Finite Group Databasebeta

← C73×#36784 #32946188

Subgroups — C73×#36784 #32946188

Order 18688.

1736 conjugacy classes of subgroups.

The subgroup lattice has 1502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2853C211yesmaximal, characteristic, complemented
2C73×#2850C211yesmaximal, characteristic, complemented
3C73×#2783C211yesmaximal, characteristic, complemented
4C73×#2779C211yesmaximal, characteristic, complemented
5C73×#2772C211yesmaximal, characteristic, complemented
6C73×#2757C211yesmaximal, characteristic, complemented
7C73×#2753C211yesmaximal, characteristic, complemented
8C73×#2744C211yesmaximal, characteristic, complemented
9C73×#2737C211yesmaximal, characteristic, complemented
10C73×#2735C211yesmaximal, characteristic, complemented
11C73×#2731C211yesmaximal, characteristic, complemented
12C73×#2701C211yesmaximal, characteristic, complemented
13C73×#2693C211yesmaximal, characteristic, complemented
14C73×#2687C211yesmaximal, characteristic, complemented
15C73×#2684C211yesmaximal, characteristic, complemented
16C73×#2684C211yesmaximal, characteristic, complemented
17C73×#2678C211yesmaximal, characteristic
18C73×#2674C211yesmaximal, characteristic, complemented
19C73×#2651C211yesmaximal, characteristic, complemented
20C73×#2650C211yesmaximal, characteristic, complemented
21C73×#2602C211yesmaximal, characteristic, complemented
22C73×#2595C211yesmaximal, characteristic, complemented
23C73×#2557C211yesmaximal, characteristic, complemented
24C73×#2534C211yesmaximal, characteristic, complemented
25C73×#2532C211yesmaximal, characteristic, complemented
26C73×#2531C211yesmaximal, characteristic, complemented
27C73×#2439C211yesmaximal, characteristic, complemented
28C73×#2411C211yesmaximal, characteristic, complemented
29C73×#2335C211yesmaximal, characteristic, complemented
30C73×#2312C211yesmaximal, characteristic, complemented
31C73×#2290C211yesmaximal, characteristic, complemented
32C2×C4⋊Q8×C73C2211yescharacteristic, complemented
33C2×#124×C73C2211yescharacteristic
34C2×#124×C73C2211yescharacteristic
35C2×#123×C73C2211yescharacteristic
36C2×#123×C73C2211yescharacteristic
37C2×#123×C73C2211yescharacteristic
38C2×#123×C73C2211yescharacteristic, complemented
39C2×C22⋊Q8×C73C2211yescharacteristic, complemented
40C2×#121×C73C2211yescharacteristic
41C2×#120×C73C2211yescharacteristic
42C2×#120×C73C2211yescharacteristic
43C2×C4×D4×C73C2211yescharacteristic
44C2×#117×C73C2211yescharacteristic
45C22×C22⋊C4×C73C2211yescharacteristic
46C22×C42×C73C2211yescharacteristic, complemented
47#400×C73C2211yescharacteristic, complemented
48#400×C73C2211yescharacteristic, complemented
49#400×C73C2211yescharacteristic, complemented
50#400×C73C2211yescharacteristic, complemented
51#400×C73C2211yescharacteristic, complemented
52#399×C73C2211yescharacteristic
53#398×C73C2211yescharacteristic, complemented
54#398×C73C2211yescharacteristic, complemented
55#398×C73C2211yescharacteristic, complemented
56#398×C73C2211yescharacteristic, complemented
57#397×C73C2211yescharacteristic
58#397×C73C2211yescharacteristic
59#397×C73C2211yescharacteristic
60#397×C73C2211yescharacteristic
61#397×C73C2211yescharacteristic
62#397×C73C2211yescharacteristic
63#397×C73C2211yescharacteristic
64#397×C73C2211yescharacteristic
65#397×C73C2211yescharacteristic, complemented
66#397×C73C2211yescharacteristic, complemented
67#397×C73C2211yescharacteristic, complemented
68#397×C73C2211yescharacteristic, complemented
69#396×C73C2211yescharacteristic
70#396×C73C2211yescharacteristic
71#396×C73C2211yescharacteristic
72#396×C73C2211yescharacteristic
73#396×C73C2211yescharacteristic
74#396×C73C2211yescharacteristic
75#396×C73C2211yescharacteristic
76#396×C73C2211yescharacteristic, complemented
77#395×C73C2211yescharacteristic, complemented
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#393×C73C2211yescharacteristic
89#393×C73C2211yescharacteristic
90#393×C73C2211yescharacteristic
91#393×C73C2211yescharacteristic
92#393×C73C2211yescharacteristic, complemented
93#392×C73C2211yescharacteristic
94#392×C73C2211yescharacteristic
95#391×C73C2211yescharacteristic, complemented
96#391×C73C2211yescharacteristic, complemented
97#391×C73C2211yescharacteristic, complemented
98#390×C73C2211yescharacteristic
99#390×C73C2211yescharacteristic
100#390×C73C2211yescharacteristic
101#390×C73C2211yescharacteristic
102#390×C73C2211yescharacteristic, complemented
103#389×C73C2211yescharacteristic, complemented
104#389×C73C2211yescharacteristic, complemented
105#389×C73C2211yescharacteristic, complemented
106#389×C73C2211yescharacteristic, complemented
107#388×C73C2211yescharacteristic
108#388×C73C2211yescharacteristic
109#388×C73C2211yescharacteristic
110#388×C73C2211yescharacteristic
111#388×C73C2211yescharacteristic
112#388×C73C2211yescharacteristic
113#388×C73C2211yescharacteristic
114#388×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, complemented
131#388×C73C2211yescharacteristic, complemented
132#388×C73C2211yescharacteristic, complemented
133#388×C73C2211yescharacteristic, complemented
134#388×C73C2211yescharacteristic, complemented
135#388×C73C2211yescharacteristic, complemented
136#388×C73C2211yescharacteristic, complemented
137#387×C73C2211yescharacteristic, complemented
138#387×C73C2211yescharacteristic, complemented
139#387×C73C2211yescharacteristic, complemented
140#387×C73C2211yescharacteristic, complemented
141#387×C73C2211yescharacteristic, complemented
142#387×C73C2211yescharacteristic, complemented
143#387×C73C2211yescharacteristic, complemented
144#387×C73C2211yescharacteristic, complemented
145#387×C73C2211yescharacteristic, complemented
146#387×C73C2211yescharacteristic, complemented
147#387×C73C2211yescharacteristic, complemented
148#387×C73C2211yescharacteristic, complemented
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#386×C73C2211yescharacteristic
158#386×C73C2211yescharacteristic
159#386×C73C2211yescharacteristic, complemented
160#386×C73C2211yescharacteristic, complemented
161#385×C73C2211yescharacteristic
162#385×C73C2211yescharacteristic, complemented
163#385×C73C2211yescharacteristic, complemented
164#385×C73C2211yescharacteristic, complemented
165#385×C73C2211yescharacteristic, complemented
166#385×C73C2211yescharacteristic, complemented
167#383×C73C2211yescharacteristic, complemented
168#382×C73C2211yescharacteristic, complemented
169#382×C73C2211yescharacteristic, complemented
170#381×C73C2211yescharacteristic
171#381×C73C2211yescharacteristic, complemented
172#380×C73C2211yescharacteristic
173#380×C73C2211yescharacteristic
174#380×C73C2211yescharacteristic
175#380×C73C2211yescharacteristic, complemented
176#379×C73C2211yescharacteristic
177#379×C73C2211yescharacteristic
178#379×C73C2211yescharacteristic
179#379×C73C2211yescharacteristic
180C4×C4⋊C4×C73C2211yescharacteristic, complemented
181C4×C4⋊C4×C73C2211yescharacteristic, complemented
182C4×C22⋊C4×C73C2211yescharacteristic
183C4×C22⋊C4×C73C2211yescharacteristic
184C4×C22⋊C4×C73C2211yescharacteristic, complemented
185C4×C22⋊C4×C73C2211yescharacteristic, complemented
186#376×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
197C23×C4×C73C2311yescharacteristic
198C23×C4×C73C2311yescharacteristic
199C23×C4×C73C2311yescharacteristic
200C23×C4×C73C2311yescharacteristic
201C23×C4×C73C2311yescharacteristic
202C23×C4×C73C2311yescharacteristic
203C4⋊Q8×C73—42no—
204#124×C73—42no—
205#124×C73—42no—
206#123×C73—24no—
207#123×C73—42no—
208#123×C73—42no—
209#123×C73—42no—
210C22⋊Q8×C73—42no—
211#121×C73—42no—
212#120×C73—42no—
213#120×C73—42no—
214C4×D4×C73—24no—
215#117×C73—42no—
216C2×C4⋊C4×C73C2311yescharacteristic
217C2×C4⋊C4×C73C2311yescharacteristic
218C2×C4⋊C4×C73C2311yescharacteristic
219C2×C4⋊C4×C73C2311yescharacteristic
220C2×C4⋊C4×C73C2311yescharacteristic
221C2×C4⋊C4×C73C2311yescharacteristic
222C2×C4⋊C4×C73C2311yescharacteristic
223C2×C4⋊C4×C73C2311yescharacteristic
224C2×C4⋊C4×C73C2311yescharacteristic
225C2×C4⋊C4×C73C2311yescharacteristic
226C2×C4⋊C4×C73C2311yescharacteristic
227C2×C4⋊C4×C73C2311yescharacteristic
228C2×C4⋊C4×C73C2311yescharacteristic
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×C22⋊C4×C73—24no—
246C2×C22⋊C4×C73C2311yescharacteristic
247C2×C22⋊C4×C73C2311yescharacteristic
248C2×C22⋊C4×C73C2311yescharacteristic
249C2×C22⋊C4×C73C2311yescharacteristic
250C2×C22⋊C4×C73C2311yescharacteristic
251C2×C22⋊C4×C73C2311yescharacteristic
252C2×C22⋊C4×C73C2311yescharacteristic
253C2×C22⋊C4×C73C2311yescharacteristic
254C2×C22⋊C4×C73C2311yescharacteristic
255C2×C22⋊C4×C73C2311yescharacteristic
256C2×C22⋊C4×C73C2311yescharacteristic
257C2×C22⋊C4×C73C2311yescharacteristic
258C2×C22⋊C4×C73C2311yescharacteristic
259C2×C22⋊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×C42×C73—42no—
299C2×C42×C73C2311yescharacteristic
300C2×C42×C73C2311yescharacteristic
301C2×C42×C73C2311yescharacteristic
302C2×C42×C73C2311yescharacteristic
303C2×C42×C73C2311yescharacteristic
304C2×C42×C73C2311yescharacteristic
305C2×C42×C73C2311yescharacteristic
306C2×C42×C73C2311yescharacteristic
307C2×C42×C73C2311yescharacteristic
308C2×C42×C73C2311yescharacteristic
309C2×C42×C73C2311yescharacteristic
310C2×C42×C73C2311yescharacteristic
311#95×C73C2311yescharacteristic
312#95×C73C2311yescharacteristic
313#95×C73C2311yescharacteristic
314#95×C73C2311yescharacteristic
315#95×C73C2311yescharacteristic
316#95×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
357C24×C73—22no—
358C24×C73—41no—
359C24×C73—41no—
360C24×C73—41no—
361C24×C73—41no—
362C24×C73—41no—
363C24×C73—41no—
364C24×C73C2411yescharacteristic
365C24×C73C2411yescharacteristic
366C24×C73C2411yescharacteristic
367C24×C73C2411yescharacteristic
368C24×C73C2411yescharacteristic
369C2×Q8×C73—22no—
370C2×Q8×C73—41no—
371C2×Q8×C73—41no—
372C2×Q8×C73—41no—
373C2×Q8×C73—41no—
374C2×Q8×C73—41no—
375C2×D4×C73—22no—
376C2×D4×C73—22no—
377C2×D4×C73—22no—
378C2×D4×C73—22no—
379C2×D4×C73—22no—
380C2×D4×C73—22no—
381C2×D4×C73—22no—
382C2×D4×C73—41no—
383C2×D4×C73—41no—
384C2×D4×C73—41no—
385C2×D4×C73—41no—
386C2×D4×C73—41no—
387C2×D4×C73—41no—
388C2×D4×C73—41no—
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—
396C22×C4×C73—22no—
397C22×C4×C73—22no—
398C22×C4×C73—22no—
399C22×C4×C73—22no—
400C22×C4×C73—41no—
401C22×C4×C73—41no—
402C22×C4×C73—41no—
403C22×C4×C73—41no—
404C22×C4×C73—41no—
405C22×C4×C73—41no—
406C22×C4×C73—41no—
407C22×C4×C73—41no—
408C22×C4×C73—41no—
409C22×C4×C73—41no—
410C22×C4×C73—41no—
411C22×C4×C73—41no—
412C22×C4×C73—41no—
413C22×C4×C73#4114yes—
414C22×C4×C73C2411yescharacteristic
415C22×C4×C73C2411yescharacteristic
416C22×C4×C73C2411yescharacteristic
417C22×C4×C73C2411yescharacteristic
418C22×C4×C73C2411yescharacteristic
419C22×C4×C73C2411yescharacteristic
420C22×C4×C73C2411yescharacteristic
421C22×C4×C73C2411yescharacteristic
422C22×C4×C73C2411yescharacteristic
423C22×C4×C73C2411yescharacteristic
424C22×C4×C73C2411yescharacteristic
425C22×C4×C73C2411yescharacteristic
426C22×C4×C73C2411yescharacteristic
427C22×C4×C73C2411yescharacteristic
428C22×C4×C73C2411yescharacteristic
429C22×C4×C73C2411yescharacteristic
430C22×C4×C73C2411yescharacteristic
431C22×C4×C73C2411yescharacteristic
432C22×C4×C73C2411yescharacteristic
433C22×C4×C73C2411yescharacteristic
434C22×C4×C73C2411yescharacteristic
435C22×C4×C73C2411yescharacteristic
436C22×C4×C73C2411yescharacteristic
437C22×C4×C73C2411yescharacteristic
438C22×C4×C73C2411yescharacteristic
439C22×C4×C73C2411yescharacteristic
440C4⋊C4×C73—22no—
441C4⋊C4×C73—22no—
442C4⋊C4×C73—22no—
443C4⋊C4×C73—22no—
444C4⋊C4×C73—22no—
445C4⋊C4×C73—41no—
446C4⋊C4×C73—41no—
447C4⋊C4×C73—41no—
448C4⋊C4×C73—41no—
449C4⋊C4×C73—41no—
450C4⋊C4×C73—41no—
451C4⋊C4×C73—41no—
452C4⋊C4×C73—41no—
453C4⋊C4×C73—41no—
454C4⋊C4×C73—41no—
455C4⋊C4×C73—41no—
456C4⋊C4×C73—41no—
457C4⋊C4×C73—41no—
458C4⋊C4×C73—41no—
459C4⋊C4×C73—41no—
460C4⋊C4×C73—41no—
461C4⋊C4×C73—41no—
462C4⋊C4×C73—41no—
463C4⋊C4×C73—41no—
464C4⋊C4×C73—41no—
465C4⋊C4×C73—41no—
466C4⋊C4×C73—41no—
467C4⋊C4×C73—41no—
468C4⋊C4×C73—41no—
469C22⋊C4×C73—22no—
470C22⋊C4×C73—22no—
471C22⋊C4×C73—22no—
472C22⋊C4×C73—22no—
473C22⋊C4×C73—22no—
474C22⋊C4×C73—22no—
475C22⋊C4×C73—22no—
476C22⋊C4×C73—22no—
477C22⋊C4×C73—22no—
478C22⋊C4×C73—22no—
479C22⋊C4×C73—22no—
480C22⋊C4×C73—22no—
481C22⋊C4×C73—22no—
482C22⋊C4×C73—22no—
483C22⋊C4×C73—22no—
484C22⋊C4×C73—41no—
485C22⋊C4×C73—41no—
486C22⋊C4×C73—41no—
487C22⋊C4×C73—41no—
488C22⋊C4×C73—41no—
489C22⋊C4×C73—41no—
490C22⋊C4×C73—41no—
491C22⋊C4×C73—41no—
492C22⋊C4×C73—41no—
493C22⋊C4×C73—41no—
494C22⋊C4×C73—41no—
495C22⋊C4×C73—41no—
496C22⋊C4×C73—41no—
497C22⋊C4×C73—41no—
498C22⋊C4×C73—41no—
499C22⋊C4×C73—41no—
500C22⋊C4×C73—41no—
501C22⋊C4×C73—41no—
502C22⋊C4×C73—41no—
503C22⋊C4×C73—41no—
504C22⋊C4×C73—41no—
505C22⋊C4×C73—41no—
506C22⋊C4×C73—41no—
507C22⋊C4×C73—41no—
508C22⋊C4×C73—41no—
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—
521C42×C73—22no—
522C42×C73—22no—
523C42×C73—22no—
524C42×C73—41no—
525C42×C73—41no—
526C42×C73—41no—
527C42×C73—41no—
528C42×C73—41no—
529C42×C73—41no—
530C42×C73—41no—
531C42×C73—41no—
532C42×C73—41no—
533C23×C73—21no—
534C23×C73—21no—
535C23×C73—21no—
536C23×C73—21no—
537C23×C73—21no—
538C23×C73—21no—
539C23×C73—21no—
540C23×C73—21no—
541C23×C73—21no—
542C23×C73—21no—
543C23×C73—21no—
544C23×C73—21no—
545C23×C73—21no—
546C23×C73—21no—
547C23×C73—21no—
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—44no—
567C23×C73—82no—
568C23×C73—82no—
569C23×C73—82no—
570C23×C73—82no—
571C23×C73—82no—
572C23×C73—82no—
573C23×C73C2×#4112yes—
574C23×C73H(5,𝔽2)12yes—
575C23×C73C2511yescharacteristic
576Q8×C73—82no—
577Q8×C73—82no—
578D4×C73—44no—
579D4×C73—82no—
580D4×C73—82no—
581D4×C73—82no—
582D4×C73—82no—
583D4×C73—82no—
584D4×C73—82no—
585C2×C4×C73—21no—
586C2×C4×C73—21no—
587C2×C4×C73—21no—
588C2×C4×C73—21no—
589C2×C4×C73—21no—
590C2×C4×C73—21no—
591C2×C4×C73—21no—
592C2×C4×C73—21no—
593C2×C4×C73—21no—
594C2×C4×C73—21no—
595C2×C4×C73—21no—
596C2×C4×C73—21no—
597C2×C4×C73—21no—
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—44no—
661C2×C4×C73—44no—
662C2×C4×C73—44no—
663C2×C4×C73—44no—
664C2×C4×C73—82no—
665C2×C4×C73—82no—
666C2×C4×C73C2×#4112yes—
667C2×C4×C73C2×#4112yes—
668C2×C4×C73H(5,𝔽2)12yes—
669C22×C73—22no—
670C22×C73—22no—
671C22×C73—22no—
672C22×C73—22no—
673C22×C73—22no—
674C22×C73—22no—
675C22×C73—41no—
676C22×C73—41no—
677C22×C73—41no—
678C22×C73—41no—
679C22×C73—41no—
680C22×C73—41no—
681C22×C73—41no—
682C22×C73—41no—
683C22×C73—41no—
684C22×C73—41no—
685C22×C73—41no—
686C22×C73—41no—
687C22×C73—41no—
688C22×C73—41no—
689C22×C73—41no—
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—88no—
705C22×C73C22×#4111yescharacteristic
706C22×C73C2×H(5,𝔽2)11yescharacteristic
707C22×C73C2×H(5,𝔽2)11yescharacteristic
708C22×C73#58511yescharacteristic
709C22×C73#58511yescharacteristic
710C22×C73#58511yescharacteristic
711C22×C73#58511yescharacteristic
712C4×C73—22no—
713C4×C73—22no—
714C4×C73—22no—
715C4×C73—41no—
716C4×C73—41no—
717C4×C73—41no—
718C4×C73—41no—
719C4×C73—41no—
720C4×C73—41no—
721C4×C73—41no—
722C4×C73—41no—
723C4×C73—41no—
724C4×C73—41no—
725C4×C73—41no—
726C4×C73—41no—
727C4×C73—41no—
728C4×C73—41no—
729C4×C73—41no—
730C4×C73—41no—
731C4×C73—41no—
732C4×C73—41no—
733C4×C73—41no—
734C4×C73—41no—
735C4×C73—41no—
736C4×C73—41no—
737C4×C73—41no—
738#36784C7311yesmaximal, characteristic, direct product factor, Sylow
739C2×C73—42no—
740C2×C73—42no—
741C2×C73—81no—
742C2×C73—81no—
743C2×C73—81no—
744C2×C73#345511yescharacteristic
745C2×C73#349411yescharacteristic
746C2×C73#350511yescharacteristic
747C2×C73#353411yescharacteristic
748C2×C73#354011yescharacteristic
749C2×C73#354511yescharacteristic
750C2×C73#356611yescharacteristic
751#2853C2×C7311yescharacteristic, complemented
752#2850C2×C7311yescharacteristic, complemented
753#2783C2×C7311yescharacteristic, complemented
754#2779C2×C7311yescharacteristic, complemented
755#2772C2×C7311yescharacteristic, complemented
756#2757C2×C7311yescharacteristic, complemented
757#2753C2×C7311yescharacteristic, complemented
758#2744C2×C7311yescharacteristic, complemented
759#2737C2×C7311yescharacteristic, complemented
760#2735C2×C7311yescharacteristic, complemented
761#2731C2×C7311yescharacteristic, complemented
762#2701C2×C7311yescharacteristic, complemented
763#2693C2×C7311yescharacteristic, complemented
764#2687C2×C7311yescharacteristic, complemented
765#2684C2×C7311yescharacteristic, complemented
766#2684C2×C7311yescharacteristic, complemented
767#2678C2×C7311yescharacteristic
768#2674C2×C7311yescharacteristic, complemented
769#2651C2×C7311yescharacteristic, complemented
770#2650C2×C7311yescharacteristic, complemented
771#2602C2×C7311yescharacteristic, complemented
772#2595C2×C7311yescharacteristic, complemented
773#2557C2×C7311yescharacteristic, complemented
774#2534C2×C7311yescharacteristic, complemented
775#2532C2×C7311yescharacteristic, complemented
776#2531C2×C7311yescharacteristic, complemented
777#2439C2×C7311yescharacteristic, complemented
778#2411C2×C7311yescharacteristic, complemented
779#2335C2×C7311yescharacteristic, complemented
780#2312C2×C7311yescharacteristic, complemented
781#2290C2×C7311yescharacteristic, complemented
782C73#3678411yescharacteristic, direct product factor, Sylow
783C2×C4⋊Q8C22×C7311yescharacteristic, complemented
784C2×#124C22×C7311yescharacteristic
785C2×#124C22×C7311yescharacteristic
786C2×#123C22×C7311yescharacteristic
787C2×#123C22×C7311yescharacteristic
788C2×#123C22×C7311yescharacteristic
789C2×#123C22×C7311yescharacteristic, complemented
790C2×C22⋊Q8C22×C7311yescharacteristic, complemented
791C2×#121C22×C7311yescharacteristic
792C2×#120C22×C7311yescharacteristic
793C2×#120C22×C7311yescharacteristic
794C2×C4×D4C22×C7311yescharacteristic
795C2×#117C22×C7311yescharacteristic
796C22×C22⋊C4C22×C7311yescharacteristic
797C22×C42C22×C7311yescharacteristic, complemented
798#400C22×C7311yescharacteristic, complemented
799#400C22×C7311yescharacteristic, complemented
800#400C22×C7311yescharacteristic, complemented
801#400C22×C7311yescharacteristic, complemented
802#400C22×C7311yescharacteristic, complemented
803#399C22×C7311yescharacteristic
804#398C22×C7311yescharacteristic, complemented
805#398C22×C7311yescharacteristic, complemented
806#398C22×C7311yescharacteristic, complemented
807#398C22×C7311yescharacteristic, complemented
808#397C22×C7311yescharacteristic
809#397C22×C7311yescharacteristic
810#397C22×C7311yescharacteristic
811#397C22×C7311yescharacteristic
812#397C22×C7311yescharacteristic
813#397C22×C7311yescharacteristic
814#397C22×C7311yescharacteristic
815#397C22×C7311yescharacteristic
816#397C22×C7311yescharacteristic, complemented
817#397C22×C7311yescharacteristic, complemented
818#397C22×C7311yescharacteristic, complemented
819#397C22×C7311yescharacteristic, complemented
820#396C22×C7311yescharacteristic
821#396C22×C7311yescharacteristic
822#396C22×C7311yescharacteristic
823#396C22×C7311yescharacteristic
824#396C22×C7311yescharacteristic
825#396C22×C7311yescharacteristic
826#396C22×C7311yescharacteristic
827#396C22×C7311yescharacteristic, complemented
828#395C22×C7311yescharacteristic, complemented
829#394C22×C7311yescharacteristic
830#394C22×C7311yescharacteristic
831#394C22×C7311yescharacteristic
832#394C22×C7311yescharacteristic
833#394C22×C7311yescharacteristic
834#394C22×C7311yescharacteristic
835#394C22×C7311yescharacteristic
836#394C22×C7311yescharacteristic
837#394C22×C7311yescharacteristic
838#394C22×C7311yescharacteristic
839#393C22×C7311yescharacteristic
840#393C22×C7311yescharacteristic
841#393C22×C7311yescharacteristic
842#393C22×C7311yescharacteristic
843#393C22×C7311yescharacteristic, complemented
844#392C22×C7311yescharacteristic
845#392C22×C7311yescharacteristic
846#391C22×C7311yescharacteristic, complemented
847#391C22×C7311yescharacteristic, complemented
848#391C22×C7311yescharacteristic, complemented
849#390C22×C7311yescharacteristic
850#390C22×C7311yescharacteristic
851#390C22×C7311yescharacteristic
852#390C22×C7311yescharacteristic
853#390C22×C7311yescharacteristic, complemented
854#389C22×C7311yescharacteristic, complemented
855#389C22×C7311yescharacteristic, complemented
856#389C22×C7311yescharacteristic, complemented
857#389C22×C7311yescharacteristic, complemented
858#388C22×C7311yescharacteristic
859#388C22×C7311yescharacteristic
860#388C22×C7311yescharacteristic
861#388C22×C7311yescharacteristic
862#388C22×C7311yescharacteristic
863#388C22×C7311yescharacteristic
864#388C22×C7311yescharacteristic
865#388C22×C7311yescharacteristic
866#388C22×C7311yescharacteristic
867#388C22×C7311yescharacteristic
868#388C22×C7311yescharacteristic
869#388C22×C7311yescharacteristic
870#388C22×C7311yescharacteristic
871#388C22×C7311yescharacteristic
872#388C22×C7311yescharacteristic
873#388C22×C7311yescharacteristic
874#388C22×C7311yescharacteristic
875#388C22×C7311yescharacteristic
876#388C22×C7311yescharacteristic
877#388C22×C7311yescharacteristic
878#388C22×C7311yescharacteristic
879#388C22×C7311yescharacteristic
880#388C22×C7311yescharacteristic
881#388C22×C7311yescharacteristic, complemented
882#388C22×C7311yescharacteristic, complemented
883#388C22×C7311yescharacteristic, complemented
884#388C22×C7311yescharacteristic, complemented
885#388C22×C7311yescharacteristic, complemented
886#388C22×C7311yescharacteristic, complemented
887#388C22×C7311yescharacteristic, complemented
888#387C22×C7311yescharacteristic, complemented
889#387C22×C7311yescharacteristic, complemented
890#387C22×C7311yescharacteristic, complemented
891#387C22×C7311yescharacteristic, complemented
892#387C22×C7311yescharacteristic, complemented
893#387C22×C7311yescharacteristic, complemented
894#387C22×C7311yescharacteristic, complemented
895#387C22×C7311yescharacteristic, complemented
896#387C22×C7311yescharacteristic, complemented
897#387C22×C7311yescharacteristic, complemented
898#387C22×C7311yescharacteristic, complemented
899#387C22×C7311yescharacteristic, complemented
900#386C22×C7311yescharacteristic
901#386C22×C7311yescharacteristic
902#386C22×C7311yescharacteristic
903#386C22×C7311yescharacteristic
904#386C22×C7311yescharacteristic
905#386C22×C7311yescharacteristic
906#386C22×C7311yescharacteristic
907#386C22×C7311yescharacteristic
908#386C22×C7311yescharacteristic
909#386C22×C7311yescharacteristic
910#386C22×C7311yescharacteristic, complemented
911#386C22×C7311yescharacteristic, complemented
912#385C22×C7311yescharacteristic
913#385C22×C7311yescharacteristic, complemented
914#385C22×C7311yescharacteristic, complemented
915#385C22×C7311yescharacteristic, complemented
916#385C22×C7311yescharacteristic, complemented
917#385C22×C7311yescharacteristic, complemented
918#383C22×C7311yescharacteristic, complemented
919#382C22×C7311yescharacteristic, complemented
920#382C22×C7311yescharacteristic, complemented
921#381C22×C7311yescharacteristic
922#381C22×C7311yescharacteristic, complemented
923#380C22×C7311yescharacteristic
924#380C22×C7311yescharacteristic
925#380C22×C7311yescharacteristic
926#380C22×C7311yescharacteristic, complemented
927#379C22×C7311yescharacteristic
928#379C22×C7311yescharacteristic
929#379C22×C7311yescharacteristic
930#379C22×C7311yescharacteristic
931C4×C4⋊C4C22×C7311yescharacteristic, complemented
932C4×C4⋊C4C22×C7311yescharacteristic, complemented
933C4×C22⋊C4C22×C7311yescharacteristic
934C4×C22⋊C4C22×C7311yescharacteristic
935C4×C22⋊C4C22×C7311yescharacteristic, complemented
936C4×C22⋊C4C22×C7311yescharacteristic, complemented
937#376C22×C7311yescharacteristic, complemented
938C25C23×C7311yescharacteristic
939C22×Q8C23×C7311yescharacteristic
940C22×Q8C23×C7311yescharacteristic
941C22×D4C23×C7311yescharacteristic
942C22×D4C23×C7311yescharacteristic
943C22×D4C23×C7311yescharacteristic
944C22×D4C23×C7311yescharacteristic
945C22×D4C23×C7311yescharacteristic
946C22×D4C23×C7311yescharacteristic
947C22×D4C23×C7311yescharacteristic
948C23×C4C23×C7311yescharacteristic
949C23×C4C23×C7311yescharacteristic
950C23×C4C23×C7311yescharacteristic
951C23×C4C23×C7311yescharacteristic
952C23×C4C23×C7311yescharacteristic
953C23×C4C23×C7311yescharacteristic
954C4⋊Q8—42no—
955#124—42no—
956#124—42no—
957#123—24no—
958#123—42no—
959#123—42no—
960#123—42no—
961C22⋊Q8—42no—
962#121—42no—
963#120—42no—
964#120—42no—
965C4×D4—24no—
966#117—42no—
967C2×C4⋊C4C23×C7311yescharacteristic
968C2×C4⋊C4C23×C7311yescharacteristic
969C2×C4⋊C4C23×C7311yescharacteristic
970C2×C4⋊C4C23×C7311yescharacteristic
971C2×C4⋊C4C23×C7311yescharacteristic
972C2×C4⋊C4C23×C7311yescharacteristic
973C2×C4⋊C4C23×C7311yescharacteristic
974C2×C4⋊C4C23×C7311yescharacteristic
975C2×C4⋊C4C23×C7311yescharacteristic
976C2×C4⋊C4C23×C7311yescharacteristic
977C2×C4⋊C4C23×C7311yescharacteristic
978C2×C4⋊C4C23×C7311yescharacteristic
979C2×C4⋊C4C23×C7311yescharacteristic
980C2×C4⋊C4C23×C7311yescharacteristic
981C2×C4⋊C4C23×C7311yescharacteristic
982C2×C4⋊C4C23×C7311yescharacteristic
983C2×C4⋊C4C23×C7311yescharacteristic
984C2×C4⋊C4C23×C7311yescharacteristic
985C2×C4⋊C4C23×C7311yescharacteristic
986C2×C4⋊C4C23×C7311yescharacteristic
987C2×C4⋊C4C23×C7311yescharacteristic
988C2×C4⋊C4C23×C7311yescharacteristic
989C2×C4⋊C4C23×C7311yescharacteristic
990C2×C4⋊C4C23×C7311yescharacteristic
991C2×C4⋊C4C23×C7311yescharacteristic
992C2×C4⋊C4C23×C7311yescharacteristic
993C2×C4⋊C4C23×C7311yescharacteristic
994C2×C4⋊C4C23×C7311yescharacteristic
995C2×C4⋊C4C23×C7311yescharacteristic
996C2×C22⋊C4—24no—
997C2×C22⋊C4C23×C7311yescharacteristic
998C2×C22⋊C4C23×C7311yescharacteristic
999C2×C22⋊C4C23×C7311yescharacteristic
1000C2×C22⋊C4C23×C7311yescharacteristic
1001C2×C22⋊C4C23×C7311yescharacteristic
1002C2×C22⋊C4C23×C7311yescharacteristic
1003C2×C22⋊C4C23×C7311yescharacteristic
1004C2×C22⋊C4C23×C7311yescharacteristic
1005C2×C22⋊C4C23×C7311yescharacteristic
1006C2×C22⋊C4C23×C7311yescharacteristic
1007C2×C22⋊C4C23×C7311yescharacteristic
1008C2×C22⋊C4C23×C7311yescharacteristic
1009C2×C22⋊C4C23×C7311yescharacteristic
1010C2×C22⋊C4C23×C7311yescharacteristic
1011C2×C22⋊C4C23×C7311yescharacteristic
1012C2×C22⋊C4C23×C7311yescharacteristic
1013C2×C22⋊C4C23×C7311yescharacteristic
1014C2×C22⋊C4C23×C7311yescharacteristic
1015C2×C22⋊C4C23×C7311yescharacteristic
1016C2×C22⋊C4C23×C7311yescharacteristic
1017C2×C22⋊C4C23×C7311yescharacteristic
1018C2×C22⋊C4C23×C7311yescharacteristic
1019C2×C22⋊C4C23×C7311yescharacteristic
1020C2×C22⋊C4C23×C7311yescharacteristic
1021C2×C22⋊C4C23×C7311yescharacteristic
1022C2×C22⋊C4C23×C7311yescharacteristic
1023C2×C22⋊C4C23×C7311yescharacteristic
1024C2×C22⋊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×C42—42no—
1050C2×C42C23×C7311yescharacteristic
1051C2×C42C23×C7311yescharacteristic
1052C2×C42C23×C7311yescharacteristic
1053C2×C42C23×C7311yescharacteristic
1054C2×C42C23×C7311yescharacteristic
1055C2×C42C23×C7311yescharacteristic
1056C2×C42C23×C7311yescharacteristic
1057C2×C42C23×C7311yescharacteristic
1058C2×C42C23×C7311yescharacteristic
1059C2×C42C23×C7311yescharacteristic
1060C2×C42C23×C7311yescharacteristic
1061C2×C42C23×C7311yescharacteristic
1062#95C23×C7311yescharacteristic
1063#95C23×C7311yescharacteristic
1064#95C23×C7311yescharacteristic
1065#95C23×C7311yescharacteristic
1066#95C23×C7311yescharacteristic
1067#95C23×C7311yescharacteristic
1068#95C23×C7311yescharacteristic
1069#95C23×C7311yescharacteristic
1070#95C23×C7311yescharacteristic
1071#95C23×C7311yescharacteristic
1072#95C23×C7311yescharacteristic
1073#95C23×C7311yescharacteristic
1074#95C23×C7311yescharacteristic
1075#95C23×C7311yescharacteristic
1076#95C23×C7311yescharacteristic
1077#95C23×C7311yescharacteristic
1078#95C23×C7311yescharacteristic
1079#95C23×C7311yescharacteristic
1080#95C23×C7311yescharacteristic
1081#95C23×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
1108C24—22no—
1109C24—41no—
1110C24—41no—
1111C24—41no—
1112C24—41no—
1113C24—41no—
1114C24—41no—
1115C24C24×C7311yescharacteristic
1116C24C24×C7311yescharacteristic
1117C24C24×C7311yescharacteristic
1118C24C24×C7311yescharacteristic
1119C24C24×C7311yescharacteristic
1120C2×Q8—22no—
1121C2×Q8—41no—
1122C2×Q8—41no—
1123C2×Q8—41no—
1124C2×Q8—41no—
1125C2×Q8—41no—
1126C2×D4—22no—
1127C2×D4—22no—
1128C2×D4—22no—
1129C2×D4—22no—
1130C2×D4—22no—
1131C2×D4—22no—
1132C2×D4—22no—
1133C2×D4—41no—
1134C2×D4—41no—
1135C2×D4—41no—
1136C2×D4—41no—
1137C2×D4—41no—
1138C2×D4—41no—
1139C2×D4—41no—
1140C2×D4—41no—
1141C2×D4—41no—
1142C2×D4—41no—
1143C2×D4—41no—
1144C2×D4—41no—
1145C2×D4—41no—
1146C2×D4—41no—
1147C22×C4—22no—
1148C22×C4—22no—
1149C22×C4—22no—
1150C22×C4—22no—
1151C22×C4—41no—
1152C22×C4—41no—
1153C22×C4—41no—
1154C22×C4—41no—
1155C22×C4—41no—
1156C22×C4—41no—
1157C22×C4—41no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—41no—
1161C22×C4—41no—
1162C22×C4—41no—
1163C22×C4—41no—
1164C22×C4#41×C7314yes—
1165C22×C4C24×C7311yescharacteristic
1166C22×C4C24×C7311yescharacteristic
1167C22×C4C24×C7311yescharacteristic
1168C22×C4C24×C7311yescharacteristic
1169C22×C4C24×C7311yescharacteristic
1170C22×C4C24×C7311yescharacteristic
1171C22×C4C24×C7311yescharacteristic
1172C22×C4C24×C7311yescharacteristic
1173C22×C4C24×C7311yescharacteristic
1174C22×C4C24×C7311yescharacteristic
1175C22×C4C24×C7311yescharacteristic
1176C22×C4C24×C7311yescharacteristic
1177C22×C4C24×C7311yescharacteristic
1178C22×C4C24×C7311yescharacteristic
1179C22×C4C24×C7311yescharacteristic
1180C22×C4C24×C7311yescharacteristic
1181C22×C4C24×C7311yescharacteristic
1182C22×C4C24×C7311yescharacteristic
1183C22×C4C24×C7311yescharacteristic
1184C22×C4C24×C7311yescharacteristic
1185C22×C4C24×C7311yescharacteristic
1186C22×C4C24×C7311yescharacteristic
1187C22×C4C24×C7311yescharacteristic
1188C22×C4C24×C7311yescharacteristic
1189C22×C4C24×C7311yescharacteristic
1190C22×C4C24×C7311yescharacteristic
1191C4⋊C4—22no—
1192C4⋊C4—22no—
1193C4⋊C4—22no—
1194C4⋊C4—22no—
1195C4⋊C4—22no—
1196C4⋊C4—41no—
1197C4⋊C4—41no—
1198C4⋊C4—41no—
1199C4⋊C4—41no—
1200C4⋊C4—41no—
1201C4⋊C4—41no—
1202C4⋊C4—41no—
1203C4⋊C4—41no—
1204C4⋊C4—41no—
1205C4⋊C4—41no—
1206C4⋊C4—41no—
1207C4⋊C4—41no—
1208C4⋊C4—41no—
1209C4⋊C4—41no—
1210C4⋊C4—41no—
1211C4⋊C4—41no—
1212C4⋊C4—41no—
1213C4⋊C4—41no—
1214C4⋊C4—41no—
1215C4⋊C4—41no—
1216C4⋊C4—41no—
1217C4⋊C4—41no—
1218C4⋊C4—41no—
1219C4⋊C4—41no—
1220C22⋊C4—22no—
1221C22⋊C4—22no—
1222C22⋊C4—22no—
1223C22⋊C4—22no—
1224C22⋊C4—22no—
1225C22⋊C4—22no—
1226C22⋊C4—22no—
1227C22⋊C4—22no—
1228C22⋊C4—22no—
1229C22⋊C4—22no—
1230C22⋊C4—22no—
1231C22⋊C4—22no—
1232C22⋊C4—22no—
1233C22⋊C4—22no—
1234C22⋊C4—22no—
1235C22⋊C4—41no—
1236C22⋊C4—41no—
1237C22⋊C4—41no—
1238C22⋊C4—41no—
1239C22⋊C4—41no—
1240C22⋊C4—41no—
1241C22⋊C4—41no—
1242C22⋊C4—41no—
1243C22⋊C4—41no—
1244C22⋊C4—41no—
1245C22⋊C4—41no—
1246C22⋊C4—41no—
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—41no—
1269C22⋊C4—41no—
1270C22⋊C4—41no—
1271C22⋊C4—41no—
1272C42—22no—
1273C42—22no—
1274C42—22no—
1275C42—41no—
1276C42—41no—
1277C42—41no—
1278C42—41no—
1279C42—41no—
1280C42—41no—
1281C42—41no—
1282C42—41no—
1283C42—41no—
1284C23—21no—
1285C23—21no—
1286C23—21no—
1287C23—21no—
1288C23—21no—
1289C23—21no—
1290C23—21no—
1291C23—21no—
1292C23—21no—
1293C23—21no—
1294C23—21no—
1295C23—21no—
1296C23—21no—
1297C23—21no—
1298C23—21no—
1299C23—21no—
1300C23—21no—
1301C23—21no—
1302C23—21no—
1303C23—21no—
1304C23—21no—
1305C23—21no—
1306C23—21no—
1307C23—21no—
1308C23—21no—
1309C23—21no—
1310C23—21no—
1311C23—21no—
1312C23—21no—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23—21no—
1317C23—44no—
1318C23—82no—
1319C23—82no—
1320C23—82no—
1321C23—82no—
1322C23—82no—
1323C23—82no—
1324C23C2×#41×C7312yes—
1325C23H(5,𝔽2)×C7312yes—
1326C23C25×C7311yescharacteristic
1327Q8—82no—
1328Q8—82no—
1329D4—44no—
1330D4—82no—
1331D4—82no—
1332D4—82no—
1333D4—82no—
1334D4—82no—
1335D4—82no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
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—44no—
1412C2×C4—44no—
1413C2×C4—44no—
1414C2×C4—44no—
1415C2×C4—82no—
1416C2×C4—82no—
1417C2×C4C2×#41×C7312yes—
1418C2×C4C2×#41×C7312yes—
1419C2×C4H(5,𝔽2)×C7312yes—
1420C22—22no—
1421C22—22no—
1422C22—22no—
1423C22—22no—
1424C22—22no—
1425C22—22no—
1426C22—41no—
1427C22—41no—
1428C22—41no—
1429C22—41no—
1430C22—41no—
1431C22—41no—
1432C22—41no—
1433C22—41no—
1434C22—41no—
1435C22—41no—
1436C22—41no—
1437C22—41no—
1438C22—41no—
1439C22—41no—
1440C22—41no—
1441C22—41no—
1442C22—41no—
1443C22—41no—
1444C22—41no—
1445C22—41no—
1446C22—41no—
1447C22—41no—
1448C22—41no—
1449C22—41no—
1450C22—41no—
1451C22—41no—
1452C22—41no—
1453C22—41no—
1454C22—41no—
1455C22—88no—
1456C22C22×#41×C7311yescharacteristic
1457C22C2×H(5,𝔽2)×C7311yescharacteristic
1458C22C2×H(5,𝔽2)×C7311yescharacteristic
1459C22#585×C7311yescharacteristic
1460C22#585×C7311yescharacteristic
1461C22#585×C7311yescharacteristic
1462C22#585×C7311yescharacteristic
1463C4—22no—
1464C4—22no—
1465C4—22no—
1466C4—41no—
1467C4—41no—
1468C4—41no—
1469C4—41no—
1470C4—41no—
1471C4—41no—
1472C4—41no—
1473C4—41no—
1474C4—41no—
1475C4—41no—
1476C4—41no—
1477C4—41no—
1478C4—41no—
1479C4—41no—
1480C4—41no—
1481C4—41no—
1482C4—41no—
1483C4—41no—
1484C4—41no—
1485C4—41no—
1486C4—41no—
1487C4—41no—
1488C4—41no—
1489C2—42no—
1490C2—42no—
1491C2—81no—
1492C2—81no—
1493C2—81no—
1494C2C73×#345511yescharacteristic
1495C2C73×#349411yescharacteristic
1496C2C73×#350511yescharacteristic
1497C2C73×#353411yescharacteristic
1498C2C73×#354011yescharacteristic
1499C2C73×#354511yescharacteristic
1500C2C73×#356611yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
prime radicalC73×#2678C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2853C2semidirect
2. C73×#2850C2semidirect
3. C73×#2783C2semidirect
4. C73×#2779C2semidirect
5. C73×#2772C2semidirect
6. C73×#2757C2semidirect
7. C73×#2753C2semidirect
8. C73×#2744C2semidirect
9. C73×#2737C2semidirect
10. C73×#2735C2semidirect
11. C73×#2731C2semidirect
12. C73×#2701C2semidirect
13. C73×#2693C2semidirect
14. C73×#2687C2semidirect
15. C73×#2684C2semidirect
16. C73×#2684C2semidirect
18. C73×#2674C2semidirect
19. C73×#2651C2semidirect
20. C73×#2650C2semidirect
21. C73×#2602C2semidirect
22. C73×#2595C2semidirect
23. C73×#2557C2semidirect
24. C73×#2534C2semidirect
25. C73×#2532C2semidirect
26. C73×#2531C2semidirect
27. C73×#2439C2semidirect
28. C73×#2411C2semidirect
29. C73×#2335C2semidirect
30. C73×#2312C2semidirect
31. C73×#2290C2semidirect
32. C2×C4⋊Q8×C73C22semidirect
38. C2×#123×C73C22semidirect
39. C2×C22⋊Q8×C73C22semidirect
46. C22×C42×C73C22semidirect
47. #400×C73C22semidirect
48. #400×C73C22semidirect
49. #400×C73C22semidirect
50. #400×C73C22semidirect
51. #400×C73C22semidirect
53. #398×C73C22semidirect
54. #398×C73C22semidirect
55. #398×C73C22semidirect
56. #398×C73C22semidirect
65. #397×C73C22semidirect
66. #397×C73C22semidirect
67. #397×C73C22semidirect
68. #397×C73C22semidirect
76. #396×C73C22semidirect
77. #395×C73C22semidirect
92. #393×C73C22semidirect
95. #391×C73C22semidirect
96. #391×C73C22semidirect
97. #391×C73C22semidirect
102. #390×C73C22semidirect
103. #389×C73C22semidirect
104. #389×C73C22semidirect
105. #389×C73C22semidirect
106. #389×C73C22semidirect
130. #388×C73C22semidirect
131. #388×C73C22semidirect
132. #388×C73C22semidirect
133. #388×C73C22semidirect
134. #388×C73C22semidirect
135. #388×C73C22semidirect
136. #388×C73C22semidirect
137. #387×C73C22semidirect
138. #387×C73C22semidirect
139. #387×C73C22semidirect
140. #387×C73C22semidirect
141. #387×C73C22semidirect
142. #387×C73C22semidirect
143. #387×C73C22semidirect
144. #387×C73C22semidirect
145. #387×C73C22semidirect
146. #387×C73C22semidirect
147. #387×C73C22semidirect
148. #387×C73C22semidirect
159. #386×C73C22semidirect
160. #386×C73C22semidirect
162. #385×C73C22semidirect
163. #385×C73C22semidirect
164. #385×C73C22semidirect
165. #385×C73C22semidirect
166. #385×C73C22semidirect
167. #383×C73C22semidirect
168. #382×C73C22semidirect
169. #382×C73C22semidirect
171. #381×C73C22semidirect
175. #380×C73C22semidirect
180. C4×C4⋊C4×C73C22semidirect
181. C4×C4⋊C4×C73C22semidirect
184. C4×C22⋊C4×C73C22semidirect
185. C4×C22⋊C4×C73C22semidirect
186. #376×C73C22semidirect
738. #36784C73direct (N × H)
751. #2853C2×C73semidirect
752. #2850C2×C73semidirect
753. #2783C2×C73semidirect
754. #2779C2×C73semidirect
755. #2772C2×C73semidirect
756. #2757C2×C73semidirect
757. #2753C2×C73semidirect
758. #2744C2×C73semidirect
759. #2737C2×C73semidirect
760. #2735C2×C73semidirect
761. #2731C2×C73semidirect
762. #2701C2×C73semidirect
763. #2693C2×C73semidirect
764. #2687C2×C73semidirect
765. #2684C2×C73semidirect
766. #2684C2×C73semidirect
768. #2674C2×C73semidirect
769. #2651C2×C73semidirect
770. #2650C2×C73semidirect
771. #2602C2×C73semidirect
772. #2595C2×C73semidirect
773. #2557C2×C73semidirect
774. #2534C2×C73semidirect
775. #2532C2×C73semidirect
776. #2531C2×C73semidirect
777. #2439C2×C73semidirect
778. #2411C2×C73semidirect
779. #2335C2×C73semidirect
780. #2312C2×C73semidirect
781. #2290C2×C73semidirect
782. C73#36784direct (N × H)
783. C2×C4⋊Q8C22×C73semidirect
789. C2×#123C22×C73semidirect
790. C2×C22⋊Q8C22×C73semidirect
797. C22×C42C22×C73semidirect
798. #400C22×C73semidirect
799. #400C22×C73semidirect
800. #400C22×C73semidirect
801. #400C22×C73semidirect
802. #400C22×C73semidirect
804. #398C22×C73semidirect
805. #398C22×C73semidirect
806. #398C22×C73semidirect
807. #398C22×C73semidirect
816. #397C22×C73semidirect
817. #397C22×C73semidirect
818. #397C22×C73semidirect
819. #397C22×C73semidirect
827. #396C22×C73semidirect
828. #395C22×C73semidirect
843. #393C22×C73semidirect
846. #391C22×C73semidirect
847. #391C22×C73semidirect
848. #391C22×C73semidirect
853. #390C22×C73semidirect
854. #389C22×C73semidirect
855. #389C22×C73semidirect
856. #389C22×C73semidirect
857. #389C22×C73semidirect
881. #388C22×C73semidirect
882. #388C22×C73semidirect
883. #388C22×C73semidirect
884. #388C22×C73semidirect
885. #388C22×C73semidirect
886. #388C22×C73semidirect
887. #388C22×C73semidirect
888. #387C22×C73semidirect
889. #387C22×C73semidirect
890. #387C22×C73semidirect
891. #387C22×C73semidirect
892. #387C22×C73semidirect
893. #387C22×C73semidirect
894. #387C22×C73semidirect
895. #387C22×C73semidirect
896. #387C22×C73semidirect
897. #387C22×C73semidirect
898. #387C22×C73semidirect
899. #387C22×C73semidirect
910. #386C22×C73semidirect
911. #386C22×C73semidirect
913. #385C22×C73semidirect
914. #385C22×C73semidirect
915. #385C22×C73semidirect
916. #385C22×C73semidirect
917. #385C22×C73semidirect
918. #383C22×C73semidirect
919. #382C22×C73semidirect
920. #382C22×C73semidirect
922. #381C22×C73semidirect
926. #380C22×C73semidirect
931. C4×C4⋊C4C22×C73semidirect
932. C4×C4⋊C4C22×C73semidirect
935. C4×C22⋊C4C22×C73semidirect
936. C4×C22⋊C4C22×C73semidirect
937. #376C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#28532
C73×#28502
C73×#27832
C73×#27792
C73×#27722
C73×#27572
C73×#27532
C73×#27442
C73×#27372
C73×#27352
C73×#27312
C73×#27012
C73×#26932
C73×#26872
C73×#26842
C73×#26782
C73×#26742
C73×#26512
C73×#26502
C73×#26022
C73×#25952
C73×#25572
C73×#25342
C73×#25322
C73×#25312
C73×#24392
C73×#24112
C73×#23352
C73×#23122
C73×#22902
#3678473