Finite Group Databasebeta

← #30552390

Subgroups — #30552390

Order 15616.

1690 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459222C211yesmaximal, characteristic, complemented
2C2×#16840386C211yesmaximal, characteristic
3#21457120C214yesmaximal, complemented
4#21457118C214yesmaximal, complemented
5#21457105C214yesmaximal, complemented
6#21457103C214yesmaximal, complemented
7#21456361C211yesmaximal, characteristic, complemented
8#21456208C211yesmaximal, characteristic, complemented
9#21456206C211yesmaximal, characteristic, complemented
10#21455769C212yesmaximal, complemented
11#21455761C212yesmaximal
12#21455623C212yesmaximal, complemented
13#21455615C212yesmaximal, complemented
14#21454455C211yesmaximal, characteristic, complemented
15C61×#3165C211yesmaximal, characteristic, complemented
16#16840392C2212yescomplemented
17#16840392C2212yescomplemented
18#16840391—21no—
19#16840391—21no—
20#16840389C2212yescomplemented
21#16840389C2212yescomplemented
22#16840387—21no—
23#16840387—21no—
24#16840386—22no—
25#16840386—22no—
26#16840386C2214yes—
27#16840386C2214yes—
28#16840319C2211yescharacteristic
29#16840316—22no—
30#16840316—22no—
31#16840315C2212yes—
32C2×#14519772—21no—
33C2×#14519766—21no—
34C2×#14519765C2211yescharacteristic
35C2×#14519762—21no—
36C2×#14519757C2211yescharacteristic
37C2×#14519753—21no—
38C2×#14519752C2211yescharacteristic
39C2×#14519742C2211yescharacteristic
40C2×#14519739C2211yescharacteristic
41C2×#14519734C2211yescharacteristic
42#117×D61C2212yes—
43#16840168C2214yescomplemented
44#16840165C2212yescomplemented
45#16840158C2212yescomplemented
46#16840124C2212yescomplemented
47#16840124C2212yescomplemented
48#16840122C2212yescomplemented
49#16840122C2212yescomplemented
50#16840119C2214yescomplemented
51#16840117C2214yescomplemented
52#16840106C2214yescomplemented
53#16840105C2214yescomplemented
54#16840099C2214yescomplemented
55#16840094C2214yescomplemented
56#16840089C2214yes—
57#16840088C2214yes—
58#16840082C2214yes—
59#16840077C2214yes—
60#16840072C2214yescomplemented
61#16840068C2214yescomplemented
62#16840065C2214yescomplemented
63#16840061C2214yescomplemented
64#16840056C2214yescomplemented
65#16840051C2214yescomplemented
66#16840046C2214yescomplemented
67#16840041C2214yescomplemented
68#16839824C2214yescomplemented
69#16839821C2214yescomplemented
70#16839802C2212yes—
71#16839802C2212yes—
72#16839785C2212yes—
73#16839772C2212yes—
74#16839770C2212yes—
75#16839768C2212yes—
76#16839766C2212yes—
77#16839725C2212yes—
78C4×#11758194C2211yescharacteristic
79C61×#533C2211yescharacteristic
80C2×C4⋊Q8×C61C2211yescharacteristic
81C61×#501C2214yescomplemented
82C61×#500C2212yescomplemented
83C61×#498C2212yescomplemented
84C61×#428C2212yes—
85C61×#428C2212yes—
86C4×M16×C61C2211yescharacteristic
87C22×Dic122C2311yescharacteristic
88C22×D244—21no—
89C22×D244C2311yescharacteristic
90C22×C4×D61—21no—
91C22×C4×D61C2311yescharacteristic
92C2×#11758194C2312yes—
93#14519777C2311yescharacteristic
94#14519777C2311yescharacteristic
95#14519776—22no—
96#14519776—22no—
97#14519776C2312yes—
98#14519776C2312yes—
99#14519775—22no—
100#14519775—22no—
101#14519772—24no—
102#14519772—24no—
103#14519769C2312yes—
104#14519768C2312yes—
105#14519768C2312yes—
106#14519767—22no—
107#14519767—22no—
108#14519767—22no—
109#14519767—22no—
110#14519766—24no—
111#14519766—24no—
112#14519765—21no—
113#14519765—21no—
114#14519765C2312yes—
115#14519765C2312yes—
116#14519762—24no—
117#14519762—24no—
118#14519757—22no—
119#14519757—22no—
120#14519757—22no—
121#14519757C2314yes—
122#14519756—21no—
123#14519756—21no—
124#14519755—22no—
125#14519755—22no—
126#14519755—22no—
127#14519755—22no—
128#14519754—22no—
129#14519754—22no—
130#14519753—22no—
131#14519753—22no—
132#14519753—24no—
133#14519753—24no—
134#14519752—22no—
135#14519752C2314yes—
136C4×Dic122—21no—
137C4×Dic122—21no—
138C4×Dic122—22no—
139C4×Dic122—22no—
140#14519742—22no—
141#14519742C2314yes—
142#14519739—22no—
143#14519739C2314yes—
144#14519736C2312yes—
145#14519735C2312yes—
146#14519735C2312yes—
147#14519734—22no—
148#14519734D412yes—
149#14519734D412yes—
150#14519734C2312yes—
151#14519734C2312yes—
152#14519733—22no—
153C2×C4⋊Dic61—21no—
154C2×#11758196—21no—
155C2×#11758196D411yescharacteristic
156C2×#11758196D411yescharacteristic
157C4⋊C4×D61C2312yes—
158C4⋊C4×D61C2312yes—
159C2×#11758198—21no—
160C2×#11758198—21no—
161C2×#11758198—21no—
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×#11758198D411yescharacteristic
165C2×#11758198D411yescharacteristic
166C22⋊C4×D61—22no—
167C2×C4×Dic61—21no—
168C2×C4×Dic61C2311yescharacteristic
169C42×D61—22no—
170#14519710C2314yes—
171#14519710C2314yes—
172#14519708C2314yes—
173#14519708C2314yes—
174#14519706C2314yes—
175#14519706C2314yes—
176#14519702C2314yes—
177#14519702C2314yes—
178#14519700C2314yes—
179#14519700C2314yes—
180#14519699C2314yes—
181#14519699C2314yes—
182#14519697C2314yes—
183#14519697C2314yes—
184#14519689C2314yes—
185#14519689C2314yes—
186#14519688C2312yes—
187C4×#92418C2312yes—
188C22×Q8×C61—21no—
189C2×M16×C61C2312yes—
190C4⋊Q8×C61—21no—
191C4⋊Q8×C61—21no—
192C4⋊Q8×C61C2312yes—
193C4⋊Q8×C61C2312yes—
194C4⋊Q8×C61C2311yescharacteristic
195C4⋊Q8×C61C2311yescharacteristic
196#125×C61C2312yes—
197C22⋊Q8×C61—21no—
198C22⋊Q8×C61—21no—
199C4×Q8×C61—21no—
200C4×Q8×C61—21no—
201#117×C61C2312yes—
202C2×C4⋊C4×C61—21no—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C4⋊C4×C61C2311yescharacteristic
205C2×C42×C61C2311yescharacteristic
206#107×C61C2314yes—
207#107×C61C2314yes—
208#106×C61C2314yes—
209#106×C61C2314yes—
210#97×C61C2312yes—
211C4×C8×C61C2312yes—
212C23×D61—21no—
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×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C2×D244—24no—
229C2×D244—21no—
230C2×D244—24no—
231C2×D244—82no—
232C2×D244C2412yes—
233C2×C4×D61—24no—
234C2×C4×D61—22no—
235C2×C4×D61—22no—
236C2×C4×D61—24no—
237C2×C4×D61—82no—
238C2×C4×D61C2×D412yes—
239C2×C4×D61C2412yes—
240C2×Dic122—24no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—22no—
245C2×Dic122—22no—
246C2×Dic122C2412yes—
247M16×C61—24no—
248C2×C8×C61C2414yes—
249C4⋊C4×C61—22no—
250C4⋊C4×C61—22no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—22no—
254C4⋊C4×C61—22no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C2412yes—
258C4⋊C4×C61C2412yes—
259C4⋊C4×C61C2412yes—
260C4⋊C4×C61C2412yes—
261C22⋊C4×C61—22no—
262C42×C61—22no—
263C42×C61C2×D411yescharacteristic
264C42×C61C2×D411yescharacteristic
265C42×C61C2411yescharacteristic
266C42×C61C2411yescharacteristic
267C22⋊Dic61—22no—
268#11758198—22no—
269#11758198—22no—
270#11758198—24no—
271#11758198—22no—
272#11758198—22no—
273#11758198—22no—
274#11758198—22no—
275#11758198—24no—
276#11758198—24no—
277#11758198C2×D412yes—
278#11758198C2×D412yes—
279#11758198C2×D412yes—
280#11758198C2×D412yes—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—24no—
284C4⋊Dic61—22no—
285C4⋊Dic61—22no—
286C4⋊Dic61C2412yes—
287C4⋊Dic61C2412yes—
288#11758196—22no—
289#11758196—22no—
290#11758196—22no—
291#11758196—22no—
292#11758196—24no—
293#11758196—22no—
294#11758196—22no—
295#11758196—22no—
296#11758196—22no—
297#11758196C2×D412yes—
298#11758196C2×D412yes—
299#11758196C2×D412yes—
300#11758196C2×D412yes—
301C4×Dic61—22no—
302C4×Dic61—22no—
303C4×Dic61—22no—
304C4×Dic61—24no—
305C4×Dic61C2×D412yes—
306C4×Dic61C2412yes—
307#11758194—24no—
308C2×#92418C2414yes—
309C23×C61C22×D411yescharacteristic
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—42no—
315C22×D61—42no—
316C22×D61—42no—
317C22×D61C22×D412yes—
318Q8×C61—81no—
319Q8×C61—81no—
320Q8×C61—82no—
321Q8×C61—82no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—42no—
329C2×C4×C61—42no—
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C612−1+414yes—
336C2×C4×C61C2511yescharacteristic
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—42no—
344C2×Dic61C22×D412yes—
345C2×Dic61C22×D412yes—
346C2×Dic61C22×D412yes—
347D244—24no—
348D244—42no—
349D244—84no—
350C4×D61—24no—
351C4×D61—24no—
352C4×D61—84no—
353C4×D61—82no—
354C4×D61—82no—
355Dic122—24no—
356Dic122—42no—
357Dic122—82no—
358Dic122—82no—
359Dic122—81no—
360Dic122—81no—
361C8×C61—24no—
362#92418—24no—
363#60870—611nomaximal, Sylow
364C22×C61—21no—
365C22×C61—21no—
366C22×C61#53612yes—
367C22×C61C23×D411yescharacteristic
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—82no—
375C2×D61—84no—
376C4×C61—21no—
377C4×C61—21no—
378C4×C61—21no—
379C4×C61—21no—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61#53612yes—
385C4×C61C2×2−1+412yes—
386Dic61—22no—
387Dic61—22no—
388Dic61—22no—
389Dic61—42no—
390Dic61—42no—
391Dic61—42no—
392#3458—611no—
393C2×#542—611no—
394#3244—614no—
395#3244—614no—
396#3243—614no—
397#3243—614no—
398#3165—611no—
399#3165D6111yescharacteristic, complemented
400#3140—611no—
401#3140—611no—
402#3095—612no—
403#3094—612no—
404#3078—612no—
405#3077—612no—
406#2921—611no—
407C2×C61—22no—
408C2×C61C2×#53611yescharacteristic
409C2×C61#358511yescharacteristic
410C2×C61#358611yescharacteristic
411D61—42no—
412D61—82no—
413#544—612no—
414#544—612no—
415#544—612no—
416#544—612no—
417#544—1221no—
418#544—1221no—
419#543—1221no—
420#543—1221no—
421#542—614no—
422#542—614no—
423#542—1222no—
424#542—1222no—
425#533—612no—
426#533—611no—
427#533—1222no—
428#533—1222no—
429#533C2×D6111yescharacteristic
430C2×C4⋊Q8C2×D6111yescharacteristic
431C2×#126—1221no—
432C2×#124—611no—
433C2×#124—1221no—
434C2×#123—1221no—
435C2×C22⋊Q8—611no—
436C2×C22⋊Q8—1221no—
437C2×#121—611no—
438C2×C4×Q8—611no—
439C2×C4×D4—611no—
440C2×#117—611no—
441C2×#117—612no—
442#501—614no—
443#501C2×D6114yescomplemented
444#500—612no—
445#500C2×D6112yescomplemented
446#498—612no—
447#498C2×D6112yescomplemented
448#489—612no—
449#489—612no—
450#489—612no—
451#489—612no—
452#488—614no—
453#488—614no—
454#485—614no—
455#485—614no—
456#484—614no—
457#483—614no—
458#482—614no—
459#482—614no—
460#481—614no—
461#480—614no—
462#479—614no—
463#479—614no—
464#478—614no—
465#478—614no—
466#477—614no—
467#476—614no—
468#475—614no—
469#474—614no—
470#433—614no—
471#433—614no—
472#428—612no—
473#428—612no—
474#428C2×D6112yes—
475#428C2×D6112yes—
476#423—612no—
477#419—612no—
478#419—612no—
479#418—612no—
480#418—612no—
481#407—612no—
482C4×M16—611no—
483C4×M16C2×D6111yescharacteristic
484C61#6087011yescharacteristic, complemented, Sylow
485C22×Q8—21no—
486C22×Q8—611no—
487C22×D4—611no—
488C22×D4—1221no—
489C23×C4—611no—
490C23×C4—1221no—
491C2×M16—612no—
492C2×M16C22×D6112yes—
493C4⋊Q8—21no—
494C4⋊Q8—21no—
495C4⋊Q8—612no—
496C4⋊Q8—612no—
497C4⋊Q8—611no—
498C4⋊Q8—611no—
499C4⋊Q8—1222no—
500C4⋊Q8—1222no—
501C4⋊Q8—1222no—
502C4⋊Q8—1222no—
503C4⋊Q8C22×D6112yes—
504C4⋊Q8C22×D6112yes—
505C4⋊Q8C22×D6111yescharacteristic
506C4⋊Q8C22×D6111yescharacteristic
507#126—1224no—
508#126—1224no—
509#125—612no—
510#125—612no—
511#125—612no—
512#125—1222no—
513#125—1222no—
514#125—1222no—
515#125—1222no—
516#125C22×D6112yes—
517#124—612no—
518#124—612no—
519#124—1224no—
520#124—1224no—
521#124—1221no—
522#124—1221no—
523#123—1224no—
524#123—1224no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527C22⋊Q8—614no—
528C22⋊Q8—1222no—
529C22⋊Q8—1222no—
530C22⋊Q8—1222no—
531C22⋊Q8—1222no—
532C22⋊Q8—1222no—
533C22⋊Q8—1222no—
534C22⋊Q8—1222no—
535C22⋊Q8—1222no—
536C22⋊Q8—1222no—
537C22⋊Q8—1222no—
538C22⋊Q8—1222no—
539C22⋊Q8—1224no—
540C22⋊Q8—1224no—
541C22⋊Q8—1221no—
542C22⋊Q8—1221no—
543#121—614no—
544#121—1222no—
545C4×Q8—21no—
546C4×Q8—21no—
547C4×Q8—614no—
548C4×Q8—1222no—
549C4×Q8—1222no—
550C4×Q8—1222no—
551C4×Q8—1221no—
552C4×Q8—1221no—
553C4×D4—614no—
554C4×D4—1222no—
555#117—612no—
556#117—612no—
557#117—612no—
558#117—612no—
559#117—612no—
560#117—612no—
561#117—612no—
562#117—1222no—
563#117—1222no—
564#117C22×D6112yes—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—612no—
569C2×C4⋊C4—612no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4C22×D6111yescharacteristic
573C2×C4⋊C4C22×D6111yescharacteristic
574C2×C22⋊C4—611no—
575C2×C22⋊C4—611no—
576C2×C22⋊C4—1222no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C42—611no—
583C2×C42—1222no—
584C2×C42—1221no—
585C2×C42C22×D6111yescharacteristic
586#107—614no—
587#107—614no—
588#107C22×D6114yes—
589#107C22×D6114yes—
590#106—614no—
591#106—614no—
592#106C22×D6114yes—
593#106C22×D6114yes—
594C4⋊C8—614no—
595C4⋊C8—614no—
596#103—614no—
597#103—614no—
598#103—614no—
599#103—614no—
600#102—614no—
601#102—614no—
602#102—614no—
603#102—614no—
604C22⋊C8—614no—
605C22⋊C8—614no—
606#97—612no—
607#97C22×D6112yes—
608C4×C8—612no—
609C4×C8C22×D6112yes—
610C24—611no—
611C24—1221no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—22no—
615C2×Q8—22no—
616C2×Q8—82no—
617C2×Q8—612no—
618C2×Q8—1222no—
619C2×Q8—1222no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1224no—
624C2×D4—612no—
625C2×D4—1224no—
626C2×D4—1221no—
627C2×D4—1224no—
628C2×D4—4882no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—612no—
635C22×C4—612no—
636C22×C4—1224no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1224no—
640C22×C4—1221no—
641C22×C4—4882no—
642C22×C4D4×D6111yescharacteristic
643C22×C4D4×D6111yescharacteristic
644C22×C4C23×D6111yescharacteristic
645M16—24no—
646M16—1224no—
647C2×C8—614no—
648C2×C8C23×D6114yes—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—612no—
658C4⋊C4—612no—
659C4⋊C4—612no—
660C4⋊C4—612no—
661C4⋊C4—612no—
662C4⋊C4—612no—
663C4⋊C4—1222no—
664C4⋊C4—1222no—
665C4⋊C4—1224no—
666C4⋊C4—1224no—
667C4⋊C4—1222no—
668C4⋊C4—1222no—
669C4⋊C4—1222no—
670C4⋊C4—1222no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—1222no—
674C4⋊C4—1222no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4C23×D6112yes—
678C4⋊C4C23×D6112yes—
679C4⋊C4C23×D6112yes—
680C4⋊C4C23×D6112yes—
681C22⋊C4—22no—
682C22⋊C4—612no—
683C22⋊C4—612no—
684C22⋊C4—612no—
685C22⋊C4—612no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—1222no—
689C22⋊C4—1222no—
690C22⋊C4—1224no—
691C22⋊C4—1222no—
692C22⋊C4—1222no—
693C22⋊C4—1222no—
694C22⋊C4—1222no—
695C22⋊C4—1222no—
696C42—22no—
697C42—612no—
698C42—612no—
699C42—1222no—
700C42—1222no—
701C42—1224no—
702C42—1222no—
703C42D4×D6111yescharacteristic
704C42D4×D6111yescharacteristic
705C42C23×D6111yescharacteristic
706C42C23×D6111yescharacteristic
707C23—612no—
708C23—1222no—
709C23—1222no—
710C23—2441no—
711C23—2441no—
712C23—2442no—
713C23—2442no—
714C23—2442no—
715C23C2×D4×D6111yescharacteristic
716Q8—81no—
717Q8—81no—
718Q8—82no—
719Q8—82no—
720Q8—1224no—
721Q8—4881no—
722Q8—4881no—
723Q8—4882no—
724Q8—4882no—
725Q8—2442no—
726D4—1224no—
727D4—4884no—
728D4—2442no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—612no—
738C2×C4—612no—
739C2×C4—612no—
740C2×C4—1222no—
741C2×C4—1224no—
742C2×C4—1224no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—4884no—
747C2×C4—4882no—
748C2×C4—4882no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2442no—
752C2×C4C2×D4×D6111yescharacteristic
753C2×C4C2×D4×D6111yescharacteristic
754C2×C4C2×D4×D6111yescharacteristic
755C2×C4C2×D4×D6111yescharacteristic
756C2×C4C2×D4×D6111yescharacteristic
757C2×C4#1451982514yes—
758C2×C4C24×D6111yescharacteristic
759C8—24no—
760C8—1224no—
761C22—21no—
762C22—21no—
763C22—1222no—
764C22—1222no—
765C22—1222no—
766C22—4884no—
767C22—4882no—
768C22—2442no—
769C22—2442no—
770C22—2442no—
771C22#1684033712yes—
772C22C22×D4×D6111yescharacteristic
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—1222no—
782C4—1222no—
783C4—1222no—
784C4—2442no—
785C4—2442no—
786C4—2442no—
787C4#1684033712yes—
788C4C2×#1451982512yes—
789C2—22no—
790C2—4882no—
791C2—2442no—
792C2C2×#1684033711yescharacteristic
793C2#2146059511yescharacteristic
794C2#2146060211yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3165C2
socleC22×C61C23×D4
prime radicalC2×#14519752C22
hypercenter#3165D61
hypocenterC61#60870
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
1. #21459222C2semidirect
3. #21457120C2semidirect
4. #21457118C2semidirect
5. #21457105C2semidirect
6. #21457103C2semidirect
7. #21456361C2semidirect
8. #21456208C2semidirect
9. #21456206C2semidirect
10. #21455769C2semidirect
12. #21455623C2semidirect
13. #21455615C2semidirect
14. #21454455C2semidirect
15. C61×#3165C2semidirect
16. #16840392C22semidirect
17. #16840392C22semidirect
20. #16840389C22semidirect
21. #16840389C22semidirect
43. #16840168C22semidirect
44. #16840165C22semidirect
45. #16840158C22semidirect
46. #16840124C22semidirect
47. #16840124C22semidirect
48. #16840122C22semidirect
49. #16840122C22semidirect
50. #16840119C22semidirect
51. #16840117C22semidirect
52. #16840106C22semidirect
53. #16840105C22semidirect
54. #16840099C22semidirect
55. #16840094C22semidirect
60. #16840072C22semidirect
61. #16840068C22semidirect
62. #16840065C22semidirect
63. #16840061C22semidirect
64. #16840056C22semidirect
65. #16840051C22semidirect
66. #16840046C22semidirect
67. #16840041C22semidirect
68. #16839824C22semidirect
69. #16839821C22semidirect
81. C61×#501C22semidirect
82. C61×#500C22semidirect
83. C61×#498C22semidirect
399. #3165D61semidirect
443. #501C2×D61semidirect
445. #500C2×D61semidirect
447. #498C2×D61semidirect
484. C61#60870semidirect

Maximal subgroups

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

subgroupindex
#214592222
C2×#168403862
#214571202
#214571182
#214571052
#214571032
#214563612
#214562082
#214562062
#214557692
#214557612
#214556232
#214556152
#214544552
C61×#31652
#6087061