Finite Group Databasebeta

← #31965117

Subgroups — #31965117

Order 18176.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22596998C211yesmaximal, characteristic, complemented
2#22591200C211yesmaximal, characteristic, complemented
3#22586917C211yesmaximal, characteristic, complemented
4#22586904C211yesmaximal, characteristic, complemented
5#22586896C211yesmaximal, characteristic
6#22586891C211yesmaximal, characteristic, complemented
7#22586878C211yesmaximal, characteristic, complemented
8#22586873C211yesmaximal, characteristic, complemented
9#22586865C211yesmaximal, characteristic, complemented
10#22586852C211yesmaximal, characteristic, complemented
11#22586844C211yesmaximal, characteristic
12#22586839C211yesmaximal, characteristic, complemented
13#22586826C211yesmaximal, characteristic, complemented
14C2×#17985736C211yesmaximal, characteristic, complemented
15C71×#3495C211yesmaximal, characteristic
16#17986060—21no—
17#17986060—21no—
18#17986056C2211yescharacteristic
19#17986056C2211yescharacteristic
20#17986052C2211yescharacteristic
21#17986052C2211yescharacteristic
22#17986026—21no—
23#17985963C2211yescharacteristic
24C2×C22⋊(C71⋊C8)C2211yescharacteristic
25#17985955—21no—
26#17985885—21no—
27#17985885—21no—
28#17985874—21no—
29#17985867C2211yescharacteristic
30#17985865C2211yescharacteristic
31#17985862C2211yescharacteristic
32C4×C4⋊Dic71C2211yescharacteristic
33C22⋊C4×Dic71—21no—
34#17985845C2211yescharacteristic
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×C71—21no—
53#554×C71—21no—
54#552×C71—21no—
55#552×C71—21no—
56#552×C71—21no—
57#552×C71—21no—
58#551×C71—21no—
59#551×C71—21no—
60#544×C71C411yescharacteristic, complemented
61#542×C71C411yescharacteristic, complemented
62#542×C71C411yescharacteristic, complemented
63#541×C71C411yescharacteristic, complemented
64#541×C71C411yescharacteristic, complemented
65#536×C71C411yescharacteristic, complemented
66#533×C71C2211yescharacteristic
67#533×C71C2211yescharacteristic
68#529×C71C2211yescharacteristic
69#529×C71C2211yescharacteristic
70#525×C71C2211yescharacteristic
71C2×C22⋊Q8×C71C2211yescharacteristic
72#520×C71C411yescharacteristic, complemented
73#519×C71C411yescharacteristic, complemented
74C2×#117×C71C2211yescharacteristic
75C23×Dic71—21no—
76C2×#11765849—21no—
77C22×C71⋊C8—21no—
78C2×C4⋊Dic71—21no—
79C2×C4⋊Dic71—21no—
80C2×C22⋊Dic71—21no—
81C2×C4×Dic71—21no—
82C2×C4×Dic71—21no—
83C4⋊(C71⋊C8)—21no—
84C4⋊(C71⋊C8)—21no—
85C4⋊(C71⋊C8)—21no—
86C4⋊(C71⋊C8)—21no—
87C22⋊(C71⋊C8)—21no—
88C22⋊(C71⋊C8)—21no—
89C22⋊(C71⋊C8)C2311yescharacteristic
90C22⋊(C71⋊C8)C2311yescharacteristic
91C22⋊(C71⋊C8)C2311yescharacteristic
92C22⋊(C71⋊C8)C2311yescharacteristic
93#14556039—21no—
94#14556039—21no—
95C4×C71⋊C8—21no—
96C4×C71⋊C8—21no—
97C71⋊#95—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×C71C2×C411yescharacteristic
108C22×Q8×C71C2×C411yescharacteristic
109C23×C4×C71C2311yescharacteristic
110C4⋊Q8×C71—21no—
111C4⋊Q8×C71C2×C411yescharacteristic, complemented
112C4⋊Q8×C71C2×C411yescharacteristic, complemented
113C4⋊Q8×C71C2×C411yescharacteristic, complemented
114C4⋊Q8×C71C2×C411yescharacteristic, complemented
115#126×C71—21no—
116#126×C71—21no—
117#126×C71—21no—
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×C71—21no—
127#125×C71—21no—
128#125×C71—21no—
129#125×C71—21no—
130#125×C71C2×C411yescharacteristic, complemented
131#125×C71C2×C411yescharacteristic, complemented
132#124×C71—21no—
133#124×C71—21no—
134#124×C71C2×C411yescharacteristic, complemented
135#124×C71C2×C411yescharacteristic, complemented
136#123×C71—21no—
137#123×C71—21no—
138#123×C71—21no—
139#123×C71—21no—
140#123×C71—21no—
141#123×C71—21no—
142#123×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×C71—21no—
151C22⋊Q8×C71—21no—
152C22⋊Q8×C71—21no—
153C22⋊Q8×C71C2×C411yescharacteristic
154C22⋊Q8×C71C2×C411yescharacteristic
155C22⋊Q8×C71C2×C411yescharacteristic
156C22⋊Q8×C71C2311yescharacteristic
157C22⋊Q8×C71C2311yescharacteristic
158C22⋊Q8×C71C2311yescharacteristic
159#121×C71C2×C411yescharacteristic
160#121×C71C2311yescharacteristic
161#120×C71—21no—
162C4×Q8×C71—21no—
163C4×Q8×C71—21no—
164C4×Q8×C71—21no—
165C4×Q8×C71—21no—
166C4×Q8×C71C2×C411yescharacteristic, complemented
167C4×Q8×C71C2×C411yescharacteristic, complemented
168C4×Q8×C71C2×C411yescharacteristic, complemented
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×C71C2×C411yescharacteristic, complemented
179C4×D4×C71C2×C411yescharacteristic, complemented
180#117×C71—21no—
181#117×C71—21no—
182#117×C71—21no—
183#117×C71—21no—
184#117×C71—21no—
185#117×C71—21no—
186#117×C71—21no—
187#117×C71C2×C411yescharacteristic
188#117×C71C2×C411yescharacteristic
189#117×C71C2×C411yescharacteristic
190#117×C71C2×C411yescharacteristic
191#117×C71C2×C411yescharacteristic
192#117×C71D411yescharacteristic
193#117×C71D411yescharacteristic
194#117×C71D411yescharacteristic
195#117×C71D411yescharacteristic
196C2×C4⋊C4×C71—21no—
197C2×C4⋊C4×C71—21no—
198C2×C4⋊C4×C71C2×C411yescharacteristic
199C2×C4⋊C4×C71D411yescharacteristic
200C2×C4⋊C4×C71D411yescharacteristic
201C2×C22⋊C4×C71—21no—
202C2×C22⋊C4×C71D411yescharacteristic
203C2×C22⋊C4×C71D411yescharacteristic
204C2×C42×C71C2311yescharacteristic
205C2×C42×C71C2311yescharacteristic
206C22×Dic71—21no—
207C22×Dic71—21no—
208C22×Dic71—21no—
209C22×Dic71—21no—
210C22×Dic71—42no—
211C22×Dic71—42no—
212C22×Dic71—81no—
213#11765849—42no—
214C2×C71⋊C8—21no—
215C2×C71⋊C8—21no—
216C2×C71⋊C8—21no—
217C2×C71⋊C8—21no—
218C2×C71⋊C8—42no—
219C4⋊Dic71—42no—
220C4⋊Dic71—81no—
221C22⋊Dic71—42no—
222C4×Dic71—42no—
223C4×Dic71—81no—
224C24×C71C2×D411yescharacteristic
225#41×C71—42no—
226C2×Q8×C71—21no—
227C2×Q8×C71—21no—
228C2×Q8×C71—21no—
229C2×Q8×C71—42no—
230C2×Q8×C71C22×C411yescharacteristic
231C2×Q8×C71C22×C411yescharacteristic
232C2×Q8×C71C22×C411yescharacteristic
233C2×D4×C71—21no—
234C2×D4×C71—21no—
235C2×D4×C71—21no—
236C2×D4×C71C22×C411yescharacteristic
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—42no—
243C22×C4×C71C22×C411yescharacteristic
244C22×C4×C71C22×C411yescharacteristic
245C22×C4×C71C2×D411yescharacteristic
246C22×C4×C71C2×D411yescharacteristic
247C22×C4×C71C2×D411yescharacteristic
248C22×C4×C71C2×D411yescharacteristic
249C22×C4×C71C2×D411yescharacteristic
250C22×C4×C71C2×D411yescharacteristic
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2411yescharacteristic
253C4⋊C4×C71—21no—
254C4⋊C4×C71—21no—
255C4⋊C4×C71—21no—
256C4⋊C4×C71—21no—
257C4⋊C4×C71—21no—
258C4⋊C4×C71—21no—
259C4⋊C4×C71—21no—
260C4⋊C4×C71—21no—
261C4⋊C4×C71—21no—
262C4⋊C4×C71—21no—
263C4⋊C4×C71—21no—
264C4⋊C4×C71—21no—
265C4⋊C4×C71—21no—
266C4⋊C4×C71—21no—
267C4⋊C4×C71—21no—
268C4⋊C4×C71—21no—
269C4⋊C4×C71—21no—
270C4⋊C4×C71—21no—
271C4⋊C4×C71—21no—
272C4⋊C4×C71—21no—
273C4⋊C4×C71—21no—
274C4⋊C4×C71—21no—
275C4⋊C4×C71—21no—
276C4⋊C4×C71C22⋊C411yescharacteristic
277C4⋊C4×C71C22⋊C411yescharacteristic
278C4⋊C4×C71C22⋊C411yescharacteristic
279C4⋊C4×C71C22⋊C411yescharacteristic
280C4⋊C4×C71C22⋊C411yescharacteristic
281C4⋊C4×C71C22⋊C411yescharacteristic
282C4⋊C4×C71C22⋊C411yescharacteristic
283C4⋊C4×C71C22⋊C411yescharacteristic
284C4⋊C4×C71C22×C411yescharacteristic
285C4⋊C4×C71C22×C411yescharacteristic
286C4⋊C4×C71C22×C411yescharacteristic
287C4⋊C4×C71C22×C411yescharacteristic
288C22⋊C4×C71—21no—
289C22⋊C4×C71—21no—
290C22⋊C4×C71—21no—
291C22⋊C4×C71—21no—
292C22⋊C4×C71—21no—
293C22⋊C4×C71—21no—
294C22⋊C4×C71—21no—
295C22⋊C4×C71—21no—
296C22⋊C4×C71—21no—
297C22⋊C4×C71—21no—
298C22⋊C4×C71—21no—
299C22⋊C4×C71—21no—
300C22⋊C4×C71—21no—
301C22⋊C4×C71—21no—
302C22⋊C4×C71—21no—
303C22⋊C4×C71C22⋊C411yescharacteristic
304C22⋊C4×C71C22⋊C411yescharacteristic
305C22⋊C4×C71C22⋊C411yescharacteristic
306C22⋊C4×C71C22⋊C411yescharacteristic
307C22⋊C4×C71C22⋊C411yescharacteristic
308C22⋊C4×C71C22⋊C411yescharacteristic
309C22⋊C4×C71C22⋊C411yescharacteristic
310C22⋊C4×C71C22⋊C411yescharacteristic
311C42×C71—21no—
312C42×C71—21no—
313C42×C71—21no—
314C42×C71—21no—
315C42×C71—21no—
316C42×C71—21no—
317C42×C71—21no—
318C42×C71C22×C411yescharacteristic
319C42×C71C22×C411yescharacteristic
320C42×C71C22×C411yescharacteristic
321C42×C71C22×C411yescharacteristic
322C42×C71C2×D411yescharacteristic
323C42×C71C2×D411yescharacteristic
324C42×C71C2×D411yescharacteristic
325C42×C71C2×D411yescharacteristic
326C23×C71—21no—
327C23×C71—21no—
328C23×C71—22no—
329C23×C71—21no—
330C23×C71—41no—
331C23×C71C2×C22⋊C411yescharacteristic
332C23×C71C2×C22⋊C411yescharacteristic
333C23×C71C22×D411yescharacteristic
334Q8×C71—41no—
335Q8×C71—41no—
336Q8×C71—41no—
337Q8×C71—42no—
338Q8×C71—81no—
339Q8×C71—81no—
340D4×C71—41no—
341D4×C71—41no—
342D4×C71—41no—
343D4×C71—42no—
344D4×C71—81no—
345C2×C4×C71—21no—
346C2×C4×C71—21no—
347C2×C4×C71—21no—
348C2×C4×C71—21no—
349C2×C4×C71—22no—
350C2×C4×C71—22no—
351C2×C4×C71—21no—
352C2×C4×C71—21no—
353C2×C4×C71—21no—
354C2×C4×C71—21no—
355C2×C4×C71—21no—
356C2×C4×C71—21no—
357C2×C4×C71—21no—
358C2×C4×C71—41no—
359C2×C4×C71—41no—
360C2×C4×C71—41no—
361C2×C4×C71—41no—
362C2×C4×C71—41no—
363C2×C4×C71—41no—
364C2×C4×C71—42no—
365C2×C4×C71—42no—
366C2×C4×C71—81no—
367C2×C4×C71—81no—
368C2×C4×C71—81no—
369C2×C4×C71C2×C22⋊C411yescharacteristic
370C2×C4×C71C2×C22⋊C411yescharacteristic
371C2×C4×C71C2×C22⋊C411yescharacteristic
372C2×C4×C71C2×C22⋊C411yescharacteristic
373C2×C4×C71C2×C22⋊C411yescharacteristic
374C2×C4×C71C2×C22⋊C411yescharacteristic
375C2×C4×C71C2×C22⋊C411yescharacteristic
376C2×C4×C71C2×C22⋊C411yescharacteristic
377C2×C4×C71C2×C22⋊C411yescharacteristic
378C2×C4×C71C2×C22⋊C411yescharacteristic
379C2×C4×C71C23×C411yescharacteristic
380C2×C4×C71C22×D411yescharacteristic
381C2×Dic71—22no—
382C2×Dic71—41no—
383C2×Dic71—41no—
384C2×Dic71—41no—
385C2×Dic71—41no—
386C2×Dic71—41no—
387C2×Dic71—41no—
388C2×Dic71—41no—
389C2×Dic71—41no—
390C2×Dic71—41no—
391C2×Dic71—41no—
392C2×Dic71—41no—
393C2×Dic71—84no—
394C71⋊C8—41no—
395C71⋊C8—41no—
396C71⋊C8—41no—
397C71⋊C8—41no—
398C22×C71—21no—
399C22×C71—21no—
400C22×C71—21no—
401C22×C71—21no—
402C22×C71—21no—
403C22×C71—21no—
404C22×C71—21no—
405C22×C71—42no—
406C22×C71—42no—
407C22×C71—41no—
408C22×C71—41no—
409C22×C71—41no—
410C22×C71#41012yes—
411C22×C71C22×C22⋊C411yescharacteristic
412C22×C71#57711yescharacteristic
413C22×C71#57811yescharacteristic
414C4×C71—21no—
415C4×C71—21no—
416C4×C71—21no—
417C4×C71—21no—
418C4×C71—21no—
419C4×C71—21no—
420C4×C71—21no—
421C4×C71—21no—
422C4×C71—21no—
423C4×C71—21no—
424C4×C71—21no—
425C4×C71—21no—
426C4×C71—41no—
427C4×C71—41no—
428C4×C71—41no—
429C4×C71—41no—
430C4×C71—41no—
431C4×C71—41no—
432C4×C71—41no—
433Dic71—42no—
434Dic71—81no—
435Dic71—81no—
436Dic71—81no—
437#17609—711nomaximal, Sylow
438C2×C71—21no—
439C2×C71—21no—
440C2×C71—22no—
441C2×C71—41no—
442C2×C71—81no—
443C2×C71C2×#41011yescharacteristic
444C2×C71#289811yescharacteristic
445C2×C71#290111yescharacteristic
446#3495D7111yescharacteristic
447#2924—711no—
448#2343—711no—
449#1521—711no—
450#1518—711no—
451#1516—711no—
452#1515—711no—
453#1512—711no—
454#1511—711no—
455#1509—711no—
456#1506—711no—
457#1504—711no—
458#1503—711no—
459#1500—711no—
460C2×#328—711no—
461C71#1760911yescharacteristic, complemented, Sylow
462#556—21no—
463#554—21no—
464#552—21no—
465#552—21no—
466#552—21no—
467#552—21no—
468#551—21no—
469#551—21no—
470#544Dic7111yescharacteristic, complemented
471#542Dic7111yescharacteristic, complemented
472#542Dic7111yescharacteristic, complemented
473#541Dic7111yescharacteristic, complemented
474#541Dic7111yescharacteristic, complemented
475#536Dic7111yescharacteristic, complemented
476#533C2×D7111yescharacteristic
477#533C2×D7111yescharacteristic
478#529C2×D7111yescharacteristic
479#529C2×D7111yescharacteristic
480#525C2×D7111yescharacteristic
481C2×C22⋊Q8C2×D7111yescharacteristic
482#520Dic7111yescharacteristic, complemented
483#519Dic7111yescharacteristic, complemented
484C2×#117C2×D7111yescharacteristic
485#433—1421no—
486#433—1421no—
487#432—711no—
488#432—711no—
489#431—711no—
490#431—711no—
491#424—1421no—
492#407—711no—
493C2×C22⋊C8—711no—
494#405—1421no—
495#387—1421no—
496#387—1421no—
497#385—1421no—
498#383—711no—
499#382—711no—
500#381—711no—
501C4×C4⋊C4—711no—
502C4×C22⋊C4—1421no—
503#376—711no—
504C2×#95—711no—
505#328—711no—
506#328—711no—
507#328—711no—
508#328—711no—
509#328—711no—
510#328—711no—
511#328—711no—
512#328—711no—
513#328—711no—
514#328—711no—
515#328—711no—
516#328—711no—
517#327—711no—
518#327—711no—
519#327—711no—
520#327—711no—
521C2×#41C2×Dic7111yescharacteristic
522C22×Q8C2×Dic7111yescharacteristic
523C23×C4—1421no—
524C23×C4C22×D7111yescharacteristic
525C2×M16—1421no—
526C22×C8—1421no—
527C4⋊Q8—21no—
528C4⋊Q8C2×Dic7111yescharacteristic, complemented
529C4⋊Q8C2×Dic7111yescharacteristic, complemented
530C4⋊Q8C2×Dic7111yescharacteristic, complemented
531C4⋊Q8C2×Dic7111yescharacteristic, complemented
532#126—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#126—21no—
538#126—21no—
539#126—21no—
540#125—21no—
541#125—21no—
542#125—21no—
543#125—21no—
544#125—21no—
545#125—21no—
546#125—21no—
547#125C2×Dic7111yescharacteristic, complemented
548#125C2×Dic7111yescharacteristic, complemented
549#124—21no—
550#124—21no—
551#124C2×Dic7111yescharacteristic, complemented
552#124C2×Dic7111yescharacteristic, complemented
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8C2×Dic7111yescharacteristic
571C22⋊Q8C2×Dic7111yescharacteristic
572C22⋊Q8C2×Dic7111yescharacteristic
573C22⋊Q8C22×D7111yescharacteristic
574C22⋊Q8C22×D7111yescharacteristic
575C22⋊Q8C22×D7111yescharacteristic
576#121C2×Dic7111yescharacteristic
577#121C22×D7111yescharacteristic
578#120—21no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8—21no—
583C4×Q8C2×Dic7111yescharacteristic, complemented
584C4×Q8C2×Dic7111yescharacteristic, complemented
585C4×Q8C2×Dic7111yescharacteristic, complemented
586C4×Q8C2×Dic7111yescharacteristic, complemented
587C4×Q8C2×Dic7111yescharacteristic, complemented
588C4×Q8C2×Dic7111yescharacteristic, complemented
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4C2×Dic7111yescharacteristic, complemented
596C4×D4C2×Dic7111yescharacteristic, complemented
597#117—21no—
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602#117—21no—
603#117—21no—
604#117C2×Dic7111yescharacteristic
605#117C2×Dic7111yescharacteristic
606#117C2×Dic7111yescharacteristic
607#117C2×Dic7111yescharacteristic
608#117C2×Dic7111yescharacteristic
609#117C22⋊D7111yescharacteristic
610#117C22⋊D7111yescharacteristic
611#117C22⋊D7111yescharacteristic
612#117C22⋊D7111yescharacteristic
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—1421no—
616C2×C4⋊C4—1421no—
617C2×C4⋊C4C2×Dic7111yescharacteristic
618C2×C4⋊C4C22⋊D7111yescharacteristic
619C2×C4⋊C4C22⋊D7111yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—1421no—
622C2×C22⋊C4C22⋊D7111yescharacteristic
623C2×C22⋊C4C22⋊D7111yescharacteristic
624C2×C42—1421no—
625C2×C42—1421no—
626C2×C42C22×D7111yescharacteristic
627C2×C42C22×D7111yescharacteristic
628C4⋊C8—1421no—
629C4⋊C8—1421no—
630C4⋊C8—1421no—
631C4⋊C8—1421no—
632C22⋊C8—711no—
633C22⋊C8—711no—
634C22⋊C8—711no—
635C22⋊C8—711no—
636C22⋊C8—1421no—
637C22⋊C8—1421no—
638#97—1421no—
639#97—1421no—
640C4×C8—1421no—
641C4×C8—1421no—
642#95—711no—
643#95—711no—
644#95—711no—
645#95—711no—
646#95—1421no—
647#95—1421no—
648#95—1421no—
649#95—1421no—
650#95—1421no—
651#95—1421no—
652C24C2×C22⋊D7111yescharacteristic
653#41—42no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—42no—
658C2×Q8C22×Dic7111yescharacteristic
659C2×Q8C22×Dic7111yescharacteristic
660C2×Q8C22×Dic7111yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4C22×Dic7111yescharacteristic
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—42no—
671C22×C4—2842no—
672C22×C4—2842no—
673C22×C4—5681no—
674C22×C4—1421no—
675C22×C4—1421no—
676C22×C4—1421no—
677C22×C4—1421no—
678C22×C4C22×Dic7111yescharacteristic
679C22×C4C22×Dic7111yescharacteristic
680C22×C4C2×C22⋊D7111yescharacteristic
681C22×C4C2×C22⋊D7111yescharacteristic
682C22×C4C2×C22⋊D7111yescharacteristic
683C22×C4C2×C22⋊D7111yescharacteristic
684C22×C4C2×C22⋊D7111yescharacteristic
685C22×C4C2×C22⋊D7111yescharacteristic
686C22×C4C2×C22⋊D7111yescharacteristic
687C22×C4C23×D7111yescharacteristic
688M16—2842no—
689C2×C8—2842no—
690C2×C8—1421no—
691C2×C8—1421no—
692C2×C8—1421no—
693C2×C8—1421no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—2842no—
718C4⋊C4—5681no—
719C4⋊C4C22⋊Dic7111yescharacteristic
720C4⋊C4C22⋊Dic7111yescharacteristic
721C4⋊C4C22⋊Dic7111yescharacteristic
722C4⋊C4C22⋊Dic7111yescharacteristic
723C4⋊C4C22⋊Dic7111yescharacteristic
724C4⋊C4C22⋊Dic7111yescharacteristic
725C4⋊C4C22⋊Dic7111yescharacteristic
726C4⋊C4C22⋊Dic7111yescharacteristic
727C4⋊C4C22×Dic7111yescharacteristic
728C4⋊C4C22×Dic7111yescharacteristic
729C4⋊C4C22×Dic7111yescharacteristic
730C4⋊C4C22×Dic7111yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—2842no—
747C22⋊C4C22⋊Dic7111yescharacteristic
748C22⋊C4C22⋊Dic7111yescharacteristic
749C22⋊C4C22⋊Dic7111yescharacteristic
750C22⋊C4C22⋊Dic7111yescharacteristic
751C22⋊C4C22⋊Dic7111yescharacteristic
752C22⋊C4C22⋊Dic7111yescharacteristic
753C22⋊C4C22⋊Dic7111yescharacteristic
754C22⋊C4C22⋊Dic7111yescharacteristic
755C42—21no—
756C42—21no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—2842no—
763C42—5681no—
764C42C22×Dic7111yescharacteristic
765C42C22×Dic7111yescharacteristic
766C42C22×Dic7111yescharacteristic
767C42C22×Dic7111yescharacteristic
768C42C2×C22⋊D7111yescharacteristic
769C42C2×C22⋊D7111yescharacteristic
770C42C2×C22⋊D7111yescharacteristic
771C42C2×C22⋊D7111yescharacteristic
772C23—22no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—41no—
777C23C2×C22⋊Dic7111yescharacteristic
778C23C2×C22⋊Dic7111yescharacteristic
779C23C22×C22⋊D7111yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—42no—
784Q8—81no—
785Q8—81no—
786D4—41no—
787D4—42no—
788D4—41no—
789D4—41no—
790D4—81no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—2841no—
816C2×C4—2841no—
817C2×C4—2841no—
818C2×C4—2841no—
819C2×C4—2841no—
820C2×C4—2841no—
821C2×C4—2841no—
822C2×C4—2841no—
823C2×C4—2841no—
824C2×C4—2841no—
825C2×C4—2841no—
826C2×C4—5684no—
827C2×C4—1422no—
828C2×C4C2×C22⋊Dic7111yescharacteristic
829C2×C4C2×C22⋊Dic7111yescharacteristic
830C2×C4C2×C22⋊Dic7111yescharacteristic
831C2×C4C2×C22⋊Dic7111yescharacteristic
832C2×C4C2×C22⋊Dic7111yescharacteristic
833C2×C4C2×C22⋊Dic7111yescharacteristic
834C2×C4C2×C22⋊Dic7111yescharacteristic
835C2×C4C2×C22⋊Dic7111yescharacteristic
836C2×C4C2×C22⋊Dic7111yescharacteristic
837C2×C4C2×C22⋊Dic7111yescharacteristic
838C2×C4C23×Dic7111yescharacteristic
839C2×C4C22×C22⋊D7111yescharacteristic
840C8—2841no—
841C8—2841no—
842C8—2841no—
843C8—2841no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22#1798597312yes—
857C22C22×C22⋊Dic7111yescharacteristic
858C22#1798680711yescharacteristic
859C22#1798681411yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—2842no—
880C4—5681no—
881C4—5681no—
882C4—5681no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—81no—
888C2C2×#1798597311yescharacteristic
889C2#2259687311yescharacteristic
890C2#2259688711yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#3495C2
socleC22×C71C22×C22⋊C4
prime radical#525×C71C22
cosocleC22×C4×C71C24
hypercenter#3495D71
hypocenterC71#17609
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3495

Complements

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

NH ≅ G/Ntype
1. #22596998C2semidirect
2. #22591200C2semidirect
3. #22586917C2semidirect
4. #22586904C2semidirect
6. #22586891C2semidirect
7. #22586878C2semidirect
8. #22586873C2semidirect
9. #22586865C2semidirect
10. #22586852C2semidirect
12. #22586839C2semidirect
13. #22586826C2semidirect
14. C2×#17985736C2semidirect
60. #544×C71C4semidirect
61. #542×C71C4semidirect
62. #542×C71C4semidirect
63. #541×C71C4semidirect
64. #541×C71C4semidirect
65. #536×C71C4semidirect
72. #520×C71C4semidirect
73. #519×C71C4semidirect
111. C4⋊Q8×C71C2×C4semidirect
112. C4⋊Q8×C71C2×C4semidirect
113. C4⋊Q8×C71C2×C4semidirect
114. C4⋊Q8×C71C2×C4semidirect
130. #125×C71C2×C4semidirect
131. #125×C71C2×C4semidirect
134. #124×C71C2×C4semidirect
135. #124×C71C2×C4semidirect
166. C4×Q8×C71C2×C4semidirect
167. C4×Q8×C71C2×C4semidirect
168. C4×Q8×C71C2×C4semidirect
169. C4×Q8×C71C2×C4semidirect
170. C4×Q8×C71C2×C4semidirect
171. C4×Q8×C71C2×C4semidirect
178. C4×D4×C71C2×C4semidirect
179. C4×D4×C71C2×C4semidirect
461. C71#17609semidirect
470. #544Dic71semidirect
471. #542Dic71semidirect
472. #542Dic71semidirect
473. #541Dic71semidirect
474. #541Dic71semidirect
475. #536Dic71semidirect
482. #520Dic71semidirect
483. #519Dic71semidirect
528. C4⋊Q8C2×Dic71semidirect
529. C4⋊Q8C2×Dic71semidirect
530. C4⋊Q8C2×Dic71semidirect
531. C4⋊Q8C2×Dic71semidirect
547. #125C2×Dic71semidirect
548. #125C2×Dic71semidirect
551. #124C2×Dic71semidirect
552. #124C2×Dic71semidirect
583. C4×Q8C2×Dic71semidirect
584. C4×Q8C2×Dic71semidirect
585. C4×Q8C2×Dic71semidirect
586. C4×Q8C2×Dic71semidirect
587. C4×Q8C2×Dic71semidirect
588. C4×Q8C2×Dic71semidirect
595. C4×D4C2×Dic71semidirect
596. C4×D4C2×Dic71semidirect

Maximal subgroups

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

subgroupindex
#225969982
#225912002
#225869172
#225869042
#225868962
#225868912
#225868782
#225868732
#225868652
#225868522
#225868442
#225868392
#225868262
C2×#179857362
C71×#34952
#1760971