Finite Group Databasebeta

← #7711774

Subgroups — #7711774

Order 512.

4578 conjugacy classes of subgroups.

The subgroup lattice has 1467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59918C212yesmaximal, complemented
2#59866C212yesmaximal, complemented
3#59856C212yesmaximal
4#59830C212yesmaximal
5#46153C211yesmaximal, characteristic, complemented
6#46152C211yesmaximal, characteristic, complemented
7#46009C212yesmaximal, complemented
8#46008C212yesmaximal, complemented
9#46006C211yesmaximal, characteristic, complemented
10#46005C211yesmaximal, characteristic, complemented
11#39698C214yesmaximal, complemented
12#39662C212yesmaximal, complemented
13#39661C212yesmaximal, complemented
14#39604C212yesmaximal, complemented
15#39604C212yesmaximal, complemented
16#39589C214yesmaximal, complemented
17#38457C214yesmaximal, complemented
18#38441C214yesmaximal, complemented
19#37609C212yesmaximal, complemented
20#37196C212yesmaximal, complemented
21#37137C212yesmaximal, complemented
22#36635C211yesmaximal, characteristic, complemented
23C2×#2859C211yesmaximal, characteristic, complemented
24#36287C212yesmaximal, complemented
25#36280C212yesmaximal, complemented
26#36278C212yesmaximal, complemented
27#36261C212yesmaximal, complemented
28#35208C212yesmaximal, complemented
29#35017C212yesmaximal, complemented
30#34390C212yesmaximal
31C4×#529C211yesmaximal, characteristic
32C2×#554C2214yes—
33C2×#529C2211yescharacteristic
34C22×#125C2212yes—
35#2864C2212yes—
36#2863C2212yes—
37#2863C2212yes—
38#2863C2212yes—
39#2862C2211yescharacteristic
40#2859C2212yes—
41#2859C2212yes—
42#2859C2212yes—
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2859C2212yes—
46#2859C2211yescharacteristic
47#2859C2212yes—
48#2859C2211yescharacteristic
49#2859C2212yes—
50#2859C2211yescharacteristic
51#2859C2212yes—
52#2857C2211yescharacteristic
53#2857C2211yescharacteristic
54#2857C2212yes—
55#2855C2212yes—
56#2855C2212yes—
57#2855C2212yes—
58#2851C2212yes—
59#2845C2212yes—
60#2845C2212yes—
61#2844C2212yes—
62#2844C2212yes—
63#2809C2212yes—
64#2807C2214yes—
65#2806C2214yes—
66#2806C2212yes—
67#2805C2212yes—
68#2802C2214yes—
69#2802C2214yes—
70#2792C2214yes—
71#2792C2214yes—
72#2792C2214yes—
73#2792C2214yes—
74#2791C2214yes—
75#2791C2214yes—
76#2790C2214yes—
77#2790C2214yes—
78#2780C2214yes—
79#2774C2214yes—
80#2768C2214yes—
81#2734C2212yes—
82#2732C2212yes—
83#2726C2212yes—
84#2726C2214yes—
85#2726C2214yes—
86#2726C2212yes—
87#2726C2214yes—
88#2720C2214yes—
89#2720C2214yes—
90#2720C2214yes—
91#2720C2214yes—
92#2720C2214yes—
93#2713C2214yes—
94#2713C2214yes—
95#2704C2214yes—
96#2704C2214yes—
97#2704C2214yes—
98#2683C2212yes—
99#2667C2214yes—
100#2666C2214yes—
101#2666C2214yes—
102#2666C2214yes—
103#2666C2214yes—
104#2666C2214yes—
105#2627C2214yes—
106#2627C2214yes—
107#2612C2214yes—
108#2612C2214yes—
109#2612C2214yes—
110#2608C2214yes—
111#2606C2214yes—
112#2606C2214yes—
113#2590C2214yes—
114#2590C2214yes—
115#2587C2214yes—
116#2587C2214yes—
117#2586C2214yes—
118#2585C2214yes—
119#2585C2214yes—
120#2584C2214yes—
121#2583C2214yes—
122#2583C2214yes—
123#2583C2214yes—
124#2582C2212yes—
125#2579C2214yes—
126#2579C2214yes—
127#2569C2214yes—
128#2569C2214yes—
129#2567C2212yes—
130#2567C2212yes—
131#2567C2212yes—
132#2556C2214yes—
133#2556C2214yes—
134#2556C2214yes—
135#2556C2214yes—
136#2552C2212yes—
137#2552C2212yes—
138#2552C2212yes—
139#2551C2212yes—
140#2550C2214yes—
141#2549C2214yes—
142#2549C2214yes—
143#2549C2214yes—
144#2522C2214yes—
145#2511C2212yes—
146#2511C2212yes—
147#2511C2212yes—
148#2507C2214yes—
149#2507C2212yes—
150#2507C2212yes—
151#2507C2212yes—
152#2507C2212yes—
153#2507C2212yes—
154#2507C2212yes—
155#2506C2214yes—
156#2506C2214yes—
157#2502C2214yes—
158#2502C2212yes—
159#2502C2212yes—
160#2497C2212yes—
161#2497C2212yes—
162#2497C2212yes—
163#2497C2212yes—
164#2487C2214yes—
165#2487C2212yes—
166#2473C2214yes—
167#2473C2214yes—
168#2473C2214yes—
169#2473C2214yes—
170#2462C2214yes—
171#2462C2214yes—
172#2462C2214yes—
173#2462C2214yes—
174#2453C2214yes—
175#2451C2212yes—
176#2451C2212yes—
177#2449C2214yes—
178#2449C2214yes—
179#2449C2214yes—
180#2446C2212yes—
181#2441C2214yes—
182#2440C2212yes—
183#2440C2212yes—
184#2440C2212yes—
185#2440C2212yes—
186#2440C2212yes—
187#2440C2212yes—
188#2438C2214yes—
189#2429C2214yes—
190#2429C2212yes—
191#2423C2212yes—
192#2423C2212yes—
193#2423C2212yes—
194#2417C2212yes—
195#2417C2212yes—
196#2417C2212yes—
197#2382C2212yes—
198#2382C2212yes—
199#2379C2212yes—
200#2379C2212yes—
201#2370C2214yes—
202#2369C2212yes—
203#2368C2214yes—
204#2364C2214yes—
205#2360C2212yes—
206#2360C2212yes—
207#2360C2214yes—
208#2360C2212yes—
209#2353C2214yes—
210Q8×C4⋊C4C2212yes—
211#2349C2214yes—
212D4×C4⋊C4C2212yes—
213D4×C4⋊C4C2212yes—
214#2346C2214yes—
215#2345C2214yes—
216#2345C2212yes—
217#2343C2214yes—
218#2334C2214yes—
219#2334C2214yes—
220#2330C2214yes—
221#2329C2214yes—
222#2322C2214yes—
223#2322C2214yes—
224#2320C2214yes—
225#2318C2214yes—
226C4×C4⋊Q8C2211yescharacteristic
227C4×C4⋊Q8C2211yescharacteristic
228C4×C4⋊Q8C2212yes—
229C4×#125C2212yes—
230C4×#125C2211yescharacteristic
231C4×#125C2211yescharacteristic
232C4×#126C2212yes—
233C4×#126C2212yes—
234C4×#124C2211yescharacteristic
235C4×#124C2211yescharacteristic
236C4×C22⋊Q8C2211yescharacteristic
237C4×C22⋊Q8C2212yes—
238C4×C22⋊Q8C2212yes—
239C4×C22⋊Q8C2212yes—
240C4×C22⋊Q8C2211yescharacteristic
241C4×#123C2212yes—
242C4×#123C2212yes—
243C4×#121C2211yescharacteristic
244C4×#121C2211yescharacteristic
245#2298C2212yes—
246#2295C2212yes—
247#2295C2212yes—
248#2295C2211yescharacteristic
249#2295C2212yes—
250#2293C2211yescharacteristic
251C2×#389C2212yes—
252C2×#389C2212yes—
253C2×#389C2212yes—
254C2×#389C2212yes—
255C2×#389C2212yes—
256#2290C2212yes—
257C2×#384C2211yescharacteristic
258C2×#384C2211yescharacteristic
259#2283C2212yes—
260#2283C2211yescharacteristic
261C2×#382C2212yes—
262C42×Q8C2211yescharacteristic
263C42×D4C2212yes—
264C42×D4C2211yescharacteristic
265C4×#117C2212yes—
266C2×C43C2211yescharacteristic
267#554—416no—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2314yes—
273#529Q8116yescomplemented
274C2×#126C2312yes—
275C2×#125—48no—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#125C2311yescharacteristic
288C2×#124C2311yescharacteristic
289C2×#123C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2311yescharacteristic
302C2×#121C2311yescharacteristic
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2312yes—
319C2×#117C2312yes—
320C2×#117C2312yes—
321C22×C4⋊C4C2314yes—
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2314yes—
325C22×C4⋊C4C2314yes—
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2312yes—
332C22×C42C2311yescharacteristic
333C22×C42C2311yescharacteristic
334C22×C42C2311yescharacteristic
335C22×C42C2312yes—
336C22×C42C2311yescharacteristic
337C22×C42C2311yescharacteristic
338C22×C42C2311yescharacteristic
339C22×C42C2311yescharacteristic
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
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#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#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2314yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#391C2311yescharacteristic
441#391C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#389C2312yes—
445#389C2312yes—
446#389C2311yescharacteristic
447#389C2311yescharacteristic
448#389C2311yescharacteristic
449#389C2311yescharacteristic
450#389C2314yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2312yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#388C2312yes—
523#388C2312yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2312yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2312yes—
537#388C2312yes—
538#387C2312yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
542#387C2312yes—
543#387C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2312yes—
547#387C2312yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
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#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2312yes—
595#386C2312yes—
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#385C2314yes—
610#385C2314yes—
611#385C2312yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2312yes—
620#384C2312yes—
621#384C2311yescharacteristic
622#384C2311yescharacteristic
623#384C2311yescharacteristic
624#384C2314yes—
625#384C2312yes—
626#384C2312yes—
627#384C2312yes—
628#384C2312yes—
629#384C2311yescharacteristic
630#384C2312yes—
631#384C2311yescharacteristic
632#384C2312yes—
633#384C2312yes—
634#384C2311yescharacteristic
635#384C2312yes—
636#384C2312yes—
637#384C2314yes—
638#383C2312yes—
639#383C2314yes—
640#383C2314yes—
641#382C2311yescharacteristic
642#382C2311yescharacteristic
643#382C2312yes—
644#382C2314yes—
645#382C2314yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2314yes—
651#382C2312yes—
652#382C2312yes—
653#381C2314yes—
654#381C2314yes—
655#381C2312yes—
656#380C2311yescharacteristic
657#380C2314yes—
658#380C2312yes—
659#380C2314yes—
660#380C2314yes—
661#380C2312yes—
662#380C2314yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2314yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2311yescharacteristic
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C4⋊C4C2311yescharacteristic
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721#376C2314yes—
722#376C2314yes—
723#376C2312yes—
724#376C2312yes—
725C2×#95C2314yes—
726C2×#95C2314yes—
727C2×#95C2314yes—
728C43C2311yescharacteristic
729C43C2311yescharacteristic
730C43C2311yescharacteristic
731C43C2311yescharacteristic
732C43C2312yes—
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C22×Q8C2412yes—
738C22×Q8C2412yes—
739C22×Q8C2414yes—
740C22×Q8C2414yes—
741C22×Q8C2411yescharacteristic
742C22×D4C2412yes—
743C22×D4C2411yescharacteristic
744C23×C4C2411yescharacteristic
745C23×C4C2412yes—
746C23×C4C2411yescharacteristic
747C23×C4C2411yescharacteristic
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2411yescharacteristic
751C23×C4C2412yes—
752C23×C4C2414yes—
753C23×C4C2414yes—
754C23×C4C2412yes—
755C23×C4C2411yescharacteristic
756C23×C4C2411yescharacteristic
757C23×C4C2411yescharacteristic
758C4⋊Q8—44no—
759C4⋊Q8—42no—
760C4⋊Q8—44no—
761C4⋊Q8—42no—
762C4⋊Q8—48no—
763#126C2×Q8116yes—
764#125—44no—
765#125—48no—
766#125—44no—
767#125—44no—
768#125—48no—
769#125—44no—
770#125—44no—
771#125—48no—
772#125—48no—
773#125—48no—
774#125—48no—
775#125C2×Q818yes—
776#124C2×Q818yes—
777#123C2×Q8116yes—
778C22⋊Q8—28no—
779C22⋊Q8—28no—
780C22⋊Q8—48no—
781C22⋊Q8—48no—
782C22⋊Q8—48no—
783C22⋊Q8—48no—
784C22⋊Q8—48no—
785C22⋊Q8—48no—
786C22⋊Q8—48no—
787C22⋊Q8—44no—
788C22⋊Q8—44no—
789C22⋊Q8C2×Q818yes—
790#121C2×Q818yes—
791C4×Q8—42no—
792C4×Q8—42no—
793C4×Q8—44no—
794C4×Q8—48no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×Q8—44no—
798C4×Q8C2×Q818yes—
799C4×D4—28no—
800C4×D4—28no—
801C4×D4—42no—
802C4×D4—42no—
803C4×D4—48no—
804C4×D4—48no—
805C4×D4C2×Q818yes—
806C4×D4C2×Q8116yes—
807#117—44no—
808#117C2×Q8116yes—
809C2×C4⋊C4—216no—
810C2×C4⋊C4—44no—
811C2×C4⋊C4—44no—
812C2×C4⋊C4—44no—
813C2×C4⋊C4—44no—
814C2×C4⋊C4—44no—
815C2×C4⋊C4—44no—
816C2×C4⋊C4—48no—
817C2×C4⋊C4—44no—
818C2×C4⋊C4—44no—
819C2×C4⋊C4—48no—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2411yescharacteristic
901C2×C4⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C42—24no—
924C2×C42—24no—
925C2×C42—44no—
926C2×C42—42no—
927C2×C42—42no—
928C2×C42—42no—
929C2×C42—42no—
930C2×C42C2×Q818yes—
931C2×C42C2411yescharacteristic
932C2×C42C2412yes—
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2412yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2411yescharacteristic
962C2×C42C2411yescharacteristic
963C2×C42C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968C2×C42C2411yescharacteristic
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2411yescharacteristic
972C2×C42C2412yes—
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975C2×C42C2411yescharacteristic
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042C24C2512yes—
1043C24C2511yescharacteristic
1044C2×Q8—24no—
1045C2×Q8—24no—
1046C2×Q8—24no—
1047C2×Q8—24no—
1048C2×Q8—41no—
1049C2×Q8—41no—
1050C2×Q8—44no—
1051C2×Q8—42no—
1052C2×Q8—44no—
1053C2×Q8—42no—
1054C2×Q8—44no—
1055C2×Q8—44no—
1056C2×Q8—44no—
1057C2×Q8—44no—
1058C2×Q8C22×Q814yes—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—41no—
1062C2×D4—41no—
1063C2×D4C22×Q818yes—
1064C2×D4C22×Q814yes—
1065C22×C4—22no—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—22no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—22no—
1072C22×C4—22no—
1073C22×C4—28no—
1074C22×C4—28no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—41no—
1080C22×C4—41no—
1081C22×C4—42no—
1082C22×C4—41no—
1083C22×C4—41no—
1084C22×C4—41no—
1085C22×C4—41no—
1086C22×C4—41no—
1087C22×C4—41no—
1088C22×C4—42no—
1089C22×C4—42no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4C22×Q814yes—
1102C22×C4C22×Q814yes—
1103C22×C4C22×Q814yes—
1104C22×C4C22×Q818yes—
1105C22×C4H(5,𝔽2)14yes—
1106C22×C42−1+414yes—
1107C22×C4C2514yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2514yes—
1111C22×C4C2514yes—
1112C22×C4C2512yes—
1113C22×C4C2514yes—
1114C22×C4C2512yes—
1115C22×C4C2514yes—
1116C22×C4C2514yes—
1117C22×C4C2514yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2514yes—
1121C22×C4C2511yescharacteristic
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C22×C4C2512yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2511yescharacteristic
1131C22×C4C2511yescharacteristic
1132C22×C4C2511yescharacteristic
1133C22×C4C2511yescharacteristic
1134C22×C4C2511yescharacteristic
1135C22×C4C2511yescharacteristic
1136C4⋊C4—28no—
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—28no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—28no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—28no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—28no—
1157C4⋊C4—24no—
1158C4⋊C4—28no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—41no—
1180C4⋊C4—41no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—41no—
1185C4⋊C4—41no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—42no—
1210C4⋊C4—42no—
1211C4⋊C4—42no—
1212C4⋊C4C22×Q818yes—
1213C4⋊C4C22×Q818yes—
1214C4⋊C4C22×Q814yes—
1215C4⋊C4C22×Q818yes—
1216C4⋊C4C22×Q814yes—
1217C4⋊C4C22×Q818yes—
1218C22⋊C4—24no—
1219C22⋊C4—28no—
1220C22⋊C4—24no—
1221C22⋊C4—28no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—24no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4C22×Q818yes—
1235C22⋊C4C22×Q818yes—
1236C22⋊C4C22×Q818yes—
1237C22⋊C4C22×Q818yes—
1238C22⋊C4C22×Q818yes—
1239C42—22no—
1240C42—22no—
1241C42—22no—
1242C42—22no—
1243C42—24no—
1244C42—22no—
1245C42—22no—
1246C42—22no—
1247C42—22no—
1248C42—24no—
1249C42—22no—
1250C42—22no—
1251C42—22no—
1252C42—22no—
1253C42—22no—
1254C42—22no—
1255C42—24no—
1256C42—22no—
1257C42—22no—
1258C42—24no—
1259C42—41no—
1260C42—41no—
1261C42—42no—
1262C42—41no—
1263C42—41no—
1264C42—41no—
1265C42—42no—
1266C42—41no—
1267C42—41no—
1268C42—41no—
1269C42—42no—
1270C42—44no—
1271C42—44no—
1272C42—44no—
1273C42—44no—
1274C42—44no—
1275C42—42no—
1276C42—44no—
1277C42—44no—
1278C42—44no—
1279C42C22×Q814yes—
1280C42C22×Q814yes—
1281C42C22×Q814yes—
1282C42C22×Q814yes—
1283C42C22×Q818yes—
1284C23—21no—
1285C23—21no—
1286C23—21no—
1287C23—21no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23C23×Q814yes—
1295C23C23×Q812yes—
1296C23C2×H(5,𝔽2)12yes—
1297C23C2×2−1+412yes—
1298C23C2611yescharacteristic
1299Q8—44no—
1300Q8—48no—
1301Q8—84no—
1302Q8—88no—
1303Q8—164no—
1304D4—216no—
1305D4—44no—
1306C2×C4—28no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—28no—
1336C2×C4—28no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—44no—
1380C2×C4—48no—
1381C2×C4—44no—
1382C2×C4—44no—
1383C2×C4—44no—
1384C2×C4—48no—
1385C2×C4—84no—
1386C2×C4—88no—
1387C2×C4—88no—
1388C2×C4—88no—
1389C2×C4—164no—
1390C2×C4C23×Q812yes—
1391C2×C4C23×Q812yes—
1392C2×C4C23×Q812yes—
1393C2×C4C23×Q812yes—
1394C2×C4C23×Q812yes—
1395C2×C4C23×Q812yes—
1396C2×C4C23×Q814yes—
1397C2×C4C23×Q814yes—
1398C2×C4C23×Q814yes—
1399C2×C4C2×H(5,𝔽2)12yes—
1400C2×C4C2×H(5,𝔽2)12yes—
1401C2×C4C2×2−1+412yes—
1402C2×C4C2×2−1+412yes—
1403C2×C4#58512yes—
1404C2×C4#58512yes—
1405C2×C4#58512yes—
1406C2×C4#58512yes—
1407C22—22no—
1408C22—22no—
1409C22—22no—
1410C22—22no—
1411C22—22no—
1412C22—22no—
1413C22—24no—
1414C22—24no—
1415C22—24no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22#350314yes—
1421C22C24×Q811yescharacteristic
1422C22C22×H(5,𝔽2)11yescharacteristic
1423C22C22×2−1+411yescharacteristic
1424C22C2×#58511yescharacteristic
1425C22C2×#58511yescharacteristic
1426C22C2×#58511yescharacteristic
1427C22C2×#58511yescharacteristic
1428C4—22no—
1429C4—22no—
1430C4—22no—
1431C4—24no—
1432C4—22no—
1433C4—22no—
1434C4—24no—
1435C4—22no—
1436C4—22no—
1437C4—24no—
1438C4—22no—
1439C4—22no—
1440C4—22no—
1441C4—22no—
1442C4—42no—
1443C4—44no—
1444C4—41no—
1445C4—41no—
1446C4—44no—
1447C4—44no—
1448C4—44no—
1449C4—42no—
1450C4—44no—
1451C4—44no—
1452C4—42no—
1453C4—44no—
1454C4—42no—
1455C4—44no—
1456C4#355314yes—
1457C2—24no—
1458C2—44no—
1459C2C2×#355311yescharacteristic
1460C2#6275911yescharacteristic
1461C2C2×#350311yescharacteristic
1462C2#6281311yescharacteristic
1463C2#6281311yescharacteristic
1464C2#6282211yescharacteristic
1465C2#6282511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59918C2semidirect
2. #59866C2semidirect
5. #46153C2semidirect
6. #46152C2semidirect
7. #46009C2semidirect
8. #46008C2semidirect
9. #46006C2semidirect
10. #46005C2semidirect
11. #39698C2semidirect
12. #39662C2semidirect
13. #39661C2semidirect
14. #39604C2semidirect
15. #39604C2semidirect
16. #39589C2semidirect
17. #38457C2semidirect
18. #38441C2semidirect
19. #37609C2semidirect
20. #37196C2semidirect
21. #37137C2semidirect
22. #36635C2semidirect
23. C2×#2859C2semidirect
24. #36287C2semidirect
25. #36280C2semidirect
26. #36278C2semidirect
27. #36261C2semidirect
28. #35208C2semidirect
29. #35017C2semidirect
273. #529Q8semidirect

Maximal subgroups

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

subgroupindex
#599182
#598662
#598562
#598302
#461532
#461522
#460092
#460082
#460062
#460052
#396982
#396622
#396612
#396042
#395892
#384572
#384412
#376092
#371962
#371372
#366352
C2×#28592
#362872
#362802
#362782
#362612
#352082
#350172
#343902
C4×#5292