Finite Group Databasebeta

← #7655772

Subgroups — #7655772

Order 512.

5428 conjugacy classes of subgroups.

The subgroup lattice has 1405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42900C213yesmaximal, complemented
2#42892C213yesmaximal, complemented
3#42852C213yesmaximal, complemented
4#42847C213yesmaximal, complemented
5#42685C213yesmaximal, complemented
6#42654C213yesmaximal, complemented
7#42519C213yesmaximal, complemented
8#42462C213yesmaximal, complemented
9#40118C213yesmaximal, complemented
10#40100C213yesmaximal, complemented
11#39242C213yesmaximal, complemented
12#39227C213yesmaximal, complemented
13#37512C213yesmaximal, complemented
14#37501C213yesmaximal, complemented
15#36467C211yesmaximal, characteristic, complemented
16#36448C211yesmaximal, characteristic, complemented
17#36444C211yesmaximal, characteristic, complemented
18#36433C211yesmaximal, characteristic, complemented
19#36018C211yesmaximal, characteristic, complemented
20#35898C211yesmaximal, characteristic, complemented
21#35854C211yesmaximal, characteristic, complemented
22#35786C211yesmaximal, characteristic, complemented
23#35771C211yesmaximal, characteristic, complemented
24#35757C211yesmaximal, characteristic, complemented
25#35723C211yesmaximal, characteristic, complemented
26#35687C211yesmaximal, characteristic, complemented
27#35036C213yesmaximal, complemented
28#34589C213yesmaximal, complemented
29#34291C211yesmaximal, characteristic, complemented
30#34257C211yesmaximal, characteristic, complemented
31C4×#548C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#519C2211yescharacteristic
42C2×#519C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45#2863C2213yes—
46#2861C2213yes—
47#2857C2213yes—
48#2854C2213yes—
49#2831C2216yes—
50#2829C2216yes—
51#2825C2216yes—
52#2824C2216yes—
53#2808C2216yes—
54#2808C2216yes—
55#2803C2216yes—
56#2803C2216yes—
57#2787C2216yes—
58#2786C2216yes—
59#2786C2216yes—
60#2784C2216yes—
61#2781C2216yes—
62#2779C2216yes—
63#2774C2216yes—
64#2759C2216yes—
65#2756C2216yes—
66#2745C2216yes—
67#2714C2216yes—
68#2695C2216yes—
69#2666C2213yes—
70#2665C2213yes—
71#2662C2213yes—
72#2661C2213yes—
73#2653C2213yes—
74#2653C2213yes—
75#2653C2216yes—
76#2651C2213yes—
77#2650C2213yes—
78#2649C2213yes—
79#2648C2216yes—
80#2648C2211yescharacteristic
81#2648C2213yes—
82#2648C2213yes—
83#2648C2216yes—
84#2648C2216yes—
85#2644C2213yes—
86#2640C2213yes—
87#2636C2213yes—
88#2635C2213yes—
89#2631C2213yes—
90#2630C2213yes—
91#2630C2216yes—
92#2629C2213yes—
93#2625C2213yes—
94#2620C2213yes—
95#2619C2213yes—
96#2616C2213yes—
97#2615C2213yes—
98#2592C2213yes—
99#2592C2213yes—
100#2587C2216yes—
101#2582C2213yes—
102#2578C2216yes—
103#2578C2216yes—
104#2574C2216yes—
105#2565C2213yes—
106#2563C2213yes—
107#2562C2213yes—
108#2557C2216yes—
109#2554C2216yes—
110#2548C2213yes—
111#2547C2213yes—
112#2545C2213yes—
113#2538C2213yes—
114#2537C2213yes—
115#2536C2213yes—
116#2518C2216yes—
117#2514C2213yes—
118#2514C2213yes—
119#2513C2213yes—
120#2512C2213yes—
121#2512C2213yes—
122#2511C2213yes—
123#2500C2213yes—
124#2499C2213yes—
125#2497C2213yes—
126#2496C2213yes—
127#2496C2213yes—
128#2495C2213yes—
129#2494C2213yes—
130#2494C2213yes—
131#2492C2213yes—
132#2491C2213yes—
133#2490C2213yes—
134#2490C2213yes—
135#2490C2213yes—
136#2489C2213yes—
137#2489C2213yes—
138#2489C2213yes—
139#2485C2213yes—
140#2485C2213yes—
141#2467C2216yes—
142#2453C2213yes—
143#2451C2213yes—
144#2446C2213yes—
145#2446C2213yes—
146#2445C2213yes—
147#2445C2213yes—
148#2441C2213yes—
149#2439C2213yes—
150#2436C2213yes—
151#2434C2213yes—
152#2432C2213yes—
153#2432C2213yes—
154#2431C2213yes—
155#2431C2213yes—
156#2429C2213yes—
157#2427C2213yes—
158#2427C2213yes—
159#2426C2213yes—
160#2426C2213yes—
161#2426C2213yes—
162#2423C2213yes—
163#2422C2213yes—
164#2421C2213yes—
165#2420C2213yes—
166#2415C2213yes—
167#2415C2213yes—
168#2415C2213yes—
169#2414C2213yes—
170#2414C2213yes—
171#2414C2213yes—
172#2409C2213yes—
173#2409C2213yes—
174#2407C2213yes—
175#2407C2213yes—
176#2407C2213yes—
177#2407C2213yes—
178#2401C2213yes—
179#2398C2213yes—
180#2396C2213yes—
181#2395C2213yes—
182#2392C2213yes—
183#2392C2213yes—
184#2388C2213yes—
185#2388C2213yes—
186#2367C2213yes—
187#2365C2213yes—
188#2362C2213yes—
189#2362C2213yes—
190#2361C2213yes—
191#2360C2213yes—
192#2352C2213yes—
193#2352C2213yes—
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2213yes—
206#2341C2211yescharacteristic
207#2341C2213yes—
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2213yes—
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2213yes—
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218#2335C2216yes—
219#2334C2216yes—
220#2327C2213yes—
221#2323C2213yes—
222#2311C2213yes—
223#2311C2213yes—
224C4×#126C2213yes—
225C4×#124C2213yes—
226C4×#124C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×C22⋊Q8C2213yes—
229C4×#123C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232#2297C2213yes—
233#2297C2213yes—
234#2290C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C2×2−1+4—28no—
239C2×2−1+4—44no—
240C2×2−1+4—44no—
241C22×#41C2311yescharacteristic
242C22×#41C2311yescharacteristic
243C22×#41C2313yes—
244C22×#41C2313yes—
245C22×#41C2313yes—
246C23×Q8C2311yescharacteristic
247C23×Q8C2311yescharacteristic
248C23×Q8C2311yescharacteristic
249C23×Q8C2313yes—
250#557—44no—
251#550—44no—
252D4×Q8—28no—
253D4×Q8—44no—
254#548—28no—
255#548—44no—
256#548—44no—
257#548—44no—
258C2×C4⋊Q8C2313yes—
259C2×C4⋊Q8C2313yes—
260C2×C4⋊Q8C2313yes—
261C2×#127C2313yes—
262C2×#126C2313yes—
263C2×#126C2316yes—
264C2×#125C2313yes—
265C2×#125C2313yes—
266C2×#124C2313yes—
267C2×#124C2313yes—
268C2×#124C2313yes—
269C2×#124C2313yes—
270C2×#124C2313yes—
271C2×#123C2316yes—
272C2×#123C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2313yes—
277C2×C22⋊Q8C2313yes—
278C2×C22⋊Q8C2313yes—
279C2×C22⋊Q8C2313yes—
280C2×C22⋊Q8C2313yes—
281C2×#121C2313yes—
282C2×#121C2313yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288#519—44no—
289#519—44no—
290C4×#41—44no—
291C2×C4×Q8—44no—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2313yes—
303C2×C4×Q8C2313yes—
304C2×C4×Q8C2313yes—
305C2×C4×Q8C2313yes—
306C2×C4×Q8C2313yes—
307C2×C4×Q8C2313yes—
308C2×C4×Q8C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2313yes—
312C2×C4×D4C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×#117C2313yes—
321C2×#117C2313yes—
322C2×#117C2313yes—
323C2×#117C2313yes—
324C2×#117C2313yes—
325C22×C4⋊C4C2313yes—
326C22×C42C2313yes—
327C22×C42C2313yes—
328#401C2316yes—
329#401C2313yes—
330#400C2316yes—
331#400C2316yes—
332#400C2316yes—
333#400C2313yes—
334#400C2316yes—
335#400C2313yes—
336#400C2313yes—
337#400C2313yes—
338#400C2313yes—
339#400C2313yes—
340#400C2311yescharacteristic
341#399C2313yes—
342#399C2313yes—
343#398C2313yes—
344#398C2316yes—
345#398C2316yes—
346#398C2316yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#397C2316yes—
352#397C2316yes—
353#397C2316yes—
354#397C2316yes—
355#397C2316yes—
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2311yescharacteristic
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2311yescharacteristic
371#396C2316yes—
372#396C2316yes—
373#396C2316yes—
374#396C2313yes—
375#396C2316yes—
376#396C2313yes—
377#396C2313yes—
378#396C2311yescharacteristic
379#396C2313yes—
380#396C2313yes—
381#396C2313yes—
382#395C2316yes—
383#395C2313yes—
384#395C2313yes—
385#395C2313yes—
386#394C2316yes—
387#394C2316yes—
388#394C2316yes—
389#394C2316yes—
390#394C2316yes—
391#394C2316yes—
392#394C2316yes—
393#394C2313yes—
394#394C2316yes—
395#394C2316yes—
396#394C2316yes—
397#394C2316yes—
398#394C2313yes—
399#394C2313yes—
400#394C2313yes—
401#394C2313yes—
402#394C2313yes—
403#394C2313yes—
404#394C2313yes—
405#394C2311yescharacteristic
406#394C2313yes—
407#394C2313yes—
408#394C2313yes—
409#394C2311yescharacteristic
410#394C2313yes—
411#394C2313yes—
412#394C2311yescharacteristic
413#393C2313yes—
414#393C2316yes—
415#393C2313yes—
416#393C2316yes—
417#393C2316yes—
418#393C2313yes—
419#393C2313yes—
420#393C2313yes—
421#392C2313yes—
422#392C2313yes—
423#392C2313yes—
424#392C2316yes—
425#392C2316yes—
426#392C2316yes—
427#392C2313yes—
428#392C2313yes—
429#392C2311yescharacteristic
430#392C2313yes—
431#392C2313yes—
432#391C2313yes—
433#391C2313yes—
434#391C2313yes—
435#391C2313yes—
436#391C2316yes—
437#391C2313yes—
438#391C2313yes—
439#391C2313yes—
440#391C2313yes—
441#391C2316yes—
442#391C2313yes—
443#391C2313yes—
444#391C2313yes—
445#391C2313yes—
446#391C2313yes—
447#391C2313yes—
448#391C2313yes—
449#391C2313yes—
450#391C2313yes—
451#391C2313yes—
452#391C2313yes—
453#390C2316yes—
454#390C2313yes—
455#390C2313yes—
456#390C2316yes—
457#390C2313yes—
458#390C2316yes—
459#390C2313yes—
460#390C2313yes—
461#390C2313yes—
462#390C2313yes—
463#390C2313yes—
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2311yescharacteristic
472#390C2316yes—
473#390C2316yes—
474#389C2313yes—
475#389C2316yes—
476#389C2316yes—
477#389C2313yes—
478#389C2313yes—
479#389C2316yes—
480#389C2316yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#388C2311yescharacteristic
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2316yes—
496#388C2316yes—
497#388C2316yes—
498#388C2316yes—
499#388C2316yes—
500#388C2316yes—
501#388C2316yes—
502#388C2316yes—
503#388C2313yes—
504#388C2316yes—
505#388C2316yes—
506#388C2313yes—
507#388C2316yes—
508#388C2313yes—
509#388C2316yes—
510#388C2316yes—
511#388C2313yes—
512#388C2316yes—
513#388C2316yes—
514#388C2313yes—
515#388C2313yes—
516#388C2313yes—
517#388C2311yescharacteristic
518#388C2316yes—
519#388C2316yes—
520#388C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2316yes—
528#387C2316yes—
529#387C2316yes—
530#387C2313yes—
531#387C2313yes—
532#387C2316yes—
533#387C2316yes—
534#387C2316yes—
535#387C2316yes—
536#387C2316yes—
537#387C2316yes—
538#387C2311yescharacteristic
539#387C2313yes—
540#386C2316yes—
541#386C2313yes—
542#386C2313yes—
543#386C2316yes—
544#386C2313yes—
545#386C2313yes—
546#386C2316yes—
547#386C2316yes—
548#386C2316yes—
549#386C2313yes—
550#386C2311yescharacteristic
551#386C2313yes—
552#386C2311yescharacteristic
553#386C2313yes—
554#386C2316yes—
555#386C2316yes—
556#385C2313yes—
557#385C2313yes—
558#385C2316yes—
559#385C2316yes—
560#385C2316yes—
561#385C2316yes—
562#385C2316yes—
563#385C2313yes—
564#384C2313yes—
565#384C2313yes—
566#384C2313yes—
567#383C2313yes—
568#383C2316yes—
569#382C2316yes—
570#382C2313yes—
571#382C2313yes—
572#382C2313yes—
573#382C2313yes—
574#381C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2316yes—
586#380C2316yes—
587#380C2316yes—
588#380C2316yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2316yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2316yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2313yes—
629C4×C22⋊C4C2316yes—
630C4×C22⋊C4C2311yescharacteristic
631#376C2313yes—
632C43C2313yes—
6332−1+4—464no—
634C2×#41—24no—
635C2×#41—212no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C2×#41—24no—
641C2×#41—212no—
642C2×#41—212no—
643C2×#41—46no—
644C2×#41—46no—
645C2×#41—46no—
646C2×#41—46no—
647C2×#41—46no—
648C2×#41—46no—
649C22×Q8—24no—
650C22×Q8—24no—
651C22×Q8—24no—
652C22×Q8—212no—
653C22×Q8—24no—
654C22×Q8—24no—
655C22×Q8—24no—
656C22×Q8—24no—
657C22×Q8—24no—
658C22×Q8—46no—
659C22×Q8—46no—
660C22×Q8#4118yes—
661C22×Q8C2413yes—
662C22×Q8C2413yes—
663C22×Q8C2413yes—
664C22×Q8C2413yes—
665C22×Q8C2413yes—
666C22×Q8C2411yescharacteristic
667C22×D4C2413yes—
668C22×D4C2413yes—
669C22×D4C2411yescharacteristic
670C22×D4C2413yes—
671C22×D4C2411yescharacteristic
672C22×D4C2411yescharacteristic
673C22×D4C2413yes—
674C22×D4C2413yes—
675C22×D4C2413yes—
676C22×D4C2413yes—
677C22×D4C2413yes—
678C22×D4C2413yes—
679C22×D4C2416yes—
680C23×C4C2413yes—
681C23×C4C2413yes—
682C23×C4C2413yes—
683C23×C4C2413yes—
684C23×C4C2413yes—
685C23×C4C2413yes—
686C23×C4C2413yes—
687C23×C4C2411yescharacteristic
688C23×C4C2416yes—
689C23×C4C2413yes—
690C4⋊Q8—212no—
691C4⋊Q8—46no—
692C4⋊Q8—46no—
693#127—46no—
694#126—46no—
695#126—412no—
696#125—46no—
697#125—46no—
698#124—212no—
699#124—46no—
700#124—46no—
701#124—46no—
702#124—46no—
703#123—412no—
704#123—46no—
705C22⋊Q8—212no—
706C22⋊Q8—212no—
707C22⋊Q8—212no—
708C22⋊Q8—46no—
709C22⋊Q8—46no—
710C22⋊Q8—46no—
711C22⋊Q8—46no—
712C22⋊Q8—46no—
713#121—212no—
714#121—46no—
715#121—46no—
716#121—46no—
717#121—46no—
718#121—46no—
719#121—46no—
720C4×Q8—24no—
721C4×Q8—24no—
722C4×Q8—24no—
723C4×Q8—24no—
724C4×Q8—24no—
725C4×Q8—24no—
726C4×Q8—24no—
727C4×Q8—24no—
728C4×Q8—24no—
729C4×Q8—24no—
730C4×Q8—46no—
731C4×Q8—46no—
732C4×Q8—46no—
733C4×Q8—46no—
734C4×Q8—46no—
735C4×Q8—46no—
736C4×Q8—46no—
737C4×D4—212no—
738C4×D4—212no—
739C4×D4—46no—
740C4×D4—46no—
741C4×D4—46no—
742C4×D4—46no—
743C4×D4—46no—
744C4×D4—46no—
745C4×D4—46no—
746C4×D4—46no—
747C4×D4—46no—
748#117—46no—
749#117—46no—
750#117—46no—
751#117—46no—
752#117—46no—
753C2×C4⋊C4—46no—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2416yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2416yes—
788C2×C4⋊C4C2416yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2416yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2416yes—
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2411yescharacteristic
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2416yes—
812C2×C22⋊C4C2411yescharacteristic
813C2×C22⋊C4C2411yescharacteristic
814C2×C22⋊C4C2411yescharacteristic
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2416yes—
826C2×C22⋊C4C2416yes—
827C2×C22⋊C4C2416yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2416yes—
833C2×C22⋊C4C2416yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2416yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2416yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2411yescharacteristic
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2411yescharacteristic
844C2×C22⋊C4C2411yescharacteristic
845C2×C22⋊C4C2411yescharacteristic
846C2×C22⋊C4C2411yescharacteristic
847C2×C22⋊C4C2416yes—
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2416yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C42—46no—
855C2×C42—46no—
856C2×C42C2413yes—
857C2×C42C2413yes—
858C2×C42C2413yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2413yes—
862C2×C42C2413yes—
863C2×C42C2413yes—
864C2×C42C2413yes—
865C2×C42C2413yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868C2×C42C2416yes—
869C2×C42C2416yes—
870C2×C42C2413yes—
871C2×C42C2413yes—
872C2×C42C2413yes—
873C2×C42C2416yes—
874C2×C42C2411yescharacteristic
875C2×C42C2413yes—
876C2×C42C2411yescharacteristic
877#95C2411yescharacteristic
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2411yescharacteristic
882#95C2411yescharacteristic
883#95C2413yes—
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2413yes—
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2416yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2416yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2416yes—
905#95C2416yes—
906#95C2413yes—
907#95C2416yes—
908#95C2416yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2411yescharacteristic
918#95C2416yes—
919#95C2411yescharacteristic
920#95C2416yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2416yes—
930#95C2416yes—
931#95C2416yes—
932#95C2416yes—
933C24C2511yescharacteristic
934C24C2513yes—
935C24C2511yescharacteristic
936C24C2513yes—
937C24C2511yescharacteristic
938#41—448no—
939#41—448no—
940#41—448no—
941#41—416no—
942#41—416no—
943C2×Q8—232no—
944C2×Q8—26no—
945C2×Q8—26no—
946C2×Q8—26no—
947C2×Q8—26no—
948C2×Q8—26no—
949C2×Q8—26no—
950C2×Q8—26no—
951C2×Q8—26no—
952C2×Q8—26no—
953C2×Q8—43no—
954C2×Q8—43no—
955C2×Q8—43no—
956C2×Q8—43no—
957C2×Q8—43no—
958C2×Q8—448no—
959C2×Q8—416no—
960C2×Q8—416no—
961C2×Q8C2×#41112yes—
962C2×Q8C2×#4114yes—
963C2×Q8H(5,𝔽2)14yes—
964C2×Q8H(5,𝔽2)14yes—
965C2×D4—22no—
966C2×D4—26no—
967C2×D4—22no—
968C2×D4—26no—
969C2×D4—26no—
970C2×D4—26no—
971C2×D4—26no—
972C2×D4—26no—
973C2×D4—26no—
974C2×D4—26no—
975C2×D4—26no—
976C2×D4—22no—
977C2×D4—41no—
978C2×D4—43no—
979C2×D4—43no—
980C2×D4—41no—
981C2×D4—41no—
982C2×D4—41no—
983C2×D4—43no—
984C2×D4—43no—
985C2×D4—41no—
986C2×D4—43no—
987C2×D4—41no—
988C2×D4—43no—
989C2×D4—43no—
990C2×D4—43no—
991C2×D4—43no—
992C2×D4—43no—
993C2×D4—43no—
994C2×D4—43no—
995C2×D4—43no—
996C2×D4—43no—
997C2×D4—43no—
998C2×D4—43no—
999C2×D4—43no—
1000C2×D4—43no—
1001C2×D4—46no—
1002C2×D4—46no—
1003C2×D4—46no—
1004C22×C4—26no—
1005C22×C4—26no—
1006C22×C4—26no—
1007C22×C4—26no—
1008C22×C4—212no—
1009C22×C4—26no—
1010C22×C4—26no—
1011C22×C4—26no—
1012C22×C4—26no—
1013C22×C4—26no—
1014C22×C4—26no—
1015C22×C4—26no—
1016C22×C4—26no—
1017C22×C4—26no—
1018C22×C4—26no—
1019C22×C4—22no—
1020C22×C4—26no—
1021C22×C4—26no—
1022C22×C4—41no—
1023C22×C4—41no—
1024C22×C4—46no—
1025C22×C4—46no—
1026C22×C4—43no—
1027C22×C4—43no—
1028C22×C4—43no—
1029C22×C4—43no—
1030C22×C4—43no—
1031C22×C4—43no—
1032C22×C4—43no—
1033C22×C4C2×#41112yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2511yescharacteristic
1036C22×C4C2513yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2511yescharacteristic
1039C22×C4C2511yescharacteristic
1040C22×C4C2513yes—
1041C22×C4C2513yes—
1042C22×C4C2513yes—
1043C22×C4C2513yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2513yes—
1046C22×C4C2513yes—
1047C22×C4C2513yes—
1048C22×C4C2513yes—
1049C22×C4C2513yes—
1050C22×C4C2513yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C22×C4C2511yescharacteristic
1055C22×C4C2513yes—
1056C22×C4C2513yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2511yescharacteristic
1059C22×C4C2513yes—
1060C4⋊C4—26no—
1061C4⋊C4—26no—
1062C4⋊C4—26no—
1063C4⋊C4—26no—
1064C4⋊C4—212no—
1065C4⋊C4—26no—
1066C4⋊C4—26no—
1067C4⋊C4—26no—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—26no—
1071C4⋊C4—26no—
1072C4⋊C4—26no—
1073C4⋊C4—26no—
1074C4⋊C4—26no—
1075C4⋊C4—22no—
1076C4⋊C4—26no—
1077C4⋊C4—46no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—43no—
1081C4⋊C4—43no—
1082C4⋊C4—46no—
1083C4⋊C4—43no—
1084C4⋊C4—43no—
1085C4⋊C4—43no—
1086C4⋊C4—43no—
1087C4⋊C4—43no—
1088C4⋊C4—41no—
1089C4⋊C4—43no—
1090C4⋊C4—43no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4—41no—
1094C4⋊C4—43no—
1095C4⋊C4—43no—
1096C4⋊C4—46no—
1097C4⋊C4—43no—
1098C4⋊C4—46no—
1099C4⋊C4—46no—
1100C4⋊C4—43no—
1101C4⋊C4—43no—
1102C4⋊C4—46no—
1103C22⋊C4—22no—
1104C22⋊C4—26no—
1105C22⋊C4—26no—
1106C22⋊C4—26no—
1107C22⋊C4—212no—
1108C22⋊C4—22no—
1109C22⋊C4—26no—
1110C22⋊C4—26no—
1111C22⋊C4—22no—
1112C22⋊C4—22no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—43no—
1116C22⋊C4—46no—
1117C22⋊C4—46no—
1118C22⋊C4—41no—
1119C22⋊C4—43no—
1120C22⋊C4—43no—
1121C22⋊C4—41no—
1122C22⋊C4—43no—
1123C22⋊C4—43no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—43no—
1130C22⋊C4—43no—
1131C22⋊C4—46no—
1132C22⋊C4—43no—
1133C22⋊C4—43no—
1134C22⋊C4—43no—
1135C22⋊C4—41no—
1136C22⋊C4—41no—
1137C22⋊C4—41no—
1138C22⋊C4—43no—
1139C22⋊C4—43no—
1140C22⋊C4—43no—
1141C22⋊C4—43no—
1142C22⋊C4—43no—
1143C22⋊C4—43no—
1144C22⋊C4—43no—
1145C22⋊C4—43no—
1146C22⋊C4—43no—
1147C22⋊C4—46no—
1148C22⋊C4—46no—
1149C22⋊C4—46no—
1150C22⋊C4—43no—
1151C22⋊C4—43no—
1152C22⋊C4—46no—
1153C22⋊C4—46no—
1154C22⋊C4—43no—
1155C22⋊C4—43no—
1156C22⋊C4—43no—
1157C22⋊C4—43no—
1158C22⋊C4—46no—
1159C22⋊C4—46no—
1160C42—26no—
1161C42—26no—
1162C42—26no—
1163C42—26no—
1164C42—26no—
1165C42—26no—
1166C42—26no—
1167C42—26no—
1168C42—26no—
1169C42—26no—
1170C42—26no—
1171C42—41no—
1172C42—43no—
1173C42—43no—
1174C42—43no—
1175C42—41no—
1176C42—43no—
1177C42—46no—
1178C42—46no—
1179C42—43no—
1180C42—46no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—23no—
1189C23—21no—
1190C23—23no—
1191C23—21no—
1192C23—23no—
1193C23—21no—
1194C23—23no—
1195C23—23no—
1196C23—21no—
1197C23—21no—
1198C23—23no—
1199C23—21no—
1200C23—23no—
1201C23—23no—
1202C23—21no—
1203C23—23no—
1204C23—21no—
1205C23—21no—
1206C23—23no—
1207C23—21no—
1208C23—23no—
1209C23—23no—
1210C23—23no—
1211C23—21no—
1212C23—21no—
1213C23—23no—
1214C23—21no—
1215C23C22×#4112yes—
1216C23C2611yescharacteristic
1217Q8—224no—
1218Q8—412no—
1219Q8—412no—
1220Q8—412no—
1221Q8—86no—
1222Q8#538116yes—
1223D4—44no—
1224D4—412no—
1225D4—412no—
1226D4—44no—
1227D4—44no—
1228D4—412no—
1229D4—412no—
1230D4—412no—
1231D4—86no—
1232D4—86no—
1233D4—86no—
1234D4—86no—
1235D4—166no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—224no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—21no—
1248C2×C4—23no—
1249C2×C4—21no—
1250C2×C4—23no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—21no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—21no—
1269C2×C4—23no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—21no—
1276C2×C4—23no—
1277C2×C4—23no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—23no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—23no—
1286C2×C4—23no—
1287C2×C4—21no—
1288C2×C4—23no—
1289C2×C4—23no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—23no—
1294C2×C4—23no—
1295C2×C4—21no—
1296C2×C4—23no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—23no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—23no—
1304C2×C4—21no—
1305C2×C4—23no—
1306C2×C4—23no—
1307C2×C4—23no—
1308C2×C4—21no—
1309C2×C4—44no—
1310C2×C4—424no—
1311C2×C4—412no—
1312C2×C4—412no—
1313C2×C4—412no—
1314C2×C4—412no—
1315C2×C4—86no—
1316C2×C4—86no—
1317C2×C4—86no—
1318C2×C4C22×#4116yes—
1319C2×C4C22×#4116yes—
1320C2×C4C2×H(5,𝔽2)16yes—
1321C2×C4C2×H(5,𝔽2)16yes—
1322C2×C4#58512yes—
1323C2×C4#58512yes—
1324C22—22no—
1325C22—22no—
1326C22—22no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—43no—
1332C22—41no—
1333C22—41no—
1334C22—43no—
1335C22—41no—
1336C22—43no—
1337C22—41no—
1338C22—43no—
1339C22—43no—
1340C22—41no—
1341C22—41no—
1342C22—43no—
1343C22—43no—
1344C22—43no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—41no—
1350C22—43no—
1351C22—43no—
1352C22—43no—
1353C22—43no—
1354C22—41no—
1355C22—43no—
1356C22—41no—
1357C22—41no—
1358C22—43no—
1359C22C23×#4111yescharacteristic
1360C22C22×H(5,𝔽2)11yescharacteristic
1361C22C22×H(5,𝔽2)11yescharacteristic
1362C22C2×#58511yescharacteristic
1363C22C2×#58511yescharacteristic
1364C222−1+611yescharacteristic
1365C222−1+611yescharacteristic
1366C4—22no—
1367C4—22no—
1368C4—26no—
1369C4—43no—
1370C4—43no—
1371C4—41no—
1372C4—41no—
1373C4—43no—
1374C4—43no—
1375C4—41no—
1376C4—41no—
1377C4—43no—
1378C4—43no—
1379C4—41no—
1380C4—41no—
1381C4—41no—
1382C4—43no—
1383C4—43no—
1384C4—43no—
1385C4—43no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—43no—
1390C4—43no—
1391C4C2×#538112yes—
1392C2—42no—
1393C2—83no—
1394C2—81no—
1395C2—81no—
1396C2—83no—
1397C2C22×#53811yescharacteristic
1398C2#6279311yescharacteristic
1399C2#6285011yescharacteristic
1400C2#6289711yescharacteristic
1401C2#6291911yescharacteristic
1402C2#6292211yescharacteristic
1403C2#6292211yescharacteristic
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. #42900C2semidirect
2. #42892C2semidirect
3. #42852C2semidirect
4. #42847C2semidirect
5. #42685C2semidirect
6. #42654C2semidirect
7. #42519C2semidirect
8. #42462C2semidirect
9. #40118C2semidirect
10. #40100C2semidirect
11. #39242C2semidirect
12. #39227C2semidirect
13. #37512C2semidirect
14. #37501C2semidirect
15. #36467C2semidirect
16. #36448C2semidirect
17. #36444C2semidirect
18. #36433C2semidirect
19. #36018C2semidirect
20. #35898C2semidirect
21. #35854C2semidirect
22. #35786C2semidirect
23. #35771C2semidirect
24. #35757C2semidirect
25. #35723C2semidirect
26. #35687C2semidirect
27. #35036C2semidirect
28. #34589C2semidirect
29. #34291C2semidirect
30. #34257C2semidirect
31. C4×#548C2semidirect

Maximal subgroups

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

subgroupindex
#429002
#428922
#428522
#428472
#426852
#426542
#425192
#424622
#401182
#401002
#392422
#392272
#375122
#375012
#364672
#364482
#364442
#364332
#360182
#358982
#358542
#357862
#357712
#357572
#357232
#356872
#350362
#345892
#342912
#342572
C4×#5482