Finite Group Databasebeta

← #7642801

Subgroups — #7642801

Order 512.

4582 conjugacy classes of subgroups.

The subgroup lattice has 1189 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39921C214yesmaximal, complemented
2#39920C214yesmaximal, complemented
3#39897C214yesmaximal, complemented
4#39896C214yesmaximal, complemented
5#38419C214yesmaximal, complemented
6#38418C214yesmaximal, complemented
7#38417C214yesmaximal, complemented
8#38416C214yesmaximal, complemented
9#36980C212yesmaximal, complemented
10#36979C211yesmaximal, characteristic, complemented
11#36978C211yesmaximal, characteristic, complemented
12#36729C212yesmaximal, complemented
13#36728C211yesmaximal, characteristic, complemented
14#36727C211yesmaximal, characteristic
15#36621C212yesmaximal, complemented
16#35459C214yesmaximal, complemented
17#35373C214yesmaximal, complemented
18#35120C211yesmaximal, characteristic, complemented
19#35119C211yesmaximal, characteristic, complemented
20#35075C214yesmaximal, complemented
21#35074C214yesmaximal, complemented
22#34219C212yesmaximal, complemented
23C2×#2283C211yesmaximal, characteristic, complemented
24C2×#529C2212yes—
25C23×C42C2211yescharacteristic
26#2855C2214yes—
27#2855C2212yes—
28#2854C2214yes—
29#2854C2212yes—
30#2853C2214yes—
31#2852C2214yes—
32#2852C2214yes—
33#2851C2212yes—
34#2851C2212yes—
35#2850C2212yes—
36#2850C2212yes—
37#2849C2214yes—
38#2848C2212yes—
39#2847C2212yes—
40#2777C2214yescomplemented
41#2776C2214yescomplemented
42#2775C2214yescomplemented
43#2770C2214yescomplemented
44#2769C2214yescomplemented
45#2766C2214yescomplemented
46#2764C2214yescomplemented
47#2762C2214yescomplemented
48#2759C2214yescomplemented
49#2758C2214yescomplemented
50#2758C2214yescomplemented
51#2757C2214yescomplemented
52#2756C2214yescomplemented
53#2749C2214yescomplemented
54#2748C2214yes—
55#2747C2214yes—
56#2747C2214yes—
57#2742C2214yes—
58#2741C2214yes—
59#2741C2214yes—
60#2738C2214yescomplemented
61#2737C2214yescomplemented
62#2722C2214yes—
63#2717C2214yes—
64#2704C2214yes—
65#2703C2214yes—
66#2702C2214yes—
67#2692C2214yes—
68#2691C2214yes—
69#2690C2214yes—
70#2672C2214yes—
71#2671C2214yes—
72#2659C2211yescharacteristic
73#2659C2212yes—
74#2656C2211yescharacteristic
75#2655C2214yescomplemented
76#2654C2214yescomplemented
77#2653C2214yes—
78#2652C2214yes—
79#2651C2214yescomplemented
80#2650C2214yescomplemented
81#2649C2214yes—
82#2648C2214yes—
83#2646C2211yescharacteristic
84#2646C2211yescharacteristic
85#2639C2212yes—
86#2612C2214yescomplemented
87#2612C2214yescomplemented
88#2611C2214yescomplemented
89#2610C2214yescomplemented
90#2606C2214yescomplemented
91#2605C2214yescomplemented
92#2604C2214yescomplemented
93#2603C2214yescomplemented
94#2597C2214yes—
95#2596C2214yescomplemented
96#2595C2214yes—
97#2594C2214yescomplemented
98#2590C2214yescomplemented
99#2589C2214yes—
100#2588C2214yescomplemented
101#2587C2214yes—
102#2578C2214yes—
103#2577C2214yescomplemented
104#2576C2214yes—
105#2576C2214yes—
106#2576C2214yescomplemented
107#2575C2214yes—
108#2575C2214yescomplemented
109#2575C2214yescomplemented
110#2574C2214yescomplemented
111#2573C2214yes—
112#2572C2214yes—
113#2560C2214yescomplemented
114#2559C2214yes—
115#2558C2214yescomplemented
116#2557C2214yes—
117#2553C2214yescomplemented
118#2529C2214yescomplemented
119#2528C2214yescomplemented
120#2527C2214yes—
121#2526C2214yes—
122#2524C2214yescomplemented
123#2520C2214yescomplemented
124#2519C2214yescomplemented
125#2518C2214yescomplemented
126#2517C2214yescomplemented
127#2516C2214yes—
128#2515C2214yes—
129#2515C2214yescomplemented
130#2510C2214yes—
131#2508C2214yescomplemented
132#2505C2214yes—
133#2505C2214yescomplemented
134#2493C2214yes—
135#2489C2214yescomplemented
136#2488C2214yes—
137#2488C2214yescomplemented
138#2481C2214yes—
139#2480C2214yes—
140#2473C2214yes—
141#2472C2214yes—
142#2468C2214yes—
143#2466C2214yes—
144#2459C2214yes—
145#2457C2214yes—
146#2450C2214yes—
147#2449C2214yes—
148#2447C2214yes—
149#2444C2214yes—
150#2444C2214yes—
151#2443C2214yes—
152#2425C2214yes—
153#2424C2214yes—
154#2420C2214yes—
155#2419C2214yes—
156#2419C2214yes—
157#2418C2214yes—
158#2373C2214yescomplemented
159#2373C2214yescomplemented
160#2372C2214yescomplemented
161#2371C2214yescomplemented
162#2356C2214yescomplemented
163#2353C2214yescomplemented
164#2346C2214yescomplemented
165#2343C2214yescomplemented
166#2337C2214yes—
167#2336C2214yescomplemented
168#2335C2214yes—
169#2335C2214yescomplemented
170#2334C2214yes—
171#2334C2214yescomplemented
172#2333C2214yes—
173#2332C2214yescomplemented
174#2329C2214yes—
175#2329C2212yes—
176#2329C2212yes—
177#2325C2214yes—
178#2325C2212yes—
179#2325C2212yes—
180#2318C2214yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2212yes—
183C4×#123C2214yes—
184C4×#123C2214yes—
185C4×#123C2214yes—
186C4×#121C2212yes—
187C4×#121C2212yes—
188C4×#120C2214yes—
189#2290C2214yes—
190#2290C2214yes—
191#2283C2212yes—
192#2283C2214yes—
193#2283C2214yes—
194#2283C2214yes—
195#2283C2214yes—
196C2×#383C2211yescharacteristic
197C2×#383C2211yescharacteristic
198C2×#382C2212yes—
199C2×#381C2212yes—
200C2×#380C2211yescharacteristic
201C2×#380C2211yescharacteristic
202#2275C2214yes—
203C2×C4×C4⋊C4C2212yes—
204C2×C4×C22⋊C4C2212yes—
205C2×#376C2211yescharacteristic
206C2×#376C2211yescharacteristic
207C24×C4C2311yescharacteristic
208C24×C4C2311yescharacteristic
209C24×C4C2311yescharacteristic
210#529—216no—
211C2×#126C2314yes—
212C2×#126C2314yes—
213C2×#126C2314yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#124C2312yes—
217C2×#124C2314yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×#121C2312yes—
228C2×#121C2314yes—
229C2×#121C2314yes—
230C2×#121C2312yes—
231C2×#121C2312yes—
232C2×#120C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×#117C2314yes—
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C22⋊C4C2312yes—
244C22×C22⋊C4C2312yes—
245C22×C42—28no—
246C22×C42C2312yes—
247C22×C42C2312yes—
248C22×C42C2312yes—
249C22×C42C2312yes—
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253C22×C42C2312yes—
254C22×C42C2312yes—
255C22×C42C2311yescharacteristic
256#401C2314yes—
257#401C2314yes—
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#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#399C2314yes—
277#399C2314yes—
278#399C2314yes—
279#399C2314yes—
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#397C2314yes—
295#397C2314yes—
296#397C2314yes—
297#397C2314yes—
298#397C2314yes—
299#397C2314yes—
300#397C2314yes—
301#397C2314yes—
302#397C2314yes—
303#397C2314yes—
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#395C2314yes—
317#395C2314yes—
318#395C2314yes—
319#395C2314yes—
320#394C2314yes—
321#394C2314yes—
322#394C2314yes—
323#394C2314yes—
324#394C2314yes—
325#394C2314yes—
326#394C2314yes—
327#394C2314yes—
328#394C2314yes—
329#394C2314yes—
330#393C2314yes—
331#393C2314yes—
332#393C2314yes—
333#393C2314yes—
334#392C2314yes—
335#392C2314yes—
336#391C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#391C2314yes—
344#391C2312yes—
345#391C2312yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2312yes—
351#390C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#388C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2314yes—
372#388C2314yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2314yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2314yes—
387#388C2314yes—
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#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
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#386C2314yes—
453#386C2314yes—
454#386C2314yes—
455#386C2314yes—
456#386C2314yes—
457#386C2314yes—
458#386C2314yes—
459#386C2314yes—
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#385C2314yes—
475#385C2314yes—
476#385C2314yes—
477#385C2314yes—
478#385C2314yes—
479#385C2314yes—
480#385C2314yes—
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#383C2314yes—
497#383C2314yes—
498#383C2314yes—
499#383C2314yes—
500#383C2314yes—
501#383C2314yes—
502#383C2314yes—
503#383C2314yes—
504#382C2314yes—
505#382C2314yes—
506#382C2314yes—
507#382C2314yes—
508#382C2314yes—
509#382C2312yes—
510#382C2312yes—
511#382C2314yes—
512#382C2314yes—
513#381C2314yes—
514#381C2314yes—
515#381C2314yes—
516#381C2314yes—
517#381C2314yes—
518#381C2314yes—
519#381C2314yes—
520#381C2314yes—
521#381C2314yes—
522#380C2314yes—
523#380C2314yes—
524#380C2314yes—
525#380C2312yes—
526#380C2312yes—
527#380C2314yes—
528#380C2314yes—
529#380C2312yes—
530#380C2312yes—
531#380C2312yes—
532#380C2312yes—
533#380C2314yes—
534#380C2314yes—
535#380C2314yes—
536#380C2314yes—
537#379C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2314yes—
546C4×C4⋊C4C2314yes—
547C4×C4⋊C4C2314yes—
548C4×C4⋊C4C2314yes—
549C4×C4⋊C4C2312yes—
550C4×C4⋊C4C2312yes—
551C4×C4⋊C4C2314yes—
552C4×C4⋊C4C2314yes—
553C4×C22⋊C4C2314yes—
554C4×C22⋊C4C2314yes—
555C4×C22⋊C4C2314yes—
556C4×C22⋊C4C2314yes—
557C4×C22⋊C4C2314yes—
558C4×C22⋊C4C2314yes—
559C4×C22⋊C4C2314yes—
560C4×C22⋊C4C2314yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2314yes—
563C4×C22⋊C4C2314yes—
564C4×C22⋊C4C2314yes—
565C4×C22⋊C4C2314yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2314yes—
568C4×C22⋊C4C2314yes—
569C4×C22⋊C4C2314yes—
570C4×C22⋊C4C2314yes—
571#376C2314yes—
572#376C2314yes—
573#376C2314yes—
574#376C2314yes—
575#376C2314yes—
576#376C2314yes—
577C2×#95C2312yes—
578C2×#95C2311yescharacteristic
579C2×#95C2311yescharacteristic
580C2×#95C2312yes—
581C2×#95C2314yes—
582C2×#95C2311yescharacteristic
583C2×#95C2311yescharacteristic
584C2×#95C2312yes—
585C2×#95C2312yes—
586C2×#95C2312yes—
587C2×#95C2312yes—
588C25C2411yescharacteristic
589C22×Q8C2412yes—
590C22×Q8C2414yes—
591C22×D4C2414yes—
592C22×D4C2414yes—
593C22×D4C2414yes—
594C22×D4C2412yes—
595C22×D4C2414yes—
596C23×C4—24no—
597C23×C4—24no—
598C23×C4—24no—
599C23×C4—44no—
600C23×C4—44no—
601C23×C4—42no—
602C23×C4—42no—
603C23×C4C2411yescharacteristic
604C23×C4C2411yescharacteristic
605C23×C4C2412yes—
606C23×C4C2412yes—
607C23×C4C2412yes—
608C23×C4C2412yes—
609C23×C4C2411yescharacteristic
610C23×C4C2412yes—
611C23×C4C2412yes—
612C23×C4C2412yes—
613C23×C4C2412yes—
614C23×C4C2414yes—
615C23×C4C2411yescharacteristic
616C23×C4C2411yescharacteristic
617C23×C4C2411yescharacteristic
618C23×C4C2411yescharacteristic
619C23×C4C2411yescharacteristic
620C23×C4C2414yes—
621C23×C4C2414yes—
622C23×C4C2411yescharacteristic
623C23×C4C2411yescharacteristic
624#126—216no—
625#126—48no—
626#126—48no—
627#125—28no—
628#125—48no—
629#124—28no—
630#124—48no—
631#123—216no—
632#123—48no—
633#123—48no—
634#123—48no—
635C22⋊Q8—28no—
636C22⋊Q8—48no—
637C22⋊Q8—48no—
638C22⋊Q8—44no—
639C22⋊Q8—44no—
640#121—28no—
641#121—44no—
642#121—44no—
643#121—48no—
644#121—48no—
645#120—48no—
646C4×Q8—28no—
647C4×D4—216no—
648C4×D4—28no—
649C4×D4—48no—
650C4×D4—48no—
651C4×D4—48no—
652C4×D4—48no—
653#117—216no—
654C2×C4⋊C4—44no—
655C2×C4⋊C4—44no—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C22⋊C4—44no—
695C2×C22⋊C4—44no—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
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×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C42—24no—
732C2×C42—24no—
733C2×C42—24no—
734C2×C42—28no—
735C2×C42—28no—
736C2×C42—28no—
737C2×C42—28no—
738C2×C42—44no—
739C2×C42—44no—
740C2×C42#4118yes—
741C2×C42C2414yes—
742C2×C42C2412yes—
743C2×C42C2412yes—
744C2×C42C2412yes—
745C2×C42C2412yes—
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2414yes—
749C2×C42C2414yes—
750C2×C42C2414yes—
751C2×C42C2414yes—
752C2×C42C2414yes—
753C2×C42C2414yes—
754C2×C42C2414yes—
755C2×C42C2414yes—
756C2×C42C2414yes—
757C2×C42C2414yes—
758C2×C42C2414yes—
759C2×C42C2414yes—
760C2×C42C2412yes—
761C2×C42C2412yes—
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—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822C24—22no—
823C24—22no—
824C24—22no—
825C24—24no—
826C24—42no—
827C24C2514yes—
828C24C2511yescharacteristic
829C24C2511yescharacteristic
830C24C2511yescharacteristic
831C2×Q8—24no—
832C2×Q8—42no—
833C2×Q8—42no—
834C2×Q8—44no—
835C2×Q8—44no—
836C2×Q8—44no—
837C2×D4—28no—
838C2×D4—28no—
839C2×D4—28no—
840C2×D4—28no—
841C2×D4—28no—
842C2×D4—24no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—44no—
850C2×D4—44no—
851C2×D4—44no—
852C22×C4—22no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—28no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—416no—
905C22×C4—416no—
906C22×C4—416no—
907C22×C4C2×#4114yes—
908C22×C4C2×#4114yes—
909C22×C4C2×#4114yes—
910C22×C4C2511yescharacteristic
911C22×C4C2511yescharacteristic
912C22×C4C2512yes—
913C22×C4C2514yes—
914C22×C4C2514yes—
915C22×C4C2514yes—
916C22×C4C2514yes—
917C22×C4C2514yes—
918C22×C4C2514yes—
919C22×C4C2514yes—
920C22×C4C2514yes—
921C22×C4C2514yes—
922C22×C4C2514yes—
923C22×C4C2514yes—
924C22×C4C2512yes—
925C22×C4C2512yes—
926C22×C4C2511yescharacteristic
927C22×C4C2511yescharacteristic
928C22×C4C2512yes—
929C4⋊C4—28no—
930C4⋊C4—28no—
931C4⋊C4—24no—
932C4⋊C4—28no—
933C4⋊C4—24no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—28no—
938C4⋊C4—28no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C22⋊C4—28no—
968C22⋊C4—28no—
969C22⋊C4—28no—
970C22⋊C4—28no—
971C22⋊C4—28no—
972C22⋊C4—28no—
973C22⋊C4—28no—
974C22⋊C4—28no—
975C22⋊C4—28no—
976C22⋊C4—28no—
977C22⋊C4—28no—
978C22⋊C4—28no—
979C22⋊C4—28no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C42—24no—
1003C42—24no—
1004C42—24no—
1005C42—24no—
1006C42—24no—
1007C42—24no—
1008C42—28no—
1009C42—44no—
1010C42—44no—
1011C42—44no—
1012C42—44no—
1013C42—44no—
1014C42—44no—
1015C42—44no—
1016C42—44no—
1017C42—44no—
1018C42—44no—
1019C42—44no—
1020C42—44no—
1021C42C2×#4118yes—
1022C42C2×#4118yes—
1023C23—22no—
1024C23—21no—
1025C23—21no—
1026C23—28no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—24no—
1036C23—24no—
1037C23—24no—
1038C23—24no—
1039C23—24no—
1040C23—24no—
1041C23—24no—
1042C23—48no—
1043C23—48no—
1044C23—44no—
1045C23—44no—
1046C23C22×#4112yes—
1047C23#58512yes—
1048C23#58512yes—
1049C23#58514yes—
1050C23C2611yescharacteristic
1051Q8—84no—
1052Q8—164no—
1053D4—416no—
1054D4—84no—
1055D4—88no—
1056D4—88no—
1057D4—164no—
1058C2×C4—28no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—28no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—44no—
1109C2×C4—44no—
1110C2×C4—48no—
1111C2×C4—48no—
1112C2×C4—48no—
1113C2×C4—48no—
1114C2×C4—44no—
1115C2×C4—44no—
1116C2×C4—44no—
1117C2×C4—44no—
1118C2×C4—44no—
1119C2×C4—44no—
1120C2×C4—88no—
1121C2×C4—84no—
1122C2×C4—84no—
1123C2×C4—84no—
1124C2×C4—84no—
1125C2×C4—164no—
1126C2×C4—164no—
1127C2×C4C22×#4114yes—
1128C2×C4C22×#4112yes—
1129C2×C4C22×#4112yes—
1130C2×C4C22×#4114yes—
1131C2×C4#58514yes—
1132C22—22no—
1133C22—22no—
1134C22—24no—
1135C22—24no—
1136C22—22no—
1137C22—22no—
1138C22—24no—
1139C22—24no—
1140C22—416no—
1141C22—41no—
1142C22—41no—
1143C22—42no—
1144C22—42no—
1145C22—41no—
1146C22—41no—
1147C22—44no—
1148C22—44no—
1149C22—44no—
1150C22—44no—
1151C22—44no—
1152C22—44no—
1153C22—44no—
1154C22#345514yes—
1155C22C23×#4111yescharacteristic
1156C22C2×#58511yescharacteristic
1157C22C2×#58511yescharacteristic
1158C22C2×#58512yes—
1159C22C2×#58512yes—
1160C4—24no—
1161C4—24no—
1162C4—24no—
1163C4—22no—
1164C4—22no—
1165C4—42no—
1166C4—44no—
1167C4—44no—
1168C4—44no—
1169C4—44no—
1170C4—44no—
1171C4—44no—
1172C4—44no—
1173C4—44no—
1174C4—44no—
1175C4—44no—
1176C4—41no—
1177C4—41no—
1178C4—44no—
1179C2—24no—
1180C2—42no—
1181C2—42no—
1182C2—84no—
1183C2C2×#345511yescharacteristic
1184C2#6281411yescharacteristic
1185C2#6281411yescharacteristic
1186C2#6282912yes—
1187C2#6282912yes—
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. #39921C2semidirect
2. #39920C2semidirect
3. #39897C2semidirect
4. #39896C2semidirect
5. #38419C2semidirect
6. #38418C2semidirect
7. #38417C2semidirect
8. #38416C2semidirect
9. #36980C2semidirect
10. #36979C2semidirect
11. #36978C2semidirect
12. #36729C2semidirect
13. #36728C2semidirect
15. #36621C2semidirect
16. #35459C2semidirect
17. #35373C2semidirect
18. #35120C2semidirect
19. #35119C2semidirect
20. #35075C2semidirect
21. #35074C2semidirect
22. #34219C2semidirect
23. C2×#2283C2semidirect
40. #2777C22semidirect
41. #2776C22semidirect
42. #2775C22semidirect
43. #2770C22semidirect
44. #2769C22semidirect
45. #2766C22semidirect
46. #2764C22semidirect
47. #2762C22semidirect
48. #2759C22semidirect
49. #2758C22semidirect
50. #2758C22semidirect
51. #2757C22semidirect
52. #2756C22semidirect
53. #2749C22semidirect
60. #2738C22semidirect
61. #2737C22semidirect
75. #2655C22semidirect
76. #2654C22semidirect
79. #2651C22semidirect
80. #2650C22semidirect
86. #2612C22semidirect
87. #2612C22semidirect
88. #2611C22semidirect
89. #2610C22semidirect
90. #2606C22semidirect
91. #2605C22semidirect
92. #2604C22semidirect
93. #2603C22semidirect
95. #2596C22semidirect
97. #2594C22semidirect
98. #2590C22semidirect
100. #2588C22semidirect
103. #2577C22semidirect
106. #2576C22semidirect
108. #2575C22semidirect
109. #2575C22semidirect
110. #2574C22semidirect
113. #2560C22semidirect
115. #2558C22semidirect
117. #2553C22semidirect
118. #2529C22semidirect
119. #2528C22semidirect
122. #2524C22semidirect
123. #2520C22semidirect
124. #2519C22semidirect
125. #2518C22semidirect
126. #2517C22semidirect
129. #2515C22semidirect
131. #2508C22semidirect
133. #2505C22semidirect
135. #2489C22semidirect
137. #2488C22semidirect
158. #2373C22semidirect
159. #2373C22semidirect
160. #2372C22semidirect
161. #2371C22semidirect
162. #2356C22semidirect
163. #2353C22semidirect
164. #2346C22semidirect
165. #2343C22semidirect
167. #2336C22semidirect
169. #2335C22semidirect
171. #2334C22semidirect
173. #2332C22semidirect

Maximal subgroups

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

subgroupindex
#399212
#399202
#398972
#398962
#384192
#384182
#384172
#384162
#369802
#369792
#369782
#367292
#367282
#367272
#366212
#354592
#353732
#351202
#351192
#350752
#350742
#342192
C2×#22832