Finite Group Databasebeta

← #7898330

Subgroups — #7898330

Order 512.

4493 conjugacy classes of subgroups.

The subgroup lattice has 1396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59924C211yesmaximal, characteristic, complemented
2#59151C212yesmaximal, complemented
3#52267C211yesmaximal, characteristic
4#51081C214yesmaximal
5#51076C214yesmaximal, complemented
6#51076C214yesmaximal, complemented
7#47732C214yesmaximal, complemented
8#46004C212yesmaximal
9#45275C212yesmaximal, complemented
10#45274C212yesmaximal, complemented
11#44954C212yesmaximal, complemented
12#44597C214yesmaximal, complemented
13#42973C212yesmaximal, complemented
14#42825C212yesmaximal, complemented
15#42825C214yesmaximal, complemented
16#39987C212yesmaximal, complemented
17#39702C212yesmaximal
18#39695C212yesmaximal, complemented
19#39621C211yesmaximal, characteristic, complemented
20#39621C212yesmaximal, complemented
21#39493C211yesmaximal, characteristic
22#37686C212yesmaximal
23#37195C212yesmaximal, complemented
24#36474C211yesmaximal, characteristic, complemented
25#35819C212yesmaximal, complemented
26#35576C212yesmaximal, complemented
27#35199C211yesmaximal, characteristic, complemented
28#34463C212yesmaximal
29#34322C211yesmaximal, characteristic
30C2×Q82C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#556C2211yescharacteristic
33C2×#544C2212yes—
34C22×C4⋊Q8C2212yes—
35#2863C2212yes—
36#2862C2211yescharacteristic
37#2862C2212yes—
38#2862C2212yes—
39#2851C2212yes—
40#2844C2214yes—
41#2844C2214yes—
42#2811C2212yes—
43#2811C2212yes—
44#2811C2212yes—
45#2807C2214yes—
46#2807C2212yes—
47#2806C2212yes—
48#2806C2211yescharacteristic
49#2806C2212yes—
50#2806C2212yes—
51#2806C2214yes—
52#2805C2214yes—
53#2805C2211yescharacteristic
54#2805C2214yes—
55#2805C2212yes—
56#2804C2212yes—
57#2804C2211yescharacteristic
58#2802C2212yes—
59#2802C2214yes—
60#2802C2214yes—
61#2799C2214yes—
62#2790C2212yes—
63#2790C2214yes—
64#2788C2212yes—
65#2788C2214yes—
66#2780C2212yes—
67#2774C2214yes—
68#2774C2214yes—
69#2763C2214yes—
70#2763C2214yes—
71#2763C2214yes—
72#2763C2214yes—
73#2755C2214yes—
74#2734C2214yes—
75#2734C2214yes—
76#2734C2214yes—
77#2734C2214yes—
78#2734C2212yes—
79#2732C2211yescharacteristic
80#2732C2212yes—
81#2729C2214yes—
82#2729C2212yes—
83#2729C2214yes—
84#2729C2214yes—
85#2720C2214yes—
86#2720C2214yes—
87#2720C2214yes—
88#2713C2214yes—
89#2713C2214yes—
90#2713C2214yes—
91#2713C2214yes—
92#2713C2214yes—
93#2704C2214yes—
94#2677C2214yes—
95#2677C2214yes—
96#2666C2214yes—
97#2666C2214yes—
98#2666C2214yes—
99#2666C2214yes—
100#2666C2214yes—
101#2660C2212yes—
102#2660C2214yes—
103#2660C2214yes—
104#2628C2212yes—
105#2628C2212yes—
106#2612C2214yes—
107#2605C2214yes—
108#2605C2214yes—
109#2590C2214yes—
110#2589C2214yes—
111#2589C2214yes—
112#2589C2214yes—
113#2589C2214yes—
114#2587C2214yes—
115#2586C2214yes—
116#2586C2214yes—
117#2586C2214yes—
118#2583C2214yes—
119#2583C2214yes—
120#2582C2211yescharacteristic
121#2570C2214yes—
122#2570C2212yes—
123#2568C2211yescharacteristic
124#2568C2214yes—
125#2568C2212yes—
126#2567C2212yes—
127#2567C2212yes—
128#2567C2214yes—
129#2567C2214yes—
130#2567C2212yes—
131#2567C2212yes—
132#2567C2211yescharacteristic
133#2556C2214yes—
134#2556C2214yes—
135#2551C2214yes—
136#2551C2212yes—
137#2551C2212yes—
138#2551C2212yes—
139#2551C2212yes—
140#2551C2212yes—
141#2551C2214yes—
142#2551C2212yes—
143#2551C2211yescharacteristic
144#2551C2214yes—
145#2550C2212yes—
146#2550C2212yes—
147#2550C2212yes—
148#2550C2214yes—
149#2550C2212yes—
150#2550C2214yes—
151#2550C2214yes—
152#2550C2214yes—
153#2550C2214yes—
154#2550C2214yes—
155#2550C2214yes—
156#2550C2212yes—
157#2550C2212yes—
158#2546C2211yescharacteristic
159#2546C2212yes—
160#2546C2211yescharacteristic
161#2522C2214yes—
162#2520C2214yes—
163#2520C2214yes—
164#2509C2212yes—
165#2509C2214yes—
166#2509C2212yes—
167#2508C2212yes—
168#2508C2212yes—
169#2508C2212yes—
170#2506C2214yes—
171#2506C2212yes—
172#2506C2212yes—
173#2492C2214yes—
174#2492C2214yes—
175#2473C2214yes—
176#2465C2214yes—
177#2465C2214yes—
178#2453C2212yes—
179#2453C2214yes—
180#2451C2212yes—
181#2451C2214yes—
182#2451C2212yes—
183#2451C2214yes—
184#2451C2212yes—
185#2451C2214yes—
186#2449C2214yes—
187#2446C2212yes—
188#2442C2212yes—
189#2440C2212yes—
190#2440C2212yes—
191#2440C2214yes—
192#2440C2212yes—
193#2439C2212yes—
194#2439C2212yes—
195#2434C2214yes—
196#2434C2214yes—
197#2434C2214yes—
198#2434C2214yes—
199#2434C2214yes—
200#2409C2214yes—
201#2402C2212yes—
202#2402C2214yes—
203#2396C2212yes—
204#2396C2212yes—
205#2383C2214yes—
206#2379C2214yes—
207#2373C2214yes—
208#2373C2214yes—
209#2370C2212yes—
210#2369C2212yes—
211#2369C2212yes—
212#2369C2212yes—
213#2369C2212yes—
214#2367C2212yes—
215#2365C2211yescharacteristic
216#2362C2212yes—
217#2360C2212yes—
218#2360C2214yes—
219#2360C2212yes—
220#2355C2211yescharacteristic
221#2355C2214yes—
222#2355C2212yes—
223#2352C2212yes—
224#2351C2212yes—
225#2351C2212yes—
226#2351C2212yes—
227D4×C4⋊C4C2211yescharacteristic
228#2347C2212yes—
229#2346C2212yes—
230#2346C2212yes—
231#2337C2214yes—
232#2334C2214yes—
233#2334C2214yes—
234#2334C2214yes—
235#2331C2214yes—
236#2331C2212yes—
237#2331C2212yes—
238#2323C2212yes—
239#2323C2212yes—
240#2320C2214yes—
241#2320C2212yes—
242#2317C2212yes—
243#2317C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×C4⋊Q8C2212yes—
248C4×#124C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251#2296C2212yes—
252#2296C2212yes—
253#2295C2212yes—
254#2295C2211yescharacteristic
255#2293C2211yescharacteristic
256#2290C2212yes—
257#2274C2212yes—
258C42×Q8C2211yescharacteristic
259C23×Q8C2314yes—
260Q82—44no—
261#557—44no—
262#556Q8116yescomplemented
263#544—48no—
264C2×C4⋊Q8—48no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2314yes—
279C2×C4⋊Q8C2314yes—
280C2×C4⋊Q8C2314yes—
281C2×C4⋊Q8C2314yes—
282C2×C4⋊Q8C2314yes—
283C2×C4⋊Q8C2314yes—
284C2×C4⋊Q8C2312yes—
285C2×C4⋊Q8C2312yes—
286C2×C4⋊Q8C2314yes—
287C2×C4⋊Q8C2314yes—
288C2×C4⋊Q8C2311yescharacteristic
289C2×#126C2314yes—
290C2×#125C2312yes—
291C2×#125C2312yes—
292C2×#125C2314yes—
293C2×#125C2314yes—
294C2×#125C2314yes—
295C2×#125C2314yes—
296C2×#124C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×#117C2312yes—
321C2×#117C2312yes—
322C2×#117C2312yes—
323C2×#117C2312yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2314yes—
327C22×C42C2312yes—
328#400C2312yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2312yes—
350#400C2312yes—
351#399C2314yes—
352#399C2312yes—
353#399C2314yes—
354#399C2312yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#396C2312yes—
388#396C2314yes—
389#396C2312yes—
390#396C2312yes—
391#396C2312yes—
392#396C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2312yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2312yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2312yes—
432#393C2312yes—
433#393C2314yes—
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2314yes—
441#391C2312yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2314yes—
448#391C2312yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2312yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2312yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2312yes—
467#391C2314yes—
468#391C2314yes—
469#391C2312yes—
470#391C2314yes—
471#391C2314yes—
472#391C2314yes—
473#391C2314yes—
474#391C2311yescharacteristic
475#391C2314yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2311yescharacteristic
480#390C2311yescharacteristic
481#390C2311yescharacteristic
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2312yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2312yes—
527#389C2314yes—
528#389C2314yes—
529#389C2312yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2311yescharacteristic
539#389C2311yescharacteristic
540#389C2314yes—
541#389C2312yes—
542#389C2311yescharacteristic
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2311yescharacteristic
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2312yes—
557#388C2312yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2312yes—
564#387C2312yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2312yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2312yes—
603#387C2314yes—
604#387C2312yes—
605#386C2312yes—
606#386C2314yes—
607#386C2312yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2312yes—
613#385C2312yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2312yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2312yes—
628#385C2312yes—
629#385C2312yes—
630#385C2312yes—
631#385C2312yes—
632#384C2312yes—
633#384C2311yescharacteristic
634#384C2311yescharacteristic
635#384C2311yescharacteristic
636#384C2314yes—
637#384C2314yes—
638#384C2312yes—
639#384C2312yes—
640#384C2314yes—
641#383C2314yes—
642#383C2314yes—
643#382C2312yes—
644#382C2314yes—
645#382C2312yes—
646#382C2312yes—
647#382C2314yes—
648#382C2312yes—
649#382C2314yes—
650#382C2314yes—
651#382C2312yes—
652#382C2314yes—
653#382C2314yes—
654#382C2314yes—
655#382C2312yes—
656#382C2314yes—
657#382C2314yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2314yes—
662#380C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2311yescharacteristic
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2314yes—
712#376C2312yes—
713#376C2314yes—
714#376C2314yes—
715C43C2311yescharacteristic
716C43C2312yes—
717C22×Q8—48no—
718C22×Q8—84no—
719C22×Q8—84no—
720C22×Q8C2411yescharacteristic
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×Q8C2414yes—
727C22×Q8C2414yes—
728C22×Q8C2412yes—
729C22×Q8C2414yes—
730C22×Q8C2414yes—
731C22×Q8C2412yes—
732C22×Q8C2411yescharacteristic
733C22×D4C2411yescharacteristic
734C23×C4C2412yes—
735C23×C4C2414yes—
736C23×C4C2412yes—
737C23×C4C2414yes—
738C23×C4C2412yes—
739C4⋊Q8—28no—
740C4⋊Q8—24no—
741C4⋊Q8—28no—
742C4⋊Q8—28no—
743C4⋊Q8—24no—
744C4⋊Q8—44no—
745C4⋊Q8—44no—
746C4⋊Q8—44no—
747C4⋊Q8—42no—
748C4⋊Q8—44no—
749C4⋊Q8—42no—
750C4⋊Q8—44no—
751C4⋊Q8—48no—
752C4⋊Q8—48no—
753C4⋊Q8—48no—
754C4⋊Q8—48no—
755C4⋊Q8—84no—
756C4⋊Q8—84no—
757C4⋊Q8—84no—
758C4⋊Q8—84no—
759C4⋊Q8—84no—
760C4⋊Q8—82no—
761C4⋊Q8—82no—
762C4⋊Q8C2×Q818yescomplemented
763#126C2×Q8132yescomplemented
764#125—28no—
765#125—44no—
766#125—48no—
767#125—48no—
768#125—84no—
769#125—84no—
770#124C2×Q8116yes—
771C22⋊Q8—28no—
772C22⋊Q8—48no—
773C22⋊Q8—48no—
774C22⋊Q8—84no—
775C22⋊Q8—84no—
776C22⋊Q8—84no—
777C22⋊Q8C2×Q8116yescomplemented
778C4×Q8—24no—
779C4×Q8—24no—
780C4×Q8—24no—
781C4×Q8—42no—
782C4×Q8—42no—
783C4×Q8—44no—
784C4×Q8—44no—
785C4×Q8—44no—
786C4×Q8—44no—
787C4×Q8—82no—
788C4×Q8—82no—
789C4×Q8—82no—
790C4×Q8C2×Q8116yescomplemented
791C4×Q8C2×Q818yescomplemented
792C4×D4—82no—
793C4×D4C2×Q818yes—
794#117—28no—
795#117—44no—
796#117—44no—
797#117C2×Q8116yescomplemented
798C2×C4⋊C4—28no—
799C2×C4⋊C4—44no—
800C2×C4⋊C4—48no—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C42—44no—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2411yescharacteristic
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2411yescharacteristic
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012C24C2512yes—
1013C2×Q8—22no—
1014C2×Q8—28no—
1015C2×Q8—28no—
1016C2×Q8—22no—
1017C2×Q8—22no—
1018C2×Q8—24no—
1019C2×Q8—22no—
1020C2×Q8—24no—
1021C2×Q8—41no—
1022C2×Q8—42no—
1023C2×Q8—42no—
1024C2×Q8—41no—
1025C2×Q8—41no—
1026C2×Q8—42no—
1027C2×Q8—42no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8—44no—
1031C2×Q8—41no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—44no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×Q8—41no—
1040C2×Q8—42no—
1041C2×Q8—41no—
1042C2×Q8—42no—
1043C2×Q8—44no—
1044C2×Q8—42no—
1045C2×Q8—44no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—44no—
1049C2×Q8—832no—
1050C2×Q8C22×Q814yes—
1051C2×Q8C22×Q818yes—
1052C2×Q82−1+414yes—
1053C2×D4—41no—
1054C2×D4—41no—
1055C2×D4C22×Q814yes—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—28no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4C22×Q818yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2514yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C22×C4C2511yescharacteristic
1097C22×C4C2512yes—
1098C22×C4C2511yescharacteristic
1099C4⋊C4—28no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—22no—
1113C4⋊C4—22no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—28no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4—41no—
1130C4⋊C4—41no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—41no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—41no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—41no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—41no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4C22×Q814yes—
1179C4⋊C4C22×Q818yes—
1180C4⋊C4C22×Q814yes—
1181C4⋊C4C22×Q8116yes—
1182C4⋊C4C22×Q818yes—
1183C4⋊C4C22×Q818yes—
1184C4⋊C4H(5,𝔽2)14yes—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—24no—
1188C22⋊C4—24no—
1189C22⋊C4—42no—
1190C22⋊C4—44no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4C22×Q8116yes—
1200C22⋊C4C22×Q818yes—
1201C22⋊C4C22×Q8116yes—
1202C42—24no—
1203C42—24no—
1204C42—24no—
1205C42—24no—
1206C42—22no—
1207C42—24no—
1208C42—24no—
1209C42—24no—
1210C42—22no—
1211C42—24no—
1212C42—42no—
1213C42—42no—
1214C42—44no—
1215C42—44no—
1216C42—44no—
1217C42—41no—
1218C42—44no—
1219C42—42no—
1220C42—44no—
1221C42—44no—
1222C42—41no—
1223C42—41no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42—42no—
1230C42C22×Q8116yes—
1231C42C22×Q814yes—
1232C42C22×Q818yes—
1233C422−1+414yes—
1234C23—22no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—22no—
1239C23—22no—
1240C23C23×Q814yes—
1241C23C2611yescharacteristic
1242Q8—28no—
1243Q8—48no—
1244Q8—44no—
1245Q8—82no—
1246Q8—84no—
1247Q8—82no—
1248Q8—84no—
1249Q8—88no—
1250Q8—88no—
1251Q8—88no—
1252Q8—88no—
1253Q8—164no—
1254Q8—162no—
1255D4—44no—
1256C2×C4—21no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—22no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—216no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—21no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—21no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—21no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—48no—
1328C2×C4—48no—
1329C2×C4—88no—
1330C2×C4—88no—
1331C2×C4C23×Q814yes—
1332C2×C4C23×Q812yes—
1333C2×C4C23×Q814yes—
1334C2×C4C23×Q812yes—
1335C2×C4C23×Q814yes—
1336C2×C4C23×Q818yes—
1337C2×C4C23×Q812yes—
1338C2×C4C2×H(5,𝔽2)14yes—
1339C2×C4C2×H(5,𝔽2)12yes—
1340C2×C4C2×2−1+412yes—
1341C2×C4C2×2−1+412yes—
1342C2×C4C2×2−1+412yes—
1343C2×C4C2×2−1+414yes—
1344C2×C4C2×2−1+412yes—
1345C22—24no—
1346C22—24no—
1347C22—24no—
1348C22—42no—
1349C22—42no—
1350C22—42no—
1351C22—42no—
1352C22C24×Q811yescharacteristic
1353C22C22×H(5,𝔽2)11yescharacteristic
1354C22C22×2−1+411yescharacteristic
1355C22C22×2−1+411yescharacteristic
1356C22H(7,𝔽2)11yescharacteristic
1357C22H(7,𝔽2)11yescharacteristic
1358C222−1+611yescharacteristic
1359C4—22no—
1360C4—24no—
1361C4—24no—
1362C4—24no—
1363C4—24no—
1364C4—22no—
1365C4—28no—
1366C4—22no—
1367C4—24no—
1368C4—22no—
1369C4—22no—
1370C4—42no—
1371C4—42no—
1372C4—44no—
1373C4—44no—
1374C4—44no—
1375C4—42no—
1376C4—41no—
1377C4—42no—
1378C4—42no—
1379C4—44no—
1380C4—42no—
1381C4—42no—
1382C4—44no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4#350314yes—
1387C2—44no—
1388C2C2×#350311yescharacteristic
1389C2#6285411yescharacteristic
1390C2#6287911yescharacteristic
1391C2#6289311yescharacteristic
1392C2#6294311yescharacteristic
1393C2Q8×2−1+411yescharacteristic
1394C2#6304511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59924C2semidirect
2. #59151C2semidirect
5. #51076C2semidirect
6. #51076C2semidirect
7. #47732C2semidirect
9. #45275C2semidirect
10. #45274C2semidirect
11. #44954C2semidirect
12. #44597C2semidirect
13. #42973C2semidirect
14. #42825C2semidirect
15. #42825C2semidirect
16. #39987C2semidirect
18. #39695C2semidirect
19. #39621C2semidirect
20. #39621C2semidirect
23. #37195C2semidirect
24. #36474C2semidirect
25. #35819C2semidirect
26. #35576C2semidirect
27. #35199C2semidirect
262. #556Q8semidirect
762. C4⋊Q8C2×Q8semidirect
763. #126C2×Q8semidirect
777. C22⋊Q8C2×Q8semidirect
790. C4×Q8C2×Q8semidirect
791. C4×Q8C2×Q8semidirect
797. #117C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#599242
#591512
#522672
#510812
#510762
#477322
#460042
#452752
#452742
#449542
#445972
#429732
#428252
#399872
#397022
#396952
#396212
#394932
#376862
#371952
#364742
#358192
#355762
#351992
#344632
#343222