Finite Group Databasebeta

← C73×#36901 #32946305

Subgroups — C73×#36901 #32946305

Order 18688.

2064 conjugacy classes of subgroups.

The subgroup lattice has 1622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2848C211yesmaximal, characteristic, complemented
2C73×#2847C211yesmaximal, characteristic, complemented
3C73×#2787C211yesmaximal, characteristic, complemented
4C73×#2784C211yesmaximal, characteristic, complemented
5C73×#2778C211yesmaximal, characteristic, complemented
6C73×#2747C211yesmaximal, characteristic, complemented
7C73×#2732C211yesmaximal, characteristic, complemented
8C73×#2708C211yesmaximal, characteristic, complemented
9C73×#2696C211yesmaximal, characteristic, complemented
10C73×#2695C211yesmaximal, characteristic, complemented
11C73×#2692C211yesmaximal, characteristic, complemented
12C73×#2685C211yesmaximal, characteristic, complemented
13C73×#2684C211yesmaximal, characteristic, complemented
14C73×#2681C211yesmaximal, characteristic, complemented
15C73×#2678C211yesmaximal, characteristic, complemented
16C73×#2676C211yesmaximal, characteristic, complemented
17C73×#2671C211yesmaximal, characteristic, complemented
18C73×#2668C211yesmaximal, characteristic, complemented
19C73×#2653C211yesmaximal, characteristic, complemented
20C73×#2649C211yesmaximal, characteristic, complemented
21C73×#2522C211yesmaximal, characteristic, complemented
22C73×#2521C211yesmaximal, characteristic, complemented
23C73×#2477C211yesmaximal, characteristic, complemented
24C73×#2476C211yesmaximal, characteristic, complemented
25C73×#2463C211yesmaximal, characteristic, complemented
26C73×#2456C211yesmaximal, characteristic, complemented
27C73×#2450C211yesmaximal, characteristic, complemented
28C73×#2425C211yesmaximal, characteristic, complemented
29C73×#2325C211yesmaximal, characteristic, complemented
30C73×#2324C211yesmaximal, characteristic, complemented
31C4×#120×C73C211yesmaximal, characteristic, complemented
32C24×C4×C73C2211yescharacteristic
33C2×#126×C73C2211yescharacteristic
34C2×#124×C73C2211yescharacteristic
35C2×#123×C73C2211yescharacteristic
36C2×#123×C73C2211yescharacteristic, complemented
37C2×#123×C73C2211yescharacteristic, complemented
38C2×C22⋊Q8×C73C2211yescharacteristic
39C2×C22⋊Q8×C73C2211yescharacteristic
40C2×C22⋊Q8×C73C2211yescharacteristic
41C2×C22⋊Q8×C73C2211yescharacteristic, complemented
42C2×C22⋊Q8×C73C2211yescharacteristic, complemented
43C2×#121×C73C2211yescharacteristic
44C2×#121×C73C2211yescharacteristic
45C2×#121×C73C2211yescharacteristic
46C2×#121×C73C2211yescharacteristic
47C2×#121×C73C2211yescharacteristic
48C2×#121×C73C2211yescharacteristic
49C2×#120×C73C2211yescharacteristic
50C2×#120×C73C2211yescharacteristic
51C2×#120×C73C2211yescharacteristic
52C2×C4×D4×C73C2211yescharacteristic
53C2×C4×D4×C73C2211yescharacteristic
54C2×C4×D4×C73C2211yescharacteristic
55C2×C4×D4×C73C2211yescharacteristic, complemented
56C2×#117×C73C2211yescharacteristic, complemented
57#401×C73C2211yescharacteristic, complemented
58#400×C73C2211yescharacteristic, complemented
59#400×C73C2211yescharacteristic, complemented
60#400×C73C2211yescharacteristic, complemented
61#400×C73C2211yescharacteristic, complemented
62#399×C73C2211yescharacteristic
63#399×C73C2211yescharacteristic
64#399×C73C2211yescharacteristic, complemented
65#398×C73C2211yescharacteristic, complemented
66#398×C73C2211yescharacteristic, complemented
67#398×C73C2211yescharacteristic, complemented
68#398×C73C2211yescharacteristic, complemented
69#398×C73C2211yescharacteristic, complemented
70#398×C73C2211yescharacteristic, complemented
71#397×C73C2211yescharacteristic
72#397×C73C2211yescharacteristic
73#397×C73C2211yescharacteristic
74#397×C73C2211yescharacteristic
75#397×C73C2211yescharacteristic
76#397×C73C2211yescharacteristic, complemented
77#397×C73C2211yescharacteristic, complemented
78#396×C73C2211yescharacteristic
79#396×C73C2211yescharacteristic
80#396×C73C2211yescharacteristic, complemented
81#396×C73C2211yescharacteristic, complemented
82#396×C73C2211yescharacteristic, complemented
83#395×C73C2211yescharacteristic, complemented
84#394×C73C2211yescharacteristic
85#394×C73C2211yescharacteristic
86#394×C73C2211yescharacteristic
87#394×C73C2211yescharacteristic
88#394×C73C2211yescharacteristic
89#394×C73C2211yescharacteristic
90#394×C73C2211yescharacteristic
91#394×C73C2211yescharacteristic
92#394×C73C2211yescharacteristic
93#394×C73C2211yescharacteristic
94#394×C73C2211yescharacteristic, complemented
95#394×C73C2211yescharacteristic, complemented
96#393×C73C2211yescharacteristic
97#393×C73C2211yescharacteristic
98#393×C73C2211yescharacteristic, complemented
99#393×C73C2211yescharacteristic, complemented
100#393×C73C2211yescharacteristic, complemented
101#392×C73C2211yescharacteristic
102#392×C73C2211yescharacteristic
103#392×C73C2211yescharacteristic
104#392×C73C2211yescharacteristic, complemented
105#391×C73C2211yescharacteristic, complemented
106#391×C73C2211yescharacteristic, complemented
107#390×C73C2211yescharacteristic
108#390×C73C2211yescharacteristic
109#390×C73C2211yescharacteristic
110#390×C73C2211yescharacteristic
111#390×C73C2211yescharacteristic, complemented
112#389×C73C2211yescharacteristic, complemented
113#389×C73C2211yescharacteristic, complemented
114#389×C73C2211yescharacteristic, complemented
115#388×C73C2211yescharacteristic
116#388×C73C2211yescharacteristic
117#388×C73C2211yescharacteristic
118#388×C73C2211yescharacteristic
119#388×C73C2211yescharacteristic
120#388×C73C2211yescharacteristic
121#388×C73C2211yescharacteristic, complemented
122#388×C73C2211yescharacteristic, complemented
123#388×C73C2211yescharacteristic, complemented
124#388×C73C2211yescharacteristic, complemented
125#388×C73C2211yescharacteristic, complemented
126#388×C73C2211yescharacteristic, complemented
127#388×C73C2211yescharacteristic, complemented
128#387×C73C2211yescharacteristic, complemented
129#387×C73C2211yescharacteristic, complemented
130#387×C73C2211yescharacteristic, complemented
131#387×C73C2211yescharacteristic, complemented
132#387×C73C2211yescharacteristic, complemented
133#387×C73C2211yescharacteristic, complemented
134#387×C73C2211yescharacteristic, complemented
135#387×C73C2211yescharacteristic, complemented
136#387×C73C2211yescharacteristic, complemented
137#386×C73C2211yescharacteristic
138#386×C73C2211yescharacteristic
139#386×C73C2211yescharacteristic
140#386×C73C2211yescharacteristic
141#386×C73C2211yescharacteristic
142#386×C73C2211yescharacteristic
143#386×C73C2211yescharacteristic
144#386×C73C2211yescharacteristic
145#386×C73C2211yescharacteristic
146#386×C73C2211yescharacteristic
147#386×C73C2211yescharacteristic
148#386×C73C2211yescharacteristic
149#386×C73C2211yescharacteristic
150#386×C73C2211yescharacteristic
151#386×C73C2211yescharacteristic
152#386×C73C2211yescharacteristic
153#386×C73C2211yescharacteristic
154#386×C73C2211yescharacteristic, complemented
155#386×C73C2211yescharacteristic, complemented
156#386×C73C2211yescharacteristic, complemented
157#385×C73C2211yescharacteristic
158#385×C73C2211yescharacteristic
159#385×C73C2211yescharacteristic
160#385×C73C2211yescharacteristic
161#385×C73C2211yescharacteristic
162#385×C73C2211yescharacteristic
163#385×C73C2211yescharacteristic
164#385×C73C2211yescharacteristic
165#385×C73C2211yescharacteristic
166#385×C73C2211yescharacteristic, complemented
167#385×C73C2211yescharacteristic, complemented
168#385×C73C2211yescharacteristic, complemented
169#385×C73C2211yescharacteristic, complemented
170#385×C73C2211yescharacteristic, complemented
171#380×C73C2211yescharacteristic
172#380×C73C2211yescharacteristic
173#380×C73C2211yescharacteristic
174#380×C73C2211yescharacteristic
175#380×C73C2211yescharacteristic
176#380×C73C2211yescharacteristic
177#380×C73C2211yescharacteristic, complemented
178#380×C73C2211yescharacteristic, complemented
179#379×C73C2211yescharacteristic
180#379×C73C2211yescharacteristic
181#379×C73C2211yescharacteristic
182C4×C4⋊C4×C73C2211yescharacteristic, complemented
183C4×C22⋊C4×C73C2211yescharacteristic
184C4×C22⋊C4×C73C2211yescharacteristic
185C4×C22⋊C4×C73C2211yescharacteristic
186C2×#95×C73C2211yescharacteristic, complemented
187C25×C73C2311yescharacteristic
188C22×Q8×C73C2311yescharacteristic
189C22×Q8×C73C2311yescharacteristic
190C22×D4×C73C2311yescharacteristic
191C22×D4×C73C2311yescharacteristic
192C22×D4×C73C2311yescharacteristic
193C22×D4×C73C2311yescharacteristic
194C22×D4×C73C2311yescharacteristic
195C22×D4×C73C2311yescharacteristic
196C22×D4×C73C2311yescharacteristic
197C22×D4×C73C2311yescharacteristic
198C22×D4×C73C2311yescharacteristic
199C22×D4×C73C2311yescharacteristic
200C22×D4×C73C2311yescharacteristic
201C22×D4×C73C2311yescharacteristic
202C23×C4×C73—42no—
203C23×C4×C73—42no—
204C23×C4×C73—42no—
205C23×C4×C73C2311yescharacteristic
206C23×C4×C73C2311yescharacteristic
207C23×C4×C73C2311yescharacteristic
208C23×C4×C73C2311yescharacteristic
209C23×C4×C73C2311yescharacteristic
210C23×C4×C73C2311yescharacteristic
211C23×C4×C73C2311yescharacteristic
212C23×C4×C73C2311yescharacteristic
213C23×C4×C73C2311yescharacteristic
214C23×C4×C73C2311yescharacteristic
215C23×C4×C73C2311yescharacteristic
216#126×C73—42no—
217#124×C73—42no—
218#123×C73—42no—
219#123×C73—42no—
220#123×C73—42no—
221C22⋊Q8×C73—42no—
222C22⋊Q8×C73—42no—
223C22⋊Q8×C73—42no—
224C22⋊Q8×C73—42no—
225C22⋊Q8×C73—42no—
226#121×C73—24no—
227#121×C73—24no—
228#121×C73—42no—
229#121×C73—42no—
230#121×C73—42no—
231#121×C73—42no—
232#120×C73—24no—
233#120×C73—42no—
234#120×C73—42no—
235C4×D4×C73—42no—
236C4×D4×C73—42no—
237C4×D4×C73—42no—
238C4×D4×C73—42no—
239#117×C73—42no—
240C2×C4⋊C4×C73C2311yescharacteristic
241C2×C4⋊C4×C73C2311yescharacteristic
242C2×C4⋊C4×C73C2311yescharacteristic
243C2×C4⋊C4×C73C2311yescharacteristic
244C2×C4⋊C4×C73C2311yescharacteristic
245C2×C4⋊C4×C73C2311yescharacteristic
246C2×C4⋊C4×C73C2311yescharacteristic
247C2×C4⋊C4×C73C2311yescharacteristic
248C2×C4⋊C4×C73C2311yescharacteristic
249C2×C4⋊C4×C73C2311yescharacteristic
250C2×C4⋊C4×C73C2311yescharacteristic
251C2×C4⋊C4×C73C2311yescharacteristic
252C2×C4⋊C4×C73C2311yescharacteristic
253C2×C4⋊C4×C73C2311yescharacteristic
254C2×C4⋊C4×C73C2311yescharacteristic
255C2×C4⋊C4×C73C2311yescharacteristic
256C2×C4⋊C4×C73C2311yescharacteristic
257C2×C4⋊C4×C73C2311yescharacteristic
258C2×C4⋊C4×C73C2311yescharacteristic
259C2×C4⋊C4×C73C2311yescharacteristic
260C2×C4⋊C4×C73C2311yescharacteristic
261C2×C4⋊C4×C73C2311yescharacteristic
262C2×C4⋊C4×C73C2311yescharacteristic
263C2×C4⋊C4×C73C2311yescharacteristic
264C2×C4⋊C4×C73C2311yescharacteristic
265C2×C4⋊C4×C73C2311yescharacteristic
266C2×C4⋊C4×C73C2311yescharacteristic
267C2×C4⋊C4×C73C2311yescharacteristic
268C2×C4⋊C4×C73C2311yescharacteristic
269C2×C4⋊C4×C73C2311yescharacteristic
270C2×C22⋊C4×C73C2311yescharacteristic
271C2×C22⋊C4×C73C2311yescharacteristic
272C2×C22⋊C4×C73C2311yescharacteristic
273C2×C22⋊C4×C73C2311yescharacteristic
274C2×C22⋊C4×C73C2311yescharacteristic
275C2×C22⋊C4×C73C2311yescharacteristic
276C2×C22⋊C4×C73C2311yescharacteristic
277C2×C22⋊C4×C73C2311yescharacteristic
278C2×C22⋊C4×C73C2311yescharacteristic
279C2×C22⋊C4×C73C2311yescharacteristic
280C2×C22⋊C4×C73C2311yescharacteristic
281C2×C22⋊C4×C73C2311yescharacteristic
282C2×C22⋊C4×C73C2311yescharacteristic
283C2×C22⋊C4×C73C2311yescharacteristic
284C2×C22⋊C4×C73C2311yescharacteristic
285C2×C22⋊C4×C73C2311yescharacteristic
286C2×C22⋊C4×C73C2311yescharacteristic
287C2×C22⋊C4×C73C2311yescharacteristic
288C2×C22⋊C4×C73C2311yescharacteristic
289C2×C22⋊C4×C73C2311yescharacteristic
290C2×C22⋊C4×C73C2311yescharacteristic
291C2×C22⋊C4×C73C2311yescharacteristic
292C2×C22⋊C4×C73C2311yescharacteristic
293C2×C22⋊C4×C73C2311yescharacteristic
294C2×C22⋊C4×C73C2311yescharacteristic
295C2×C22⋊C4×C73C2311yescharacteristic
296C2×C22⋊C4×C73C2311yescharacteristic
297C2×C22⋊C4×C73C2311yescharacteristic
298C2×C22⋊C4×C73C2311yescharacteristic
299C2×C22⋊C4×C73C2311yescharacteristic
300C2×C22⋊C4×C73C2311yescharacteristic
301C2×C22⋊C4×C73C2311yescharacteristic
302C2×C22⋊C4×C73C2311yescharacteristic
303C2×C22⋊C4×C73C2311yescharacteristic
304C2×C22⋊C4×C73C2311yescharacteristic
305C2×C22⋊C4×C73C2311yescharacteristic
306C2×C22⋊C4×C73C2311yescharacteristic
307C2×C22⋊C4×C73C2311yescharacteristic
308C2×C22⋊C4×C73C2311yescharacteristic
309C2×C22⋊C4×C73C2311yescharacteristic
310C2×C22⋊C4×C73C2311yescharacteristic
311C2×C22⋊C4×C73C2311yescharacteristic
312C2×C22⋊C4×C73C2311yescharacteristic
313C2×C22⋊C4×C73C2311yescharacteristic
314C2×C22⋊C4×C73C2311yescharacteristic
315C2×C22⋊C4×C73C2311yescharacteristic
316C2×C22⋊C4×C73C2311yescharacteristic
317C2×C22⋊C4×C73C2311yescharacteristic
318C2×C22⋊C4×C73C2311yescharacteristic
319C2×C22⋊C4×C73C2311yescharacteristic
320C2×C22⋊C4×C73C2311yescharacteristic
321C2×C22⋊C4×C73C2311yescharacteristic
322C2×C42×C73C2311yescharacteristic
323C2×C42×C73C2311yescharacteristic
324C2×C42×C73C2311yescharacteristic
325C2×C42×C73C2311yescharacteristic
326C2×C42×C73C2311yescharacteristic
327C2×C42×C73C2311yescharacteristic
328C2×C42×C73C2311yescharacteristic
329#95×C73C2311yescharacteristic
330#95×C73C2311yescharacteristic
331#95×C73C2311yescharacteristic
332#95×C73C2311yescharacteristic
333#95×C73C2311yescharacteristic
334#95×C73C2311yescharacteristic
335#95×C73C2311yescharacteristic
336#95×C73C2311yescharacteristic
337#95×C73C2311yescharacteristic
338#95×C73C2311yescharacteristic
339#95×C73C2311yescharacteristic
340#95×C73C2311yescharacteristic
341#95×C73C2311yescharacteristic
342#95×C73C2311yescharacteristic
343#95×C73C2311yescharacteristic
344#95×C73C2311yescharacteristic
345#95×C73C2311yescharacteristic
346#95×C73C2311yescharacteristic
347#95×C73C2311yescharacteristic
348#95×C73C2311yescharacteristic
349#95×C73C2311yescharacteristic
350#95×C73C2311yescharacteristic
351#95×C73C2311yescharacteristic
352#95×C73C2311yescharacteristic
353#95×C73C2311yescharacteristic
354#95×C73C2311yescharacteristic
355#95×C73C2311yescharacteristic
356#95×C73C2311yescharacteristic
357#95×C73C2311yescharacteristic
358#95×C73C2311yescharacteristic
359#95×C73C2311yescharacteristic
360#95×C73C2311yescharacteristic
361#95×C73C2311yescharacteristic
362#95×C73C2311yescharacteristic
363#95×C73C2311yescharacteristic
364#95×C73C2311yescharacteristic
365#95×C73C2311yescharacteristic
366#95×C73C2311yescharacteristic
367#95×C73C2311yescharacteristic
368#95×C73C2311yescharacteristic
369C24×C73—22no—
370C24×C73—22no—
371C24×C73—22no—
372C24×C73—41no—
373C24×C73—41no—
374C24×C73—41no—
375C24×C73—41no—
376C24×C73C2411yescharacteristic
377C24×C73C2411yescharacteristic
378C24×C73C2411yescharacteristic
379C24×C73C2411yescharacteristic
380C24×C73C2411yescharacteristic
381C24×C73C2411yescharacteristic
382C2×Q8×C73—22no—
383C2×Q8×C73—41no—
384C2×Q8×C73—41no—
385C2×Q8×C73—41no—
386C2×Q8×C73—41no—
387C2×Q8×C73—41no—
388C2×D4×C73—22no—
389C2×D4×C73—22no—
390C2×D4×C73—22no—
391C2×D4×C73—22no—
392C2×D4×C73—22no—
393C2×D4×C73—22no—
394C2×D4×C73—22no—
395C2×D4×C73—22no—
396C2×D4×C73—22no—
397C2×D4×C73—22no—
398C2×D4×C73—22no—
399C2×D4×C73—22no—
400C2×D4×C73—22no—
401C2×D4×C73—41no—
402C2×D4×C73—41no—
403C2×D4×C73—41no—
404C2×D4×C73—41no—
405C2×D4×C73—41no—
406C2×D4×C73—41no—
407C2×D4×C73—41no—
408C2×D4×C73—41no—
409C2×D4×C73—41no—
410C2×D4×C73—41no—
411C2×D4×C73—41no—
412C2×D4×C73—41no—
413C2×D4×C73—41no—
414C2×D4×C73—41no—
415C2×D4×C73—41no—
416C2×D4×C73—41no—
417C2×D4×C73—41no—
418C2×D4×C73—41no—
419C2×D4×C73—41no—
420C2×D4×C73—41no—
421C2×D4×C73—41no—
422C2×D4×C73—41no—
423C2×D4×C73#4114yes—
424C22×C4×C73—22no—
425C22×C4×C73—22no—
426C22×C4×C73—22no—
427C22×C4×C73—22no—
428C22×C4×C73—22no—
429C22×C4×C73—22no—
430C22×C4×C73—22no—
431C22×C4×C73—22no—
432C22×C4×C73—22no—
433C22×C4×C73—22no—
434C22×C4×C73—22no—
435C22×C4×C73—22no—
436C22×C4×C73—41no—
437C22×C4×C73—41no—
438C22×C4×C73—41no—
439C22×C4×C73—41no—
440C22×C4×C73—41no—
441C22×C4×C73—41no—
442C22×C4×C73—41no—
443C22×C4×C73—41no—
444C22×C4×C73—41no—
445C22×C4×C73—41no—
446C22×C4×C73—41no—
447C22×C4×C73—41no—
448C22×C4×C73—41no—
449C22×C4×C73—41no—
450C22×C4×C73—41no—
451C22×C4×C73—41no—
452C22×C4×C73—41no—
453C22×C4×C73—41no—
454C22×C4×C73—41no—
455C22×C4×C73—41no—
456C22×C4×C73—41no—
457C22×C4×C73—416no—
458C22×C4×C73C2411yescharacteristic
459C22×C4×C73C2411yescharacteristic
460C22×C4×C73C2411yescharacteristic
461C22×C4×C73C2411yescharacteristic
462C22×C4×C73C2411yescharacteristic
463C22×C4×C73C2411yescharacteristic
464C22×C4×C73C2411yescharacteristic
465C22×C4×C73C2411yescharacteristic
466C22×C4×C73C2411yescharacteristic
467C22×C4×C73C2411yescharacteristic
468C22×C4×C73C2411yescharacteristic
469C22×C4×C73C2411yescharacteristic
470C22×C4×C73C2411yescharacteristic
471C22×C4×C73C2411yescharacteristic
472C22×C4×C73C2411yescharacteristic
473C22×C4×C73C2411yescharacteristic
474C22×C4×C73C2411yescharacteristic
475C22×C4×C73C2411yescharacteristic
476C22×C4×C73C2411yescharacteristic
477C22×C4×C73C2411yescharacteristic
478C22×C4×C73C2411yescharacteristic
479C22×C4×C73C2411yescharacteristic
480C22×C4×C73C2411yescharacteristic
481C22×C4×C73C2411yescharacteristic
482C22×C4×C73C2411yescharacteristic
483C4⋊C4×C73—22no—
484C4⋊C4×C73—22no—
485C4⋊C4×C73—22no—
486C4⋊C4×C73—22no—
487C4⋊C4×C73—22no—
488C4⋊C4×C73—22no—
489C4⋊C4×C73—22no—
490C4⋊C4×C73—22no—
491C4⋊C4×C73—22no—
492C4⋊C4×C73—22no—
493C4⋊C4×C73—41no—
494C4⋊C4×C73—41no—
495C4⋊C4×C73—41no—
496C4⋊C4×C73—41no—
497C4⋊C4×C73—41no—
498C4⋊C4×C73—41no—
499C4⋊C4×C73—41no—
500C4⋊C4×C73—41no—
501C4⋊C4×C73—41no—
502C4⋊C4×C73—41no—
503C4⋊C4×C73—41no—
504C4⋊C4×C73—41no—
505C4⋊C4×C73—41no—
506C4⋊C4×C73—41no—
507C4⋊C4×C73—41no—
508C4⋊C4×C73—41no—
509C4⋊C4×C73—41no—
510C4⋊C4×C73—41no—
511C4⋊C4×C73—41no—
512C4⋊C4×C73—41no—
513C22⋊C4×C73—22no—
514C22⋊C4×C73—22no—
515C22⋊C4×C73—22no—
516C22⋊C4×C73—22no—
517C22⋊C4×C73—22no—
518C22⋊C4×C73—22no—
519C22⋊C4×C73—22no—
520C22⋊C4×C73—22no—
521C22⋊C4×C73—22no—
522C22⋊C4×C73—22no—
523C22⋊C4×C73—22no—
524C22⋊C4×C73—22no—
525C22⋊C4×C73—22no—
526C22⋊C4×C73—22no—
527C22⋊C4×C73—22no—
528C22⋊C4×C73—22no—
529C22⋊C4×C73—22no—
530C22⋊C4×C73—22no—
531C22⋊C4×C73—22no—
532C22⋊C4×C73—41no—
533C22⋊C4×C73—41no—
534C22⋊C4×C73—41no—
535C22⋊C4×C73—41no—
536C22⋊C4×C73—41no—
537C22⋊C4×C73—41no—
538C22⋊C4×C73—41no—
539C22⋊C4×C73—41no—
540C22⋊C4×C73—41no—
541C22⋊C4×C73—41no—
542C22⋊C4×C73—41no—
543C22⋊C4×C73—41no—
544C22⋊C4×C73—41no—
545C22⋊C4×C73—41no—
546C22⋊C4×C73—41no—
547C22⋊C4×C73—41no—
548C22⋊C4×C73—41no—
549C22⋊C4×C73—41no—
550C22⋊C4×C73—41no—
551C22⋊C4×C73—41no—
552C22⋊C4×C73—41no—
553C22⋊C4×C73—41no—
554C22⋊C4×C73—41no—
555C22⋊C4×C73—41no—
556C22⋊C4×C73—41no—
557C22⋊C4×C73—41no—
558C22⋊C4×C73—41no—
559C22⋊C4×C73—41no—
560C22⋊C4×C73—41no—
561C22⋊C4×C73—41no—
562C22⋊C4×C73—41no—
563C22⋊C4×C73—41no—
564C22⋊C4×C73—41no—
565C42×C73—22no—
566C42×C73—41no—
567C42×C73—41no—
568C42×C73—41no—
569C42×C73—41no—
570C42×C73—41no—
571C42×C73—41no—
572C23×C73—21no—
573C23×C73—21no—
574C23×C73—21no—
575C23×C73—21no—
576C23×C73—21no—
577C23×C73—21no—
578C23×C73—21no—
579C23×C73—21no—
580C23×C73—21no—
581C23×C73—21no—
582C23×C73—21no—
583C23×C73—21no—
584C23×C73—21no—
585C23×C73—21no—
586C23×C73—21no—
587C23×C73—21no—
588C23×C73—21no—
589C23×C73—21no—
590C23×C73—21no—
591C23×C73—21no—
592C23×C73—21no—
593C23×C73—21no—
594C23×C73—21no—
595C23×C73—21no—
596C23×C73—21no—
597C23×C73—21no—
598C23×C73—21no—
599C23×C73—21no—
600C23×C73—21no—
601C23×C73—21no—
602C23×C73—21no—
603C23×C73—21no—
604C23×C73—21no—
605C23×C73—21no—
606C23×C73—21no—
607C23×C73—21no—
608C23×C73—21no—
609C23×C73—21no—
610C23×C73—44no—
611C23×C73—44no—
612C23×C73—44no—
613C23×C73—44no—
614C23×C73—44no—
615C23×C73—44no—
616C23×C73—44no—
617C23×C73C2×#4112yes—
618C23×C73C2×#4112yes—
619C23×C73H(5,𝔽2)12yes—
620C23×C732−1+412yes—
621C23×C73C2511yescharacteristic
622Q8×C73—82no—
623Q8×C73—82no—
624D4×C73—44no—
625D4×C73—44no—
626D4×C73—44no—
627D4×C73—44no—
628D4×C73—82no—
629D4×C73—82no—
630D4×C73—82no—
631D4×C73—82no—
632D4×C73—82no—
633D4×C73—82no—
634D4×C73—82no—
635D4×C73—82no—
636C2×C4×C73—21no—
637C2×C4×C73—21no—
638C2×C4×C73—21no—
639C2×C4×C73—21no—
640C2×C4×C73—21no—
641C2×C4×C73—21no—
642C2×C4×C73—21no—
643C2×C4×C73—21no—
644C2×C4×C73—21no—
645C2×C4×C73—21no—
646C2×C4×C73—21no—
647C2×C4×C73—21no—
648C2×C4×C73—21no—
649C2×C4×C73—21no—
650C2×C4×C73—21no—
651C2×C4×C73—21no—
652C2×C4×C73—21no—
653C2×C4×C73—21no—
654C2×C4×C73—21no—
655C2×C4×C73—21no—
656C2×C4×C73—21no—
657C2×C4×C73—21no—
658C2×C4×C73—21no—
659C2×C4×C73—21no—
660C2×C4×C73—21no—
661C2×C4×C73—21no—
662C2×C4×C73—21no—
663C2×C4×C73—21no—
664C2×C4×C73—21no—
665C2×C4×C73—21no—
666C2×C4×C73—21no—
667C2×C4×C73—21no—
668C2×C4×C73—21no—
669C2×C4×C73—21no—
670C2×C4×C73—21no—
671C2×C4×C73—21no—
672C2×C4×C73—21no—
673C2×C4×C73—21no—
674C2×C4×C73—21no—
675C2×C4×C73—21no—
676C2×C4×C73—21no—
677C2×C4×C73—21no—
678C2×C4×C73—21no—
679C2×C4×C73—21no—
680C2×C4×C73—21no—
681C2×C4×C73—21no—
682C2×C4×C73—21no—
683C2×C4×C73—21no—
684C2×C4×C73—21no—
685C2×C4×C73—21no—
686C2×C4×C73—21no—
687C2×C4×C73—21no—
688C2×C4×C73—21no—
689C2×C4×C73—21no—
690C2×C4×C73—21no—
691C2×C4×C73—21no—
692C2×C4×C73—21no—
693C2×C4×C73—21no—
694C2×C4×C73—21no—
695C2×C4×C73—21no—
696C2×C4×C73—21no—
697C2×C4×C73—21no—
698C2×C4×C73—21no—
699C2×C4×C73—21no—
700C2×C4×C73—21no—
701C2×C4×C73—21no—
702C2×C4×C73—21no—
703C2×C4×C73—21no—
704C2×C4×C73—21no—
705C2×C4×C73—21no—
706C2×C4×C73—21no—
707C2×C4×C73—44no—
708C2×C4×C73—44no—
709C2×C4×C73—44no—
710C2×C4×C73—44no—
711C2×C4×C73—44no—
712C2×C4×C73—44no—
713C2×C4×C73—44no—
714C2×C4×C73—82no—
715C2×C4×C73—82no—
716C2×C4×C73—82no—
717C2×C4×C73—82no—
718C2×C4×C73C2×#4112yes—
719C2×C4×C73H(5,𝔽2)12yes—
720C2×C4×C73H(5,𝔽2)12yes—
721C2×C4×C73H(5,𝔽2)12yes—
722C22×C73—22no—
723C22×C73—22no—
724C22×C73—22no—
725C22×C73—22no—
726C22×C73—22no—
727C22×C73—22no—
728C22×C73—22no—
729C22×C73—22no—
730C22×C73—22no—
731C22×C73—22no—
732C22×C73—22no—
733C22×C73—22no—
734C22×C73—416no—
735C22×C73—41no—
736C22×C73—41no—
737C22×C73—41no—
738C22×C73—41no—
739C22×C73—41no—
740C22×C73—41no—
741C22×C73—41no—
742C22×C73—41no—
743C22×C73—41no—
744C22×C73—41no—
745C22×C73—41no—
746C22×C73—41no—
747C22×C73—41no—
748C22×C73—41no—
749C22×C73—41no—
750C22×C73—41no—
751C22×C73—41no—
752C22×C73—41no—
753C22×C73—41no—
754C22×C73—41no—
755C22×C73—41no—
756C22×C73—41no—
757C22×C73—41no—
758C22×C73—41no—
759C22×C73—41no—
760C22×C73—41no—
761C22×C73—41no—
762C22×C73—41no—
763C22×C73—41no—
764C22×C73—41no—
765C22×C73C22×#4111yescharacteristic
766C22×C73C2×H(5,𝔽2)11yescharacteristic
767C22×C73C2×H(5,𝔽2)11yescharacteristic
768C22×C73C2×H(5,𝔽2)11yescharacteristic
769C22×C73C2×H(5,𝔽2)11yescharacteristic
770C22×C73C2×2−1+411yescharacteristic
771C22×C73#58511yescharacteristic
772C4×C73—22no—
773C4×C73—22no—
774C4×C73—22no—
775C4×C73—22no—
776C4×C73—41no—
777C4×C73—41no—
778C4×C73—41no—
779C4×C73—41no—
780C4×C73—41no—
781C4×C73—41no—
782C4×C73—41no—
783C4×C73—41no—
784C4×C73—41no—
785C4×C73—41no—
786C4×C73—41no—
787C4×C73—41no—
788C4×C73—41no—
789C4×C73—41no—
790C4×C73—41no—
791C4×C73—41no—
792C4×C73—41no—
793C4×C73—41no—
794C4×C73—41no—
795C4×C73—41no—
796C4×C73—41no—
797#36901C7311yesmaximal, characteristic, direct product factor, Sylow
798C2×C73—42no—
799C2×C73—42no—
800C2×C73—42no—
801C2×C73—42no—
802C2×C73—81no—
803C2×C73—81no—
804C2×C73#345911yescharacteristic
805C2×C73#351911yescharacteristic
806C2×C73#352011yescharacteristic
807C2×C73#353211yescharacteristic
808C2×C73#353611yescharacteristic
809C2×C73#354111yescharacteristic
810C2×C73#354211yescharacteristic
811#2848C2×C7311yescharacteristic, complemented
812#2847C2×C7311yescharacteristic, complemented
813#2787C2×C7311yescharacteristic, complemented
814#2784C2×C7311yescharacteristic, complemented
815#2778C2×C7311yescharacteristic, complemented
816#2747C2×C7311yescharacteristic, complemented
817#2732C2×C7311yescharacteristic, complemented
818#2708C2×C7311yescharacteristic, complemented
819#2696C2×C7311yescharacteristic, complemented
820#2695C2×C7311yescharacteristic, complemented
821#2692C2×C7311yescharacteristic, complemented
822#2685C2×C7311yescharacteristic, complemented
823#2684C2×C7311yescharacteristic, complemented
824#2681C2×C7311yescharacteristic, complemented
825#2678C2×C7311yescharacteristic, complemented
826#2676C2×C7311yescharacteristic, complemented
827#2671C2×C7311yescharacteristic, complemented
828#2668C2×C7311yescharacteristic, complemented
829#2653C2×C7311yescharacteristic, complemented
830#2649C2×C7311yescharacteristic, complemented
831#2522C2×C7311yescharacteristic, complemented
832#2521C2×C7311yescharacteristic, complemented
833#2477C2×C7311yescharacteristic, complemented
834#2476C2×C7311yescharacteristic, complemented
835#2463C2×C7311yescharacteristic, complemented
836#2456C2×C7311yescharacteristic, complemented
837#2450C2×C7311yescharacteristic, complemented
838#2425C2×C7311yescharacteristic, complemented
839#2325C2×C7311yescharacteristic, complemented
840#2324C2×C7311yescharacteristic, complemented
841C4×#120C2×C7311yescharacteristic, complemented
842C73#3690111yescharacteristic, direct product factor, Sylow
843C24×C4C22×C7311yescharacteristic
844C2×#126C22×C7311yescharacteristic
845C2×#124C22×C7311yescharacteristic
846C2×#123C22×C7311yescharacteristic
847C2×#123C22×C7311yescharacteristic, complemented
848C2×#123C22×C7311yescharacteristic, complemented
849C2×C22⋊Q8C22×C7311yescharacteristic
850C2×C22⋊Q8C22×C7311yescharacteristic
851C2×C22⋊Q8C22×C7311yescharacteristic
852C2×C22⋊Q8C22×C7311yescharacteristic, complemented
853C2×C22⋊Q8C22×C7311yescharacteristic, complemented
854C2×#121C22×C7311yescharacteristic
855C2×#121C22×C7311yescharacteristic
856C2×#121C22×C7311yescharacteristic
857C2×#121C22×C7311yescharacteristic
858C2×#121C22×C7311yescharacteristic
859C2×#121C22×C7311yescharacteristic
860C2×#120C22×C7311yescharacteristic
861C2×#120C22×C7311yescharacteristic
862C2×#120C22×C7311yescharacteristic
863C2×C4×D4C22×C7311yescharacteristic
864C2×C4×D4C22×C7311yescharacteristic
865C2×C4×D4C22×C7311yescharacteristic
866C2×C4×D4C22×C7311yescharacteristic, complemented
867C2×#117C22×C7311yescharacteristic, complemented
868#401C22×C7311yescharacteristic, complemented
869#400C22×C7311yescharacteristic, complemented
870#400C22×C7311yescharacteristic, complemented
871#400C22×C7311yescharacteristic, complemented
872#400C22×C7311yescharacteristic, complemented
873#399C22×C7311yescharacteristic
874#399C22×C7311yescharacteristic
875#399C22×C7311yescharacteristic, complemented
876#398C22×C7311yescharacteristic, complemented
877#398C22×C7311yescharacteristic, complemented
878#398C22×C7311yescharacteristic, complemented
879#398C22×C7311yescharacteristic, complemented
880#398C22×C7311yescharacteristic, complemented
881#398C22×C7311yescharacteristic, complemented
882#397C22×C7311yescharacteristic
883#397C22×C7311yescharacteristic
884#397C22×C7311yescharacteristic
885#397C22×C7311yescharacteristic
886#397C22×C7311yescharacteristic
887#397C22×C7311yescharacteristic, complemented
888#397C22×C7311yescharacteristic, complemented
889#396C22×C7311yescharacteristic
890#396C22×C7311yescharacteristic
891#396C22×C7311yescharacteristic, complemented
892#396C22×C7311yescharacteristic, complemented
893#396C22×C7311yescharacteristic, complemented
894#395C22×C7311yescharacteristic, complemented
895#394C22×C7311yescharacteristic
896#394C22×C7311yescharacteristic
897#394C22×C7311yescharacteristic
898#394C22×C7311yescharacteristic
899#394C22×C7311yescharacteristic
900#394C22×C7311yescharacteristic
901#394C22×C7311yescharacteristic
902#394C22×C7311yescharacteristic
903#394C22×C7311yescharacteristic
904#394C22×C7311yescharacteristic
905#394C22×C7311yescharacteristic, complemented
906#394C22×C7311yescharacteristic, complemented
907#393C22×C7311yescharacteristic
908#393C22×C7311yescharacteristic
909#393C22×C7311yescharacteristic, complemented
910#393C22×C7311yescharacteristic, complemented
911#393C22×C7311yescharacteristic, complemented
912#392C22×C7311yescharacteristic
913#392C22×C7311yescharacteristic
914#392C22×C7311yescharacteristic
915#392C22×C7311yescharacteristic, complemented
916#391C22×C7311yescharacteristic, complemented
917#391C22×C7311yescharacteristic, complemented
918#390C22×C7311yescharacteristic
919#390C22×C7311yescharacteristic
920#390C22×C7311yescharacteristic
921#390C22×C7311yescharacteristic
922#390C22×C7311yescharacteristic, complemented
923#389C22×C7311yescharacteristic, complemented
924#389C22×C7311yescharacteristic, complemented
925#389C22×C7311yescharacteristic, complemented
926#388C22×C7311yescharacteristic
927#388C22×C7311yescharacteristic
928#388C22×C7311yescharacteristic
929#388C22×C7311yescharacteristic
930#388C22×C7311yescharacteristic
931#388C22×C7311yescharacteristic
932#388C22×C7311yescharacteristic, complemented
933#388C22×C7311yescharacteristic, complemented
934#388C22×C7311yescharacteristic, complemented
935#388C22×C7311yescharacteristic, complemented
936#388C22×C7311yescharacteristic, complemented
937#388C22×C7311yescharacteristic, complemented
938#388C22×C7311yescharacteristic, complemented
939#387C22×C7311yescharacteristic, complemented
940#387C22×C7311yescharacteristic, complemented
941#387C22×C7311yescharacteristic, complemented
942#387C22×C7311yescharacteristic, complemented
943#387C22×C7311yescharacteristic, complemented
944#387C22×C7311yescharacteristic, complemented
945#387C22×C7311yescharacteristic, complemented
946#387C22×C7311yescharacteristic, complemented
947#387C22×C7311yescharacteristic, complemented
948#386C22×C7311yescharacteristic
949#386C22×C7311yescharacteristic
950#386C22×C7311yescharacteristic
951#386C22×C7311yescharacteristic
952#386C22×C7311yescharacteristic
953#386C22×C7311yescharacteristic
954#386C22×C7311yescharacteristic
955#386C22×C7311yescharacteristic
956#386C22×C7311yescharacteristic
957#386C22×C7311yescharacteristic
958#386C22×C7311yescharacteristic
959#386C22×C7311yescharacteristic
960#386C22×C7311yescharacteristic
961#386C22×C7311yescharacteristic
962#386C22×C7311yescharacteristic
963#386C22×C7311yescharacteristic
964#386C22×C7311yescharacteristic
965#386C22×C7311yescharacteristic, complemented
966#386C22×C7311yescharacteristic, complemented
967#386C22×C7311yescharacteristic, complemented
968#385C22×C7311yescharacteristic
969#385C22×C7311yescharacteristic
970#385C22×C7311yescharacteristic
971#385C22×C7311yescharacteristic
972#385C22×C7311yescharacteristic
973#385C22×C7311yescharacteristic
974#385C22×C7311yescharacteristic
975#385C22×C7311yescharacteristic
976#385C22×C7311yescharacteristic
977#385C22×C7311yescharacteristic, complemented
978#385C22×C7311yescharacteristic, complemented
979#385C22×C7311yescharacteristic, complemented
980#385C22×C7311yescharacteristic, complemented
981#385C22×C7311yescharacteristic, complemented
982#380C22×C7311yescharacteristic
983#380C22×C7311yescharacteristic
984#380C22×C7311yescharacteristic
985#380C22×C7311yescharacteristic
986#380C22×C7311yescharacteristic
987#380C22×C7311yescharacteristic
988#380C22×C7311yescharacteristic, complemented
989#380C22×C7311yescharacteristic, complemented
990#379C22×C7311yescharacteristic
991#379C22×C7311yescharacteristic
992#379C22×C7311yescharacteristic
993C4×C4⋊C4C22×C7311yescharacteristic, complemented
994C4×C22⋊C4C22×C7311yescharacteristic
995C4×C22⋊C4C22×C7311yescharacteristic
996C4×C22⋊C4C22×C7311yescharacteristic
997C2×#95C22×C7311yescharacteristic, complemented
998C25C23×C7311yescharacteristic
999C22×Q8C23×C7311yescharacteristic
1000C22×Q8C23×C7311yescharacteristic
1001C22×D4C23×C7311yescharacteristic
1002C22×D4C23×C7311yescharacteristic
1003C22×D4C23×C7311yescharacteristic
1004C22×D4C23×C7311yescharacteristic
1005C22×D4C23×C7311yescharacteristic
1006C22×D4C23×C7311yescharacteristic
1007C22×D4C23×C7311yescharacteristic
1008C22×D4C23×C7311yescharacteristic
1009C22×D4C23×C7311yescharacteristic
1010C22×D4C23×C7311yescharacteristic
1011C22×D4C23×C7311yescharacteristic
1012C22×D4C23×C7311yescharacteristic
1013C23×C4—42no—
1014C23×C4—42no—
1015C23×C4—42no—
1016C23×C4C23×C7311yescharacteristic
1017C23×C4C23×C7311yescharacteristic
1018C23×C4C23×C7311yescharacteristic
1019C23×C4C23×C7311yescharacteristic
1020C23×C4C23×C7311yescharacteristic
1021C23×C4C23×C7311yescharacteristic
1022C23×C4C23×C7311yescharacteristic
1023C23×C4C23×C7311yescharacteristic
1024C23×C4C23×C7311yescharacteristic
1025C23×C4C23×C7311yescharacteristic
1026C23×C4C23×C7311yescharacteristic
1027#126—42no—
1028#124—42no—
1029#123—42no—
1030#123—42no—
1031#123—42no—
1032C22⋊Q8—42no—
1033C22⋊Q8—42no—
1034C22⋊Q8—42no—
1035C22⋊Q8—42no—
1036C22⋊Q8—42no—
1037#121—24no—
1038#121—24no—
1039#121—42no—
1040#121—42no—
1041#121—42no—
1042#121—42no—
1043#120—24no—
1044#120—42no—
1045#120—42no—
1046C4×D4—42no—
1047C4×D4—42no—
1048C4×D4—42no—
1049C4×D4—42no—
1050#117—42no—
1051C2×C4⋊C4C23×C7311yescharacteristic
1052C2×C4⋊C4C23×C7311yescharacteristic
1053C2×C4⋊C4C23×C7311yescharacteristic
1054C2×C4⋊C4C23×C7311yescharacteristic
1055C2×C4⋊C4C23×C7311yescharacteristic
1056C2×C4⋊C4C23×C7311yescharacteristic
1057C2×C4⋊C4C23×C7311yescharacteristic
1058C2×C4⋊C4C23×C7311yescharacteristic
1059C2×C4⋊C4C23×C7311yescharacteristic
1060C2×C4⋊C4C23×C7311yescharacteristic
1061C2×C4⋊C4C23×C7311yescharacteristic
1062C2×C4⋊C4C23×C7311yescharacteristic
1063C2×C4⋊C4C23×C7311yescharacteristic
1064C2×C4⋊C4C23×C7311yescharacteristic
1065C2×C4⋊C4C23×C7311yescharacteristic
1066C2×C4⋊C4C23×C7311yescharacteristic
1067C2×C4⋊C4C23×C7311yescharacteristic
1068C2×C4⋊C4C23×C7311yescharacteristic
1069C2×C4⋊C4C23×C7311yescharacteristic
1070C2×C4⋊C4C23×C7311yescharacteristic
1071C2×C4⋊C4C23×C7311yescharacteristic
1072C2×C4⋊C4C23×C7311yescharacteristic
1073C2×C4⋊C4C23×C7311yescharacteristic
1074C2×C4⋊C4C23×C7311yescharacteristic
1075C2×C4⋊C4C23×C7311yescharacteristic
1076C2×C4⋊C4C23×C7311yescharacteristic
1077C2×C4⋊C4C23×C7311yescharacteristic
1078C2×C4⋊C4C23×C7311yescharacteristic
1079C2×C4⋊C4C23×C7311yescharacteristic
1080C2×C4⋊C4C23×C7311yescharacteristic
1081C2×C22⋊C4C23×C7311yescharacteristic
1082C2×C22⋊C4C23×C7311yescharacteristic
1083C2×C22⋊C4C23×C7311yescharacteristic
1084C2×C22⋊C4C23×C7311yescharacteristic
1085C2×C22⋊C4C23×C7311yescharacteristic
1086C2×C22⋊C4C23×C7311yescharacteristic
1087C2×C22⋊C4C23×C7311yescharacteristic
1088C2×C22⋊C4C23×C7311yescharacteristic
1089C2×C22⋊C4C23×C7311yescharacteristic
1090C2×C22⋊C4C23×C7311yescharacteristic
1091C2×C22⋊C4C23×C7311yescharacteristic
1092C2×C22⋊C4C23×C7311yescharacteristic
1093C2×C22⋊C4C23×C7311yescharacteristic
1094C2×C22⋊C4C23×C7311yescharacteristic
1095C2×C22⋊C4C23×C7311yescharacteristic
1096C2×C22⋊C4C23×C7311yescharacteristic
1097C2×C22⋊C4C23×C7311yescharacteristic
1098C2×C22⋊C4C23×C7311yescharacteristic
1099C2×C22⋊C4C23×C7311yescharacteristic
1100C2×C22⋊C4C23×C7311yescharacteristic
1101C2×C22⋊C4C23×C7311yescharacteristic
1102C2×C22⋊C4C23×C7311yescharacteristic
1103C2×C22⋊C4C23×C7311yescharacteristic
1104C2×C22⋊C4C23×C7311yescharacteristic
1105C2×C22⋊C4C23×C7311yescharacteristic
1106C2×C22⋊C4C23×C7311yescharacteristic
1107C2×C22⋊C4C23×C7311yescharacteristic
1108C2×C22⋊C4C23×C7311yescharacteristic
1109C2×C22⋊C4C23×C7311yescharacteristic
1110C2×C22⋊C4C23×C7311yescharacteristic
1111C2×C22⋊C4C23×C7311yescharacteristic
1112C2×C22⋊C4C23×C7311yescharacteristic
1113C2×C22⋊C4C23×C7311yescharacteristic
1114C2×C22⋊C4C23×C7311yescharacteristic
1115C2×C22⋊C4C23×C7311yescharacteristic
1116C2×C22⋊C4C23×C7311yescharacteristic
1117C2×C22⋊C4C23×C7311yescharacteristic
1118C2×C22⋊C4C23×C7311yescharacteristic
1119C2×C22⋊C4C23×C7311yescharacteristic
1120C2×C22⋊C4C23×C7311yescharacteristic
1121C2×C22⋊C4C23×C7311yescharacteristic
1122C2×C22⋊C4C23×C7311yescharacteristic
1123C2×C22⋊C4C23×C7311yescharacteristic
1124C2×C22⋊C4C23×C7311yescharacteristic
1125C2×C22⋊C4C23×C7311yescharacteristic
1126C2×C22⋊C4C23×C7311yescharacteristic
1127C2×C22⋊C4C23×C7311yescharacteristic
1128C2×C22⋊C4C23×C7311yescharacteristic
1129C2×C22⋊C4C23×C7311yescharacteristic
1130C2×C22⋊C4C23×C7311yescharacteristic
1131C2×C22⋊C4C23×C7311yescharacteristic
1132C2×C22⋊C4C23×C7311yescharacteristic
1133C2×C42C23×C7311yescharacteristic
1134C2×C42C23×C7311yescharacteristic
1135C2×C42C23×C7311yescharacteristic
1136C2×C42C23×C7311yescharacteristic
1137C2×C42C23×C7311yescharacteristic
1138C2×C42C23×C7311yescharacteristic
1139C2×C42C23×C7311yescharacteristic
1140#95C23×C7311yescharacteristic
1141#95C23×C7311yescharacteristic
1142#95C23×C7311yescharacteristic
1143#95C23×C7311yescharacteristic
1144#95C23×C7311yescharacteristic
1145#95C23×C7311yescharacteristic
1146#95C23×C7311yescharacteristic
1147#95C23×C7311yescharacteristic
1148#95C23×C7311yescharacteristic
1149#95C23×C7311yescharacteristic
1150#95C23×C7311yescharacteristic
1151#95C23×C7311yescharacteristic
1152#95C23×C7311yescharacteristic
1153#95C23×C7311yescharacteristic
1154#95C23×C7311yescharacteristic
1155#95C23×C7311yescharacteristic
1156#95C23×C7311yescharacteristic
1157#95C23×C7311yescharacteristic
1158#95C23×C7311yescharacteristic
1159#95C23×C7311yescharacteristic
1160#95C23×C7311yescharacteristic
1161#95C23×C7311yescharacteristic
1162#95C23×C7311yescharacteristic
1163#95C23×C7311yescharacteristic
1164#95C23×C7311yescharacteristic
1165#95C23×C7311yescharacteristic
1166#95C23×C7311yescharacteristic
1167#95C23×C7311yescharacteristic
1168#95C23×C7311yescharacteristic
1169#95C23×C7311yescharacteristic
1170#95C23×C7311yescharacteristic
1171#95C23×C7311yescharacteristic
1172#95C23×C7311yescharacteristic
1173#95C23×C7311yescharacteristic
1174#95C23×C7311yescharacteristic
1175#95C23×C7311yescharacteristic
1176#95C23×C7311yescharacteristic
1177#95C23×C7311yescharacteristic
1178#95C23×C7311yescharacteristic
1179#95C23×C7311yescharacteristic
1180C24—22no—
1181C24—22no—
1182C24—22no—
1183C24—41no—
1184C24—41no—
1185C24—41no—
1186C24—41no—
1187C24C24×C7311yescharacteristic
1188C24C24×C7311yescharacteristic
1189C24C24×C7311yescharacteristic
1190C24C24×C7311yescharacteristic
1191C24C24×C7311yescharacteristic
1192C24C24×C7311yescharacteristic
1193C2×Q8—22no—
1194C2×Q8—41no—
1195C2×Q8—41no—
1196C2×Q8—41no—
1197C2×Q8—41no—
1198C2×Q8—41no—
1199C2×D4—22no—
1200C2×D4—22no—
1201C2×D4—22no—
1202C2×D4—22no—
1203C2×D4—22no—
1204C2×D4—22no—
1205C2×D4—22no—
1206C2×D4—22no—
1207C2×D4—22no—
1208C2×D4—22no—
1209C2×D4—22no—
1210C2×D4—22no—
1211C2×D4—22no—
1212C2×D4—41no—
1213C2×D4—41no—
1214C2×D4—41no—
1215C2×D4—41no—
1216C2×D4—41no—
1217C2×D4—41no—
1218C2×D4—41no—
1219C2×D4—41no—
1220C2×D4—41no—
1221C2×D4—41no—
1222C2×D4—41no—
1223C2×D4—41no—
1224C2×D4—41no—
1225C2×D4—41no—
1226C2×D4—41no—
1227C2×D4—41no—
1228C2×D4—41no—
1229C2×D4—41no—
1230C2×D4—41no—
1231C2×D4—41no—
1232C2×D4—41no—
1233C2×D4—41no—
1234C2×D4#41×C7314yes—
1235C22×C4—22no—
1236C22×C4—22no—
1237C22×C4—22no—
1238C22×C4—22no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—22no—
1247C22×C4—41no—
1248C22×C4—41no—
1249C22×C4—41no—
1250C22×C4—41no—
1251C22×C4—41no—
1252C22×C4—41no—
1253C22×C4—41no—
1254C22×C4—41no—
1255C22×C4—41no—
1256C22×C4—41no—
1257C22×C4—41no—
1258C22×C4—41no—
1259C22×C4—41no—
1260C22×C4—41no—
1261C22×C4—41no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—41no—
1265C22×C4—41no—
1266C22×C4—41no—
1267C22×C4—41no—
1268C22×C4—416no—
1269C22×C4C24×C7311yescharacteristic
1270C22×C4C24×C7311yescharacteristic
1271C22×C4C24×C7311yescharacteristic
1272C22×C4C24×C7311yescharacteristic
1273C22×C4C24×C7311yescharacteristic
1274C22×C4C24×C7311yescharacteristic
1275C22×C4C24×C7311yescharacteristic
1276C22×C4C24×C7311yescharacteristic
1277C22×C4C24×C7311yescharacteristic
1278C22×C4C24×C7311yescharacteristic
1279C22×C4C24×C7311yescharacteristic
1280C22×C4C24×C7311yescharacteristic
1281C22×C4C24×C7311yescharacteristic
1282C22×C4C24×C7311yescharacteristic
1283C22×C4C24×C7311yescharacteristic
1284C22×C4C24×C7311yescharacteristic
1285C22×C4C24×C7311yescharacteristic
1286C22×C4C24×C7311yescharacteristic
1287C22×C4C24×C7311yescharacteristic
1288C22×C4C24×C7311yescharacteristic
1289C22×C4C24×C7311yescharacteristic
1290C22×C4C24×C7311yescharacteristic
1291C22×C4C24×C7311yescharacteristic
1292C22×C4C24×C7311yescharacteristic
1293C22×C4C24×C7311yescharacteristic
1294C4⋊C4—22no—
1295C4⋊C4—22no—
1296C4⋊C4—22no—
1297C4⋊C4—22no—
1298C4⋊C4—22no—
1299C4⋊C4—22no—
1300C4⋊C4—22no—
1301C4⋊C4—22no—
1302C4⋊C4—22no—
1303C4⋊C4—22no—
1304C4⋊C4—41no—
1305C4⋊C4—41no—
1306C4⋊C4—41no—
1307C4⋊C4—41no—
1308C4⋊C4—41no—
1309C4⋊C4—41no—
1310C4⋊C4—41no—
1311C4⋊C4—41no—
1312C4⋊C4—41no—
1313C4⋊C4—41no—
1314C4⋊C4—41no—
1315C4⋊C4—41no—
1316C4⋊C4—41no—
1317C4⋊C4—41no—
1318C4⋊C4—41no—
1319C4⋊C4—41no—
1320C4⋊C4—41no—
1321C4⋊C4—41no—
1322C4⋊C4—41no—
1323C4⋊C4—41no—
1324C22⋊C4—22no—
1325C22⋊C4—22no—
1326C22⋊C4—22no—
1327C22⋊C4—22no—
1328C22⋊C4—22no—
1329C22⋊C4—22no—
1330C22⋊C4—22no—
1331C22⋊C4—22no—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—22no—
1335C22⋊C4—22no—
1336C22⋊C4—22no—
1337C22⋊C4—22no—
1338C22⋊C4—22no—
1339C22⋊C4—22no—
1340C22⋊C4—22no—
1341C22⋊C4—22no—
1342C22⋊C4—22no—
1343C22⋊C4—41no—
1344C22⋊C4—41no—
1345C22⋊C4—41no—
1346C22⋊C4—41no—
1347C22⋊C4—41no—
1348C22⋊C4—41no—
1349C22⋊C4—41no—
1350C22⋊C4—41no—
1351C22⋊C4—41no—
1352C22⋊C4—41no—
1353C22⋊C4—41no—
1354C22⋊C4—41no—
1355C22⋊C4—41no—
1356C22⋊C4—41no—
1357C22⋊C4—41no—
1358C22⋊C4—41no—
1359C22⋊C4—41no—
1360C22⋊C4—41no—
1361C22⋊C4—41no—
1362C22⋊C4—41no—
1363C22⋊C4—41no—
1364C22⋊C4—41no—
1365C22⋊C4—41no—
1366C22⋊C4—41no—
1367C22⋊C4—41no—
1368C22⋊C4—41no—
1369C22⋊C4—41no—
1370C22⋊C4—41no—
1371C22⋊C4—41no—
1372C22⋊C4—41no—
1373C22⋊C4—41no—
1374C22⋊C4—41no—
1375C22⋊C4—41no—
1376C42—22no—
1377C42—41no—
1378C42—41no—
1379C42—41no—
1380C42—41no—
1381C42—41no—
1382C42—41no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—21no—
1407C23—21no—
1408C23—21no—
1409C23—21no—
1410C23—21no—
1411C23—21no—
1412C23—21no—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—44no—
1422C23—44no—
1423C23—44no—
1424C23—44no—
1425C23—44no—
1426C23—44no—
1427C23—44no—
1428C23C2×#41×C7312yes—
1429C23C2×#41×C7312yes—
1430C23H(5,𝔽2)×C7312yes—
1431C232−1+4×C7312yes—
1432C23C25×C7311yescharacteristic
1433Q8—82no—
1434Q8—82no—
1435D4—44no—
1436D4—44no—
1437D4—44no—
1438D4—44no—
1439D4—82no—
1440D4—82no—
1441D4—82no—
1442D4—82no—
1443D4—82no—
1444D4—82no—
1445D4—82no—
1446D4—82no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—44no—
1519C2×C4—44no—
1520C2×C4—44no—
1521C2×C4—44no—
1522C2×C4—44no—
1523C2×C4—44no—
1524C2×C4—44no—
1525C2×C4—82no—
1526C2×C4—82no—
1527C2×C4—82no—
1528C2×C4—82no—
1529C2×C4C2×#41×C7312yes—
1530C2×C4H(5,𝔽2)×C7312yes—
1531C2×C4H(5,𝔽2)×C7312yes—
1532C2×C4H(5,𝔽2)×C7312yes—
1533C22—22no—
1534C22—22no—
1535C22—22no—
1536C22—22no—
1537C22—22no—
1538C22—22no—
1539C22—22no—
1540C22—22no—
1541C22—22no—
1542C22—22no—
1543C22—22no—
1544C22—22no—
1545C22—416no—
1546C22—41no—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—41no—
1560C22—41no—
1561C22—41no—
1562C22—41no—
1563C22—41no—
1564C22—41no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—41no—
1569C22—41no—
1570C22—41no—
1571C22—41no—
1572C22—41no—
1573C22—41no—
1574C22—41no—
1575C22—41no—
1576C22C22×#41×C7311yescharacteristic
1577C22C2×H(5,𝔽2)×C7311yescharacteristic
1578C22C2×H(5,𝔽2)×C7311yescharacteristic
1579C22C2×H(5,𝔽2)×C7311yescharacteristic
1580C22C2×H(5,𝔽2)×C7311yescharacteristic
1581C22C2×2−1+4×C7311yescharacteristic
1582C22#585×C7311yescharacteristic
1583C4—22no—
1584C4—22no—
1585C4—22no—
1586C4—22no—
1587C4—41no—
1588C4—41no—
1589C4—41no—
1590C4—41no—
1591C4—41no—
1592C4—41no—
1593C4—41no—
1594C4—41no—
1595C4—41no—
1596C4—41no—
1597C4—41no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—41no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—41no—
1608C2—42no—
1609C2—42no—
1610C2—42no—
1611C2—42no—
1612C2—81no—
1613C2—81no—
1614C2C73×#345911yescharacteristic
1615C2C73×#351911yescharacteristic
1616C2C73×#352011yescharacteristic
1617C2C73×#353211yescharacteristic
1618C2C73×#353611yescharacteristic
1619C2C73×#354111yescharacteristic
1620C2C73×#354211yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C73×#2848C2semidirect
2. C73×#2847C2semidirect
3. C73×#2787C2semidirect
4. C73×#2784C2semidirect
5. C73×#2778C2semidirect
6. C73×#2747C2semidirect
7. C73×#2732C2semidirect
8. C73×#2708C2semidirect
9. C73×#2696C2semidirect
10. C73×#2695C2semidirect
11. C73×#2692C2semidirect
12. C73×#2685C2semidirect
13. C73×#2684C2semidirect
14. C73×#2681C2semidirect
15. C73×#2678C2semidirect
16. C73×#2676C2semidirect
17. C73×#2671C2semidirect
18. C73×#2668C2semidirect
19. C73×#2653C2semidirect
20. C73×#2649C2semidirect
21. C73×#2522C2semidirect
22. C73×#2521C2semidirect
23. C73×#2477C2semidirect
24. C73×#2476C2semidirect
25. C73×#2463C2semidirect
26. C73×#2456C2semidirect
27. C73×#2450C2semidirect
28. C73×#2425C2semidirect
29. C73×#2325C2semidirect
30. C73×#2324C2semidirect
31. C4×#120×C73C2semidirect
36. C2×#123×C73C22semidirect
37. C2×#123×C73C22semidirect
41. C2×C22⋊Q8×C73C22semidirect
42. C2×C22⋊Q8×C73C22semidirect
55. C2×C4×D4×C73C22semidirect
56. C2×#117×C73C22semidirect
57. #401×C73C22semidirect
58. #400×C73C22semidirect
59. #400×C73C22semidirect
60. #400×C73C22semidirect
61. #400×C73C22semidirect
64. #399×C73C22semidirect
65. #398×C73C22semidirect
66. #398×C73C22semidirect
67. #398×C73C22semidirect
68. #398×C73C22semidirect
69. #398×C73C22semidirect
70. #398×C73C22semidirect
76. #397×C73C22semidirect
77. #397×C73C22semidirect
80. #396×C73C22semidirect
81. #396×C73C22semidirect
82. #396×C73C22semidirect
83. #395×C73C22semidirect
94. #394×C73C22semidirect
95. #394×C73C22semidirect
98. #393×C73C22semidirect
99. #393×C73C22semidirect
100. #393×C73C22semidirect
104. #392×C73C22semidirect
105. #391×C73C22semidirect
106. #391×C73C22semidirect
111. #390×C73C22semidirect
112. #389×C73C22semidirect
113. #389×C73C22semidirect
114. #389×C73C22semidirect
121. #388×C73C22semidirect
122. #388×C73C22semidirect
123. #388×C73C22semidirect
124. #388×C73C22semidirect
125. #388×C73C22semidirect
126. #388×C73C22semidirect
127. #388×C73C22semidirect
128. #387×C73C22semidirect
129. #387×C73C22semidirect
130. #387×C73C22semidirect
131. #387×C73C22semidirect
132. #387×C73C22semidirect
133. #387×C73C22semidirect
134. #387×C73C22semidirect
135. #387×C73C22semidirect
136. #387×C73C22semidirect
154. #386×C73C22semidirect
155. #386×C73C22semidirect
156. #386×C73C22semidirect
166. #385×C73C22semidirect
167. #385×C73C22semidirect
168. #385×C73C22semidirect
169. #385×C73C22semidirect
170. #385×C73C22semidirect
177. #380×C73C22semidirect
178. #380×C73C22semidirect
182. C4×C4⋊C4×C73C22semidirect
186. C2×#95×C73C22semidirect
797. #36901C73direct (N × H)
811. #2848C2×C73semidirect
812. #2847C2×C73semidirect
813. #2787C2×C73semidirect
814. #2784C2×C73semidirect
815. #2778C2×C73semidirect
816. #2747C2×C73semidirect
817. #2732C2×C73semidirect
818. #2708C2×C73semidirect
819. #2696C2×C73semidirect
820. #2695C2×C73semidirect
821. #2692C2×C73semidirect
822. #2685C2×C73semidirect
823. #2684C2×C73semidirect
824. #2681C2×C73semidirect
825. #2678C2×C73semidirect
826. #2676C2×C73semidirect
827. #2671C2×C73semidirect
828. #2668C2×C73semidirect
829. #2653C2×C73semidirect
830. #2649C2×C73semidirect
831. #2522C2×C73semidirect
832. #2521C2×C73semidirect
833. #2477C2×C73semidirect
834. #2476C2×C73semidirect
835. #2463C2×C73semidirect
836. #2456C2×C73semidirect
837. #2450C2×C73semidirect
838. #2425C2×C73semidirect
839. #2325C2×C73semidirect
840. #2324C2×C73semidirect
841. C4×#120C2×C73semidirect
842. C73#36901direct (N × H)
847. C2×#123C22×C73semidirect
848. C2×#123C22×C73semidirect
852. C2×C22⋊Q8C22×C73semidirect
853. C2×C22⋊Q8C22×C73semidirect
866. C2×C4×D4C22×C73semidirect
867. C2×#117C22×C73semidirect
868. #401C22×C73semidirect
869. #400C22×C73semidirect
870. #400C22×C73semidirect
871. #400C22×C73semidirect
872. #400C22×C73semidirect
875. #399C22×C73semidirect
876. #398C22×C73semidirect
877. #398C22×C73semidirect
878. #398C22×C73semidirect
879. #398C22×C73semidirect
880. #398C22×C73semidirect
881. #398C22×C73semidirect
887. #397C22×C73semidirect
888. #397C22×C73semidirect
891. #396C22×C73semidirect
892. #396C22×C73semidirect
893. #396C22×C73semidirect
894. #395C22×C73semidirect
905. #394C22×C73semidirect
906. #394C22×C73semidirect
909. #393C22×C73semidirect
910. #393C22×C73semidirect
911. #393C22×C73semidirect
915. #392C22×C73semidirect
916. #391C22×C73semidirect
917. #391C22×C73semidirect
922. #390C22×C73semidirect
923. #389C22×C73semidirect
924. #389C22×C73semidirect
925. #389C22×C73semidirect
932. #388C22×C73semidirect
933. #388C22×C73semidirect
934. #388C22×C73semidirect
935. #388C22×C73semidirect
936. #388C22×C73semidirect
937. #388C22×C73semidirect
938. #388C22×C73semidirect
939. #387C22×C73semidirect
940. #387C22×C73semidirect
941. #387C22×C73semidirect
942. #387C22×C73semidirect
943. #387C22×C73semidirect
944. #387C22×C73semidirect
945. #387C22×C73semidirect
946. #387C22×C73semidirect
947. #387C22×C73semidirect
965. #386C22×C73semidirect
966. #386C22×C73semidirect
967. #386C22×C73semidirect
977. #385C22×C73semidirect
978. #385C22×C73semidirect
979. #385C22×C73semidirect
980. #385C22×C73semidirect
981. #385C22×C73semidirect
988. #380C22×C73semidirect
989. #380C22×C73semidirect
993. C4×C4⋊C4C22×C73semidirect
997. C2×#95C22×C73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C73×#28482
C73×#28472
C73×#27872
C73×#27842
C73×#27782
C73×#27472
C73×#27322
C73×#27082
C73×#26962
C73×#26952
C73×#26922
C73×#26852
C73×#26842
C73×#26812
C73×#26782
C73×#26762
C73×#26712
C73×#26682
C73×#26532
C73×#26492
C73×#25222
C73×#25212
C73×#24772
C73×#24762
C73×#24632
C73×#24562
C73×#24502
C73×#24252
C73×#23252
C73×#23242
C4×#120×C732
#3690173