Finite Group Databasebeta

← #7697183

Subgroups — #7697183

Order 512.

4771 conjugacy classes of subgroups.

The subgroup lattice has 1423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59832C211yesmaximal, characteristic, complemented
2#59831C212yesmaximal, complemented
3#59830C212yesmaximal, complemented
4#59655C214yesmaximal, complemented
5#52290C212yesmaximal, complemented
6#52267C211yesmaximal, characteristic, complemented
7#45359C212yesmaximal, complemented
8#45280C212yesmaximal, complemented
9#45110C212yesmaximal, complemented
10#44653C214yesmaximal, complemented
11#44277C214yesmaximal, complemented
12#43570C214yesmaximal, complemented
13#39969C214yesmaximal, complemented
14#39708C212yesmaximal, complemented
15#39688C212yesmaximal, complemented
16#39646C214yesmaximal, complemented
17#39637C211yesmaximal, characteristic, complemented
18#39365C211yesmaximal, characteristic, complemented
19#38447C212yesmaximal, complemented
20#38098C212yesmaximal, complemented
21#36481C212yesmaximal, complemented
22#36477C211yesmaximal, characteristic, complemented
23#35871C212yesmaximal, complemented
24#35819C212yesmaximal, complemented
25#35747C212yesmaximal, complemented
26#34332C211yesmaximal, characteristic, complemented
27#34321C211yesmaximal, characteristic
28#34306C212yesmaximal
29#34272C212yesmaximal, complemented
30C2×Q82C2212yes—
31C2×#555C2211yescharacteristic
32C2×#554C2211yescharacteristic
33C2×#554C2214yes—
34C2×#544C2212yes—
35#2863C2214yes—
36#2859C2211yescharacteristic
37#2857C2212yes—
38#2855C2212yes—
39#2809C2214yes—
40#2809C2212yes—
41#2807C2212yes—
42#2807C2214yes—
43#2806C2211yescharacteristic
44#2806C2212yes—
45#2805C2212yes—
46#2805C2211yescharacteristic
47#2804C2211yescharacteristic
48#2802C2212yes—
49#2802C2214yes—
50#2799C2214yes—
51#2792C2214yes—
52#2791C2214yes—
53#2790C2214yes—
54#2790C2212yes—
55#2788C2214yes—
56#2788C2212yes—
57#2784C2214yes—
58#2780C2214yes—
59#2780C2212yes—
60#2774C2214yes—
61#2768C2214yes—
62#2748C2214yes—
63#2734C2212yes—
64#2734C2212yes—
65#2734C2212yes—
66#2732C2211yescharacteristic
67#2732C2214yes—
68#2732C2212yes—
69#2732C2214yes—
70#2729C2212yes—
71#2729C2214yes—
72#2729C2214yes—
73#2729C2214yes—
74#2729C2214yes—
75#2726C2212yes—
76#2726C2212yes—
77#2720C2214yes—
78#2704C2214yes—
79#2692C2214yes—
80#2683C2212yes—
81#2666C2214yes—
82#2666C2214yes—
83#2665C2214yes—
84#2647C2212yes—
85#2629C2212yes—
86#2628C2212yes—
87#2608C2214yes—
88#2606C2214yes—
89#2606C2214yes—
90#2606C2214yes—
91#2605C2214yes—
92#2589C2214yes—
93#2589C2214yes—
94#2588C2214yes—
95#2587C2214yes—
96#2587C2214yes—
97#2587C2214yes—
98#2587C2214yes—
99#2585C2214yes—
100#2584C2212yes—
101#2583C2214yes—
102#2582C2214yes—
103#2582C2212yes—
104#2579C2214yes—
105#2579C2214yes—
106#2574C2214yes—
107#2570C2212yes—
108#2566C2212yes—
109#2564C2214yes—
110#2556C2214yes—
111#2556C2214yes—
112#2556C2214yes—
113#2552C2212yes—
114#2551C2212yes—
115#2551C2212yes—
116#2550C2214yes—
117#2550C2214yes—
118#2550C2212yes—
119#2550C2212yes—
120#2549C2214yes—
121#2546C2212yes—
122#2546C2212yes—
123#2538C2214yes—
124#2538C2211yescharacteristic
125#2538C2211yescharacteristic
126#2522C2214yes—
127#2522C2214yes—
128#2522C2214yes—
129#2509C2212yes—
130#2507C2212yes—
131#2507C2212yes—
132#2507C2212yes—
133#2506C2212yes—
134#2506C2212yes—
135#2505C2214yes—
136#2497C2212yes—
137#2492C2214yes—
138#2492C2214yes—
139#2473C2214yes—
140#2473C2214yes—
141#2465C2214yes—
142#2465C2214yes—
143#2462C2214yes—
144#2454C2212yes—
145#2453C2214yes—
146#2453C2214yes—
147#2452C2214yes—
148#2452C2214yes—
149#2452C2212yes—
150#2452C2212yes—
151#2452C2212yes—
152#2451C2214yes—
153#2451C2214yes—
154#2450C2214yes—
155#2450C2214yes—
156#2449C2214yes—
157#2449C2214yes—
158#2449C2214yes—
159#2442C2212yes—
160#2441C2212yes—
161#2441C2212yes—
162#2440C2214yes—
163#2440C2214yes—
164#2440C2212yes—
165#2440C2212yes—
166#2440C2212yes—
167#2438C2214yes—
168#2429C2212yes—
169#2429C2214yes—
170#2429C2214yes—
171#2429C2214yes—
172#2429C2214yes—
173#2429C2214yes—
174#2423C2214yes—
175#2402C2212yes—
176#2402C2214yes—
177#2399C2214yes—
178#2396C2214yes—
179#2396C2212yes—
180#2396C2212yes—
181#2372C2214yes—
182#2370C2212yes—
183#2370C2212yes—
184#2370C2212yes—
185#2370C2212yes—
186#2370C2212yes—
187#2369C2211yescharacteristic
188#2369C2211yescharacteristic
189#2369C2212yes—
190#2369C2212yes—
191#2368C2214yes—
192#2368C2214yes—
193#2367C2214yes—
194#2367C2214yes—
195#2365C2212yes—
196#2365C2212yes—
197#2365C2212yes—
198#2365C2212yes—
199#2364C2214yes—
200#2363C2212yes—
201#2363C2212yes—
202#2361C2212yes—
203#2361C2212yes—
204#2360C2214yes—
205#2360C2214yes—
206#2360C2212yes—
207#2360C2214yes—
208#2357C2212yes—
209#2355C2211yescharacteristic
210#2354C2211yescharacteristic
211#2352C2212yes—
212Q8×C4⋊C4C2211yescharacteristic
213Q8×C4⋊C4C2211yescharacteristic
214D4×C4⋊C4C2211yescharacteristic
215D4×C4⋊C4C2211yescharacteristic
216D4×C4⋊C4C2212yes—
217#2347C2212yes—
218#2347C2212yes—
219#2347C2212yes—
220#2346C2212yes—
221#2345C2212yes—
222#2343C2214yes—
223#2337C2214yes—
224#2337C2214yes—
225#2333C2214yes—
226#2331C2212yes—
227#2331C2214yes—
228#2330C2212yes—
229#2330C2214yes—
230#2329C2214yes—
231#2324C2212yes—
232#2324C2212yes—
233#2317C2212yes—
234C4×C4⋊Q8C2214yes—
235C4×C4⋊Q8C2214yes—
236C4×C4⋊Q8C2211yescharacteristic
237C4×C4⋊Q8C2211yescharacteristic
238C4×C4⋊Q8C2211yescharacteristic
239C4×#125C2214yes—
240C4×#124C2214yes—
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×#121C2212yes—
245C4×#121C2212yes—
246#2298C2214yes—
247#2296C2212yes—
248#2296C2212yes—
249#2295C2211yescharacteristic
250#2293C2211yescharacteristic
251C2×#389C2212yes—
252C2×#389C2212yes—
253#2290C2212yes—
254#2275C2212yes—
255#2274C2212yes—
256#2274C2212yes—
257C42×D4C2211yescharacteristic
258C4×#117C2212yes—
259Q82—48no—
260#555Q8116yescomplemented
261#554—28no—
262#554—416no—
263#544—216no—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×#125C2314yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#124C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2314yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2314yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2314yes—
308C2×C4×Q8C2312yes—
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2312yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2314yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2311yescharacteristic
319C2×#117C2312yes—
320C2×#117C2312yes—
321C2×#117C2312yes—
322C2×#117C2312yes—
323C2×#117C2312yes—
324C2×#117C2312yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2314yes—
329C22×C4⋊C4C2314yes—
330C22×C4⋊C4C2312yes—
331C22×C42C2312yes—
332C22×C42C2312yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2312yes—
339#400C2314yes—
340#400C2312yes—
341#400C2314yes—
342#400C2312yes—
343#400C2314yes—
344#400C2312yes—
345#400C2312yes—
346#400C2314yes—
347#400C2312yes—
348#399C2314yes—
349#399C2312yes—
350#399C2314yes—
351#399C2314yes—
352#399C2312yes—
353#399C2314yes—
354#398C2314yes—
355#398C2312yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2312yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2314yes—
382#398C2314yes—
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2312yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2312yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2312yes—
401#396C2312yes—
402#396C2314yes—
403#396C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2312yes—
412#395C2312yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2312yes—
421#393C2314yes—
422#393C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2311yescharacteristic
428#391C2314yes—
429#391C2314yes—
430#391C2311yescharacteristic
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2311yescharacteristic
447#391C2311yescharacteristic
448#390C2312yes—
449#390C2312yes—
450#390C2314yes—
451#390C2312yes—
452#390C2314yes—
453#390C2314yes—
454#390C2311yescharacteristic
455#390C2311yescharacteristic
456#389C2312yes—
457#389C2314yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#389C2314yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2314yes—
498#389C2312yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#389C2312yes—
508#389C2311yescharacteristic
509#389C2312yes—
510#389C2311yescharacteristic
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2311yescharacteristic
523#389C2311yescharacteristic
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2312yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2312yes—
541#388C2312yes—
542#388C2314yes—
543#388C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2312yes—
577#387C2314yes—
578#387C2312yes—
579#387C2312yes—
580#387C2314yes—
581#387C2312yes—
582#387C2314yes—
583#387C2312yes—
584#386C2312yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2312yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2312yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2312yes—
614#385C2312yes—
615#385C2314yes—
616#385C2312yes—
617#385C2312yes—
618#385C2312yes—
619#385C2312yes—
620#385C2312yes—
621#384C2314yes—
622#384C2311yescharacteristic
623#384C2314yes—
624#384C2311yescharacteristic
625#384C2311yescharacteristic
626#384C2312yes—
627#384C2312yes—
628#384C2311yescharacteristic
629#384C2311yescharacteristic
630#383C2314yes—
631#383C2314yes—
632#382C2314yes—
633#382C2312yes—
634#382C2312yes—
635#382C2314yes—
636#381C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2312yes—
645#380C2312yes—
646#380C2312yes—
647#380C2312yes—
648#380C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710#376C2314yes—
711#376C2312yes—
712#376C2314yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C43C2314yes—
716C43C2311yescharacteristic
717C22×Q8C2411yescharacteristic
718C22×Q8C2414yes—
719C22×Q8C2414yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2414yes—
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×D4C2411yescharacteristic
726C22×D4C2414yes—
727C22×D4C2411yescharacteristic
728C23×C4C2412yes—
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2414yes—
732C23×C4C2414yes—
733C23×C4C2412yes—
734C23×C4C2414yes—
735C23×C4C2414yes—
736C23×C4C2412yes—
737C23×C4C2412yes—
738C4⋊Q8—216no—
739C4⋊Q8—216no—
740C4⋊Q8—24no—
741C4⋊Q8—28no—
742C4⋊Q8—44no—
743C4⋊Q8—44no—
744C4⋊Q8—48no—
745C4⋊Q8—48no—
746C4⋊Q8—48no—
747C4⋊Q8C2×Q818yes—
748C4⋊Q8#4118yes—
749#125—216no—
750#125—28no—
751#125—28no—
752#125—28no—
753#125—48no—
754#125—48no—
755#124C2×Q8132yes—
756C22⋊Q8—216no—
757C22⋊Q8—216no—
758C22⋊Q8—28no—
759C22⋊Q8—28no—
760C22⋊Q8—216no—
761C22⋊Q8—28no—
762C22⋊Q8—48no—
763C22⋊Q8—48no—
764C22⋊Q8—48no—
765C22⋊Q8—48no—
766C22⋊Q8—84no—
767C22⋊Q8—84no—
768C22⋊Q8—84no—
769C22⋊Q8—82no—
770#121C2×Q8116yes—
771#121C2×Q8116yes—
772C4×Q8—24no—
773C4×Q8—42no—
774C4×Q8—42no—
775C4×Q8—48no—
776C4×Q8—48no—
777C4×Q8—48no—
778C4×Q8—44no—
779C4×Q8—44no—
780C4×Q8—82no—
781C4×Q8—82no—
782C4×Q8—84no—
783C4×D4—28no—
784C4×D4—24no—
785C4×D4—48no—
786C4×D4—44no—
787C4×D4—42no—
788C4×D4—48no—
789C4×D4—48no—
790C4×D4—82no—
791C4×D4C2×Q818yes—
792C4×D4C2×Q818yes—
793#117—28no—
794#117—28no—
795#117—44no—
796#117—82no—
797#117C2×Q8116yes—
798#117C2×Q8116yes—
799C2×C4⋊C4—28no—
800C2×C4⋊C4—28no—
801C2×C4⋊C4—44no—
802C2×C4⋊C4—48no—
803C2×C4⋊C4—48no—
804C2×C4⋊C4—82no—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C42—44no—
916C2×C42—82no—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2414yes—
922C2×C42C2411yescharacteristic
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2412yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2414yes—
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941C2×C42C2414yes—
942C2×C42C2411yescharacteristic
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015C24C2512yes—
1016C24C2512yes—
1017C2×Q8—22no—
1018C2×Q8—28no—
1019C2×Q8—28no—
1020C2×Q8—22no—
1021C2×Q8—42no—
1022C2×Q8—42no—
1023C2×Q8—41no—
1024C2×Q8—41no—
1025C2×Q8—41no—
1026C2×Q8—42no—
1027C2×Q8—42no—
1028C2×Q8—41no—
1029C2×Q8—44no—
1030C2×Q8—41no—
1031C2×Q8—44no—
1032C2×Q8—41no—
1033C2×Q8—44no—
1034C2×Q8—44no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8C22×Q818yes—
1039C2×Q8C2×#4118yes—
1040C2×Q8H(5,𝔽2)14yes—
1041C2×D4—22no—
1042C2×D4—22no—
1043C2×D4—44no—
1044C2×D4—41no—
1045C2×D4—44no—
1046C2×D4—41no—
1047C2×D4C22×Q814yes—
1048C2×D4C22×Q814yes—
1049C2×D4C22×Q8116yes—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—28no—
1054C22×C4—28no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—44no—
1069C22×C4—44no—
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×C4C22×Q818yes—
1079C22×C4C22×Q818yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2514yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2514yes—
1095C22×C4C2514yes—
1096C22×C4C2511yescharacteristic
1097C22×C4C2512yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2514yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2512yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2511yescharacteristic
1107C4⋊C4—22no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—22no—
1115C4⋊C4—24no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—22no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—41no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—41no—
1148C4⋊C4—41no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—41no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—41no—
1164C4⋊C4—41no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4C22×Q814yes—
1184C4⋊C4C22×Q814yes—
1185C4⋊C4C22×Q818yes—
1186C4⋊C4C22×Q818yes—
1187C4⋊C4C2×#4118yes—
1188C4⋊C4C2×#4118yes—
1189C22⋊C4—28no—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—28no—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—28no—
1196C22⋊C4—24no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4C22×Q8116yes—
1214C22⋊C4C22×Q8116yes—
1215C22⋊C4C22×Q818yes—
1216C22⋊C4C22×Q818yes—
1217C42—28no—
1218C42—24no—
1219C42—24no—
1220C42—28no—
1221C42—22no—
1222C42—24no—
1223C42—24no—
1224C42—24no—
1225C42—22no—
1226C42—42no—
1227C42—42no—
1228C42—41no—
1229C42—42no—
1230C42—42no—
1231C42—42no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C42—41no—
1236C42—41no—
1237C42—44no—
1238C42—44no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42—44no—
1245C42C22×Q8116yes—
1246C42C22×Q814yes—
1247C42C2×#4114yes—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23—22no—
1259C23—22no—
1260C23C23×Q814yes—
1261C23C23×Q814yes—
1262C23C2611yescharacteristic
1263Q8—48no—
1264Q8—48no—
1265Q8—44no—
1266Q8—44no—
1267Q8—88no—
1268Q8—82no—
1269Q8—88no—
1270Q8—164no—
1271D4—28no—
1272D4—416no—
1273D4—44no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—24no—
1294C2×C4—216no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—21no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—21no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—21no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—48no—
1344C2×C4—48no—
1345C2×C4—88no—
1346C2×C4—88no—
1347C2×C4—84no—
1348C2×C4—84no—
1349C2×C4—84no—
1350C2×C4—164no—
1351C2×C4—164no—
1352C2×C4C23×Q814yes—
1353C2×C4C23×Q814yes—
1354C2×C4C23×Q812yes—
1355C2×C4C23×Q818yes—
1356C2×C4C23×Q812yes—
1357C2×C4C23×Q812yes—
1358C2×C4C22×#4118yes—
1359C2×C4C22×#4112yes—
1360C2×C4C22×#4112yes—
1361C2×C4C22×#4112yes—
1362C2×C4C2×H(5,𝔽2)14yes—
1363C2×C4C2×H(5,𝔽2)12yes—
1364C2×C4#58512yes—
1365C22—24no—
1366C22—24no—
1367C22—24no—
1368C22—24no—
1369C22—24no—
1370C22—24no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22C24×Q811yescharacteristic
1380C22C23×#4111yescharacteristic
1381C22C22×H(5,𝔽2)11yescharacteristic
1382C22C2×#58511yescharacteristic
1383C22H(7,𝔽2)11yescharacteristic
1384C222−1+611yescharacteristic
1385C222−1+611yescharacteristic
1386C4—28no—
1387C4—22no—
1388C4—28no—
1389C4—22no—
1390C4—22no—
1391C4—22no—
1392C4—24no—
1393C4—22no—
1394C4—24no—
1395C4—24no—
1396C4—42no—
1397C4—44no—
1398C4—42no—
1399C4—41no—
1400C4—42no—
1401C4—42no—
1402C4—42no—
1403C4—42no—
1404C4—44no—
1405C4—42no—
1406C4—42no—
1407C4—42no—
1408C4—42no—
1409C4—44no—
1410C4—44no—
1411C4—42no—
1412C4Q8×#4114yes—
1413C2—44no—
1414C2—44no—
1415C2C2×Q8×#4111yescharacteristic
1416C2#6285111yescharacteristic
1417C2#6285411yescharacteristic
1418C2#6290511yescharacteristic
1419C2Q8×H(5,𝔽2)11yescharacteristic
1420C2#6298411yescharacteristic
1421C2#6305311yescharacteristic
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. #59832C2semidirect
2. #59831C2semidirect
3. #59830C2semidirect
4. #59655C2semidirect
5. #52290C2semidirect
6. #52267C2semidirect
7. #45359C2semidirect
8. #45280C2semidirect
9. #45110C2semidirect
10. #44653C2semidirect
11. #44277C2semidirect
12. #43570C2semidirect
13. #39969C2semidirect
14. #39708C2semidirect
15. #39688C2semidirect
16. #39646C2semidirect
17. #39637C2semidirect
18. #39365C2semidirect
19. #38447C2semidirect
20. #38098C2semidirect
21. #36481C2semidirect
22. #36477C2semidirect
23. #35871C2semidirect
24. #35819C2semidirect
25. #35747C2semidirect
26. #34332C2semidirect
29. #34272C2semidirect
260. #555Q8semidirect

Maximal subgroups

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

subgroupindex
#598322
#598312
#598302
#596552
#522902
#522672
#453592
#452802
#451102
#446532
#442772
#435702
#399692
#397082
#396882
#396462
#396372
#393652
#384472
#380982
#364812
#364772
#358712
#358192
#357472
#343322
#343212
#343062
#342722