Finite Group Databasebeta

← #7900912

Subgroups — #7900912

Order 512.

4529 conjugacy classes of subgroups.

The subgroup lattice has 1426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59454C212yesmaximal, complemented
3#52162C211yesmaximal, characteristic, complemented
4#50907C214yesmaximal, complemented
5#50707C214yesmaximal, complemented
6#47969C214yesmaximal, complemented
7#47726C214yesmaximal, complemented
8#45793C212yesmaximal, complemented
9#45358C212yesmaximal, complemented
10#45086C214yesmaximal, complemented
11#44950C212yesmaximal, complemented
12#44941C212yesmaximal, complemented
13#42933C212yesmaximal, complemented
14#42493C212yesmaximal, complemented
15#42189C214yesmaximal, complemented
16#39986C212yesmaximal, complemented
17#39637C211yesmaximal, characteristic, complemented
18#39631C212yesmaximal, complemented
19#39590C212yesmaximal, complemented
20#39365C211yesmaximal, characteristic, complemented
21#38447C212yesmaximal, complemented
22#38101C212yesmaximal, complemented
23#37308C212yesmaximal, complemented
24#36261C211yesmaximal, characteristic, complemented
25#36039C212yesmaximal, complemented
26#35566C212yesmaximal, complemented
27#35176C211yesmaximal, characteristic, complemented
28#34467C212yesmaximal
29#34321C211yesmaximal, characteristic
30C2×#555C2211yescharacteristic
31C2×#554C2212yes—
32C2×#544C2212yes—
33C2×#533C2212yes—
34#2859C2211yescharacteristic
35#2857C2212yes—
36#2857C2212yes—
37#2855C2212yes—
38#2851C2212yes—
39#2843C2214yes—
40#2841C2214yes—
41#2809C2212yes—
42#2807C2214yes—
43#2807C2214yes—
44#2807C2214yes—
45#2807C2214yes—
46#2806C2214yes—
47#2806C2214yes—
48#2806C2212yes—
49#2805C2212yes—
50#2805C2214yes—
51#2805C2212yes—
52#2805C2212yes—
53#2802C2214yes—
54#2792C2214yes—
55#2790C2214yes—
56#2790C2214yes—
57#2784C2214yes—
58#2768C2214yes—
59#2768C2214yes—
60#2768C2214yes—
61#2763C2214yes—
62#2748C2214yes—
63#2742C2214yes—
64#2742C2214yes—
65#2742C2214yes—
66#2734C2212yes—
67#2734C2214yes—
68#2734C2211yescharacteristic
69#2732C2214yes—
70#2732C2211yescharacteristic
71#2732C2212yes—
72#2729C2214yes—
73#2729C2214yes—
74#2729C2214yes—
75#2729C2214yes—
76#2729C2212yes—
77#2726C2211yescharacteristic
78#2726C2212yes—
79#2726C2212yes—
80#2720C2214yes—
81#2720C2212yes—
82#2720C2214yes—
83#2713C2212yes—
84#2704C2212yes—
85#2692C2214yes—
86#2692C2212yes—
87#2692C2214yes—
88#2683C2212yes—
89#2683C2214yes—
90#2683C2211yescharacteristic
91#2677C2212yes—
92#2677C2214yes—
93#2677C2214yes—
94#2677C2214yes—
95#2667C2214yes—
96#2666C2214yes—
97#2666C2214yes—
98#2666C2214yes—
99#2666C2214yes—
100#2647C2212yes—
101#2646C2214yes—
102#2629C2212yes—
103#2628C2214yes—
104#2628C2212yes—
105#2606C2214yes—
106#2606C2214yes—
107#2589C2214yes—
108#2587C2214yes—
109#2587C2214yes—
110#2586C2214yes—
111#2585C2214yes—
112#2584C2212yes—
113#2584C2212yes—
114#2584C2212yes—
115#2584C2212yes—
116#2584C2212yes—
117#2583C2214yes—
118#2583C2214yes—
119#2583C2214yes—
120#2581C2214yes—
121#2580C2212yes—
122#2580C2212yes—
123#2574C2214yes—
124#2571C2212yes—
125#2570C2214yes—
126#2570C2214yes—
127#2568C2212yes—
128#2567C2214yes—
129#2567C2212yes—
130#2567C2212yes—
131#2564C2214yes—
132#2556C2214yes—
133#2556C2214yes—
134#2556C2214yes—
135#2552C2214yes—
136#2552C2211yescharacteristic
137#2552C2212yes—
138#2552C2211yescharacteristic
139#2551C2214yes—
140#2551C2214yes—
141#2551C2212yes—
142#2551C2211yescharacteristic
143#2550C2214yes—
144#2550C2214yes—
145#2550C2212yes—
146#2550C2212yes—
147#2549C2214yes—
148#2549C2214yes—
149#2549C2214yes—
150#2546C2211yescharacteristic
151#2546C2212yes—
152#2546C2212yes—
153#2542C2214yes—
154#2542C2211yescharacteristic
155#2538C2211yescharacteristic
156#2522C2214yes—
157#2522C2214yes—
158#2511C2214yes—
159#2509C2212yes—
160#2509C2212yes—
161#2509C2212yes—
162#2508C2212yes—
163#2507C2212yes—
164#2507C2212yes—
165#2507C2214yes—
166#2506C2212yes—
167#2505C2214yes—
168#2497C2214yes—
169#2487C2214yes—
170#2487C2214yes—
171#2473C2214yes—
172#2473C2214yes—
173#2454C2214yes—
174#2454C2212yes—
175#2454C2212yes—
176#2453C2214yes—
177#2452C2214yes—
178#2452C2212yes—
179#2451C2214yes—
180#2450C2214yes—
181#2450C2214yes—
182#2449C2214yes—
183#2449C2214yes—
184#2449C2214yes—
185#2442C2212yes—
186#2442C2212yes—
187#2441C2212yes—
188#2441C2212yes—
189#2440C2212yes—
190#2440C2212yes—
191#2440C2214yes—
192#2440C2214yes—
193#2440C2212yes—
194#2440C2214yes—
195#2440C2212yes—
196#2438C2214yes—
197#2429C2212yes—
198#2429C2214yes—
199#2423C2212yes—
200#2402C2214yes—
201#2399C2212yes—
202#2396C2212yes—
203#2396C2212yes—
204#2379C2214yes—
205#2377C2214yes—
206#2370C2212yes—
207#2370C2212yes—
208#2370C2212yes—
209#2369C2211yescharacteristic
210#2367C2214yes—
211#2367C2214yes—
212#2365C2212yes—
213#2363C2212yes—
214#2363C2212yes—
215#2361C2212yes—
216#2361C2212yes—
217#2355C2212yes—
218#2354C2211yescharacteristic
219#2352C2212yes—
220Q8×C4⋊C4C2212yes—
221#2349C2212yes—
222D4×C4⋊C4C2211yescharacteristic
223D4×C4⋊C4C2214yes—
224D4×C4⋊C4C2211yescharacteristic
225D4×C4⋊C4C2211yescharacteristic
226#2347C2212yes—
227#2347C2212yes—
228#2347C2212yes—
229#2346C2212yes—
230#2343C2214yes—
231#2337C2214yes—
232#2337C2214yes—
233#2331C2212yes—
234#2330C2214yes—
235#2330C2212yes—
236#2326C2214yes—
237#2325C2214yes—
238#2324C2212yes—
239#2324C2212yes—
240#2319C2212yes—
241#2317C2212yes—
242#2316C2212yes—
243#2314C2214yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×C22⋊Q8C2212yes—
248C4×#121C2212yes—
249C4×#121C2212yes—
250#2296C2212yes—
251#2296C2212yes—
252#2295C2211yescharacteristic
253#2293C2211yescharacteristic
254C2×#389C2212yes—
255C2×#389C2212yes—
256#2290C2212yes—
257#2274C2212yes—
258C42×D4C2211yescharacteristic
259#555Q8116yescomplemented
260#554—48no—
261#544—48no—
262#533—48no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2314yes—
275C2×C4⋊Q8C2311yescharacteristic
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#124C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2314yes—
310C2×C4×D4C2311yescharacteristic
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2311yescharacteristic
320C2×#117C2312yes—
321C2×#117C2312yes—
322C2×#117C2312yes—
323C2×#117C2312yes—
324C2×#117C2312yes—
325C2×#117C2312yes—
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2314yes—
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2314yes—
332C22×C42C2312yes—
333C22×C42C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2312yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2312yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2312yes—
357#399C2312yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2312yes—
388#398C2314yes—
389#398C2312yes—
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2312yes—
403#396C2314yes—
404#396C2314yes—
405#396C2312yes—
406#396C2312yes—
407#396C2312yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#395C2314yes—
412#395C2312yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2312yes—
427#395C2312yes—
428#395C2314yes—
429#395C2312yes—
430#395C2312yes—
431#395C2312yes—
432#395C2314yes—
433#395C2314yes—
434#393C2314yes—
435#393C2312yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#391C2312yes—
454#391C2311yescharacteristic
455#391C2314yes—
456#391C2311yescharacteristic
457#391C2314yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2314yes—
462#390C2314yes—
463#390C2314yes—
464#390C2311yescharacteristic
465#390C2311yescharacteristic
466#389C2312yes—
467#389C2311yescharacteristic
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2311yescharacteristic
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2311yescharacteristic
523#389C2312yes—
524#389C2311yescharacteristic
525#389C2312yes—
526#389C2312yes—
527#389C2314yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2312yes—
534#389C2314yes—
535#389C2311yescharacteristic
536#389C2311yescharacteristic
537#389C2314yes—
538#389C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
553#388C2312yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2312yes—
558#388C2312yes—
559#387C2314yes—
560#387C2314yes—
561#387C2312yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
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#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2312yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2312yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2312yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2312yes—
624#385C2314yes—
625#385C2314yes—
626#385C2312yes—
627#385C2314yes—
628#385C2314yes—
629#385C2312yes—
630#384C2311yescharacteristic
631#384C2311yescharacteristic
632#384C2311yescharacteristic
633#384C2314yes—
634#384C2314yes—
635#384C2314yes—
636#384C2314yes—
637#384C2312yes—
638#384C2312yes—
639#384C2312yes—
640#384C2311yescharacteristic
641#384C2311yescharacteristic
642#383C2314yes—
643#383C2314yes—
644#382C2314yes—
645#382C2314yes—
646#382C2314yes—
647#382C2312yes—
648#382C2312yes—
649#382C2314yes—
650#382C2312yes—
651#381C2314yes—
652#380C2312yes—
653#380C2314yes—
654#380C2314yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2314yes—
666#380C2312yes—
667#380C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711#376C2312yes—
712#376C2314yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C43C2311yescharacteristic
716C22×Q8C2411yescharacteristic
717C22×Q8C2412yes—
718C22×Q8C2412yes—
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×Q8C2414yes—
723C22×Q8C2412yes—
724C22×D4C2411yescharacteristic
725C22×D4C2414yes—
726C22×D4C2411yescharacteristic
727C23×C4C2412yes—
728C23×C4C2412yes—
729C23×C4C2414yes—
730C23×C4C2412yes—
731C23×C4C2414yes—
732C23×C4C2412yes—
733C23×C4C2414yes—
734C23×C4C2414yes—
735C23×C4C2412yes—
736C23×C4C2412yes—
737C4⋊Q8—24no—
738C4⋊Q8—42no—
739C4⋊Q8—44no—
740C4⋊Q8—44no—
741C4⋊Q8—44no—
742C4⋊Q8—44no—
743C4⋊Q8—48no—
744C4⋊Q8—82no—
745C4⋊Q8—82no—
746C4⋊Q8—84no—
747C4⋊Q8—84no—
748C4⋊Q8—84no—
749C4⋊Q8C2×Q818yes—
750#125—28no—
751#125—28no—
752#125—44no—
753#125—44no—
754#125—48no—
755#125—44no—
756#125—44no—
757#125—48no—
758#124C2×Q8132yes—
759C22⋊Q8—44no—
760C22⋊Q8—44no—
761C22⋊Q8—44no—
762C22⋊Q8—48no—
763C22⋊Q8—48no—
764C22⋊Q8—44no—
765C22⋊Q8—44no—
766C22⋊Q8—48no—
767C22⋊Q8—48no—
768C22⋊Q8—48no—
769C22⋊Q8—84no—
770C22⋊Q8—82no—
771C22⋊Q8—82no—
772C22⋊Q8—84no—
773C22⋊Q8—84no—
774C22⋊Q8—82no—
775#121C2×Q8116yes—
776#121C2×Q8116yes—
777C4×Q8—24no—
778C4×Q8—28no—
779C4×Q8—44no—
780C4×Q8—44no—
781C4×Q8—44no—
782C4×Q8—84no—
783C4×Q8—82no—
784C4×D4—24no—
785C4×D4—24no—
786C4×D4—44no—
787C4×D4—44no—
788C4×D4—48no—
789C4×D4—82no—
790C4×D4—84no—
791C4×D4—84no—
792C4×D4C2×Q818yes—
793C4×D4C2×Q818yes—
794#117—28no—
795#117—44no—
796#117—44no—
797#117—82no—
798#117C2×Q8116yes—
799#117C2×Q8116yes—
800C2×C4⋊C4—28no—
801C2×C4⋊C4—44no—
802C2×C4⋊C4—44no—
803C2×C4⋊C4—48no—
804C2×C4⋊C4—82no—
805C2×C4⋊C4—84no—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C42—44no—
923C2×C42—82no—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930C2×C42C2412yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2412yes—
937C2×C42C2411yescharacteristic
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2412yes—
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2414yes—
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2412yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24C2512yes—
1017C24C2512yes—
1018C2×Q8—24no—
1019C2×Q8—22no—
1020C2×Q8—24no—
1021C2×Q8—42no—
1022C2×Q8—42no—
1023C2×Q8—42no—
1024C2×Q8—42no—
1025C2×Q8—42no—
1026C2×Q8—42no—
1027C2×Q8—41no—
1028C2×Q8—42no—
1029C2×Q8—42no—
1030C2×Q8—41no—
1031C2×Q8—42no—
1032C2×Q8—42no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×Q8—44no—
1040C2×Q8—44no—
1041C2×Q8C22×Q818yes—
1042C2×D4—22no—
1043C2×D4—22no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—41no—
1047C2×D4—41no—
1048C2×D4C22×Q814yes—
1049C2×D4C22×Q814yes—
1050C2×D4C22×Q8116yes—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—28no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4C22×Q818yes—
1080C22×C4C22×Q818yes—
1081C22×C4C2511yescharacteristic
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2514yes—
1097C22×C4C2512yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2511yescharacteristic
1100C22×C4C2514yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2512yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—22no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—22no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—24no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—22no—
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—22no—
1131C4⋊C4—24no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—41no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—41no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—41no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—41no—
1173C4⋊C4—41no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—41no—
1189C4⋊C4—44no—
1190C4⋊C4—42no—
1191C4⋊C4C22×Q814yes—
1192C4⋊C4C22×Q814yes—
1193C4⋊C4C22×Q818yes—
1194C4⋊C4C22×Q818yes—
1195C4⋊C42−1+414yes—
1196C22⋊C4—24no—
1197C22⋊C4—24no—
1198C22⋊C4—24no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—44no—
1219C22⋊C4—42no—
1220C22⋊C4C22×Q8116yes—
1221C22⋊C4C22×Q8116yes—
1222C22⋊C4C22×Q818yes—
1223C22⋊C4C22×Q818yes—
1224C42—24no—
1225C42—24no—
1226C42—24no—
1227C42—24no—
1228C42—22no—
1229C42—24no—
1230C42—22no—
1231C42—42no—
1232C42—42no—
1233C42—41no—
1234C42—42no—
1235C42—42no—
1236C42—42no—
1237C42—41no—
1238C42—44no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42—41no—
1245C42—44no—
1246C42—44no—
1247C42—44no—
1248C42C22×Q8116yes—
1249C42C22×Q814yes—
1250C42H(5,𝔽2)14yes—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23C23×Q814yes—
1264C23C23×Q814yes—
1265C23C2611yescharacteristic
1266Q8—48no—
1267Q8—82no—
1268Q8—84no—
1269Q8—84no—
1270Q8—84no—
1271Q8—84no—
1272Q8—164no—
1273Q8—164no—
1274D4—28no—
1275D4—416no—
1276D4—44no—
1277C2×C4—22no—
1278C2×C4—21no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—21no—
1285C2×C4—22no—
1286C2×C4—21no—
1287C2×C4—24no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—22no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—216no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—21no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—21no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—48no—
1348C2×C4—48no—
1349C2×C4—84no—
1350C2×C4—88no—
1351C2×C4—84no—
1352C2×C4—88no—
1353C2×C4—84no—
1354C2×C4—164no—
1355C2×C4—164no—
1356C2×C4C23×Q814yes—
1357C2×C4C23×Q814yes—
1358C2×C4C23×Q812yes—
1359C2×C4C23×Q818yes—
1360C2×C4C23×Q812yes—
1361C2×C4C23×Q812yes—
1362C2×C4C2×H(5,𝔽2)12yes—
1363C2×C4C2×H(5,𝔽2)12yes—
1364C2×C4C2×H(5,𝔽2)12yes—
1365C2×C4C2×2−1+414yes—
1366C2×C4C2×2−1+412yes—
1367C2×C4#58512yes—
1368C22—24no—
1369C22—24no—
1370C22—24no—
1371C22—24no—
1372C22—24no—
1373C22—24no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—42no—
1382C22C24×Q811yescharacteristic
1383C22C22×H(5,𝔽2)11yescharacteristic
1384C22C22×2−1+411yescharacteristic
1385C22C2×#58511yescharacteristic
1386C22H(7,𝔽2)11yescharacteristic
1387C22H(7,𝔽2)11yescharacteristic
1388C222−1+611yescharacteristic
1389C4—28no—
1390C4—22no—
1391C4—24no—
1392C4—22no—
1393C4—24no—
1394C4—22no—
1395C4—22no—
1396C4—24no—
1397C4—22no—
1398C4—41no—
1399C4—42no—
1400C4—44no—
1401C4—42no—
1402C4—42no—
1403C4—42no—
1404C4—44no—
1405C4—44no—
1406C4—42no—
1407C4—42no—
1408C4—42no—
1409C4—44no—
1410C4—44no—
1411C4—42no—
1412C4—42no—
1413C4—42no—
1414C4—42no—
1415C4#350314yes—
1416C2—44no—
1417C2—44no—
1418C2C2×#350311yescharacteristic
1419C2#6285411yescharacteristic
1420C2#6288011yescharacteristic
1421C2#6294811yescharacteristic
1422C2#6296011yescharacteristic
1423C2#6298911yescharacteristic
1424C2#6306111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#555C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59870C2semidirect
2. #59454C2semidirect
3. #52162C2semidirect
4. #50907C2semidirect
5. #50707C2semidirect
6. #47969C2semidirect
7. #47726C2semidirect
8. #45793C2semidirect
9. #45358C2semidirect
10. #45086C2semidirect
11. #44950C2semidirect
12. #44941C2semidirect
13. #42933C2semidirect
14. #42493C2semidirect
15. #42189C2semidirect
16. #39986C2semidirect
17. #39637C2semidirect
18. #39631C2semidirect
19. #39590C2semidirect
20. #39365C2semidirect
21. #38447C2semidirect
22. #38101C2semidirect
23. #37308C2semidirect
24. #36261C2semidirect
25. #36039C2semidirect
26. #35566C2semidirect
27. #35176C2semidirect
259. #555Q8semidirect

Maximal subgroups

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

subgroupindex
#598702
#594542
#521622
#509072
#507072
#479692
#477262
#457932
#453582
#450862
#449502
#449412
#429332
#424932
#421892
#399862
#396372
#396312
#395902
#393652
#384472
#381012
#373082
#362612
#360392
#355662
#351762
#344672
#343212