Finite Group Databasebeta

← #30552366

Subgroups — #30552366

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×#16840392C211yesmaximal, characteristic, complemented
2#21459211C211yesmaximal, characteristic
3#21457118C214yesmaximal, complemented
4#21457103C214yesmaximal, complemented
5#21457090C214yesmaximal, complemented
6#21457075C214yesmaximal, complemented
7#21456366C211yesmaximal, characteristic, complemented
8#21456222C211yesmaximal, characteristic, complemented
9#21456213C211yesmaximal, characteristic, complemented
10#21455753C212yesmaximal, complemented
11#21455745C212yesmaximal, complemented
12#21455640C212yesmaximal, complemented
13#21455632C212yesmaximal, complemented
14#21454455C211yesmaximal, characteristic, complemented
15C61×#3166C211yesmaximal, characteristic, complemented
16#16840392—22no—
17#16840392—22no—
18#16840392C2214yes—
19#16840392C2214yes—
20#16840386C2212yes—
21#16840386C2212yes—
22#16840375C2212yes—
23#16840368C2212yes—
24#16840361—21no—
25#16840361—21no—
26#16840352—21no—
27#16840352—21no—
28#16840312C2211yescharacteristic
29C2×#14519777C2211yescharacteristic
30C2×#14519776—21no—
31C2×#14519776C2211yescharacteristic
32#16840299—22no—
33#16840299—22no—
34C2×#14519768C2211yescharacteristic
35C2×#14519767—21no—
36#16840274C2212yes—
37C2×#14519757—21no—
38C2×#14519755—21no—
39#16840230C2212yes—
40C2×#14519735C2211yescharacteristic
41C2×#14519734C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43#16840172C2214yescomplemented
44#16840165C2212yescomplemented
45#16840158C2212yescomplemented
46#16840132C2212yescomplemented
47#16840128C2212yescomplemented
48#16840122C2214yescomplemented
49#16840119C2214yescomplemented
50#16840113C2212yescomplemented
51#16840109C2212yescomplemented
52#16840106C2214yes—
53#16840105C2214yes—
54#16840099C2214yes—
55#16840094C2214yes—
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#16839824C2214yes—
69#16839821C2214yes—
70#16839805C2212yes—
71#16839805C2212yes—
72#16839785C2212yes—
73#16839764C2212yes—
74#16839764C2212yes—
75#16839761C2212yes—
76#16839761C2212yes—
77#16839725C2212yes—
78C4×#11758194C2211yescharacteristic
79C61×#533C2211yescharacteristic
80C2×#125×C61C2211yescharacteristic
81C61×#501C2212yescomplemented
82C61×#501C2212yescomplemented
83C61×#499C2214yescomplemented
84C61×#428C2212yes—
85C61×#428C2212yes—
86C4×M16×C61C2211yescharacteristic
87C2×#11758222C2312yes—
88C22×Dic122—21no—
89C22×Dic122—21no—
90C22×C4×D61—21no—
91C22×C4×D61C2311yescharacteristic
92C2×#11758194C2312yes—
93#14519777—21no—
94#14519777—21no—
95#14519777C2311yescharacteristic
96#14519777C2312yes—
97#14519777C2312yes—
98#14519776—24no—
99#14519776—24no—
100#14519776—22no—
101#14519776C2314yes—
102#14519774C2311yescharacteristic
103#14519772—22no—
104#14519772—22no—
105#14519772—22no—
106#14519772—22no—
107#14519768—22no—
108#14519768—22no—
109#14519768—22no—
110#14519768C2314yes—
111#14519767—24no—
112#14519767—24no—
113#14519766—22no—
114#14519766—22no—
115#14519765C2312yes—
116#14519762—22no—
117#14519762—22no—
118#14519762—22no—
119#14519762—22no—
120#14519761—22no—
121#14519757—24no—
122#14519757—24no—
123#14519757C2312yes—
124#14519757C2312yes—
125#14519755—24no—
126#14519755—24no—
127#14519753—22no—
128#14519753—22no—
129#14519752—22no—
130#14519752—22no—
131#14519752C2312yes—
132#14519752C2312yes—
133#14519751—21no—
134#14519751—21no—
135#14519747—22no—
136#14519742C2312yes—
137#14519742C2312yes—
138C4×D244—22no—
139C4×D244—22no—
140C4×D244—21no—
141C4×D244—21no—
142#14519739C2312yes—
143#14519739C2312yes—
144#14519737—22no—
145#14519737—22no—
146#14519735—22no—
147#14519735C2314yes—
148#14519734—22no—
149#14519734D412yes—
150#14519734D412yes—
151#14519734C2312yes—
152#14519734C2312yes—
153C2×C4⋊Dic61—21no—
154C2×C4⋊Dic61—21no—
155C2×C4⋊Dic61C2311yescharacteristic
156C2×C4⋊Dic61C2311yescharacteristic
157C2×#11758196—21no—
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196D411yescharacteristic
161C2×#11758196D411yescharacteristic
162C4⋊C4×D61—22no—
163C4⋊C4×D61C2314yes—
164C2×#11758198—21no—
165C2×#11758198D411yescharacteristic
166C2×#11758198D411yescharacteristic
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—
188C2×M16×C61C2312yes—
189C4⋊Q8×C61C2311yescharacteristic
190C4⋊Q8×C61C2311yescharacteristic
191#125×C61—21no—
192#125×C61—21no—
193#125×C61C2312yes—
194#125×C61C2312yes—
195#125×C61C2312yes—
196C22⋊Q8×C61—21no—
197C22⋊Q8×C61—21no—
198C4×Q8×C61—21no—
199C4×Q8×C61—21no—
200#117×C61C2312yes—
201C2×C4⋊C4×C61—21no—
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×D61C2×D411yescharacteristic
213C2×Q8×C61—21no—
214C2×Q8×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2411yescharacteristic
220C2×C22⋊D61—22no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226#11758222—28no—
227C2×D244—22no—
228C2×D244—22no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244C2412yes—
232C2×C4×D61—24no—
233C2×C4×D61—22no—
234C2×C4×D61—24no—
235C2×C4×D61—22no—
236C2×C4×D61—22no—
237C2×C4×D61—82no—
238C2×C4×D61C2×D412yes—
239C2×C4×D61C2412yes—
240C2×Dic122—22no—
241C2×Dic122—22no—
242C2×Dic122—24no—
243C2×Dic122—82no—
244C2×Dic122—82no—
245C2×Dic122C2412yes—
246M16×C61—24no—
247C2×C8×C61C2414yes—
248C4⋊C4×C61—22no—
249C4⋊C4×C61—22no—
250C4⋊C4×C61—22no—
251C4⋊C4×C61—22no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—22no—
255C4⋊C4×C61—22no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61C2412yes—
259C4⋊C4×C61C2412yes—
260C4⋊C4×C61C2412yes—
261C4⋊C4×C61C2412yes—
262C22⋊C4×C61—22no—
263C42×C61—22no—
264C42×C61C2×D411yescharacteristic
265C42×C61C2×D411yescharacteristic
266C42×C61C2411yescharacteristic
267C42×C61C2411yescharacteristic
268#11758198—24no—
269#11758198—22no—
270#11758198—22no—
271#11758198—22no—
272#11758198—22no—
273#11758198—22no—
274#11758198—22no—
275#11758198—22no—
276#11758198—22no—
277#11758198C2×D412yes—
278#11758198C2×D412yes—
279#11758198C2×D412yes—
280#11758198C2×D412yes—
281C4⋊Dic61—21no—
282C4⋊Dic61—22no—
283C4⋊Dic61—22no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—24no—
288C4⋊Dic61—22no—
289C4⋊Dic61—22no—
290C4⋊Dic61C2412yes—
291C4⋊Dic61C2412yes—
292#11758196—24no—
293#11758196—24no—
294#11758196—24no—
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—24no—
304C4×Dic61C2×D412yes—
305C4×Dic61C2412yes—
306#11758194—24no—
307C2×#92418C2414yes—
308C23×C61C22×D411yescharacteristic
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61C22×D412yes—
314Q8×C61—81no—
315Q8×C61—81no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
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—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61C22×D412yes—
341C2×Dic61C22×D412yes—
342C2×Dic61C22×D412yes—
343D244—24no—
344D244—81no—
345D244—81no—
346D244—82no—
347D244—82no—
348C4×D61—24no—
349C4×D61—24no—
350C4×D61—44no—
351C4×D61—82no—
352C4×D61—82no—
353C4×D61—84no—
354Dic122—24no—
355Dic122—84no—
356Dic122—82no—
357Dic122—82no—
358C8×C61—24no—
359#92418—24no—
360#60867—611nomaximal, Sylow
361C22×C61—21no—
362C22×C61—21no—
363C22×C61#53612yes—
364C22×C61C23×D411yescharacteristic
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—44no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C4×C61—21no—
373C4×C61—21no—
374C4×C61—21no—
375C4×C61—21no—
376C4×C61—42no—
377C4×C61—42no—
378C4×C61—42no—
379C4×C61—42no—
380C4×C61#53612yes—
381C4×C61C2×2−1+412yes—
382Dic61—22no—
383Dic61—22no—
384Dic61—22no—
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#3166D6111yescharacteristic, complemented
395#3165—611no—
396#3142—611no—
397#3141—611no—
398#3093—612no—
399#3092—612no—
400#3080—612no—
401#3079—612no—
402#2921—611no—
403C2×C61—22no—
404C2×C61C2×#53611yescharacteristic
405C2×C61#358511yescharacteristic
406C2×C61#358611yescharacteristic
407D61—42no—
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#533C2×D6111yescharacteristic
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—1221no—
430C2×#125C2×D6111yescharacteristic
431#525—612no—
432C2×C22⋊Q8—1221no—
433C2×C22⋊Q8—1221no—
434C4×#41—612no—
435C2×#117—611no—
436C2×#117—611no—
437C22×C4⋊C4—611no—
438#501—614no—
439#501C2×D6112yescomplemented
440#501C2×D6112yescomplemented
441#500—612no—
442#499C2×D6114yescomplemented
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#433—614no—
467#433—614no—
468#428—612no—
469#428—612no—
470#428C2×D6112yes—
471#428C2×D6112yes—
472#423—612no—
473#417—612no—
474#417—612no—
475#417—612no—
476#417—612no—
477#407—612no—
478C4×M16—611no—
479C4×M16C2×D6111yescharacteristic
480C61#6086711yescharacteristic, complemented, Sylow
481C2×#41—612no—
482C22×Q8—1221no—
483C22×Q8—1221no—
484C23×C4—611no—
485C23×C4—1221no—
486C2×M16—612no—
487C2×M16C22×D6112yes—
488C4⋊Q8—614no—
489C4⋊Q8—612no—
490C4⋊Q8—612no—
491C4⋊Q8—611no—
492C4⋊Q8—1222no—
493C4⋊Q8—1224no—
494C4⋊Q8—1224no—
495C4⋊Q8—1221no—
496C4⋊Q8—1221no—
497C4⋊Q8C22×D6111yescharacteristic
498C4⋊Q8C22×D6111yescharacteristic
499#127—611no—
500#126—1222no—
501#126—1222no—
502#126—1222no—
503#126—1222no—
504#125—21no—
505#125—21no—
506#125—614no—
507#125—1222no—
508#125—1224no—
509#125—1224no—
510#125—1222no—
511#125—1222no—
512#125C22×D6112yes—
513#125C22×D6112yes—
514#125C22×D6112yes—
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—21no—
524C22⋊Q8—21no—
525C22⋊Q8—612no—
526C22⋊Q8—612no—
527C22⋊Q8—1224no—
528C22⋊Q8—1224no—
529C22⋊Q8—1224no—
530C22⋊Q8—1224no—
531C22⋊Q8—1222no—
532C22⋊Q8—1222no—
533#121—612no—
534#121—612no—
535#121—1222no—
536#121—1222no—
537#121—1221no—
538#121—1221no—
539#120—1222no—
540C4×Q8—21no—
541C4×Q8—21no—
542C4×Q8—612no—
543C4×Q8—612no—
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—612no—
553#117—612no—
554#117—612no—
555#117—612no—
556#117—614no—
557#117—1222no—
558#117—1222no—
559#117C22×D6112yes—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—614no—
567C2×C4⋊C4—1222no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4C22×D6111yescharacteristic
574C2×C4⋊C4C22×D6111yescharacteristic
575C2×C22⋊C4—611no—
576C2×C22⋊C4—611no—
577C2×C22⋊C4—1221no—
578C2×C42—611no—
579C2×C42—1222no—
580C2×C42—1221no—
581C2×C42C22×D6111yescharacteristic
582#107—614no—
583#107—614no—
584#107C22×D6114yes—
585#107C22×D6114yes—
586#106—614no—
587#106—614no—
588#106C22×D6114yes—
589#106C22×D6114yes—
590C4⋊C8—614no—
591C4⋊C8—614no—
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⋊C8—614no—
601C22⋊C8—614no—
602#97—612no—
603#97C22×D6112yes—
604C4×C8—612no—
605C4×C8C22×D6112yes—
606C24—611no—
607#41—1228no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—612no—
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—21no—
623C22×C4—21no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—612no—
628C22×C4—612no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1224no—
632C22×C4—1224no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1222no—
636C22×C4—4882no—
637C22×C4D4×D6111yescharacteristic
638C22×C4D4×D6111yescharacteristic
639C22×C4C23×D6111yescharacteristic
640M16—24no—
641M16—1224no—
642C2×C8—614no—
643C2×C8C23×D6114yes—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—612no—
655C4⋊C4—612no—
656C4⋊C4—612no—
657C4⋊C4—612no—
658C4⋊C4—612no—
659C4⋊C4—612no—
660C4⋊C4—1224no—
661C4⋊C4—1224no—
662C4⋊C4—1224no—
663C4⋊C4—1224no—
664C4⋊C4—1222no—
665C4⋊C4—1222no—
666C4⋊C4—1222no—
667C4⋊C4—1222no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1222no—
671C4⋊C4—1222no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4C23×D6112yes—
675C4⋊C4C23×D6112yes—
676C4⋊C4C23×D6112yes—
677C4⋊C4C23×D6112yes—
678C22⋊C4—22no—
679C22⋊C4—612no—
680C22⋊C4—612no—
681C22⋊C4—612no—
682C22⋊C4—612no—
683C22⋊C4—1222no—
684C22⋊C4—1222no—
685C22⋊C4—1222no—
686C22⋊C4—1222no—
687C22⋊C4—1224no—
688C22⋊C4—1222no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C42—22no—
693C42—612no—
694C42—612no—
695C42—1224no—
696C42—1222no—
697C42—1222no—
698C42D4×D6111yescharacteristic
699C42D4×D6111yescharacteristic
700C42C23×D6111yescharacteristic
701C42C23×D6111yescharacteristic
702C23—612no—
703C23—1222no—
704C23—1222no—
705C23—2441no—
706C23—2441no—
707C23C2×D4×D6111yescharacteristic
708Q8—81no—
709Q8—81no—
710Q8—1224no—
711Q8—4882no—
712Q8—4882no—
713Q8—4884no—
714D4—1224no—
715D4—4881no—
716D4—4881no—
717D4—4882no—
718D4—4882no—
719D4—2444no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—612no—
729C2×C4—612no—
730C2×C4—612no—
731C2×C4—1222no—
732C2×C4—1224no—
733C2×C4—1224no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—4882no—
738C2×C4—4882no—
739C2×C4—4884no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2444no—
745C2×C4C2×D4×D6111yescharacteristic
746C2×C4C2×D4×D6111yescharacteristic
747C2×C4C2×D4×D6111yescharacteristic
748C2×C4C2×D4×D6111yescharacteristic
749C2×C4C2×D4×D6111yescharacteristic
750C2×C4#1451982514yes—
751C2×C4C24×D6111yescharacteristic
752C8—24no—
753C8—1224no—
754C22—21no—
755C22—21no—
756C22—1222no—
757C22—1222no—
758C22—1222no—
759C22—2444no—
760C22—2442no—
761C22—2442no—
762C22—2442no—
763C22#1684033712yes—
764C22C22×D4×D6111yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—21no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—1222no—
774C4—1222no—
775C4—1222no—
776C4—2442no—
777C4—2442no—
778C4—2442no—
779C4#1684033712yes—
780C4C2×#1451982512yes—
781C2—22no—
782C2—4882no—
783C2—2442no—
784C2C2×#1684033711yescharacteristic
785C2#2146059611yescharacteristic
786C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3166C2
socleC22×C61C23×D4
prime radical#21459211C2
hypercenter#3166D61
hypocenterC61#60867
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
1. C2×#16840392C2semidirect
3. #21457118C2semidirect
4. #21457103C2semidirect
5. #21457090C2semidirect
6. #21457075C2semidirect
7. #21456366C2semidirect
8. #21456222C2semidirect
9. #21456213C2semidirect
10. #21455753C2semidirect
11. #21455745C2semidirect
12. #21455640C2semidirect
13. #21455632C2semidirect
14. #21454455C2semidirect
15. C61×#3166C2semidirect
43. #16840172C22semidirect
44. #16840165C22semidirect
45. #16840158C22semidirect
46. #16840132C22semidirect
47. #16840128C22semidirect
48. #16840122C22semidirect
49. #16840119C22semidirect
50. #16840113C22semidirect
51. #16840109C22semidirect
60. #16840072C22semidirect
61. #16840068C22semidirect
62. #16840065C22semidirect
63. #16840061C22semidirect
64. #16840056C22semidirect
65. #16840051C22semidirect
66. #16840046C22semidirect
67. #16840041C22semidirect
81. C61×#501C22semidirect
82. C61×#501C22semidirect
83. C61×#499C22semidirect
394. #3166D61semidirect
439. #501C2×D61semidirect
440. #501C2×D61semidirect
442. #499C2×D61semidirect
480. C61#60867semidirect

Maximal subgroups

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

subgroupindex
C2×#168403922
#214592112
#214571182
#214571032
#214570902
#214570752
#214563662
#214562222
#214562132
#214557532
#214557452
#214556402
#214556322
#214544552
C61×#31662
#6086761