Finite Group Databasebeta

← #7726983

Subgroups — #7726983

Order 512.

4168 conjugacy classes of subgroups.

The subgroup lattice has 1385 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48873C214yesmaximal, complemented
2#48872C214yesmaximal, complemented
3#47230C214yesmaximal, complemented
4#47017C214yesmaximal, complemented
5#45431C211yesmaximal, characteristic, complemented
6#45425C211yesmaximal, characteristic, complemented
7#45318C211yesmaximal, characteristic, complemented
8#45306C211yesmaximal, characteristic, complemented
9#45306C211yesmaximal, characteristic, complemented
10#45276C211yesmaximal, characteristic, complemented
11#45083C211yesmaximal, characteristic, complemented
12#44979C211yesmaximal, characteristic, complemented
13#40034C212yesmaximal
14#40028C212yesmaximal, complemented
15#39809C212yesmaximal, complemented
16#39801C212yesmaximal, complemented
17#39757C212yesmaximal, complemented
18#39754C212yesmaximal, complemented
19#38742C214yesmaximal, complemented
20#38731C214yesmaximal, complemented
21#37635C211yesmaximal, characteristic, complemented
22#37006C214yesmaximal, complemented
23#36420C212yesmaximal
24#36314C212yesmaximal, complemented
25#35511C214yesmaximal, complemented
26#35326C211yesmaximal, characteristic
27#35201C211yesmaximal, characteristic
28#34878C211yesmaximal, characteristic, complemented
29#34392C211yesmaximal, characteristic
30#34225C211yesmaximal, characteristic, complemented
31#34074C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#529C2211yescharacteristic
35#2865C2214yes—
36#2864C2214yes—
37#2861C2212yes—
38#2859C2212yes—
39#2857C2211yescharacteristic
40#2857C2211yescharacteristic
41#2850C2211yescharacteristic
42#2850C2211yescharacteristic
43#2817C2212yes—
44#2817C2212yes—
45#2810C2214yes—
46#2810C2214yes—
47#2807C2214yes—
48#2805C2214yes—
49#2805C2214yes—
50#2802C2214yes—
51#2802C2214yes—
52#2798C2214yes—
53#2796C2214yes—
54#2788C2214yes—
55#2787C2214yes—
56#2787C2214yes—
57#2782C2214yes—
58#2777C2214yes—
59#2777C2214yes—
60#2774C2214yes—
61#2774C2214yes—
62#2774C2214yes—
63#2773C2214yes—
64#2771C2214yes—
65#2770C2214yes—
66#2767C2214yes—
67#2767C2214yes—
68#2763C2214yes—
69#2762C2214yes—
70#2759C2214yes—
71#2758C2214yes—
72#2758C2214yes—
73#2758C2214yes—
74#2755C2214yes—
75#2754C2214yes—
76#2750C2214yes—
77#2747C2214yes—
78#2742C2214yes—
79#2738C2214yes—
80#2738C2214yes—
81#2723C2214yes—
82#2690C2214yes—
83#2690C2214yes—
84#2689C2214yes—
85#2663C2212yes—
86#2663C2212yes—
87#2660C2212yes—
88#2660C2211yescharacteristic
89#2658C2211yescharacteristic
90#2655C2214yes—
91#2650C2214yes—
92#2642C2212yes—
93#2642C2211yescharacteristic
94#2640C2211yescharacteristic
95#2634C2212yes—
96#2634C2212yes—
97#2625C2214yes—
98#2612C2212yes—
99#2612C2212yes—
100#2612C2214yes—
101#2612C2214yes—
102#2611C2214yes—
103#2611C2214yes—
104#2606C2212yes—
105#2605C2212yes—
106#2605C2214yes—
107#2604C2214yes—
108#2604C2212yes—
109#2604C2212yes—
110#2604C2214yes—
111#2604C2214yes—
112#2599C2214yes—
113#2596C2214yes—
114#2596C2214yes—
115#2596C2214yes—
116#2595C2214yes—
117#2592C2212yes—
118#2590C2214yes—
119#2590C2214yes—
120#2589C2214yes—
121#2589C2214yes—
122#2588C2214yes—
123#2586C2214yes—
124#2584C2214yes—
125#2582C2212yes—
126#2581C2214yes—
127#2581C2214yes—
128#2581C2212yes—
129#2581C2212yes—
130#2580C2212yes—
131#2578C2214yes—
132#2575C2214yes—
133#2575C2214yes—
134#2571C2212yes—
135#2571C2212yes—
136#2571C2212yes—
137#2570C2212yes—
138#2570C2212yes—
139#2569C2212yes—
140#2568C2211yescharacteristic
141#2568C2211yescharacteristic
142#2568C2212yes—
143#2568C2211yescharacteristic
144#2567C2211yescharacteristic
145#2567C2211yescharacteristic
146#2567C2211yescharacteristic
147#2564C2214yes—
148#2563C2211yescharacteristic
149#2552C2212yes—
150#2549C2212yes—
151#2542C2211yescharacteristic
152#2533C2214yes—
153#2533C2214yes—
154#2533C2214yes—
155#2533C2214yes—
156#2533C2214yes—
157#2533C2214yes—
158#2533C2214yes—
159#2533C2214yes—
160#2532C2214yes—
161#2532C2214yes—
162#2532C2214yes—
163#2531C2214yes—
164#2530C2214yes—
165#2530C2214yes—
166#2530C2214yes—
167#2530C2214yes—
168#2528C2214yes—
169#2514C2212yes—
170#2513C2212yes—
171#2512C2212yes—
172#2511C2212yes—
173#2511C2212yes—
174#2511C2212yes—
175#2511C2212yes—
176#2511C2212yes—
177#2508C2214yes—
178#2505C2214yes—
179#2500C2212yes—
180#2499C2212yes—
181#2499C2212yes—
182#2499C2212yes—
183#2498C2214yes—
184#2495C2214yes—
185#2478C2214yes—
186#2477C2214yes—
187#2465C2214yes—
188#2453C2214yes—
189#2448C2212yes—
190#2447C2212yes—
191#2446C2212yes—
192#2446C2212yes—
193#2438C2214yes—
194#2438C2212yes—
195#2438C2212yes—
196#2421C2214yes—
197#2415C2214yes—
198#2402C2211yescharacteristic
199#2402C2211yescharacteristic
200#2399C2211yescharacteristic
201#2399C2211yescharacteristic
202#2376C2214yes—
203#2370C2214yes—
204#2367C2212yes—
205#2365C2212yes—
206#2363C2212yes—
207#2362C2212yes—
208#2362C2212yes—
209#2362C2212yes—
210#2357C2211yescharacteristic
211#2356C2212yes—
212#2356C2211yescharacteristic
213#2356C2212yes—
214#2356C2211yescharacteristic
215#2356C2212yes—
216#2356C2211yescharacteristic
217#2355C2212yes—
218#2354C2212yes—
219#2351C2211yescharacteristic
220#2351C2211yescharacteristic
221#2351C2211yescharacteristic
222Q8×C4⋊C4C2212yes—
223#2349C2211yescharacteristic
224#2347C2212yes—
225#2347C2212yes—
226#2346C2212yes—
227#2343C2212yes—
228#2336C2214yes—
229#2334C2214yes—
230#2334C2214yes—
231#2331C2211yescharacteristic
232#2331C2211yescharacteristic
233#2331C2211yescharacteristic
234#2331C2211yescharacteristic
235#2330C2212yes—
236#2330C2212yes—
237#2330C2212yes—
238#2329C2214yes—
239#2329C2214yes—
240#2327C2211yescharacteristic
241#2327C2211yescharacteristic
242#2326C2211yescharacteristic
243#2326C2212yes—
244#2326C2211yescharacteristic
245#2323C2214yes—
246#2323C2214yes—
247#2320C2212yes—
248#2319C2212yes—
249#2318C2212yes—
250C4×C4⋊Q8C2212yes—
251C4×C4⋊Q8C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254#2298C2214yes—
255#2296C2212yes—
256#2295C2214yes—
257#2295C2214yes—
258#2295C2212yes—
259#2295C2212yes—
260#2295C2214yes—
261#2285C2211yescharacteristic
262#2283C2211yescharacteristic
263#2276C2212yes—
264C4×#117C2212yes—
265C4×#117C2211yescharacteristic
266C2×#376C2211yescharacteristic
267#533—28no—
268#533—28no—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275#529—28no—
276C2×#126C2312yes—
277C2×#126C2314yes—
278C2×#125C2311yescharacteristic
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#124C2311yescharacteristic
283C2×#124C2311yescharacteristic
284C2×#124C2311yescharacteristic
285C2×#123C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2311yescharacteristic
290C2×C22⋊Q8C2311yescharacteristic
291C2×C22⋊Q8C2311yescharacteristic
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×#121C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2314yes—
308C2×C4×Q8C2312yes—
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×#117C2312yes—
313C2×#117C2312yes—
314C2×#117C2312yes—
315C2×#117C2312yes—
316C2×#117C2314yes—
317C2×#117C2312yes—
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321#401C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2312yes—
325#400C2312yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2312yes—
334#400C2312yes—
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#400C2314yes—
355#400C2312yes—
356#400C2312yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#399C2314yes—
364#399C2314yes—
365#399C2314yes—
366#399C2314yes—
367#399C2312yes—
368#399C2312yes—
369#398C2312yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#396C2314yes—
403#395C2312yes—
404#395C2312yes—
405#395C2312yes—
406#395C2312yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2312yes—
411#395C2312yes—
412#395C2314yes—
413#395C2314yes—
414#395C2312yes—
415#395C2312yes—
416#395C2312yes—
417#395C2312yes—
418#394C2314yes—
419#394C2314yes—
420#393C2312yes—
421#393C2312yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#391C2312yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2314yes—
439#391C2311yescharacteristic
440#391C2311yescharacteristic
441#391C2312yes—
442#391C2314yes—
443#391C2311yescharacteristic
444#391C2311yescharacteristic
445#391C2314yes—
446#391C2311yescharacteristic
447#391C2311yescharacteristic
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#390C2312yes—
458#390C2314yes—
459#390C2311yescharacteristic
460#390C2312yes—
461#390C2311yescharacteristic
462#390C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
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#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2312yes—
541#387C2312yes—
542#387C2312yes—
543#387C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
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#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2312yes—
592#387C2314yes—
593#387C2314yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2312yes—
607#387C2312yes—
608#387C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2312yes—
615#385C2312yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2312yes—
625#385C2314yes—
626#385C2312yes—
627#384C2312yes—
628#384C2312yes—
629#384C2312yes—
630#384C2312yes—
631#384C2311yescharacteristic
632#384C2311yescharacteristic
633#384C2312yes—
634#383C2312yes—
635#383C2312yes—
636#383C2312yes—
637#383C2314yes—
638#383C2314yes—
639#383C2311yescharacteristic
640#383C2311yescharacteristic
641#383C2314yes—
642#383C2314yes—
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2314yes—
648#382C2311yescharacteristic
649#382C2311yescharacteristic
650#382C2314yes—
651#382C2314yes—
652#382C2314yes—
653#382C2312yes—
654#382C2312yes—
655#382C2312yes—
656#382C2312yes—
657#382C2311yescharacteristic
658#382C2311yescharacteristic
659#381C2311yescharacteristic
660#381C2311yescharacteristic
661#381C2312yes—
662#381C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2314yes—
672#380C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2311yescharacteristic
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⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C22⋊C4C2311yescharacteristic
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2311yescharacteristic
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716#376C2312yes—
717#376C2311yescharacteristic
718#376C2311yescharacteristic
719#376C2311yescharacteristic
720#376C2312yes—
721#376C2311yescharacteristic
722#376C2311yescharacteristic
723#376C2312yes—
724#376C2312yes—
725#376C2312yes—
726#376C2311yescharacteristic
727#376C2314yes—
728#376C2312yes—
729#376C2314yes—
730#376C2314yes—
731#376C2314yes—
732C2×#95C2312yes—
733C2×#95C2312yes—
734C2×#95C2312yes—
735C43C2312yes—
736C43C2314yes—
737C22×Q8C2411yescharacteristic
738C22×Q8C2411yescharacteristic
739C22×Q8C2411yescharacteristic
740C22×Q8C2412yes—
741C22×Q8C2412yes—
742C22×Q8C2412yes—
743C22×Q8C2412yes—
744C22×Q8C2412yes—
745C22×D4C2411yescharacteristic
746C22×D4C2412yes—
747C23×C4C2411yescharacteristic
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2414yes—
751C23×C4C2412yes—
752C23×C4C2411yescharacteristic
753C23×C4C2411yescharacteristic
754C4⋊Q8—24no—
755C4⋊Q8—24no—
756C4⋊Q8—24no—
757C4⋊Q8—24no—
758C4⋊Q8—24no—
759C4⋊Q8—42no—
760#126—28no—
761#126—48no—
762#125—24no—
763#125—28no—
764#125—28no—
765#125—48no—
766#124—24no—
767#124—24no—
768#124—42no—
769#123—28no—
770C22⋊Q8—24no—
771C22⋊Q8—24no—
772C22⋊Q8—24no—
773C22⋊Q8—28no—
774C22⋊Q8—28no—
775C22⋊Q8—28no—
776C22⋊Q8—44no—
777C22⋊Q8—48no—
778C22⋊Q8—44no—
779#121—24no—
780C4×Q8—24no—
781C4×Q8—28no—
782C4×Q8—24no—
783C4×Q8—24no—
784C4×Q8—28no—
785C4×Q8—28no—
786C4×Q8—28no—
787C4×Q8—44no—
788C4×Q8—48no—
789C4×Q8—44no—
790C4×Q8—44no—
791C4×Q8—44no—
792C4×Q8—48no—
793C4×D4—28no—
794C4×D4—24no—
795C4×D4—44no—
796#117—28no—
797#117—28no—
798#117—28no—
799#117—44no—
800#117—48no—
801#117—44no—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C42—24no—
897C2×C42—42no—
898C2×C42#4118yes—
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2411yescharacteristic
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2411yescharacteristic
912C2×C42C2412yes—
913C2×C42C2411yescharacteristic
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932C2×C42C2411yescharacteristic
933#95C2411yescharacteristic
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2411yescharacteristic
945#95C2412yes—
946#95C2411yescharacteristic
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2411yescharacteristic
951#95C2414yes—
952#95C2411yescharacteristic
953#95C2411yescharacteristic
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2411yescharacteristic
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2411yescharacteristic
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023C24C2512yes—
1024C24C2511yescharacteristic
1025C2×Q8—22no—
1026C2×Q8—24no—
1027C2×Q8—22no—
1028C2×Q8—22no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—22no—
1033C2×Q8—22no—
1034C2×Q8—22no—
1035C2×Q8—24no—
1036C2×Q8—22no—
1037C2×Q8—22no—
1038C2×Q8—22no—
1039C2×Q8—44no—
1040C2×Q8—42no—
1041C2×Q8—42no—
1042C2×Q8—44no—
1043C2×Q8—42no—
1044C2×Q8—44no—
1045C2×Q8—42no—
1046C2×D4—24no—
1047C2×D4—22no—
1048C2×D4—22no—
1049C2×D4—22no—
1050C2×D4—44no—
1051C22×C4—22no—
1052C22×C4—22no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—42no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—42no—
1061C22×C4—44no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—42no—
1066C22×C4C2×#4114yes—
1067C22×C4C2×#4114yes—
1068C22×C4C2×#4114yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2511yescharacteristic
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2511yescharacteristic
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—22no—
1105C4⋊C4—24no—
1106C4⋊C4—22no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—22no—
1117C4⋊C4—22no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C22⋊C4—28no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—24no—
1174C22⋊C4—24no—
1175C22⋊C4—24no—
1176C22⋊C4—28no—
1177C22⋊C4—24no—
1178C22⋊C4—28no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—42no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—42no—
1187C22⋊C4—44no—
1188C22⋊C4—42no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C42—24no—
1193C42—28no—
1194C42—24no—
1195C42—24no—
1196C42—24no—
1197C42—22no—
1198C42—24no—
1199C42—24no—
1200C42—22no—
1201C42—22no—
1202C42—24no—
1203C42—28no—
1204C42—24no—
1205C42—24no—
1206C42—28no—
1207C42—42no—
1208C42—42no—
1209C42—42no—
1210C42—44no—
1211C42—44no—
1212C42—44no—
1213C42—42no—
1214C42—44no—
1215C42—44no—
1216C42—44no—
1217C42—44no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42C2×#4114yes—
1222C42C2×#4114yes—
1223C42C2×#4114yes—
1224C42C2×#4114yes—
1225C422−1+414yes—
1226C23—21no—
1227C23—22no—
1228C23—21no—
1229C23—22no—
1230C23—22no—
1231C23—22no—
1232C23—24no—
1233C23—22no—
1234C23—24no—
1235C23C22×#4112yes—
1236C23C2611yescharacteristic
1237Q8—48no—
1238Q8—48no—
1239Q8—44no—
1240Q8—44no—
1241Q8—44no—
1242Q8—84no—
1243Q8—84no—
1244Q8—84no—
1245D4—44no—
1246D4—84no—
1247C2×C4—21no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—28no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
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—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—44no—
1318C2×C4—44no—
1319C2×C4—84no—
1320C2×C4—84no—
1321C2×C4—88no—
1322C2×C4—84no—
1323C2×C4C22×#4112yes—
1324C2×C4C22×#4112yes—
1325C2×C4C22×#4112yes—
1326C2×C4C22×#4112yes—
1327C2×C4C22×#4112yes—
1328C2×C4C22×#4112yes—
1329C2×C4C2×2−1+414yes—
1330C2×C4C2×2−1+412yes—
1331C2×C4#58514yes—
1332C2×C4#58512yes—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—44no—
1342C22—44no—
1343C22C23×#4111yescharacteristic
1344C22C22×2−1+411yescharacteristic
1345C22C2×#58511yescharacteristic
1346C22C2×#58512yes—
1347C222−1+612yes—
1348C4—22no—
1349C4—22no—
1350C4—22no—
1351C4—22no—
1352C4—22no—
1353C4—24no—
1354C4—24no—
1355C4—42no—
1356C4—42no—
1357C4—42no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—44no—
1362C4—42no—
1363C4—44no—
1364C4—42no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—44no—
1370C4—42no—
1371C4—44no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4#350714yes—
1377C2—42no—
1378C2—82no—
1379C2C2×#350711yescharacteristic
1380C2#6281511yescharacteristic
1381C2#6286011yescharacteristic
1382C2#6292812yes—
1383C2#6293612yes—
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. #48873C2semidirect
2. #48872C2semidirect
3. #47230C2semidirect
4. #47017C2semidirect
5. #45431C2semidirect
6. #45425C2semidirect
7. #45318C2semidirect
8. #45306C2semidirect
9. #45306C2semidirect
10. #45276C2semidirect
11. #45083C2semidirect
12. #44979C2semidirect
14. #40028C2semidirect
15. #39809C2semidirect
16. #39801C2semidirect
17. #39757C2semidirect
18. #39754C2semidirect
19. #38742C2semidirect
20. #38731C2semidirect
21. #37635C2semidirect
22. #37006C2semidirect
24. #36314C2semidirect
25. #35511C2semidirect
28. #34878C2semidirect
30. #34225C2semidirect
31. #34074C2semidirect

Maximal subgroups

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

subgroupindex
#488732
#488722
#472302
#470172
#454312
#454252
#453182
#453062
#452762
#450832
#449792
#400342
#400282
#398092
#398012
#397572
#397542
#387422
#387312
#376352
#370062
#364202
#363142
#355112
#353262
#352012
#348782
#343922
#342252
#340742