Finite Group Databasebeta

← #30549678

Subgroups — #30549678

Order 15616.

1798 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459222C211yesmaximal, characteristic
2C2×#16840389C211yesmaximal, characteristic
3#21456372C211yesmaximal, characteristic, complemented
4#21456371C211yesmaximal, characteristic, complemented
5#21456369C212yesmaximal, complemented
6#21456363C212yesmaximal, complemented
7#21456361C211yesmaximal, characteristic, complemented
8#21456354C214yesmaximal, complemented
9#21456352C214yesmaximal, complemented
10#21456346C214yesmaximal, complemented
11#21456344C214yesmaximal, complemented
12#21454406C212yesmaximal
13#428×D61C212yesmaximal
14#21454236C211yesmaximal, characteristic
15C61×#3165C211yesmaximal, characteristic, complemented
16C2×M16×D61C2212yes—
17#16840392C2212yes—
18#16840392C2212yes—
19#16840391—21no—
20#16840391—21no—
21#16840389—22no—
22#16840389—22no—
23#16840389C2214yes—
24#16840389C2214yes—
25#16840389C2212yes—
26#16840389C2212yes—
27#16840387—21no—
28#16840387—21no—
29#16840319C2211yescharacteristic
30#16840316—22no—
31#16840316—22no—
32#16840315C2212yes—
33C2×#14519776C2211yescharacteristic
34C2×#14519775—21no—
35C2×#14519769C2211yescharacteristic
36C2×#14519768C2211yescharacteristic
37C2×#14519767—21no—
38C2×#14519755—21no—
39C2×#14519753—21no—
40C2×#14519735C2211yescharacteristic
41C2×#14519734C2211yescharacteristic
42#117×D61C2212yes—
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840171C2212yescomplemented
45#16840171C2212yescomplemented
46#16840170C2214yescomplemented
47#16840170C2214yescomplemented
48#16840169C2214yescomplemented
49#16840169C2214yescomplemented
50#16840168C2212yescomplemented
51#16840168C2214yescomplemented
52#16840168C2212yescomplemented
53#16840166C2214yescomplemented
54#16840165C2212yescomplemented
55#16840164C2214yescomplemented
56#16840163C2214yescomplemented
57#16840162C2214yescomplemented
58#16840161C2214yescomplemented
59#16840159C2214yescomplemented
60#16840158C2212yescomplemented
61#16839805C2212yes—
62#16839805C2212yes—
63#16839804C2212yes—
64#16839804C2212yes—
65#16839803C2214yes—
66#16839803C2214yes—
67#16839802C2212yes—
68#16839802C2212yes—
69#16839801C2214yes—
70#16839801C2214yes—
71#16839799C2214yes—
72#16839797C2214yes—
73#107×D61C2214yes—
74#106×D61C2214yes—
75#16839719C2214yes—
76#16839716C2214yes—
77C4×#11758194C2211yescharacteristic
78M16×Dic61C2212yes—
79C61×#533C2211yescharacteristic
80C2×C4⋊Q8×C61C2211yescharacteristic
81C61×#501C2214yescomplemented
82C61×#500C2212yescomplemented
83C61×#498C2212yescomplemented
84C61×#428C2212yes—
85C61×#428C2212yes—
86C4×M16×C61C2211yescharacteristic
87C22×Dic122—21no—
88C22×C4×D61—21no—
89C22×C4×D61C2311yescharacteristic
90C2×#11758194C2312yes—
91C2×#11758189C2314yes—
92M16×D61Q8116yescomplemented
93C2×C8×D61C2314yes—
94#14519777C2311yescharacteristic
95#14519777C2311yescharacteristic
96#14519776—22no—
97#14519776—22no—
98#14519776—22no—
99#14519776C2314yes—
100#14519776C2312yes—
101#14519776C2312yes—
102#14519775—24no—
103#14519775—24no—
104#14519775—22no—
105#14519775—22no—
106#14519769—21no—
107#14519769—21no—
108#14519769C2312yes—
109#14519769C2312yes—
110#14519769C2312yes—
111#14519768—22no—
112#14519768C2314yes—
113#14519768C2312yes—
114#14519768C2312yes—
115#14519767—24no—
116#14519767—24no—
117#14519767—22no—
118#14519767—22no—
119#14519767—22no—
120#14519767—22no—
121#14519757—22no—
122#14519757—22no—
123#14519756—21no—
124#14519756—21no—
125#14519755—24no—
126#14519755—24no—
127#14519755—22no—
128#14519755—22no—
129#14519755—22no—
130#14519755—22no—
131#14519754—22no—
132#14519754—22no—
133#14519753—24no—
134#14519753—24no—
135#14519753—22no—
136#14519753—22no—
137C4×Dic122—21no—
138C4×Dic122—21no—
139C4×Dic122—22no—
140C4×Dic122—22no—
141#14519736C2312yes—
142#14519735—22no—
143#14519735C2312yes—
144#14519735C2312yes—
145#14519735C2314yes—
146#14519734—22no—
147#14519734D412yes—
148#14519734D412yes—
149#14519734C2312yes—
150#14519734C2312yes—
151#14519733—22no—
152C2×C4⋊Dic61—21no—
153C2×C4⋊Dic61C2311yescharacteristic
154C2×C4⋊Dic61C2311yescharacteristic
155C2×#11758196—21no—
156C2×#11758196—21no—
157C2×#11758196—21no—
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196D411yescharacteristic
161C2×#11758196D411yescharacteristic
162C4⋊C4×D61—22no—
163C4⋊C4×D61C2314yes—
164C4⋊C4×D61C2312yes—
165C4⋊C4×D61C2312yes—
166C2×#11758198—21no—
167C2×#11758198D411yescharacteristic
168C2×#11758198D411yescharacteristic
169C22⋊C4×D61—22no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61C2311yescharacteristic
172C42×D61—22no—
173#14519711C2314yes—
174#14519711C2314yes—
175#14519710C2314yes—
176#14519710C2314yes—
177#14519710C2314yes—
178#14519710C2314yes—
179#14519709C2314yes—
180#14519709C2314yes—
181#14519708C2314yes—
182#14519708C2314yes—
183#14519708C2314yes—
184#14519708C2314yes—
185#14519688C2312yes—
186#14519687C2314yes—
187C4×#92418C2312yes—
188C8×Dic61C2314yes—
189C22×Q8×C61—21no—
190C2×M16×C61C2312yes—
191C4⋊Q8×C61—21no—
192C4⋊Q8×C61—21no—
193C4⋊Q8×C61C2312yes—
194C4⋊Q8×C61C2312yes—
195C4⋊Q8×C61C2311yescharacteristic
196C4⋊Q8×C61C2311yescharacteristic
197#125×C61C2312yes—
198C22⋊Q8×C61—21no—
199C22⋊Q8×C61—21no—
200C4×Q8×C61—21no—
201C4×Q8×C61—21no—
202#117×C61C2312yes—
203C2×C4⋊C4×C61—21no—
204C2×C4⋊C4×C61C2311yescharacteristic
205C2×C4⋊C4×C61C2311yescharacteristic
206C2×C42×C61C2311yescharacteristic
207#107×C61C2314yes—
208#107×C61C2314yes—
209#106×C61C2314yes—
210#106×C61C2314yes—
211#97×C61C2312yes—
212C4×C8×C61C2312yes—
213C23×D61C2×D411yescharacteristic
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—22no—
217C2×Q8×C61—22no—
218C2×Q8×C61—82no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2411yescharacteristic
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C2×C4×D61—24no—
230C2×C4×D61—22no—
231C2×C4×D61—22no—
232C2×C4×D61—82no—
233C2×C4×D61C2×D412yes—
234C2×C4×D61C2×Q818yes—
235C2×C4×D61C2412yes—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—24no—
239C2×Dic122—22no—
240C2×Dic122—22no—
241C2×Dic122—82no—
242M16×C61C2×Q818yes—
243C2×C8×C61C2414yes—
244C4⋊C4×C61—22no—
245C4⋊C4×C61—22no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—22no—
249C4⋊C4×C61—22no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61C2412yes—
253C4⋊C4×C61C2412yes—
254C4⋊C4×C61C2412yes—
255C4⋊C4×C61C2412yes—
256C22⋊C4×C61—22no—
257C42×C61—22no—
258C42×C61C2×D411yescharacteristic
259C42×C61C2×D411yescharacteristic
260C42×C61C2411yescharacteristic
261C42×C61C2411yescharacteristic
262C22⋊Dic61—22no—
263#11758198—22no—
264#11758198—22no—
265#11758198—24no—
266#11758198C2×D412yes—
267#11758198C2×D412yes—
268#11758198C2×D412yes—
269#11758198C2×D412yes—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—24no—
275C4⋊Dic61—22no—
276C4⋊Dic61—22no—
277C4⋊Dic61C2412yes—
278C4⋊Dic61C2412yes—
279C4⋊Dic61C2412yes—
280C4⋊Dic61C2412yes—
281#11758196—22no—
282#11758196—22no—
283#11758196—22no—
284#11758196—22no—
285#11758196—22no—
286#11758196—22no—
287#11758196—24no—
288#11758196—22no—
289#11758196—22no—
290#11758196—24no—
291#11758196—24no—
292#11758196—22no—
293#11758196—22no—
294#11758196—22no—
295#11758196—22no—
296#11758196C2×D412yes—
297#11758196C2×D412yes—
298#11758196C2×D412yes—
299#11758196C2×D412yes—
300C4×Dic61—22no—
301C4×Dic61—22no—
302C4×Dic61—22no—
303C4×Dic61—24no—
304C4×Dic61C2×D412yes—
305C4×Dic61C2412yes—
306#11758194C2×Q818yes—
307C2×#92418C2414yes—
308#11758189C2×Q8116yescomplemented
309C8×D61C2×Q8116yescomplemented
310C23×C61C22×D411yescharacteristic
311C22×D61—41no—
312C22×D61—41no—
313C22×D61C4⋊Q814yes—
314C22×D61C22×D412yes—
315Q8×C61—81no—
316Q8×C61—81no—
317Q8×C61—82no—
318Q8×C61—82no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—42no—
326C2×C4×C61—42no—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C22×Q814yes—
333C2×C4×C61C2511yescharacteristic
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61C4⋊Q814yes—
343C2×Dic61C22×D412yes—
344C2×Dic61C22×D412yes—
345C2×Dic61C22×D412yes—
346C4×D61—82no—
347C4×D61—82no—
348C4×D61—84no—
349C4×D61C4⋊Q818yes—
350C4×D61C22×Q814yes—
351C4×D61C22×Q814yes—
352Dic122—82no—
353Dic122—82no—
354Dic122—84no—
355Dic122—81no—
356Dic122—81no—
357C8×C61C22×Q818yes—
358#92418C22×Q818yes—
359#60664—611nomaximal, Sylow
360C22×C61—21no—
361C22×C61—21no—
362C22×C61C2×C4⋊Q812yes—
363C22×C61C23×D411yescharacteristic
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—44no—
367C2×D61C2×C4⋊Q814yes—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—42no—
373C4×C61—42no—
374C4×C61—42no—
375C4×C61—42no—
376C4×C61C2×C4⋊Q812yes—
377C4×C61C23×Q812yes—
378Dic61—22no—
379Dic61—22no—
380Dic61—42no—
381Dic61—42no—
382Dic61—42no—
383Dic61—42no—
384Dic61C2×C4⋊Q814yes—
385#3458—611no—
386C2×#544—611no—
387#3166—612no—
388#3166—611no—
389#3166—611no—
390#3165—612no—
391#3165—611no—
392#3165D6111yescharacteristic, complemented
393#3164—614no—
394#3164—614no—
395#3163—614no—
396#3163—614no—
397#2911—612no—
398C2×#428—612no—
399#2873—611no—
400C2×C61—22no—
401C2×C61C22×C4⋊Q811yescharacteristic
402C2×C61#358511yescharacteristic
403C2×C61#358611yescharacteristic
404D61—24no—
405C22×M16—612no—
406#544—612no—
407#544—614no—
408#544—614no—
409#544—612no—
410#544—612no—
411#544—612no—
412#544—1221no—
413#544—1221no—
414#544—1222no—
415#544—1222no—
416#543—1221no—
417#543—1221no—
418#533—612no—
419#533—611no—
420#533—1222no—
421#533—1222no—
422#533C2×D6111yescharacteristic
423C2×C4⋊Q8—611no—
424C2×C4⋊Q8—1221no—
425C2×C4⋊Q8C2×D6111yescharacteristic
426C2×#125—611no—
427C2×#125—611no—
428C2×#125—1221no—
429C2×C22⋊Q8—1221no—
430C2×C22⋊Q8—1221no—
431C2×#117—611no—
432C2×#117—612no—
433C2×#117—611no—
434C22×C4⋊C4—611no—
435#501—612no—
436#501—614no—
437#501—612no—
438#501—614no—
439#501—614no—
440#501—614no—
441#501—614no—
442#501—612no—
443#501—612no—
444#501C2×D6114yescomplemented
445#500—612no—
446#500—614no—
447#500C2×D6112yescomplemented
448#499—614no—
449#499—614no—
450#499—614no—
451#499—614no—
452#498—612no—
453#498—614no—
454#498C2×D6112yescomplemented
455#428—612no—
456#428—612no—
457#428—612no—
458#428—612no—
459#428—612no—
460#428—612no—
461#428—614no—
462#428—614no—
463#428—614no—
464#428—614no—
465#428C2×D6112yes—
466#428C2×D6112yes—
467#427—614no—
468#427—614no—
469C2×#107—614no—
470C2×#106—614no—
471#405—614no—
472#405—614no—
473C4×M16—612no—
474C4×M16—611no—
475C4×M16C2×D6111yescharacteristic
476C61#6066411yescharacteristic, complemented, Sylow
477C22×Q8—21no—
478C22×Q8—1221no—
479C23×C4—611no—
480C23×C4—1221no—
481C2×M16—612no—
482C2×M16—6116no—
483C2×M16—614no—
484C2×M16C22×D6112yes—
485C22×C8—614no—
486C4⋊Q8—21no—
487C4⋊Q8—21no—
488C4⋊Q8—614no—
489C4⋊Q8—612no—
490C4⋊Q8—612no—
491C4⋊Q8—611no—
492C4⋊Q8—611no—
493C4⋊Q8—1222no—
494C4⋊Q8—1222no—
495C4⋊Q8—1222no—
496C4⋊Q8—1224no—
497C4⋊Q8—1224no—
498C4⋊Q8—1222no—
499C4⋊Q8—1222no—
500C4⋊Q8C22×D6112yes—
501C4⋊Q8C22×D6112yes—
502C4⋊Q8C22×D6111yescharacteristic
503C4⋊Q8C22×D6111yescharacteristic
504#125—614no—
505#125—612no—
506#125—612no—
507#125—612no—
508#125—612no—
509#125—612no—
510#125—1222no—
511#125—1224no—
512#125—1224no—
513#125—1222no—
514#125—1222no—
515#125—1222no—
516#125—1222no—
517#125—1221no—
518#125—1221no—
519#125C22×D6112yes—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—1222no—
523C22⋊Q8—1222no—
524C22⋊Q8—1224no—
525C22⋊Q8—1224no—
526C22⋊Q8—1222no—
527C22⋊Q8—1222no—
528C22⋊Q8—1222no—
529C22⋊Q8—1222no—
530C22⋊Q8—1222no—
531C22⋊Q8—1222no—
532C22⋊Q8—1224no—
533C22⋊Q8—1224no—
534C22⋊Q8—1222no—
535C22⋊Q8—1222no—
536C22⋊Q8—1221no—
537C22⋊Q8—1221no—
538C4×Q8—21no—
539C4×Q8—21no—
540C4×Q8—1222no—
541C4×Q8—1222no—
542C4×Q8—1221no—
543C4×Q8—1221no—
544#117—612no—
545#117—612no—
546#117—612no—
547#117—612no—
548#117—612no—
549#117—612no—
550#117—614no—
551#117—612no—
552#117—1222no—
553#117—1222no—
554#117—1222no—
555#117C22×D6112yes—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—614no—
562C2×C4⋊C4—612no—
563C2×C4⋊C4—612no—
564C2×C4⋊C4—1222no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4C22×D6111yescharacteristic
572C2×C4⋊C4C22×D6111yescharacteristic
573C2×C22⋊C4—611no—
574C2×C22⋊C4—611no—
575C2×C22⋊C4—1222no—
576C2×C22⋊C4—1221no—
577C2×C42—611no—
578C2×C42—1222no—
579C2×C42—1221no—
580C2×C42C22×D6111yescharacteristic
581#107—614no—
582#107—614no—
583#107—614no—
584#107—614no—
585#107—614no—
586#107—614no—
587#107C22×D6114yes—
588#107C22×D6114yes—
589#106—614no—
590#106—614no—
591#106—614no—
592#106—614no—
593#106—614no—
594#106—614no—
595#106C22×D6114yes—
596#106C22×D6114yes—
597#97—614no—
598#97—612no—
599#97C22×D6112yes—
600C4×C8—614no—
601C4×C8—612no—
602C4×C8C22×D6112yes—
603C24—611no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—82no—
609C2×Q8—1222no—
610C2×Q8—1222no—
611C2×Q8—1224no—
612C2×Q8—1221no—
613C2×Q8—1221no—
614C2×Q8—4882no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—611no—
618C22×C4—612no—
619C22×C4—618no—
620C22×C4—612no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1224no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—4882no—
629C22×C4D4×D6111yescharacteristic
630C22×C4D4×D6111yescharacteristic
631C22×C4C23×D6111yescharacteristic
632M16—618no—
633M16—6116no—
634M16Q8×D6118yes—
635C2×C8—614no—
636C2×C8—6116no—
637C2×C8C23×D6114yes—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—612no—
647C4⋊C4—612no—
648C4⋊C4—612no—
649C4⋊C4—612no—
650C4⋊C4—612no—
651C4⋊C4—612no—
652C4⋊C4—612no—
653C4⋊C4—612no—
654C4⋊C4—1224no—
655C4⋊C4—1222no—
656C4⋊C4—1222no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1222no—
661C4⋊C4—1222no—
662C4⋊C4—1222no—
663C4⋊C4—1222no—
664C4⋊C4—1222no—
665C4⋊C4—1222no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1222no—
669C4⋊C4—1222no—
670C4⋊C4—1222no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—1222no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4C23×D6112yes—
677C4⋊C4C23×D6112yes—
678C4⋊C4C23×D6112yes—
679C4⋊C4C23×D6112yes—
680C22⋊C4—22no—
681C22⋊C4—612no—
682C22⋊C4—612no—
683C22⋊C4—612no—
684C22⋊C4—612no—
685C22⋊C4—1222no—
686C22⋊C4—1222no—
687C22⋊C4—1224no—
688C22⋊C4—1222no—
689C42—22no—
690C42—612no—
691C42—612no—
692C42—1222no—
693C42—1222no—
694C42—1224no—
695C42—1222no—
696C42D4×D6111yescharacteristic
697C42D4×D6111yescharacteristic
698C42C23×D6111yescharacteristic
699C42C23×D6111yescharacteristic
700C23—612no—
701C23—614no—
702C23—2441no—
703C23—2441no—
704C23C2×D4×D6111yescharacteristic
705Q8—81no—
706Q8—81no—
707Q8—82no—
708Q8—82no—
709Q8—4881no—
710Q8—4881no—
711Q8—4882no—
712Q8—4882no—
713Q8—4884no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—614no—
723C2×C4—612no—
724C2×C4—618no—
725C2×C4—614no—
726C2×C4—614no—
727C2×C4—612no—
728C2×C4—612no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—4882no—
734C2×C4—4882no—
735C2×C4—4884no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4C2×D4×D6111yescharacteristic
741C2×C4C2×D4×D6111yescharacteristic
742C2×C4C2×D4×D6111yescharacteristic
743C2×C4C2×D4×D6111yescharacteristic
744C2×C4C2×D4×D6111yescharacteristic
745C2×C4C2×Q8×D6114yes—
746C2×C4C24×D6111yescharacteristic
747C8—618no—
748C8C2×Q8×D6118yes—
749C22—21no—
750C22—21no—
751C22—614no—
752C22—1222no—
753C22—1222no—
754C22—2444no—
755C22C4⋊Q8×D6112yes—
756C22C22×D4×D6111yescharacteristic
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—42no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—614no—
766C4—1222no—
767C4—1222no—
768C4—2442no—
769C4—2442no—
770C4—2442no—
771C4—2442no—
772C4C4⋊Q8×D6112yes—
773C4C22×Q8×D6112yes—
774C2—22no—
775C2—1224no—
776C2C2×C4⋊Q8×D6111yescharacteristic
777C2#2146059511yescharacteristic
778C2#2146060211yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3165C2
socleC22×C61C23×D4
prime radicalC23×D61C2×D4
hypercenter#3165D61
hypocenterC61#60664
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
3. #21456372C2semidirect
4. #21456371C2semidirect
5. #21456369C2semidirect
6. #21456363C2semidirect
7. #21456361C2semidirect
8. #21456354C2semidirect
9. #21456352C2semidirect
10. #21456346C2semidirect
11. #21456344C2semidirect
15. C61×#3165C2semidirect
44. #16840171C22semidirect
45. #16840171C22semidirect
46. #16840170C22semidirect
47. #16840170C22semidirect
48. #16840169C22semidirect
49. #16840169C22semidirect
50. #16840168C22semidirect
51. #16840168C22semidirect
52. #16840168C22semidirect
53. #16840166C22semidirect
54. #16840165C22semidirect
55. #16840164C22semidirect
56. #16840163C22semidirect
57. #16840162C22semidirect
58. #16840161C22semidirect
59. #16840159C22semidirect
60. #16840158C22semidirect
81. C61×#501C22semidirect
82. C61×#500C22semidirect
83. C61×#498C22semidirect
92. M16×D61Q8semidirect
308. #11758189C2×Q8semidirect
309. C8×D61C2×Q8semidirect
392. #3165D61semidirect
444. #501C2×D61semidirect
447. #500C2×D61semidirect
454. #498C2×D61semidirect
476. C61#60664semidirect

Maximal subgroups

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

subgroupindex
#214592222
C2×#168403892
#214563722
#214563712
#214563692
#214563632
#214563612
#214563542
#214563522
#214563462
#214563442
#214544062
#428×D612
#214542362
C61×#31652
#6066461