Finite Group Databasebeta

← #7659772

Subgroups — #7659772

Order 512.

5357 conjugacy classes of subgroups.

The subgroup lattice has 1399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52277C213yesmaximal, complemented
2#42993C213yesmaximal, complemented
3#42919C213yesmaximal, complemented
4#42900C213yesmaximal, complemented
5#42855C213yesmaximal, complemented
6#42853C213yesmaximal, complemented
7#42828C213yesmaximal, complemented
8#40225C213yesmaximal, complemented
9#40218C213yesmaximal, complemented
10#40031C213yesmaximal, complemented
11#40006C213yesmaximal, complemented
12#39654C213yesmaximal, complemented
13#39244C213yesmaximal, complemented
14#37406C213yesmaximal, complemented
15#37402C213yesmaximal, complemented
16#37324C213yesmaximal, complemented
17#36577C211yesmaximal, characteristic, complemented
18Q8×#123C211yesmaximal, characteristic, complemented
19Q8×#121C211yesmaximal, characteristic, complemented
20#36467C211yesmaximal, characteristic, complemented
21#36448C211yesmaximal, characteristic, complemented
22#36434C211yesmaximal, characteristic, complemented
23#35910C211yesmaximal, characteristic, complemented
24#35898C211yesmaximal, characteristic, complemented
25#35801C211yesmaximal, characteristic, complemented
26#35700C211yesmaximal, characteristic, complemented
27#35687C211yesmaximal, characteristic, complemented
28#35687C211yesmaximal, characteristic, complemented
29#34311C211yesmaximal, characteristic, complemented
30#34291C211yesmaximal, characteristic, complemented
31#34257C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×D4×Q8C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#519C2211yescharacteristic
42C2×#519C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45#2863C2213yes—
46#2861C2213yes—
47#2857C2213yes—
48#2857C2213yes—
49#2855C2213yes—
50#2850C2213yes—
51#2833C2216yes—
52#2829C2216yes—
53#2808C2216yes—
54#2806C2216yes—
55#2805C2216yes—
56#2803C2213yes—
57#2800C2213yes—
58#2797C2213yes—
59#2788C2213yes—
60#2787C2216yes—
61#2786C2216yes—
62#2781C2216yes—
63#2780C2216yes—
64#2779C2216yes—
65#2779C2216yes—
66#2778C2216yes—
67#2778C2213yes—
68#2774C2213yes—
69#2770C2216yes—
70#2770C2216yes—
71#2768C2216yes—
72#2759C2213yes—
73#2756C2216yes—
74#2753C2213yes—
75#2751C2213yes—
76#2750C2216yes—
77#2749C2213yes—
78#2741C2216yes—
79#2741C2213yes—
80#2741C2216yes—
81#2727C2216yes—
82#2714C2213yes—
83#2710C2213yes—
84#2703C2211yescharacteristic
85#2702C2213yes—
86#2702C2216yes—
87#2676C2213yes—
88#2666C2216yes—
89#2653C2216yes—
90#2652C2216yes—
91#2651C2216yes—
92#2650C2216yes—
93#2648C2216yes—
94#2644C2213yes—
95#2642C2213yes—
96#2624C2213yes—
97#2621C2213yes—
98#2616C2213yes—
99#2616C2213yes—
100#2593C2216yes—
101#2592C2213yes—
102#2589C2216yes—
103#2587C2216yes—
104#2587C2216yes—
105#2582C2213yes—
106#2574C2216yes—
107#2568C2213yes—
108#2568C2213yes—
109#2562C2213yes—
110#2562C2213yes—
111#2559C2216yes—
112#2546C2213yes—
113#2546C2213yes—
114#2545C2213yes—
115#2538C2213yes—
116#2536C2213yes—
117#2536C2213yes—
118#2514C2213yes—
119#2514C2213yes—
120#2513C2213yes—
121#2512C2213yes—
122#2512C2213yes—
123#2511C2213yes—
124#2502C2213yes—
125#2500C2213yes—
126#2497C2213yes—
127#2496C2213yes—
128#2496C2213yes—
129#2495C2213yes—
130#2494C2213yes—
131#2494C2213yes—
132#2492C2213yes—
133#2492C2213yes—
134#2492C2213yes—
135#2491C2213yes—
136#2490C2213yes—
137#2489C2213yes—
138#2489C2213yes—
139#2489C2213yes—
140#2487C2213yes—
141#2485C2213yes—
142#2453C2213yes—
143#2453C2213yes—
144#2448C2213yes—
145#2448C2213yes—
146#2446C2213yes—
147#2446C2213yes—
148#2442C2213yes—
149#2442C2213yes—
150#2434C2213yes—
151#2434C2213yes—
152#2432C2213yes—
153#2432C2213yes—
154#2432C2213yes—
155#2432C2213yes—
156#2429C2213yes—
157#2429C2213yes—
158#2429C2213yes—
159#2429C2213yes—
160#2429C2213yes—
161#2426C2213yes—
162#2423C2213yes—
163#2423C2213yes—
164#2423C2213yes—
165#2421C2213yes—
166#2417C2213yes—
167#2417C2213yes—
168#2417C2213yes—
169#2416C2213yes—
170#2415C2213yes—
171#2415C2213yes—
172#2409C2213yes—
173#2409C2213yes—
174#2407C2213yes—
175#2407C2213yes—
176#2407C2213yes—
177#2407C2213yes—
178#2401C2213yes—
179#2398C2213yes—
180#2395C2213yes—
181#2392C2213yes—
182#2388C2213yes—
183#2388C2213yes—
184#2365C2213yes—
185#2365C2213yes—
186#2362C2213yes—
187#2362C2213yes—
188#2362C2213yes—
189#2360C2213yes—
190#2354C2213yes—
191#2352C2213yes—
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198#2341C2213yes—
199#2341C2213yes—
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2213yes—
210Q8×C22⋊C4C2213yes—
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216#2337C2216yes—
217#2334C2216yes—
218#2327C2213yes—
219#2323C2213yes—
220#2323C2213yes—
221#2323C2213yes—
222#2311C2213yes—
223#2311C2213yes—
224C4×C4⋊Q8C2213yes—
225C4×#126C2213yes—
226C4×#124C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×C22⋊Q8C2213yes—
229C4×#123C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232#2297C2213yes—
233#2297C2213yes—
234#2293C2213yes—
235#2290C2213yes—
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C2×2−1+4—28no—
239C2×2−1+4—44no—
240C2×2−1+4—44no—
241C22×#41C2311yescharacteristic
242C22×#41C2313yes—
243C22×#41C2313yes—
244C22×#41C2313yes—
245C23×Q8C2311yescharacteristic
246C23×Q8C2311yescharacteristic
247C23×Q8C2311yescharacteristic
248C23×Q8C2311yescharacteristic
249C23×Q8C2313yes—
250#557—44no—
251D4×Q8—28no—
252D4×Q8—28no—
253D4×Q8—44no—
254D4×Q8—44no—
255D4×Q8—44no—
256#548—44no—
257#548—44no—
258C2×C4⋊Q8C2313yes—
259C2×C4⋊Q8C2313yes—
260C2×C4⋊Q8C2313yes—
261C2×C4⋊Q8C2313yes—
262C2×C4⋊Q8C2313yes—
263C2×C4⋊Q8C2313yes—
264C2×#126C2313yes—
265C2×#126C2316yes—
266C2×#125C2313yes—
267C2×#125C2313yes—
268C2×#124C2313yes—
269C2×#124C2313yes—
270C2×#124C2313yes—
271C2×#123C2311yescharacteristic
272C2×C22⋊Q8C2313yes—
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×C22⋊Q8C2313yes—
282C2×C22⋊Q8C2313yes—
283C2×C22⋊Q8C2313yes—
284C2×C22⋊Q8C2313yes—
285C2×#121C2311yescharacteristic
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#121C2313yes—
289#519—44no—
290#519—44no—
291C2×C4×Q8—44no—
292C2×C4×Q8—44no—
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×Q8C2311yescharacteristic
303C2×C4×Q8C2313yes—
304C2×C4×Q8C2313yes—
305C2×C4×Q8C2313yes—
306C2×C4×Q8C2313yes—
307C2×C4×Q8C2313yes—
308C2×C4×Q8C2313yes—
309C2×C4×Q8C2313yes—
310C2×C4×Q8C2313yes—
311C2×C4×Q8C2313yes—
312C2×C4×D4C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×#117C2313yes—
320C2×#117C2313yes—
321C2×#117C2313yes—
322C2×#117C2313yes—
323C22×C4⋊C4C2313yes—
324C22×C4⋊C4C2313yes—
325C22×C42C2313yes—
326C22×C42C2313yes—
327#401C2313yes—
328#401C2316yes—
329#400C2316yes—
330#400C2316yes—
331#400C2313yes—
332#400C2316yes—
333#400C2316yes—
334#400C2313yes—
335#400C2316yes—
336#400C2316yes—
337#400C2316yes—
338#400C2313yes—
339#400C2316yes—
340#400C2316yes—
341#400C2311yescharacteristic
342#400C2313yes—
343#400C2313yes—
344#399C2316yes—
345#399C2313yes—
346#399C2316yes—
347#398C2316yes—
348#398C2316yes—
349#398C2316yes—
350#398C2316yes—
351#398C2316yes—
352#398C2316yes—
353#398C2316yes—
354#398C2316yes—
355#398C2316yes—
356#398C2313yes—
357#398C2313yes—
358#397C2316yes—
359#397C2316yes—
360#397C2313yes—
361#397C2316yes—
362#397C2316yes—
363#397C2313yes—
364#397C2316yes—
365#397C2316yes—
366#397C2313yes—
367#397C2311yescharacteristic
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#396C2316yes—
374#396C2316yes—
375#396C2316yes—
376#396C2313yes—
377#396C2316yes—
378#396C2316yes—
379#396C2313yes—
380#396C2313yes—
381#395C2316yes—
382#395C2313yes—
383#395C2316yes—
384#395C2313yes—
385#394C2313yes—
386#394C2316yes—
387#394C2313yes—
388#394C2316yes—
389#394C2316yes—
390#394C2316yes—
391#394C2313yes—
392#394C2313yes—
393#394C2313yes—
394#394C2316yes—
395#394C2316yes—
396#394C2316yes—
397#394C2313yes—
398#394C2313yes—
399#394C2313yes—
400#394C2313yes—
401#394C2313yes—
402#394C2313yes—
403#394C2313yes—
404#394C2311yescharacteristic
405#393C2313yes—
406#393C2316yes—
407#393C2313yes—
408#393C2313yes—
409#393C2313yes—
410#392C2313yes—
411#392C2311yescharacteristic
412#392C2311yescharacteristic
413#392C2313yes—
414#392C2313yes—
415#392C2313yes—
416#392C2311yescharacteristic
417#391C2313yes—
418#391C2313yes—
419#391C2316yes—
420#391C2313yes—
421#391C2313yes—
422#391C2313yes—
423#391C2313yes—
424#391C2316yes—
425#391C2316yes—
426#391C2313yes—
427#391C2313yes—
428#391C2313yes—
429#391C2313yes—
430#391C2313yes—
431#391C2313yes—
432#391C2313yes—
433#391C2313yes—
434#391C2313yes—
435#391C2313yes—
436#391C2313yes—
437#391C2313yes—
438#391C2313yes—
439#391C2313yes—
440#391C2313yes—
441#391C2313yes—
442#391C2313yes—
443#391C2313yes—
444#390C2316yes—
445#390C2313yes—
446#390C2313yes—
447#390C2313yes—
448#390C2313yes—
449#390C2313yes—
450#390C2313yes—
451#390C2313yes—
452#390C2313yes—
453#390C2313yes—
454#390C2313yes—
455#390C2313yes—
456#390C2313yes—
457#390C2311yescharacteristic
458#390C2313yes—
459#390C2313yes—
460#389C2313yes—
461#389C2316yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2316yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2316yes—
471#389C2316yes—
472#389C2316yes—
473#389C2316yes—
474#389C2316yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#388C2311yescharacteristic
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2316yes—
489#388C2316yes—
490#388C2316yes—
491#388C2316yes—
492#388C2316yes—
493#388C2313yes—
494#388C2313yes—
495#388C2313yes—
496#388C2316yes—
497#388C2316yes—
498#388C2313yes—
499#388C2316yes—
500#388C2316yes—
501#388C2316yes—
502#388C2316yes—
503#388C2316yes—
504#388C2313yes—
505#388C2316yes—
506#388C2313yes—
507#388C2316yes—
508#388C2313yes—
509#388C2316yes—
510#388C2316yes—
511#388C2313yes—
512#388C2316yes—
513#388C2313yes—
514#388C2313yes—
515#388C2313yes—
516#388C2313yes—
517#388C2313yes—
518#388C2313yes—
519#388C2311yescharacteristic
520#387C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2316yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2316yes—
528#387C2316yes—
529#387C2316yes—
530#387C2316yes—
531#387C2313yes—
532#387C2313yes—
533#387C2313yes—
534#387C2316yes—
535#387C2316yes—
536#387C2316yes—
537#387C2313yes—
538#387C2313yes—
539#387C2313yes—
540#386C2313yes—
541#386C2313yes—
542#386C2316yes—
543#386C2316yes—
544#386C2316yes—
545#386C2313yes—
546#386C2313yes—
547#386C2313yes—
548#386C2316yes—
549#386C2313yes—
550#386C2313yes—
551#386C2313yes—
552#386C2311yescharacteristic
553#386C2311yescharacteristic
554#386C2311yescharacteristic
555#385C2316yes—
556#385C2316yes—
557#385C2316yes—
558#385C2316yes—
559#385C2316yes—
560#385C2316yes—
561#385C2316yes—
562#385C2313yes—
563#385C2313yes—
564#385C2313yes—
565#385C2313yes—
566#385C2313yes—
567#384C2313yes—
568#384C2313yes—
569#384C2313yes—
570#383C2313yes—
571#383C2316yes—
572#382C2316yes—
573#382C2313yes—
574#382C2313yes—
575#382C2313yes—
576#382C2313yes—
577#381C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2316yes—
589#380C2316yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2313yes—
595#380C2313yes—
596#380C2316yes—
597#380C2316yes—
598#380C2311yescharacteristic
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2316yes—
605C4×C4⋊C4C2316yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2316yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2316yes—
618C4×C22⋊C4C2316yes—
619C4×C22⋊C4C2316yes—
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⋊C4C2313yes—
630C4×C22⋊C4C2313yes—
631#376C2313yes—
632C43C2313yes—
6332−1+4—464no—
634C2×#41—212no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—212no—
639C2×#41—212no—
640C2×#41—46no—
641C2×#41—46no—
642C2×#41—46no—
643C2×#41—46no—
644C2×#41—46no—
645C2×#41—46no—
646C22×Q8—24no—
647C22×Q8—24no—
648C22×Q8—24no—
649C22×Q8—24no—
650C22×Q8—212no—
651C22×Q8—24no—
652C22×Q8—24no—
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×Q8C2413yes—
667C22×Q8C2411yescharacteristic
668C22×D4C2413yes—
669C22×D4C2411yescharacteristic
670C22×D4C2411yescharacteristic
671C22×D4C2411yescharacteristic
672C22×D4C2411yescharacteristic
673C22×D4C2413yes—
674C22×D4C2411yescharacteristic
675C22×D4C2413yes—
676C22×D4C2413yes—
677C22×D4C2411yescharacteristic
678C22×D4C2413yes—
679C23×C4C2413yes—
680C23×C4C2413yes—
681C23×C4C2413yes—
682C23×C4C2413yes—
683C23×C4C2411yescharacteristic
684C23×C4C2413yes—
685C23×C4C2411yescharacteristic
686C23×C4C2416yes—
687C23×C4C2413yes—
688C23×C4C2413yes—
689C4⋊Q8—212no—
690C4⋊Q8—212no—
691C4⋊Q8—46no—
692C4⋊Q8—46no—
693C4⋊Q8—46no—
694C4⋊Q8—46no—
695#126—412no—
696#126—46no—
697#125—46no—
698#125—46no—
699#124—212no—
700#124—46no—
701#124—46no—
702#123—24no—
703C22⋊Q8—212no—
704C22⋊Q8—212no—
705C22⋊Q8—212no—
706C22⋊Q8—212no—
707C22⋊Q8—46no—
708C22⋊Q8—46no—
709C22⋊Q8—46no—
710C22⋊Q8—46no—
711C22⋊Q8—46no—
712C22⋊Q8—46no—
713C22⋊Q8—46no—
714C22⋊Q8—46no—
715C22⋊Q8—46no—
716#121—24no—
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×Q8—46no—
738C4×Q8—46no—
739C4×D4—212no—
740C4×D4—212no—
741C4×D4—46no—
742C4×D4—46no—
743C4×D4—46no—
744C4×D4—46no—
745C4×D4—46no—
746#117—46no—
747#117—46no—
748#117—46no—
749#117—46no—
750C2×C4⋊C4—46no—
751C2×C4⋊C4—46no—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
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⋊C4C2411yescharacteristic
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2416yes—
787C2×C4⋊C4C2416yes—
788C2×C4⋊C4C2416yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2416yes—
791C2×C4⋊C4C2416yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2416yes—
798C2×C4⋊C4C2416yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2411yescharacteristic
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2411yescharacteristic
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2411yescharacteristic
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2411yescharacteristic
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⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2416yes—
833C2×C22⋊C4C2416yes—
834C2×C22⋊C4C2411yescharacteristic
835C2×C22⋊C4C2411yescharacteristic
836C2×C22⋊C4C2411yescharacteristic
837C2×C22⋊C4C2411yescharacteristic
838C2×C22⋊C4C2411yescharacteristic
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2416yes—
841C2×C22⋊C4C2413yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2416yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2411yescharacteristic
851C2×C42—46no—
852C2×C42—46no—
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2413yes—
857C2×C42C2413yes—
858C2×C42C2413yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2413yes—
862C2×C42C2413yes—
863C2×C42C2413yes—
864C2×C42C2416yes—
865C2×C42C2416yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2416yes—
872C2×C42C2411yescharacteristic
873C2×C42C2413yes—
874#95C2411yescharacteristic
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2411yescharacteristic
879#95C2413yes—
880#95C2411yescharacteristic
881#95C2413yes—
882#95C2411yescharacteristic
883#95C2411yescharacteristic
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2416yes—
890#95C2413yes—
891#95C2413yes—
892#95C2416yes—
893#95C2413yes—
894#95C2413yes—
895#95C2416yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2416yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2411yescharacteristic
911#95C2411yescharacteristic
912#95C2411yescharacteristic
913#95C2416yes—
914#95C2416yes—
915#95C2416yes—
916#95C2416yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2416yes—
927#95C2416yes—
928#95C2416yes—
929#95C2416yes—
930#95C2416yes—
931#95C2416yes—
932C24C2511yescharacteristic
933C24C2511yescharacteristic
934C24C2513yes—
935C24C2511yescharacteristic
936C24C2511yescharacteristic
937#41—448no—
938#41—448no—
939#41—448no—
940#41—416no—
941C2×Q8—232no—
942C2×Q8—26no—
943C2×Q8—26no—
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—26no—
954C2×Q8—26no—
955C2×Q8—43no—
956C2×Q8—43no—
957C2×Q8—43no—
958C2×Q8—43no—
959C2×Q8—448no—
960C2×Q8—416no—
961C2×Q8—416no—
962C2×Q8—416no—
963C2×Q8C2×#41112yes—
964C2×Q8C2×#4114yes—
965C2×Q8H(5,𝔽2)14yes—
966C2×Q8H(5,𝔽2)14yes—
967C2×D4—22no—
968C2×D4—22no—
969C2×D4—22no—
970C2×D4—26no—
971C2×D4—22no—
972C2×D4—22no—
973C2×D4—22no—
974C2×D4—26no—
975C2×D4—26no—
976C2×D4—26no—
977C2×D4—26no—
978C2×D4—26no—
979C2×D4—22no—
980C2×D4—22no—
981C2×D4—41no—
982C2×D4—41no—
983C2×D4—41no—
984C2×D4—41no—
985C2×D4—41no—
986C2×D4—41no—
987C2×D4—41no—
988C2×D4—41no—
989C2×D4—43no—
990C2×D4—43no—
991C2×D4—41no—
992C2×D4—41no—
993C2×D4—43no—
994C2×D4—43no—
995C2×D4—43no—
996C2×D4—43no—
997C2×D4—43no—
998C2×D4—43no—
999C2×D4—43no—
1000C22×C4—26no—
1001C22×C4—26no—
1002C22×C4—22no—
1003C22×C4—26no—
1004C22×C4—26no—
1005C22×C4—212no—
1006C22×C4—26no—
1007C22×C4—26no—
1008C22×C4—26no—
1009C22×C4—26no—
1010C22×C4—26no—
1011C22×C4—26no—
1012C22×C4—26no—
1013C22×C4—26no—
1014C22×C4—26no—
1015C22×C4—26no—
1016C22×C4—22no—
1017C22×C4—22no—
1018C22×C4—41no—
1019C22×C4—41no—
1020C22×C4—41no—
1021C22×C4—46no—
1022C22×C4—46no—
1023C22×C4—43no—
1024C22×C4—43no—
1025C22×C4—43no—
1026C22×C4—43no—
1027C22×C4—43no—
1028C22×C4—43no—
1029C22×C4C2×#41112yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2511yescharacteristic
1032C22×C4C2513yes—
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2511yescharacteristic
1036C22×C4C2513yes—
1037C22×C4C2513yes—
1038C22×C4C2513yes—
1039C22×C4C2513yes—
1040C22×C4C2513yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2513yes—
1043C22×C4C2513yes—
1044C22×C4C2513yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2513yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2513yes—
1049C22×C4C2513yes—
1050C22×C4C2513yes—
1051C22×C4C2513yes—
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C22×C4C2511yescharacteristic
1055C22×C4C2513yes—
1056C4⋊C4—26no—
1057C4⋊C4—26no—
1058C4⋊C4—26no—
1059C4⋊C4—26no—
1060C4⋊C4—212no—
1061C4⋊C4—212no—
1062C4⋊C4—26no—
1063C4⋊C4—26no—
1064C4⋊C4—26no—
1065C4⋊C4—26no—
1066C4⋊C4—26no—
1067C4⋊C4—26no—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—22no—
1071C4⋊C4—22no—
1072C4⋊C4—22no—
1073C4⋊C4—26no—
1074C4⋊C4—26no—
1075C4⋊C4—26no—
1076C4⋊C4—46no—
1077C4⋊C4—46no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—46no—
1081C4⋊C4—43no—
1082C4⋊C4—43no—
1083C4⋊C4—46no—
1084C4⋊C4—43no—
1085C4⋊C4—43no—
1086C4⋊C4—43no—
1087C4⋊C4—43no—
1088C4⋊C4—43no—
1089C4⋊C4—43no—
1090C4⋊C4—43no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4—41no—
1094C4⋊C4—43no—
1095C4⋊C4—43no—
1096C4⋊C4—43no—
1097C4⋊C4—46no—
1098C4⋊C4—46no—
1099C4⋊C4—46no—
1100C4⋊C4—46no—
1101C4⋊C4—43no—
1102C4⋊C4—46no—
1103C22⋊C4—26no—
1104C22⋊C4—26no—
1105C22⋊C4—26no—
1106C22⋊C4—26no—
1107C22⋊C4—26no—
1108C22⋊C4—22no—
1109C22⋊C4—22no—
1110C22⋊C4—22no—
1111C22⋊C4—26no—
1112C22⋊C4—26no—
1113C22⋊C4—26no—
1114C22⋊C4—22no—
1115C22⋊C4—41no—
1116C22⋊C4—41no—
1117C22⋊C4—43no—
1118C22⋊C4—41no—
1119C22⋊C4—46no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—41no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—43no—
1127C22⋊C4—43no—
1128C22⋊C4—41no—
1129C22⋊C4—46no—
1130C22⋊C4—43no—
1131C22⋊C4—41no—
1132C22⋊C4—41no—
1133C22⋊C4—43no—
1134C22⋊C4—43no—
1135C22⋊C4—41no—
1136C22⋊C4—41no—
1137C22⋊C4—43no—
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—46no—
1147C22⋊C4—46no—
1148C22⋊C4—43no—
1149C22⋊C4—43no—
1150C22⋊C4—43no—
1151C22⋊C4—46no—
1152C22⋊C4—46no—
1153C22⋊C4—43no—
1154C22⋊C42−1+414yescomplemented
1155C42—26no—
1156C42—26no—
1157C42—26no—
1158C42—26no—
1159C42—26no—
1160C42—26no—
1161C42—26no—
1162C42—26no—
1163C42—26no—
1164C42—26no—
1165C42—26no—
1166C42—43no—
1167C42—43no—
1168C42—43no—
1169C42—43no—
1170C42—41no—
1171C42—43no—
1172C42—46no—
1173C42—46no—
1174C42—43no—
1175C42—46no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—23no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—23no—
1196C23—23no—
1197C23—23no—
1198C23—21no—
1199C23—21no—
1200C23—21no—
1201C23—23no—
1202C23—21no—
1203C23—23no—
1204C23—21no—
1205C23—23no—
1206C23—21no—
1207C23—21no—
1208C23—21no—
1209C23C22×#4112yes—
1210C23C2×2−1+412yes—
1211C23C2611yescharacteristic
1212Q8—224no—
1213Q8—412no—
1214Q8—412no—
1215Q8—412no—
1216Q8—412no—
1217Q8—86no—
1218Q8#538116yes—
1219D4—44no—
1220D4—44no—
1221D4—412no—
1222D4—44no—
1223D4—44no—
1224D4—44no—
1225D4—412no—
1226D4—44no—
1227D4—412no—
1228D4—86no—
1229D4—86no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—224no—
1239C2×C4—21no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—21no—
1245C2×C4—23no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—23no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—23no—
1277C2×C4—23no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—23no—
1282C2×C4—23no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—23no—
1286C2×C4—23no—
1287C2×C4—21no—
1288C2×C4—23no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—23no—
1294C2×C4—23no—
1295C2×C4—23no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—23no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—23no—
1302C2×C4—44no—
1303C2×C4—424no—
1304C2×C4—44no—
1305C2×C4—412no—
1306C2×C4—412no—
1307C2×C4—412no—
1308C2×C4—412no—
1309C2×C4—86no—
1310C2×C4—86no—
1311C2×C4C22×#4116yes—
1312C2×C4C22×#4116yes—
1313C2×C4C2×H(5,𝔽2)16yes—
1314C2×C4C2×H(5,𝔽2)16yes—
1315C2×C4C2×2−1+412yes—
1316C2×C4C2×2−1+412yes—
1317C2×C4#58512yes—
1318C22—22no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—22no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—43no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—43no—
1338C22—41no—
1339C22—43no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—43no—
1344C22—41no—
1345C22—41no—
1346C22—43no—
1347C22—41no—
1348C22—43no—
1349C22—41no—
1350C22—43no—
1351C22—41no—
1352C22—41no—
1353C22C23×#4111yescharacteristic
1354C22C22×H(5,𝔽2)11yescharacteristic
1355C22C22×H(5,𝔽2)11yescharacteristic
1356C22C22×2−1+411yescharacteristic
1357C22C2×#58511yescharacteristic
1358C222−1+611yescharacteristic
1359C222−1+611yescharacteristic
1360C4—22no—
1361C4—22no—
1362C4—22no—
1363C4—26no—
1364C4—41no—
1365C4—43no—
1366C4—43no—
1367C4—43no—
1368C4—43no—
1369C4—41no—
1370C4—43no—
1371C4—43no—
1372C4—41no—
1373C4—43no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—43no—
1379C4—43no—
1380C4—43no—
1381C4—41no—
1382C4—43no—
1383C4—43no—
1384C4—43no—
1385C4C2×#538112yes—
1386C2—42no—
1387C2—42no—
1388C2—81no—
1389C2—83no—
1390C2—81no—
1391C2C22×#53811yescharacteristic
1392C2#6291311yescharacteristic
1393C2#6292211yescharacteristic
1394C2#6299811yescharacteristic
1395C2#6300711yescharacteristic
1396C2#6301511yescharacteristic
1397C2#6304411yescharacteristic
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. #52277C2semidirect
2. #42993C2semidirect
3. #42919C2semidirect
4. #42900C2semidirect
5. #42855C2semidirect
6. #42853C2semidirect
7. #42828C2semidirect
8. #40225C2semidirect
9. #40218C2semidirect
10. #40031C2semidirect
11. #40006C2semidirect
12. #39654C2semidirect
13. #39244C2semidirect
14. #37406C2semidirect
15. #37402C2semidirect
16. #37324C2semidirect
17. #36577C2semidirect
18. Q8×#123C2semidirect
19. Q8×#121C2semidirect
20. #36467C2semidirect
21. #36448C2semidirect
22. #36434C2semidirect
23. #35910C2semidirect
24. #35898C2semidirect
25. #35801C2semidirect
26. #35700C2semidirect
27. #35687C2semidirect
28. #35687C2semidirect
29. #34311C2semidirect
30. #34291C2semidirect
31. #34257C2semidirect
1154. C22⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#522772
#429932
#429192
#429002
#428552
#428532
#428282
#402252
#402182
#400312
#400062
#396542
#392442
#374062
#374022
#373242
#365772
Q8×#1232
Q8×#1212
#364672
#364482
#364342
#359102
#358982
#358012
#357002
#356872
#343112
#342912
#342572