Finite Group Databasebeta

← #30610808

Subgroups — #30610808

Order 15616.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462627C211yesmaximal, characteristic, complemented
2#21462519C211yesmaximal, characteristic, complemented
3#21461183C211yesmaximal, characteristic, complemented
4#21461177C211yesmaximal, characteristic, complemented
5#21461173C211yesmaximal, characteristic, complemented
6#21461159C211yesmaximal, characteristic, complemented
7#21461155C211yesmaximal, characteristic, complemented
8#21461151C211yesmaximal, characteristic, complemented
9#21461143C211yesmaximal, characteristic, complemented
10#21461137C211yesmaximal, characteristic, complemented
11#21461133C211yesmaximal, characteristic, complemented
12#21461119C211yesmaximal, characteristic, complemented
13#21461115C211yesmaximal, characteristic, complemented
14#21461111C211yesmaximal, characteristic, complemented
15#21459385C211yesmaximal, characteristic
16#16840813—21no—
17#16840796—21no—
18#16840792—21no—
19#16840792—21no—
20#16840787—21no—
21#16840787—21no—
22#16840784C2211yescharacteristic
23#16840784C2211yescharacteristic, complemented
24#16840781C2211yescharacteristic
25#16840781C2211yescharacteristic, complemented
26#16840781C2211yescharacteristic, complemented
27#16840780C2211yescharacteristic
28#16840780C2211yescharacteristic, complemented
29#16840766C2211yescharacteristic, complemented
30D61⋊(C4⋊C8)C2211yescharacteristic, complemented
31#16840737—21no—
32#16840727—21no—
33C4×#11758213C2211yescharacteristic
34C4×#11758213C2211yescharacteristic, complemented
35C4×D61⋊C8C2211yescharacteristic, complemented
36#16840612C2211yescharacteristic, complemented
37#16840612C2211yescharacteristic, complemented
38#16840612C2211yescharacteristic, complemented
39#16840612C2211yescharacteristic, complemented
40#16840612C2211yescharacteristic, complemented
41#16840612C2211yescharacteristic, complemented
42#16840612C2211yescharacteristic, complemented
43#16840612C2211yescharacteristic, complemented
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46#16840610C2211yescharacteristic
47#16840610C2211yescharacteristic
48D4⋊#92420C2211yescharacteristic
49D4⋊#92420C2211yescharacteristic
50D4⋊#92420C2211yescharacteristic
51D4⋊#92420C2211yescharacteristic
52#16840485C411yescharacteristic
53#16840478C411yescharacteristic
54#16840460—21no—
55#16840454—21no—
56#16840450C411yescharacteristic
57#16840450C411yescharacteristic
58#16840439—21no—
59#16840439—21no—
60#16840416C411yescharacteristic
61#16840407C411yescharacteristic
62#16840407C411yescharacteristic
63#16840317C2211yescharacteristic
64#16840298—21no—
65#16840298—21no—
66#16840297C2211yescharacteristic
67#16840297C2211yescharacteristic
68#16840275—21no—
69C4×#11758226C2211yescharacteristic
70C4×#11758224C2211yescharacteristic
71C4×#11758224C2211yescharacteristic
72C4×D4×D61C2211yescharacteristic
73C2×#14519735—21no—
74C61×#554C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758213—21no—
77C2×#11758213—21no—
78C2×D61⋊C8—21no—
79C2×D61⋊C8—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83C4⋊#92420—21no—
84C4⋊#92420—21no—
85C4⋊#92420C2311yescharacteristic
86C4⋊#92420C2311yescharacteristic
87C4⋊#92420C2311yescharacteristic
88C4⋊#92420C2311yescharacteristic
89#14519834—21no—
90#14519834—21no—
91#14519834—21no—
92#14519834—21no—
93#14519834—21no—
94#14519834—21no—
95#14519834—21no—
96#14519832—21no—
97#14519832—21no—
98#14519832—21no—
99#14519832—21no—
100C4×#92420—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420C2311yescharacteristic
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C2×#11758226D411yescharacteristic
108C2×#11758224C2×C411yescharacteristic
109C2×#11758224C2×C411yescharacteristic
110C2×D4×D61C2×C411yescharacteristic
111C22×C4×D61—21no—
112#14519777C2×C411yescharacteristic
113#14519772—21no—
114#14519772—21no—
115#14519772—21no—
116#14519772—21no—
117#14519772—21no—
118#14519772—21no—
119#14519768—21no—
120#14519768—21no—
121#14519768—21no—
122#14519766—21no—
123#14519766—21no—
124#14519765C2×C411yescharacteristic
125#14519765C2×C411yescharacteristic
126#14519762—21no—
127#14519762—21no—
128#14519762—21no—
129#14519762—21no—
130#14519761—21no—
131#14519761—21no—
132#14519761—21no—
133#14519761—21no—
134#14519757C2×C411yescharacteristic
135#14519757C2×C411yescharacteristic
136#14519757C2×C411yescharacteristic
137#14519757C2×C411yescharacteristic
138#14519753—21no—
139#14519753—21no—
140#14519752—21no—
141#14519752C2×C411yescharacteristic
142#14519752C2×C411yescharacteristic
143#14519751—21no—
144#14519751—21no—
145#14519751—21no—
146#14519747—21no—
147#14519747—21no—
148Q8×Dic61—21no—
149Q8×Dic61D411yescharacteristic
150C4×Dic122C2×C411yescharacteristic
151C4×Dic122C2×C411yescharacteristic
152#14519742C2311yescharacteristic
153#14519742C2311yescharacteristic
154C4×D244C2×C411yescharacteristic
155C4×D244C2×C411yescharacteristic
156C4×D244C2×C411yescharacteristic
157C4×D244C2×C411yescharacteristic
158D4×Dic61C2311yescharacteristic
159#14519739—21no—
160#14519739—21no—
161#14519739D411yescharacteristic
162#14519739D411yescharacteristic
163#14519739D411yescharacteristic
164#14519739C2311yescharacteristic
165C4×C22⋊D61—21no—
166C4×C22⋊D61—21no—
167C4×C22⋊D61—21no—
168#14519737—21no—
169#14519737—21no—
170#14519737—21no—
171#14519735—21no—
172#14519735—21no—
173#14519735—21no—
174#14519735—21no—
175#14519735—21no—
176#14519735—21no—
177#14519735—21no—
178#14519735C2×C411yescharacteristic
179#14519735C2×C411yescharacteristic
180#14519735D411yescharacteristic
181#14519735D411yescharacteristic
182#14519735D411yescharacteristic
183#14519733—21no—
184#14519733—21no—
185C2×C4⋊Dic61—21no—
186C4⋊C4×D61C2×C411yescharacteristic
187C2×#11758198—21no—
188C2×#11758198—21no—
189C22⋊C4×D61—21no—
190C2×C4×Dic61—21no—
191C2×C4×Dic61—21no—
192C42×D61C2311yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic
196#125×C61C2×C411yescharacteristic
197#125×C61C2×C411yescharacteristic
198C22⋊Q8×C61—21no—
199C22⋊Q8×C61—21no—
200C22⋊Q8×C61—21no—
201C4×Q8×C61C2×C411yescharacteristic
202C4×D4×C61C2×C411yescharacteristic
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61—21no—
206C23×D61—21no—
207C2×Q8×C61—21no—
208C2×Q8×C61C22⋊C411yescharacteristic
209C2×D4×C61C22×C411yescharacteristic
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219#11758226—41no—
220#11758226—41no—
221#11758224—22no—
222#11758224—22no—
223#11758224—41no—
224#11758224—41no—
225D4×D61—22no—
226D4×D61—41no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244C22⋊C411yescharacteristic
230C2×D244C22⋊C411yescharacteristic
231C2×D244C22⋊C411yescharacteristic
232C2×D244C22×C411yescharacteristic
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—42no—
237C2×C4×D61—42no—
238C2×C4×D61C22×C411yescharacteristic
239C2×C4×D61C22×C411yescharacteristic
240C2×C4×D61C22×C411yescharacteristic
241C2×C4×D61C2×D411yescharacteristic
242C2×C4×D61C2×D411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×Dic122C22×C411yescharacteristic
248C2×Dic122C22×C411yescharacteristic
249C2×#92420—21no—
250C2×#92420—21no—
251C2×#92420—21no—
252C2×#92420—21no—
253C2×#92420—21no—
254C2×#92420—21no—
255C2×#92420—21no—
256C2×#92420—21no—
257#11758213—42no—
258#11758213—42no—
259#11758213—42no—
260D61⋊C8—42no—
261D61⋊C8—42no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61C22⋊C411yescharacteristic
268C4⋊C4×C61C22⋊C411yescharacteristic
269C4⋊C4×C61C22⋊C411yescharacteristic
270C4⋊C4×C61C22×C411yescharacteristic
271C4⋊C4×C61C22×C411yescharacteristic
272C4⋊C4×C61C22×C411yescharacteristic
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C42×C61C22×C411yescharacteristic
277C42×C61C22×C411yescharacteristic
278C42×C61C22×C411yescharacteristic
279C22⋊Dic61—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198C22⋊C411yescharacteristic
295#11758198C22⋊C411yescharacteristic
296#11758198C22⋊C411yescharacteristic
297#11758198C22⋊C411yescharacteristic
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61C22⋊C411yescharacteristic
307C4⋊Dic61C22⋊C411yescharacteristic
308C4⋊Dic61C22⋊C411yescharacteristic
309C4⋊Dic61C22×C411yescharacteristic
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61—21no—
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2411yescharacteristic
328C23×C61—21no—
329C22×D61—21no—
330C22×D61—42no—
331C22×D61—42no—
332C22×D61—81no—
333C22×D61C2×C22⋊C411yescharacteristic
334C22×D61C2×C22⋊C411yescharacteristic
335C22×D61C2×C22⋊C411yescharacteristic
336Q8×C61—41no—
337Q8×C61—81no—
338D4×C61—21no—
339D4×C61#13112yes—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—42no—
344C2×C4×C61—81no—
345C2×C4×C61—81no—
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—42no—
354C22⋊D61—42no—
355C22⋊D61—42no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—42no—
360C2×Dic61—42no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61C2×C22⋊C411yescharacteristic
364C2×Dic61C2×C22⋊C411yescharacteristic
365C2×Dic61C2×C22⋊C411yescharacteristic
366C2×Dic61C22×D411yescharacteristic
367C2×Dic61C22×D411yescharacteristic
368D244—21no—
369D244—21no—
370D244—41no—
371D244—41no—
372D244—41no—
373D244—81no—
374D244—81no—
375C4×D61—21no—
376C4×D61—21no—
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—21no—
380C4×D61—21no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—21no—
385C4×D61—21no—
386C4×D61—21no—
387C4×D61—41no—
388C4×D61—41no—
389C4×D61—41no—
390C4×D61—42no—
391C4×D61—42no—
392C4×D61—41no—
393C4×D61—41no—
394Dic122—21no—
395Dic122—21no—
396Dic122—21no—
397Dic122—21no—
398#92420—22no—
399#92420—41no—
400#92420—41no—
401#92420—41no—
402#92420—41no—
403#92420—41no—
404#92420—41no—
405#92420—41no—
406#17513—611nomaximal, Sylow
407C22×C61—22no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61C22×C22⋊C411yescharacteristic
411C2×D61—21no—
412C2×D61—21no—
413C2×D61—21no—
414C2×D61—21no—
415C2×D61—21no—
416C2×D61—21no—
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—21no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—41no—
423C2×D61—84no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—41no—
431C4×C61—41no—
432C4×C61—41no—
433C4×C61C2×#13111yescharacteristic
434C4×C61#56811yescharacteristic
435Dic61—21no—
436Dic61—21no—
437Dic61—21no—
438Dic61—21no—
439Dic61—41no—
440Dic61—41no—
441Dic61—41no—
442Dic61#57511yescharacteristic
443Dic61#57511yescharacteristic
444#3475—611no—
445#2965—611no—
446#2925—611no—
447#1497—611no—
448#1495—611no—
449#1494—611no—
450#1490—611no—
451#1489—611no—
452#1488—611no—
453#1485—611no—
454#1483—611no—
455#1482—611no—
456#1478—611no—
457#1477—611no—
458#1476—611no—
459C2×C61—42no—
460C2×C61#288011yescharacteristic
461C2×C61#289611yescharacteristic
462C2×C61#290111yescharacteristic
463D61—41no—
464D61—41no—
465D61—41no—
466D61—81no—
467#556—611no—
468#555—611no—
469#554#692311yescharacteristic
470#553—1221no—
471#552—611no—
472#552—611no—
473#552—1221no—
474#551—1221no—
475#551—1221no—
476#547—611no—
477#546—611no—
478#546—611no—
479#533—611no—
480#529—611no—
481#529—611no—
482#529—1221no—
483#529—1221no—
484#525—1221no—
485C4×#41—611no—
486C4×#41—611no—
487C4×#41—611no—
488C2×C4×D4—611no—
489C2×#117—1221no—
490#446—1221no—
491#436—1221no—
492#435—1221no—
493#435—1221no—
494#433—1221no—
495#433—1221no—
496#432—611no—
497#432—611no—
498#431—611no—
499#431—611no—
500#431—611no—
501#431—611no—
502#431—611no—
503#423—611no—
504C2×C4⋊C8—611no—
505#408—1221no—
506#405—1221no—
507C4×M16—611no—
508C4×M16—611no—
509C2×C4×C8—611no—
510Q8⋊C8—611no—
511Q8⋊C8—611no—
512Q8⋊C8—611no—
513Q8⋊C8—611no—
514Q8⋊C8—611no—
515Q8⋊C8—611no—
516Q8⋊C8—611no—
517Q8⋊C8—611no—
518D4⋊C8—611no—
519D4⋊C8—611no—
520D4⋊C8—611no—
521D4⋊C8—611no—
522D4⋊C8—611no—
523D4⋊C8—611no—
524D4⋊C8—611no—
525D4⋊C8—611no—
526C61#1751311yescharacteristic, complemented, Sylow
527C2×#41—611no—
528C2×#41—611no—
529C2×#41—611no—
530C22×D4—611no—
531C23×C4—1221no—
532C2×M16—1221no—
533C2×M16—1221no—
534C2×M16—1221no—
535C22×C8—1221no—
536C22×C8—1221no—
537C4⋊Q8—611no—
538C4⋊Q8C2×#692311yescharacteristic
539#126—1221no—
540#126—1221no—
541#126—1221no—
542#126—1221no—
543#126—1221no—
544#126—1221no—
545#125—1221no—
546#125—1221no—
547#125—1221no—
548#125C2×#692311yescharacteristic
549#125C2×#692311yescharacteristic
550#124—611no—
551#124—611no—
552#124—1221no—
553#124—1221no—
554#123—1221no—
555#123—1221no—
556#123—1221no—
557#123—1221no—
558#123—1221no—
559#123—1221no—
560#123—1221no—
561#123—1221no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—611no—
566C22⋊Q8—611no—
567C22⋊Q8—611no—
568C22⋊Q8—611no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571#121—611no—
572#121—611no—
573#121—1221no—
574#121—1221no—
575#121—1221no—
576#121—1221no—
577#120—1221no—
578#120—1221no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—611no—
582C4×Q8—611no—
583C4×Q8—611no—
584C4×Q8—1221no—
585C4×Q8C2×#692311yescharacteristic
586C4×D4—611no—
587C4×D4—611no—
588C4×D4—611no—
589C4×D4—611no—
590C4×D4—611no—
591C4×D4—611no—
592C4×D4—611no—
593C4×D4—611no—
594C4×D4—611no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4—1221no—
598C4×D4—1221no—
599C4×D4—1221no—
600C4×D4—1221no—
601C4×D4—1221no—
602C4×D4—1221no—
603C4×D4C2×#692311yescharacteristic
604C4×D4C2×#692311yescharacteristic
605C4×D4C2×#692311yescharacteristic
606#117—611no—
607#117—611no—
608#117—611no—
609#117—611no—
610#117—611no—
611#117—1221no—
612#117—1221no—
613#117—1221no—
614#117—1221no—
615#117—1221no—
616#117—1221no—
617#117—1221no—
618#117—1221no—
619#117—1221no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C42—611no—
627C2×C42—611no—
628C2×C42—611no—
629C2×C42—1221no—
630C2×C42—1221no—
631C4⋊C8—611no—
632C4⋊C8—611no—
633C4⋊C8—611no—
634C4⋊C8—611no—
635C4⋊C8—1221no—
636C4⋊C8—1221no—
637C4⋊C8—1221no—
638C4⋊C8—1221no—
639C4⋊C8—1221no—
640C22⋊C8—1221no—
641C22⋊C8—1221no—
642C22⋊C8—1221no—
643C22⋊C8—1221no—
644C22⋊C8—1221no—
645C22⋊C8—1221no—
646C22⋊C8—1221no—
647#97—1221no—
648#97—1221no—
649#97—1221no—
650#97—1221no—
651C4×C8—611no—
652C4×C8—611no—
653C4×C8—611no—
654C4×C8—611no—
655C4×C8—1221no—
656C4×C8—1221no—
657C4×C8—1221no—
658C24—1221no—
659#41—1222no—
660#41—1222no—
661#41—2441no—
662#41—2441no—
663#41—2441no—
664#41—2441no—
665C2×Q8—21no—
666C2×Q8—611no—
667C2×Q8—611no—
668C2×Q8C22⋊#692311yescharacteristic
669C2×D4—611no—
670C2×D4—611no—
671C2×D4—611no—
672C2×D4—611no—
673C2×D4—1221no—
674C2×D4—1221no—
675C2×D4—1221no—
676C2×D4—1222no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4—2441no—
680C2×D4C22×#692311yescharacteristic
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—611no—
685C22×C4—611no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—2442no—
700C22×C4—2442no—
701M16—2442no—
702M16—2442no—
703M16—2442no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—2442no—
713C2×C8—2442no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—611no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—611no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4C22⋊#692311yescharacteristic
735C4⋊C4C22⋊#692311yescharacteristic
736C4⋊C4C22⋊#692311yescharacteristic
737C4⋊C4C22×#692311yescharacteristic
738C4⋊C4C22×#692311yescharacteristic
739C4⋊C4C22×#692311yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—611no—
744C22⋊C4—611no—
745C22⋊C4—611no—
746C22⋊C4—611no—
747C22⋊C4—611no—
748C22⋊C4—611no—
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—
761C22⋊C4—1221no—
762C22⋊C4—1221no—
763C22⋊C4—1221no—
764C42—611no—
765C42—611no—
766C42—611no—
767C42—611no—
768C42—611no—
769C42—611no—
770C42—611no—
771C42—1221no—
772C42—1221no—
773C42—1221no—
774C42—1221no—
775C42—1221no—
776C42—1221no—
777C42C22×#692311yescharacteristic
778C42C22×#692311yescharacteristic
779C42C22×#692311yescharacteristic
780C23—21no—
781C23—611no—
782C23—611no—
783C23—611no—
784C23—1221no—
785C23—4881no—
786C23—2442no—
787C23—2442no—
788Q8—41no—
789Q8—81no—
790Q8—1221no—
791Q8—1221no—
792Q8—1221no—
793Q8—1221no—
794D4—21no—
795D4—1221no—
796D4—1221no—
797D4—4881no—
798D4—4881no—
799D4—2441no—
800D4—2441no—
801D4—2441no—
802D4—2442no—
803D4—2442no—
804D4—2442no—
805D4#1451986512yes—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—42no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—611no—
813C2×C4—611no—
814C2×C4—611no—
815C2×C4—611no—
816C2×C4—611no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2441no—
835C2×C4—2442no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4—2442no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2442no—
842C2×C4—2442no—
843C2×C4C2×C22⋊#692311yescharacteristic
844C2×C4C2×C22⋊#692311yescharacteristic
845C2×C4C2×C22⋊#692311yescharacteristic
846C2×C4C2×C22⋊#692311yescharacteristic
847C2×C4C2×C22⋊#692311yescharacteristic
848C2×C4C2×C22⋊#692311yescharacteristic
849C2×C4C23×#692311yescharacteristic
850C8—1222no—
851C8—2441no—
852C8—2441no—
853C8—2441no—
854C8—2441no—
855C8—2441no—
856C8—2441no—
857C8—2441no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—1221no—
862C22—1221no—
863C22—1221no—
864C22—1221no—
865C22—1221no—
866C22—1221no—
867C22—1221no—
868C22—1221no—
869C22—1221no—
870C22—4884no—
871C22—2441no—
872C22—2441no—
873C22—2441no—
874C22C22×C22⋊#692311yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—611no—
885C4—611no—
886C4—1221no—
887C4—1221no—
888C4—1221no—
889C4—1221no—
890C4—2441no—
891C4—2441no—
892C4—2441no—
893C4C2×#1451986511yescharacteristic
894C4#1684084211yescharacteristic
895C2—42no—
896C2—4881no—
897C2—2441no—
898C2—2441no—
899C2—2441no—
900C2#2146240811yescharacteristic
901C2#2146243911yescharacteristic
902C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#554C4
socleC22×C61C22×C22⋊C4
prime radical#21459385C2
cosocleC4×Dic61C24
hypercenter#554#6923
hypocenterC61#17513
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #21462627C2semidirect
2. #21462519C2semidirect
3. #21461183C2semidirect
4. #21461177C2semidirect
5. #21461173C2semidirect
6. #21461159C2semidirect
7. #21461155C2semidirect
8. #21461151C2semidirect
9. #21461143C2semidirect
10. #21461137C2semidirect
11. #21461133C2semidirect
12. #21461119C2semidirect
13. #21461115C2semidirect
14. #21461111C2semidirect
23. #16840784C22semidirect
25. #16840781C22semidirect
26. #16840781C22semidirect
28. #16840780C22semidirect
29. #16840766C22semidirect
30. D61⋊(C4⋊C8)C22semidirect
34. C4×#11758213C22semidirect
35. C4×D61⋊C8C22semidirect
36. #16840612C22semidirect
37. #16840612C22semidirect
38. #16840612C22semidirect
39. #16840612C22semidirect
40. #16840612C22semidirect
41. #16840612C22semidirect
42. #16840612C22semidirect
43. #16840612C22semidirect
526. C61#17513semidirect

Maximal subgroups

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

subgroupindex
#214626272
#214625192
#214611832
#214611772
#214611732
#214611592
#214611552
#214611512
#214611432
#214611372
#214611332
#214611192
#214611152
#214611112
#214593852
#1751361