Finite Group Databasebeta

← C73×#36817 #32946221

Subgroups — C73×#36817 #32946221

Order 18688.

1852 conjugacy classes of subgroups.

The subgroup lattice has 1530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2851C211yesmaximal, characteristic, complemented
2C73×#2850C211yesmaximal, characteristic, complemented
3C73×#2778C211yesmaximal, characteristic, complemented
4C73×#2763C211yesmaximal, characteristic, complemented
5C73×#2762C211yesmaximal, characteristic, complemented
6C73×#2756C211yesmaximal, characteristic, complemented
7C73×#2753C211yesmaximal, characteristic, complemented
8C73×#2728C211yesmaximal, characteristic, complemented
9C73×#2723C211yesmaximal, characteristic, complemented
10C73×#2723C211yesmaximal, characteristic, complemented
11C73×#2711C211yesmaximal, characteristic, complemented
12C73×#2708C211yesmaximal, characteristic, complemented
13C73×#2704C211yesmaximal, characteristic, complemented
14C73×#2700C211yesmaximal, characteristic, complemented
15C73×#2686C211yesmaximal, characteristic, complemented
16C73×#2676C211yesmaximal, characteristic, complemented
17C73×#2676C211yesmaximal, characteristic, complemented
18C73×#2671C211yesmaximal, characteristic, complemented
19C73×#2653C211yesmaximal, characteristic, complemented
20C73×#2649C211yesmaximal, characteristic, complemented
21C73×#2602C211yesmaximal, characteristic, complemented
22C73×#2589C211yesmaximal, characteristic, complemented
23C73×#2559C211yesmaximal, characteristic, complemented
24C73×#2549C211yesmaximal, characteristic, complemented
25C73×#2474C211yesmaximal, characteristic, complemented
26C73×#2470C211yesmaximal, characteristic, complemented
27C73×#2430C211yesmaximal, characteristic, complemented
28C73×#2407C211yesmaximal, characteristic, complemented
29C73×#2335C211yesmaximal, characteristic, complemented
30C73×#2318C211yesmaximal, characteristic, complemented
31C73×#2297C211yesmaximal, characteristic, complemented
32C22×#41×C73C2211yescharacteristic
33C2×#126×C73C2211yescharacteristic
34C2×#125×C73C2211yescharacteristic
35C2×#124×C73C2211yescharacteristic
36C2×#124×C73C2211yescharacteristic
37C2×#123×C73C2211yescharacteristic
38C2×#123×C73C2211yescharacteristic
39C2×C22⋊Q8×C73C2211yescharacteristic
40C2×C22⋊Q8×C73C2211yescharacteristic
41C2×C22⋊Q8×C73C2211yescharacteristic
42C2×C22⋊Q8×C73C2211yescharacteristic
43C2×#121×C73C2211yescharacteristic
44C2×#121×C73C2211yescharacteristic
45C2×#121×C73C2211yescharacteristic
46C2×#121×C73C2211yescharacteristic
47C2×#121×C73C2211yescharacteristic
48C2×C4×D4×C73C2211yescharacteristic
49C2×#117×C73C2211yescharacteristic
50C22×C42×C73C2211yescharacteristic
51#401×C73C2211yescharacteristic
52#400×C73C2211yescharacteristic
53#400×C73C2211yescharacteristic
54#400×C73C2211yescharacteristic
55#400×C73C2211yescharacteristic
56#400×C73C2211yescharacteristic
57#399×C73C2211yescharacteristic
58#399×C73C2211yescharacteristic
59#398×C73C2211yescharacteristic
60#398×C73C2211yescharacteristic
61#398×C73C2211yescharacteristic
62#398×C73C2211yescharacteristic
63#397×C73C2211yescharacteristic
64#397×C73C2211yescharacteristic
65#397×C73C2211yescharacteristic
66#397×C73C2211yescharacteristic
67#397×C73C2211yescharacteristic
68#397×C73C2211yescharacteristic
69#397×C73C2211yescharacteristic
70#396×C73C2211yescharacteristic
71#396×C73C2211yescharacteristic
72#396×C73C2211yescharacteristic
73#395×C73C2211yescharacteristic
74#395×C73C2211yescharacteristic
75#395×C73C2211yescharacteristic
76#395×C73C2211yescharacteristic
77#394×C73C2211yescharacteristic
78#394×C73C2211yescharacteristic
79#394×C73C2211yescharacteristic
80#394×C73C2211yescharacteristic
81#394×C73C2211yescharacteristic
82#394×C73C2211yescharacteristic
83#394×C73C2211yescharacteristic
84#394×C73C2211yescharacteristic
85#394×C73C2211yescharacteristic
86#394×C73C2211yescharacteristic
87#394×C73C2211yescharacteristic
88#394×C73C2211yescharacteristic
89#394×C73C2211yescharacteristic
90#394×C73C2211yescharacteristic
91#393×C73C2211yescharacteristic
92#393×C73C2211yescharacteristic
93#393×C73C2211yescharacteristic
94#393×C73C2211yescharacteristic
95#392×C73C2211yescharacteristic
96#392×C73C2211yescharacteristic
97#392×C73C2211yescharacteristic
98#392×C73C2211yescharacteristic
99#391×C73C2211yescharacteristic
100#391×C73C2211yescharacteristic
101#391×C73C2211yescharacteristic
102#391×C73C2211yescharacteristic
103#391×C73C2211yescharacteristic
104#391×C73C2211yescharacteristic
105#390×C73C2211yescharacteristic
106#390×C73C2211yescharacteristic
107#390×C73C2211yescharacteristic
108#390×C73C2211yescharacteristic
109#390×C73C2211yescharacteristic
110#389×C73C2211yescharacteristic
111#389×C73C2211yescharacteristic
112#389×C73C2211yescharacteristic
113#389×C73C2211yescharacteristic
114#389×C73C2211yescharacteristic
115#388×C73C2211yescharacteristic
116#388×C73C2211yescharacteristic
117#388×C73C2211yescharacteristic
118#388×C73C2211yescharacteristic
119#388×C73C2211yescharacteristic
120#388×C73C2211yescharacteristic
121#388×C73C2211yescharacteristic
122#388×C73C2211yescharacteristic
123#388×C73C2211yescharacteristic
124#388×C73C2211yescharacteristic
125#388×C73C2211yescharacteristic
126#388×C73C2211yescharacteristic
127#388×C73C2211yescharacteristic
128#388×C73C2211yescharacteristic
129#388×C73C2211yescharacteristic
130#388×C73C2211yescharacteristic
131#388×C73C2211yescharacteristic
132#387×C73C2211yescharacteristic
133#387×C73C2211yescharacteristic
134#387×C73C2211yescharacteristic
135#387×C73C2211yescharacteristic
136#387×C73C2211yescharacteristic
137#387×C73C2211yescharacteristic
138#387×C73C2211yescharacteristic
139#387×C73C2211yescharacteristic
140#387×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
155#386×C73C2211yescharacteristic
156#386×C73C2211yescharacteristic
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
167#385×C73C2211yescharacteristic
168#385×C73C2211yescharacteristic
169#385×C73C2211yescharacteristic
170#385×C73C2211yescharacteristic
171#383×C73C2211yescharacteristic
172#382×C73C2211yescharacteristic
173#382×C73C2211yescharacteristic
174#382×C73C2211yescharacteristic
175#381×C73C2211yescharacteristic
176#380×C73C2211yescharacteristic
177#380×C73C2211yescharacteristic
178#380×C73C2211yescharacteristic
179#380×C73C2211yescharacteristic
180C4×C4⋊C4×C73C2211yescharacteristic
181C4×C22⋊C4×C73C2211yescharacteristic
182C4×C22⋊C4×C73C2211yescharacteristic
183C4×C22⋊C4×C73C2211yescharacteristic
184C4×C22⋊C4×C73C2211yescharacteristic
185C4×C22⋊C4×C73C2211yescharacteristic
186C2×#95×C73C2211yescharacteristic
187C2×#41×C73—24no—
188C2×#41×C73—42no—
189C2×#41×C73—42no—
190C22×Q8×C73C2311yescharacteristic
191C22×Q8×C73C2311yescharacteristic
192C22×Q8×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
202C22×D4×C73C2311yescharacteristic
203C23×C4×C73C2311yescharacteristic
204C23×C4×C73C2311yescharacteristic
205C23×C4×C73C2311yescharacteristic
206C23×C4×C73C2311yescharacteristic
207C23×C4×C73C2311yescharacteristic
208C23×C4×C73C2311yescharacteristic
209C23×C4×C73C2311yescharacteristic
210C23×C4×C73C2311yescharacteristic
211C23×C4×C73C2311yescharacteristic
212#126×C73—42no—
213#125×C73—42no—
214#124×C73—42no—
215#124×C73—42no—
216#123×C73—24no—
217#123×C73—42no—
218C22⋊Q8×C73—42no—
219C22⋊Q8×C73—42no—
220C22⋊Q8×C73—42no—
221C22⋊Q8×C73—42no—
222#121×C73—42no—
223#121×C73—42no—
224#121×C73—42no—
225#121×C73—42no—
226#121×C73—42no—
227C4×D4×C73—24no—
228#117×C73—42no—
229C2×C4⋊C4×C73C2311yescharacteristic
230C2×C4⋊C4×C73C2311yescharacteristic
231C2×C4⋊C4×C73C2311yescharacteristic
232C2×C4⋊C4×C73C2311yescharacteristic
233C2×C4⋊C4×C73C2311yescharacteristic
234C2×C4⋊C4×C73C2311yescharacteristic
235C2×C4⋊C4×C73C2311yescharacteristic
236C2×C4⋊C4×C73C2311yescharacteristic
237C2×C4⋊C4×C73C2311yescharacteristic
238C2×C4⋊C4×C73C2311yescharacteristic
239C2×C4⋊C4×C73C2311yescharacteristic
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×C22⋊C4×C73C2311yescharacteristic
261C2×C22⋊C4×C73C2311yescharacteristic
262C2×C22⋊C4×C73C2311yescharacteristic
263C2×C22⋊C4×C73C2311yescharacteristic
264C2×C22⋊C4×C73C2311yescharacteristic
265C2×C22⋊C4×C73C2311yescharacteristic
266C2×C22⋊C4×C73C2311yescharacteristic
267C2×C22⋊C4×C73C2311yescharacteristic
268C2×C22⋊C4×C73C2311yescharacteristic
269C2×C22⋊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×C42×C73—42no—
307C2×C42×C73C2311yescharacteristic
308C2×C42×C73C2311yescharacteristic
309C2×C42×C73C2311yescharacteristic
310C2×C42×C73C2311yescharacteristic
311C2×C42×C73C2311yescharacteristic
312C2×C42×C73C2311yescharacteristic
313C2×C42×C73C2311yescharacteristic
314C2×C42×C73C2311yescharacteristic
315C2×C42×C73C2311yescharacteristic
316C2×C42×C73C2311yescharacteristic
317#95×C73C2311yescharacteristic
318#95×C73C2311yescharacteristic
319#95×C73C2311yescharacteristic
320#95×C73C2311yescharacteristic
321#95×C73C2311yescharacteristic
322#95×C73C2311yescharacteristic
323#95×C73C2311yescharacteristic
324#95×C73C2311yescharacteristic
325#95×C73C2311yescharacteristic
326#95×C73C2311yescharacteristic
327#95×C73C2311yescharacteristic
328#95×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
363C24×C73C2411yescharacteristic
364C24×C73C2411yescharacteristic
365C24×C73C2411yescharacteristic
366C24×C73C2411yescharacteristic
367C24×C73C2411yescharacteristic
368#41×C73—416no—
369C2×Q8×C73—22no—
370C2×Q8×C73—22no—
371C2×Q8×C73—22no—
372C2×Q8×C73—41no—
373C2×Q8×C73—41no—
374C2×Q8×C73—41no—
375C2×Q8×C73—41no—
376C2×Q8×C73—41no—
377C2×Q8×C73—41no—
378C2×D4×C73—22no—
379C2×D4×C73—22no—
380C2×D4×C73—22no—
381C2×D4×C73—22no—
382C2×D4×C73—22no—
383C2×D4×C73—22no—
384C2×D4×C73—22no—
385C2×D4×C73—22no—
386C2×D4×C73—22no—
387C2×D4×C73—22no—
388C2×D4×C73—22no—
389C2×D4×C73—41no—
390C2×D4×C73—41no—
391C2×D4×C73—41no—
392C2×D4×C73—41no—
393C2×D4×C73—41no—
394C2×D4×C73—41no—
395C2×D4×C73—41no—
396C2×D4×C73—41no—
397C2×D4×C73—41no—
398C2×D4×C73—41no—
399C2×D4×C73—41no—
400C2×D4×C73—41no—
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—
408C22×C4×C73—22no—
409C22×C4×C73—22no—
410C22×C4×C73—22no—
411C22×C4×C73—22no—
412C22×C4×C73—22no—
413C22×C4×C73—22no—
414C22×C4×C73—22no—
415C22×C4×C73—41no—
416C22×C4×C73—41no—
417C22×C4×C73—41no—
418C22×C4×C73—41no—
419C22×C4×C73—41no—
420C22×C4×C73—41no—
421C22×C4×C73—41no—
422C22×C4×C73—41no—
423C22×C4×C73—41no—
424C22×C4×C73—41no—
425C22×C4×C73—41no—
426C22×C4×C73—41no—
427C22×C4×C73—41no—
428C22×C4×C73—41no—
429C22×C4×C73—41no—
430C22×C4×C73—41no—
431C22×C4×C73—41no—
432C22×C4×C73—41no—
433C22×C4×C73—41no—
434C22×C4×C73#4114yes—
435C22×C4×C73C2411yescharacteristic
436C22×C4×C73C2411yescharacteristic
437C22×C4×C73C2411yescharacteristic
438C22×C4×C73C2411yescharacteristic
439C22×C4×C73C2411yescharacteristic
440C22×C4×C73C2411yescharacteristic
441C22×C4×C73C2411yescharacteristic
442C22×C4×C73C2411yescharacteristic
443C22×C4×C73C2411yescharacteristic
444C22×C4×C73C2411yescharacteristic
445C22×C4×C73C2411yescharacteristic
446C22×C4×C73C2411yescharacteristic
447C22×C4×C73C2411yescharacteristic
448C22×C4×C73C2411yescharacteristic
449C22×C4×C73C2411yescharacteristic
450C22×C4×C73C2411yescharacteristic
451C22×C4×C73C2411yescharacteristic
452C22×C4×C73C2411yescharacteristic
453C22×C4×C73C2411yescharacteristic
454C22×C4×C73C2411yescharacteristic
455C22×C4×C73C2411yescharacteristic
456C22×C4×C73C2411yescharacteristic
457C22×C4×C73C2411yescharacteristic
458C22×C4×C73C2411yescharacteristic
459C22×C4×C73C2411yescharacteristic
460C22×C4×C73C2411yescharacteristic
461C4⋊C4×C73—22no—
462C4⋊C4×C73—22no—
463C4⋊C4×C73—22no—
464C4⋊C4×C73—22no—
465C4⋊C4×C73—22no—
466C4⋊C4×C73—22no—
467C4⋊C4×C73—22no—
468C4⋊C4×C73—22no—
469C4⋊C4×C73—22no—
470C4⋊C4×C73—41no—
471C4⋊C4×C73—41no—
472C4⋊C4×C73—41no—
473C4⋊C4×C73—41no—
474C4⋊C4×C73—41no—
475C4⋊C4×C73—41no—
476C4⋊C4×C73—41no—
477C4⋊C4×C73—41no—
478C4⋊C4×C73—41no—
479C4⋊C4×C73—41no—
480C4⋊C4×C73—41no—
481C4⋊C4×C73—41no—
482C4⋊C4×C73—41no—
483C4⋊C4×C73—41no—
484C4⋊C4×C73—41no—
485C4⋊C4×C73—41no—
486C4⋊C4×C73—41no—
487C4⋊C4×C73—41no—
488C4⋊C4×C73—41no—
489C4⋊C4×C73—41no—
490C4⋊C4×C73—41no—
491C4⋊C4×C73—41no—
492C22⋊C4×C73—22no—
493C22⋊C4×C73—22no—
494C22⋊C4×C73—22no—
495C22⋊C4×C73—22no—
496C22⋊C4×C73—22no—
497C22⋊C4×C73—22no—
498C22⋊C4×C73—22no—
499C22⋊C4×C73—22no—
500C22⋊C4×C73—22no—
501C22⋊C4×C73—22no—
502C22⋊C4×C73—22no—
503C22⋊C4×C73—22no—
504C22⋊C4×C73—22no—
505C22⋊C4×C73—22no—
506C22⋊C4×C73—22no—
507C22⋊C4×C73—22no—
508C22⋊C4×C73—22no—
509C22⋊C4×C73—41no—
510C22⋊C4×C73—41no—
511C22⋊C4×C73—41no—
512C22⋊C4×C73—41no—
513C22⋊C4×C73—41no—
514C22⋊C4×C73—41no—
515C22⋊C4×C73—41no—
516C22⋊C4×C73—41no—
517C22⋊C4×C73—41no—
518C22⋊C4×C73—41no—
519C22⋊C4×C73—41no—
520C22⋊C4×C73—41no—
521C22⋊C4×C73—41no—
522C22⋊C4×C73—41no—
523C22⋊C4×C73—41no—
524C22⋊C4×C73—41no—
525C22⋊C4×C73—41no—
526C22⋊C4×C73—41no—
527C22⋊C4×C73—41no—
528C22⋊C4×C73—41no—
529C22⋊C4×C73—41no—
530C22⋊C4×C73—41no—
531C22⋊C4×C73—41no—
532C22⋊C4×C73—41no—
533C22⋊C4×C73—41no—
534C22⋊C4×C73—41no—
535C22⋊C4×C73—41no—
536C22⋊C4×C73—41no—
537C22⋊C4×C73—41no—
538C42×C73—22no—
539C42×C73—22no—
540C42×C73—22no—
541C42×C73—41no—
542C42×C73—41no—
543C42×C73—41no—
544C42×C73—41no—
545C42×C73—41no—
546C42×C73—41no—
547C42×C73—41no—
548C23×C73—21no—
549C23×C73—21no—
550C23×C73—21no—
551C23×C73—21no—
552C23×C73—21no—
553C23×C73—21no—
554C23×C73—21no—
555C23×C73—21no—
556C23×C73—21no—
557C23×C73—21no—
558C23×C73—21no—
559C23×C73—21no—
560C23×C73—21no—
561C23×C73—21no—
562C23×C73—21no—
563C23×C73—21no—
564C23×C73—21no—
565C23×C73—21no—
566C23×C73—21no—
567C23×C73—21no—
568C23×C73—21no—
569C23×C73—21no—
570C23×C73—21no—
571C23×C73—21no—
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×C73C2×#4112yes—
582C23×C73H(5,𝔽2)12yes—
583C23×C73C2511yescharacteristic
584Q8×C73—44no—
585Q8×C73—82no—
586Q8×C73—82no—
587D4×C73—44no—
588D4×C73—44no—
589D4×C73—44no—
590D4×C73—44no—
591D4×C73—82no—
592D4×C73—82no—
593D4×C73—82no—
594D4×C73—82no—
595D4×C73—82no—
596D4×C73—82no—
597C2×C4×C73—28no—
598C2×C4×C73—21no—
599C2×C4×C73—21no—
600C2×C4×C73—21no—
601C2×C4×C73—21no—
602C2×C4×C73—21no—
603C2×C4×C73—21no—
604C2×C4×C73—21no—
605C2×C4×C73—21no—
606C2×C4×C73—21no—
607C2×C4×C73—21no—
608C2×C4×C73—21no—
609C2×C4×C73—21no—
610C2×C4×C73—21no—
611C2×C4×C73—21no—
612C2×C4×C73—21no—
613C2×C4×C73—21no—
614C2×C4×C73—21no—
615C2×C4×C73—21no—
616C2×C4×C73—21no—
617C2×C4×C73—21no—
618C2×C4×C73—21no—
619C2×C4×C73—21no—
620C2×C4×C73—21no—
621C2×C4×C73—21no—
622C2×C4×C73—21no—
623C2×C4×C73—21no—
624C2×C4×C73—21no—
625C2×C4×C73—21no—
626C2×C4×C73—21no—
627C2×C4×C73—21no—
628C2×C4×C73—21no—
629C2×C4×C73—21no—
630C2×C4×C73—21no—
631C2×C4×C73—21no—
632C2×C4×C73—21no—
633C2×C4×C73—21no—
634C2×C4×C73—21no—
635C2×C4×C73—21no—
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—44no—
672C2×C4×C73—44no—
673C2×C4×C73—44no—
674C2×C4×C73—44no—
675C2×C4×C73—82no—
676C2×C4×C73—82no—
677C2×C4×C73—82no—
678C2×C4×C73—82no—
679C2×C4×C73C2×#4112yes—
680C2×C4×C73C2×#4112yes—
681C2×C4×C73H(5,𝔽2)12yes—
682C2×C4×C73H(5,𝔽2)12yes—
683C2×C4×C732−1+412yes—
684C22×C73—22no—
685C22×C73—22no—
686C22×C73—22no—
687C22×C73—22no—
688C22×C73—22no—
689C22×C73—22no—
690C22×C73—41no—
691C22×C73—41no—
692C22×C73—41no—
693C22×C73—41no—
694C22×C73—41no—
695C22×C73—41no—
696C22×C73—41no—
697C22×C73—41no—
698C22×C73—41no—
699C22×C73—41no—
700C22×C73—41no—
701C22×C73—41no—
702C22×C73—41no—
703C22×C73—41no—
704C22×C73—41no—
705C22×C73—41no—
706C22×C73—41no—
707C22×C73—41no—
708C22×C73—41no—
709C22×C73—41no—
710C22×C73—41no—
711C22×C73—41no—
712C22×C73—41no—
713C22×C73—41no—
714C22×C73—41no—
715C22×C73—41no—
716C22×C73—41no—
717C22×C73—41no—
718C22×C73—41no—
719C22×C73C22×#4111yescharacteristic
720C22×C73C2×H(5,𝔽2)11yescharacteristic
721C22×C73C2×H(5,𝔽2)11yescharacteristic
722C22×C73C2×H(5,𝔽2)11yescharacteristic
723C22×C73C2×2−1+411yescharacteristic
724C22×C73#58511yescharacteristic
725C22×C73#58511yescharacteristic
726C4×C73—22no—
727C4×C73—22no—
728C4×C73—22no—
729C4×C73—22no—
730C4×C73—22no—
731C4×C73—41no—
732C4×C73—41no—
733C4×C73—41no—
734C4×C73—41no—
735C4×C73—41no—
736C4×C73—41no—
737C4×C73—41no—
738C4×C73—41no—
739C4×C73—41no—
740C4×C73—41no—
741C4×C73—41no—
742C4×C73—41no—
743C4×C73—41no—
744C4×C73—41no—
745C4×C73—41no—
746C4×C73—41no—
747C4×C73—41no—
748C4×C73—41no—
749C4×C73—41no—
750C4×C73—41no—
751C4×C73—41no—
752#36817C7311yesmaximal, characteristic, direct product factor, Sylow
753C2×C73—42no—
754C2×C73—42no—
755C2×C73—81no—
756C2×C73—81no—
757C2×C73—81no—
758C2×C73#345511yescharacteristic
759C2×C73#349011yescharacteristic
760C2×C73#351111yescharacteristic
761C2×C73#354111yescharacteristic
762C2×C73#354211yescharacteristic
763C2×C73#355811yescharacteristic
764C2×C73#355911yescharacteristic
765#2851C2×C7311yescharacteristic, complemented
766#2850C2×C7311yescharacteristic, complemented
767#2778C2×C7311yescharacteristic, complemented
768#2763C2×C7311yescharacteristic, complemented
769#2762C2×C7311yescharacteristic, complemented
770#2756C2×C7311yescharacteristic, complemented
771#2753C2×C7311yescharacteristic, complemented
772#2728C2×C7311yescharacteristic, complemented
773#2723C2×C7311yescharacteristic, complemented
774#2723C2×C7311yescharacteristic, complemented
775#2711C2×C7311yescharacteristic, complemented
776#2708C2×C7311yescharacteristic, complemented
777#2704C2×C7311yescharacteristic, complemented
778#2700C2×C7311yescharacteristic, complemented
779#2686C2×C7311yescharacteristic, complemented
780#2676C2×C7311yescharacteristic, complemented
781#2676C2×C7311yescharacteristic, complemented
782#2671C2×C7311yescharacteristic, complemented
783#2653C2×C7311yescharacteristic, complemented
784#2649C2×C7311yescharacteristic, complemented
785#2602C2×C7311yescharacteristic, complemented
786#2589C2×C7311yescharacteristic, complemented
787#2559C2×C7311yescharacteristic, complemented
788#2549C2×C7311yescharacteristic, complemented
789#2474C2×C7311yescharacteristic, complemented
790#2470C2×C7311yescharacteristic, complemented
791#2430C2×C7311yescharacteristic, complemented
792#2407C2×C7311yescharacteristic, complemented
793#2335C2×C7311yescharacteristic, complemented
794#2318C2×C7311yescharacteristic, complemented
795#2297C2×C7311yescharacteristic, complemented
796C73#3681711yescharacteristic, direct product factor, Sylow
797C22×#41C22×C7311yescharacteristic
798C2×#126C22×C7311yescharacteristic
799C2×#125C22×C7311yescharacteristic
800C2×#124C22×C7311yescharacteristic
801C2×#124C22×C7311yescharacteristic
802C2×#123C22×C7311yescharacteristic
803C2×#123C22×C7311yescharacteristic
804C2×C22⋊Q8C22×C7311yescharacteristic
805C2×C22⋊Q8C22×C7311yescharacteristic
806C2×C22⋊Q8C22×C7311yescharacteristic
807C2×C22⋊Q8C22×C7311yescharacteristic
808C2×#121C22×C7311yescharacteristic
809C2×#121C22×C7311yescharacteristic
810C2×#121C22×C7311yescharacteristic
811C2×#121C22×C7311yescharacteristic
812C2×#121C22×C7311yescharacteristic
813C2×C4×D4C22×C7311yescharacteristic
814C2×#117C22×C7311yescharacteristic
815C22×C42C22×C7311yescharacteristic
816#401C22×C7311yescharacteristic
817#400C22×C7311yescharacteristic
818#400C22×C7311yescharacteristic
819#400C22×C7311yescharacteristic
820#400C22×C7311yescharacteristic
821#400C22×C7311yescharacteristic
822#399C22×C7311yescharacteristic
823#399C22×C7311yescharacteristic
824#398C22×C7311yescharacteristic
825#398C22×C7311yescharacteristic
826#398C22×C7311yescharacteristic
827#398C22×C7311yescharacteristic
828#397C22×C7311yescharacteristic
829#397C22×C7311yescharacteristic
830#397C22×C7311yescharacteristic
831#397C22×C7311yescharacteristic
832#397C22×C7311yescharacteristic
833#397C22×C7311yescharacteristic
834#397C22×C7311yescharacteristic
835#396C22×C7311yescharacteristic
836#396C22×C7311yescharacteristic
837#396C22×C7311yescharacteristic
838#395C22×C7311yescharacteristic
839#395C22×C7311yescharacteristic
840#395C22×C7311yescharacteristic
841#395C22×C7311yescharacteristic
842#394C22×C7311yescharacteristic
843#394C22×C7311yescharacteristic
844#394C22×C7311yescharacteristic
845#394C22×C7311yescharacteristic
846#394C22×C7311yescharacteristic
847#394C22×C7311yescharacteristic
848#394C22×C7311yescharacteristic
849#394C22×C7311yescharacteristic
850#394C22×C7311yescharacteristic
851#394C22×C7311yescharacteristic
852#394C22×C7311yescharacteristic
853#394C22×C7311yescharacteristic
854#394C22×C7311yescharacteristic
855#394C22×C7311yescharacteristic
856#393C22×C7311yescharacteristic
857#393C22×C7311yescharacteristic
858#393C22×C7311yescharacteristic
859#393C22×C7311yescharacteristic
860#392C22×C7311yescharacteristic
861#392C22×C7311yescharacteristic
862#392C22×C7311yescharacteristic
863#392C22×C7311yescharacteristic
864#391C22×C7311yescharacteristic
865#391C22×C7311yescharacteristic
866#391C22×C7311yescharacteristic
867#391C22×C7311yescharacteristic
868#391C22×C7311yescharacteristic
869#391C22×C7311yescharacteristic
870#390C22×C7311yescharacteristic
871#390C22×C7311yescharacteristic
872#390C22×C7311yescharacteristic
873#390C22×C7311yescharacteristic
874#390C22×C7311yescharacteristic
875#389C22×C7311yescharacteristic
876#389C22×C7311yescharacteristic
877#389C22×C7311yescharacteristic
878#389C22×C7311yescharacteristic
879#389C22×C7311yescharacteristic
880#388C22×C7311yescharacteristic
881#388C22×C7311yescharacteristic
882#388C22×C7311yescharacteristic
883#388C22×C7311yescharacteristic
884#388C22×C7311yescharacteristic
885#388C22×C7311yescharacteristic
886#388C22×C7311yescharacteristic
887#388C22×C7311yescharacteristic
888#388C22×C7311yescharacteristic
889#388C22×C7311yescharacteristic
890#388C22×C7311yescharacteristic
891#388C22×C7311yescharacteristic
892#388C22×C7311yescharacteristic
893#388C22×C7311yescharacteristic
894#388C22×C7311yescharacteristic
895#388C22×C7311yescharacteristic
896#388C22×C7311yescharacteristic
897#387C22×C7311yescharacteristic
898#387C22×C7311yescharacteristic
899#387C22×C7311yescharacteristic
900#387C22×C7311yescharacteristic
901#387C22×C7311yescharacteristic
902#387C22×C7311yescharacteristic
903#387C22×C7311yescharacteristic
904#387C22×C7311yescharacteristic
905#387C22×C7311yescharacteristic
906#386C22×C7311yescharacteristic
907#386C22×C7311yescharacteristic
908#386C22×C7311yescharacteristic
909#386C22×C7311yescharacteristic
910#386C22×C7311yescharacteristic
911#386C22×C7311yescharacteristic
912#386C22×C7311yescharacteristic
913#386C22×C7311yescharacteristic
914#386C22×C7311yescharacteristic
915#386C22×C7311yescharacteristic
916#386C22×C7311yescharacteristic
917#386C22×C7311yescharacteristic
918#386C22×C7311yescharacteristic
919#386C22×C7311yescharacteristic
920#386C22×C7311yescharacteristic
921#386C22×C7311yescharacteristic
922#385C22×C7311yescharacteristic
923#385C22×C7311yescharacteristic
924#385C22×C7311yescharacteristic
925#385C22×C7311yescharacteristic
926#385C22×C7311yescharacteristic
927#385C22×C7311yescharacteristic
928#385C22×C7311yescharacteristic
929#385C22×C7311yescharacteristic
930#385C22×C7311yescharacteristic
931#385C22×C7311yescharacteristic
932#385C22×C7311yescharacteristic
933#385C22×C7311yescharacteristic
934#385C22×C7311yescharacteristic
935#385C22×C7311yescharacteristic
936#383C22×C7311yescharacteristic
937#382C22×C7311yescharacteristic
938#382C22×C7311yescharacteristic
939#382C22×C7311yescharacteristic
940#381C22×C7311yescharacteristic
941#380C22×C7311yescharacteristic
942#380C22×C7311yescharacteristic
943#380C22×C7311yescharacteristic
944#380C22×C7311yescharacteristic
945C4×C4⋊C4C22×C7311yescharacteristic
946C4×C22⋊C4C22×C7311yescharacteristic
947C4×C22⋊C4C22×C7311yescharacteristic
948C4×C22⋊C4C22×C7311yescharacteristic
949C4×C22⋊C4C22×C7311yescharacteristic
950C4×C22⋊C4C22×C7311yescharacteristic
951C2×#95C22×C7311yescharacteristic
952C2×#41—24no—
953C2×#41—42no—
954C2×#41—42no—
955C22×Q8C23×C7311yescharacteristic
956C22×Q8C23×C7311yescharacteristic
957C22×Q8C23×C7311yescharacteristic
958C22×D4C23×C7311yescharacteristic
959C22×D4C23×C7311yescharacteristic
960C22×D4C23×C7311yescharacteristic
961C22×D4C23×C7311yescharacteristic
962C22×D4C23×C7311yescharacteristic
963C22×D4C23×C7311yescharacteristic
964C22×D4C23×C7311yescharacteristic
965C22×D4C23×C7311yescharacteristic
966C22×D4C23×C7311yescharacteristic
967C22×D4C23×C7311yescharacteristic
968C23×C4C23×C7311yescharacteristic
969C23×C4C23×C7311yescharacteristic
970C23×C4C23×C7311yescharacteristic
971C23×C4C23×C7311yescharacteristic
972C23×C4C23×C7311yescharacteristic
973C23×C4C23×C7311yescharacteristic
974C23×C4C23×C7311yescharacteristic
975C23×C4C23×C7311yescharacteristic
976C23×C4C23×C7311yescharacteristic
977#126—42no—
978#125—42no—
979#124—42no—
980#124—42no—
981#123—24no—
982#123—42no—
983C22⋊Q8—42no—
984C22⋊Q8—42no—
985C22⋊Q8—42no—
986C22⋊Q8—42no—
987#121—42no—
988#121—42no—
989#121—42no—
990#121—42no—
991#121—42no—
992C4×D4—24no—
993#117—42no—
994C2×C4⋊C4C23×C7311yescharacteristic
995C2×C4⋊C4C23×C7311yescharacteristic
996C2×C4⋊C4C23×C7311yescharacteristic
997C2×C4⋊C4C23×C7311yescharacteristic
998C2×C4⋊C4C23×C7311yescharacteristic
999C2×C4⋊C4C23×C7311yescharacteristic
1000C2×C4⋊C4C23×C7311yescharacteristic
1001C2×C4⋊C4C23×C7311yescharacteristic
1002C2×C4⋊C4C23×C7311yescharacteristic
1003C2×C4⋊C4C23×C7311yescharacteristic
1004C2×C4⋊C4C23×C7311yescharacteristic
1005C2×C4⋊C4C23×C7311yescharacteristic
1006C2×C4⋊C4C23×C7311yescharacteristic
1007C2×C4⋊C4C23×C7311yescharacteristic
1008C2×C4⋊C4C23×C7311yescharacteristic
1009C2×C4⋊C4C23×C7311yescharacteristic
1010C2×C4⋊C4C23×C7311yescharacteristic
1011C2×C4⋊C4C23×C7311yescharacteristic
1012C2×C4⋊C4C23×C7311yescharacteristic
1013C2×C4⋊C4C23×C7311yescharacteristic
1014C2×C4⋊C4C23×C7311yescharacteristic
1015C2×C4⋊C4C23×C7311yescharacteristic
1016C2×C4⋊C4C23×C7311yescharacteristic
1017C2×C4⋊C4C23×C7311yescharacteristic
1018C2×C4⋊C4C23×C7311yescharacteristic
1019C2×C4⋊C4C23×C7311yescharacteristic
1020C2×C4⋊C4C23×C7311yescharacteristic
1021C2×C4⋊C4C23×C7311yescharacteristic
1022C2×C4⋊C4C23×C7311yescharacteristic
1023C2×C4⋊C4C23×C7311yescharacteristic
1024C2×C4⋊C4C23×C7311yescharacteristic
1025C2×C22⋊C4C23×C7311yescharacteristic
1026C2×C22⋊C4C23×C7311yescharacteristic
1027C2×C22⋊C4C23×C7311yescharacteristic
1028C2×C22⋊C4C23×C7311yescharacteristic
1029C2×C22⋊C4C23×C7311yescharacteristic
1030C2×C22⋊C4C23×C7311yescharacteristic
1031C2×C22⋊C4C23×C7311yescharacteristic
1032C2×C22⋊C4C23×C7311yescharacteristic
1033C2×C22⋊C4C23×C7311yescharacteristic
1034C2×C22⋊C4C23×C7311yescharacteristic
1035C2×C22⋊C4C23×C7311yescharacteristic
1036C2×C22⋊C4C23×C7311yescharacteristic
1037C2×C22⋊C4C23×C7311yescharacteristic
1038C2×C22⋊C4C23×C7311yescharacteristic
1039C2×C22⋊C4C23×C7311yescharacteristic
1040C2×C22⋊C4C23×C7311yescharacteristic
1041C2×C22⋊C4C23×C7311yescharacteristic
1042C2×C22⋊C4C23×C7311yescharacteristic
1043C2×C22⋊C4C23×C7311yescharacteristic
1044C2×C22⋊C4C23×C7311yescharacteristic
1045C2×C22⋊C4C23×C7311yescharacteristic
1046C2×C22⋊C4C23×C7311yescharacteristic
1047C2×C22⋊C4C23×C7311yescharacteristic
1048C2×C22⋊C4C23×C7311yescharacteristic
1049C2×C22⋊C4C23×C7311yescharacteristic
1050C2×C22⋊C4C23×C7311yescharacteristic
1051C2×C22⋊C4C23×C7311yescharacteristic
1052C2×C22⋊C4C23×C7311yescharacteristic
1053C2×C22⋊C4C23×C7311yescharacteristic
1054C2×C22⋊C4C23×C7311yescharacteristic
1055C2×C22⋊C4C23×C7311yescharacteristic
1056C2×C22⋊C4C23×C7311yescharacteristic
1057C2×C22⋊C4C23×C7311yescharacteristic
1058C2×C22⋊C4C23×C7311yescharacteristic
1059C2×C22⋊C4C23×C7311yescharacteristic
1060C2×C22⋊C4C23×C7311yescharacteristic
1061C2×C22⋊C4C23×C7311yescharacteristic
1062C2×C22⋊C4C23×C7311yescharacteristic
1063C2×C22⋊C4C23×C7311yescharacteristic
1064C2×C22⋊C4C23×C7311yescharacteristic
1065C2×C22⋊C4C23×C7311yescharacteristic
1066C2×C22⋊C4C23×C7311yescharacteristic
1067C2×C22⋊C4C23×C7311yescharacteristic
1068C2×C22⋊C4C23×C7311yescharacteristic
1069C2×C22⋊C4C23×C7311yescharacteristic
1070C2×C22⋊C4C23×C7311yescharacteristic
1071C2×C42—42no—
1072C2×C42C23×C7311yescharacteristic
1073C2×C42C23×C7311yescharacteristic
1074C2×C42C23×C7311yescharacteristic
1075C2×C42C23×C7311yescharacteristic
1076C2×C42C23×C7311yescharacteristic
1077C2×C42C23×C7311yescharacteristic
1078C2×C42C23×C7311yescharacteristic
1079C2×C42C23×C7311yescharacteristic
1080C2×C42C23×C7311yescharacteristic
1081C2×C42C23×C7311yescharacteristic
1082#95C23×C7311yescharacteristic
1083#95C23×C7311yescharacteristic
1084#95C23×C7311yescharacteristic
1085#95C23×C7311yescharacteristic
1086#95C23×C7311yescharacteristic
1087#95C23×C7311yescharacteristic
1088#95C23×C7311yescharacteristic
1089#95C23×C7311yescharacteristic
1090#95C23×C7311yescharacteristic
1091#95C23×C7311yescharacteristic
1092#95C23×C7311yescharacteristic
1093#95C23×C7311yescharacteristic
1094#95C23×C7311yescharacteristic
1095#95C23×C7311yescharacteristic
1096#95C23×C7311yescharacteristic
1097#95C23×C7311yescharacteristic
1098#95C23×C7311yescharacteristic
1099#95C23×C7311yescharacteristic
1100#95C23×C7311yescharacteristic
1101#95C23×C7311yescharacteristic
1102#95C23×C7311yescharacteristic
1103#95C23×C7311yescharacteristic
1104#95C23×C7311yescharacteristic
1105#95C23×C7311yescharacteristic
1106#95C23×C7311yescharacteristic
1107#95C23×C7311yescharacteristic
1108#95C23×C7311yescharacteristic
1109#95C23×C7311yescharacteristic
1110#95C23×C7311yescharacteristic
1111#95C23×C7311yescharacteristic
1112#95C23×C7311yescharacteristic
1113#95C23×C7311yescharacteristic
1114#95C23×C7311yescharacteristic
1115#95C23×C7311yescharacteristic
1116#95C23×C7311yescharacteristic
1117#95C23×C7311yescharacteristic
1118#95C23×C7311yescharacteristic
1119#95C23×C7311yescharacteristic
1120#95C23×C7311yescharacteristic
1121#95C23×C7311yescharacteristic
1122#95C23×C7311yescharacteristic
1123#95C23×C7311yescharacteristic
1124#95C23×C7311yescharacteristic
1125#95C23×C7311yescharacteristic
1126#95C23×C7311yescharacteristic
1127#95C23×C7311yescharacteristic
1128C24C24×C7311yescharacteristic
1129C24C24×C7311yescharacteristic
1130C24C24×C7311yescharacteristic
1131C24C24×C7311yescharacteristic
1132C24C24×C7311yescharacteristic
1133#41—416no—
1134C2×Q8—22no—
1135C2×Q8—22no—
1136C2×Q8—22no—
1137C2×Q8—41no—
1138C2×Q8—41no—
1139C2×Q8—41no—
1140C2×Q8—41no—
1141C2×Q8—41no—
1142C2×Q8—41no—
1143C2×D4—22no—
1144C2×D4—22no—
1145C2×D4—22no—
1146C2×D4—22no—
1147C2×D4—22no—
1148C2×D4—22no—
1149C2×D4—22no—
1150C2×D4—22no—
1151C2×D4—22no—
1152C2×D4—22no—
1153C2×D4—22no—
1154C2×D4—41no—
1155C2×D4—41no—
1156C2×D4—41no—
1157C2×D4—41no—
1158C2×D4—41no—
1159C2×D4—41no—
1160C2×D4—41no—
1161C2×D4—41no—
1162C2×D4—41no—
1163C2×D4—41no—
1164C2×D4—41no—
1165C2×D4—41no—
1166C2×D4—41no—
1167C2×D4—41no—
1168C2×D4—41no—
1169C2×D4—41no—
1170C2×D4—41no—
1171C2×D4—41no—
1172C2×D4—41no—
1173C22×C4—22no—
1174C22×C4—22no—
1175C22×C4—22no—
1176C22×C4—22no—
1177C22×C4—22no—
1178C22×C4—22no—
1179C22×C4—22no—
1180C22×C4—41no—
1181C22×C4—41no—
1182C22×C4—41no—
1183C22×C4—41no—
1184C22×C4—41no—
1185C22×C4—41no—
1186C22×C4—41no—
1187C22×C4—41no—
1188C22×C4—41no—
1189C22×C4—41no—
1190C22×C4—41no—
1191C22×C4—41no—
1192C22×C4—41no—
1193C22×C4—41no—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—41no—
1198C22×C4—41no—
1199C22×C4#41×C7314yes—
1200C22×C4C24×C7311yescharacteristic
1201C22×C4C24×C7311yescharacteristic
1202C22×C4C24×C7311yescharacteristic
1203C22×C4C24×C7311yescharacteristic
1204C22×C4C24×C7311yescharacteristic
1205C22×C4C24×C7311yescharacteristic
1206C22×C4C24×C7311yescharacteristic
1207C22×C4C24×C7311yescharacteristic
1208C22×C4C24×C7311yescharacteristic
1209C22×C4C24×C7311yescharacteristic
1210C22×C4C24×C7311yescharacteristic
1211C22×C4C24×C7311yescharacteristic
1212C22×C4C24×C7311yescharacteristic
1213C22×C4C24×C7311yescharacteristic
1214C22×C4C24×C7311yescharacteristic
1215C22×C4C24×C7311yescharacteristic
1216C22×C4C24×C7311yescharacteristic
1217C22×C4C24×C7311yescharacteristic
1218C22×C4C24×C7311yescharacteristic
1219C22×C4C24×C7311yescharacteristic
1220C22×C4C24×C7311yescharacteristic
1221C22×C4C24×C7311yescharacteristic
1222C22×C4C24×C7311yescharacteristic
1223C22×C4C24×C7311yescharacteristic
1224C22×C4C24×C7311yescharacteristic
1225C22×C4C24×C7311yescharacteristic
1226C4⋊C4—22no—
1227C4⋊C4—22no—
1228C4⋊C4—22no—
1229C4⋊C4—22no—
1230C4⋊C4—22no—
1231C4⋊C4—22no—
1232C4⋊C4—22no—
1233C4⋊C4—22no—
1234C4⋊C4—22no—
1235C4⋊C4—41no—
1236C4⋊C4—41no—
1237C4⋊C4—41no—
1238C4⋊C4—41no—
1239C4⋊C4—41no—
1240C4⋊C4—41no—
1241C4⋊C4—41no—
1242C4⋊C4—41no—
1243C4⋊C4—41no—
1244C4⋊C4—41no—
1245C4⋊C4—41no—
1246C4⋊C4—41no—
1247C4⋊C4—41no—
1248C4⋊C4—41no—
1249C4⋊C4—41no—
1250C4⋊C4—41no—
1251C4⋊C4—41no—
1252C4⋊C4—41no—
1253C4⋊C4—41no—
1254C4⋊C4—41no—
1255C4⋊C4—41no—
1256C4⋊C4—41no—
1257C22⋊C4—22no—
1258C22⋊C4—22no—
1259C22⋊C4—22no—
1260C22⋊C4—22no—
1261C22⋊C4—22no—
1262C22⋊C4—22no—
1263C22⋊C4—22no—
1264C22⋊C4—22no—
1265C22⋊C4—22no—
1266C22⋊C4—22no—
1267C22⋊C4—22no—
1268C22⋊C4—22no—
1269C22⋊C4—22no—
1270C22⋊C4—22no—
1271C22⋊C4—22no—
1272C22⋊C4—22no—
1273C22⋊C4—22no—
1274C22⋊C4—41no—
1275C22⋊C4—41no—
1276C22⋊C4—41no—
1277C22⋊C4—41no—
1278C22⋊C4—41no—
1279C22⋊C4—41no—
1280C22⋊C4—41no—
1281C22⋊C4—41no—
1282C22⋊C4—41no—
1283C22⋊C4—41no—
1284C22⋊C4—41no—
1285C22⋊C4—41no—
1286C22⋊C4—41no—
1287C22⋊C4—41no—
1288C22⋊C4—41no—
1289C22⋊C4—41no—
1290C22⋊C4—41no—
1291C22⋊C4—41no—
1292C22⋊C4—41no—
1293C22⋊C4—41no—
1294C22⋊C4—41no—
1295C22⋊C4—41no—
1296C22⋊C4—41no—
1297C22⋊C4—41no—
1298C22⋊C4—41no—
1299C22⋊C4—41no—
1300C22⋊C4—41no—
1301C22⋊C4—41no—
1302C22⋊C4—41no—
1303C42—22no—
1304C42—22no—
1305C42—22no—
1306C42—41no—
1307C42—41no—
1308C42—41no—
1309C42—41no—
1310C42—41no—
1311C42—41no—
1312C42—41no—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—21no—
1319C23—21no—
1320C23—21no—
1321C23—21no—
1322C23—21no—
1323C23—21no—
1324C23—21no—
1325C23—21no—
1326C23—21no—
1327C23—21no—
1328C23—21no—
1329C23—21no—
1330C23—21no—
1331C23—21no—
1332C23—21no—
1333C23—21no—
1334C23—21no—
1335C23—21no—
1336C23—21no—
1337C23—21no—
1338C23—21no—
1339C23—21no—
1340C23—21no—
1341C23—21no—
1342C23—21no—
1343C23—21no—
1344C23—21no—
1345C23—21no—
1346C23C2×#41×C7312yes—
1347C23H(5,𝔽2)×C7312yes—
1348C23C25×C7311yescharacteristic
1349Q8—44no—
1350Q8—82no—
1351Q8—82no—
1352D4—44no—
1353D4—44no—
1354D4—44no—
1355D4—44no—
1356D4—82no—
1357D4—82no—
1358D4—82no—
1359D4—82no—
1360D4—82no—
1361D4—82no—
1362C2×C4—28no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—44no—
1437C2×C4—44no—
1438C2×C4—44no—
1439C2×C4—44no—
1440C2×C4—82no—
1441C2×C4—82no—
1442C2×C4—82no—
1443C2×C4—82no—
1444C2×C4C2×#41×C7312yes—
1445C2×C4C2×#41×C7312yes—
1446C2×C4H(5,𝔽2)×C7312yes—
1447C2×C4H(5,𝔽2)×C7312yes—
1448C2×C42−1+4×C7312yes—
1449C22—22no—
1450C22—22no—
1451C22—22no—
1452C22—22no—
1453C22—22no—
1454C22—22no—
1455C22—41no—
1456C22—41no—
1457C22—41no—
1458C22—41no—
1459C22—41no—
1460C22—41no—
1461C22—41no—
1462C22—41no—
1463C22—41no—
1464C22—41no—
1465C22—41no—
1466C22—41no—
1467C22—41no—
1468C22—41no—
1469C22—41no—
1470C22—41no—
1471C22—41no—
1472C22—41no—
1473C22—41no—
1474C22—41no—
1475C22—41no—
1476C22—41no—
1477C22—41no—
1478C22—41no—
1479C22—41no—
1480C22—41no—
1481C22—41no—
1482C22—41no—
1483C22—41no—
1484C22C22×#41×C7311yescharacteristic
1485C22C2×H(5,𝔽2)×C7311yescharacteristic
1486C22C2×H(5,𝔽2)×C7311yescharacteristic
1487C22C2×H(5,𝔽2)×C7311yescharacteristic
1488C22C2×2−1+4×C7311yescharacteristic
1489C22#585×C7311yescharacteristic
1490C22#585×C7311yescharacteristic
1491C4—22no—
1492C4—22no—
1493C4—22no—
1494C4—22no—
1495C4—22no—
1496C4—41no—
1497C4—41no—
1498C4—41no—
1499C4—41no—
1500C4—41no—
1501C4—41no—
1502C4—41no—
1503C4—41no—
1504C4—41no—
1505C4—41no—
1506C4—41no—
1507C4—41no—
1508C4—41no—
1509C4—41no—
1510C4—41no—
1511C4—41no—
1512C4—41no—
1513C4—41no—
1514C4—41no—
1515C4—41no—
1516C4—41no—
1517C2—42no—
1518C2—42no—
1519C2—81no—
1520C2—81no—
1521C2—81no—
1522C2C73×#345511yescharacteristic
1523C2C73×#349011yescharacteristic
1524C2C73×#351111yescharacteristic
1525C2C73×#354111yescharacteristic
1526C2C73×#354211yescharacteristic
1527C2C73×#355811yescharacteristic
1528C2C73×#355911yescharacteristic
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×#2851C2semidirect
2. C73×#2850C2semidirect
3. C73×#2778C2semidirect
4. C73×#2763C2semidirect
5. C73×#2762C2semidirect
6. C73×#2756C2semidirect
7. C73×#2753C2semidirect
8. C73×#2728C2semidirect
9. C73×#2723C2semidirect
10. C73×#2723C2semidirect
11. C73×#2711C2semidirect
12. C73×#2708C2semidirect
13. C73×#2704C2semidirect
14. C73×#2700C2semidirect
15. C73×#2686C2semidirect
16. C73×#2676C2semidirect
17. C73×#2676C2semidirect
18. C73×#2671C2semidirect
19. C73×#2653C2semidirect
20. C73×#2649C2semidirect
21. C73×#2602C2semidirect
22. C73×#2589C2semidirect
23. C73×#2559C2semidirect
24. C73×#2549C2semidirect
25. C73×#2474C2semidirect
26. C73×#2470C2semidirect
27. C73×#2430C2semidirect
28. C73×#2407C2semidirect
29. C73×#2335C2semidirect
30. C73×#2318C2semidirect
31. C73×#2297C2semidirect
752. #36817C73direct (N × H)
765. #2851C2×C73semidirect
766. #2850C2×C73semidirect
767. #2778C2×C73semidirect
768. #2763C2×C73semidirect
769. #2762C2×C73semidirect
770. #2756C2×C73semidirect
771. #2753C2×C73semidirect
772. #2728C2×C73semidirect
773. #2723C2×C73semidirect
774. #2723C2×C73semidirect
775. #2711C2×C73semidirect
776. #2708C2×C73semidirect
777. #2704C2×C73semidirect
778. #2700C2×C73semidirect
779. #2686C2×C73semidirect
780. #2676C2×C73semidirect
781. #2676C2×C73semidirect
782. #2671C2×C73semidirect
783. #2653C2×C73semidirect
784. #2649C2×C73semidirect
785. #2602C2×C73semidirect
786. #2589C2×C73semidirect
787. #2559C2×C73semidirect
788. #2549C2×C73semidirect
789. #2474C2×C73semidirect
790. #2470C2×C73semidirect
791. #2430C2×C73semidirect
792. #2407C2×C73semidirect
793. #2335C2×C73semidirect
794. #2318C2×C73semidirect
795. #2297C2×C73semidirect
796. C73#36817direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#28512
C73×#28502
C73×#27782
C73×#27632
C73×#27622
C73×#27562
C73×#27532
C73×#27282
C73×#27232
C73×#27112
C73×#27082
C73×#27042
C73×#27002
C73×#26862
C73×#26762
C73×#26712
C73×#26532
C73×#26492
C73×#26022
C73×#25892
C73×#25592
C73×#25492
C73×#24742
C73×#24702
C73×#24302
C73×#24072
C73×#23352
C73×#23182
C73×#22972
#3681773