Finite Group Databasebeta

← #29657313

Subgroups — #29657313

Order 15616.

956 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457145C211yesmaximal, characteristic, complemented
2#21456144C211yesmaximal, characteristic, complemented
3#21455910C211yesmaximal, characteristic, complemented
4#21444991C211yesmaximal, characteristic, complemented
5#21444984C211yesmaximal, characteristic, complemented
6#21444970C211yesmaximal, characteristic, complemented
7#21444970C211yesmaximal, characteristic, complemented
8#21444929C211yesmaximal, characteristic, complemented
9#21444922C211yesmaximal, characteristic, complemented
10#21444908C211yesmaximal, characteristic, complemented
11#21444908C211yesmaximal, characteristic, complemented
12#21444519C211yesmaximal, characteristic, complemented
13#21444279C211yesmaximal, characteristic, complemented
14C2×D4⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3520C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840119—22no—
18#16840114C2211yescharacteristic, complemented
19#16840114C2211yescharacteristic, complemented
20#16840110C2211yescharacteristic, complemented
21#16840110C2211yescharacteristic, complemented
22#16840080—21no—
23#16840059—21no—
24#16840057C2211yescharacteristic, complemented
25#16840052C2211yescharacteristic
26#16840052C2211yescharacteristic
27#16840052C2211yescharacteristic, complemented
28#16839996—21no—
29#16839993—21no—
30#16839974—21no—
31#16839962C2211yescharacteristic, complemented
32#16839957C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839957C2211yescharacteristic, complemented
35#16839896—21no—
36#16839872—21no—
37#16839872—21no—
38#16839819C2211yescharacteristic
39C2×C4⋊#92418C2211yescharacteristic
40#16839756—22no—
41C2×C4×#92418C2211yescharacteristic
42#16839508C2211yescharacteristic, complemented
43#16839508C2211yescharacteristic, complemented
44#16839508C2211yescharacteristic, complemented
45#16839508C2211yescharacteristic, complemented
46Q8⋊#92418C2211yescharacteristic, complemented
47Q8⋊#92418C2211yescharacteristic, complemented
48D4⋊#92418C2211yescharacteristic
49D4⋊#92418C2211yescharacteristic
50D4⋊#92418C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54C61×#556C2211yescharacteristic
55C61×#554—21no—
56C61×#552—21no—
57C61×#551—22no—
58D4×Q8×C61C2211yescharacteristic
59C61×#548—21no—
60C61×#547C2211yescharacteristic
61C61×#547C2211yescharacteristic
62C61×#546—21no—
63C61×#542—21no—
64C61×#539—22no—
65C61×#533C2211yescharacteristic
66C61×#529C2211yescharacteristic
67C61×#525—21no—
68C2×C22⋊Q8×C61—21no—
69C61×#520—21no—
70C2×C4×D4×C61C2211yescharacteristic
71C2×#11758222—21no—
72C2×#11758201—21no—
73C2×#11758199—21no—
74C2×#11758199—21no—
75C2×#11758199—21no—
76C22×#92418—21no—
77C22×#92418—21no—
78#14519777C2311yescharacteristic
79#14519774C2311yescharacteristic
80#14519765—21no—
81#14519751—21no—
82#14519751—21no—
83C4×D244—21no—
84C4×D244—21no—
85#14519710—21no—
86#14519708—21no—
87#14519708—21no—
88#14519708—21no—
89C4⋊#92418—21no—
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519701—21no—
95#14519700—22no—
96#14519700—22no—
97#14519698—21no—
98#14519698—21no—
99#14519698—21no—
100#14519697—21no—
101#14519697—21no—
102#14519697—21no—
103#14519697—21no—
104#14519697—22no—
105#14519697—22no—
106C22⋊#92418—21no—
107#14519688—21no—
108C4×#92418—21no—
109C4×#92418C2311yescharacteristic
110C4×#92418C2311yescharacteristic
111C2×#41×C61—21no—
112C2×#41×C61—21no—
113C22×Q8×C61—21no—
114C22×D4×C61D411yescharacteristic
115C23×C4×C61—21no—
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119#126×C61—22no—
120#126×C61—22no—
121#126×C61—21no—
122#125×C61—22no—
123#125×C61D412yes—
124#125×C61D411yescharacteristic
125#124×C61—22no—
126#124×C61—21no—
127#124×C61D411yescharacteristic
128#123×C61—22no—
129#123×C61—22no—
130#123×C61—21no—
131#123×C61—22no—
132#123×C61—22no—
133C22⋊Q8×C61—22no—
134C22⋊Q8×C61—22no—
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61—21no—
137C22⋊Q8×C61—21no—
138C22⋊Q8×C61—21no—
139C22⋊Q8×C61—22no—
140C22⋊Q8×C61—21no—
141C22⋊Q8×C61—21no—
142C22⋊Q8×C61—21no—
143C22⋊Q8×C61D411yescharacteristic
144#121×C61—22no—
145#121×C61—21no—
146#121×C61—21no—
147#121×C61D411yescharacteristic
148#120×C61—22no—
149C4×Q8×C61—21no—
150C4×Q8×C61—21no—
151C4×Q8×C61—21no—
152C4×Q8×C61C2311yescharacteristic
153C4×D4×C61—22no—
154C4×D4×C61—22no—
155C4×D4×C61—22no—
156C4×D4×C61—21no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61D411yescharacteristic
161C4×D4×C61D411yescharacteristic
162C4×D4×C61C2311yescharacteristic
163C4×D4×C61C2311yescharacteristic
164C4×D4×C61C2311yescharacteristic
165#117×C61—22no—
166#117×C61—21no—
167#117×C61—21no—
168#117×C61D412yes—
169C2×C4⋊C4×C61—22no—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61D411yescharacteristic
173C2×C22⋊C4×C61—22no—
174C2×C22⋊C4×C61—21no—
175C2×C42×C61C2311yescharacteristic
176C24×C61—21no—
177#41×C61—42no—
178#41×C61—42no—
179#41×C61—81no—
180#41×C61—81no—
181C2×Q8×C61—22no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—81no—
185C2×Q8×C61—81no—
186C2×Q8×C61C2×D411yescharacteristic
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61—21no—
190C2×D4×C61—22no—
191C2×D4×C61—21no—
192C2×D4×C61—41no—
193C2×D4×C61C2×D411yescharacteristic
194C2×D4×C61C2×D411yescharacteristic
195C2×D4×C61C2×D411yescharacteristic
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—81no—
206C22×C4×C61—81no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C2×C22⋊D61—41no—
211#11758222—44no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×C4×D61—41no—
216C2×Dic122—21no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—22no—
219C4⋊C4×C61—22no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—22no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—22no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61C2×D411yescharacteristic
231C4⋊C4×C61C2×D411yescharacteristic
232C4⋊C4×C61C2×D411yescharacteristic
233C4⋊C4×C61C2×D411yescharacteristic
234C4⋊C4×C61C2×D412yes—
235C4⋊C4×C61C2×D412yes—
236C22⋊C4×C61—22no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—22no—
243C22⋊C4×C61—21no—
244C22⋊C4×C61—21no—
245C22⋊C4×C61—21no—
246C22⋊C4×C61—21no—
247C22⋊C4×C61—21no—
248C22⋊C4×C61—21no—
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C42×C61—22no—
252C42×C61—22no—
253C42×C61—21no—
254C42×C61C2×D411yescharacteristic
255C42×C61C2×D411yescharacteristic
256C42×C61C2×D411yescharacteristic
257C42×C61C2411yescharacteristic
258#11758201—81no—
259#11758199—42no—
260#11758199—42no—
261#11758199—81no—
262#11758198—41no—
263#11758198—41no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—42no—
273C2×#92418—81no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—42no—
278C23×C61—42no—
279C23×C61—81no—
280C23×C61#12011yescharacteristic
281C22×D61—41no—
282Q8×C61—21no—
283Q8×C61—21no—
284Q8×C61—41no—
285Q8×C61—41no—
286Q8×C61—41no—
287Q8×C61—41no—
288Q8×C61—82no—
289D4×C61—21no—
290D4×C61—21no—
291D4×C61—21no—
292D4×C61—21no—
293D4×C61—21no—
294D4×C61—42no—
295D4×C61—44no—
296D4×C61—42no—
297D4×C61—82no—
298D4×C61#13512yes—
299C2×C4×C61—22no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—22no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—44no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—81no—
319C2×C4×C61—81no—
320C2×C4×C61—81no—
321C2×C4×C61—82no—
322C2×C4×C61—82no—
323C2×C4×C61#12011yescharacteristic
324C2×C4×C61#12011yescharacteristic
325C2×C4×C61#12011yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C22⋊D61—82no—
330C2×Dic61—41no—
331D244—42no—
332D244—41no—
333D244—41no—
334D244—41no—
335D244—41no—
336C4×D61—82no—
337Dic122—42no—
338#92418—41no—
339#92418—41no—
340#92418—41no—
341#92418—41no—
342#92418—41no—
343#92418—41no—
344#18638—611nomaximal, Sylow
345C22×C61—21no—
346C22×C61—21no—
347C22×C61—22no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—84no—
357C22×C61#45412yes—
358C22×C61C2×#12011yescharacteristic
359C2×D61—81no—
360C2×D61—81no—
361C2×D61—81no—
362C4×C61—21no—
363C4×C61—21no—
364C4×C61—21no—
365C4×C61—21no—
366C4×C61—41no—
367C4×C61—42no—
368C4×C61—41no—
369C4×C61—41no—
370C4×C61—42no—
371C4×C61—41no—
372C4×C61—41no—
373C4×C61C2×#13511yescharacteristic
374C4×C61#57511yescharacteristic
375C4×C61#57611yescharacteristic
376C4×C61#57711yescharacteristic
377Dic61—81no—
378#3520D6111yescharacteristic, complemented
379#3247—611no—
380#3131—611no—
381#3109—611no—
382#1638—611no—
383#1637—611no—
384#1635—611no—
385#1635—611no—
386#1628—611no—
387#1627—611no—
388#1625—611no—
389#1625—611no—
390#1552—611no—
391#1494—611no—
392C2×D4⋊C8—611no—
393C2×C61—22no—
394C2×C61—42no—
395C2×C61—81no—
396C2×C61—81no—
397C2×C61#300211yescharacteristic
398C2×C61#301211yescharacteristic
399C2×C61C2×#45411yescharacteristic
400D61—161no—
401#556C2×D6111yescharacteristic
402#554—21no—
403#552—21no—
404#551—22no—
405D4×Q8C2×D6111yescharacteristic
406#548—21no—
407#547C2×D6111yescharacteristic
408#547C2×D6111yescharacteristic
409#546—21no—
410#542—21no—
411#539—22no—
412#533C2×D6111yescharacteristic
413#532—611no—
414#529C2×D6111yescharacteristic
415#525—21no—
416C2×C22⋊Q8—21no—
417#520—21no—
418C2×C4×D4C2×D6111yescharacteristic
419#488—1222no—
420#487—611no—
421#487—611no—
422#486—611no—
423#486—611no—
424#481—1221no—
425#478—1221no—
426#477—611no—
427#476—611no—
428#476—611no—
429#476—611no—
430#466—1221no—
431#465—1221no—
432#463—1221no—
433#460—611no—
434#459—611no—
435#459—611no—
436#459—611no—
437#447—1221no—
438#442—1221no—
439#442—1221no—
440#432—611no—
441C2×C4⋊C8—611no—
442#416—1222no—
443C2×C4×C8—611no—
444#332—611no—
445#332—611no—
446#332—611no—
447#332—611no—
448Q8⋊C8—611no—
449Q8⋊C8—611no—
450D4⋊C8—611no—
451D4⋊C8—611no—
452D4⋊C8—611no—
453D4⋊C8—611no—
454D4⋊C8—611no—
455D4⋊C8—611no—
456C61#1863811yescharacteristic, complemented, Sylow
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—1221no—
460C22×Q8—21no—
461C22×D4C22⋊D6111yescharacteristic
462C23×C4—21no—
463C2×SD16—1221no—
464C2×D8—1221no—
465C2×D8—1221no—
466C2×D8—1221no—
467C22×C8—1221no—
468C22×C8—1221no—
469C4⋊Q8—21no—
470C4⋊Q8—611no—
471C4⋊Q8C22×D6111yescharacteristic
472C4⋊Q8C22×D6111yescharacteristic
473#127—611no—
474#126—22no—
475#126—22no—
476#126—21no—
477#125—22no—
478#125C22⋊D6111yescharacteristic
479#125C22⋊D6112yes—
480#124—22no—
481#124—21no—
482#124—1221no—
483#124C22⋊D6111yescharacteristic
484#123—22no—
485#123—22no—
486#123—21no—
487#123—22no—
488#123—22no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—22no—
498C22⋊Q8—21no—
499C22⋊Q8C22⋊D6111yescharacteristic
500#121—22no—
501#121—21no—
502#121—21no—
503#121—1221no—
504#121—1221no—
505#121C22⋊D6111yescharacteristic
506#120—22no—
507C4×Q8—21no—
508C4×Q8—21no—
509C4×Q8—21no—
510C4×Q8C22×D6111yescharacteristic
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—1221no—
519C4×D4—1221no—
520C4×D4C22⋊D6111yescharacteristic
521C4×D4C22⋊D6111yescharacteristic
522C4×D4C22×D6111yescharacteristic
523C4×D4C22×D6111yescharacteristic
524C4×D4C22×D6111yescharacteristic
525#117—22no—
526#117—21no—
527#117—21no—
528#117C22⋊D6112yes—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4C22⋊D6111yescharacteristic
533C2×C22⋊C4—22no—
534C2×C22⋊C4—21no—
535C2×C42C22×D6111yescharacteristic
536#107—1221no—
537#106—1221no—
538#106—1221no—
539#106—1221no—
540C4⋊C8—611no—
541C4⋊C8—611no—
542C4⋊C8—611no—
543C4⋊C8—611no—
544C4⋊C8—1221no—
545#103—1221no—
546#103—1222no—
547#103—1222no—
548#102—1221no—
549#102—1221no—
550#102—1221no—
551#102—1222no—
552#102—1222no—
553#102—1221no—
554#102—1221no—
555#102—1221no—
556#102—1221no—
557C22⋊C8—1221no—
558#97—1221no—
559C4×C8—611no—
560C4×C8—611no—
561C4×C8—1221no—
562C24—21no—
563#41—42no—
564#41—42no—
565#41—81no—
566#41—81no—
567#41—2444no—
568C2×Q8—22no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—81no—
572C2×Q8—81no—
573C2×Q8—1221no—
574C2×Q8C2×C22⋊D6111yescharacteristic
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—2441no—
585C2×D4C2×C22⋊D6111yescharacteristic
586C2×D4C2×C22⋊D6111yescharacteristic
587C2×D4C2×C22⋊D6111yescharacteristic
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—81no—
598C22×C4—81no—
599C22×C4—2441no—
600C22×C4C2×C22⋊D6111yescharacteristic
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C2×C22⋊D6111yescharacteristic
603SD16—4881no—
604D8—4881no—
605D8—2442no—
606D8—2442no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—4881no—
614C2×C8—2442no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—22no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4C2×C22⋊D6112yes—
631C4⋊C4C2×C22⋊D6112yes—
632C4⋊C4C2×C22⋊D6111yescharacteristic
633C4⋊C4C2×C22⋊D6111yescharacteristic
634C4⋊C4C2×C22⋊D6111yescharacteristic
635C4⋊C4C2×C22⋊D6111yescharacteristic
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—2441no—
652C22⋊C4—2441no—
653C42—22no—
654C42—21no—
655C42—22no—
656C42C2×C22⋊D6111yescharacteristic
657C42C2×C22⋊D6111yescharacteristic
658C42C2×C22⋊D6111yescharacteristic
659C42C23×D6111yescharacteristic
660C23—21no—
661C23—21no—
662C23—21no—
663C23—42no—
664C23—42no—
665C23—81no—
666C23—2441no—
667C23#1451974611yescharacteristic
668Q8—21no—
669Q8—21no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—82no—
675Q8—2442no—
676D4—21no—
677D4—21no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—42no—
682D4—44no—
683D4—42no—
684D4—82no—
685D4—4882no—
686D4—2442no—
687D4—2441no—
688D4—2441no—
689D4—2441no—
690D4—2441no—
691D4#1451979712yes—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—44no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—82no—
715C2×C4—82no—
716C2×C4—4882no—
717C2×C4—2441no—
718C2×C4#1451974611yescharacteristic
719C2×C4#1451974611yescharacteristic
720C2×C4#1451974611yescharacteristic
721C2×C4C22×C22⋊D6111yescharacteristic
722C2×C4C22×C22⋊D6111yescharacteristic
723C2×C4C22×C22⋊D6111yescharacteristic
724C8—2441no—
725C8—2441no—
726C8—2441no—
727C8—2441no—
728C8—2441no—
729C8—2441no—
730C22—21no—
731C22—21no—
732C22—22no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—84no—
742C22—4881no—
743C22—4881no—
744C22—4881no—
745C22#1683993512yes—
746C22C2×#1451974611yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—41no—
752C4—41no—
753C4—42no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—42no—
758C4—4881no—
759C4C2×#1451979711yescharacteristic
760C4#1684056011yescharacteristic
761C4#1684056511yescharacteristic
762C4#1684057311yescharacteristic
763C2—22no—
764C2—42no—
765C2—81no—
766C2—81no—
767C2—9761no—
768C2#2145503711yescharacteristic
769C2#2145512311yescharacteristic
770C2C2×#1683993511yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3520C2
socleC22×C61C2×#120
hypercenter#3520D61
hypocenterC61#18638
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3520

Complements

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

NH ≅ G/Ntype
1. #21457145C2semidirect
2. #21456144C2semidirect
3. #21455910C2semidirect
4. #21444991C2semidirect
5. #21444984C2semidirect
6. #21444970C2semidirect
7. #21444970C2semidirect
8. #21444929C2semidirect
9. #21444922C2semidirect
10. #21444908C2semidirect
11. #21444908C2semidirect
12. #21444519C2semidirect
13. #21444279C2semidirect
14. C2×D4⋊#92418C2semidirect
15. C61×#3520C2semidirect
18. #16840114C22semidirect
19. #16840114C22semidirect
20. #16840110C22semidirect
21. #16840110C22semidirect
24. #16840057C22semidirect
27. #16840052C22semidirect
31. #16839962C22semidirect
34. #16839957C22semidirect
42. #16839508C22semidirect
43. #16839508C22semidirect
44. #16839508C22semidirect
45. #16839508C22semidirect
46. Q8⋊#92418C22semidirect
47. Q8⋊#92418C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
378. #3520D61semidirect
456. C61#18638semidirect

Maximal subgroups

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

subgroupindex
#214571452
#214561442
#214559102
#214449912
#214449842
#214449702
#214449292
#214449222
#214449082
#214445192
#214442792
C2×D4⋊#924182
C61×#35202
#1863861