Finite Group Databasebeta

← #29656371

Subgroups — #29656371

Order 15616.

954 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456538C211yesmaximal, characteristic, complemented
2#21455970C211yesmaximal, characteristic
3#21455291C211yesmaximal, characteristic, complemented
4#21445068C211yesmaximal, characteristic, complemented
5#21445061C211yesmaximal, characteristic, complemented
6#21445040C211yesmaximal, characteristic, complemented
7#21445033C211yesmaximal, characteristic, complemented
8#21444922C211yesmaximal, characteristic, complemented
9#21444915C211yesmaximal, characteristic, complemented
10#21444897C211yesmaximal, characteristic, complemented
11#21444891C211yesmaximal, characteristic, complemented
12#21444549C211yesmaximal, characteristic, complemented
13#21444266C211yesmaximal, characteristic, complemented
14#21444258C211yesmaximal, characteristic, complemented
15Q8×#41×C61C211yesmaximal, characteristic, complemented
16C2×#14519808—21no—
17#16840312C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840136C2211yescharacteristic
20#16840112C2211yescharacteristic
21#16840110C2211yescharacteristic
22#16840086—21no—
23#16840047C2211yescharacteristic
24#16840042C2211yescharacteristic
25#16840010—22no—
26#16839984—21no—
27#16839984—21no—
28#16839972C2211yescharacteristic
29#16839972C2211yescharacteristic
30#16839962C2211yescharacteristic
31#16839962C2211yescharacteristic
32#16839962C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839907—21no—
35#16839872—21no—
36#16839860—21no—
37#16839860—22no—
38#16839819C2211yescharacteristic
39#16839786C2211yescharacteristic
40#16839761—21no—
41C4×#11758194C2211yescharacteristic
42#16839511C2211yescharacteristic
43#16839511C2211yescharacteristic
44#16839508C2211yescharacteristic
45#16839508C2211yescharacteristic
46Q8⋊#92418C2211yescharacteristic
47Q8⋊#92418C2211yescharacteristic
48Q8⋊#92418C2211yescharacteristic
49Q8⋊#92418C2211yescharacteristic
50Q8⋊#92418C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54Q82×C61C2211yescharacteristic
55C61×#557—21no—
56C61×#557C2211yescharacteristic
57C61×#554—22no—
58C61×#554—21no—
59C61×#554—21no—
60C61×#554C2211yescharacteristic
61D4×Q8×C61—21no—
62D4×Q8×C61C2211yescharacteristic
63C61×#533—22no—
64C61×#533—21no—
65C61×#533—21no—
66C61×#533C2211yescharacteristic
67C4×#41×C61—21no—
68C4×#41×C61C2211yescharacteristic
69C2×C4×Q8×C61—21no—
70C2×C4×Q8×C61C2211yescharacteristic
71C2×#11758222—21no—
72#14519808—44no—
73C2×#11758202—21no—
74C2×#11758202—21no—
75C2×#11758201—21no—
76C2×#11758201—21no—
77C2×#11758201—21no—
78C2×#11758201—22no—
79C2×#11758199—21no—
80C2×#11758194—21no—
81C2×#11758194—21no—
82#14519777C2311yescharacteristic
83#14519774C2311yescharacteristic
84#14519765—21no—
85#14519751—21no—
86#14519751—21no—
87C4×D244—21no—
88C4×D244—21no—
89#14519710—22no—
90#14519710—21no—
91#14519708—21no—
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519701—22no—
98#14519701—21no—
99#14519700—21no—
100#14519700—21no—
101#14519698—21no—
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—22no—
107C22⋊#92418—21no—
108#14519688—21no—
109#14519688—21no—
110C4×#92418C2311yescharacteristic
111C4×#92418C2311yescharacteristic
112C2×#41×C61D411yescharacteristic
113C22×Q8×C61—21no—
114C22×Q8×C61D411yescharacteristic
115C4⋊Q8×C61—22no—
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61—22no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122C4⋊Q8×C61C2311yescharacteristic
123#125×C61—22no—
124#125×C61—22no—
125#125×C61—22no—
126#125×C61—21no—
127#125×C61—21no—
128#125×C61—21no—
129C22⋊Q8×C61—22no—
130C22⋊Q8×C61—22no—
131C22⋊Q8×C61—22no—
132C22⋊Q8×C61—22no—
133C22⋊Q8×C61—22no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61—22no—
136C22⋊Q8×C61—21no—
137C22⋊Q8×C61—21no—
138C22⋊Q8×C61—22no—
139C22⋊Q8×C61D412yes—
140C4×Q8×C61—22no—
141C4×Q8×C61—22no—
142C4×Q8×C61—22no—
143C4×Q8×C61—21no—
144C4×Q8×C61—21no—
145C4×Q8×C61—21no—
146C4×Q8×C61—21no—
147C4×Q8×C61—21no—
148C4×Q8×C61—21no—
149C4×Q8×C61—21no—
150C4×Q8×C61D412yes—
151C4×Q8×C61D411yescharacteristic
152C4×Q8×C61D411yescharacteristic
153C4×Q8×C61D411yescharacteristic
154C4×Q8×C61C2311yescharacteristic
155C4×Q8×C61C2311yescharacteristic
156C4×Q8×C61C2311yescharacteristic
157C4×D4×C61—22no—
158C4×D4×C61—22no—
159C4×D4×C61—21no—
160C4×D4×C61—21no—
161C4×D4×C61—21no—
162C4×D4×C61—21no—
163C4×D4×C61D411yescharacteristic
164C4×D4×C61C2311yescharacteristic
165#117×C61—22no—
166#117×C61—21no—
167#117×C61—21no—
168#117×C61D411yescharacteristic
169C2×C4⋊C4×C61—22no—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61D411yescharacteristic
173C2×C42×C61—22no—
174C2×C42×C61—21no—
175C2×C42×C61—21no—
176C2×C42×C61C2311yescharacteristic
177#41×C61—22no—
178#41×C61—22no—
179C2×Q8×C61—22no—
180C2×Q8×C61—22no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—22no—
184C2×Q8×C61—41no—
185C2×Q8×C61—42no—
186C2×Q8×C61—42no—
187C2×Q8×C61C2×D411yescharacteristic
188C2×Q8×C61C2×D411yescharacteristic
189C2×Q8×C61C2×D411yescharacteristic
190C2×Q8×C61C2×D412yes—
191C2×D4×C61—21no—
192C2×D4×C61C2×D411yescharacteristic
193C22×C4×C61—21no—
194C22×C4×C61—22no—
195C22×C4×C61—21no—
196C22×C4×C61—22no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C2×C22⋊D61—41no—
204#11758222—42no—
205#11758222—42no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×C4×D61—41no—
210C2×Dic122—21no—
211C4⋊C4×C61—22no—
212C4⋊C4×C61—22no—
213C4⋊C4×C61—22no—
214C4⋊C4×C61—22no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—22no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—22no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61C2×D411yescharacteristic
232C4⋊C4×C61C2×D411yescharacteristic
233C4⋊C4×C61C2×D411yescharacteristic
234C4⋊C4×C61C2×D411yescharacteristic
235C4⋊C4×C61C2×D412yes—
236C22⋊C4×C61—22no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C42×C61—22no—
243C42×C61—22no—
244C42×C61—21no—
245C42×C61—22no—
246C42×C61—21no—
247C42×C61—21no—
248C42×C61—21no—
249C42×C61—21no—
250C42×C61—21no—
251C42×C61—21no—
252C42×C61C2×D411yescharacteristic
253C42×C61C2×D411yescharacteristic
254C42×C61C2×D411yescharacteristic
255C42×C61C2411yescharacteristic
256#11758202—42no—
257#11758202—42no—
258#11758201—44no—
259#11758201—42no—
260#11758201—42no—
261#11758201—42no—
262#11758199—42no—
263#11758198—41no—
264#11758198—41no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267#11758194—42no—
268#11758194—42no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C23×C61—21no—
276C23×C61#12011yescharacteristic
277C22×D61—41no—
278Q8×C61—21no—
279Q8×C61—21no—
280Q8×C61—21no—
281Q8×C61—21no—
282Q8×C61—42no—
283Q8×C61—44no—
284Q8×C61—42no—
285Q8×C61—41no—
286Q8×C61—41no—
287Q8×C61—82no—
288Q8×C61AGL(1,ℤ/8)12yes—
289Q8×C61#13712yescomplemented
290D4×C61—24no—
291D4×C61—21no—
292D4×C61#13712yescomplemented
293C2×C4×C61—24no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—41no—
308C2×C4×C61—42no—
309C2×C4×C61—44no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—81no—
313C2×C4×C61—81no—
314C2×C4×C61—82no—
315C2×C4×C61#12011yescharacteristic
316C2×C4×C61#12011yescharacteristic
317C2×C4×C61#12011yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C22⋊D61—82no—
322C2×Dic61—41no—
323D244—42no—
324D244—41no—
325D244—41no—
326D244—41no—
327D244—41no—
328C4×D61—82no—
329Dic122—41no—
330Dic122—41no—
331#92418—22no—
332#92418—41no—
333#92418—41no—
334#92418—41no—
335#92418—41no—
336#92418—41no—
337#18556—611nomaximal, Sylow
338C22×C61—21no—
339C22×C61—22no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61C2×#12011yescharacteristic
345C2×D61—81no—
346C2×D61—81no—
347C2×D61—81no—
348C4×C61—21no—
349C4×C61—22no—
350C4×C61—21no—
351C4×C61—22no—
352C4×C61—21no—
353C4×C61—21no—
354C4×C61—41no—
355C4×C61—42no—
356C4×C61—41no—
357C4×C61—41no—
358C4×C61—42no—
359C4×C61—41no—
360C4×C61—41no—
361C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
362C4×C61C2×#13711yescharacteristic
363C4×C61C2×#13711yescharacteristic
364C4×C61#57511yescharacteristic
365Dic61—81no—
366Q8×#41D6111yescharacteristic, complemented
367#3182—611no—
368#3115—611no—
369#3037—611no—
370#1649—611no—
371#1648—611no—
372#1645—611no—
373#1644—611no—
374#1627—611no—
375#1626—611no—
376#1623—611no—
377#1622—611no—
378#1559—611no—
379#1491—611no—
380#1489—611no—
381C2×C61—41no—
382C2×C61—42no—
383C2×C61#300411yescharacteristic
384C2×C61#300611yescharacteristic
385C2×C61#301811yescharacteristic
386D61—161no—
387C2×#137—1221no—
388Q82C2×D6111yescharacteristic
389#557—21no—
390#557C2×D6111yescharacteristic
391#554—22no—
392#554—21no—
393#554—21no—
394#554C2×D6111yescharacteristic
395D4×Q8—21no—
396D4×Q8C2×D6111yescharacteristic
397#533—22no—
398#533—21no—
399#533—21no—
400#533C2×D6111yescharacteristic
401#532—611no—
402C4×#41—21no—
403C4×#41C2×D6111yescharacteristic
404C2×C4×Q8—21no—
405C2×C4×Q8C2×D6111yescharacteristic
406#500—611no—
407#492—611no—
408#487—611no—
409#486—611no—
410#482—1221no—
411#475—611no—
412#474—611no—
413#468—1222no—
414#464—1221no—
415#464—1221no—
416#462—611no—
417#462—611no—
418#460—611no—
419#460—611no—
420#460—611no—
421#459—611no—
422#449—1221no—
423#442—1221no—
424#440—1221no—
425#440—1222no—
426#432—611no—
427#423—611no—
428#417—1221no—
429C4×M16—611no—
430#333—611no—
431#333—611no—
432#332—611no—
433#332—611no—
434Q8⋊C8—611no—
435Q8⋊C8—611no—
436Q8⋊C8—611no—
437Q8⋊C8—611no—
438Q8⋊C8—611no—
439Q8⋊C8—611no—
440D4⋊C8—611no—
441D4⋊C8—611no—
442C61#1855611yescharacteristic, complemented, Sylow
443C2×#41—1221no—
444C2×#41C22⋊D6111yescharacteristic
445C22×Q8—21no—
446C22×Q8C22⋊D6111yescharacteristic
447#137—2444no—
448C2×Q16—1221no—
449C2×Q16—1221no—
450C2×SD16—1221no—
451C2×SD16—1221no—
452C2×SD16—1221no—
453C2×SD16—1222no—
454C2×D8—1221no—
455C2×M16—1221no—
456C2×M16—1221no—
457C4⋊Q8—22no—
458C4⋊Q8—21no—
459C4⋊Q8—22no—
460C4⋊Q8—21no—
461C4⋊Q8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—611no—
464C4⋊Q8C22×D6111yescharacteristic
465C4⋊Q8C22×D6111yescharacteristic
466#127—611no—
467#125—22no—
468#125—22no—
469#125—22no—
470#125—21no—
471#125—21no—
472#125—21no—
473#124—1221no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—21no—
480C22⋊Q8—22no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—22no—
484C22⋊Q8C22⋊D6112yes—
485#121—1221no—
486#121—1221no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—21no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8C22⋊D6111yescharacteristic
498C4×Q8C22⋊D6111yescharacteristic
499C4×Q8C22⋊D6111yescharacteristic
500C4×Q8C22⋊D6112yes—
501C4×Q8C22×D6111yescharacteristic
502C4×Q8C22×D6111yescharacteristic
503C4×Q8C22×D6111yescharacteristic
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—1221no—
511C4×D4—1221no—
512C4×D4C22⋊D6111yescharacteristic
513C4×D4C22×D6111yescharacteristic
514#117—22no—
515#117—21no—
516#117—21no—
517#117C22⋊D6111yescharacteristic
518C2×C4⋊C4—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4C22⋊D6111yescharacteristic
522C2×C42—22no—
523C2×C42—21no—
524C2×C42—21no—
525C2×C42C22×D6111yescharacteristic
526#107—1222no—
527#107—1221no—
528#106—1221no—
529C4⋊C8—611no—
530C4⋊C8—611no—
531C4⋊C8—611no—
532C4⋊C8—611no—
533C4⋊C8—1221no—
534#103—1221no—
535#103—1222no—
536#103—1221no—
537#103—1221no—
538#102—1221no—
539#102—1221no—
540#102—1221no—
541#102—1221no—
542#102—1222no—
543#102—1221no—
544C22⋊C8—1221no—
545#97—1221no—
546#97—1221no—
547C4×C8—611no—
548C4×C8—611no—
549#41—22no—
550#41—22no—
551#41—2442no—
552#41—2442no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—41no—
559C2×Q8—42no—
560C2×Q8—42no—
561C2×Q8—1221no—
562C2×Q8C2×C22⋊D6111yescharacteristic
563C2×Q8C2×C22⋊D6111yescharacteristic
564C2×Q8C2×C22⋊D6111yescharacteristic
565C2×Q8C2×C22⋊D6112yes—
566C2×D4—21no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—2441no—
571C2×D4C2×C22⋊D6111yescharacteristic
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—2441no—
580C22×C4C2×C22⋊D6111yescharacteristic
581C22×C4C2×C22⋊D6111yescharacteristic
582C22×C4C2×C22⋊D6111yescharacteristic
583Q16—2442no—
584Q16—2442no—
585SD16—2444no—
586SD16—2442no—
587SD16—2442no—
588SD16—2442no—
589D8—2442no—
590M16—2442no—
591M16—2442no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—22no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4C2×C22⋊D6111yescharacteristic
621C4⋊C4C2×C22⋊D6111yescharacteristic
622C4⋊C4C2×C22⋊D6111yescharacteristic
623C4⋊C4C2×C22⋊D6111yescharacteristic
624C4⋊C4C2×C22⋊D6112yes—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—2441no—
632C22⋊C4—2441no—
633C42—22no—
634C42—22no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—22no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42C2×C22⋊D6111yescharacteristic
644C42C2×C22⋊D6111yescharacteristic
645C42C2×C22⋊D6111yescharacteristic
646C42C23×D6111yescharacteristic
647C23—21no—
648C23—2441no—
649C23#1451974611yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—42no—
655Q8—42no—
656Q8—44no—
657Q8—41no—
658Q8—41no—
659Q8—82no—
660Q8—2441no—
661Q8—2441no—
662Q8#1451980212yes—
663Q8#1451980812yescomplemented
664D4—24no—
665D4—21no—
666D4—4882no—
667D4—2442no—
668D4—2441no—
669D4—2441no—
670D4—2441no—
671D4—2441no—
672D4#1451980812yescomplemented
673C2×C4—24no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—82no—
695C2×C4—4882no—
696C2×C4—2441no—
697C2×C4#1451974611yescharacteristic
698C2×C4#1451974611yescharacteristic
699C2×C4#1451974611yescharacteristic
700C2×C4C22×C22⋊D6111yescharacteristic
701C2×C4C22×C22⋊D6111yescharacteristic
702C2×C4C22×C22⋊D6111yescharacteristic
703C8—1222no—
704C8—2441no—
705C8—2441no—
706C8—2441no—
707C8—2441no—
708C8—2441no—
709C22—21no—
710C22—21no—
711C22—22no—
712C22—21no—
713C22—41no—
714C22—41no—
715C22—4881no—
716C22—4881no—
717C22—4881no—
718C22C2×#1451974611yescharacteristic
719C4—21no—
720C4—21no—
721C4—21no—
722C4—22no—
723C4—21no—
724C4—22no—
725C4—41no—
726C4—42no—
727C4—41no—
728C4—41no—
729C4—41no—
730C4—42no—
731C4—41no—
732C4—4881no—
733C4C2×#1451980211yescharacteristic
734C4C2×#1451980811yescharacteristic
735C4C2×#1451980811yescharacteristic
736C4#1684056011yescharacteristic
737C2—41no—
738C2—42no—
739C2—9761no—
740C2#2145505311yescharacteristic
741C2#2145507111yescharacteristic
742C2#2145516811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingQ8×#41×C61C2
socleC22×C61C2×#120
prime radical#21455970C2
hypercenterQ8×#41D61
hypocenterC61#18556
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. #21456538C2semidirect
3. #21455291C2semidirect
4. #21445068C2semidirect
5. #21445061C2semidirect
6. #21445040C2semidirect
7. #21445033C2semidirect
8. #21444922C2semidirect
9. #21444915C2semidirect
10. #21444897C2semidirect
11. #21444891C2semidirect
12. #21444549C2semidirect
13. #21444266C2semidirect
14. #21444258C2semidirect
15. Q8×#41×C61C2semidirect
289. Q8×C61#137semidirect
292. D4×C61#137semidirect
366. Q8×#41D61semidirect
442. C61#18556semidirect
663. Q8#14519808semidirect
672. D4#14519808semidirect

Maximal subgroups

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

subgroupindex
#214565382
#214559702
#214552912
#214450682
#214450612
#214450402
#214450332
#214449222
#214449152
#214448972
#214448912
#214445492
#214442662
#214442582
Q8×#41×C612
#1855661