Finite Group Databasebeta

← #7697195

Subgroups — #7697195

Order 512.

4867 conjugacy classes of subgroups.

The subgroup lattice has 1246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59926C211yesmaximal, characteristic, complemented
2#59923C212yesmaximal, complemented
3#59744C212yesmaximal, complemented
4#59726C214yesmaximal, complemented
5#52307C211yesmaximal, characteristic, complemented
6#52280C212yesmaximal, complemented
7#44325C212yesmaximal, complemented
8#44203C214yesmaximal, complemented
9#44068C214yesmaximal, complemented
10#44031C214yesmaximal, complemented
11#43903C214yesmaximal, complemented
12#40300C214yesmaximal, complemented
13#40098C214yesmaximal, complemented
14#39455C212yesmaximal, complemented
15#38811C212yesmaximal, complemented
16#38486C212yesmaximal, complemented
17#38155C214yesmaximal, complemented
18#36566C212yesmaximal, complemented
19#36539C211yesmaximal, characteristic, complemented
20#35913C212yesmaximal, complemented
21#35696C214yesmaximal, complemented
22#34327C212yesmaximal, complemented
23#34285C214yesmaximal, complemented
24C2×#548C2212yes—
25C2×#542C2214yes—
26#2864C2214yes—
27#2864C2211yescharacteristic
28#2862C2212yes—
29#2854C2212yes—
30#2811C2211yescharacteristic
31#2808C2212yes—
32#2806C2212yes—
33#2806C2212yes—
34#2804C2211yescharacteristic
35#2803C2214yes—
36#2801C2214yes—
37#2800C2214yes—
38#2789C2212yes—
39#2785C2214yes—
40#2785C2212yes—
41#2782C2212yes—
42#2781C2214yes—
43#2781C2214yes—
44#2775C2214yes—
45#2775C2214yes—
46#2767C2214yes—
47#2759C2214yes—
48#2759C2214yes—
49#2759C2214yes—
50#2756C2214yes—
51#2734C2212yes—
52#2733C2212yes—
53#2733C2214yes—
54#2733C2211yescharacteristic
55#2733C2212yes—
56#2731C2214yes—
57#2730C2214yes—
58#2727C2212yes—
59#2723C2214yes—
60#2715C2214yes—
61#2715C2214yes—
62#2714C2214yes—
63#2712C2212yes—
64#2712C2214yes—
65#2710C2214yes—
66#2683C2211yescharacteristic
67#2676C2214yes—
68#2676C2214yes—
69#2675C2212yes—
70#2665C2212yes—
71#2665C2214yes—
72#2653C2214yes—
73#2650C2214yes—
74#2630C2214yes—
75#2612C2212yes—
76#2604C2214yes—
77#2602C2214yes—
78#2602C2214yes—
79#2600C2214yes—
80#2594C2214yes—
81#2593C2212yes—
82#2589C2214yes—
83#2589C2214yes—
84#2587C2214yes—
85#2586C2214yes—
86#2586C2214yes—
87#2586C2214yes—
88#2583C2214yes—
89#2581C2212yes—
90#2580C2212yes—
91#2579C2212yes—
92#2576C2214yes—
93#2576C2214yes—
94#2575C2214yes—
95#2574C2214yes—
96#2574C2214yes—
97#2574C2214yes—
98#2560C2214yes—
99#2559C2214yes—
100#2559C2214yes—
101#2557C2214yes—
102#2555C2214yes—
103#2555C2214yes—
104#2555C2212yes—
105#2554C2214yes—
106#2549C2214yes—
107#2549C2214yes—
108#2545C2214yes—
109#2545C2214yes—
110#2543C2214yes—
111#2536C2211yescharacteristic
112#2535C2211yescharacteristic
113#2529C2214yes—
114#2527C2214yes—
115#2526C2214yes—
116#2525C2214yes—
117#2523C2212yes—
118#2521C2214yes—
119#2518C2214yes—
120#2514C2214yes—
121#2510C2214yes—
122#2494C2212yes—
123#2491C2214yes—
124#2477C2214yes—
125#2477C2214yes—
126#2471C2214yes—
127#2470C2214yes—
128#2469C2214yes—
129#2469C2214yes—
130#2468C2214yes—
131#2466C2214yes—
132#2465C2214yes—
133#2465C2214yes—
134#2465C2214yes—
135#2463C2212yes—
136#2463C2214yes—
137#2461C2214yes—
138#2461C2214yes—
139#2459C2214yes—
140#2456C2214yes—
141#2452C2214yes—
142#2451C2214yes—
143#2451C2214yes—
144#2447C2214yes—
145#2443C2214yes—
146#2436C2214yes—
147#2434C2214yes—
148#2430C2214yes—
149#2427C2214yes—
150#2426C2212yes—
151#2421C2214yes—
152#2407C2214yes—
153#2406C2212yes—
154#2395C2214yes—
155#2392C2214yes—
156#2388C2212yes—
157#2388C2214yes—
158#2388C2214yes—
159#2374C2214yes—
160#2374C2214yes—
161#2372C2212yes—
162#2372C2214yes—
163#2369C2214yes—
164#2368C2214yes—
165#2368C2214yes—
166#2368C2214yes—
167#2368C2214yes—
168#2367C2212yes—
169#2367C2214yes—
170#2367C2214yes—
171#2365C2214yes—
172#2364C2214yes—
173#2363C2214yes—
174#2362C2214yes—
175#2362C2212yes—
176#2362C2214yes—
177#2361C2212yes—
178#2361C2214yes—
179#2360C2214yes—
180#2359C2214yes—
181#2359C2214yes—
182#2357C2211yescharacteristic
183#2356C2212yes—
184#2353C2214yes—
185#2352C2212yes—
186#2351C2211yescharacteristic
187#2349C2212yes—
188Q8×C22⋊C4C2212yes—
189#2339C2212yes—
190#2339C2212yes—
191#2337C2214yes—
192#2337C2214yes—
193#2337C2214yes—
194#2334C2214yes—
195#2334C2214yes—
196#2332C2214yes—
197#2325C2214yes—
198#2320C2214yes—
199C4×#126C2214yes—
200C4×#126C2214yes—
201C4×#124C2211yescharacteristic
202C4×#124C2212yes—
203C4×#124C2214yes—
204C4×#124C2214yes—
205C4×#124C2212yes—
206C4×#124C2214yes—
207C4×C22⋊Q8C2212yes—
208C4×C22⋊Q8C2212yes—
209C4×#121C2212yes—
210#2298C2214yes—
211#2297C2212yes—
212#2295C2212yes—
213C2×#391C2212yes—
214#2293C2214yes—
215#2275C2214yes—
216#2274C2212yes—
217C42×Q8C2212yes—
218C42×D4C2211yescharacteristic
219C22×#41C2312yes—
220C22×#41C2312yes—
221C23×Q8C2312yes—
222#548—216no—
223#542—232no—
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2314yes—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#124C2314yes—
230C2×#124C2314yes—
231C2×#124C2314yes—
232C2×#124C2314yes—
233C2×#124C2312yes—
234C2×#124C2311yescharacteristic
235C2×#124C2312yes—
236C2×#124C2314yes—
237C2×#124C2314yes—
238C2×#123C2314yes—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2312yes—
248C2×#121C2314yes—
249C2×#121C2314yes—
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2314yes—
253C2×#121C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2314yes—
261C2×C4×Q8C2312yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2312yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2312yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×#117C2314yes—
276C2×#117C2312yes—
277C2×#117C2314yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2312yes—
280C22×C42C2312yes—
281#401C2314yes—
282#401C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2312yes—
286#400C2312yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#399C2314yes—
291#399C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2312yes—
299#397C2314yes—
300#397C2314yes—
301#397C2314yes—
302#397C2314yes—
303#397C2312yes—
304#397C2314yes—
305#397C2314yes—
306#397C2314yes—
307#397C2314yes—
308#397C2314yes—
309#397C2314yes—
310#396C2314yes—
311#396C2314yes—
312#396C2314yes—
313#396C2314yes—
314#396C2314yes—
315#396C2314yes—
316#396C2314yes—
317#396C2314yes—
318#396C2314yes—
319#395C2314yes—
320#395C2314yes—
321#395C2314yes—
322#395C2312yes—
323#395C2312yes—
324#395C2314yes—
325#395C2314yes—
326#395C2312yes—
327#395C2314yes—
328#395C2314yes—
329#395C2314yes—
330#394C2314yes—
331#394C2314yes—
332#394C2314yes—
333#394C2314yes—
334#394C2314yes—
335#394C2312yes—
336#394C2314yes—
337#394C2314yes—
338#394C2312yes—
339#394C2314yes—
340#394C2314yes—
341#394C2314yes—
342#394C2314yes—
343#394C2314yes—
344#394C2314yes—
345#394C2314yes—
346#394C2314yes—
347#393C2314yes—
348#393C2314yes—
349#393C2314yes—
350#393C2314yes—
351#393C2314yes—
352#393C2312yes—
353#393C2314yes—
354#393C2314yes—
355#393C2314yes—
356#392C2314yes—
357#392C2312yes—
358#392C2314yes—
359#392C2314yes—
360#392C2314yes—
361#392C2312yes—
362#392C2314yes—
363#392C2314yes—
364#392C2314yes—
365#391C2314yes—
366#391C2312yes—
367#391C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2312yes—
372#391C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2312yes—
382#391C2314yes—
383#391C2314yes—
384#391C2312yes—
385#391C2312yes—
386#391C2314yes—
387#391C2312yes—
388#391C2311yescharacteristic
389#391C2312yes—
390#390C2314yes—
391#390C2314yes—
392#390C2312yes—
393#390C2311yescharacteristic
394#390C2312yes—
395#390C2314yes—
396#390C2314yes—
397#390C2314yes—
398#390C2312yes—
399#390C2314yes—
400#390C2314yes—
401#390C2312yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2312yes—
414#389C2314yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2314yes—
419#389C2312yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2312yes—
506#386C2312yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2312yes—
526#385C2312yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#383C2314yes—
538#383C2314yes—
539#383C2314yes—
540#382C2311yescharacteristic
541#382C2312yes—
542#382C2312yes—
543#382C2311yescharacteristic
544#382C2314yes—
545#382C2314yes—
546#382C2314yes—
547#382C2312yes—
548#382C2312yes—
549#382C2311yescharacteristic
550#381C2314yes—
551#381C2312yes—
552#381C2314yes—
553#380C2312yes—
554#380C2314yes—
555#380C2314yes—
556#380C2312yes—
557#380C2312yes—
558#380C2312yes—
559#380C2312yes—
560C4×C4⋊C4C2312yes—
561C4×C4⋊C4C2314yes—
562C4×C4⋊C4C2314yes—
563C4×C4⋊C4C2314yes—
564C4×C4⋊C4C2314yes—
565C4×C4⋊C4C2314yes—
566C4×C4⋊C4C2312yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2314yes—
569C4×C4⋊C4C2312yes—
570C4×C4⋊C4C2314yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2314yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2311yescharacteristic
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C22⋊C4C2314yes—
582C4×C22⋊C4C2314yes—
583C4×C22⋊C4C2314yes—
584C4×C22⋊C4C2314yes—
585C4×C22⋊C4C2314yes—
586C4×C22⋊C4C2314yes—
587C4×C22⋊C4C2314yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2312yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608#376C2314yes—
609#376C2314yes—
610C2×#95C2314yes—
611C2×#95C2314yes—
612C2×#95C2314yes—
613C43C2312yes—
614C43C2314yes—
615C43C2311yescharacteristic
616C2×#41—28no—
617C2×#41—44no—
618C2×#41—82no—
619C2×#41—82no—
620C2×#41—84no—
621C22×Q8—28no—
622C22×Q8—82no—
623C22×Q8—82no—
624C22×Q8C2412yes—
625C22×Q8C2414yes—
626C22×Q8C2412yes—
627C22×Q8C2414yes—
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2411yescharacteristic
631C22×D4C2411yescharacteristic
632C22×D4C2414yes—
633C22×D4C2412yes—
634C22×D4C2412yes—
635C22×D4C2414yes—
636C22×D4C2414yes—
637C22×D4C2411yescharacteristic
638C22×D4C2414yes—
639C22×D4C2412yes—
640C22×D4C2414yes—
641C23×C4C2412yes—
642C23×C4C2412yes—
643C23×C4C2412yes—
644C23×C4C2414yes—
645C23×C4C2414yes—
646C23×C4C2414yes—
647C23×C4C2414yes—
648C23×C4C2412yes—
649C23×C4C2414yes—
650C23×C4C2412yes—
651C23×C4C2412yes—
652C4⋊Q8—216no—
653C4⋊Q8—84no—
654#126—216no—
655#126—216no—
656#126—84no—
657#124—216no—
658#124—28no—
659#124—28no—
660#124—24no—
661#124—216no—
662#124—216no—
663#124—216no—
664#124—84no—
665#124—84no—
666#123—216no—
667#123—216no—
668#123—84no—
669C22⋊Q8—28no—
670C22⋊Q8—216no—
671C22⋊Q8—216no—
672C22⋊Q8—216no—
673C22⋊Q8—84no—
674C22⋊Q8—84no—
675C22⋊Q8#41116yescomplemented
676#121—28no—
677#121—216no—
678#121—216no—
679#121—84no—
680#121—82no—
681#121—84no—
682C4×Q8—216no—
683C4×Q8—28no—
684C4×Q8—42no—
685C4×Q8—44no—
686C4×Q8—82no—
687C4×Q8—82no—
688C4×Q8—82no—
689C4×Q8—84no—
690C4×D4—216no—
691C4×D4—28no—
692C4×D4—216no—
693C4×D4—42no—
694C4×D4—42no—
695C4×D4—44no—
696C4×D4—48no—
697C4×D4—82no—
698C4×D4—84no—
699C4×D4—84no—
700C4×D4—84no—
701C4×D4—84no—
702C4×D4—82no—
703#117—216no—
704#117—82no—
705#117—84no—
706C2×C4⋊C4—44no—
707C2×C4⋊C4—82no—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2412yes—
753C2×C22⋊C4C2412yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C42—82no—
793C2×C42C2414yes—
794C2×C42C2414yes—
795C2×C42C2411yescharacteristic
796C2×C42C2412yes—
797C2×C42C2412yes—
798C2×C42C2414yes—
799C2×C42C2414yes—
800C2×C42C2414yes—
801C2×C42C2412yes—
802C2×C42C2411yescharacteristic
803C2×C42C2414yes—
804C2×C42C2414yes—
805C2×C42C2412yes—
806C2×C42C2414yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2411yescharacteristic
819#95C2411yescharacteristic
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2412yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2411yescharacteristic
838#95C2412yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2412yes—
844#95C2412yes—
845#95C2414yes—
846#95C2414yes—
847#95C2412yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2412yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2412yes—
872#95C2412yes—
873#95C2414yes—
874#95C2412yes—
875#95C2412yes—
876C24C2512yes—
877C24C2514yes—
878C24C2512yes—
879#41—816no—
880#41—816no—
881C2×Q8—28no—
882C2×Q8—24no—
883C2×Q8—28no—
884C2×Q8—28no—
885C2×Q8—41no—
886C2×Q8—42no—
887C2×Q8—41no—
888C2×Q8—42no—
889C2×Q8—42no—
890C2×Q8—42no—
891C2×Q8—42no—
892C2×Q8—44no—
893C2×Q8—44no—
894C2×Q8—44no—
895C2×Q8—44no—
896C2×Q8—44no—
897C2×Q8—42no—
898C2×Q8—816no—
899C2×Q8C2×#4118yes—
900C2×Q82−1+414yes—
901C2×D4—24no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—24no—
907C2×D4—28no—
908C2×D4—24no—
909C2×D4—22no—
910C2×D4—42no—
911C2×D4—44no—
912C2×D4—41no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—44no—
917C2×D4—42no—
918C2×D4—41no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—41no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C22×C4—28no—
930C22×C4—24no—
931C22×C4—28no—
932C22×C4—28no—
933C22×C4—28no—
934C22×C4—24no—
935C22×C4—24no—
936C22×C4—28no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—44no—
944C22×C4—42no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—44no—
953C22×C4—42no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4C2×#4118yes—
959C22×C4C2514yes—
960C22×C4C2512yes—
961C22×C4C2514yes—
962C22×C4C2512yes—
963C22×C4C2514yes—
964C22×C4C2514yes—
965C22×C4C2512yes—
966C22×C4C2511yescharacteristic
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2514yes—
970C22×C4C2514yes—
971C22×C4C2514yes—
972C22×C4C2512yes—
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2512yes—
976C22×C4C2511yescharacteristic
977C22×C4C2512yes—
978C22×C4C2511yescharacteristic
979C4⋊C4—28no—
980C4⋊C4—24no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—28no—
987C4⋊C4—28no—
988C4⋊C4—24no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—44no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—44no—
995C4⋊C4—42no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—42no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—42no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—42no—
1007C4⋊C4—41no—
1008C4⋊C4—42no—
1009C4⋊C4—44no—
1010C4⋊C4—42no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4C2×#41116yes—
1019C4⋊C4C2×#4118yes—
1020C22⋊C4—24no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—28no—
1024C22⋊C4—28no—
1025C22⋊C4—24no—
1026C22⋊C4—28no—
1027C22⋊C4—28no—
1028C22⋊C4—28no—
1029C22⋊C4—28no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—28no—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—24no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—42no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—42no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—42no—
1062C22⋊C4C2×#41116yes—
1063C42—28no—
1064C42—28no—
1065C42—24no—
1066C42—28no—
1067C42—28no—
1068C42—28no—
1069C42—24no—
1070C42—22no—
1071C42—22no—
1072C42—24no—
1073C42—41no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42—44no—
1078C42—44no—
1079C42—44no—
1080C42—44no—
1081C42—44no—
1082C42—42no—
1083C42—44no—
1084C42—44no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C42—42no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—24no—
1096C23—24no—
1097C23—24no—
1098C23—24no—
1099C23—22no—
1100C23—24no—
1101C23—22no—
1102C23—24no—
1103C23—22no—
1104C23—24no—
1105C23—24no—
1106C23—24no—
1107C23C22×#4114yes—
1108C23C2611yescharacteristic
1109Q8—48no—
1110Q8—44no—
1111Q8—48no—
1112Q8—48no—
1113Q8—88no—
1114Q8—88no—
1115Q8—84no—
1116D4—416no—
1117D4—48no—
1118D4—48no—
1119D4—44no—
1120D4—48no—
1121D4—88no—
1122D4—82no—
1123D4—88no—
1124D4—88no—
1125D4—88no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—21no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—21no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—48no—
1176C2×C4—48no—
1177C2×C4—48no—
1178C2×C4—88no—
1179C2×C4—84no—
1180C2×C4—88no—
1181C2×C4—88no—
1182C2×C4—84no—
1183C2×C4—88no—
1184C2×C4—164no—
1185C2×C4—162no—
1186C2×C4C22×#4118yes—
1187C2×C4C22×#4118yes—
1188C2×C4C22×#4114yes—
1189C2×C4C22×#4114yes—
1190C2×C4C2×2−1+414yes—
1191C2×C4C2×2−1+412yes—
1192C2×C4#58512yes—
1193C22—24no—
1194C22—24no—
1195C22—24no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—44no—
1201C22—44no—
1202C22—44no—
1203C22—42no—
1204C22—44no—
1205C22—44no—
1206C22—44no—
1207C22—44no—
1208C22—44no—
1209C22—42no—
1210C22—42no—
1211C22—44no—
1212C22C23×#4112yes—
1213C22C22×2−1+411yescharacteristic
1214C22C2×#58511yescharacteristic
1215C22H(7,𝔽2)12yes—
1216C22H(7,𝔽2)11yescharacteristic
1217C4—22no—
1218C4—24no—
1219C4—24no—
1220C4—28no—
1221C4—22no—
1222C4—24no—
1223C4—28no—
1224C4—42no—
1225C4—44no—
1226C4—44no—
1227C4—44no—
1228C4—42no—
1229C4—44no—
1230C4—42no—
1231C4—44no—
1232C4—44no—
1233C4—44no—
1234C4—42no—
1235C4—41no—
1236C4—42no—
1237C2—44no—
1238C2—82no—
1239C2—84no—
1240C2#41211yescharacteristic
1241C2#6284612yes—
1242C2#6290211yescharacteristic
1243C2#6299912yes—
1244C2#6304611yescharacteristic
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. #59926C2semidirect
2. #59923C2semidirect
3. #59744C2semidirect
4. #59726C2semidirect
5. #52307C2semidirect
6. #52280C2semidirect
7. #44325C2semidirect
8. #44203C2semidirect
9. #44068C2semidirect
10. #44031C2semidirect
11. #43903C2semidirect
12. #40300C2semidirect
13. #40098C2semidirect
14. #39455C2semidirect
15. #38811C2semidirect
16. #38486C2semidirect
17. #38155C2semidirect
18. #36566C2semidirect
19. #36539C2semidirect
20. #35913C2semidirect
21. #35696C2semidirect
22. #34327C2semidirect
23. #34285C2semidirect
675. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#599262
#599232
#597442
#597262
#523072
#522802
#443252
#442032
#440682
#440312
#439032
#403002
#400982
#394552
#388112
#384862
#381552
#365662
#365392
#359132
#356962
#343272
#342852