Finite Group Databasebeta

← #8119666

Subgroups — #8119666

Order 512.

4228 conjugacy classes of subgroups.

The subgroup lattice has 1149 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#55793C214yesmaximal, complemented
2#55078C214yesmaximal, complemented
3#54129C214yesmaximal, complemented
4#53641C214yesmaximal, complemented
5#52431C214yesmaximal, complemented
6#47253C214yesmaximal, complemented
7#46926C214yesmaximal, complemented
8#46886C214yesmaximal, complemented
9#46637C214yesmaximal, complemented
10#43619C214yesmaximal, complemented
11#39806C212yesmaximal, complemented
12#39799C212yesmaximal, complemented
13#39636C212yesmaximal, complemented
14#39627C212yesmaximal, complemented
15#38535C214yesmaximal, complemented
16#37908C214yesmaximal, complemented
17#36728C211yesmaximal, characteristic, complemented
18#36727C211yesmaximal, characteristic
19#35080C212yesmaximal, complemented
20#34997C212yesmaximal, complemented
21C2×#2569C211yesmaximal, characteristic, complemented
22#2857C2212yes—
23#2850C2212yes—
24#2849C2214yes—
25#2848C2212yes—
26#2847C2212yes—
27#2836C2214yescomplemented
28#2836C2214yescomplemented
29#2834C2214yescomplemented
30#2834C2214yescomplemented
31#2831C2214yescomplemented
32#2831C2214yescomplemented
33#2830C2214yescomplemented
34#2822C2214yescomplemented
35#2802C2214yescomplemented
36#2799C2214yescomplemented
37#2797C2214yescomplemented
38#2796C2214yes—
39#2791C2214yescomplemented
40#2790C2214yescomplemented
41#2789C2214yescomplemented
42#2789C2214yescomplemented
43#2787C2214yes—
44#2787C2214yescomplemented
45#2786C2214yescomplemented
46#2781C2214yes—
47#2781C2214yescomplemented
48#2780C2214yescomplemented
49#2777C2214yescomplemented
50#2775C2214yescomplemented
51#2773C2214yescomplemented
52#2770C2214yescomplemented
53#2770C2214yescomplemented
54#2767C2214yescomplemented
55#2766C2214yescomplemented
56#2766C2214yescomplemented
57#2766C2214yescomplemented
58#2765C2214yes—
59#2763C2214yes—
60#2762C2214yescomplemented
61#2761C2214yes—
62#2757C2214yes—
63#2755C2214yescomplemented
64#2754C2214yescomplemented
65#2752C2214yescomplemented
66#2750C2214yescomplemented
67#2748C2214yes—
68#2747C2214yes—
69#2746C2214yes—
70#2745C2214yescomplemented
71#2744C2214yes—
72#2741C2214yes—
73#2729C2214yescomplemented
74#2724C2214yescomplemented
75#2722C2214yes—
76#2717C2214yes—
77#2713C2214yescomplemented
78#2710C2214yes—
79#2708C2214yes—
80#2707C2214yescomplemented
81#2707C2214yescomplemented
82#2704C2214yes—
83#2703C2214yes—
84#2695C2214yes—
85#2694C2214yes—
86#2693C2214yes—
87#2691C2214yes—
88#2690C2214yes—
89#2687C2214yescomplemented
90#2671C2214yes—
91#2667C2214yes—
92#2659C2211yescharacteristic
93#2656C2211yescharacteristic
94#2653C2214yes—
95#2653C2214yes—
96#2649C2214yes—
97#2646C2211yescharacteristic
98#2646C2211yescharacteristic
99#2646C2212yes—
100#2643C2214yes—
101#2639C2212yes—
102#2638C2214yes—
103#2630C2214yes—
104#2602C2214yescomplemented
105#2599C2214yescomplemented
106#2596C2214yescomplemented
107#2594C2214yescomplemented
108#2585C2214yescomplemented
109#2585C2214yescomplemented
110#2583C2214yes—
111#2579C2214yes—
112#2579C2214yes—
113#2577C2214yes—
114#2575C2214yescomplemented
115#2575C2214yescomplemented
116#2569C2214yes—
117#2569C2214yes—
118#2569C2214yes—
119#2569C2214yes—
120#2557C2214yescomplemented
121#2553C2214yes—
122#2524C2214yescomplemented
123#2524C2214yescomplemented
124#2522C2214yescomplemented
125#2520C2214yescomplemented
126#2517C2214yescomplemented
127#2515C2214yes—
128#2510C2214yes—
129#2510C2214yes—
130#2510C2214yes—
131#2510C2214yes—
132#2509C2214yescomplemented
133#2505C2214yes—
134#2505C2214yes—
135#2505C2214yescomplemented
136#2504C2214yes—
137#2498C2214yescomplemented
138#2495C2212yes—
139#2495C2214yescomplemented
140#2494C2212yes—
141#2493C2214yes—
142#2493C2214yescomplemented
143#2492C2212yes—
144#2491C2212yes—
145#2489C2214yescomplemented
146#2488C2214yes—
147#2480C2214yes—
148#2475C2214yescomplemented
149#2474C2214yescomplemented
150#2473C2214yes—
151#2473C2214yes—
152#2472C2214yes—
153#2470C2214yes—
154#2461C2214yes—
155#2460C2214yes—
156#2453C2214yescomplemented
157#2450C2214yes—
158#2450C2214yes—
159#2450C2214yes—
160#2450C2214yescomplemented
161#2449C2214yes—
162#2447C2214yes—
163#2444C2214yes—
164#2444C2214yes—
165#2443C2214yes—
166#2443C2214yes—
167#2427C2212yes—
168#2426C2212yes—
169#2425C2214yes—
170#2425C2214yes—
171#2424C2214yes—
172#2423C2212yes—
173#2422C2212yes—
174#2419C2214yes—
175#2418C2214yes—
176C2×#400C2212yes—
177C2×#398C2212yes—
178#2368C2214yes—
179#2364C2214yes—
180#2352C2214yes—
181#2349C2214yes—
182#2337C2214yes—
183#2335C2214yes—
184#2335C2214yes—
185#2334C2214yes—
186#2329C2212yes—
187#2329C2212yes—
188#2325C2212yes—
189#2325C2212yes—
190#2324C2214yes—
191#2318C2214yes—
192#2318C2214yes—
193C4×C22⋊Q8C2212yes—
194C4×#121C2212yes—
195C4×#120C2214yes—
196C2×#387C2212yes—
197C2×#387C2212yes—
198C2×#385C2212yes—
199C2×#380C2212yes—
200C2×#380C2211yescharacteristic
201C2×C4×C22⋊C4C2211yescharacteristic
202C22×#95C2211yescharacteristic
203C24×C4C2311yescharacteristic
204C24×C4C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×#126C2314yes—
207C2×#125C2314yes—
208C2×#125C2314yes—
209C2×#124C2314yes—
210C2×#124C2312yes—
211C2×#123C2314yes—
212C2×#123C2314yes—
213C2×#123C2314yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2314yes—
221C2×#121C2312yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#120C2314yes—
227C2×C4×Q8C2312yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2312yes—
234C2×#117C2314yes—
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2312yes—
240C22×C22⋊C4C2311yescharacteristic
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2311yescharacteristic
243C22×C42C2312yes—
244#401C2314yes—
245#401C2314yes—
246#401C2314yes—
247#401C2314yes—
248#400C2314yes—
249#400C2314yes—
250#400C2314yes—
251#400C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#399C2314yes—
272#399C2314yes—
273#399C2314yes—
274#399C2314yes—
275#399C2314yes—
276#398C2314yes—
277#398C2314yes—
278#398C2314yes—
279#398C2314yes—
280#398C2314yes—
281#398C2314yes—
282#398C2314yes—
283#398C2314yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#397C2314yes—
304#397C2314yes—
305#397C2314yes—
306#397C2314yes—
307#397C2314yes—
308#397C2314yes—
309#397C2314yes—
310#397C2314yes—
311#397C2314yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#396C2314yes—
327#396C2314yes—
328#396C2314yes—
329#396C2314yes—
330#396C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#395C2314yes—
337#395C2314yes—
338#395C2314yes—
339#395C2314yes—
340#394C2314yes—
341#394C2314yes—
342#394C2314yes—
343#394C2314yes—
344#394C2314yes—
345#394C2314yes—
346#394C2314yes—
347#394C2314yes—
348#394C2314yes—
349#394C2314yes—
350#393C2314yes—
351#393C2314yes—
352#393C2314yes—
353#393C2314yes—
354#392C2314yes—
355#392C2314yes—
356#391C2314yes—
357#391C2314yes—
358#391C2314yes—
359#391C2314yes—
360#391C2314yes—
361#391C2312yes—
362#391C2314yes—
363#391C2314yes—
364#391C2312yes—
365#390C2314yes—
366#390C2314yes—
367#390C2314yes—
368#390C2314yes—
369#390C2312yes—
370#390C2312yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2312yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2312yes—
383#389C2314yes—
384#389C2314yes—
385#389C2312yes—
386#389C2312yes—
387#389C2314yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#388C2314yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#386C2314yes—
461#386C2314yes—
462#386C2314yes—
463#386C2314yes—
464#386C2314yes—
465#386C2314yes—
466#386C2314yes—
467#386C2314yes—
468#386C2314yes—
469#386C2314yes—
470#386C2314yes—
471#386C2314yes—
472#386C2314yes—
473#386C2314yes—
474#386C2314yes—
475#386C2314yes—
476#386C2314yes—
477#386C2314yes—
478#386C2314yes—
479#386C2314yes—
480#386C2314yes—
481#385C2314yes—
482#385C2314yes—
483#385C2314yes—
484#385C2314yes—
485#385C2314yes—
486#385C2314yes—
487#385C2314yes—
488#385C2314yes—
489#385C2314yes—
490#385C2314yes—
491#385C2314yes—
492#385C2314yes—
493#385C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2314yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#384C2312yes—
513#383C2314yes—
514#383C2314yes—
515#383C2314yes—
516#383C2314yes—
517#382C2314yes—
518#382C2314yes—
519#382C2314yes—
520#382C2314yes—
521#382C2314yes—
522#382C2312yes—
523#382C2314yes—
524#381C2314yes—
525#381C2314yes—
526#381C2314yes—
527#381C2314yes—
528#380C2314yes—
529#380C2314yes—
530#380C2314yes—
531#380C2314yes—
532#380C2314yes—
533#380C2314yes—
534#380C2314yes—
535#380C2314yes—
536#380C2314yes—
537#380C2314yes—
538#380C2312yes—
539#380C2312yes—
540#380C2314yes—
541#380C2312yes—
542#380C2312yes—
543#380C2312yes—
544#380C2312yes—
545#380C2314yes—
546#380C2314yes—
547#379C2314yes—
548C4×C4⋊C4C2312yes—
549C4×C4⋊C4C2314yes—
550C4×C4⋊C4C2314yes—
551C4×C4⋊C4C2312yes—
552C4×C4⋊C4C2314yes—
553C4×C4⋊C4C2314yes—
554C4×C4⋊C4C2314yes—
555C4×C22⋊C4C2312yes—
556C4×C22⋊C4C2312yes—
557C4×C22⋊C4C2312yes—
558C4×C22⋊C4C2312yes—
559C4×C22⋊C4C2314yes—
560C4×C22⋊C4C2314yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2314yes—
563C4×C22⋊C4C2314yes—
564C4×C22⋊C4C2314yes—
565C4×C22⋊C4C2314yes—
566C4×C22⋊C4C2314yes—
567C2×#95C2314yes—
568C2×#95C2314yes—
569C2×#95C2311yescharacteristic
570C2×#95C2314yes—
571C2×#95C2311yescharacteristic
572C2×#95C2312yes—
573C2×#95C2311yescharacteristic
574C2×#95C2312yes—
575C2×#95C2312yes—
576C2×#95C2312yes—
577C2×#95C2311yescharacteristic
578C2×#95C2312yes—
579C2×#95C2312yes—
580C25C2411yescharacteristic
581C22×Q8C2412yes—
582C22×Q8C2414yes—
583C22×D4C2414yes—
584C22×D4C2414yes—
585C22×D4C2414yes—
586C22×D4C2412yes—
587C22×D4C2414yes—
588C23×C4—24no—
589C23×C4—44no—
590C23×C4—44no—
591C23×C4—82no—
592C23×C4—82no—
593C23×C4C2412yes—
594C23×C4C2412yes—
595C23×C4C2412yes—
596C23×C4C2412yes—
597C23×C4C2412yes—
598C23×C4C2411yescharacteristic
599C23×C4C2412yes—
600C23×C4C2414yes—
601C23×C4C2412yes—
602C23×C4C2412yes—
603C23×C4C2414yes—
604C23×C4C2414yes—
605C23×C4C2414yes—
606C23×C4C2414yes—
607C23×C4C2411yescharacteristic
608C4⋊Q8—82no—
609#126—48no—
610#125—84no—
611#125—84no—
612#124—48no—
613#124—82no—
614#123—48no—
615#123—48no—
616#123—84no—
617#123—84no—
618#123—84no—
619C22⋊Q8—28no—
620C22⋊Q8—48no—
621C22⋊Q8—82no—
622C22⋊Q8—84no—
623C22⋊Q8—82no—
624#121—28no—
625#121—48no—
626#121—48no—
627#121—82no—
628#121—82no—
629#120—48no—
630C4×Q8—82no—
631C4×D4—48no—
632C4×D4—48no—
633C4×D4—48no—
634C4×D4—48no—
635C4×D4—82no—
636C4×D4—84no—
637#117—84no—
638C2×C4⋊C4—44no—
639C2×C4⋊C4—44no—
640C2×C4⋊C4—82no—
641C2×C4⋊C4—82no—
642C2×C4⋊C4—82no—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C22⋊C4—44no—
688C2×C22⋊C4—42no—
689C2×C22⋊C4—42no—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2411yescharacteristic
700C2×C22⋊C4C2411yescharacteristic
701C2×C22⋊C4C2411yescharacteristic
702C2×C22⋊C4C2411yescharacteristic
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C42—82no—
730C2×C42C2414yes—
731C2×C42C2414yes—
732C2×C42C2414yes—
733C2×C42C2414yes—
734C2×C42C2414yes—
735C2×C42C2412yes—
736C2×C42C2414yes—
737C2×C42C2412yes—
738C2×C42C2412yes—
739C2×C42C2414yes—
740C2×C42C2414yes—
741C2×C42C2414yes—
742C2×C42C2412yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805C24—22no—
806C24—22no—
807C24—22no—
808C24—24no—
809C24—42no—
810C24C2514yes—
811C24C2511yescharacteristic
812C24C2511yescharacteristic
813C24C2511yescharacteristic
814C2×Q8—24no—
815C2×Q8—42no—
816C2×Q8—42no—
817C2×Q8—44no—
818C2×Q8—44no—
819C2×Q8—44no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—28no—
823C2×D4—28no—
824C2×D4—28no—
825C2×D4—24no—
826C2×D4—42no—
827C2×D4—44no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—42no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—44no—
835C22×C4—22no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—28no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—44no—
867C22×C4—42no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—88no—
878C22×C4—816no—
879C22×C42−1+414yes—
880C22×C4C2514yes—
881C22×C4C2514yes—
882C22×C4C2512yes—
883C22×C4C2512yes—
884C22×C4C2514yes—
885C22×C4C2512yes—
886C22×C4C2514yes—
887C22×C4C2514yes—
888C22×C4C2514yes—
889C22×C4C2514yes—
890C22×C4C2514yes—
891C22×C4C2514yes—
892C22×C4C2514yes—
893C22×C4C2512yes—
894C22×C4C2514yes—
895C22×C4C2512yes—
896C22×C4C2512yes—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—28no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—42no—
916C4⋊C4—44no—
917C4⋊C4—42no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—42no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—42no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—41no—
951C22⋊C4—44no—
952C22⋊C4—41no—
953C22⋊C4—41no—
954C22⋊C4—41no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C42—42no—
981C42—42no—
982C42—42no—
983C42—42no—
984C42—44no—
985C42—44no—
986C42—44no—
987C42—44no—
988C42—44no—
989C42—44no—
990C42—44no—
991C42—44no—
992C42—44no—
993C23—21no—
994C23—21no—
995C23—22no—
996C23—28no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—48no—
1013C23—48no—
1014C23—44no—
1015C23—44no—
1016C23C2×2−1+412yes—
1017C23#58512yes—
1018C23#58512yes—
1019C23#58514yes—
1020C23C2611yescharacteristic
1021Q8—84no—
1022Q8—164no—
1023D4—416no—
1024D4—84no—
1025D4—88no—
1026D4—88no—
1027D4—164no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—44no—
1079C2×C4—44no—
1080C2×C4—48no—
1081C2×C4—84no—
1082C2×C4—84no—
1083C2×C4—84no—
1084C2×C4—84no—
1085C2×C4—84no—
1086C2×C4—84no—
1087C2×C4—88no—
1088C2×C4—84no—
1089C2×C4—88no—
1090C2×C4—88no—
1091C2×C4—164no—
1092C2×C4—164no—
1093C2×C4C2×2−1+414yes—
1094C22—22no—
1095C22—22no—
1096C22—24no—
1097C22—24no—
1098C22—22no—
1099C22—22no—
1100C22—24no—
1101C22—24no—
1102C22—416no—
1103C22—41no—
1104C22—41no—
1105C22—41no—
1106C22—41no—
1107C22—42no—
1108C22—42no—
1109C22—44no—
1110C22—44no—
1111C22—44no—
1112C22—44no—
1113C22—44no—
1114C22—44no—
1115C22—44no—
1116C22#355714yes—
1117C22C22×2−1+411yescharacteristic
1118C22C2×#58512yes—
1119C22C2×#58511yescharacteristic
1120C22C2×#58511yescharacteristic
1121C22H(7,𝔽2)12yes—
1122C4—24no—
1123C4—44no—
1124C4—44no—
1125C4—42no—
1126C4—44no—
1127C4—44no—
1128C4—42no—
1129C4—44no—
1130C4—42no—
1131C4—44no—
1132C4—44no—
1133C4—42no—
1134C4—44no—
1135C4—42no—
1136C4—44no—
1137C4—44no—
1138C4—44no—
1139C2—24no—
1140C2—42no—
1141C2—42no—
1142C2—84no—
1143C2C2×#355711yescharacteristic
1144C2#6282511yescharacteristic
1145C2#6286411yescharacteristic
1146C2#6290612yes—
1147C2#6296312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36727C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #55793C2semidirect
2. #55078C2semidirect
3. #54129C2semidirect
4. #53641C2semidirect
5. #52431C2semidirect
6. #47253C2semidirect
7. #46926C2semidirect
8. #46886C2semidirect
9. #46637C2semidirect
10. #43619C2semidirect
11. #39806C2semidirect
12. #39799C2semidirect
13. #39636C2semidirect
14. #39627C2semidirect
15. #38535C2semidirect
16. #37908C2semidirect
17. #36728C2semidirect
19. #35080C2semidirect
20. #34997C2semidirect
21. C2×#2569C2semidirect
27. #2836C22semidirect
28. #2836C22semidirect
29. #2834C22semidirect
30. #2834C22semidirect
31. #2831C22semidirect
32. #2831C22semidirect
33. #2830C22semidirect
34. #2822C22semidirect
35. #2802C22semidirect
36. #2799C22semidirect
37. #2797C22semidirect
39. #2791C22semidirect
40. #2790C22semidirect
41. #2789C22semidirect
42. #2789C22semidirect
44. #2787C22semidirect
45. #2786C22semidirect
47. #2781C22semidirect
48. #2780C22semidirect
49. #2777C22semidirect
50. #2775C22semidirect
51. #2773C22semidirect
52. #2770C22semidirect
53. #2770C22semidirect
54. #2767C22semidirect
55. #2766C22semidirect
56. #2766C22semidirect
57. #2766C22semidirect
60. #2762C22semidirect
63. #2755C22semidirect
64. #2754C22semidirect
65. #2752C22semidirect
66. #2750C22semidirect
70. #2745C22semidirect
73. #2729C22semidirect
74. #2724C22semidirect
77. #2713C22semidirect
80. #2707C22semidirect
81. #2707C22semidirect
89. #2687C22semidirect
104. #2602C22semidirect
105. #2599C22semidirect
106. #2596C22semidirect
107. #2594C22semidirect
108. #2585C22semidirect
109. #2585C22semidirect
114. #2575C22semidirect
115. #2575C22semidirect
120. #2557C22semidirect
122. #2524C22semidirect
123. #2524C22semidirect
124. #2522C22semidirect
125. #2520C22semidirect
126. #2517C22semidirect
132. #2509C22semidirect
135. #2505C22semidirect
137. #2498C22semidirect
139. #2495C22semidirect
142. #2493C22semidirect
145. #2489C22semidirect
148. #2475C22semidirect
149. #2474C22semidirect
156. #2453C22semidirect
160. #2450C22semidirect

Maximal subgroups

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

subgroupindex
#557932
#550782
#541292
#536412
#524312
#472532
#469262
#468862
#466372
#436192
#398062
#397992
#396362
#396272
#385352
#379082
#367282
#367272
#350802
#349972
C2×#25692