Finite Group Databasebeta

← #7688349

Subgroups — #7688349

Order 512.

4709 conjugacy classes of subgroups.

The subgroup lattice has 1107 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59876C214yesmaximal, complemented
2#59863C212yesmaximal, complemented
3#59863C211yesmaximal, characteristic, complemented
4#59717C214yesmaximal, complemented
5#59640C212yesmaximal
6#59211C212yesmaximal, complemented
7#45262C214yesmaximal, complemented
8#44117C218yesmaximal, complemented
9#40020C214yesmaximal, complemented
10#39515C212yesmaximal, complemented
11#39249C214yesmaximal, complemented
12#39125C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36590C212yesmaximal, complemented
15#36559C211yesmaximal, characteristic, complemented
16#36535C212yesmaximal, complemented
17#36534C212yesmaximal, complemented
18#36301C212yesmaximal, complemented
19#36194C211yesmaximal, characteristic, complemented
20#35774C214yesmaximal, complemented
21#34954C212yesmaximal, complemented
22#34934C211yesmaximal, characteristic
23#34317C212yesmaximal, complemented
24#34242C212yesmaximal, complemented
25C4×Q82C211yesmaximal, characteristic, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×Q82C2211yescharacteristic
28C2×#556C2211yescharacteristic
29C2×#554C2212yes—
30C2×#529C2212yes—
31#2868C2211yescharacteristic
32#2864C2214yes—
33#2862C2212yes—
34#2861C2214yes—
35#2859C2212yes—
36#2857C2212yes—
37#2808C2218yes—
38#2808C2214yes—
39#2803C2218yes—
40#2800C2218yes—
41#2798C2218yes—
42#2795C2218yes—
43#2793C2218yes—
44#2779C2218yes—
45#2759C2218yes—
46#2716C2218yes—
47#2674C2218yes—
48#2649C2218yes—
49#2628C2214yes—
50#2594C2218yes—
51#2594C2218yes—
52#2593C2218yes—
53#2592C2218yes—
54#2592C2214yes—
55#2592C2214yes—
56#2590C2218yes—
57#2588C2218yes—
58#2582C2212yes—
59#2581C2214yes—
60#2573C2218yes—
61#2571C2212yes—
62#2571C2212yes—
63#2570C2214yes—
64#2570C2214yes—
65#2568C2212yes—
66#2566C2214yes—
67#2565C2214yes—
68#2563C2212yes—
69#2563C2212yes—
70#2563C2212yes—
71#2560C2218yes—
72#2560C2218yes—
73#2554C2214yes—
74#2552C2211yescharacteristic
75#2550C2214yes—
76#2548C2214yes—
77#2548C2211yescharacteristic
78#2548C2212yes—
79#2547C2212yes—
80#2547C2214yes—
81#2544C2214yes—
82#2541C2211yescharacteristic
83#2538C2212yes—
84#2538C2212yes—
85#2538C2211yescharacteristic
86#2538C2212yes—
87#2536C2214yes—
88#2536C2214yes—
89#2527C2218yes—
90#2525C2218yes—
91#2525C2218yes—
92#2523C2218yes—
93#2514C2214yes—
94#2513C2214yes—
95#2513C2214yes—
96#2513C2214yes—
97#2513C2214yes—
98#2512C2212yes—
99#2511C2214yes—
100#2500C2214yes—
101#2497C2214yes—
102#2495C2214yes—
103#2494C2214yes—
104#2494C2214yes—
105#2492C2214yes—
106#2491C2214yes—
107#2490C2212yes—
108#2485C2214yes—
109#2485C2214yes—
110#2485C2214yes—
111#2477C2218yes—
112#2474C2218yes—
113#2459C2218yes—
114#2452C2214yes—
115#2452C2214yes—
116#2448C2214yes—
117#2448C2214yes—
118#2446C2214yes—
119#2445C2212yes—
120#2439C2214yes—
121#2426C2212yes—
122#2421C2214yes—
123#2420C2214yes—
124#2395C2218yes—
125#2392C2214yes—
126#2373C2214yes—
127#2373C2218yes—
128#2370C2214yes—
129#2369C2212yes—
130#2369C2212yes—
131#2369C2214yes—
132#2369C2212yes—
133#2369C2211yescharacteristic
134#2367C2212yes—
135#2365C2212yes—
136#2365C2211yescharacteristic
137#2363C2214yes—
138#2362C2218yes—
139#2362C2214yes—
140#2362C2214yes—
141#2362C2212yes—
142#2357C2214yes—
143#2356C2212yes—
144#2355C2211yescharacteristic
145#2355C2212yes—
146#2355C2214yes—
147#2355C2212yes—
148#2355C2212yes—
149#2355C2212yes—
150#2354C2212yes—
151#2354C2212yes—
152#2354C2212yes—
153#2354C2211yescharacteristic
154#2354C2214yes—
155#2352C2214yes—
156#2352C2214yes—
157Q8×C4⋊C4C2211yescharacteristic
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2211yescharacteristic
160Q8×C4⋊C4C2212yes—
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2212yes—
163#2347C2214yes—
164#2347C2212yes—
165#2344C2214yes—
166#2335C2218yes—
167#2332C2218yes—
168#2323C2214yes—
169#2314C2214yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2214yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2212yes—
176C4×#127C2212yes—
177C4×#127C2211yescharacteristic
178C4×#127C2212yes—
179C4×#125C2214yes—
180C4×#125C2214yes—
181C4×#126C2214yes—
182C4×#124C2214yes—
183C4×#124C2212yes—
184C4×#124C2214yes—
185C4×C22⋊Q8C2212yes—
186C4×#121C2212yes—
187#2293C2214yes—
188#2293C2212yes—
189#2293C2214yes—
190#2285C2212yes—
191#2274C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2212yes—
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199Q82—28no—
200#556—28no—
201#554—216no—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×#127C2311yescharacteristic
211C2×#127C2312yes—
212#529—216no—
213C2×#126C2314yes—
214C2×#126C2314yes—
215C2×#125C2312yes—
216C2×#125C2314yes—
217C2×#124C2312yes—
218C2×#124C2312yes—
219C2×#124C2314yes—
220C2×#124C2318yes—
221C2×#123C2314yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×#121C2312yes—
228C2×#121C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2314yes—
256C2×#117C2314yes—
257C2×#117C2312yes—
258C2×#117C2314yes—
259C2×#117C2312yes—
260C2×#117C2314yes—
261C2×#117C2318yes—
262C22×C4⋊C4C2314yes—
263C22×C42C2312yes—
264#401C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#399C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2314yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2314yes—
282#397C2318yes—
283#397C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2314yes—
287#396C2314yes—
288#396C2318yes—
289#395C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2314yes—
293#394C2318yes—
294#394C2314yes—
295#394C2314yes—
296#394C2318yes—
297#394C2318yes—
298#393C2318yes—
299#393C2318yes—
300#393C2318yes—
301#393C2318yes—
302#392C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#391C2312yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2312yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2312yes—
316#391C2314yes—
317#391C2318yes—
318#391C2318yes—
319#391C2312yes—
320#391C2314yes—
321#390C2314yes—
322#390C2314yes—
323#390C2314yes—
324#390C2312yes—
325#390C2314yes—
326#390C2312yes—
327#390C2312yes—
328#390C2314yes—
329#390C2312yes—
330#390C2312yes—
331#390C2314yes—
332#390C2314yes—
333#390C2318yes—
334#390C2312yes—
335#390C2314yes—
336#390C2314yes—
337#390C2312yes—
338#390C2312yes—
339#390C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2312yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2318yes—
364#389C2314yes—
365#389C2312yes—
366#389C2314yes—
367#389C2314yes—
368#389C2312yes—
369#388C2314yes—
370#388C2314yes—
371#388C2314yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2314yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2314yes—
395#388C2318yes—
396#388C2314yes—
397#388C2314yes—
398#388C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2314yes—
419#386C2318yes—
420#386C2318yes—
421#386C2314yes—
422#385C2318yes—
423#385C2318yes—
424#385C2314yes—
425#384C2312yes—
426#384C2312yes—
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2312yes—
430#384C2312yes—
431#384C2311yescharacteristic
432#384C2314yes—
433#384C2312yes—
434#384C2312yes—
435#384C2312yes—
436#383C2314yes—
437#383C2318yes—
438#382C2312yes—
439#382C2314yes—
440#382C2314yes—
441#382C2314yes—
442#382C2314yes—
443#382C2314yes—
444#382C2314yes—
445#382C2314yes—
446#381C2318yes—
447#380C2314yes—
448#380C2314yes—
449#380C2314yes—
450#380C2314yes—
451#380C2314yes—
452#380C2314yes—
453#380C2314yes—
454#380C2314yes—
455#380C2314yes—
456#380C2312yes—
457#380C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2318yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2312yes—
517#376C2314yes—
518C43C2314yes—
519C43C2314yes—
520C43C2312yes—
521C43C2311yescharacteristic
522C43C2312yes—
523C22×Q8C2412yes—
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2412yes—
527C22×Q8C2414yes—
528C22×Q8C2414yes—
529C22×D4C2412yes—
530C22×D4C2412yes—
531C22×D4C2411yescharacteristic
532C22×D4C2412yes—
533C22×D4C2414yes—
534C22×D4C2414yes—
535C23×C4C2414yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2418yes—
539C23×C4C2412yes—
540C4⋊Q8—28no—
541C4⋊Q8—216no—
542C4⋊Q8—28no—
543C4⋊Q8—24no—
544C4⋊Q8—24no—
545C4⋊Q8—28no—
546C4⋊Q8—44no—
547C4⋊Q8—82no—
548#127—24no—
549#127—44no—
550#126—216no—
551#126—216no—
552#125—28no—
553#125—216no—
554#124—28no—
555#124—28no—
556#124—48no—
557#124—88no—
558#123—216no—
559C22⋊Q8—28no—
560C22⋊Q8—216no—
561C22⋊Q8—28no—
562C22⋊Q8—232no—
563C22⋊Q8—84no—
564#121—28no—
565#121—44no—
566C4×Q8—28no—
567C4×Q8—28no—
568C4×Q8—24no—
569C4×Q8—28no—
570C4×Q8—24no—
571C4×Q8—28no—
572C4×Q8—44no—
573C4×Q8—48no—
574C4×Q8—44no—
575C4×Q8—42no—
576C4×Q8—44no—
577C4×Q8—44no—
578C4×Q8—42no—
579C4×Q8—84no—
580C4×Q8#4118yes—
581C4×Q8#4118yes—
582C4×D4—28no—
583C4×D4—216no—
584C4×D4—28no—
585C4×D4—216no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—48no—
589C4×D4—42no—
590C4×D4—44no—
591C4×D4—48no—
592C4×D4—84no—
593#117—28no—
594#117—216no—
595#117—44no—
596#117—48no—
597#117—48no—
598#117—88no—
599C2×C4⋊C4—216no—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C42—28no—
681C2×C42C2412yes—
682C2×C42C2414yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2412yes—
688C2×C42C2414yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2414yes—
692C2×C42C2411yescharacteristic
693C2×C42C2412yes—
694C2×C42C2414yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2418yes—
701C2×C42C2418yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2418yes—
705C2×C42C2414yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2411yescharacteristic
711C2×C42C2412yes—
712C2×C42C2411yescharacteristic
713C2×C42C2412yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#95C2412yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2412yes—
722#95C2412yes—
723#95C2412yes—
724#95C2418yes—
725#95C2418yes—
726#95C2414yes—
727#95C2414yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2412yes—
737#95C2414yes—
738#95C2414yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2414yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756C24C2512yes—
757C24C2514yes—
758C2×Q8—22no—
759C2×Q8—24no—
760C2×Q8—28no—
761C2×Q8—24no—
762C2×Q8—28no—
763C2×Q8—22no—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—24no—
768C2×Q8—42no—
769C2×Q8—44no—
770C2×Q8—44no—
771C2×Q8—42no—
772C2×Q8—44no—
773C2×Q8—44no—
774C2×Q8C2×#4114yes—
775C2×Q8C2×#4114yes—
776C2×D4—24no—
777C2×D4—24no—
778C2×D4—22no—
779C2×D4—28no—
780C2×D4—22no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—22no—
786C2×D4—24no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—28no—
797C22×C4—28no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—28no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—216no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4C2512yes—
810C22×C4C2514yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2514yes—
814C22×C4C2512yes—
815C22×C4C2514yes—
816C22×C4C2512yes—
817C22×C4C2514yes—
818C22×C4C2518yes—
819C22×C4C2512yes—
820C22×C4C2514yes—
821C22×C4C2512yes—
822C22×C4C2511yescharacteristic
823C22×C4C2512yes—
824C22×C4C2512yes—
825C22×C4C2511yescharacteristic
826C22×C4C2512yes—
827C22×C4C2511yescharacteristic
828C22×C4C2512yes—
829C22×C4C2511yescharacteristic
830C22×C4C2511yescharacteristic
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C4⋊C4—216no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—24no—
837C4⋊C4—28no—
838C4⋊C4—22no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—28no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—24no—
850C4⋊C4—216no—
851C4⋊C4—24no—
852C4⋊C4—22no—
853C4⋊C4—24no—
854C4⋊C4—22no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—24no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—28no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—48no—
865C4⋊C4—48no—
866C4⋊C4—42no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—42no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—42no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4C2×#4114yes—
883C4⋊C4C2×#4114yes—
884C4⋊C4C2×#4118yes—
885C4⋊C4C2×#4118yes—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—216no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—24no—
895C22⋊C4—28no—
896C22⋊C4—24no—
897C22⋊C4—44no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—44no—
901C22⋊C4—48no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—48no—
906C22⋊C4—42no—
907C22⋊C4—48no—
908C22⋊C4—44no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—44no—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—28no—
917C42—28no—
918C42—24no—
919C42—24no—
920C42—28no—
921C42—22no—
922C42—24no—
923C42—24no—
924C42—22no—
925C42—24no—
926C42—28no—
927C42—24no—
928C42—22no—
929C42—48no—
930C42—44no—
931C42—48no—
932C42—44no—
933C42—44no—
934C42—42no—
935C42—42no—
936C42—44no—
937C42—42no—
938C42—44no—
939C42—44no—
940C42—42no—
941C42—48no—
942C42—41no—
943C42C2×#4114yes—
944C42C2×#4118yes—
945C42C2×#4114yes—
946C42C2×#4118yes—
947C422−1+414yes—
948C23—22no—
949C23—24no—
950C23—24no—
951C23—22no—
952C23—22no—
953C23—24no—
954C23—22no—
955C23—22no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23C2611yescharacteristic
963Q8—28no—
964Q8—28no—
965Q8—48no—
966Q8—84no—
967Q8—88no—
968Q8—88no—
969D4—48no—
970D4—48no—
971D4—48no—
972D4—44no—
973D4—88no—
974D4—88no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—28no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—28no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—28no—
1031C2×C4—48no—
1032C2×C4—416no—
1033C2×C4—48no—
1034C2×C4—84no—
1035C2×C4—816no—
1036C2×C4C22×#4114yes—
1037C2×C4C22×#4112yes—
1038C2×C4C22×#4114yes—
1039C2×C4C22×#4114yes—
1040C2×C4C22×#4112yes—
1041C2×C4C22×#4114yes—
1042C2×C4C22×#4112yes—
1043C2×C4C22×#4112yes—
1044C2×C4C22×#4112yes—
1045C2×C4C22×#4112yes—
1046C2×C4C2×2−1+412yes—
1047C2×C4C2×2−1+412yes—
1048C2×C4C2×2−1+412yes—
1049C2×C4#58512yes—
1050C2×C4#58512yes—
1051C2×C4#58512yes—
1052C22—42no—
1053C22—44no—
1054C22—44no—
1055C22—42no—
1056C22—42no—
1057C22—44no—
1058C22—42no—
1059C22—44no—
1060C22—42no—
1061C22—44no—
1062C22—44no—
1063C22—42no—
1064C22—42no—
1065C22—44no—
1066C22C23×#4111yescharacteristic
1067C22C23×#4111yescharacteristic
1068C22C22×2−1+411yescharacteristic
1069C22C2×#58511yescharacteristic
1070C22C2×#58511yescharacteristic
1071C22C2×#58511yescharacteristic
1072C22H(7,𝔽2)11yescharacteristic
1073C4—22no—
1074C4—24no—
1075C4—24no—
1076C4—22no—
1077C4—24no—
1078C4—22no—
1079C4—24no—
1080C4—42no—
1081C4—44no—
1082C4—42no—
1083C4—48no—
1084C4—42no—
1085C4—41no—
1086C4—44no—
1087C4—42no—
1088C4—42no—
1089C4—44no—
1090C4—42no—
1091C4—44no—
1092C4—42no—
1093C4—44no—
1094C4#348014yes—
1095C4#350714yes—
1096C4#351814yes—
1097C2—82no—
1098C2—84no—
1099C2C2×#348011yescharacteristic
1100C2C2×#350711yescharacteristic
1101C2C2×#351811yescharacteristic
1102C2#6292611yescharacteristic
1103C2#6299411yescharacteristic
1104C2#6301011yescharacteristic
1105C2#6303111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2541C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59876C2semidirect
2. #59863C2semidirect
3. #59863C2semidirect
4. #59717C2semidirect
6. #59211C2semidirect
7. #45262C2semidirect
8. #44117C2semidirect
9. #40020C2semidirect
10. #39515C2semidirect
11. #39249C2semidirect
12. #39125C2semidirect
13. #36598C2semidirect
14. #36590C2semidirect
15. #36559C2semidirect
16. #36535C2semidirect
17. #36534C2semidirect
18. #36301C2semidirect
19. #36194C2semidirect
20. #35774C2semidirect
21. #34954C2semidirect
23. #34317C2semidirect
24. #34242C2semidirect
25. C4×Q82C2semidirect
26. C4×#556C2semidirect

Maximal subgroups

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

subgroupindex
#598762
#598632
#597172
#596402
#592112
#452622
#441172
#400202
#395152
#392492
#391252
#365982
#365902
#365592
#365352
#365342
#363012
#361942
#357742
#349542
#349342
#343172
#342422
C4×Q822
C4×#5562