Finite Group Databasebeta

← #7657271

Subgroups — #7657271

Order 512.

5588 conjugacy classes of subgroups.

The subgroup lattice has 1422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42961C213yesmaximal, complemented
2#42945C213yesmaximal, complemented
3#42936C213yesmaximal, complemented
4#42923C213yesmaximal, complemented
5#42760C213yesmaximal, complemented
6#42732C213yesmaximal, complemented
7#42602C213yesmaximal, complemented
8#42595C213yesmaximal, complemented
9#40153C213yesmaximal, complemented
10#40140C213yesmaximal, complemented
11#39004C213yesmaximal, complemented
12#38997C213yesmaximal, complemented
13#37515C213yesmaximal, complemented
14#37494C213yesmaximal, complemented
15#36467C211yesmaximal, characteristic, complemented
16#36448C211yesmaximal, characteristic, complemented
17#36432C211yesmaximal, characteristic, complemented
18#36430C211yesmaximal, characteristic, complemented
19#36029C211yesmaximal, characteristic, complemented
20#35996C211yesmaximal, characteristic, complemented
21#35883C211yesmaximal, characteristic, complemented
22#35854C211yesmaximal, characteristic, complemented
23#35831C211yesmaximal, characteristic, complemented
24#35816C211yesmaximal, characteristic, complemented
25#35757C211yesmaximal, characteristic, complemented
26#35757C211yesmaximal, characteristic, complemented
27#35030C213yesmaximal, complemented
28#34589C213yesmaximal, complemented
29#34295C211yesmaximal, characteristic, complemented
30#34259C211yesmaximal, characteristic, complemented
31C4×#550C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45#2863C2213yes—
46#2861C2213yes—
47#2855C2213yes—
48#2850C2213yes—
49#2832C2216yes—
50#2831C2216yes—
51#2825C2216yes—
52#2825C2216yes—
53#2765C2216yes—
54#2761C2216yes—
55#2760C2216yes—
56#2756C2216yes—
57#2753C2216yes—
58#2752C2216yes—
59#2750C2216yes—
60#2749C2216yes—
61#2749C2216yes—
62#2749C2216yes—
63#2749C2216yes—
64#2714C2216yes—
65#2703C2216yes—
66#2696C2216yes—
67#2688C2216yes—
68#2676C2216yes—
69#2666C2213yes—
70#2665C2213yes—
71#2662C2213yes—
72#2661C2213yes—
73#2661C2216yes—
74#2653C2213yes—
75#2653C2213yes—
76#2653C2216yes—
77#2653C2216yes—
78#2651C2211yescharacteristic
79#2650C2213yes—
80#2649C2213yes—
81#2648C2213yes—
82#2648C2213yes—
83#2648C2213yes—
84#2645C2213yes—
85#2643C2216yes—
86#2640C2213yes—
87#2639C2216yes—
88#2636C2213yes—
89#2635C2213yes—
90#2631C2213yes—
91#2630C2213yes—
92#2629C2213yes—
93#2625C2213yes—
94#2620C2213yes—
95#2619C2213yes—
96#2615C2213yes—
97#2615C2213yes—
98#2592C2213yes—
99#2592C2213yes—
100#2574C2216yes—
101#2572C2216yes—
102#2566C2213yes—
103#2563C2213yes—
104#2562C2213yes—
105#2544C2213yes—
106#2544C2213yes—
107#2541C2213yes—
108#2538C2213yes—
109#2537C2213yes—
110#2535C2213yes—
111#2535C2213yes—
112#2514C2213yes—
113#2514C2213yes—
114#2514C2213yes—
115#2514C2213yes—
116#2511C2213yes—
117#2511C2213yes—
118#2510C2216yes—
119#2502C2213yes—
120#2499C2213yes—
121#2497C2213yes—
122#2496C2213yes—
123#2495C2213yes—
124#2495C2213yes—
125#2494C2213yes—
126#2494C2213yes—
127#2492C2213yes—
128#2491C2213yes—
129#2490C2213yes—
130#2490C2213yes—
131#2490C2213yes—
132#2489C2213yes—
133#2489C2213yes—
134#2489C2213yes—
135#2486C2213yes—
136#2485C2213yes—
137#2456C2216yes—
138#2456C2216yes—
139#2454C2213yes—
140#2452C2213yes—
141#2450C2216yes—
142#2447C2213yes—
143#2447C2213yes—
144#2447C2213yes—
145#2447C2213yes—
146#2444C2216yes—
147#2444C2216yes—
148#2442C2213yes—
149#2440C2213yes—
150#2436C2213yes—
151#2436C2213yes—
152#2431C2213yes—
153#2431C2213yes—
154#2431C2213yes—
155#2431C2213yes—
156#2428C2213yes—
157#2428C2213yes—
158#2428C2213yes—
159#2428C2213yes—
160#2427C2213yes—
161#2427C2213yes—
162#2422C2213yes—
163#2422C2213yes—
164#2422C2213yes—
165#2420C2213yes—
166#2417C2213yes—
167#2416C2213yes—
168#2416C2213yes—
169#2416C2213yes—
170#2415C2213yes—
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#2366C2213yes—
187#2366C2213yes—
188#2363C2213yes—
189#2363C2213yes—
190#2363C2213yes—
191#2361C2213yes—
192#2354C2213yes—
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#2341C2211yescharacteristic
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214#2339C2213yes—
215#2339C2213yes—
216#2339C2213yes—
217#2339C2213yes—
218#2328C2213yes—
219#2325C2216yes—
220#2324C2213yes—
221#2318C2216yes—
222#2311C2213yes—
223#2310C2213yes—
224C4×#127C2213yes—
225C4×#126C2213yes—
226C4×#124C2213yes—
227C4×#123C2213yes—
228C4×#121C2213yes—
229C4×#121C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232#2297C2213yes—
233C2×#391C2213yes—
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×#41C2311yescharacteristic
244C22×#41C2313yes—
245C22×#41C2313yes—
246C22×#41C2313yes—
247C23×Q8C2311yescharacteristic
248C23×Q8C2311yescharacteristic
249C23×Q8C2313yes—
250#557—44no—
251#550—28no—
252#550—28no—
253#550—44no—
254#548—44no—
255#548—44no—
256#548—44no—
257#548—44no—
258C2×C4⋊Q8C2313yes—
259C2×#127C2313yes—
260C2×#127C2313yes—
261C2×#127C2313yes—
262C2×#126C2313yes—
263C2×#125C2313yes—
264C2×#125C2313yes—
265C2×#124C2313yes—
266C2×#124C2313yes—
267C2×#124C2313yes—
268C2×#124C2313yes—
269C2×#124C2313yes—
270C2×#123C2313yes—
271C2×#123C2316yes—
272C2×C22⋊Q8C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2316yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280C2×#121C2313yes—
281C2×#121C2316yes—
282C2×#121C2313yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#121C2313yes—
289C2×#121C2316yes—
290C2×#121C2316yes—
291#520—44no—
292#520—44no—
293C4×#41—44no—
294C4×#41—44no—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2313yes—
312C2×C4×D4C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2316yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×C4×D4C2313yes—
321C2×C4×D4C2313yes—
322C2×C4×D4C2313yes—
323C2×C4×D4C2313yes—
324C2×C4×D4C2316yes—
325C2×#117C2313yes—
326C2×#117C2313yes—
327C2×#117C2313yes—
328C2×#117C2313yes—
329C22×C4⋊C4C2313yes—
330C22×C4⋊C4C2313yes—
331C22×C42C2313yes—
332C22×C42C2313yes—
333#401C2316yes—
334#401C2316yes—
335#401C2313yes—
336#400C2316yes—
337#400C2313yes—
338#400C2316yes—
339#400C2316yes—
340#400C2316yes—
341#400C2316yes—
342#400C2313yes—
343#400C2313yes—
344#400C2313yes—
345#400C2313yes—
346#400C2313yes—
347#400C2313yes—
348#399C2313yes—
349#399C2311yescharacteristic
350#398C2316yes—
351#398C2316yes—
352#398C2313yes—
353#398C2313yes—
354#398C2311yescharacteristic
355#398C2313yes—
356#398C2311yescharacteristic
357#397C2313yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#397C2316yes—
362#397C2316yes—
363#397C2316yes—
364#397C2316yes—
365#397C2316yes—
366#397C2316yes—
367#397C2316yes—
368#397C2313yes—
369#397C2311yescharacteristic
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#397C2311yescharacteristic
374#397C2313yes—
375#397C2313yes—
376#397C2313yes—
377#396C2313yes—
378#396C2316yes—
379#396C2316yes—
380#396C2313yes—
381#396C2313yes—
382#396C2316yes—
383#396C2313yes—
384#396C2313yes—
385#396C2313yes—
386#396C2311yescharacteristic
387#395C2313yes—
388#395C2313yes—
389#395C2313yes—
390#394C2316yes—
391#394C2313yes—
392#394C2313yes—
393#394C2316yes—
394#394C2316yes—
395#394C2316yes—
396#394C2316yes—
397#394C2316yes—
398#394C2316yes—
399#394C2313yes—
400#394C2313yes—
401#394C2313yes—
402#394C2313yes—
403#394C2313yes—
404#394C2313yes—
405#394C2313yes—
406#394C2313yes—
407#394C2311yescharacteristic
408#394C2311yescharacteristic
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#393C2313yes—
414#393C2316yes—
415#393C2313yes—
416#393C2316yes—
417#393C2316yes—
418#393C2313yes—
419#393C2316yes—
420#393C2313yes—
421#393C2313yes—
422#392C2313yes—
423#392C2316yes—
424#392C2316yes—
425#392C2316yes—
426#392C2316yes—
427#392C2316yes—
428#392C2316yes—
429#392C2316yes—
430#392C2313yes—
431#392C2313yes—
432#392C2313yes—
433#392C2313yes—
434#392C2313yes—
435#392C2313yes—
436#392C2313yes—
437#391C2313yes—
438#391C2316yes—
439#391C2313yes—
440#391C2313yes—
441#391C2313yes—
442#391C2313yes—
443#391C2313yes—
444#391C2313yes—
445#391C2313yes—
446#391C2313yes—
447#391C2313yes—
448#391C2313yes—
449#391C2313yes—
450#391C2313yes—
451#391C2313yes—
452#391C2313yes—
453#391C2313yes—
454#391C2313yes—
455#391C2313yes—
456#391C2313yes—
457#390C2313yes—
458#390C2313yes—
459#390C2316yes—
460#390C2316yes—
461#390C2316yes—
462#390C2313yes—
463#390C2313yes—
464#390C2313yes—
465#390C2316yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2313yes—
472#390C2313yes—
473#390C2313yes—
474#390C2313yes—
475#390C2313yes—
476#390C2311yescharacteristic
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#388C2311yescharacteristic
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2316yes—
495#388C2316yes—
496#388C2313yes—
497#388C2316yes—
498#388C2316yes—
499#388C2316yes—
500#388C2316yes—
501#388C2313yes—
502#388C2316yes—
503#388C2313yes—
504#388C2313yes—
505#388C2316yes—
506#388C2316yes—
507#388C2311yescharacteristic
508#388C2311yescharacteristic
509#388C2313yes—
510#388C2313yes—
511#388C2311yescharacteristic
512#388C2316yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2316yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2313yes—
522#387C2313yes—
523#387C2311yescharacteristic
524#387C2316yes—
525#386C2316yes—
526#386C2316yes—
527#386C2316yes—
528#386C2313yes—
529#386C2313yes—
530#386C2316yes—
531#386C2316yes—
532#386C2316yes—
533#386C2316yes—
534#386C2316yes—
535#386C2316yes—
536#386C2316yes—
537#386C2316yes—
538#386C2313yes—
539#386C2316yes—
540#386C2316yes—
541#386C2313yes—
542#386C2313yes—
543#386C2316yes—
544#386C2313yes—
545#386C2313yes—
546#386C2313yes—
547#386C2313yes—
548#386C2316yes—
549#386C2316yes—
550#386C2316yes—
551#386C2316yes—
552#386C2316yes—
553#385C2316yes—
554#385C2316yes—
555#385C2316yes—
556#385C2316yes—
557#385C2313yes—
558#385C2316yes—
559#385C2313yes—
560#385C2313yes—
561#385C2316yes—
562#385C2316yes—
563#384C2313yes—
564#384C2313yes—
565#384C2313yes—
566#383C2313yes—
567#383C2316yes—
568#383C2316yes—
569#382C2316yes—
570#382C2313yes—
571#382C2313yes—
572#382C2313yes—
573#382C2313yes—
574#381C2316yes—
575#381C2316yes—
576#381C2316yes—
577#381C2316yes—
578#381C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2316yes—
590#380C2316yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2313yes—
595#380C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2311yescharacteristic
609C4×C4⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2313yes—
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—
629#376C2313yes—
630C2×#95C2316yes—
631C2×#95C2316yes—
632C43C2313yes—
6332−1+4—464no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C2×#41—24no—
641C2×#41—24no—
642C2×#41—212no—
643C2×#41—212no—
644C2×#41—212no—
645C2×#41—46no—
646C2×#41—46no—
647C2×#41—46no—
648C2×#41—46no—
649C2×#41—46no—
650C2×#41—46no—
651C2×#41#4118yes—
652C22×Q8—24no—
653C22×Q8—24no—
654C22×Q8—24no—
655C22×Q8—24no—
656C22×Q8—24no—
657C22×Q8—24no—
658C22×Q8—212no—
659C22×Q8—46no—
660C22×Q8—46no—
661C22×Q8C2413yes—
662C22×Q8C2413yes—
663C22×Q8C2413yes—
664C22×Q8C2413yes—
665C22×Q8C2411yescharacteristic
666C22×D4C2413yes—
667C22×D4C2413yes—
668C22×D4C2413yes—
669C22×D4C2413yes—
670C22×D4C2416yes—
671C22×D4C2416yes—
672C22×D4C2413yes—
673C22×D4C2413yes—
674C22×D4C2413yes—
675C22×D4C2411yescharacteristic
676C22×D4C2413yes—
677C22×D4C2413yes—
678C22×D4C2413yes—
679C22×D4C2413yes—
680C22×D4C2413yes—
681C22×D4C2416yes—
682C23×C4C2413yes—
683C23×C4C2413yes—
684C23×C4C2413yes—
685C23×C4C2413yes—
686C23×C4C2413yes—
687C23×C4C2413yes—
688C23×C4C2413yes—
689C23×C4C2416yes—
690C23×C4C2416yes—
691C23×C4C2416yes—
692C23×C4C2413yes—
693C23×C4C2413yes—
694C4⋊Q8—46no—
695#127—212no—
696#127—212no—
697#127—46no—
698#126—46no—
699#125—46no—
700#125—46no—
701#124—46no—
702#124—46no—
703#124—46no—
704#124—46no—
705#124—46no—
706#123—46no—
707#123—86no—
708C22⋊Q8—46no—
709C22⋊Q8—46no—
710C22⋊Q8—46no—
711C22⋊Q8—46no—
712C22⋊Q8—86no—
713#121—212no—
714#121—212no—
715#121—212no—
716#121—212no—
717#121—46no—
718#121—412no—
719#121—46no—
720#121—46no—
721#121—46no—
722#121—46no—
723#121—46no—
724#121—46no—
725#121—86no—
726#121—86no—
727C4×Q8—24no—
728C4×Q8—24no—
729C4×Q8—24no—
730C4×Q8—24no—
731C4×Q8—24no—
732C4×Q8—24no—
733C4×Q8—24no—
734C4×Q8—24no—
735C4×Q8—24no—
736C4×Q8—24no—
737C4×Q8—46no—
738C4×D4—212no—
739C4×D4—212no—
740C4×D4—46no—
741C4×D4—46no—
742C4×D4—46no—
743C4×D4—46no—
744C4×D4—46no—
745C4×D4—46no—
746C4×D4—46no—
747C4×D4—46no—
748C4×D4—46no—
749C4×D4—46no—
750C4×D4—46no—
751C4×D4—46no—
752C4×D4—46no—
753C4×D4—46no—
754C4×D4—46no—
755C4×D4—412no—
756C4×D4—86no—
757#117—46no—
758#117—46no—
759#117—46no—
760#117—46no—
761C2×C4⋊C4—46no—
762C2×C4⋊C4—46no—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2416yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2416yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2416yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2416yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2411yescharacteristic
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2411yescharacteristic
812C2×C22⋊C4C2411yescharacteristic
813C2×C22⋊C4C2416yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2411yescharacteristic
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2411yescharacteristic
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2416yes—
826C2×C22⋊C4C2416yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2416yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2416yes—
839C2×C22⋊C4C2416yes—
840C2×C22⋊C4C2416yes—
841C2×C22⋊C4C2416yes—
842C2×C22⋊C4C2416yes—
843C2×C22⋊C4C2416yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2411yescharacteristic
854C2×C22⋊C4C2411yescharacteristic
855C2×C22⋊C4C2411yescharacteristic
856C2×C22⋊C4C2411yescharacteristic
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2416yes—
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2413yes—
861C2×C42—46no—
862C2×C42—46no—
863C2×C42C2413yes—
864C2×C42C2413yes—
865C2×C42C2413yes—
866C2×C42C2413yes—
867C2×C42C2411yescharacteristic
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2413yes—
872C2×C42C2413yes—
873C2×C42C2413yes—
874C2×C42C2413yes—
875C2×C42C2413yes—
876C2×C42C2413yes—
877C2×C42C2413yes—
878C2×C42C2416yes—
879C2×C42C2413yes—
880C2×C42C2411yescharacteristic
881C2×C42C2411yescharacteristic
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2416yes—
887#95C2416yes—
888#95C2416yes—
889#95C2416yes—
890#95C2411yescharacteristic
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2411yescharacteristic
895#95C2411yescharacteristic
896#95C2411yescharacteristic
897#95C2413yes—
898#95C2411yescharacteristic
899#95C2411yescharacteristic
900#95C2411yescharacteristic
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2416yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2411yescharacteristic
922#95C2411yescharacteristic
923#95C2411yescharacteristic
924#95C2416yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2413yes—
931#95C2413yes—
932#95C2416yes—
933#95C2416yes—
934#95C2416yes—
935#95C2416yes—
936#95C2416yes—
937#95C2416yes—
938C24C2513yes—
939C24C2513yes—
940C24C2511yescharacteristic
941C24C2511yescharacteristic
942C24C2513yes—
943#41—232no—
944#41—448no—
945#41—448no—
946#41—448no—
947#41—416no—
948#41—416no—
949C2×Q8—26no—
950C2×Q8—26no—
951C2×Q8—26no—
952C2×Q8—26no—
953C2×Q8—26no—
954C2×Q8—26no—
955C2×Q8—26no—
956C2×Q8—43no—
957C2×Q8—43no—
958C2×Q8—43no—
959C2×Q8—43no—
960C2×Q8—43no—
961C2×Q8—448no—
962C2×Q8—416no—
963C2×Q8—416no—
964C2×Q8C2×#4114yes—
965C2×Q8H(5,𝔽2)14yes—
966C2×Q8H(5,𝔽2)14yes—
967C2×D4—26no—
968C2×D4—26no—
969C2×D4—26no—
970C2×D4—26no—
971C2×D4—212no—
972C2×D4—212no—
973C2×D4—26no—
974C2×D4—26no—
975C2×D4—22no—
976C2×D4—26no—
977C2×D4—26no—
978C2×D4—26no—
979C2×D4—26no—
980C2×D4—26no—
981C2×D4—26no—
982C2×D4—26no—
983C2×D4—43no—
984C2×D4—41no—
985C2×D4—41no—
986C2×D4—43no—
987C2×D4—43no—
988C2×D4—43no—
989C2×D4—43no—
990C2×D4—43no—
991C2×D4—43no—
992C2×D4—43no—
993C2×D4—43no—
994C2×D4—43no—
995C2×D4—46no—
996C2×D4—46no—
997C2×D4—43no—
998C2×D4—43no—
999C2×D4—46no—
1000C2×D4—43no—
1001C2×D4—43no—
1002C2×D4—43no—
1003C2×D4—43no—
1004C2×D4—43no—
1005C2×D4—43no—
1006C2×D4—43no—
1007C2×D4—46no—
1008C2×D4—43no—
1009C2×D4—43no—
1010C2×D4—43no—
1011C2×D4—46no—
1012C2×D4—46no—
1013C2×D4—46no—
1014C2×D4C2×#41112yes—
1015C22×C4—26no—
1016C22×C4—26no—
1017C22×C4—212no—
1018C22×C4—26no—
1019C22×C4—26no—
1020C22×C4—26no—
1021C22×C4—26no—
1022C22×C4—26no—
1023C22×C4—26no—
1024C22×C4—26no—
1025C22×C4—26no—
1026C22×C4—26no—
1027C22×C4—26no—
1028C22×C4—26no—
1029C22×C4—26no—
1030C22×C4—26no—
1031C22×C4—26no—
1032C22×C4—46no—
1033C22×C4—46no—
1034C22×C4—43no—
1035C22×C4—43no—
1036C22×C4—43no—
1037C22×C4—43no—
1038C22×C4—43no—
1039C22×C4—43no—
1040C22×C4—43no—
1041C22×C4—43no—
1042C22×C4—43no—
1043C22×C4—43no—
1044C22×C4—46no—
1045C22×C4—46no—
1046C22×C4—46no—
1047C22×C4—46no—
1048C22×C4—46no—
1049C22×C4—46no—
1050C22×C4C2×#41112yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2513yes—
1053C22×C4C2513yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C22×C4C2513yes—
1057C22×C4C2513yes—
1058C22×C4C2511yescharacteristic
1059C22×C4C2513yes—
1060C22×C4C2513yes—
1061C22×C4C2513yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2513yes—
1064C22×C4C2513yes—
1065C22×C4C2513yes—
1066C22×C4C2511yescharacteristic
1067C22×C4C2511yescharacteristic
1068C22×C4C2511yescharacteristic
1069C22×C4C2511yescharacteristic
1070C22×C4C2513yes—
1071C22×C4C2513yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C22×C4C2513yes—
1077C4⋊C4—22no—
1078C4⋊C4—22no—
1079C4⋊C4—26no—
1080C4⋊C4—26no—
1081C4⋊C4—26no—
1082C4⋊C4—26no—
1083C4⋊C4—26no—
1084C4⋊C4—26no—
1085C4⋊C4—26no—
1086C4⋊C4—26no—
1087C4⋊C4—26no—
1088C4⋊C4—26no—
1089C4⋊C4—22no—
1090C4⋊C4—26no—
1091C4⋊C4—26no—
1092C4⋊C4—43no—
1093C4⋊C4—43no—
1094C4⋊C4—41no—
1095C4⋊C4—41no—
1096C4⋊C4—41no—
1097C4⋊C4—41no—
1098C4⋊C4—43no—
1099C4⋊C4—41no—
1100C4⋊C4—43no—
1101C4⋊C4—43no—
1102C4⋊C4—43no—
1103C4⋊C4—43no—
1104C4⋊C4—46no—
1105C4⋊C4—41no—
1106C4⋊C4—43no—
1107C4⋊C4—43no—
1108C4⋊C4—43no—
1109C4⋊C4—43no—
1110C4⋊C4—46no—
1111C4⋊C4—43no—
1112C4⋊C4—46no—
1113C4⋊C4—43no—
1114C4⋊C4—46no—
1115C4⋊C4—43no—
1116C4⋊C4—43no—
1117C22⋊C4—26no—
1118C22⋊C4—26no—
1119C22⋊C4—26no—
1120C22⋊C4—26no—
1121C22⋊C4—26no—
1122C22⋊C4—22no—
1123C22⋊C4—26no—
1124C22⋊C4—22no—
1125C22⋊C4—22no—
1126C22⋊C4—22no—
1127C22⋊C4—41no—
1128C22⋊C4—46no—
1129C22⋊C4—43no—
1130C22⋊C4—43no—
1131C22⋊C4—41no—
1132C22⋊C4—43no—
1133C22⋊C4—41no—
1134C22⋊C4—41no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—43no—
1138C22⋊C4—43no—
1139C22⋊C4—46no—
1140C22⋊C4—46no—
1141C22⋊C4—43no—
1142C22⋊C4—43no—
1143C22⋊C4—43no—
1144C22⋊C4—43no—
1145C22⋊C4—46no—
1146C22⋊C4—41no—
1147C22⋊C4—41no—
1148C22⋊C4—41no—
1149C22⋊C4—41no—
1150C22⋊C4—43no—
1151C22⋊C4—43no—
1152C22⋊C4—43no—
1153C22⋊C4—43no—
1154C22⋊C4—43no—
1155C22⋊C4—43no—
1156C22⋊C4—46no—
1157C22⋊C4—46no—
1158C22⋊C4—46no—
1159C22⋊C4—46no—
1160C22⋊C4—46no—
1161C22⋊C4—46no—
1162C22⋊C4—46no—
1163C22⋊C4—43no—
1164C22⋊C4—43no—
1165C22⋊C4—46no—
1166C22⋊C4—43no—
1167C22⋊C4—43no—
1168C22⋊C4—43no—
1169C22⋊C4—43no—
1170C22⋊C4—43no—
1171C22⋊C4—43no—
1172C22⋊C4—43no—
1173C22⋊C4—43no—
1174C22⋊C4—43no—
1175C42—26no—
1176C42—26no—
1177C42—26no—
1178C42—26no—
1179C42—26no—
1180C42—26no—
1181C42—26no—
1182C42—26no—
1183C42—26no—
1184C42—26no—
1185C42—22no—
1186C42—26no—
1187C42—41no—
1188C42—41no—
1189C42—43no—
1190C42—43no—
1191C42—43no—
1192C42—46no—
1193C42—43no—
1194C23—23no—
1195C23—23no—
1196C23—23no—
1197C23—23no—
1198C23—23no—
1199C23—23no—
1200C23—23no—
1201C23—23no—
1202C23—21no—
1203C23—21no—
1204C23—23no—
1205C23—23no—
1206C23—23no—
1207C23—23no—
1208C23—21no—
1209C23—21no—
1210C23—21no—
1211C23—21no—
1212C23—21no—
1213C23—21no—
1214C23—21no—
1215C23—23no—
1216C23—23no—
1217C23—21no—
1218C23—23no—
1219C23—23no—
1220C23—21no—
1221C23—23no—
1222C23—21no—
1223C23—23no—
1224C23—21no—
1225C23—23no—
1226C23—21no—
1227C23—23no—
1228C23C22×#4116yes—
1229C23C2611yescharacteristic
1230Q8—412no—
1231Q8—412no—
1232Q8—412no—
1233Q8—86no—
1234Q8#538116yes—
1235D4—224no—
1236D4—412no—
1237D4—44no—
1238D4—412no—
1239D4—412no—
1240D4—412no—
1241D4—412no—
1242D4—812no—
1243D4—812no—
1244D4—86no—
1245D4—86no—
1246D4—86no—
1247D4—86no—
1248D4—86no—
1249D4—86no—
1250D4—166no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—224no—
1258C2×C4—21no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—23no—
1277C2×C4—23no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—23no—
1286C2×C4—23no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—23no—
1290C2×C4—23no—
1291C2×C4—23no—
1292C2×C4—23no—
1293C2×C4—23no—
1294C2×C4—21no—
1295C2×C4—23no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—23no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—23no—
1303C2×C4—23no—
1304C2×C4—23no—
1305C2×C4—23no—
1306C2×C4—23no—
1307C2×C4—23no—
1308C2×C4—23no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—23no—
1312C2×C4—23no—
1313C2×C4—23no—
1314C2×C4—21no—
1315C2×C4—23no—
1316C2×C4—23no—
1317C2×C4—21no—
1318C2×C4—23no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—424no—
1325C2×C4—412no—
1326C2×C4—412no—
1327C2×C4—412no—
1328C2×C4—412no—
1329C2×C4—86no—
1330C2×C4—86no—
1331C2×C4—86no—
1332C2×C4—86no—
1333C2×C4—166no—
1334C2×C4—166no—
1335C2×C4C22×#4112yes—
1336C2×C4C22×#4116yes—
1337C2×C4C2×H(5,𝔽2)16yes—
1338C2×C4C2×H(5,𝔽2)16yes—
1339C2×C4#58512yes—
1340C2×C4#58512yes—
1341C22—26no—
1342C22—26no—
1343C22—26no—
1344C22—43no—
1345C22—43no—
1346C22—43no—
1347C22—43no—
1348C22—43no—
1349C22—43no—
1350C22—41no—
1351C22—41no—
1352C22—43no—
1353C22—43no—
1354C22—41no—
1355C22—41no—
1356C22—43no—
1357C22—43no—
1358C22—41no—
1359C22—41no—
1360C22—43no—
1361C22—41no—
1362C22—43no—
1363C22—43no—
1364C22—43no—
1365C22—41no—
1366C22—41no—
1367C22—41no—
1368C22—41no—
1369C22—43no—
1370C22—43no—
1371C22—41no—
1372C22—41no—
1373C22—41no—
1374C22—43no—
1375C22—43no—
1376C22C23×#4111yescharacteristic
1377C22C22×H(5,𝔽2)11yescharacteristic
1378C22C22×H(5,𝔽2)11yescharacteristic
1379C22C2×#58511yescharacteristic
1380C22C2×#58511yescharacteristic
1381C22H(7,𝔽2)11yescharacteristic
1382C222−1+611yescharacteristic
1383C4—22no—
1384C4—22no—
1385C4—22no—
1386C4—43no—
1387C4—43no—
1388C4—41no—
1389C4—43no—
1390C4—43no—
1391C4—43no—
1392C4—41no—
1393C4—41no—
1394C4—41no—
1395C4—43no—
1396C4—41no—
1397C4—41no—
1398C4—43no—
1399C4—41no—
1400C4—43no—
1401C4—43no—
1402C4—43no—
1403C4—41no—
1404C4—41no—
1405C4—41no—
1406C4—43no—
1407C4—43no—
1408C4C2×#538112yes—
1409C2—46no—
1410C2—83no—
1411C2—83no—
1412C2—81no—
1413C2—81no—
1414C2C22×#53811yescharacteristic
1415C2#6281011yescharacteristic
1416C2#6285711yescharacteristic
1417C2#6289911yescharacteristic
1418C2#6292211yescharacteristic
1419C2#6292211yescharacteristic
1420C2#6292311yescharacteristic
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. #42961C2semidirect
2. #42945C2semidirect
3. #42936C2semidirect
4. #42923C2semidirect
5. #42760C2semidirect
6. #42732C2semidirect
7. #42602C2semidirect
8. #42595C2semidirect
9. #40153C2semidirect
10. #40140C2semidirect
11. #39004C2semidirect
12. #38997C2semidirect
13. #37515C2semidirect
14. #37494C2semidirect
15. #36467C2semidirect
16. #36448C2semidirect
17. #36432C2semidirect
18. #36430C2semidirect
19. #36029C2semidirect
20. #35996C2semidirect
21. #35883C2semidirect
22. #35854C2semidirect
23. #35831C2semidirect
24. #35816C2semidirect
25. #35757C2semidirect
26. #35757C2semidirect
27. #35030C2semidirect
28. #34589C2semidirect
29. #34295C2semidirect
30. #34259C2semidirect
31. C4×#550C2semidirect

Maximal subgroups

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

subgroupindex
#429612
#429452
#429362
#429232
#427602
#427322
#426022
#425952
#401532
#401402
#390042
#389972
#375152
#374942
#364672
#364482
#364322
#364302
#360292
#359962
#358832
#358542
#358312
#358162
#357572
#350302
#345892
#342952
#342592
C4×#5502