Finite Group Databasebeta

← #7688635

Subgroups — #7688635

Order 512.

4727 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59720C214yesmaximal, complemented
3#59660C212yesmaximal, complemented
4#59436C212yesmaximal, complemented
5#59242C212yesmaximal, complemented
6#59211C214yesmaximal, complemented
7#45224C214yesmaximal, complemented
8#43756C218yesmaximal, complemented
9#40035C214yesmaximal, complemented
10#39224C214yesmaximal, complemented
11#39203C212yesmaximal, complemented
12#39193C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36590C212yesmaximal, complemented
15#36587C212yesmaximal, complemented
16#36563C211yesmaximal, characteristic, complemented
17#36302C212yesmaximal, complemented
18#36187C211yesmaximal, characteristic
19#36185C212yesmaximal, complemented
20#36069C214yesmaximal, complemented
21#34954C211yesmaximal, characteristic, complemented
22#34948C212yesmaximal, complemented
23#34321C212yesmaximal, complemented
24#34317C212yesmaximal, complemented
25C4×#554C211yesmaximal, characteristic, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×#556C2211yescharacteristic
28C2×#555C2212yes—
29C2×#554C2211yescharacteristic
30C2×#554C2212yes—
31#2868C2211yescharacteristic
32#2862C2212yes—
33#2861C2214yes—
34#2859C2212yes—
35#2856C2212yes—
36#2850C2214yes—
37#2798C2218yes—
38#2787C2218yes—
39#2786C2218yes—
40#2779C2218yes—
41#2779C2218yes—
42#2757C2218yes—
43#2754C2218yes—
44#2746C2218yes—
45#2745C2218yes—
46#2732C2214yes—
47#2728C2218yes—
48#2654C2218yes—
49#2625C2214yes—
50#2599C2218yes—
51#2597C2218yes—
52#2594C2218yes—
53#2593C2214yes—
54#2582C2212yes—
55#2582C2212yes—
56#2582C2211yescharacteristic
57#2577C2218yes—
58#2571C2214yes—
59#2571C2211yescharacteristic
60#2571C2212yes—
61#2570C2214yes—
62#2570C2214yes—
63#2570C2214yes—
64#2569C2218yes—
65#2568C2212yes—
66#2567C2212yes—
67#2563C2212yes—
68#2552C2212yes—
69#2552C2212yes—
70#2550C2214yes—
71#2548C2211yescharacteristic
72#2548C2211yescharacteristic
73#2542C2212yes—
74#2538C2212yes—
75#2538C2214yes—
76#2537C2212yes—
77#2537C2212yes—
78#2536C2218yes—
79#2531C2218yes—
80#2525C2218yes—
81#2525C2218yes—
82#2524C2218yes—
83#2521C2218yes—
84#2521C2218yes—
85#2514C2214yes—
86#2514C2214yes—
87#2513C2214yes—
88#2513C2214yes—
89#2513C2212yes—
90#2513C2214yes—
91#2513C2212yes—
92#2511C2214yes—
93#2507C2214yes—
94#2504C2214yes—
95#2500C2214yes—
96#2500C2214yes—
97#2499C2214yes—
98#2495C2214yes—
99#2495C2214yes—
100#2495C2218yes—
101#2494C2214yes—
102#2491C2214yes—
103#2491C2214yes—
104#2490C2214yes—
105#2489C2214yes—
106#2489C2214yes—
107#2485C2218yes—
108#2476C2218yes—
109#2454C2214yes—
110#2451C2214yes—
111#2448C2212yes—
112#2448C2212yes—
113#2447C2214yes—
114#2446C2214yes—
115#2444C2218yes—
116#2442C2214yes—
117#2442C2214yes—
118#2442C2214yes—
119#2427C2214yes—
120#2427C2214yes—
121#2427C2214yes—
122#2421C2214yes—
123#2417C2214yes—
124#2402C2218yes—
125#2395C2214yes—
126#2373C2214yes—
127#2370C2214yes—
128#2370C2212yes—
129#2369C2211yescharacteristic
130#2369C2212yes—
131#2368C2214yes—
132#2367C2218yes—
133#2367C2212yes—
134#2366C2212yes—
135#2365C2211yescharacteristic
136#2365C2212yes—
137#2363C2214yes—
138#2362C2218yes—
139#2362C2214yes—
140#2362C2214yes—
141#2362C2212yes—
142#2361C2214yes—
143#2361C2214yes—
144#2360C2212yes—
145#2357C2214yes—
146#2356C2212yes—
147#2355C2212yes—
148#2355C2211yescharacteristic
149#2355C2212yes—
150#2355C2212yes—
151#2355C2211yescharacteristic
152#2354C2212yes—
153#2354C2211yescharacteristic
154#2354C2214yes—
155#2354C2212yes—
156Q8×C4⋊C4C2212yes—
157#2349C2212yes—
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2211yescharacteristic
160#2347C2214yes—
161#2347C2214yes—
162#2347C2212yes—
163#2345C2212yes—
164#2344C2214yes—
165#2337C2218yes—
166#2332C2218yes—
167#2324C2214yes—
168#2323C2214yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2211yescharacteristic
172C4×C4⋊Q8C2211yescharacteristic
173C4×#127C2211yescharacteristic
174C4×#125C2214yes—
175C4×#125C2212yes—
176C4×#125C2214yes—
177C4×#126C2214yes—
178C4×#124C2212yes—
179C4×#124C2212yes—
180C4×#124C2212yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×#121C2214yes—
185#2296C2214yes—
186#2293C2212yes—
187#2293C2214yes—
188#2293C2212yes—
189#2285C2214yes—
190#2285C2212yes—
191#2274C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2211yescharacteristic
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C4×#117C2212yes—
198C2×C4×C4⋊C4C2212yes—
199#556—28no—
200#555—216no—
201#554—28no—
202#554—216no—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×#127C2311yescharacteristic
209C2×#126C2314yes—
210C2×#125C2312yes—
211C2×#125C2314yes—
212C2×#125C2314yes—
213C2×#124C2318yes—
214C2×#124C2312yes—
215C2×#124C2312yes—
216C2×#124C2312yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×#121C2314yes—
224C2×#121C2314yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2312yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2318yes—
249C2×C4×D4C2311yescharacteristic
250C2×#117C2314yes—
251C2×#117C2314yes—
252C2×#117C2312yes—
253C2×#117C2314yes—
254C2×#117C2312yes—
255C2×#117C2318yes—
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C42C2312yes—
260C22×C42C2314yes—
261#401C2318yes—
262#400C2318yes—
263#400C2314yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#399C2314yes—
271#399C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2314yes—
279#397C2314yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2314yes—
285#397C2314yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#396C2318yes—
291#396C2318yes—
292#395C2318yes—
293#394C2314yes—
294#394C2314yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#393C2318yes—
300#391C2314yes—
301#391C2314yes—
302#391C2312yes—
303#391C2312yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2312yes—
310#391C2312yes—
311#391C2314yes—
312#391C2318yes—
313#391C2312yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#390C2312yes—
318#390C2312yes—
319#390C2312yes—
320#390C2314yes—
321#390C2312yes—
322#390C2318yes—
323#390C2314yes—
324#390C2314yes—
325#390C2314yes—
326#390C2314yes—
327#390C2312yes—
328#390C2312yes—
329#390C2312yes—
330#390C2312yes—
331#390C2312yes—
332#390C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2314yes—
336#389C2312yes—
337#389C2312yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2312yes—
342#389C2314yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2314yes—
347#389C2312yes—
348#389C2314yes—
349#389C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2318yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2318yes—
359#389C2314yes—
360#388C2314yes—
361#388C2314yes—
362#388C2314yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2314yes—
369#388C2318yes—
370#388C2318yes—
371#388C2314yes—
372#388C2318yes—
373#388C2318yes—
374#388C2314yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2314yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2314yes—
397#387C2314yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2318yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2314yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2314yes—
420#385C2314yes—
421#385C2314yes—
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2312yes—
425#384C2311yescharacteristic
426#384C2314yes—
427#384C2312yes—
428#384C2314yes—
429#384C2312yes—
430#384C2312yes—
431#383C2314yes—
432#383C2318yes—
433#383C2318yes—
434#382C2312yes—
435#382C2314yes—
436#382C2312yes—
437#382C2314yes—
438#382C2314yes—
439#382C2312yes—
440#382C2314yes—
441#382C2318yes—
442#382C2314yes—
443#382C2312yes—
444#381C2318yes—
445#380C2314yes—
446#380C2314yes—
447#380C2314yes—
448#380C2318yes—
449#380C2318yes—
450#380C2318yes—
451#380C2314yes—
452#380C2312yes—
453#380C2314yes—
454#380C2312yes—
455#380C2318yes—
456#380C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2318yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2318yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517#376C2314yes—
518C2×#95C2314yes—
519C43C2314yes—
520C43C2312yes—
521C43C2311yescharacteristic
522C43C2312yes—
523C22×Q8C2412yes—
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2414yes—
527C22×Q8C2412yes—
528C22×D4C2412yes—
529C22×D4C2412yes—
530C22×D4C2411yescharacteristic
531C22×D4C2418yes—
532C22×D4C2412yes—
533C23×C4C2412yes—
534C23×C4C2414yes—
535C23×C4C2412yes—
536C23×C4C2418yes—
537C23×C4C2414yes—
538C23×C4C2412yes—
539C23×C4C2414yes—
540C4⋊Q8—28no—
541C4⋊Q8—24no—
542C4⋊Q8—44no—
543C4⋊Q8—82no—
544C4⋊Q8#4118yes—
545#127—24no—
546#126—216no—
547#125—28no—
548#125—216no—
549#125—48no—
550#124—28no—
551#124—232no—
552#124—44no—
553#124—44no—
554C22⋊Q8—232no—
555C22⋊Q8—216no—
556C22⋊Q8—28no—
557C22⋊Q8—216no—
558C22⋊Q8—28no—
559C22⋊Q8—48no—
560#121—216no—
561#121—216no—
562#121—48no—
563#121—84no—
564C4×Q8—28no—
565C4×Q8—28no—
566C4×Q8—24no—
567C4×Q8—24no—
568C4×Q8—24no—
569C4×Q8—24no—
570C4×Q8—44no—
571C4×Q8—44no—
572C4×Q8—42no—
573C4×Q8—42no—
574C4×Q8—84no—
575C4×Q8—84no—
576C4×D4—28no—
577C4×D4—216no—
578C4×D4—24no—
579C4×D4—28no—
580C4×D4—28no—
581C4×D4—48no—
582C4×D4—44no—
583C4×D4—42no—
584C4×D4—44no—
585C4×D4—88no—
586C4×D4#4118yes—
587#117—216no—
588#117—28no—
589#117—216no—
590#117—48no—
591#117—44no—
592#117—88no—
593C2×C4⋊C4—216no—
594C2×C4⋊C4—28no—
595C2×C4⋊C4—44no—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2412yes—
674C2×C42—28no—
675C2×C42—48no—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2418yes—
679C2×C42C2414yes—
680C2×C42C2411yescharacteristic
681C2×C42C2412yes—
682C2×C42C2414yes—
683C2×C42C2414yes—
684C2×C42C2411yescharacteristic
685C2×C42C2412yes—
686C2×C42C2411yescharacteristic
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2414yes—
695C2×C42C2418yes—
696C2×C42C2414yes—
697C2×C42C2418yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2414yes—
702C2×C42C2412yes—
703C2×C42C2411yescharacteristic
704C2×C42C2414yes—
705C2×C42C2414yes—
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709#95C2412yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2412yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2412yes—
720#95C2412yes—
721#95C2414yes—
722#95C2414yes—
723#95C2412yes—
724#95C2414yes—
725#95C2414yes—
726#95C2418yes—
727#95C2414yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2412yes—
735#95C2414yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2414yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753C24C2514yes—
754C24C2512yes—
755C2×Q8—24no—
756C2×Q8—22no—
757C2×Q8—22no—
758C2×Q8—24no—
759C2×Q8—28no—
760C2×Q8—22no—
761C2×Q8—22no—
762C2×Q8—24no—
763C2×Q8—22no—
764C2×Q8—22no—
765C2×Q8—42no—
766C2×Q8—42no—
767C2×Q8—44no—
768C2×Q8—44no—
769C2×Q8C2×#4118yes—
770C2×D4—216no—
771C2×D4—22no—
772C2×D4—24no—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—42no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—42no—
784C2×D4C2×#4114yes—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—28no—
788C22×C4—24no—
789C22×C4—28no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—216no—
795C22×C4—24no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—48no—
800C22×C4—48no—
801C22×C4—42no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—42no—
805C22×C4C2×#4118yes—
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2518yes—
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2511yescharacteristic
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2511yescharacteristic
824C22×C4C2514yes—
825C22×C4C2511yescharacteristic
826C22×C4C2511yescharacteristic
827C22×C4C2511yescharacteristic
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C4⋊C4—24no—
831C4⋊C4—22no—
832C4⋊C4—28no—
833C4⋊C4—216no—
834C4⋊C4—24no—
835C4⋊C4—22no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—24no—
839C4⋊C4—22no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—28no—
843C4⋊C4—28no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—216no—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—22no—
853C4⋊C4—24no—
854C4⋊C4—22no—
855C4⋊C4—24no—
856C4⋊C4—22no—
857C4⋊C4—24no—
858C4⋊C4—28no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—48no—
864C4⋊C4—42no—
865C4⋊C4—48no—
866C4⋊C4—42no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—44no—
878C4⋊C4C2×#4118yes—
879C4⋊C4C2×#4118yes—
880C4⋊C4C2×#4114yes—
881C22⋊C4—216no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—216no—
885C22⋊C4—28no—
886C22⋊C4—216no—
887C22⋊C4—24no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—42no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4C2×#4118yes—
908C42—216no—
909C42—28no—
910C42—24no—
911C42—28no—
912C42—24no—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—24no—
917C42—24no—
918C42—24no—
919C42—28no—
920C42—24no—
921C42—24no—
922C42—22no—
923C42—22no—
924C42—22no—
925C42—24no—
926C42—44no—
927C42—44no—
928C42—44no—
929C42—44no—
930C42—48no—
931C42—48no—
932C42—42no—
933C42—42no—
934C42—44no—
935C42—42no—
936C42—42no—
937C42—41no—
938C42C2×#4114yes—
939C42C2×#4114yes—
940C422−1+414yes—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23C22×#4114yes—
955C23C2611yescharacteristic
956Q8—48no—
957Q8—48no—
958Q8—44no—
959Q8—44no—
960Q8—88no—
961D4—28no—
962D4—48no—
963D4—48no—
964D4—84no—
965D4—816no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—24no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—24no—
975C2×C4—21no—
976C2×C4—216no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—28no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—21no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—28no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—28no—
1024C2×C4—22no—
1025C2×C4—416no—
1026C2×C4—48no—
1027C2×C4—88no—
1028C2×C4—816no—
1029C2×C4—84no—
1030C2×C4—88no—
1031C2×C4C22×#4114yes—
1032C2×C4C22×#4112yes—
1033C2×C4C22×#4112yes—
1034C2×C4C22×#4118yes—
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4112yes—
1037C2×C4C22×#4112yes—
1038C2×C4C22×#4112yes—
1039C2×C4C2×2−1+412yes—
1040C2×C4C2×2−1+412yes—
1041C2×C4C2×2−1+412yes—
1042C2×C4#58512yes—
1043C2×C4#58512yes—
1044C2×C4#58512yes—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—44no—
1053C22—44no—
1054C22—44no—
1055C22—44no—
1056C22—44no—
1057C22—44no—
1058C22—44no—
1059C22C23×#4111yescharacteristic
1060C22C23×#4111yescharacteristic
1061C22C22×2−1+411yescharacteristic
1062C22C2×#58511yescharacteristic
1063C22C2×#58511yescharacteristic
1064C22C2×#58511yescharacteristic
1065C22H(7,𝔽2)11yescharacteristic
1066C4—28no—
1067C4—22no—
1068C4—22no—
1069C4—24no—
1070C4—22no—
1071C4—42no—
1072C4—44no—
1073C4—42no—
1074C4—48no—
1075C4—42no—
1076C4—41no—
1077C4—44no—
1078C4—42no—
1079C4—42no—
1080C4—42no—
1081C4—42no—
1082C4—42no—
1083C4—42no—
1084C4—42no—
1085C4—44no—
1086C4—44no—
1087C4#348014yes—
1088C4#351514yes—
1089C4#351814yes—
1090C2—44no—
1091C2—84no—
1092C2C2×#348011yescharacteristic
1093C2C2×#351511yescharacteristic
1094C2C2×#351811yescharacteristic
1095C2#6292911yescharacteristic
1096C2#6299211yescharacteristic
1097C2#6301011yescharacteristic
1098C2#6303111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36187C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59823C2semidirect
2. #59720C2semidirect
3. #59660C2semidirect
4. #59436C2semidirect
5. #59242C2semidirect
6. #59211C2semidirect
7. #45224C2semidirect
8. #43756C2semidirect
9. #40035C2semidirect
10. #39224C2semidirect
11. #39203C2semidirect
12. #39193C2semidirect
13. #36598C2semidirect
14. #36590C2semidirect
15. #36587C2semidirect
16. #36563C2semidirect
17. #36302C2semidirect
19. #36185C2semidirect
20. #36069C2semidirect
21. #34954C2semidirect
22. #34948C2semidirect
23. #34321C2semidirect
24. #34317C2semidirect
25. C4×#554C2semidirect
26. C4×#556C2semidirect

Maximal subgroups

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

subgroupindex
#598232
#597202
#596602
#594362
#592422
#592112
#452242
#437562
#400352
#392242
#392032
#391932
#365982
#365902
#365872
#365632
#363022
#361872
#361852
#360692
#349542
#349482
#343212
#343172
C4×#5542
C4×#5562