Finite Group Databasebeta

← #29647685

Subgroups — #29647685

Order 15616.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459559C211yesmaximal, characteristic
2#21454472C211yesmaximal, characteristic, complemented
3#21448676C211yesmaximal, characteristic, complemented
4#21444381C211yesmaximal, characteristic, complemented
5#21444372C211yesmaximal, characteristic
6#21444369C211yesmaximal, characteristic, complemented
7#21444354C211yesmaximal, characteristic, complemented
8#21444350C211yesmaximal, characteristic, complemented
9#21444344C211yesmaximal, characteristic, complemented
10#21444329C211yesmaximal, characteristic, complemented
11#21444320C211yesmaximal, characteristic
12#21444319C211yesmaximal, characteristic, complemented
13#21444302C211yesmaximal, characteristic, complemented
14#328×D61C211yesmaximal, characteristic, complemented
15C61×#1521C211yesmaximal, characteristic, complemented
16#16840479—21no—
17#16840471—21no—
18#16840451—21no—
19#16840449—21no—
20#16840448—21no—
21#16840445—21no—
22#16840441—21no—
23#16840435—21no—
24#16840392C411yescharacteristic, complemented
25#16840381C411yescharacteristic, complemented
26#16840377C411yescharacteristic, complemented
27#16840375C411yescharacteristic, complemented
28#16840370C411yescharacteristic, complemented
29#16840332C411yescharacteristic, complemented
30#16840319C2211yescharacteristic
31#16840314C2211yescharacteristic
32#16840293C2211yescharacteristic
33#16840272C2211yescharacteristic
34C22⋊Q8×D61C2211yescharacteristic
35#16840241C411yescharacteristic, complemented
36#16840238C411yescharacteristic, complemented
37C2×#14519734C2211yescharacteristic
38#16839822—21no—
39#16839821—21no—
40#16839819C2211yescharacteristic
41#16839816C2211yescharacteristic
42#16839812C2211yescharacteristic
43#16839787—21no—
44#16839724C2211yescharacteristic
45C22⋊C8×D61C2211yescharacteristic
46#16839716—21no—
47#16839649—21no—
48#16839644—21no—
49#16839636—21no—
50#16839626C2211yescharacteristic
51#16839624C2211yescharacteristic
52C4×C4⋊Dic61C2211yescharacteristic
53#16839609—21no—
54#16839607C2211yescharacteristic
55#95×D61C2211yescharacteristic
56#16839500C2211yescharacteristic
57#16839500C2211yescharacteristic
58#16839500C2211yescharacteristic
59#16839500C2211yescharacteristic
60#16839499C2211yescharacteristic
61#16839499C2211yescharacteristic
62#16839498C2211yescharacteristic
63#16839498C2211yescharacteristic
64#16839498C2211yescharacteristic
65#16839498C2211yescharacteristic
66#16839496C2211yescharacteristic
67#16839496C2211yescharacteristic
68C61×#529C2211yescharacteristic
69C61×#431C2211yescharacteristic
70C61×#383C2211yescharacteristic
71C61×#328C2211yescharacteristic
72C61×#328C2211yescharacteristic
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758224C2×C411yescharacteristic
76C2×Q8×D61C2×C411yescharacteristic
77C22×C4×D61—21no—
78C22×C4×D61C2311yescharacteristic
79C2×#11758189—21no—
80C2×C8×D61—21no—
81#14519777C2×C411yescharacteristic, complemented
82#14519777C2×C411yescharacteristic, complemented
83#14519776—21no—
84#14519776C2×C411yescharacteristic, complemented
85#14519775C2×C411yescharacteristic, complemented
86#14519772—21no—
87#14519772—21no—
88#14519772—21no—
89#14519771—21no—
90#14519770—21no—
91#14519770—21no—
92#14519770—21no—
93#14519769—21no—
94#14519769—21no—
95#14519768—21no—
96#14519768—21no—
97#14519768C2×C411yescharacteristic, complemented
98#14519767—21no—
99#14519767—21no—
100#14519767—21no—
101#14519764C2×C411yescharacteristic, complemented
102#14519763—21no—
103#14519763—21no—
104#14519761—21no—
105#14519760—21no—
106#14519759—21no—
107#14519759—21no—
108#14519759—21no—
109#14519758—21no—
110#14519757—21no—
111#14519757C2×C411yescharacteristic
112#14519757C2×C411yescharacteristic
113#14519756—21no—
114#14519756—21no—
115#14519756C2311yescharacteristic
116#14519756C2311yescharacteristic
117#14519755—21no—
118#14519755—21no—
119#14519754—21no—
120#14519754—21no—
121#14519754—21no—
122#14519754—21no—
123#14519754—21no—
124#14519753C2×C411yescharacteristic
125#14519748C2×C411yescharacteristic
126#14519745—21no—
127Q8×Dic61C2×C411yescharacteristic, complemented
128C4×Dic122—21no—
129C4×Dic122—21no—
130C4×Dic122C2×C411yescharacteristic, complemented
131C4×Dic122C2×C411yescharacteristic, complemented
132#14519742—21no—
133#14519742—21no—
134#14519742C2×C411yescharacteristic, complemented
135#14519742C2×C411yescharacteristic, complemented
136D4×Dic61—21no—
137D4×Dic61—21no—
138D4×Dic61C2×C411yescharacteristic, complemented
139C4×C22⋊D61—21no—
140#14519737—21no—
141#14519737—21no—
142#14519736—21no—
143#14519735—21no—
144#14519735C2×C411yescharacteristic
145#14519734—21no—
146#14519734C2×C411yescharacteristic
147#14519734C2×C411yescharacteristic
148#14519734C2×C411yescharacteristic
149#14519734C2×C411yescharacteristic
150#14519734D411yescharacteristic
151#14519734D411yescharacteristic
152#14519734D411yescharacteristic
153#14519734D411yescharacteristic
154#14519733—21no—
155#14519733—21no—
156#14519733—21no—
157C2×C4⋊Dic61—21no—
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196D411yescharacteristic
161C2×#11758196D411yescharacteristic
162C4⋊C4×D61—21no—
163C4⋊C4×D61C2×C411yescharacteristic
164C2×#11758198—21no—
165C2×#11758198D411yescharacteristic
166C2×#11758198D411yescharacteristic
167C22⋊C4×D61—21no—
168C2×C4×Dic61—21no—
169C2×C4×Dic61—21no—
170C2×C4×Dic61C2311yescharacteristic
171C4⋊#92418—21no—
172#14519706—21no—
173#14519706—21no—
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176#14519689—21no—
177#14519689—21no—
178#14519688—21no—
179#14519687—21no—
180C8×Dic61—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187#126×C61—21no—
188#125×C61C2×C411yescharacteristic, complemented
189#124×C61C2×C411yescharacteristic, complemented
190#123×C61—21no—
191C22⋊Q8×C61C2311yescharacteristic
192#121×C61C2311yescharacteristic
193C4×Q8×C61C2×C411yescharacteristic, complemented
194C4×D4×C61—21no—
195C4×D4×C61C2×C411yescharacteristic, complemented
196#117×C61—21no—
197C2×C42×C61C2311yescharacteristic
198C4⋊C8×C61—21no—
199C22⋊C8×C61C2311yescharacteristic
200C22⋊C8×C61C2311yescharacteristic
201C4×C8×C61—21no—
202#95×C61—21no—
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C23×D61C2×D411yescharacteristic
207C2×Q8×C61C22×C411yescharacteristic
208C2×D4×C61—21no—
209C2×D4×C61C22×C411yescharacteristic
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2411yescharacteristic
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225Q8×D61—42no—
226#11758224—42no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—81no—
233C2×C4×D61C22×C411yescharacteristic
234C2×C4×D61C22×C411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122C22×C411yescharacteristic
241C2×Dic122C22×C411yescharacteristic
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61C22×C411yescharacteristic
249C4⋊C4×C61C22×C411yescharacteristic
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C22⋊C4×C61—21no—
254C22⋊C4×C61—21no—
255C42×C61—21no—
256C42×C61C22×C411yescharacteristic
257C42×C61C22×C411yescharacteristic
258C42×C61C2×D411yescharacteristic
259C42×C61C2×D411yescharacteristic
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—21no—
265C22⋊Dic61—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—42no—
271#11758198C22⋊C411yescharacteristic
272#11758198C22⋊C411yescharacteristic
273#11758198C22⋊C411yescharacteristic
274#11758198C22⋊C411yescharacteristic
275#11758198C22⋊C411yescharacteristic
276#11758198C22⋊C411yescharacteristic
277#11758198C22⋊C411yescharacteristic
278#11758198C22⋊C411yescharacteristic
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—42no—
287C4⋊Dic61C22×C411yescharacteristic
288C4⋊Dic61C22×C411yescharacteristic
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—81no—
302#11758196C22⋊C411yescharacteristic
303#11758196C22⋊C411yescharacteristic
304#11758196C22⋊C411yescharacteristic
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309#11758196C22⋊C411yescharacteristic
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—42no—
317C4×Dic61—81no—
318C4×Dic61C22×C411yescharacteristic
319C4×Dic61C22×C411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C2×#92418—21no—
323C2×#92418—21no—
324#11758189—42no—
325C8×D61—42no—
326C23×C61—21no—
327C23×C61C22×D411yescharacteristic
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—22no—
331C22×D61—41no—
332C22×D61C2×C22⋊C411yescharacteristic
333C22×D61C2×C22⋊C411yescharacteristic
334Q8×C61—41no—
335D4×C61—41no—
336D4×C61—41no—
337D4×C61—41no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—81no—
352C2×C4×C61C2×C22⋊C411yescharacteristic
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C23×C411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C22⋊D61—42no—
359C22⋊D61—81no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—22no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—42no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—81no—
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C2×C22⋊C411yescharacteristic
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—41no—
385C4×D61—41no—
386C4×D61—42no—
387C4×D61—81no—
388C4×D61—84no—
389Dic122—42no—
390Dic122—41no—
391Dic122—41no—
392Dic122—81no—
393Dic122—81no—
394C8×C61—41no—
395C8×C61—41no—
396#92418—41no—
397#92418—41no—
398#17609—611nomaximal, Sylow
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61C22×C22⋊C411yescharacteristic
405C22×C61#57711yescharacteristic
406C22×C61#57811yescharacteristic
407C2×D61—21no—
408C2×D61—21no—
409C2×D61—21no—
410C2×D61—21no—
411C2×D61—21no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61#41012yes—
415C4×C61—21no—
416C4×C61—21no—
417C4×C61—21no—
418C4×C61—21no—
419C4×C61—21no—
420C4×C61—21no—
421C4×C61—41no—
422C4×C61—41no—
423C4×C61—41no—
424C4×C61—81no—
425C4×C61—81no—
426Dic61—21no—
427Dic61—21no—
428Dic61—21no—
429Dic61—21no—
430Dic61—21no—
431Dic61—21no—
432Dic61—42no—
433Dic61—41no—
434Dic61—41no—
435Dic61—41no—
436Dic61—41no—
437Dic61—81no—
438#3495—611no—
439#2924—611no—
440#2343—611no—
441#1521D6111yescharacteristic, complemented
442#1518—611no—
443#1516—611no—
444#1515—611no—
445#1512—611no—
446#1511—611no—
447#1509—611no—
448#1506—611no—
449#1504—611no—
450#1503—611no—
451#1500—611no—
452C2×#328—611no—
453C2×C61—21no—
454C2×C61—21no—
455C2×C61—81no—
456C2×C61C2×#41011yescharacteristic
457C2×C61#289811yescharacteristic
458C2×C61#290111yescharacteristic
459D61—22no—
460D61—41no—
461#556—1221no—
462#554—1221no—
463#552—1221no—
464#552—1221no—
465#552—1221no—
466#552—1221no—
467#551—1221no—
468#551—1221no—
469#544—611no—
470#542—611no—
471#542—611no—
472#541—611no—
473#541—611no—
474#536—611no—
475#533—611no—
476#533—611no—
477#529—611no—
478#529C2×D6111yescharacteristic
479#525—611no—
480C2×C22⋊Q8—611no—
481#520—611no—
482#519—611no—
483C2×#117—611no—
484#433—1221no—
485#433—1221no—
486#432—611no—
487#432—611no—
488#431—611no—
489#431C2×D6111yescharacteristic
490#424—1221no—
491#407—611no—
492C2×C22⋊C8—611no—
493#405—1221no—
494#387—1221no—
495#387—1221no—
496#385—1221no—
497#383C2×D6111yescharacteristic
498#382—611no—
499#381—611no—
500C4×C4⋊C4—611no—
501C4×C22⋊C4—1221no—
502#376—611no—
503C2×#95—611no—
504#328—611no—
505#328—611no—
506#328—611no—
507#328—611no—
508#328—611no—
509#328—611no—
510#328—611no—
511#328—611no—
512#328—611no—
513#328—611no—
514#328C2×D6111yescharacteristic
515#328C2×D6111yescharacteristic
516#327—611no—
517#327—611no—
518#327C2×D6111yescharacteristic
519#327C2×D6111yescharacteristic
520C61#1760911yescharacteristic, complemented, Sylow
521C2×#41—611no—
522C22×Q8—611no—
523C23×C4—611no—
524C23×C4—1221no—
525C2×M16—1221no—
526C22×C8—1221no—
527C4⋊Q8—611no—
528C4⋊Q8—611no—
529C4⋊Q8—611no—
530C4⋊Q8—611no—
531C4⋊Q8—1221no—
532#126—21no—
533#126—1221no—
534#126—1221no—
535#126—1221no—
536#126—1221no—
537#126—1221no—
538#126—1221no—
539#126—1221no—
540#125—611no—
541#125—1221no—
542#125—1221no—
543#125—1221no—
544#125—1221no—
545#125—1221no—
546#125—1221no—
547#125—1221no—
548#125C4×D6111yescharacteristic, complemented
549#124—611no—
550#124—1221no—
551#124—1221no—
552#124C4×D6111yescharacteristic, complemented
553#123—21no—
554#123—1221no—
555#123—1221no—
556#123—1221no—
557#123—1221no—
558#123—1221no—
559#123—1221no—
560C22⋊Q8—611no—
561C22⋊Q8—611no—
562C22⋊Q8—611no—
563C22⋊Q8—611no—
564C22⋊Q8—611no—
565C22⋊Q8—1221no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8—1221no—
574C22⋊Q8—1221no—
575C22⋊Q8C22×D6111yescharacteristic
576#121—611no—
577#121C22×D6111yescharacteristic
578#120—1221no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—611no—
582C4×Q8—611no—
583C4×Q8—611no—
584C4×Q8—1221no—
585C4×Q8—1221no—
586C4×Q8—1221no—
587C4×Q8—1221no—
588C4×Q8C4×D6111yescharacteristic, complemented
589C4×D4—21no—
590C4×D4—611no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4C4×D6111yescharacteristic, complemented
597#117—21no—
598#117—611no—
599#117—611no—
600#117—611no—
601#117—611no—
602#117—611no—
603#117—611no—
604#117—611no—
605#117—611no—
606#117—611no—
607#117—1221no—
608#117—1221no—
609#117—1221no—
610#117—1221no—
611#117—1221no—
612#117—1221no—
613C2×C4⋊C4—611no—
614C2×C4⋊C4—611no—
615C2×C4⋊C4—611no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4—1221no—
619C2×C4⋊C4—1221no—
620C2×C22⋊C4—611no—
621C2×C22⋊C4—611no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C42—611no—
625C2×C42—1221no—
626C2×C42—1221no—
627C2×C42C22×D6111yescharacteristic
628C4⋊C8—21no—
629C4⋊C8—1221no—
630C4⋊C8—1221no—
631C4⋊C8—1221no—
632C22⋊C8—611no—
633C22⋊C8—611no—
634C22⋊C8—1221no—
635C22⋊C8—1221no—
636C22⋊C8C22×D6111yescharacteristic
637C22⋊C8C22×D6111yescharacteristic
638#97—1221no—
639#97—1221no—
640C4×C8—21no—
641C4×C8—1221no—
642#95—21no—
643#95—21no—
644#95—611no—
645#95—611no—
646#95—1221no—
647#95—1221no—
648#95—1221no—
649#95—1221no—
650#95C22×D6111yescharacteristic
651#95C22×D6111yescharacteristic
652C24—611no—
653#41—2442no—
654C2×Q8—611no—
655C2×Q8—611no—
656C2×Q8—1221no—
657C2×Q8—1221no—
658C2×Q8—1221no—
659C2×Q8—2442no—
660C2×Q8C2×C4×D6111yescharacteristic
661C2×D4—21no—
662C2×D4—1221no—
663C2×D4—1221no—
664C2×D4C2×C4×D6111yescharacteristic
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—4881no—
682C22×C4—2442no—
683C22×C4—2442no—
684C22×C4—2442no—
685C22×C4D4×D6111yescharacteristic
686C22×C4D4×D6111yescharacteristic
687C22×C4C23×D6111yescharacteristic
688M16—2442no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—2442no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—611no—
699C4⋊C4—611no—
700C4⋊C4—611no—
701C4⋊C4—611no—
702C4⋊C4—611no—
703C4⋊C4—611no—
704C4⋊C4—611no—
705C4⋊C4—611no—
706C4⋊C4—611no—
707C4⋊C4—611no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—4881no—
728C4⋊C4—2442no—
729C4⋊C4C2×C4×D6111yescharacteristic
730C4⋊C4C2×C4×D6111yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—611no—
737C22⋊C4—611no—
738C22⋊C4—611no—
739C22⋊C4—611no—
740C22⋊C4—611no—
741C22⋊C4—611no—
742C22⋊C4—611no—
743C22⋊C4—611no—
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—2442no—
755C42—21no—
756C42—611no—
757C42—611no—
758C42—611no—
759C42—611no—
760C42—1221no—
761C42—1221no—
762C42—1221no—
763C42—1221no—
764C42—1221no—
765C42—1221no—
766C42—4881no—
767C42—2442no—
768C42C2×C4×D6111yescharacteristic
769C42C2×C4×D6111yescharacteristic
770C42D4×D6111yescharacteristic
771C42D4×D6111yescharacteristic
772C23—21no—
773C23—611no—
774C23—611no—
775C23—1222no—
776C23—1221no—
777C23—1221no—
778C23—2441no—
779C23C2×D4×D6111yescharacteristic
780Q8—41no—
781Q8—4881no—
782Q8—4881no—
783Q8—2441no—
784Q8—2441no—
785Q8—2442no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—4881no—
790D4—2442no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—81no—
805C2×C4—611no—
806C2×C4—611no—
807C2×C4—611no—
808C2×C4—611no—
809C2×C4—611no—
810C2×C4—611no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1222no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—4881no—
821C2×C4—4884no—
822C2×C4—4881no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2442no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2442no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4C22⋊C4×D6111yescharacteristic
835C2×C4C22⋊C4×D6111yescharacteristic
836C2×C4C22⋊C4×D6111yescharacteristic
837C2×C4C22⋊C4×D6111yescharacteristic
838C2×C4C22×C4×D6111yescharacteristic
839C2×C4C2×D4×D6111yescharacteristic
840C8—41no—
841C8—41no—
842C8—2441no—
843C8—2441no—
844C22—21no—
845C22—21no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—612no—
850C22—1221no—
851C22—1221no—
852C22—1221no—
853C22—1221no—
854C22—1221no—
855C22—2442no—
856C22—2442no—
857C22C2×C22⋊C4×D6111yescharacteristic
858C22#1684056911yescharacteristic
859C22#1684057611yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—81no—
870C4—81no—
871C4—1221no—
872C4—1221no—
873C4—1221no—
874C4—1221no—
875C4—1221no—
876C4—1221no—
877C4—4881no—
878C4—2442no—
879C4—2441no—
880C4—2441no—
881C4—2441no—
882C4—2441no—
883C2—21no—
884C2—21no—
885C2—81no—
886C2—1222no—
887C2—2441no—
888C2#410×D6111yescharacteristic
889C2#2145434811yescharacteristic
890C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1521C2
socleC22×C61C22×C22⋊C4
prime radical#16840272C22
cosocleC22×C4×C61C24
hypercenter#1521D61
hypocenterC61#17609
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1521

Complements

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

NH ≅ G/Ntype
2. #21454472C2semidirect
3. #21448676C2semidirect
4. #21444381C2semidirect
6. #21444369C2semidirect
7. #21444354C2semidirect
8. #21444350C2semidirect
9. #21444344C2semidirect
10. #21444329C2semidirect
12. #21444319C2semidirect
13. #21444302C2semidirect
14. #328×D61C2semidirect
15. C61×#1521C2semidirect
24. #16840392C4semidirect
25. #16840381C4semidirect
26. #16840377C4semidirect
27. #16840375C4semidirect
28. #16840370C4semidirect
29. #16840332C4semidirect
35. #16840241C4semidirect
36. #16840238C4semidirect
81. #14519777C2×C4semidirect
82. #14519777C2×C4semidirect
84. #14519776C2×C4semidirect
85. #14519775C2×C4semidirect
97. #14519768C2×C4semidirect
101. #14519764C2×C4semidirect
127. Q8×Dic61C2×C4semidirect
130. C4×Dic122C2×C4semidirect
131. C4×Dic122C2×C4semidirect
134. #14519742C2×C4semidirect
135. #14519742C2×C4semidirect
138. D4×Dic61C2×C4semidirect
188. #125×C61C2×C4semidirect
189. #124×C61C2×C4semidirect
193. C4×Q8×C61C2×C4semidirect
195. C4×D4×C61C2×C4semidirect
441. #1521D61semidirect
520. C61#17609semidirect
548. #125C4×D61semidirect
552. #124C4×D61semidirect
588. C4×Q8C4×D61semidirect
596. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214595592
#214544722
#214486762
#214443812
#214443722
#214443692
#214443542
#214443502
#214443442
#214443292
#214443202
#214443192
#214443022
#328×D612
C61×#15212
#1760961