Finite Group Databasebeta

← #7710087

Subgroups — #7710087

Order 512.

4422 conjugacy classes of subgroups.

The subgroup lattice has 1457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59909C212yesmaximal, complemented
2#59876C212yesmaximal, complemented
3#59449C212yesmaximal, complemented
4#59448C212yesmaximal, complemented
5#46245C212yesmaximal, complemented
6#46244C212yesmaximal, complemented
7#46163C212yesmaximal, complemented
8#46025C212yesmaximal, complemented
9#39803C212yesmaximal, complemented
10#39802C212yesmaximal, complemented
11#39766C212yesmaximal, complemented
12#39750C212yesmaximal, complemented
13#39586C214yesmaximal, complemented
14#39519C214yesmaximal, complemented
15#39199C212yesmaximal, complemented
16#38982C212yesmaximal, complemented
17#38115C214yesmaximal, complemented
18#37540C211yesmaximal, characteristic, complemented
19#37539C211yesmaximal, characteristic
20#36764C212yesmaximal, complemented
21#36763C212yesmaximal, complemented
22#36639C211yesmaximal, characteristic
23#36635C211yesmaximal, characteristic, complemented
24#36487C212yesmaximal, complemented
25#36352C214yesmaximal, complemented
26#36255C212yesmaximal, complemented
27#35098C212yesmaximal, complemented
28#35035C212yesmaximal, complemented
29#34399C211yesmaximal, characteristic, complemented
30#34398C211yesmaximal, characteristic
31C2×C4×#125C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C22×#125C2211yescharacteristic
35#2864C2211yescharacteristic
36#2864C2211yescharacteristic
37#2863C2212yes—
38#2863C2212yes—
39#2862C2211yescharacteristic
40#2862C2211yescharacteristic
41#2862C2211yescharacteristic
42#2861C2212yes—
43#2861C2212yes—
44#2859C2211yescharacteristic
45#2858C2211yescharacteristic
46#2858C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2855C2212yes—
50#2855C2212yes—
51#2853C2214yes—
52#2852C2214yes—
53#2851C2211yescharacteristic
54#2851C2211yescharacteristic
55#2850C2212yes—
56#2850C2212yes—
57#2850C2212yes—
58#2850C2212yes—
59#2822C2212yes—
60#2822C2212yes—
61#2820C2212yes—
62#2820C2212yes—
63#2807C2214yes—
64#2799C2214yes—
65#2799C2214yes—
66#2798C2214yes—
67#2796C2214yes—
68#2796C2214yes—
69#2793C2214yes—
70#2790C2214yes—
71#2789C2214yes—
72#2787C2214yes—
73#2786C2214yes—
74#2783C2214yes—
75#2777C2214yes—
76#2777C2214yes—
77#2773C2214yes—
78#2772C2214yes—
79#2771C2214yes—
80#2767C2214yes—
81#2765C2214yes—
82#2762C2214yes—
83#2758C2214yes—
84#2755C2214yes—
85#2755C2214yes—
86#2751C2214yes—
87#2751C2214yes—
88#2740C2214yes—
89#2739C2214yes—
90#2729C2214yes—
91#2716C2214yes—
92#2715C2214yes—
93#2700C2214yes—
94#2689C2214yes—
95#2660C2212yes—
96#2660C2212yes—
97#2643C2214yes—
98#2642C2212yes—
99#2641C2212yes—
100#2634C2214yes—
101#2633C2214yes—
102#2627C2212yes—
103#2627C2212yes—
104#2623C2214yes—
105#2618C2212yes—
106#2618C2212yes—
107#2605C2214yes—
108#2601C2214yes—
109#2596C2214yes—
110#2596C2214yes—
111#2595C2214yes—
112#2595C2214yes—
113#2594C2214yes—
114#2594C2214yes—
115#2592C2212yes—
116#2592C2212yes—
117#2589C2214yes—
118#2588C2214yes—
119#2588C2214yes—
120#2588C2214yes—
121#2587C2214yes—
122#2582C2212yes—
123#2581C2212yes—
124#2580C2212yes—
125#2577C2214yes—
126#2577C2214yes—
127#2575C2214yes—
128#2575C2214yes—
129#2574C2214yes—
130#2573C2214yes—
131#2571C2212yes—
132#2571C2212yes—
133#2570C2212yes—
134#2570C2212yes—
135#2570C2212yes—
136#2570C2212yes—
137#2566C2212yes—
138#2566C2212yes—
139#2565C2212yes—
140#2565C2212yes—
141#2560C2214yes—
142#2538C2212yes—
143#2532C2214yes—
144#2530C2214yes—
145#2529C2214yes—
146#2528C2214yes—
147#2527C2214yes—
148#2525C2214yes—
149#2524C2214yes—
150#2523C2214yes—
151#2522C2214yes—
152#2522C2214yes—
153#2521C2214yes—
154#2520C2214yes—
155#2520C2214yes—
156#2519C2214yes—
157#2517C2214yes—
158#2516C2214yes—
159#2516C2214yes—
160#2515C2214yes—
161#2515C2214yes—
162#2514C2212yes—
163#2514C2212yes—
164#2513C2212yes—
165#2513C2212yes—
166#2512C2212yes—
167#2512C2212yes—
168#2511C2212yes—
169#2511C2212yes—
170#2510C2214yes—
171#2505C2214yes—
172#2504C2212yes—
173#2503C2212yes—
174#2502C2212yes—
175#2501C2212yes—
176#2493C2214yes—
177#2488C2214yes—
178#2488C2214yes—
179#2484C2214yes—
180#2481C2214yes—
181#2478C2214yes—
182#2475C2214yes—
183#2474C2214yes—
184#2450C2214yes—
185#2449C2214yes—
186#2448C2212yes—
187#2448C2212yes—
188#2447C2212yes—
189#2447C2212yes—
190#2419C2214yes—
191#2419C2214yes—
192#2406C2214yes—
193#2382C2212yes—
194#2382C2212yes—
195#2379C2212yes—
196#2379C2212yes—
197#2373C2214yes—
198#2373C2214yes—
199#2368C2214yes—
200#2367C2212yes—
201#2367C2212yes—
202#2361C2212yes—
203#2361C2212yes—
204#2360C2212yes—
205#2360C2212yes—
206#2357C2212yes—
207#2357C2212yes—
208#2356C2212yes—
209#2356C2212yes—
210#2355C2212yes—
211#2355C2212yes—
212#2355C2212yes—
213#2354C2212yes—
214#2351C2212yes—
215#2349C2212yes—
216#2343C2214yes—
217#2343C2214yes—
218#2339C2214yes—
219#2331C2212yes—
220#2331C2212yes—
221#2329C2212yes—
222#2329C2212yes—
223#2328C2212yes—
224#2327C2212yes—
225#2325C2212yes—
226#2325C2212yes—
227#2322C2214yes—
228#2320C2214yes—
229#2318C2214yes—
230#2318C2214yes—
231C4×C4⋊Q8C2211yescharacteristic
232C4×C4⋊Q8C2211yescharacteristic
233C4×#125C2212yes—
234C4×#125C2211yescharacteristic
235C4×#125C2211yescharacteristic
236C4×#125C2212yes—
237C4×#125C2212yes—
238C4×#125C2212yes—
239C4×#125C2212yes—
240C4×#125C2212yes—
241C4×#125C2212yes—
242C4×#125C2212yes—
243C4×#124C2212yes—
244C4×#124C2212yes—
245C4×#124C2212yes—
246C4×#124C2212yes—
247C4×C22⋊Q8C2212yes—
248C4×C22⋊Q8C2212yes—
249C4×#123C2214yes—
250#2297C2212yes—
251#2297C2212yes—
252#2295C2212yes—
253#2295C2212yes—
254C2×#389C2211yescharacteristic
255C2×#389C2211yescharacteristic
256#2290C2214yes—
257C2×#387C2212yes—
258C2×#387C2212yes—
259#2283C2211yescharacteristic
260#2283C2211yescharacteristic
261C2×#382C2211yescharacteristic
262C2×C4×C4⋊C4C2212yes—
263C2×C4×C4⋊C4C2212yes—
264C2×C4×C4⋊C4C2211yescharacteristic
265C2×C4×C4⋊C4C2211yescharacteristic
266C2×C43C2211yescharacteristic
267C22×#41C2312yes—
268#533—28no—
269#532—28no—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×#127C2311yescharacteristic
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125—28no—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2311yescharacteristic
285C2×#125C2311yescharacteristic
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×#117C2312yes—
313C2×#117C2314yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2311yescharacteristic
317C22×C4⋊C4C2311yescharacteristic
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2311yescharacteristic
320C22×C4⋊C4C2311yescharacteristic
321C22×C4⋊C4C2312yes—
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2312yes—
327C22×C42C2312yes—
328C22×C42C2311yescharacteristic
329C22×C42C2311yescharacteristic
330C22×C42C2311yescharacteristic
331#401C2314yes—
332#401C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
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#400C2314yes—
353#400C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
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#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2314yes—
419#391C2314yes—
420#391C2312yes—
421#391C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2311yescharacteristic
463#389C2311yescharacteristic
464#389C2311yescharacteristic
465#389C2311yescharacteristic
466#389C2312yes—
467#389C2311yescharacteristic
468#389C2311yescharacteristic
469#389C2311yescharacteristic
470#389C2311yescharacteristic
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2312yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2312yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2312yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2314yes—
580#387C2314yes—
581#387C2312yes—
582#387C2312yes—
583#387C2314yes—
584#387C2312yes—
585#387C2312yes—
586#387C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2312yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2312yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2312yes—
618#385C2312yes—
619#385C2314yes—
620#385C2314yes—
621#384C2311yescharacteristic
622#384C2311yescharacteristic
623#384C2312yes—
624#384C2312yes—
625#384C2312yes—
626#384C2312yes—
627#383C2314yes—
628#383C2312yes—
629#383C2314yes—
630#383C2312yes—
631#383C2314yes—
632#383C2314yes—
633#382C2312yes—
634#382C2312yes—
635#382C2312yes—
636#382C2312yes—
637#382C2311yescharacteristic
638#382C2311yescharacteristic
639#382C2311yescharacteristic
640#382C2311yescharacteristic
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2311yescharacteristic
646#382C2311yescharacteristic
647#382C2312yes—
648#382C2312yes—
649#382C2314yes—
650#382C2314yes—
651#382C2314yes—
652#382C2314yes—
653#382C2312yes—
654#382C2312yes—
655#381C2314yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#381C2312yes—
660#381C2312yes—
661#381C2314yes—
662#381C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2311yescharacteristic
667#380C2311yescharacteristic
668#380C2311yescharacteristic
669#380C2311yescharacteristic
670#380C2312yes—
671#380C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2314yes—
718#376C2314yes—
719#376C2312yes—
720#376C2312yes—
721#376C2314yes—
722C2×#95C2312yes—
723C2×#95C2314yes—
724C2×#95C2312yes—
725C2×#95C2312yes—
726C2×#95C2312yes—
727C2×#95C2312yes—
728C2×#95C2312yes—
729C43C2311yescharacteristic
730C43C2311yescharacteristic
731C43C2311yescharacteristic
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C2×#41—28no—
738C2×#41—44no—
739C2×#41—44no—
740C22×Q8C2412yes—
741C22×Q8C2412yes—
742C22×Q8C2412yes—
743C22×Q8C2412yes—
744C22×Q8C2412yes—
745C22×D4C2412yes—
746C22×D4C2414yes—
747C22×D4C2412yes—
748C22×D4C2412yes—
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C23×C4C2411yescharacteristic
752C23×C4C2411yescharacteristic
753C23×C4C2411yescharacteristic
754C23×C4C2411yescharacteristic
755C23×C4C2412yes—
756C23×C4C2412yes—
757C23×C4C2412yes—
758C23×C4C2411yescharacteristic
759C23×C4C2414yes—
760C23×C4C2414yes—
761C23×C4C2414yes—
762C23×C4C2411yescharacteristic
763C4⋊Q8—24no—
764C4⋊Q8—24no—
765C4⋊Q8—24no—
766C4⋊Q8—42no—
767C4⋊Q8—42no—
768#127—24no—
769#126—48no—
770#126—48no—
771#125—28no—
772#125—28no—
773#125—28no—
774#125—28no—
775#125—28no—
776#125—42no—
777#125—42no—
778#124—28no—
779#124—28no—
780#124—44no—
781#124—44no—
782#124—44no—
783#123—48no—
784#123—48no—
785C22⋊Q8—28no—
786C22⋊Q8—28no—
787C22⋊Q8—44no—
788C22⋊Q8—44no—
789C22⋊Q8—48no—
790#121—28no—
791#121—28no—
792C4×Q8—28no—
793C4×Q8—28no—
794C4×Q8—28no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×Q8—44no—
798C4×D4—28no—
799C4×D4—28no—
800C4×D4—44no—
801C4×D4—44no—
802C4×D4—48no—
803C4×D4—48no—
804#117—28no—
805#117—48no—
806C2×C4⋊C4—28no—
807C2×C4⋊C4—24no—
808C2×C4⋊C4—24no—
809C2×C4⋊C4—28no—
810C2×C4⋊C4—42no—
811C2×C4⋊C4—42no—
812C2×C4⋊C4—44no—
813C2×C4⋊C4—44no—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C42—24no—
908C2×C42—44no—
909C2×C42—42no—
910C2×C42—42no—
911C2×C42—42no—
912C2×C42—42no—
913C2×C42—44no—
914C2×C42—42no—
915C2×C42#4118yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2411yescharacteristic
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958C2×C42C2411yescharacteristic
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035C24C2514yes—
1036C24C2511yescharacteristic
1037#41—816no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—24no—
1041C2×Q8—24no—
1042C2×Q8—24no—
1043C2×Q8—24no—
1044C2×Q8—24no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—42no—
1049C2×Q8—42no—
1050C2×Q8—42no—
1051C2×Q8—42no—
1052C2×Q8—42no—
1053C2×D4—28no—
1054C2×D4—28no—
1055C2×D4—28no—
1056C2×D4—24no—
1057C2×D4—24no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C22×C4—22no—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—22no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—22no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—22no—
1075C22×C4—22no—
1076C22×C4—22no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—22no—
1082C22×C4—22no—
1083C22×C4—28no—
1084C22×C4—41no—
1085C22×C4—41no—
1086C22×C4—41no—
1087C22×C4—41no—
1088C22×C4—41no—
1089C22×C4—41no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4C2×#4114yes—
1105C22×C4C2×#4114yes—
1106C22×C4C2×#4114yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2514yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2514yes—
1112C22×C4C2512yes—
1113C22×C4C2514yes—
1114C22×C4C2514yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C22×C4C2514yes—
1122C22×C4C2512yes—
1123C22×C4C2514yes—
1124C22×C4C2514yes—
1125C22×C4C2512yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C22×C4C2511yescharacteristic
1129C22×C4C2511yescharacteristic
1130C22×C4C2511yescharacteristic
1131C22×C4C2511yescharacteristic
1132C22×C4C2511yescharacteristic
1133C22×C4C2511yescharacteristic
1134C22×C4C2511yescharacteristic
1135C22×C4C2511yescharacteristic
1136C4⋊C4—28no—
1137C4⋊C4—28no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—28no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—28no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—41no—
1187C4⋊C4—41no—
1188C4⋊C4—41no—
1189C4⋊C4—41no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—41no—
1196C4⋊C4—41no—
1197C4⋊C4—41no—
1198C4⋊C4—41no—
1199C4⋊C4—42no—
1200C22⋊C4—28no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—28no—
1206C22⋊C4—28no—
1207C22⋊C4—28no—
1208C22⋊C4—28no—
1209C22⋊C4—28no—
1210C22⋊C4—28no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C42—28no—
1230C42—22no—
1231C42—22no—
1232C42—22no—
1233C42—24no—
1234C42—24no—
1235C42—28no—
1236C42—22no—
1237C42—22no—
1238C42—22no—
1239C42—22no—
1240C42—22no—
1241C42—22no—
1242C42—24no—
1243C42—24no—
1244C42—41no—
1245C42—41no—
1246C42—41no—
1247C42—41no—
1248C42—41no—
1249C42—41no—
1250C42—41no—
1251C42—41no—
1252C42—41no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—41no—
1257C42—41no—
1258C42—41no—
1259C42—41no—
1260C42—41no—
1261C42—44no—
1262C42—44no—
1263C42—44no—
1264C42—44no—
1265C42—44no—
1266C42—44no—
1267C42C2×#4114yes—
1268C42C2×#4114yes—
1269C42C2×#4114yes—
1270C42C2×#4114yes—
1271C422−1+414yes—
1272C23—21no—
1273C23—21no—
1274C23—21no—
1275C23—21no—
1276C23—24no—
1277C23—24no—
1278C23—24no—
1279C23—24no—
1280C23—24no—
1281C23—24no—
1282C23—24no—
1283C23C22×#4112yes—
1284C23#58512yes—
1285C23#58512yes—
1286C23C2611yescharacteristic
1287Q8—48no—
1288Q8—84no—
1289Q8—84no—
1290Q8—84no—
1291Q8—84no—
1292D4—416no—
1293D4—48no—
1294D4—84no—
1295D4—84no—
1296C2×C4—28no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—28no—
1316C2×C4—28no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—21no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—24no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—44no—
1375C2×C4—44no—
1376C2×C4—44no—
1377C2×C4—44no—
1378C2×C4—48no—
1379C2×C4—48no—
1380C2×C4—88no—
1381C2×C4—84no—
1382C2×C4—84no—
1383C2×C4—88no—
1384C2×C4—164no—
1385C2×C4C22×#4112yes—
1386C2×C4C22×#4112yes—
1387C2×C4C22×#4112yes—
1388C2×C4C22×#4112yes—
1389C2×C4C22×#4112yes—
1390C2×C4C22×#4112yes—
1391C2×C4C2×2−1+412yes—
1392C2×C4C2×2−1+412yes—
1393C2×C4C2×2−1+412yes—
1394C2×C4#58512yes—
1395C2×C4#58512yes—
1396C2×C4#58512yes—
1397C22—22no—
1398C22—22no—
1399C22—22no—
1400C22—22no—
1401C22—22no—
1402C22—22no—
1403C22—44no—
1404C22—44no—
1405C22—44no—
1406C22—44no—
1407C22—44no—
1408C22—44no—
1409C22—44no—
1410C22#351014yes—
1411C22C23×#4111yescharacteristic
1412C22C22×2−1+411yescharacteristic
1413C22C2×#58511yescharacteristic
1414C22C2×#58511yescharacteristic
1415C22C2×#58511yescharacteristic
1416C22C2×#58511yescharacteristic
1417C22C2×#58511yescharacteristic
1418C4—22no—
1419C4—22no—
1420C4—22no—
1421C4—22no—
1422C4—22no—
1423C4—22no—
1424C4—22no—
1425C4—22no—
1426C4—22no—
1427C4—42no—
1428C4—41no—
1429C4—41no—
1430C4—44no—
1431C4—42no—
1432C4—41no—
1433C4—42no—
1434C4—42no—
1435C4—44no—
1436C4—44no—
1437C4—44no—
1438C4—44no—
1439C4—44no—
1440C4—42no—
1441C4—42no—
1442C4—41no—
1443C4—44no—
1444C4—42no—
1445C4—42no—
1446C4#350714yes—
1447C2—24no—
1448C2—84no—
1449C2#6274311yescharacteristic
1450C2#6275211yescharacteristic
1451C2C2×#350711yescharacteristic
1452C2C2×#351011yescharacteristic
1453C2#6281511yescharacteristic
1454C2#6282511yescharacteristic
1455C2#6282811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59909C2semidirect
2. #59876C2semidirect
3. #59449C2semidirect
4. #59448C2semidirect
5. #46245C2semidirect
6. #46244C2semidirect
7. #46163C2semidirect
8. #46025C2semidirect
9. #39803C2semidirect
10. #39802C2semidirect
11. #39766C2semidirect
12. #39750C2semidirect
13. #39586C2semidirect
14. #39519C2semidirect
15. #39199C2semidirect
16. #38982C2semidirect
17. #38115C2semidirect
18. #37540C2semidirect
20. #36764C2semidirect
21. #36763C2semidirect
23. #36635C2semidirect
24. #36487C2semidirect
25. #36352C2semidirect
26. #36255C2semidirect
27. #35098C2semidirect
28. #35035C2semidirect
29. #34399C2semidirect
31. C2×C4×#125C2semidirect

Maximal subgroups

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

subgroupindex
#599092
#598762
#594492
#594482
#462452
#462442
#461632
#460252
#398032
#398022
#397662
#397502
#395862
#395192
#391992
#389822
#381152
#375402
#375392
#367642
#367632
#366392
#366352
#364872
#363522
#362552
#350982
#350352
#343992
#343982
C2×C4×#1252