Finite Group Databasebeta

← #30552365

Subgroups — #30552365

Order 15616.

1686 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840390C211yesmaximal, characteristic, complemented
2#21459209C211yesmaximal, characteristic
3#21457119C214yesmaximal, complemented
4#21457104C214yesmaximal, complemented
5#21457089C214yesmaximal, complemented
6#21457074C214yesmaximal, complemented
7#21456371C211yesmaximal, characteristic, complemented
8#21456365C211yesmaximal, characteristic, complemented
9#21456220C211yesmaximal, characteristic, complemented
10#21456213C211yesmaximal, characteristic, complemented
11#21455752C212yesmaximal, complemented
12#21455744C212yesmaximal, complemented
13#21455642C212yesmaximal, complemented
14#21455635C212yesmaximal, complemented
15C61×#2921C211yesmaximal, characteristic, complemented
16#16840390—22no—
17#16840390—22no—
18#16840390C2214yes—
19#16840390C2214yes—
20#16840383C2212yes—
21#16840383C2212yes—
22#16840374C2212yes—
23#16840367C2212yes—
24#16840359—21no—
25#16840359—21no—
26#16840350—21no—
27#16840350—21no—
28#16840319C2211yescharacteristic
29#16840312C2211yescharacteristic
30C2×#14519777C2211yescharacteristic
31C2×#14519777C2211yescharacteristic
32C2×#14519776—21no—
33#16840290—22no—
34#16840290—22no—
35C2×#14519769C2211yescharacteristic
36C2×#14519769C2211yescharacteristic
37C2×#14519768—21no—
38#16840273C2212yes—
39C2×#14519754—21no—
40C2×#14519754—21no—
41C4×#11758222C2212yes—
42C2×#14519736C2211yescharacteristic
43C22×C4⋊Dic61C2211yescharacteristic
44#16840171C2214yescomplemented
45#16840171C2212yescomplemented
46#16840171C2212yescomplemented
47#16840167C2212yescomplemented
48#16840164C2214yescomplemented
49#16840160C2212yescomplemented
50#16840131C2212yescomplemented
51#16840127C2212yescomplemented
52#16840122C2214yescomplemented
53#16840117C2214yescomplemented
54#16840113C2212yescomplemented
55#16840109C2212yescomplemented
56#16840104C2214yes—
57#16840104C2214yes—
58#16840098C2214yes—
59#16840093C2214yes—
60#16840087C2214yes—
61#16840087C2214yes—
62#16840081C2214yes—
63#16840076C2214yes—
64#16840070C2214yescomplemented
65#16840070C2214yescomplemented
66#16840063C2214yescomplemented
67#16840063C2214yescomplemented
68#16840058C2214yescomplemented
69#16840053C2214yescomplemented
70#16840048C2214yescomplemented
71#16840043C2214yescomplemented
72#16839804C2212yes—
73#16839804C2212yes—
74#16839804C2212yes—
75#16839804C2212yes—
76#16839764C2212yes—
77#16839764C2212yes—
78#16839764C2212yes—
79#16839764C2212yes—
80C2×#117×C61C2211yescharacteristic
81C61×#433C2214yes—
82C61×#433C2214yes—
83C61×#423C2212yes—
84C61×#407C2212yes—
85C4×M16×C61C2211yescharacteristic
86C4×M16×C61C2211yescharacteristic
87C2×#11758222C2312yes—
88C22×Dic122—21no—
89C22×Dic122—21no—
90C23×Dic61—21no—
91#14519777—22no—
92#14519777—21no—
93#14519777—21no—
94#14519777C2311yescharacteristic
95#14519777C2314yes—
96#14519777C2312yes—
97#14519777C2312yes—
98#14519777C2311yescharacteristic
99#14519777C2311yescharacteristic
100#14519776—24no—
101#14519776—24no—
102#14519774C2311yescharacteristic
103#14519772—22no—
104#14519772—22no—
105#14519770—22no—
106#14519770—22no—
107#14519769—22no—
108#14519769—21no—
109#14519769—21no—
110#14519769C2314yes—
111#14519769C2312yes—
112#14519769C2312yes—
113#14519769C2312yes—
114#14519768—24no—
115#14519768—24no—
116#14519767—22no—
117#14519767—22no—
118#14519765C2312yes—
119#14519763—22no—
120#14519763—22no—
121#14519762—22no—
122#14519762—22no—
123#14519760—22no—
124#14519759—22no—
125#14519759—22no—
126#14519756—21no—
127#14519756—21no—
128#14519756C2312yes—
129#14519756C2312yes—
130#14519755—22no—
131#14519755—22no—
132#14519754—24no—
133#14519754—24no—
134#14519754—24no—
135#14519754—24no—
136#14519751—21no—
137#14519751—21no—
138#14519751C2312yes—
139#14519751C2312yes—
140#14519750—22no—
141#14519750—22no—
142#14519746—22no—
143C4×Dic122—21no—
144C4×Dic122—21no—
145C4×Dic122C2312yes—
146C4×Dic122C2312yes—
147C4×D244—21no—
148C4×D244—21no—
149C4×D244C2312yes—
150C4×D244C2312yes—
151C4×C22⋊D61—22no—
152C4×C22⋊D61—22no—
153C4×C22⋊D61—22no—
154C4×C22⋊D61—22no—
155#14519736—22no—
156#14519736C2314yes—
157#14519736C2312yes—
158#14519734—22no—
159C2×C4⋊Dic61—21no—
160C2×C4⋊Dic61—22no—
161C2×C4⋊Dic61—21no—
162C2×C4⋊Dic61—21no—
163C2×C4⋊Dic61C2311yescharacteristic
164C2×C4⋊Dic61C2311yescharacteristic
165C2×C4⋊Dic61C2314yes—
166C2×C4⋊Dic61C2311yescharacteristic
167C2×C4⋊Dic61C2311yescharacteristic
168C2×#11758196—21no—
169C2×#11758196—21no—
170C2×#11758196—21no—
171C2×#11758196—21no—
172C2×C22⋊Dic61—21no—
173C2×C4×Dic61—21no—
174C42×D61—22no—
175#14519711C2314yes—
176#14519711C2314yes—
177#14519711C2314yes—
178#14519711C2314yes—
179#14519709C2314yes—
180#14519709C2314yes—
181#14519709C2314yes—
182#14519709C2314yes—
183#14519702C2314yes—
184#14519702C2314yes—
185#14519702C2314yes—
186#14519702C2314yes—
187#14519699C2314yes—
188#14519699C2314yes—
189#14519699C2314yes—
190#14519699C2314yes—
191C23×C4×C61C2311yescharacteristic
192C2×M16×C61C2312yes—
193C2×M16×C61C2312yes—
194#117×C61D412yes—
195#117×C61D412yes—
196#117×C61C2312yes—
197#117×C61C2312yes—
198C2×C4⋊C4×C61D411yescharacteristic
199C2×C4⋊C4×C61D411yescharacteristic
200C2×C22⋊C4×C61D411yescharacteristic
201C2×C22⋊C4×C61D411yescharacteristic
202C2×C42×C61C2311yescharacteristic
203C2×C42×C61C2311yescharacteristic
204C4⋊C8×C61C2314yes—
205C4⋊C8×C61C2314yes—
206C22⋊C8×C61C2314yes—
207C22⋊C8×C61C2314yes—
208#97×C61C2312yes—
209#97×C61C2312yes—
210C4×C8×C61C2312yes—
211C4×C8×C61C2312yes—
212C24×C61C2×D411yescharacteristic
213C22×C4×C61—24no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2412yes—
221C22×C4×C61C2411yescharacteristic
222C2×C22⋊D61—22no—
223C2×C22⋊D61—22no—
224C2×C22⋊D61—22no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—24no—
230C22×Dic61—82no—
231#11758222—28no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244C2412yes—
235C2×C4×D61—22no—
236C2×C4×D61—22no—
237C2×C4×D61—22no—
238C2×Dic122—24no—
239C2×Dic122—22no—
240C2×Dic122—22no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—82no—
244C2×Dic122—82no—
245C2×Dic122C2412yes—
246M16×C61—24no—
247M16×C61—24no—
248C2×C8×C61C2414yes—
249C2×C8×C61C2414yes—
250C4⋊C4×C61C2×D412yes—
251C4⋊C4×C61C2×D412yes—
252C4⋊C4×C61C2×D412yes—
253C4⋊C4×C61C2×D412yes—
254C22⋊C4×C61C2×D412yes—
255C22⋊C4×C61C2×D412yes—
256C22⋊C4×C61C2×D412yes—
257C22⋊C4×C61C2×D412yes—
258C42×C61C2×D412yes—
259C42×C61C2×D411yescharacteristic
260C42×C61C2×D411yescharacteristic
261C42×C61C2411yescharacteristic
262C42×C61C2411yescharacteristic
263C42×C61C2412yes—
264C22⋊Dic61—24no—
265C22⋊Dic61—22no—
266C22⋊Dic61—22no—
267C22⋊Dic61—22no—
268#11758198—22no—
269#11758198—22no—
270#11758198—22no—
271#11758198—22no—
272#11758198—22no—
273#11758198—22no—
274C4⋊Dic61—24no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—24no—
278C4⋊Dic61—22no—
279C4⋊Dic61—22no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61C2412yes—
287C4⋊Dic61C2412yes—
288C4⋊Dic61C2412yes—
289C4⋊Dic61C2412yes—
290C4⋊Dic61C2412yes—
291C4⋊Dic61C2412yes—
292#11758196—24no—
293#11758196—22no—
294#11758196—22no—
295#11758196—24no—
296#11758196—22no—
297#11758196—22no—
298#11758196—22no—
299#11758196—22no—
300#11758196—22no—
301#11758196—22no—
302#11758196—22no—
303#11758196—22no—
304C4×Dic61—22no—
305C4×Dic61—22no—
306C4×Dic61—22no—
307C4×Dic61—24no—
308C23×C61—22no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61C22×D412yes—
312C23×C61C22×D411yescharacteristic
313C22×D61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—24no—
316C2×C4×C61—24no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61C22×D412yes—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D412yes—
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C612−1+414yes—
330C2×C4×C61C2511yescharacteristic
331C22⋊D61—44no—
332C22⋊D61—82no—
333C22⋊D61—82no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—84no—
346D244—24no—
347D244—81no—
348D244—81no—
349C4×D61—44no—
350C4×D61—82no—
351C4×D61—82no—
352Dic122—24no—
353Dic122—81no—
354Dic122—81no—
355Dic122—82no—
356Dic122—84no—
357Dic122—82no—
358C8×C61—24no—
359C8×C61—24no—
360#60867—611nomaximal, Sylow
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—44no—
367C22×C61#53612yes—
368C22×C61C23×D411yescharacteristic
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C4×C61—21no—
373C4×C61—22no—
374C4×C61—21no—
375C4×C61—21no—
376C4×C61—22no—
377C4×C61—21no—
378C4×C61—22no—
379C4×C61#53612yes—
380C4×C61C2×2−1+412yes—
381Dic61—42no—
382Dic61—42no—
383Dic61—42no—
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388C2×#544—611no—
389#3455—611no—
390#3244—614no—
391#3243—614no—
392#3242—614no—
393#3241—614no—
394#3166—611no—
395#3165—611no—
396#3142—611no—
397#3141—611no—
398#3093—612no—
399#3092—612no—
400#3080—612no—
401#3079—612no—
402#2921D6111yescharacteristic, complemented
403C2×C61—22no—
404C2×C61—42no—
405C2×C61C2×#53611yescharacteristic
406C2×C61#358511yescharacteristic
407C2×C61#358611yescharacteristic
408D61—82no—
409#544—614no—
410#544—614no—
411#544—1222no—
412#544—1222no—
413#542—612no—
414#542—612no—
415#541—612no—
416#540—612no—
417#539—1221no—
418#539—1221no—
419#538—1221no—
420#538—1221no—
421#533—611no—
422#532—611no—
423C2×C4⋊Q8—611no—
424C2×C4⋊Q8—611no—
425C2×C4⋊Q8—1221no—
426#529—1222no—
427#529—1222no—
428C2×#125—611no—
429C2×#125—611no—
430C2×#125—1221no—
431#525—612no—
432C2×C22⋊Q8—1221no—
433C2×C22⋊Q8—1221no—
434C4×#41—612no—
435C2×#117—611no—
436C2×#117C2×D6111yescharacteristic
437C22×C4⋊C4—611no—
438#501—614no—
439#501—612no—
440#501—612no—
441#500—612no—
442#499—614no—
443#498—612no—
444#491—612no—
445#490—612no—
446#489—614no—
447#488—614no—
448#487—612no—
449#486—612no—
450#485—614no—
451#485—614no—
452#484—614no—
453#483—614no—
454#482—614no—
455#482—614no—
456#481—614no—
457#480—614no—
458#479—614no—
459#479—614no—
460#478—614no—
461#478—614no—
462#477—614no—
463#476—614no—
464#475—614no—
465#474—614no—
466#433C2×D6114yes—
467#433C2×D6114yes—
468#428—612no—
469#428—612no—
470#428—612no—
471#428—612no—
472#423C2×D6112yes—
473#417—612no—
474#417—612no—
475#417—612no—
476#417—612no—
477#407C2×D6112yes—
478C4×M16C2×D6111yescharacteristic
479C4×M16C2×D6111yescharacteristic
480C61#6086711yescharacteristic, complemented, Sylow
481C2×#41—612no—
482C22×Q8—1221no—
483C22×Q8—1221no—
484C23×C4—1221no—
485C23×C4C22×D6111yescharacteristic
486C2×M16C22×D6112yes—
487C2×M16C22×D6112yes—
488C4⋊Q8—614no—
489C4⋊Q8—612no—
490C4⋊Q8—612no—
491C4⋊Q8—611no—
492C4⋊Q8—611no—
493C4⋊Q8—611no—
494C4⋊Q8—1224no—
495C4⋊Q8—1224no—
496C4⋊Q8—1222no—
497C4⋊Q8—1221no—
498C4⋊Q8—1221no—
499#127—611no—
500#126—1222no—
501#126—1222no—
502#126—1222no—
503#126—1222no—
504#125—614no—
505#125—612no—
506#125—612no—
507#125—612no—
508#125—1224no—
509#125—1224no—
510#125—1222no—
511#125—1222no—
512#125—1222no—
513#125—1221no—
514#125—1221no—
515#124—612no—
516#124—1222no—
517#124—1222no—
518#123—1222no—
519#123—1222no—
520#123—1222no—
521#123—1222no—
522#123—1222no—
523C22⋊Q8—612no—
524C22⋊Q8—612no—
525C22⋊Q8—1221no—
526C22⋊Q8—1221no—
527C22⋊Q8—1222no—
528C22⋊Q8—1222no—
529C22⋊Q8—1224no—
530C22⋊Q8—1224no—
531C22⋊Q8—1224no—
532C22⋊Q8—1224no—
533#121—612no—
534#121—612no—
535#121—1221no—
536#121—1221no—
537#121—1222no—
538#121—1222no—
539#120—1222no—
540C4×Q8—612no—
541C4×Q8—612no—
542C4×Q8—1221no—
543C4×Q8—1221no—
544C4×D4—612no—
545C4×D4—612no—
546C4×D4—1222no—
547C4×D4—1222no—
548C4×D4—1222no—
549C4×D4—1222no—
550C4×D4—1221no—
551C4×D4—1221no—
552#117—614no—
553#117—612no—
554#117—1222no—
555#117—1222no—
556#117D24412yes—
557#117D24412yes—
558#117C22×D6112yes—
559#117C22×D6112yes—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—614no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1222no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4D24411yescharacteristic
574C2×C4⋊C4D24411yescharacteristic
575C2×C22⋊C4—1221no—
576C2×C22⋊C4D24411yescharacteristic
577C2×C22⋊C4D24411yescharacteristic
578C2×C42—1221no—
579C2×C42—1222no—
580C2×C42C22×D6111yescharacteristic
581C2×C42C22×D6111yescharacteristic
582#107—614no—
583#107—614no—
584#107—614no—
585#107—614no—
586#106—614no—
587#106—614no—
588#106—614no—
589#106—614no—
590C4⋊C8C22×D6114yes—
591C4⋊C8C22×D6114yes—
592#103—614no—
593#103—614no—
594#103—614no—
595#103—614no—
596#102—614no—
597#102—614no—
598#102—614no—
599#102—614no—
600C22⋊C8C22×D6114yes—
601C22⋊C8C22×D6114yes—
602#97C22×D6112yes—
603#97C22×D6112yes—
604C4×C8C22×D6112yes—
605C4×C8C22×D6112yes—
606C24C2×D24411yescharacteristic
607#41—1228no—
608C2×Q8—612no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1224no—
612C2×Q8—1222no—
613C2×Q8—1222no—
614C2×Q8—4882no—
615C2×Q8—4882no—
616C2×D4—612no—
617C2×D4—1222no—
618C2×D4—1222no—
619C2×D4—1222no—
620C2×D4—1221no—
621C2×D4—1221no—
622C22×C4—24no—
623C22×C4—1224no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—4882no—
632C22×C4C2×D24411yescharacteristic
633C22×C4C2×D24412yes—
634C22×C4C2×D24411yescharacteristic
635C22×C4C2×D24411yescharacteristic
636C22×C4C2×D24411yescharacteristic
637C22×C4C2×D24411yescharacteristic
638C22×C4C23×D6112yes—
639C22×C4C23×D6111yescharacteristic
640M16—24no—
641M16—24no—
642C2×C8C23×D6114yes—
643C2×C8C23×D6114yes—
644C4⋊C4—612no—
645C4⋊C4—612no—
646C4⋊C4—612no—
647C4⋊C4—612no—
648C4⋊C4—612no—
649C4⋊C4—612no—
650C4⋊C4—1224no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1224no—
656C4⋊C4—1222no—
657C4⋊C4—1222no—
658C4⋊C4—1224no—
659C4⋊C4—1222no—
660C4⋊C4—1222no—
661C4⋊C4—1224no—
662C4⋊C4—1222no—
663C4⋊C4—1222no—
664C4⋊C4—1222no—
665C4⋊C4—1222no—
666C4⋊C4—1222no—
667C4⋊C4—1222no—
668C4⋊C4—1222no—
669C4⋊C4—1222no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4C2×D24412yes—
675C4⋊C4C2×D24412yes—
676C4⋊C4C2×D24412yes—
677C4⋊C4C2×D24412yes—
678C22⋊C4—1224no—
679C22⋊C4—1222no—
680C22⋊C4—1222no—
681C22⋊C4—1222no—
682C22⋊C4—1222no—
683C22⋊C4—1222no—
684C22⋊C4—1222no—
685C22⋊C4—1222no—
686C22⋊C4—1222no—
687C22⋊C4—1222no—
688C22⋊C4C2×D24412yes—
689C22⋊C4C2×D24412yes—
690C22⋊C4C2×D24412yes—
691C22⋊C4C2×D24412yes—
692C42—1222no—
693C42—1224no—
694C42—1222no—
695C42—1222no—
696C42C2×D24412yes—
697C42C2×D24411yescharacteristic
698C42C2×D24411yescharacteristic
699C42C23×D6111yescharacteristic
700C42C23×D6111yescharacteristic
701C42C23×D6112yes—
702C23—22no—
703C23—41no—
704C23—41no—
705C23—1222no—
706C23C22×D24412yes—
707C23C22×D24411yescharacteristic
708Q8—1224no—
709Q8—4881no—
710Q8—4881no—
711Q8—4884no—
712Q8—4882no—
713Q8—4882no—
714D4—1224no—
715D4—4881no—
716D4—4881no—
717D4—4882no—
718D4—4882no—
719D4—2444no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—4882no—
735C2×C4—4882no—
736C2×C4—4884no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2444no—
742C2×C4C22×D24412yes—
743C2×C4C22×D24412yes—
744C2×C4C22×D24412yes—
745C2×C4C22×D24411yescharacteristic
746C2×C4C22×D24411yescharacteristic
747C2×C4C22×D24411yescharacteristic
748C2×C4C22×D24411yescharacteristic
749C2×C4C22×D24411yescharacteristic
750C2×C4#1451982414yes—
751C2×C4C24×D6111yescharacteristic
752C8—24no—
753C8—24no—
754C22—21no—
755C22—21no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—2442no—
761C22—2442no—
762C22—2442no—
763C22#1684033812yes—
764C22C23×D24411yescharacteristic
765C4—22no—
766C4—21no—
767C4—21no—
768C4—22no—
769C4—21no—
770C4—21no—
771C4—22no—
772C4—2442no—
773C4—2442no—
774C4—2442no—
775C4—2442no—
776C4—2442no—
777C4—2442no—
778C4—2442no—
779C4#1684033812yes—
780C4C2×#1451982412yes—
781C2—22no—
782C2—42no—
783C2—4882no—
784C2C2×#1684033811yescharacteristic
785C2#2146060011yescharacteristic
786C2#2146060711yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2921C2
socleC22×C61C23×D4
prime radical#21459209C2
hypercenter#2921D61
hypocenterC61#60867
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2921

Complements

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

NH ≅ G/Ntype
1. C2×#16840390C2semidirect
3. #21457119C2semidirect
4. #21457104C2semidirect
5. #21457089C2semidirect
6. #21457074C2semidirect
7. #21456371C2semidirect
8. #21456365C2semidirect
9. #21456220C2semidirect
10. #21456213C2semidirect
11. #21455752C2semidirect
12. #21455744C2semidirect
13. #21455642C2semidirect
14. #21455635C2semidirect
15. C61×#2921C2semidirect
44. #16840171C22semidirect
45. #16840171C22semidirect
46. #16840171C22semidirect
47. #16840167C22semidirect
48. #16840164C22semidirect
49. #16840160C22semidirect
50. #16840131C22semidirect
51. #16840127C22semidirect
52. #16840122C22semidirect
53. #16840117C22semidirect
54. #16840113C22semidirect
55. #16840109C22semidirect
64. #16840070C22semidirect
65. #16840070C22semidirect
66. #16840063C22semidirect
67. #16840063C22semidirect
68. #16840058C22semidirect
69. #16840053C22semidirect
70. #16840048C22semidirect
71. #16840043C22semidirect
402. #2921D61semidirect
480. C61#60867semidirect

Maximal subgroups

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

subgroupindex
C2×#168403902
#214592092
#214571192
#214571042
#214570892
#214570742
#214563712
#214563652
#214562202
#214562132
#214557522
#214557442
#214556422
#214556352
C61×#29212
#6086761