Finite Group Databasebeta

← #29696778

Subgroups — #29696778

Order 15616.

1002 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840481C211yesmaximal, characteristic
2M16×Dic122C211yesmaximal, characteristic, complemented
3#21454770C211yesmaximal, characteristic, complemented
4#21446669C211yesmaximal, characteristic
5#21446665C211yesmaximal, characteristic
6#21446665C211yesmaximal, characteristic
7#21446661C211yesmaximal, characteristic, complemented
8#21446661C211yesmaximal, characteristic, complemented
9#21445813C211yesmaximal, characteristic, complemented
10#21445812C211yesmaximal, characteristic, complemented
11#21445809C211yesmaximal, characteristic
12#101×Dic61C211yesmaximal, characteristic, complemented
13C4×#14519695C211yesmaximal, characteristic, complemented
14#100×Dic61C211yesmaximal, characteristic
15C61×#1967C211yesmaximal, characteristic
16#16840481—21no—
17#16840481—21no—
18#16840481—21no—
19#16840481—21no—
20#16840481—21no—
21#16840481—21no—
22#16840481—21no—
23#16840481—21no—
24C2×#14519775C2211yescharacteristic
25C2×#14519770C412yes—
26C2×#14519770C412yes—
27C2×#14519764C2211yescharacteristic
28C2×#14519754C412yes—
29C2×Q8×Dic61C2211yescharacteristic
30C2×C4×Dic122C2211yescharacteristic
31C2×C4×Dic122C2211yescharacteristic
32C2×D4×Dic61C2211yescharacteristic
33C2×#14519733C412yes—
34#16839892—21no—
35#16839891—21no—
36#16839891—21no—
37#16839890—21no—
38#16839890—21no—
39#16839889—21no—
40C8×Dic122—21no—
41#16839886—21no—
42#16839786C2211yescharacteristic
43#16839785C2211yescharacteristic
44#16839785C2211yescharacteristic
45#16839785C2211yescharacteristic
46#16839785C2211yescharacteristic
47C2×#14519696C2211yescharacteristic
48C2×#14519696C2211yescharacteristic
49C2×#14519695C2211yescharacteristic
50C2×#14519695C2211yescharacteristic
51C2×#14519695C2211yescharacteristic
52C2×#14519695C2211yescharacteristic
53C2×#14519694C2211yescharacteristic
54C2×#14519694C2211yescharacteristic
55C4×#11758194C2211yescharacteristic
56M16×Dic61C2211yescharacteristic
57M16×Dic61C2211yescharacteristic
58M16×Dic61C2211yescharacteristic
59M16×Dic61C2211yescharacteristic
60#16839530C2211yescharacteristic
61#16839530C2211yescharacteristic
62#16839530C2211yescharacteristic
63#16839530C2211yescharacteristic
64C2×#124×C61C2211yescharacteristic
65C61×#423C2211yescharacteristic
66C2×#101×C61C2211yescharacteristic
67C2×#101×C61C2211yescharacteristic
68C2×#100×C61C2211yescharacteristic
69C2×#100×C61C2211yescharacteristic
70C4×M16×C61C2211yescharacteristic
71C22×Dic122C2×C411yescharacteristic
72C22×Dic122C2311yescharacteristic
73C23×Dic61C2×C412yes—
74C2×#11758194C2311yescharacteristic
75C2×#11758194C2311yescharacteristic
76C2×#11758194C2311yescharacteristic
77C2×#11758194C2311yescharacteristic
78#14519775—21no—
79#14519775—21no—
80#14519775—21no—
81#14519775—21no—
82#14519770—22no—
83#14519770—22no—
84#14519770—22no—
85#14519770—22no—
86#14519770—22no—
87#14519770—22no—
88#14519770—22no—
89#14519770—22no—
90#14519764—21no—
91#14519764—21no—
92#14519764—21no—
93#14519764—21no—
94#14519754—22no—
95#14519754—22no—
96#14519754—22no—
97#14519754—22no—
98Q8×Dic61—21no—
99Q8×Dic61—21no—
100Q8×Dic61—21no—
101Q8×Dic61—21no—
102C4×Dic122—21no—
103C4×Dic122—21no—
104C4×Dic122—21no—
105C4×Dic122—21no—
106C4×Dic122D411yescharacteristic
107C4×Dic122D411yescharacteristic
108C4×Dic122D411yescharacteristic
109C4×Dic122D411yescharacteristic
110C4×Dic122D411yescharacteristic
111C4×Dic122D411yescharacteristic
112C4×Dic122D411yescharacteristic
113C4×Dic122D411yescharacteristic
114D4×Dic61—21no—
115D4×Dic61—21no—
116D4×Dic61—21no—
117D4×Dic61—21no—
118#14519733—22no—
119#14519733—22no—
120#14519733—22no—
121#14519733—22no—
122C2×C4⋊Dic61C2×C412yes—
123C2×C4⋊Dic61C2×C411yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196C2×C412yes—
126C2×#11758196C2×C412yes—
127C2×#11758196C2×C412yes—
128C2×#11758196C2×C411yescharacteristic
129C2×#11758196C2×C411yescharacteristic
130C2×C22⋊Dic61C2×C412yes—
131C2×C22⋊Dic61C2×C412yes—
132C2×C22⋊Dic61C2×C412yes—
133C2×C4×Dic61C2×C412yes—
134C2×C4×Dic61C2×C412yes—
135C2×C4×Dic61C2311yescharacteristic
136C2×C4×Dic61C2311yescharacteristic
137C4⋊#92418—21no—
138C4⋊#92418—21no—
139#14519706—21no—
140#14519706—21no—
141#14519706—21no—
142#14519706—21no—
143#14519706—21no—
144#14519706—21no—
145#14519706—21no—
146#14519706—21no—
147#14519696—22no—
148#14519696—41no—
149#14519695—22no—
150#14519695—22no—
151#14519695—41no—
152#14519695—41no—
153#14519694—22no—
154#14519694—41no—
155#14519688—21no—
156#14519687—21no—
157#14519687—21no—
158#14519687—21no—
159#14519687—21no—
160C4×#92418—21no—
161C8×Dic61—21no—
162C8×Dic61—21no—
163C8×Dic61—21no—
164C8×Dic61—21no—
165C22×Q8×C61C2311yescharacteristic
166C22×D4×C61C2311yescharacteristic
167C2×M16×C61C2311yescharacteristic
168C2×M16×C61C2311yescharacteristic
169C2×M16×C61C2311yescharacteristic
170C2×M16×C61C2311yescharacteristic
171#124×C61—21no—
172#124×C61—21no—
173#124×C61—21no—
174#124×C61—21no—
175C2×C22⋊C4×C61C2×C412yes—
176C2×C22⋊C4×C61C2×C412yes—
177C2×C42×C61C2311yescharacteristic
178C4⋊C8×C61—21no—
179C4⋊C8×C61—21no—
180#101×C61—22no—
181#101×C61—41no—
182#100×C61—22no—
183#100×C61—41no—
184#97×C61—21no—
185C4×C8×C61—21no—
186C24×C61C22×C412yes—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—21no—
192C2×Q8×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C22×C4×C61C22×C412yes—
200C22×C4×C61C22×C411yescharacteristic
201C22×C4×C61C22×C411yescharacteristic
202C22×C4×C61C2411yescharacteristic
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—44no—
206C22×Dic61C22×C412yes—
207C22×Dic61C22×C411yescharacteristic
208C22×Dic61C22×C412yes—
209C22×Dic61C22×C411yescharacteristic
210C22×Dic61C22×C411yescharacteristic
211C22×Dic61C22×C411yescharacteristic
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—42no—
219C2×Dic122C22⋊C411yescharacteristic
220C2×Dic122C22⋊C411yescharacteristic
221C2×Dic122C22⋊C411yescharacteristic
222C2×Dic122C22⋊C411yescharacteristic
223M16×C61—21no—
224M16×C61—21no—
225M16×C61—21no—
226M16×C61—21no—
227M16×C61—21no—
228M16×C61—21no—
229M16×C61—21no—
230M16×C61#4112yes—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—22no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—22no—
239C42×C61C2×D411yescharacteristic
240C42×C61C2×D411yescharacteristic
241C42×C61C2×D411yescharacteristic
242C42×C61C2×D411yescharacteristic
243C22⋊Dic61—22no—
244C22⋊Dic61—22no—
245C22⋊Dic61—22no—
246C22⋊Dic61—22no—
247C22⋊Dic61—22no—
248C22⋊Dic61—22no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—22no—
252C4⋊Dic61—22no—
253C4⋊Dic61C22⋊C411yescharacteristic
254C4⋊Dic61C22⋊C411yescharacteristic
255C4⋊Dic61C22⋊C411yescharacteristic
256C4⋊Dic61C22⋊C411yescharacteristic
257#11758196—22no—
258#11758196—22no—
259#11758196—22no—
260#11758196—22no—
261#11758196—22no—
262#11758196—22no—
263#11758196C22⋊C411yescharacteristic
264#11758196C22⋊C411yescharacteristic
265#11758196C22⋊C411yescharacteristic
266#11758196C22⋊C411yescharacteristic
267#11758196C22⋊C411yescharacteristic
268#11758196C22⋊C411yescharacteristic
269#11758196C22⋊C411yescharacteristic
270#11758196C22⋊C411yescharacteristic
271C4×Dic61—22no—
272C4×Dic61—22no—
273C4×Dic61—22no—
274C4×Dic61—22no—
275C4×Dic61C2×D411yescharacteristic
276C4×Dic61C2×D411yescharacteristic
277C4×Dic61C2×D411yescharacteristic
278C4×Dic61C2×D411yescharacteristic
279C4×Dic61C2×D411yescharacteristic
280C4×Dic61C2×D411yescharacteristic
281C4×Dic61C2×D411yescharacteristic
282C4×Dic61C2×D411yescharacteristic
283#11758194—21no—
284#11758194—21no—
285#11758194—21no—
286#11758194—21no—
287#11758194—21no—
288#11758194—21no—
289#11758194—21no—
290#11758194#4112yes—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61C23×C411yescharacteristic
301Q8×C61—41no—
302Q8×C61—41no—
303Q8×C61—41no—
304Q8×C61—41no—
305D4×C61—41no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—41no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61C2×#4111yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C2×C4×C612−1+411yescharacteristic
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—44no—
333C2×Dic61—44no—
334C2×Dic61—42no—
335C2×Dic61C2×C22⋊C411yescharacteristic
336C2×Dic61C2×C22⋊C411yescharacteristic
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343Dic122—22no—
344Dic122—22no—
345Dic122—41no—
346Dic122—41no—
347Dic122—41no—
348Dic122—41no—
349Dic122—41no—
350Dic122—41no—
351C8×C61—22no—
352C8×C61—41no—
353C8×C61—41no—
354C8×C61—41no—
355#92418—22no—
356#92418—41no—
357#92418—41no—
358#92418—41no—
359#22537—611nomaximal, Sylow
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—82no—
366C22×C61—82no—
367C22×C61C22×C22⋊C411yescharacteristic
368C22×C61C4×#4111yescharacteristic
369C22×C61#52011yescharacteristic
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—21no—
373C4×C61—21no—
374C4×C61—42no—
375C4×C61#54811yescharacteristic
376C4×C61#54811yescharacteristic
377C4×C61#55011yescharacteristic
378C4×C61#55011yescharacteristic
379Dic61—21no—
380Dic61—21no—
381Dic61—21no—
382Dic61—21no—
383Dic61—21no—
384Dic61—21no—
385Dic61—21no—
386Dic61—42no—
387Dic61—42no—
388Dic61#41312yes—
389C2×#556—611no—
390Q8×M16—611no—
391Q8×M16—611no—
392#1967—611no—
393#1967—611no—
394#1967—611no—
395#1967D6111yescharacteristic
396#1966—611no—
397#1966—611no—
398#1801—611no—
399#1801—611no—
400#1800—611no—
401C4×#101—611no—
402C4×#101—611no—
403C4×#100—611no—
404C2×C61—21no—
405C2×C61—21no—
406C2×C61—82no—
407C2×C61#234111yescharacteristic
408C2×C61C2×#41311yescharacteristic
409C2×C61#288911yescharacteristic
410#556—1221no—
411#556—1221no—
412#556—1221no—
413#556—1221no—
414#556—1221no—
415#556—1221no—
416#556—1221no—
417#556—1221no—
418C2×C4⋊Q8—611no—
419C2×#126—612no—
420C2×#126—612no—
421C2×#124—611no—
422C2×#124C2×D6111yescharacteristic
423C2×C22⋊Q8—612no—
424C2×C4×Q8—611no—
425C2×C4×Q8—611no—
426C2×C4×Q8—611no—
427C2×C4×D4—611no—
428C2×#117—612no—
429#446—1221no—
430#446—1221no—
431#446—1221no—
432#446—1221no—
433#446—1221no—
434#446—1221no—
435C8×Q8—1221no—
436C8×Q8—1221no—
437#423—611no—
438#423—611no—
439#423—611no—
440#423—611no—
441#423—611no—
442#423C2×D6111yescharacteristic
443C2×#101—611no—
444C2×#101—611no—
445C2×#101—611no—
446C2×#101—611no—
447C2×#101—611no—
448C2×#101—611no—
449C2×#101C2×D6111yescharacteristic
450C2×#101C2×D6111yescharacteristic
451C2×#100—611no—
452C2×#100—611no—
453C2×#100C2×D6111yescharacteristic
454C2×#100C2×D6111yescharacteristic
455C4×M16—611no—
456C4×M16—611no—
457C4×M16—611no—
458C4×M16—611no—
459C4×M16—611no—
460C4×M16C2×D6111yescharacteristic
461#343—611no—
462#343—611no—
463#343—611no—
464#343—611no—
465C61#2253711yescharacteristic, complemented, Sylow
466C22×Q8—611no—
467C22×Q8—611no—
468C22×Q8C22×D6111yescharacteristic
469C22×D4C22×D6111yescharacteristic
470C23×C4—612no—
471C2×M16—611no—
472C2×M16—611no—
473C2×M16—611no—
474C2×M16—611no—
475C2×M16C22×D6111yescharacteristic
476C2×M16C22×D6111yescharacteristic
477C2×M16C22×D6111yescharacteristic
478C2×M16C22×D6111yescharacteristic
479C4⋊Q8—1221no—
480C4⋊Q8—1221no—
481C4⋊Q8—1221no—
482C4⋊Q8—1221no—
483#126—1222no—
484#126—1222no—
485#126—1222no—
486#126—1222no—
487#126—1222no—
488#126—1222no—
489#126—1222no—
490#126—1222no—
491#124—21no—
492#124—21no—
493#124—21no—
494#124—21no—
495#124—1221no—
496#124—1221no—
497#124—1221no—
498#124—1221no—
499C22⋊Q8—1222no—
500C22⋊Q8—1222no—
501C22⋊Q8—1222no—
502C22⋊Q8—1222no—
503C4×Q8—611no—
504C4×Q8—611no—
505C4×Q8—611no—
506C4×Q8—611no—
507C4×Q8—611no—
508C4×Q8—611no—
509C4×Q8—611no—
510C4×Q8—611no—
511C4×Q8—1221no—
512C4×Q8—1221no—
513C4×Q8—1221no—
514C4×Q8—1221no—
515C4×Q8—1221no—
516C4×Q8—1221no—
517C4×Q8—1221no—
518C4×Q8—1221no—
519C4×D4—1221no—
520C4×D4—1221no—
521C4×D4—1221no—
522C4×D4—1221no—
523#117—1222no—
524#117—1222no—
525#117—1222no—
526#117—1222no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—612no—
531C2×C4⋊C4—612no—
532C2×C4⋊C4—612no—
533C2×C4⋊C4—612no—
534C2×C4⋊C4—611no—
535C2×C22⋊C4—612no—
536C2×C22⋊C4—612no—
537C2×C22⋊C4—612no—
538C2×C22⋊C4C4×D6112yes—
539C2×C22⋊C4C4×D6112yes—
540C2×C42—611no—
541C2×C42—611no—
542C2×C42—612no—
543C2×C42—612no—
544C2×C42C22×D6111yescharacteristic
545C4⋊C8—21no—
546C4⋊C8—21no—
547C4⋊C8—1221no—
548C4⋊C8—1221no—
549C4⋊C8—1221no—
550C4⋊C8—1221no—
551C4⋊C8—1221no—
552C4⋊C8—1221no—
553C4⋊C8—1221no—
554C4⋊C8—1221no—
555C4⋊C8—1221no—
556C4⋊C8—1221no—
557#101—22no—
558#101—41no—
559#101—1222no—
560#101—1222no—
561#101—1222no—
562#101—2441no—
563#101—2441no—
564#101—2441no—
565#100—22no—
566#100—41no—
567#100—1222no—
568#100—2441no—
569#97—21no—
570#97—1221no—
571#97—1221no—
572#97—1221no—
573#97—1221no—
574#97—1221no—
575C4×C8—21no—
576C4×C8—1221no—
577C4×C8—1221no—
578C4×C8—1221no—
579C4×C8—1221no—
580C4×C8—1221no—
581C24C2×C4×D6112yes—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—611no—
589C2×Q8—611no—
590C2×Q8—611no—
591C2×Q8—611no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—2442no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—612no—
610C22×C4—612no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—2444no—
614C22×C4C2×C4×D6112yes—
615C22×C4C2×C4×D6111yescharacteristic
616C22×C4C2×C4×D6111yescharacteristic
617C22×C4C23×D6111yescharacteristic
618M16—21no—
619M16—21no—
620M16—21no—
621M16—21no—
622M16—21no—
623M16—21no—
624M16—21no—
625M16—612no—
626M16—1221no—
627M16—1221no—
628M16—1221no—
629M16—1221no—
630M16—1221no—
631M16—1221no—
632M16—1221no—
633M16#1175822412yes—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C4⋊C4—611no—
643C4⋊C4—611no—
644C4⋊C4—611no—
645C4⋊C4—611no—
646C4⋊C4—611no—
647C4⋊C4—611no—
648C4⋊C4—611no—
649C4⋊C4—611no—
650C4⋊C4—611no—
651C4⋊C4—611no—
652C4⋊C4—611no—
653C4⋊C4—611no—
654C4⋊C4—1222no—
655C4⋊C4—1222no—
656C4⋊C4—1222no—
657C4⋊C4—1222no—
658C4⋊C4—1222no—
659C4⋊C4—1222no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1222no—
663C4⋊C4—1222no—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—1222no—
669C22⋊C4—1222no—
670C22⋊C4—1222no—
671C22⋊C4—1222no—
672C22⋊C4—1222no—
673C22⋊C4—1222no—
674C42—611no—
675C42—611no—
676C42—611no—
677C42—611no—
678C42—611no—
679C42—611no—
680C42—611no—
681C42—611no—
682C42—1222no—
683C42—1222no—
684C42—1222no—
685C42—1222no—
686C42D4×D6111yescharacteristic
687C42D4×D6111yescharacteristic
688C42D4×D6111yescharacteristic
689C42D4×D6111yescharacteristic
690C23—22no—
691C23—22no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23C22×C4×D6111yescharacteristic
696Q8—41no—
697Q8—41no—
698Q8—41no—
699Q8—41no—
700Q8—1222no—
701Q8—1222no—
702Q8—2441no—
703Q8—2441no—
704Q8—2441no—
705Q8—2441no—
706Q8—2441no—
707Q8—2441no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—611no—
718C2×C4—611no—
719C2×C4—611no—
720C2×C4—611no—
721C2×C4—611no—
722C2×C4—611no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—2444no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2444no—
735C2×C4—2442no—
736C2×C4C22⋊C4×D6111yescharacteristic
737C2×C4C22⋊C4×D6111yescharacteristic
738C2×C4C22⋊C4×D6111yescharacteristic
739C2×C4C22⋊C4×D6111yescharacteristic
740C2×C4C2×D4×D6111yescharacteristic
741C2×C4C2×D4×D6111yescharacteristic
742C2×C4#41×D6111yescharacteristic
743C2×C4C2×#1175822411yescharacteristic
744C2×C4#1451982211yescharacteristic
745C2×C4#1451982411yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C8—1222no—
751C8—2441no—
752C8—2441no—
753C8—2441no—
754C22—21no—
755C22—21no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—82no—
760C22—82no—
761C22C2×C22⋊C4×D6111yescharacteristic
762C22C4×#1175822411yescharacteristic
763C22#1684024111yescharacteristic
764C4—21no—
765C4—21no—
766C4—21no—
767C4—21no—
768C4—42no—
769C4—612no—
770C4—1221no—
771C4—1221no—
772C4—1221no—
773C4—1221no—
774C4—1221no—
775C4—1221no—
776C4—1221no—
777C4—2442no—
778C4—2442no—
779C4#1684041811yescharacteristic
780C4#1684042011yescharacteristic
781C4#1684043011yescharacteristic
782C4#1684043211yescharacteristic
783C2—21no—
784C2—21no—
785C2—82no—
786C2#2144865811yescharacteristic
787C2#413×D6111yescharacteristic
788C2#2145430011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1967C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×C61C23
cosocleC22×C4×C61C24
hypercenter#1967D61
hypocenterC61#22537
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1967

Complements

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

NH ≅ G/Ntype
2. M16×Dic122C2semidirect
3. #21454770C2semidirect
7. #21446661C2semidirect
8. #21446661C2semidirect
9. #21445813C2semidirect
10. #21445812C2semidirect
12. #101×Dic61C2semidirect
13. C4×#14519695C2semidirect
465. C61#22537semidirect

Maximal subgroups

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

subgroupindex
C2×#168404812
M16×Dic1222
#214547702
#214466692
#214466652
#214466612
#214458132
#214458122
#214458092
#101×Dic612
C4×#145196952
#100×Dic612
C61×#19672
#2253761