Finite Group Databasebeta

← #31964992

Subgroups — #31964992

Order 18176.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22597375C211yesmaximal, characteristic, complemented
2#22590973C211yesmaximal, characteristic, complemented
3#22586917C211yesmaximal, characteristic, complemented
4#22586912C211yesmaximal, characteristic, complemented
5#22586904C211yesmaximal, characteristic, complemented
6#22586896C211yesmaximal, characteristic, complemented
7#22586891C211yesmaximal, characteristic, complemented
8#22586883C211yesmaximal, characteristic, complemented
9#22586878C211yesmaximal, characteristic, complemented
10#22586873C211yesmaximal, characteristic, complemented
11#22586860C211yesmaximal, characteristic, complemented
12#22586844C211yesmaximal, characteristic, complemented
13#22586831C211yesmaximal, characteristic, complemented
14C2×#17985736C211yesmaximal, characteristic, complemented
15C71×#3520C211yesmaximal, characteristic
16#17986077—21no—
17#17986071—21no—
18#17986071—21no—
19D4×C71⋊C8—21no—
20#17986056C2211yescharacteristic
21#17986052C2211yescharacteristic
22#17985963C2211yescharacteristic
23#17985963C2211yescharacteristic
24C2×C22⋊(C71⋊C8)C2211yescharacteristic
25C2×C22⋊(C71⋊C8)C2211yescharacteristic
26#17985892—21no—
27#17985885—21no—
28#17985879—21no—
29#17985874—21no—
30#17985867C2211yescharacteristic
31#17985865C2211yescharacteristic
32#17985862C2211yescharacteristic
33#17985859C2211yescharacteristic
34C4×C22⋊Dic71C2211yescharacteristic
35C2×C71⋊#95C2211yescharacteristic
36#17985736C2211yescharacteristic
37#17985736C2211yescharacteristic
38#17985736C2211yescharacteristic
39#17985736C2211yescharacteristic
40#17985736C2211yescharacteristic
41#17985736C2211yescharacteristic
42#17985736C2211yescharacteristic
43#17985736C2211yescharacteristic
44#17985736C2211yescharacteristic
45#17985736C2211yescharacteristic
46#17985736C2211yescharacteristic
47#17985736C2211yescharacteristic
48#17985733C2211yescharacteristic
49#17985733C2211yescharacteristic
50#17985733C2211yescharacteristic
51#17985733C2211yescharacteristic
52#556×C71C411yescharacteristic, complemented
53#554×C71—21no—
54#552×C71C411yescharacteristic, complemented
55#552×C71C411yescharacteristic, complemented
56#551×C71—21no—
57#551×C71—21no—
58D4×Q8×C71C411yescharacteristic, complemented
59#548×C71C411yescharacteristic, complemented
60#548×C71C411yescharacteristic, complemented
61#547×C71C411yescharacteristic, complemented
62#547×C71C411yescharacteristic, complemented
63#546×C71—21no—
64#542×C71—21no—
65#539×C71—21no—
66#539×C71—21no—
67#533×C71C2211yescharacteristic
68#529×C71C2211yescharacteristic
69#525×C71C2211yescharacteristic
70#525×C71C2211yescharacteristic
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×C22⋊Q8×C71C2211yescharacteristic
73#520×C71—21no—
74C2×C4×D4×C71C2211yescharacteristic
75C23×Dic71—21no—
76C2×#11765849—21no—
77C2×#11765849—21no—
78C22×C71⋊C8—21no—
79C22×C71⋊C8—21no—
80C2×C4⋊Dic71—21no—
81C2×C4⋊Dic71—21no—
82C2×C22⋊Dic71—21no—
83C2×C22⋊Dic71—21no—
84C2×C22⋊Dic71—21no—
85C2×C4×Dic71—21no—
86C4⋊(C71⋊C8)—21no—
87C4⋊(C71⋊C8)—21no—
88C22⋊(C71⋊C8)—21no—
89C22⋊(C71⋊C8)—21no—
90C22⋊(C71⋊C8)—21no—
91C22⋊(C71⋊C8)—21no—
92C22⋊(C71⋊C8)C2311yescharacteristic
93C22⋊(C71⋊C8)C2311yescharacteristic
94C22⋊(C71⋊C8)C2311yescharacteristic
95C22⋊(C71⋊C8)C2311yescharacteristic
96#14556039—21no—
97C4×C71⋊C8—21no—
98C71⋊#95—21no—
99C71⋊#95—21no—
100C71⋊#95—21no—
101C71⋊#95—21no—
102C71⋊#95—21no—
103C71⋊#95C2311yescharacteristic
104C71⋊#95C2311yescharacteristic
105C71⋊#95C2311yescharacteristic
106C71⋊#95C2311yescharacteristic
107C2×#41×C71—21no—
108C2×#41×C71C2×C411yescharacteristic
109C2×#41×C71C2×C411yescharacteristic, complemented
110C22×Q8×C71C2×C411yescharacteristic
111C22×Q8×C71C2×C411yescharacteristic, complemented
112C22×D4×C71D411yescharacteristic
113C23×C4×C71C2311yescharacteristic
114C23×C4×C71C2311yescharacteristic
115C4⋊Q8×C71—21no—
116C4⋊Q8×C71C2×C411yescharacteristic, complemented
117C4⋊Q8×C71C2×C411yescharacteristic, complemented
118#126×C71—21no—
119#126×C71—21no—
120#126×C71—21no—
121#126×C71—21no—
122#126×C71—21no—
123#125×C71—21no—
124#125×C71—21no—
125#125×C71—21no—
126#125×C71C2×C411yescharacteristic, complemented
127#124×C71—21no—
128#124×C71—21no—
129#124×C71—21no—
130#124×C71C2×C411yescharacteristic, complemented
131#123×C71—21no—
132#123×C71—21no—
133#123×C71—21no—
134#123×C71—21no—
135#123×C71—21no—
136#123×C71—21no—
137#123×C71—21no—
138#123×C71—21no—
139#123×C71—21no—
140C22⋊Q8×C71—21no—
141C22⋊Q8×C71—21no—
142C22⋊Q8×C71—21no—
143C22⋊Q8×C71—21no—
144C22⋊Q8×C71—21no—
145C22⋊Q8×C71—21no—
146C22⋊Q8×C71—21no—
147C22⋊Q8×C71—21no—
148C22⋊Q8×C71—21no—
149C22⋊Q8×C71—21no—
150C22⋊Q8×C71C2×C411yescharacteristic
151C22⋊Q8×C71C2×C411yescharacteristic
152C22⋊Q8×C71C2×C411yescharacteristic
153C22⋊Q8×C71C2×C411yescharacteristic, complemented
154C22⋊Q8×C71C2×C411yescharacteristic, complemented
155C22⋊Q8×C71C2×C411yescharacteristic, complemented
156C22⋊Q8×C71C2311yescharacteristic
157C22⋊Q8×C71C2311yescharacteristic
158C22⋊Q8×C71C2311yescharacteristic
159#121×C71—21no—
160#121×C71—21no—
161#121×C71—21no—
162#121×C71C2×C411yescharacteristic
163#121×C71C2×C411yescharacteristic, complemented
164#121×C71C2311yescharacteristic
165#120×C71—21no—
166#120×C71—21no—
167C4×Q8×C71—21no—
168C4×Q8×C71—21no—
169C4×Q8×C71C2×C411yescharacteristic, complemented
170C4×Q8×C71C2×C411yescharacteristic, complemented
171C4×Q8×C71C2×C411yescharacteristic, complemented
172C4×D4×C71—21no—
173C4×D4×C71—21no—
174C4×D4×C71—21no—
175C4×D4×C71—21no—
176C4×D4×C71—21no—
177C4×D4×C71—21no—
178C4×D4×C71—21no—
179C4×D4×C71—21no—
180C4×D4×C71C2×C411yescharacteristic
181C4×D4×C71C2×C411yescharacteristic
182C4×D4×C71C2×C411yescharacteristic
183C4×D4×C71C2×C411yescharacteristic
184C4×D4×C71C2×C411yescharacteristic, complemented
185C4×D4×C71D411yescharacteristic
186C4×D4×C71D411yescharacteristic
187C4×D4×C71D411yescharacteristic
188C4×D4×C71D411yescharacteristic
189#117×C71—21no—
190#117×C71—21no—
191#117×C71—21no—
192#117×C71—21no—
193#117×C71C2×C411yescharacteristic
194#117×C71C2×C411yescharacteristic, complemented
195C2×C4⋊C4×C71—21no—
196C2×C4⋊C4×C71—21no—
197C2×C4⋊C4×C71—21no—
198C2×C4⋊C4×C71C2×C411yescharacteristic
199C2×C4⋊C4×C71C2×C411yescharacteristic, complemented
200C2×C4⋊C4×C71D411yescharacteristic
201C2×C22⋊C4×C71—21no—
202C2×C22⋊C4×C71—21no—
203C2×C22⋊C4×C71D411yescharacteristic
204C2×C22⋊C4×C71D411yescharacteristic
205C2×C42×C71C2311yescharacteristic
206C22×Dic71—21no—
207C22×Dic71—21no—
208C22×Dic71—21no—
209C22×Dic71—21no—
210C22×Dic71—42no—
211C22×Dic71—81no—
212C22×Dic71—81no—
213#11765849—81no—
214#11765849—81no—
215C2×C71⋊C8—21no—
216C2×C71⋊C8—21no—
217C2×C71⋊C8—21no—
218C2×C71⋊C8—21no—
219C2×C71⋊C8—81no—
220C2×C71⋊C8—81no—
221C4⋊Dic71—81no—
222C4⋊Dic71—81no—
223C22⋊Dic71—42no—
224C22⋊Dic71—81no—
225C22⋊Dic71—81no—
226C4×Dic71—81no—
227C24×C71C2×D411yescharacteristic
228C24×C71C2×D411yescharacteristic
229#41×C71—44no—
230#41×C71—81no—
231#41×C71—81no—
232C2×Q8×C71—21no—
233C2×Q8×C71—21no—
234C2×Q8×C71—21no—
235C2×Q8×C71—81no—
236C2×Q8×C71—81no—
237C2×Q8×C71C22×C411yescharacteristic
238C2×Q8×C71C22×C411yescharacteristic
239C2×Q8×C71C22×C411yescharacteristic
240C2×D4×C71—21no—
241C2×D4×C71—21no—
242C2×D4×C71—21no—
243C2×D4×C71—21no—
244C2×D4×C71—21no—
245C2×D4×C71—42no—
246C2×D4×C71C22⋊C411yescharacteristic
247C2×D4×C71C22⋊C411yescharacteristic
248C2×D4×C71C22⋊C411yescharacteristic
249C2×D4×C71C22⋊C411yescharacteristic
250C2×D4×C71C22×C411yescharacteristic
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—81no—
259C22×C4×C71—81no—
260C22×C4×C71C22×C411yescharacteristic
261C22×C4×C71C22×C411yescharacteristic
262C22×C4×C71C22×C411yescharacteristic
263C22×C4×C71C22×C411yescharacteristic
264C22×C4×C71C2×D411yescharacteristic
265C22×C4×C71C2×D411yescharacteristic
266C22×C4×C71C2×D411yescharacteristic
267C22×C4×C71C2×D411yescharacteristic
268C22×C4×C71C2×D411yescharacteristic
269C22×C4×C71C2×D411yescharacteristic
270C22×C4×C71C2×D411yescharacteristic
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2411yescharacteristic
273C4⋊C4×C71—21no—
274C4⋊C4×C71—21no—
275C4⋊C4×C71—21no—
276C4⋊C4×C71—21no—
277C4⋊C4×C71—21no—
278C4⋊C4×C71—21no—
279C4⋊C4×C71—21no—
280C4⋊C4×C71—21no—
281C4⋊C4×C71—21no—
282C4⋊C4×C71—21no—
283C4⋊C4×C71—21no—
284C4⋊C4×C71—21no—
285C4⋊C4×C71—21no—
286C4⋊C4×C71—21no—
287C4⋊C4×C71—21no—
288C4⋊C4×C71—21no—
289C4⋊C4×C71—21no—
290C4⋊C4×C71—21no—
291C4⋊C4×C71—21no—
292C4⋊C4×C71C22⋊C411yescharacteristic
293C4⋊C4×C71C22⋊C411yescharacteristic
294C4⋊C4×C71C22⋊C411yescharacteristic
295C4⋊C4×C71C22⋊C411yescharacteristic
296C4⋊C4×C71C22×C411yescharacteristic
297C4⋊C4×C71C22×C411yescharacteristic
298C4⋊C4×C71C22×C411yescharacteristic
299C4⋊C4×C71C22×C411yescharacteristic
300C22⋊C4×C71—21no—
301C22⋊C4×C71—21no—
302C22⋊C4×C71—21no—
303C22⋊C4×C71—21no—
304C22⋊C4×C71—21no—
305C22⋊C4×C71—21no—
306C22⋊C4×C71—21no—
307C22⋊C4×C71—21no—
308C22⋊C4×C71—21no—
309C22⋊C4×C71—21no—
310C22⋊C4×C71—21no—
311C22⋊C4×C71—21no—
312C22⋊C4×C71—21no—
313C22⋊C4×C71—21no—
314C22⋊C4×C71—21no—
315C22⋊C4×C71—21no—
316C22⋊C4×C71—21no—
317C22⋊C4×C71C22⋊C411yescharacteristic
318C22⋊C4×C71C22⋊C411yescharacteristic
319C22⋊C4×C71C22⋊C411yescharacteristic
320C22⋊C4×C71C22⋊C411yescharacteristic
321C22⋊C4×C71C22⋊C411yescharacteristic
322C22⋊C4×C71C22⋊C411yescharacteristic
323C22⋊C4×C71C22⋊C411yescharacteristic
324C22⋊C4×C71C22⋊C411yescharacteristic
325C42×C71—21no—
326C42×C71—21no—
327C42×C71—21no—
328C42×C71—21no—
329C42×C71—21no—
330C42×C71C22×C411yescharacteristic
331C42×C71C22×C411yescharacteristic
332C42×C71C2×D411yescharacteristic
333C42×C71C2×D411yescharacteristic
334C23×C71—21no—
335C23×C71—21no—
336C23×C71—22no—
337C23×C71—21no—
338C23×C71—21no—
339C23×C71—21no—
340C23×C71—41no—
341C23×C71—41no—
342C23×C71—41no—
343C23×C71C2×C22⋊C411yescharacteristic
344C23×C71C2×C22⋊C411yescharacteristic
345C23×C71C2×C22⋊C411yescharacteristic
346C23×C71C2×C22⋊C411yescharacteristic
347C23×C71C22×D411yescharacteristic
348Q8×C71—41no—
349Q8×C71—41no—
350Q8×C71—41no—
351Q8×C71—42no—
352Q8×C71—81no—
353Q8×C71—81no—
354D4×C71—22no—
355D4×C71—22no—
356D4×C71—41no—
357D4×C71—41no—
358D4×C71—41no—
359D4×C71—42no—
360D4×C71—41no—
361D4×C71—41no—
362D4×C71—42no—
363D4×C71—81no—
364D4×C71—81no—
365C2×C4×C71—21no—
366C2×C4×C71—21no—
367C2×C4×C71—21no—
368C2×C4×C71—21no—
369C2×C4×C71—21no—
370C2×C4×C71—21no—
371C2×C4×C71—21no—
372C2×C4×C71—21no—
373C2×C4×C71—21no—
374C2×C4×C71—41no—
375C2×C4×C71—41no—
376C2×C4×C71—41no—
377C2×C4×C71—41no—
378C2×C4×C71—41no—
379C2×C4×C71—41no—
380C2×C4×C71—41no—
381C2×C4×C71—41no—
382C2×C4×C71—41no—
383C2×C4×C71—41no—
384C2×C4×C71—41no—
385C2×C4×C71—41no—
386C2×C4×C71—42no—
387C2×C4×C71—42no—
388C2×C4×C71—42no—
389C2×C4×C71—81no—
390C2×C4×C71—81no—
391C2×C4×C71—81no—
392C2×C4×C71—81no—
393C2×C4×C71C2×C22⋊C411yescharacteristic
394C2×C4×C71C2×C22⋊C411yescharacteristic
395C2×C4×C71C2×C22⋊C411yescharacteristic
396C2×C4×C71C2×C22⋊C411yescharacteristic
397C2×C4×C71C2×C22⋊C411yescharacteristic
398C2×C4×C71C2×C22⋊C411yescharacteristic
399C2×C4×C71C2×C22⋊C411yescharacteristic
400C2×C4×C71C2×C22⋊C411yescharacteristic
401C2×C4×C71C23×C411yescharacteristic
402C2×C4×C71C22×D411yescharacteristic
403C2×Dic71—41no—
404C2×Dic71—41no—
405C2×Dic71—41no—
406C2×Dic71—41no—
407C2×Dic71—41no—
408C2×Dic71—41no—
409C2×Dic71—41no—
410C2×Dic71—41no—
411C2×Dic71—41no—
412C2×Dic71—41no—
413C2×Dic71—41no—
414C2×Dic71—41no—
415C2×Dic71—84no—
416C71⋊C8—41no—
417C71⋊C8—41no—
418C71⋊C8—41no—
419C71⋊C8—41no—
420C22×C71—21no—
421C22×C71—21no—
422C22×C71—21no—
423C22×C71—21no—
424C22×C71—21no—
425C22×C71—21no—
426C22×C71—21no—
427C22×C71—21no—
428C22×C71—21no—
429C22×C71—21no—
430C22×C71—21no—
431C22×C71—21no—
432C22×C71—21no—
433C22×C71—42no—
434C22×C71—42no—
435C22×C71—41no—
436C22×C71—41no—
437C22×C71—41no—
438C22×C71—81no—
439C22×C71—81no—
440C22×C71#42112yes—
441C22×C71C22×C22⋊C411yescharacteristic
442C22×C71#57711yescharacteristic
443C22×C71#57811yescharacteristic
444C4×C71—21no—
445C4×C71—21no—
446C4×C71—21no—
447C4×C71—21no—
448C4×C71—21no—
449C4×C71—21no—
450C4×C71—21no—
451C4×C71—21no—
452C4×C71—21no—
453C4×C71—21no—
454C4×C71—41no—
455C4×C71—41no—
456C4×C71—41no—
457C4×C71—41no—
458C4×C71—41no—
459C4×C71—41no—
460C4×C71—41no—
461Dic71—81no—
462Dic71—81no—
463Dic71—81no—
464Dic71—81no—
465#17598—711nomaximal, Sylow
466C2×C71—21no—
467C2×C71—21no—
468C2×C71—22no—
469C2×C71—41no—
470C2×C71—41no—
471C2×C71—41no—
472C2×C71—81no—
473C2×C71#288311yescharacteristic
474C2×C71#289811yescharacteristic
475C2×C71C2×#42111yescharacteristic
476#3520D7111yescharacteristic
477#2974—711no—
478#2318—711no—
479#1521—711no—
480#1520—711no—
481#1518—711no—
482#1516—711no—
483#1515—711no—
484#1513—711no—
485#1512—711no—
486#1511—711no—
487#1508—711no—
488#1504—711no—
489#1501—711no—
490C2×#328—711no—
491C71#1759811yescharacteristic, complemented, Sylow
492#556Dic7111yescharacteristic, complemented
493#554—21no—
494#552Dic7111yescharacteristic, complemented
495#552Dic7111yescharacteristic, complemented
496#551—21no—
497#551—21no—
498D4×Q8Dic7111yescharacteristic, complemented
499#548Dic7111yescharacteristic, complemented
500#548Dic7111yescharacteristic, complemented
501#547Dic7111yescharacteristic, complemented
502#547Dic7111yescharacteristic, complemented
503#546—21no—
504#542—21no—
505#539—21no—
506#539—21no—
507#533C2×D7111yescharacteristic
508#529C2×D7111yescharacteristic
509#525C2×D7111yescharacteristic
510#525C2×D7111yescharacteristic
511C2×C22⋊Q8C2×D7111yescharacteristic
512C2×C22⋊Q8C2×D7111yescharacteristic
513#520—21no—
514C2×C4×D4C2×D7111yescharacteristic
515#436—1421no—
516#435—1421no—
517#435—1421no—
518C8×D4—1421no—
519#432—711no—
520#431—711no—
521#407—711no—
522#407—711no—
523C2×C22⋊C8—711no—
524C2×C22⋊C8—711no—
525#388—1421no—
526#387—1421no—
527#386—1421no—
528#385—1421no—
529#383—711no—
530#382—711no—
531#381—711no—
532#380—711no—
533C4×C22⋊C4—711no—
534C2×#95—711no—
535#328—711no—
536#328—711no—
537#328—711no—
538#328—711no—
539#328—711no—
540#328—711no—
541#328—711no—
542#328—711no—
543#328—711no—
544#328—711no—
545#328—711no—
546#328—711no—
547#327—711no—
548#327—711no—
549#327—711no—
550#327—711no—
551C2×#41—21no—
552C2×#41C2×Dic7111yescharacteristic
553C2×#41C2×Dic7111yescharacteristic, complemented
554C22×Q8C2×Dic7111yescharacteristic
555C22×Q8C2×Dic7111yescharacteristic, complemented
556C22×D4C22⋊D7111yescharacteristic
557C23×C4—1421no—
558C23×C4C22×D7111yescharacteristic
559C23×C4C22×D7111yescharacteristic
560C2×M16—1421no—
561C2×M16—1421no—
562C22×C8—1421no—
563C22×C8—1421no—
564C4⋊Q8—21no—
565C4⋊Q8C2×Dic7111yescharacteristic, complemented
566C4⋊Q8C2×Dic7111yescharacteristic, complemented
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#125C2×Dic7111yescharacteristic, complemented
576#124—21no—
577#124—21no—
578#124—21no—
579#124C2×Dic7111yescharacteristic, complemented
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8C2×Dic7111yescharacteristic
600C22⋊Q8C2×Dic7111yescharacteristic
601C22⋊Q8C2×Dic7111yescharacteristic
602C22⋊Q8C2×Dic7111yescharacteristic, complemented
603C22⋊Q8C2×Dic7111yescharacteristic, complemented
604C22⋊Q8C2×Dic7111yescharacteristic, complemented
605C22⋊Q8C22×D7111yescharacteristic
606C22⋊Q8C22×D7111yescharacteristic
607C22⋊Q8C22×D7111yescharacteristic
608#121—21no—
609#121—21no—
610#121—21no—
611#121C2×Dic7111yescharacteristic
612#121C2×Dic7111yescharacteristic, complemented
613#121C22×D7111yescharacteristic
614#120—21no—
615#120—21no—
616C4×Q8—21no—
617C4×Q8—21no—
618C4×Q8C2×Dic7111yescharacteristic, complemented
619C4×Q8C2×Dic7111yescharacteristic, complemented
620C4×Q8C2×Dic7111yescharacteristic, complemented
621C4×D4—21no—
622C4×D4—21no—
623C4×D4—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4C2×Dic7111yescharacteristic
630C4×D4C2×Dic7111yescharacteristic
631C4×D4C2×Dic7111yescharacteristic
632C4×D4C2×Dic7111yescharacteristic
633C4×D4C2×Dic7111yescharacteristic, complemented
634C4×D4C22⋊D7111yescharacteristic
635C4×D4C22⋊D7111yescharacteristic
636C4×D4C22⋊D7111yescharacteristic
637C4×D4C22⋊D7111yescharacteristic
638#117—21no—
639#117—21no—
640#117—21no—
641#117—21no—
642#117C2×Dic7111yescharacteristic
643#117C2×Dic7111yescharacteristic, complemented
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—1421no—
648C2×C4⋊C4—1421no—
649C2×C4⋊C4C2×Dic7111yescharacteristic
650C2×C4⋊C4C2×Dic7111yescharacteristic, complemented
651C2×C4⋊C4C22⋊D7111yescharacteristic
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—1421no—
655C2×C22⋊C4—1421no—
656C2×C22⋊C4—1421no—
657C2×C22⋊C4C22⋊D7111yescharacteristic
658C2×C22⋊C4C22⋊D7111yescharacteristic
659C2×C42—1421no—
660C2×C42C22×D7111yescharacteristic
661C4⋊C8—1421no—
662C4⋊C8—1421no—
663C22⋊C8—711no—
664C22⋊C8—711no—
665C22⋊C8—711no—
666C22⋊C8—711no—
667C22⋊C8—1421no—
668C22⋊C8—1421no—
669C22⋊C8—1421no—
670C22⋊C8—1421no—
671#97—1421no—
672C4×C8—1421no—
673#95—711no—
674#95—711no—
675#95—711no—
676#95—711no—
677#95—1421no—
678#95—1421no—
679#95—1421no—
680#95—1421no—
681#95—1421no—
682C24C2×C22⋊D7111yescharacteristic
683C24C2×C22⋊D7111yescharacteristic
684#41—44no—
685#41—81no—
686#41—81no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—81no—
691C2×Q8—81no—
692C2×Q8C22×Dic7111yescharacteristic
693C2×Q8C22×Dic7111yescharacteristic
694C2×Q8C22×Dic7111yescharacteristic
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—42no—
701C2×D4C22⋊Dic7111yescharacteristic
702C2×D4C22⋊Dic7111yescharacteristic
703C2×D4C22⋊Dic7111yescharacteristic
704C2×D4C22⋊Dic7111yescharacteristic
705C2×D4C22×Dic7111yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—81no—
714C22×C4—81no—
715C22×C4—2842no—
716C22×C4—5681no—
717C22×C4—5681no—
718C22×C4—1421no—
719C22×C4—1421no—
720C22×C4—1421no—
721C22×C4—1421no—
722C22×C4C22×Dic7111yescharacteristic
723C22×C4C22×Dic7111yescharacteristic
724C22×C4C22×Dic7111yescharacteristic
725C22×C4C22×Dic7111yescharacteristic
726C22×C4C2×C22⋊D7111yescharacteristic
727C22×C4C2×C22⋊D7111yescharacteristic
728C22×C4C2×C22⋊D7111yescharacteristic
729C22×C4C2×C22⋊D7111yescharacteristic
730C22×C4C2×C22⋊D7111yescharacteristic
731C22×C4C2×C22⋊D7111yescharacteristic
732C22×C4C2×C22⋊D7111yescharacteristic
733C22×C4C2×C22⋊D7111yescharacteristic
734C22×C4C23×D7111yescharacteristic
735M16—5681no—
736M16—5681no—
737C2×C8—5681no—
738C2×C8—5681no—
739C2×C8—1421no—
740C2×C8—1421no—
741C2×C8—1421no—
742C2×C8—1421no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—5681no—
763C4⋊C4—5681no—
764C4⋊C4C22⋊Dic7111yescharacteristic
765C4⋊C4C22⋊Dic7111yescharacteristic
766C4⋊C4C22⋊Dic7111yescharacteristic
767C4⋊C4C22⋊Dic7111yescharacteristic
768C4⋊C4C22×Dic7111yescharacteristic
769C4⋊C4C22×Dic7111yescharacteristic
770C4⋊C4C22×Dic7111yescharacteristic
771C4⋊C4C22×Dic7111yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—2842no—
790C22⋊C4—5681no—
791C22⋊C4—5681no—
792C22⋊C4C22⋊Dic7111yescharacteristic
793C22⋊C4C22⋊Dic7111yescharacteristic
794C22⋊C4C22⋊Dic7111yescharacteristic
795C22⋊C4C22⋊Dic7111yescharacteristic
796C22⋊C4C22⋊Dic7111yescharacteristic
797C22⋊C4C22⋊Dic7111yescharacteristic
798C22⋊C4C22⋊Dic7111yescharacteristic
799C22⋊C4C22⋊Dic7111yescharacteristic
800C42—21no—
801C42—21no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—5681no—
806C42C22×Dic7111yescharacteristic
807C42C22×Dic7111yescharacteristic
808C42C2×C22⋊D7111yescharacteristic
809C42C2×C22⋊D7111yescharacteristic
810C23—22no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23C2×C22⋊Dic7111yescharacteristic
820C23C2×C22⋊Dic7111yescharacteristic
821C23C2×C22⋊Dic7111yescharacteristic
822C23C2×C22⋊Dic7111yescharacteristic
823C23C22×C22⋊D7111yescharacteristic
824Q8—41no—
825Q8—41no—
826Q8—41no—
827Q8—42no—
828Q8—81no—
829Q8—81no—
830D4—22no—
831D4—22no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—42no—
836D4—42no—
837D4—41no—
838D4—41no—
839D4—81no—
840D4—81no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—2841no—
870C2×C4—2841no—
871C2×C4—2841no—
872C2×C4—2841no—
873C2×C4—2841no—
874C2×C4—2841no—
875C2×C4—2841no—
876C2×C4—2841no—
877C2×C4—2841no—
878C2×C4—2841no—
879C2×C4—2841no—
880C2×C4—2841no—
881C2×C4—5684no—
882C2×C4C2×C22⋊Dic7111yescharacteristic
883C2×C4C2×C22⋊Dic7111yescharacteristic
884C2×C4C2×C22⋊Dic7111yescharacteristic
885C2×C4C2×C22⋊Dic7111yescharacteristic
886C2×C4C2×C22⋊Dic7111yescharacteristic
887C2×C4C2×C22⋊Dic7111yescharacteristic
888C2×C4C2×C22⋊Dic7111yescharacteristic
889C2×C4C2×C22⋊Dic7111yescharacteristic
890C2×C4C23×Dic7111yescharacteristic
891C2×C4C22×C22⋊D7111yescharacteristic
892C8—2841no—
893C8—2841no—
894C8—2841no—
895C8—2841no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—42no—
910C22—42no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—81no—
915C22—81no—
916C22#1798601612yes—
917C22C22×C22⋊Dic7111yescharacteristic
918C22#1798680711yescharacteristic
919C22#1798681411yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—5681no—
938C4—5681no—
939C4—5681no—
940C4—5681no—
941C2—21no—
942C2—21no—
943C2—22no—
944C2—41no—
945C2—41no—
946C2—41no—
947C2—81no—
948C2#2259680111yescharacteristic
949C2#2259687311yescharacteristic
950C2C2×#1798601611yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
Fitting, prime radicalC71×#3520C2
socleC22×C71C22×C22⋊C4
cosocleC22×C4×C71C24
hypercenter#3520D71
hypocenterC71#17598
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3520

Complements

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

NH ≅ G/Ntype
1. #22597375C2semidirect
2. #22590973C2semidirect
3. #22586917C2semidirect
4. #22586912C2semidirect
5. #22586904C2semidirect
6. #22586896C2semidirect
7. #22586891C2semidirect
8. #22586883C2semidirect
9. #22586878C2semidirect
10. #22586873C2semidirect
11. #22586860C2semidirect
12. #22586844C2semidirect
13. #22586831C2semidirect
14. C2×#17985736C2semidirect
52. #556×C71C4semidirect
54. #552×C71C4semidirect
55. #552×C71C4semidirect
58. D4×Q8×C71C4semidirect
59. #548×C71C4semidirect
60. #548×C71C4semidirect
61. #547×C71C4semidirect
62. #547×C71C4semidirect
109. C2×#41×C71C2×C4semidirect
111. C22×Q8×C71C2×C4semidirect
116. C4⋊Q8×C71C2×C4semidirect
117. C4⋊Q8×C71C2×C4semidirect
126. #125×C71C2×C4semidirect
130. #124×C71C2×C4semidirect
153. C22⋊Q8×C71C2×C4semidirect
154. C22⋊Q8×C71C2×C4semidirect
155. C22⋊Q8×C71C2×C4semidirect
163. #121×C71C2×C4semidirect
169. C4×Q8×C71C2×C4semidirect
170. C4×Q8×C71C2×C4semidirect
171. C4×Q8×C71C2×C4semidirect
184. C4×D4×C71C2×C4semidirect
194. #117×C71C2×C4semidirect
199. C2×C4⋊C4×C71C2×C4semidirect
491. C71#17598semidirect
492. #556Dic71semidirect
494. #552Dic71semidirect
495. #552Dic71semidirect
498. D4×Q8Dic71semidirect
499. #548Dic71semidirect
500. #548Dic71semidirect
501. #547Dic71semidirect
502. #547Dic71semidirect
553. C2×#41C2×Dic71semidirect
555. C22×Q8C2×Dic71semidirect
565. C4⋊Q8C2×Dic71semidirect
566. C4⋊Q8C2×Dic71semidirect
575. #125C2×Dic71semidirect
579. #124C2×Dic71semidirect
602. C22⋊Q8C2×Dic71semidirect
603. C22⋊Q8C2×Dic71semidirect
604. C22⋊Q8C2×Dic71semidirect
612. #121C2×Dic71semidirect
618. C4×Q8C2×Dic71semidirect
619. C4×Q8C2×Dic71semidirect
620. C4×Q8C2×Dic71semidirect
633. C4×D4C2×Dic71semidirect
643. #117C2×Dic71semidirect
650. C2×C4⋊C4C2×Dic71semidirect

Maximal subgroups

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

subgroupindex
#225973752
#225909732
#225869172
#225869122
#225869042
#225868962
#225868912
#225868832
#225868782
#225868732
#225868602
#225868442
#225868312
C2×#179857362
C71×#35202
#1759871