Finite Group Databasebeta

← #7697100

Subgroups — #7697100

Order 512.

5072 conjugacy classes of subgroups.

The subgroup lattice has 1347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59854C213yesmaximal, complemented
2#59585C213yesmaximal, complemented
3#59582C213yesmaximal, complemented
4#52262C213yesmaximal, complemented
5#45161C213yesmaximal, complemented
6#45158C213yesmaximal, complemented
7#45090C213yesmaximal, complemented
8#45045C213yesmaximal, complemented
9#45035C213yesmaximal, complemented
10#45015C213yesmaximal, complemented
11#39816C213yesmaximal, complemented
12#39554C213yesmaximal, complemented
13#39284C213yesmaximal, complemented
14#39193C213yesmaximal, complemented
15#38219C213yesmaximal, complemented
16#38122C213yesmaximal, complemented
17#36458C211yesmaximal, characteristic, complemented
18#36447C211yesmaximal, characteristic, complemented
19#36444C211yesmaximal, characteristic, complemented
20#35983C211yesmaximal, characteristic, complemented
21#35883C211yesmaximal, characteristic, complemented
22#35831C211yesmaximal, characteristic, complemented
23#35831C211yesmaximal, characteristic, complemented
24#35771C211yesmaximal, characteristic, complemented
25#35723C211yesmaximal, characteristic, complemented
26#34312C211yesmaximal, characteristic, complemented
27#34312C211yesmaximal, characteristic, complemented
28#34312C211yesmaximal, characteristic, complemented
29#34295C211yesmaximal, characteristic, complemented
30#34262C211yesmaximal, characteristic, complemented
31#34250C211yesmaximal, characteristic, complemented
32C2×#550C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#520C2211yescharacteristic
40C2×#520C2211yescharacteristic
41C2×#519C2211yescharacteristic
42C2×#519C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44#2860C2213yes—
45#2859C2213yes—
46#2857C2213yes—
47#2803C2213yes—
48#2802C2213yes—
49#2801C2213yes—
50#2800C2211yescharacteristic
51#2800C2213yes—
52#2797C2213yes—
53#2796C2213yes—
54#2787C2213yes—
55#2783C2216yes—
56#2781C2216yes—
57#2779C2216yes—
58#2779C2216yes—
59#2779C2213yes—
60#2778C2216yes—
61#2777C2213yes—
62#2776C2216yes—
63#2772C2213yes—
64#2757C2213yes—
65#2757C2216yes—
66#2753C2213yes—
67#2750C2216yes—
68#2749C2216yes—
69#2741C2216yes—
70#2725C2213yes—
71#2725C2216yes—
72#2714C2213yes—
73#2711C2216yes—
74#2711C2213yes—
75#2691C2216yes—
76#2645C2213yes—
77#2625C2213yes—
78#2625C2213yes—
79#2620C2213yes—
80#2620C2213yes—
81#2620C2213yes—
82#2608C2216yes—
83#2591C2216yes—
84#2587C2216yes—
85#2578C2216yes—
86#2576C2216yes—
87#2576C2216yes—
88#2571C2213yes—
89#2569C2216yes—
90#2559C2216yes—
91#2552C2213yes—
92#2547C2213yes—
93#2545C2213yes—
94#2544C2213yes—
95#2544C2213yes—
96#2543C2216yes—
97#2538C2213yes—
98#2537C2213yes—
99#2537C2213yes—
100#2537C2213yes—
101#2531C2216yes—
102#2530C2216yes—
103#2526C2216yes—
104#2518C2216yes—
105#2514C2213yes—
106#2514C2213yes—
107#2513C2213yes—
108#2512C2213yes—
109#2512C2213yes—
110#2511C2213yes—
111#2510C2216yes—
112#2508C2213yes—
113#2508C2213yes—
114#2506C2213yes—
115#2506C2213yes—
116#2504C2216yes—
117#2503C2213yes—
118#2499C2213yes—
119#2497C2213yes—
120#2497C2213yes—
121#2496C2213yes—
122#2495C2213yes—
123#2495C2213yes—
124#2495C2216yes—
125#2494C2213yes—
126#2490C2216yes—
127#2487C2213yes—
128#2485C2213yes—
129#2481C2216yes—
130#2468C2216yes—
131#2460C2216yes—
132#2447C2213yes—
133#2447C2213yes—
134#2446C2213yes—
135#2446C2213yes—
136#2442C2216yes—
137#2429C2213yes—
138#2428C2213yes—
139#2428C2213yes—
140#2427C2213yes—
141#2427C2213yes—
142#2427C2213yes—
143#2427C2213yes—
144#2426C2213yes—
145#2423C2213yes—
146#2421C2213yes—
147#2420C2213yes—
148#2420C2213yes—
149#2417C2213yes—
150#2417C2213yes—
151#2416C2213yes—
152#2416C2213yes—
153#2415C2213yes—
154#2415C2213yes—
155#2415C2213yes—
156#2414C2213yes—
157#2401C2213yes—
158#2395C2213yes—
159#2395C2213yes—
160#2392C2213yes—
161#2392C2213yes—
162#2392C2213yes—
163#2367C2213yes—
164#2367C2213yes—
165#2367C2213yes—
166#2366C2213yes—
167#2363C2213yes—
168#2363C2213yes—
169#2363C2213yes—
170#2363C2213yes—
171#2361C2213yes—
172#2360C2213yes—
173#2360C2213yes—
174#2360C2213yes—
175#2356C2213yes—
176#2355C2213yes—
177#2353C2216yes—
178#2352C2213yes—
179#2352C2213yes—
180#2352C2213yes—
181#2352C2213yes—
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192#2349C2213yes—
193#2349C2213yes—
194D4×C4⋊C4C2213yes—
195D4×C4⋊C4C2213yes—
196#2347C2213yes—
197#2346C2213yes—
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208#2328C2213yes—
209#2324C2213yes—
210#2324C2213yes—
211#2324C2213yes—
212#2324C2213yes—
213#2323C2213yes—
214#2323C2213yes—
215#2323C2213yes—
216#2320C2213yes—
217#2317C2213yes—
218#2316C2213yes—
219#2314C2213yes—
220C4×#125C2213yes—
221C4×#126C2213yes—
222C4×#124C2213yes—
223C4×#124C2213yes—
224C4×#124C2213yes—
225C4×#121C2213yes—
226C4×#121C2213yes—
227#2298C2213yes—
228#2296C2213yes—
229#2295C2213yes—
230#2293C2213yes—
231#2293C2213yes—
232#2293C2213yes—
233C2×#389C2213yes—
234#2290C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242#550—28no—
243D4×Q8—44no—
244#548—28no—
245#548—28no—
246#548—28no—
247#548—44no—
248C2×C4⋊Q8C2313yes—
249C2×#127C2313yes—
250C2×#126C2313yes—
251C2×#126C2316yes—
252C2×#125C2313yes—
253C2×#125C2316yes—
254C2×#124C2313yes—
255C2×#124C2313yes—
256C2×#124C2313yes—
257C2×#124C2313yes—
258C2×C22⋊Q8C2313yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2313yes—
264C2×#121C2313yes—
265C2×#121C2313yes—
266C2×#121C2313yes—
267C2×#121C2313yes—
268C2×#121C2313yes—
269C2×#121C2313yes—
270C2×#121C2313yes—
271C2×#121C2316yes—
272C2×#121C2316yes—
273#520—28no—
274#520—44no—
275#520—44no—
276#519—28no—
277#519—44no—
278C4×#41—44no—
279C2×C4×Q8C2313yes—
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2316yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C2×#117C2313yes—
313C2×#117C2313yes—
314C2×#117C2313yes—
315C2×#117C2313yes—
316C2×#117C2313yes—
317C22×C4⋊C4C2313yes—
318C22×C4⋊C4C2313yes—
319C22×C4⋊C4C2313yes—
320C22×C4⋊C4C2316yes—
321C22×C42C2313yes—
322#401C2313yes—
323#401C2316yes—
324#400C2316yes—
325#400C2316yes—
326#400C2316yes—
327#400C2316yes—
328#400C2313yes—
329#400C2316yes—
330#400C2316yes—
331#400C2313yes—
332#400C2313yes—
333#400C2313yes—
334#400C2313yes—
335#400C2316yes—
336#399C2313yes—
337#399C2313yes—
338#398C2313yes—
339#398C2316yes—
340#398C2316yes—
341#398C2313yes—
342#398C2316yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#397C2316yes—
347#397C2316yes—
348#397C2316yes—
349#397C2313yes—
350#397C2316yes—
351#397C2316yes—
352#397C2316yes—
353#397C2313yes—
354#397C2313yes—
355#397C2313yes—
356#397C2311yescharacteristic
357#397C2313yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2311yescharacteristic
362#397C2313yes—
363#397C2313yes—
364#397C2316yes—
365#396C2316yes—
366#396C2316yes—
367#396C2313yes—
368#396C2316yes—
369#396C2313yes—
370#396C2316yes—
371#396C2316yes—
372#396C2311yescharacteristic
373#396C2311yescharacteristic
374#396C2313yes—
375#396C2313yes—
376#396C2313yes—
377#394C2313yes—
378#394C2316yes—
379#394C2313yes—
380#394C2313yes—
381#394C2316yes—
382#394C2313yes—
383#394C2316yes—
384#394C2316yes—
385#394C2316yes—
386#394C2311yescharacteristic
387#394C2313yes—
388#394C2313yes—
389#394C2313yes—
390#394C2313yes—
391#394C2313yes—
392#394C2311yescharacteristic
393#394C2313yes—
394#394C2313yes—
395#394C2316yes—
396#394C2316yes—
397#392C2313yes—
398#392C2313yes—
399#392C2313yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#390C2313yes—
413#390C2313yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2316yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2316yes—
428#390C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2313yes—
431#389C2316yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2316yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2316yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2316yes—
464#389C2311yescharacteristic
465#389C2313yes—
466#388C2313yes—
467#388C2313yes—
468#388C2313yes—
469#388C2313yes—
470#388C2316yes—
471#388C2313yes—
472#388C2316yes—
473#388C2316yes—
474#388C2316yes—
475#388C2316yes—
476#388C2316yes—
477#388C2316yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2316yes—
482#388C2313yes—
483#388C2316yes—
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2316yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2316yes—
496#388C2313yes—
497#388C2311yescharacteristic
498#388C2313yes—
499#388C2311yescharacteristic
500#388C2313yes—
501#388C2311yescharacteristic
502#388C2311yescharacteristic
503#387C2311yescharacteristic
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2313yes—
509#387C2313yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2313yes—
515#387C2313yes—
516#387C2316yes—
517#387C2316yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2313yes—
522#387C2316yes—
523#387C2313yes—
524#387C2313yes—
525#387C2311yescharacteristic
526#386C2316yes—
527#386C2316yes—
528#386C2316yes—
529#386C2316yes—
530#386C2316yes—
531#386C2316yes—
532#386C2316yes—
533#386C2316yes—
534#386C2316yes—
535#386C2313yes—
536#386C2313yes—
537#386C2316yes—
538#386C2313yes—
539#386C2316yes—
540#386C2313yes—
541#385C2313yes—
542#385C2316yes—
543#385C2316yes—
544#385C2316yes—
545#385C2316yes—
546#385C2313yes—
547#385C2316yes—
548#385C2316yes—
549#385C2313yes—
550#385C2313yes—
551#385C2313yes—
552#385C2313yes—
553#384C2313yes—
554#384C2313yes—
555#384C2313yes—
556#384C2313yes—
557#384C2313yes—
558#383C2313yes—
559#383C2316yes—
560#383C2316yes—
561#382C2313yes—
562#382C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2316yes—
567#382C2316yes—
568#382C2313yes—
569#381C2316yes—
570#381C2316yes—
571#380C2316yes—
572#380C2316yes—
573#380C2316yes—
574#380C2313yes—
575#380C2313yes—
576#380C2316yes—
577#380C2316yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2316yes—
587#380C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2316yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2316yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2316yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2316yes—
616C4×C22⋊C4C2316yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2316yes—
625#376C2313yes—
626#376C2316yes—
627C2×#95C2316yes—
628C43C2313yes—
629C43C2313yes—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41#4118yes—
636C22×Q8—24no—
637C22×Q8—24no—
638C22×Q8—24no—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8C2413yes—
643C22×Q8C2413yes—
644C22×Q8C2411yescharacteristic
645C22×D4C2413yes—
646C22×D4C2413yes—
647C22×D4C2411yescharacteristic
648C22×D4C2413yes—
649C22×D4C2413yes—
650C22×D4C2416yes—
651C22×D4C2413yes—
652C22×D4C2413yes—
653C22×D4C2413yes—
654C23×C4C2413yes—
655C23×C4C2413yes—
656C23×C4C2413yes—
657C23×C4C2413yes—
658C23×C4C2416yes—
659C23×C4C2413yes—
660C23×C4C2416yes—
661C23×C4C2413yes—
662C23×C4C2416yes—
663C4⋊Q8—46no—
664#127—212no—
665#126—46no—
666#126—86no—
667#125—46no—
668#125—86no—
669#124—212no—
670#124—212no—
671#124—212no—
672#124—46no—
673C22⋊Q8—212no—
674C22⋊Q8—212no—
675C22⋊Q8—212no—
676C22⋊Q8—46no—
677C22⋊Q8—46no—
678C22⋊Q8—46no—
679#121—212no—
680#121—212no—
681#121—212no—
682#121—212no—
683#121—212no—
684#121—46no—
685#121—46no—
686#121—86no—
687#121—86no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—24no—
694C4×Q8—24no—
695C4×Q8—24no—
696C4×Q8—24no—
697C4×Q8—24no—
698C4×Q8—212no—
699C4×Q8—212no—
700C4×Q8—46no—
701C4×Q8—46no—
702C4×Q8#4118yes—
703C4×D4—212no—
704C4×D4—212no—
705C4×D4—212no—
706C4×D4—212no—
707C4×D4—212no—
708C4×D4—212no—
709C4×D4—46no—
710C4×D4—46no—
711C4×D4—46no—
712C4×D4—46no—
713C4×D4—46no—
714C4×D4—46no—
715C4×D4—46no—
716C4×D4—46no—
717C4×D4—412no—
718#117—212no—
719#117—212no—
720#117—212no—
721#117—46no—
722#117—46no—
723#117—46no—
724#117—46no—
725#117—46no—
726C2×C4⋊C4—212no—
727C2×C4⋊C4—46no—
728C2×C4⋊C4—46no—
729C2×C4⋊C4—86no—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2416yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2411yescharacteristic
788C2×C22⋊C4C2411yescharacteristic
789C2×C22⋊C4C2411yescharacteristic
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2416yes—
797C2×C22⋊C4C2416yes—
798C2×C22⋊C4C2416yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2411yescharacteristic
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2416yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2416yes—
814C2×C22⋊C4C2416yes—
815C2×C22⋊C4C2416yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2411yescharacteristic
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2411yescharacteristic
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2411yescharacteristic
829C2×C22⋊C4C2411yescharacteristic
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2416yes—
833C2×C22⋊C4C2413yes—
834C2×C42—46no—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2416yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2416yes—
848C2×C42C2416yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2411yescharacteristic
854C2×C42C2411yescharacteristic
855C2×C42C2413yes—
856C2×C42C2413yes—
857C2×C42C2411yescharacteristic
858C2×C42C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2416yes—
862#95C2416yes—
863#95C2411yescharacteristic
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2416yes—
870#95C2413yes—
871#95C2413yes—
872#95C2411yescharacteristic
873#95C2411yescharacteristic
874#95C2411yescharacteristic
875#95C2411yescharacteristic
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2416yes—
887#95C2413yes—
888#95C2416yes—
889#95C2416yes—
890#95C2413yes—
891#95C2416yes—
892#95C2416yes—
893#95C2416yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2416yes—
899#95C2411yescharacteristic
900#95C2411yescharacteristic
901#95C2416yes—
902#95C2411yescharacteristic
903#95C2411yescharacteristic
904#95C2411yescharacteristic
905#95C2416yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2416yes—
916C24C2511yescharacteristic
917C24C2513yes—
918C24C2511yescharacteristic
919C24C2513yes—
920#41—232no—
921#41—416no—
922C2×Q8—26no—
923C2×Q8—26no—
924C2×Q8—26no—
925C2×Q8—26no—
926C2×Q8—26no—
927C2×Q8—26no—
928C2×Q8—416no—
929C2×Q8—416no—
930C2×Q8C2×#4114yes—
931C2×Q8C2×#4114yes—
932C2×Q8H(5,𝔽2)14yes—
933C2×D4—26no—
934C2×D4—26no—
935C2×D4—26no—
936C2×D4—212no—
937C2×D4—26no—
938C2×D4—26no—
939C2×D4—26no—
940C2×D4—26no—
941C2×D4—26no—
942C2×D4—26no—
943C2×D4—22no—
944C2×D4—41no—
945C2×D4—41no—
946C2×D4—43no—
947C2×D4—46no—
948C2×D4—43no—
949C2×D4—43no—
950C2×D4—43no—
951C2×D4—43no—
952C2×D4—43no—
953C2×D4—46no—
954C2×D4—43no—
955C2×D4—43no—
956C2×D4—43no—
957C2×D4—43no—
958C2×D4—43no—
959C2×D4C2×#41112yes—
960C22×C4—26no—
961C22×C4—26no—
962C22×C4—26no—
963C22×C4—26no—
964C22×C4—26no—
965C22×C4—26no—
966C22×C4—26no—
967C22×C4—26no—
968C22×C4—26no—
969C22×C4—26no—
970C22×C4—26no—
971C22×C4—212no—
972C22×C4—26no—
973C22×C4—43no—
974C22×C4—43no—
975C22×C4—43no—
976C22×C4—46no—
977C22×C4—46no—
978C22×C4—43no—
979C22×C4—43no—
980C22×C4—46no—
981C22×C4—46no—
982C22×C4—46no—
983C22×C4—46no—
984C22×C4—46no—
985C22×C4—46no—
986C22×C4C2×#41112yes—
987C22×C4C2511yescharacteristic
988C22×C4C2511yescharacteristic
989C22×C4C2511yescharacteristic
990C22×C4C2513yes—
991C22×C4C2513yes—
992C22×C4C2513yes—
993C22×C4C2513yes—
994C22×C4C2511yescharacteristic
995C22×C4C2511yescharacteristic
996C22×C4C2513yes—
997C22×C4C2513yes—
998C22×C4C2513yes—
999C22×C4C2513yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2511yescharacteristic
1002C22×C4C2513yes—
1003C22×C4C2513yes—
1004C22×C4C2513yes—
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C22×C4C2513yes—
1008C22×C4C2511yescharacteristic
1009C22×C4C2513yes—
1010C22×C4C2511yescharacteristic
1011C22×C4C2511yescharacteristic
1012C22×C4C2511yescharacteristic
1013C22×C4C2513yes—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—22no—
1017C4⋊C4—26no—
1018C4⋊C4—26no—
1019C4⋊C4—26no—
1020C4⋊C4—22no—
1021C4⋊C4—26no—
1022C4⋊C4—26no—
1023C4⋊C4—26no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—26no—
1027C4⋊C4—26no—
1028C4⋊C4—26no—
1029C4⋊C4—26no—
1030C4⋊C4—26no—
1031C4⋊C4—26no—
1032C4⋊C4—26no—
1033C4⋊C4—26no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—46no—
1041C4⋊C4—46no—
1042C4⋊C4—41no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—41no—
1046C4⋊C4—41no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—43no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—46no—
1056C4⋊C4—46no—
1057C4⋊C4—46no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—46no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4C2×#41112yes—
1067C22⋊C4—26no—
1068C22⋊C4—26no—
1069C22⋊C4—26no—
1070C22⋊C4—212no—
1071C22⋊C4—212no—
1072C22⋊C4—26no—
1073C22⋊C4—22no—
1074C22⋊C4—26no—
1075C22⋊C4—26no—
1076C22⋊C4—22no—
1077C22⋊C4—22no—
1078C22⋊C4—22no—
1079C22⋊C4—26no—
1080C22⋊C4—26no—
1081C22⋊C4—212no—
1082C22⋊C4—26no—
1083C22⋊C4—41no—
1084C22⋊C4—43no—
1085C22⋊C4—43no—
1086C22⋊C4—43no—
1087C22⋊C4—41no—
1088C22⋊C4—46no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—43no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—41no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—43no—
1100C22⋊C4—43no—
1101C22⋊C4—43no—
1102C22⋊C4—46no—
1103C22⋊C4—46no—
1104C22⋊C4—41no—
1105C22⋊C4—43no—
1106C22⋊C4—43no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—43no—
1110C22⋊C4—46no—
1111C22⋊C4—43no—
1112C22⋊C4—43no—
1113C22⋊C4—46no—
1114C22⋊C4—46no—
1115C22⋊C4—43no—
1116C22⋊C4—43no—
1117C22⋊C4—43no—
1118C42—26no—
1119C42—26no—
1120C42—212no—
1121C42—26no—
1122C42—26no—
1123C42—26no—
1124C42—26no—
1125C42—26no—
1126C42—26no—
1127C42—26no—
1128C42—26no—
1129C42—41no—
1130C42—43no—
1131C42—41no—
1132C42—43no—
1133C42—43no—
1134C42—41no—
1135C42—46no—
1136C42—46no—
1137C42—43no—
1138C42—43no—
1139C42—43no—
1140C42—43no—
1141C42C2×#41112yes—
1142C23—23no—
1143C23—23no—
1144C23—23no—
1145C23—23no—
1146C23—23no—
1147C23—23no—
1148C23—21no—
1149C23—23no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—23no—
1154C23—21no—
1155C23—23no—
1156C23—21no—
1157C23—23no—
1158C23—21no—
1159C23—21no—
1160C23—23no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—23no—
1166C23—21no—
1167C23—23no—
1168C23—21no—
1169C23C22×#4116yes—
1170C23C2611yescharacteristic
1171Q8—412no—
1172Q8—412no—
1173Q8#553116yes—
1174D4—224no—
1175D4—44no—
1176D4—412no—
1177D4—86no—
1178D4—86no—
1179D4—86no—
1180D4—812no—
1181D4—86no—
1182D4—86no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—23no—
1188C2×C4—21no—
1189C2×C4—23no—
1190C2×C4—21no—
1191C2×C4—224no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—23no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—21no—
1220C2×C4—23no—
1221C2×C4—21no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—23no—
1237C2×C4—21no—
1238C2×C4—23no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—23no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—23no—
1247C2×C4—21no—
1248C2×C4—23no—
1249C2×C4—21no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—23no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—23no—
1258C2×C4—412no—
1259C2×C4—412no—
1260C2×C4—412no—
1261C2×C4—812no—
1262C2×C4—86no—
1263C2×C4—86no—
1264C2×C4—166no—
1265C2×C4—166no—
1266C2×C4C22×#4116yes—
1267C2×C4C22×#4112yes—
1268C2×C4C22×#4112yes—
1269C2×C4C22×#4116yes—
1270C2×C4C22×#4116yes—
1271C2×C4C2×H(5,𝔽2)16yes—
1272C2×C4#58512yes—
1273C22—26no—
1274C22—26no—
1275C22—26no—
1276C22—43no—
1277C22—43no—
1278C22—43no—
1279C22—43no—
1280C22—41no—
1281C22—41no—
1282C22—43no—
1283C22—41no—
1284C22—43no—
1285C22—41no—
1286C22—41no—
1287C22—43no—
1288C22—41no—
1289C22—41no—
1290C22—43no—
1291C22—41no—
1292C22—43no—
1293C22—41no—
1294C22—41no—
1295C22—43no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—43no—
1301C22C23×#4111yescharacteristic
1302C22C23×#4111yescharacteristic
1303C22C22×H(5,𝔽2)11yescharacteristic
1304C22C2×#58511yescharacteristic
1305C22H(7,𝔽2)11yescharacteristic
1306C222−1+611yescharacteristic
1307C222−1+611yescharacteristic
1308C4—22no—
1309C4—26no—
1310C4—22no—
1311C4—22no—
1312C4—43no—
1313C4—43no—
1314C4—43no—
1315C4—41no—
1316C4—43no—
1317C4—41no—
1318C4—43no—
1319C4—41no—
1320C4—43no—
1321C4—43no—
1322C4—41no—
1323C4—43no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—43no—
1330C4—43no—
1331C4—41no—
1332C4—43no—
1333C4—43no—
1334C4C2×#553112yes—
1335C2—46no—
1336C2—81no—
1337C2—81no—
1338C2—83no—
1339C2C22×#55311yescharacteristic
1340C2#6285711yescharacteristic
1341C2#6286111yescharacteristic
1342C2#6291911yescharacteristic
1343C2#6299411yescharacteristic
1344C2#6300711yescharacteristic
1345C2#6305211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59854C2semidirect
2. #59585C2semidirect
3. #59582C2semidirect
4. #52262C2semidirect
5. #45161C2semidirect
6. #45158C2semidirect
7. #45090C2semidirect
8. #45045C2semidirect
9. #45035C2semidirect
10. #45015C2semidirect
11. #39816C2semidirect
12. #39554C2semidirect
13. #39284C2semidirect
14. #39193C2semidirect
15. #38219C2semidirect
16. #38122C2semidirect
17. #36458C2semidirect
18. #36447C2semidirect
19. #36444C2semidirect
20. #35983C2semidirect
21. #35883C2semidirect
22. #35831C2semidirect
23. #35831C2semidirect
24. #35771C2semidirect
25. #35723C2semidirect
26. #34312C2semidirect
27. #34312C2semidirect
28. #34312C2semidirect
29. #34295C2semidirect
30. #34262C2semidirect
31. #34250C2semidirect

Maximal subgroups

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

subgroupindex
#598542
#595852
#595822
#522622
#451612
#451582
#450902
#450452
#450352
#450152
#398162
#395542
#392842
#391932
#382192
#381222
#364582
#364472
#364442
#359832
#358832
#358312
#357712
#357232
#343122
#342952
#342622
#342502