Finite Group Databasebeta

← #30611629

Subgroups — #30611629

Order 15616.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462661C211yesmaximal, characteristic, complemented
2#21462507C211yesmaximal, characteristic, complemented
3#21461309C211yesmaximal, characteristic, complemented
4#21461305C211yesmaximal, characteristic, complemented
5#21461303C211yesmaximal, characteristic, complemented
6#21461299C211yesmaximal, characteristic, complemented
7#21461296C211yesmaximal, characteristic, complemented
8#21461294C211yesmaximal, characteristic, complemented
9#21461290C211yesmaximal, characteristic, complemented
10#21461286C211yesmaximal, characteristic, complemented
11#21461279C211yesmaximal, characteristic, complemented
12#21461279C211yesmaximal, characteristic, complemented
13#21461271C211yesmaximal, characteristic, complemented
14D61⋊#329C211yesmaximal, characteristic, complemented
15#21459783C211yesmaximal, characteristic
16#16840813—21no—
17#16840792—21no—
18#16840792—21no—
19#16840790—21no—
20#16840787—21no—
21#16840787—21no—
22#16840785C2211yescharacteristic, complemented
23#16840785C2211yescharacteristic, complemented
24#16840785C2211yescharacteristic, complemented
25#16840785C2211yescharacteristic, complemented
26#16840784C2211yescharacteristic, complemented
27#16840784C2211yescharacteristic, complemented
28#16840784C2211yescharacteristic, complemented
29#16840769—21no—
30#16840737—21no—
31C4×#11758213C2211yescharacteristic, complemented
32C4×#11758213C2211yescharacteristic, complemented
33#16840721C2211yescharacteristic, complemented
34#16840721C2211yescharacteristic, complemented
35#16840721C2211yescharacteristic, complemented
36#16840619C2211yescharacteristic, complemented
37#16840619C2211yescharacteristic, complemented
38#16840619C2211yescharacteristic, complemented
39#16840619C2211yescharacteristic, complemented
40#16840618C2211yescharacteristic, complemented
41#16840618C2211yescharacteristic, complemented
42#16840618C2211yescharacteristic, complemented
43#16840618C2211yescharacteristic, complemented
44#16840618C2211yescharacteristic, complemented
45#16840618C2211yescharacteristic, complemented
46#16840618C2211yescharacteristic, complemented
47#16840618C2211yescharacteristic, complemented
48#16840617C2211yescharacteristic
49#16840617C2211yescharacteristic
50#16840617C2211yescharacteristic
51#16840617C2211yescharacteristic
52#16840497C411yescharacteristic
53#16840475—21no—
54#16840437—21no—
55#16840437—21no—
56#16840427C411yescharacteristic
57#16840424C411yescharacteristic
58#16840424C411yescharacteristic
59#16840405C411yescharacteristic
60#16840405C411yescharacteristic
61#16840403—21no—
62D4×D244C411yescharacteristic
63#16840385—21no—
64#16840351—21no—
65#16840351—21no—
66#16840313C2211yescharacteristic
67#16840299C2211yescharacteristic
68#16840299C2211yescharacteristic
69#16840294C2211yescharacteristic
70#124×D61C2211yescharacteristic
71#124×D61C2211yescharacteristic
72#16840236—21no—
73C4×#11758226C2211yescharacteristic
74C61×#556C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758213—21no—
77C2×D61⋊C8—21no—
78C2×D61⋊C8—21no—
79C2×D61⋊C8—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84C4⋊#92420—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834—21no—
91#14519834—21no—
92#14519834—21no—
93#14519834—21no—
94#14519832—21no—
95#14519832—21no—
96#14519832—21no—
97#14519832C2311yescharacteristic
98#14519832C2311yescharacteristic
99#14519832C2311yescharacteristic
100#14519832C2311yescharacteristic
101#14519832C2311yescharacteristic
102#14519832C2311yescharacteristic
103#14519832C2311yescharacteristic
104#14519832C2311yescharacteristic
105C4×#92420—21no—
106C4×#92420—21no—
107C2×#11758226C2×C411yescharacteristic
108C2×#11758226C2×C411yescharacteristic
109C2×#11758226D411yescharacteristic
110C2×Q8×D61C2×C411yescharacteristic
111C2×Q8×D61C2×C411yescharacteristic
112C22×D244—21no—
113C2×D4×D61C2×C411yescharacteristic
114C2×D4×D61C2×C411yescharacteristic
115#14519776—21no—
116#14519774C2×C411yescharacteristic
117#14519772—21no—
118#14519772—21no—
119#14519770—21no—
120#14519768C2311yescharacteristic
121#14519766—21no—
122#14519766C2311yescharacteristic
123#14519766C2311yescharacteristic
124#14519765—21no—
125#14519765—21no—
126#14519765C2×C411yescharacteristic
127#14519765C2×C411yescharacteristic
128#14519764C2311yescharacteristic
129#14519763—21no—
130#14519763—21no—
131#14519763—21no—
132#14519763—21no—
133#14519762—21no—
134#14519762—21no—
135#14519762—21no—
136#14519762—21no—
137#14519759—21no—
138#14519759—21no—
139#14519759—21no—
140#14519757—21no—
141#14519757—21no—
142#14519757C2×C411yescharacteristic
143#14519755—21no—
144#14519755—21no—
145#14519753C2×C411yescharacteristic
146#14519753C2×C411yescharacteristic
147#14519752—21no—
148#14519752—21no—
149#14519752—21no—
150#14519752—21no—
151#14519752C2×C411yescharacteristic
152#14519752C2×C411yescharacteristic
153#14519751—21no—
154#14519750—21no—
155#14519750—21no—
156#14519748C2×C411yescharacteristic
157#14519747—21no—
158#14519747—21no—
159#14519747—21no—
160#14519747—21no—
161Q8×Dic61D411yescharacteristic
162C4×Dic122C2×C411yescharacteristic
163C4×D244—21no—
164C4×D244—21no—
165C4×D244—21no—
166C4×D244—21no—
167C4×D244C2×C411yescharacteristic
168C4×D244C2×C411yescharacteristic
169C4×D244C2×C411yescharacteristic
170C4×D244C2×C411yescharacteristic
171C4×D244C2×C411yescharacteristic
172#14519739—21no—
173#14519739—21no—
174#14519739—21no—
175#14519739—21no—
176#14519739D411yescharacteristic
177#14519739D411yescharacteristic
178#14519739D411yescharacteristic
179C4×C22⋊D61—21no—
180#14519736—21no—
181#14519735D411yescharacteristic
182#14519735D411yescharacteristic
183#14519735D411yescharacteristic
184#14519734—21no—
185#14519734—21no—
186C22⋊C4×D61—21no—
187C22⋊C4×D61—21no—
188C22⋊C4×D61—21no—
189C22⋊C4×D61—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C42×D61C2311yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic
196#126×C61—21no—
197#126×C61—21no—
198#124×C61C2×C411yescharacteristic
199#124×C61C2×C411yescharacteristic
200C22⋊Q8×C61—21no—
201C4×Q8×C61C2×C411yescharacteristic
202C4×Q8×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205#117×C61—21no—
206C23×D61—21no—
207C23×D61—21no—
208C2×Q8×C61C22⋊C411yescharacteristic
209C2×Q8×C61C22×C411yescharacteristic
210C2×Q8×C61C22×C411yescharacteristic
211C2×D4×C61C22×C411yescharacteristic
212C22×C4×C61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216#11758226—42no—
217#11758226—81no—
218#11758226—81no—
219Q8×D61—81no—
220Q8×D61—81no—
221D4×D61—81no—
222D4×D61—81no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—44no—
230C2×D244C22⋊C411yescharacteristic
231C2×D244C22⋊C411yescharacteristic
232C2×D244C22⋊C411yescharacteristic
233C2×D244C22×C411yescharacteristic
234C2×D244C22×C411yescharacteristic
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61C22×C411yescharacteristic
242C2×C4×D61C22×C411yescharacteristic
243C2×C4×D61C22×C411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×C4×D61C2×D411yescharacteristic
248C2×C4×D61C2×D411yescharacteristic
249C2×C4×D61C2×D411yescharacteristic
250C2×Dic122—21no—
251C2×Dic122—21no—
252C2×Dic122C22×C411yescharacteristic
253C2×#92420—21no—
254C2×#92420—21no—
255C2×#92420—21no—
256C2×#92420—21no—
257C2×#92420—21no—
258C2×#92420—21no—
259C2×#92420—21no—
260C2×#92420—21no—
261#11758213—42no—
262#11758213—42no—
263D61⋊C8—42no—
264D61⋊C8—42no—
265D61⋊C8—42no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61C22⋊C411yescharacteristic
271C4⋊C4×C61C22⋊C411yescharacteristic
272C4⋊C4×C61C22⋊C411yescharacteristic
273C4⋊C4×C61C22×C411yescharacteristic
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C22⋊C4×C61—21no—
279C42×C61—21no—
280C42×C61—21no—
281C42×C61C22×C411yescharacteristic
282C42×C61C22×C411yescharacteristic
283C42×C61C22×C411yescharacteristic
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198C22⋊C411yescharacteristic
303#11758198C22⋊C411yescharacteristic
304#11758198C22⋊C411yescharacteristic
305#11758198C22⋊C411yescharacteristic
306#11758198C22⋊C411yescharacteristic
307#11758198C22⋊C411yescharacteristic
308C4⋊Dic61—21no—
309C4⋊Dic61—21no—
310C4⋊Dic61C22⋊C411yescharacteristic
311C4⋊Dic61C22⋊C411yescharacteristic
312C4⋊Dic61C22⋊C411yescharacteristic
313C4⋊Dic61C22×C411yescharacteristic
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318C4×Dic61—21no—
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2411yescharacteristic
326C23×C61—21no—
327C22×D61—21no—
328C22×D61—21no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—81no—
332C22×D61—81no—
333C22×D61—81no—
334C22×D61—81no—
335C22×D61C2×C22⋊C411yescharacteristic
336C22×D61C2×C22⋊C411yescharacteristic
337C22×D61C2×C22⋊C411yescharacteristic
338Q8×C61—41no—
339Q8×C61—41no—
340Q8×C61—41no—
341D4×C61—41no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—42no—
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C2×C22⋊C411yescharacteristic
352C2×C4×C61C23×C411yescharacteristic
353C22⋊D61—81no—
354C22⋊D61—81no—
355C22⋊D61—81no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61C2×C22⋊C411yescharacteristic
359C2×Dic61C2×C22⋊C411yescharacteristic
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C22×D411yescharacteristic
362C2×Dic61C22×D411yescharacteristic
363D244—22no—
364D244—22no—
365D244—41no—
366D244—41no—
367D244—41no—
368D244—42no—
369D244—42no—
370D244—42no—
371D244—81no—
372D244—81no—
373D244—81no—
374C4×D61—22no—
375C4×D61—41no—
376C4×D61—41no—
377C4×D61—41no—
378C4×D61—41no—
379C4×D61—41no—
380C4×D61—41no—
381C4×D61—41no—
382C4×D61—41no—
383C4×D61—81no—
384C4×D61—81no—
385C4×D61—81no—
386C4×D61—81no—
387C4×D61—81no—
388C4×D61—81no—
389Dic122—41no—
390Dic122—81no—
391Dic122—81no—
392#92420—22no—
393#92420—41no—
394#92420—41no—
395#92420—41no—
396#92420—41no—
397#92420—41no—
398#92420—41no—
399#92420—41no—
400#17679—611nomaximal, Sylow
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61C22×C22⋊C411yescharacteristic
405C2×D61—21no—
406C2×D61—21no—
407C2×D61—21no—
408C2×D61—21no—
409C2×D61—21no—
410C2×D61—21no—
411C2×D61—21no—
412C2×D61—21no—
413C2×D61—41no—
414C2×D61—41no—
415C2×D61—41no—
416C2×D61—41no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—162no—
420C2×D61—162no—
421C2×D61#42112yes—
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—21no—
429C4×C61—41no—
430C4×C61—41no—
431C4×C61—41no—
432Dic61—21no—
433Dic61—21no—
434Dic61—21no—
435Dic61—21no—
436Dic61—21no—
437Dic61—41no—
438Dic61—41no—
439#3514—611no—
440#2970—611no—
441#2923—611no—
442#1536—611no—
443#1535—611no—
444#1535—611no—
445#1533—611no—
446#1532—611no—
447#1532—611no—
448#1530—611no—
449#1529—611no—
450#1527—611no—
451#1527—611no—
452#1524—611no—
453C2×#329—611no—
454C2×C61—81no—
455C2×C61#288811yescharacteristic
456C2×C61C2×#42111yescharacteristic
457C2×C61#290111yescharacteristic
458D61—22no—
459D61—41no—
460D61—41no—
461D61—81no—
462D61—81no—
463#559—611no—
464#556#692311yescharacteristic
465#555—1221no—
466#551—1221no—
467#551—1221no—
468D4×Q8—611no—
469#548—611no—
470#548—611no—
471#546—611no—
472#546—611no—
473#546—1221no—
474D42—611no—
475#542—1221no—
476#538—1221no—
477#538—1221no—
478#532—611no—
479#529—611no—
480#529—611no—
481#529—611no—
482C2×#124—611no—
483C2×#124—611no—
484#518—1221no—
485C4×#41—611no—
486#446—1221no—
487#435—1221no—
488#435—1221no—
489C8×D4—1221no—
490#433—1221no—
491#433—1221no—
492#432—611no—
493#432—611no—
494#432—611no—
495#432—611no—
496#432—611no—
497#432—611no—
498#432—611no—
499#424—1221no—
500#408—1221no—
501C4×M16—611no—
502C4×M16—611no—
503C2×#97—611no—
504C2×#97—611no—
505C2×#97—611no—
506#330—611no—
507#330—611no—
508#330—611no—
509#330—611no—
510#329—611no—
511#329—611no—
512#329—611no—
513#329—611no—
514#329—611no—
515#329—611no—
516#329—611no—
517#329—611no—
518#329—611no—
519#329—611no—
520#329—611no—
521#329—611no—
522C61#1767911yescharacteristic, complemented, Sylow
523C2×#41—611no—
524C2×#41—611no—
525C2×#41—611no—
526C22×Q8—611no—
527C22×Q8—611no—
528C22×D4—611no—
529C22×D4—611no—
530C22×D4—1221no—
531C2×M16—1221no—
532C2×M16—1221no—
533C22×C8—1221no—
534C22×C8—1221no—
535C22×C8—1221no—
536C4⋊Q8—1221no—
537C4⋊Q8C2×#692311yescharacteristic
538#127—611no—
539#126—21no—
540#126—21no—
541#126—1221no—
542#126—1221no—
543#126—1221no—
544#125—611no—
545#124—611no—
546#124—611no—
547#124—611no—
548#124—611no—
549#124—611no—
550#124—1221no—
551#124—1221no—
552#124—1221no—
553#124—1221no—
554#124—1221no—
555#124—1221no—
556#124—1221no—
557#124C2×#692311yescharacteristic
558#124C2×#692311yescharacteristic
559#123—1221no—
560#123—1221no—
561#123—1221no—
562#123—1221no—
563#123—1221no—
564#123—1221no—
565#123—1221no—
566C22⋊Q8—21no—
567C22⋊Q8—611no—
568C22⋊Q8—611no—
569C22⋊Q8—611no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8—1221no—
574#121—611no—
575#121—611no—
576#121—611no—
577#121—1221no—
578#121—1221no—
579#121—1221no—
580#121—1221no—
581#121—1221no—
582#121—1221no—
583#121—1221no—
584#120—1221no—
585#120—1221no—
586#120—1221no—
587#120—1221no—
588C4×Q8—611no—
589C4×Q8—611no—
590C4×Q8C2×#692311yescharacteristic
591C4×Q8C2×#692311yescharacteristic
592C4×Q8C2×#692311yescharacteristic
593C4×D4—611no—
594C4×D4—611no—
595C4×D4—611no—
596C4×D4—611no—
597C4×D4—611no—
598C4×D4—611no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—1221no—
602C4×D4—1221no—
603C4×D4—1221no—
604C4×D4—1221no—
605C4×D4—1221no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4C2×#692311yescharacteristic
611#117—21no—
612#117—611no—
613#117—611no—
614#117—611no—
615#117—1221no—
616#117—1221no—
617#117—1221no—
618C2×C22⋊C4—1221no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C42—611no—
625C2×C42—611no—
626C2×C42—611no—
627C4⋊C8—1221no—
628C4⋊C8—1221no—
629C4⋊C8—1221no—
630C4⋊C8—1221no—
631C4⋊C8—1221no—
632C4⋊C8—1221no—
633C4⋊C8—1221no—
634C22⋊C8—1221no—
635C22⋊C8—1221no—
636C22⋊C8—1221no—
637C22⋊C8—1221no—
638C22⋊C8—1221no—
639C22⋊C8—1221no—
640C22⋊C8—1221no—
641#97—611no—
642#97—611no—
643#97—611no—
644#97—611no—
645#97—611no—
646#97—611no—
647#97—611no—
648#97—611no—
649#97—1221no—
650#97—1221no—
651#97—1221no—
652C4×C8—1221no—
653C4×C8—1221no—
654C24—1221no—
655C24—1221no—
656#41—4881no—
657#41—4881no—
658#41—2442no—
659C2×Q8—611no—
660C2×Q8—1221no—
661C2×Q8—1221no—
662C2×Q8—4881no—
663C2×Q8—4881no—
664C2×Q8C22⋊#692311yescharacteristic
665C2×Q8C22×#692311yescharacteristic
666C2×Q8C22×#692311yescharacteristic
667C2×D4—611no—
668C2×D4—611no—
669C2×D4—611no—
670C2×D4—611no—
671C2×D4—611no—
672C2×D4—1221no—
673C2×D4—1221no—
674C2×D4—1221no—
675C2×D4—1221no—
676C2×D4—1221no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—4881no—
682C2×D4—4881no—
683C2×D4—2444no—
684C2×D4C22×#692311yescharacteristic
685C22×C4—21no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701M16—2442no—
702M16—2442no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—2442no—
712C2×C8—2442no—
713C2×C8—2442no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—611no—
719C4⋊C4—611no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4C22⋊#692311yescharacteristic
729C4⋊C4C22⋊#692311yescharacteristic
730C4⋊C4C22⋊#692311yescharacteristic
731C4⋊C4C22×#692311yescharacteristic
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—611no—
738C22⋊C4—611no—
739C22⋊C4—611no—
740C22⋊C4—611no—
741C22⋊C4—611no—
742C22⋊C4—611no—
743C22⋊C4—1221no—
744C22⋊C4—1221no—
745C22⋊C4—1221no—
746C22⋊C4—1221no—
747C22⋊C4—1221no—
748C22⋊C4—1221no—
749C22⋊C4—1221no—
750C22⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—1221no—
757C22⋊C4—1221no—
758C22⋊C4—1221no—
759C22⋊C4—1221no—
760C22⋊C4—1221no—
761C42—21no—
762C42—21no—
763C42—611no—
764C42—611no—
765C42—611no—
766C42—611no—
767C42—611no—
768C42—611no—
769C42—611no—
770C42—1221no—
771C42C22×#692311yescharacteristic
772C42C22×#692311yescharacteristic
773C42C22×#692311yescharacteristic
774C23—21no—
775C23—611no—
776C23—611no—
777C23—611no—
778C23—1221no—
779C23—1221no—
780C23—4881no—
781C23—4881no—
782C23—4881no—
783C23—4881no—
784C23—2442no—
785C23—2442no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—4881no—
790Q8—4881no—
791Q8—2441no—
792D4—41no—
793D4—1222no—
794D4—1222no—
795D4—4881no—
796D4—4881no—
797D4—4881no—
798D4—4881no—
799D4—4881no—
800D4—4881no—
801D4—2441no—
802D4—2441no—
803D4—2441no—
804D4—2442no—
805D4—2442no—
806D4—2442no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—42no—
811C2×C4—611no—
812C2×C4—611no—
813C2×C4—611no—
814C2×C4—611no—
815C2×C4—611no—
816C2×C4—1222no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—4881no—
820C2×C4—4881no—
821C2×C4—4881no—
822C2×C4—4881no—
823C2×C4—4881no—
824C2×C4—4881no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4C2×C22⋊#692311yescharacteristic
834C2×C4C2×C22⋊#692311yescharacteristic
835C2×C4C2×C22⋊#692311yescharacteristic
836C2×C4C2×C22⋊#692311yescharacteristic
837C2×C4C2×C22⋊#692311yescharacteristic
838C2×C4C2×C22⋊#692311yescharacteristic
839C2×C4C23×#692311yescharacteristic
840C8—1222no—
841C8—2441no—
842C8—2441no—
843C8—2441no—
844C8—2441no—
845C8—2441no—
846C8—2441no—
847C8—2441no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—612no—
852C22—1221no—
853C22—1221no—
854C22—1221no—
855C22—1221no—
856C22—1221no—
857C22—1221no—
858C22—1221no—
859C22—1221no—
860C22—9762no—
861C22—9762no—
862C22—2441no—
863C22—2441no—
864C22—2441no—
865C22—2441no—
866C22—2441no—
867C22—2441no—
868C22C22×C22⋊#692311yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—1221no—
880C4—1221no—
881C4—1221no—
882C4—1221no—
883C4—1221no—
884C4—2441no—
885C4—2441no—
886C2—81no—
887C2—1222no—
888C2—4881no—
889C2—4881no—
890C2—2441no—
891C2—2441no—
892C2#2146243011yescharacteristic
893C2D61⋊#42111yescharacteristic
894C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#556C4
socleC22×C61C22×C22⋊C4
prime radical#21459783C2
cosocleC4×Dic61C24
hypercenter#556#6923
hypocenterC61#17679
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #21462661C2semidirect
2. #21462507C2semidirect
3. #21461309C2semidirect
4. #21461305C2semidirect
5. #21461303C2semidirect
6. #21461299C2semidirect
7. #21461296C2semidirect
8. #21461294C2semidirect
9. #21461290C2semidirect
10. #21461286C2semidirect
11. #21461279C2semidirect
12. #21461279C2semidirect
13. #21461271C2semidirect
14. D61⋊#329C2semidirect
22. #16840785C22semidirect
23. #16840785C22semidirect
24. #16840785C22semidirect
25. #16840785C22semidirect
26. #16840784C22semidirect
27. #16840784C22semidirect
28. #16840784C22semidirect
31. C4×#11758213C22semidirect
32. C4×#11758213C22semidirect
33. #16840721C22semidirect
34. #16840721C22semidirect
35. #16840721C22semidirect
36. #16840619C22semidirect
37. #16840619C22semidirect
38. #16840619C22semidirect
39. #16840619C22semidirect
40. #16840618C22semidirect
41. #16840618C22semidirect
42. #16840618C22semidirect
43. #16840618C22semidirect
44. #16840618C22semidirect
45. #16840618C22semidirect
46. #16840618C22semidirect
47. #16840618C22semidirect
522. C61#17679semidirect

Maximal subgroups

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

subgroupindex
#214626612
#214625072
#214613092
#214613052
#214613032
#214612992
#214612962
#214612942
#214612902
#214612862
#214612792
#214612712
D61⋊#3292
#214597832
#1767961