Finite Group Databasebeta

← #7658931

Subgroups — #7658931

Order 512.

4730 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42343C214yesmaximal, complemented
2#42051C214yesmaximal, complemented
3#42024C214yesmaximal, complemented
4#41663C214yesmaximal, complemented
5#41653C214yesmaximal, complemented
6#40999C214yesmaximal, complemented
7#40985C214yesmaximal, complemented
8#40669C214yesmaximal, complemented
9#40667C214yesmaximal, complemented
10#37610C212yesmaximal, complemented
11#37608C211yesmaximal, characteristic, complemented
12#37604C212yesmaximal, complemented
13#37600C212yesmaximal, complemented
14#37554C212yesmaximal, complemented
15#36695C212yesmaximal, complemented
16C2×#2845C211yesmaximal, characteristic, complemented
17#35953C214yesmaximal, complemented
18#35859C214yesmaximal, complemented
19#35807C214yesmaximal, complemented
20#34229C212yesmaximal, complemented
21#34208C211yesmaximal, characteristic, complemented
22C2×#553C2214yes—
23C2×#532C2211yescharacteristic
24C2×#529C2212yes—
25C2×#520C2212yes—
26#2845C2214yes—
27#2845C2214yes—
28#2845C2214yes—
29#2845C2211yescharacteristic
30#2845C2212yes—
31#2845C2211yescharacteristic
32#2837C2214yes—
33#2837C2214yes—
34#2831C2214yes—
35#2831C2214yes—
36#2829C2214yes—
37#2829C2214yes—
38#2822C2211yescharacteristic
39#2820C2212yes—
40#2820C2212yes—
41#2820C2212yes—
42#2819C2212yes—
43#2819C2212yes—
44#2819C2211yescharacteristic
45#2787C2214yes—
46#2786C2214yes—
47#2781C2214yes—
48#2780C2214yes—
49#2777C2214yes—
50#2768C2214yes—
51#2768C2214yes—
52#2767C2214yes—
53#2766C2214yes—
54#2761C2214yes—
55#2757C2214yes—
56#2756C2214yes—
57#2756C2214yes—
58#2748C2214yes—
59#2747C2214yes—
60#2740C2214yes—
61#2738C2214yes—
62#2708C2214yes—
63#2706C2214yes—
64#2701C2214yes—
65#2699C2214yes—
66#2695C2214yes—
67#2691C2214yes—
68#2671C2214yes—
69#2667C2214yes—
70#2666C2214yes—
71#2664C2214yes—
72#2661C2214yes—
73#2661C2214yes—
74#2661C2214yes—
75#2656C2214yes—
76#2654C2214yes—
77#2653C2214yes—
78#2653C2214yes—
79#2653C2214yes—
80#2652C2214yes—
81#2651C2214yes—
82#2651C2214yes—
83#2651C2214yes—
84#2639C2214yes—
85#2637C2214yes—
86#2637C2214yes—
87#2637C2214yes—
88#2636C2214yes—
89#2636C2214yes—
90#2636C2214yes—
91#2630C2214yes—
92#2630C2214yes—
93#2628C2214yes—
94#2619C2214yes—
95#2618C2214yes—
96#2611C2214yes—
97#2609C2214yes—
98#2609C2214yes—
99#2603C2214yes—
100#2601C2214yes—
101#2591C2214yes—
102#2590C2214yes—
103#2580C2214yes—
104#2579C2214yes—
105#2579C2214yes—
106#2577C2214yes—
107#2574C2214yes—
108#2574C2214yes—
109#2564C2214yes—
110#2554C2214yes—
111#2554C2214yes—
112#2554C2214yes—
113#2553C2214yes—
114#2553C2214yes—
115#2553C2214yes—
116#2543C2214yes—
117#2543C2214yes—
118#2543C2214yes—
119#2535C2214yes—
120#2531C2214yes—
121#2528C2214yes—
122#2525C2214yes—
123#2522C2214yes—
124#2519C2214yes—
125#2519C2214yes—
126#2515C2214yes—
127#2510C2214yes—
128#2505C2214yes—
129#2504C2214yes—
130#2498C2214yes—
131#2481C2214yes—
132#2479C2214yes—
133#2478C2214yes—
134#2476C2214yes—
135#2476C2214yes—
136#2473C2214yes—
137#2468C2214yes—
138#2464C2214yes—
139#2464C2214yes—
140#2464C2214yes—
141#2464C2214yes—
142#2462C2214yes—
143#2458C2214yes—
144#2458C2214yes—
145#2458C2214yes—
146#2444C2214yes—
147#2443C2214yes—
148#2443C2214yes—
149#2443C2214yes—
150#2443C2214yes—
151#2430C2214yes—
152#2430C2214yes—
153#2425C2214yes—
154#2416C2214yes—
155#2416C2214yes—
156#2416C2214yes—
157#2416C2214yes—
158#2413C2214yes—
159#2396C2214yes—
160#2396C2214yes—
161#2395C2214yes—
162#2395C2214yes—
163#2392C2214yes—
164#2392C2214yes—
165C2×#398C2214yes—
166C2×#398C2214yes—
167C2×#398C2214yes—
168#2364C2214yes—
169#2364C2214yes—
170#2364C2214yes—
171#2361C2214yes—
172#2361C2212yes—
173#2361C2212yes—
174#2360C2212yes—
175#2360C2212yes—
176#2359C2214yes—
177#2359C2214yes—
178#2357C2212yes—
179#2356C2212yes—
180#2352C2214yes—
181#2352C2214yes—
182#2352C2214yes—
183#2351C2212yes—
184#2349C2212yes—
185#2346C2214yes—
186#2343C2214yes—
187#2334C2214yes—
188#2334C2214yes—
189#2328C2212yes—
190#2327C2212yes—
191#2318C2214yes—
192#2311C2212yes—
193C4×#125C2212yes—
194C4×#125C2212yes—
195C4×#124C2212yes—
196C4×#124C2212yes—
197C4×#124C2212yes—
198C4×#124C2212yes—
199C2×#382C2211yescharacteristic
200C2×#382C2212yes—
201#2275C2214yes—
202C4×#117C2211yescharacteristic
203C22×#41C2312yes—
204#553—416no—
205#532—28no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×#127C2311yescharacteristic
208#529—216no—
209C2×#126C2314yes—
210C2×#126C2314yes—
211C2×#126C2314yes—
212C2×#126C2314yes—
213C2×#125C2312yes—
214C2×#125C2314yes—
215C2×#124C2312yes—
216C2×#124C2312yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×#123C2314yes—
223C2×C22⋊Q8C2312yes—
224C2×#121C2312yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2314yes—
228C2×#121C2314yes—
229C2×#121C2314yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236#520—48no—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2314yes—
255C2×#117C2314yes—
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2314yes—
259C2×#117C2314yes—
260C2×#117C2314yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2314yes—
268C22×C42C2311yescharacteristic
269#401C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#399C2314yes—
280#399C2314yes—
281#399C2314yes—
282#399C2314yes—
283#399C2314yes—
284#399C2314yes—
285#399C2314yes—
286#399C2314yes—
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#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#394C2314yes—
355#394C2314yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#393C2314yes—
381#392C2314yes—
382#392C2314yes—
383#392C2314yes—
384#392C2314yes—
385#392C2314yes—
386#392C2314yes—
387#392C2314yes—
388#392C2314yes—
389#391C2312yes—
390#391C2312yes—
391#391C2312yes—
392#391C2312yes—
393#390C2312yes—
394#390C2312yes—
395#390C2312yes—
396#390C2314yes—
397#390C2314yes—
398#390C2314yes—
399#390C2314yes—
400#390C2312yes—
401#390C2314yes—
402#390C2314yes—
403#390C2314yes—
404#389C2312yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
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#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#386C2314yes—
478#386C2314yes—
479#386C2314yes—
480#386C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2314yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#383C2314yes—
522#383C2314yes—
523#382C2312yes—
524#382C2312yes—
525#382C2311yescharacteristic
526#382C2311yescharacteristic
527#382C2314yes—
528#382C2314yes—
529#382C2314yes—
530#382C2314yes—
531#382C2312yes—
532#382C2314yes—
533#382C2312yes—
534#382C2312yes—
535#382C2314yes—
536#382C2314yes—
537#381C2314yes—
538#381C2314yes—
539#380C2314yes—
540#380C2314yes—
541#380C2314yes—
542#380C2314yes—
543#380C2314yes—
544#380C2314yes—
545#380C2314yes—
546#380C2314yes—
547#380C2314yes—
548C4×C4⋊C4C2314yes—
549C4×C4⋊C4C2314yes—
550C4×C4⋊C4C2314yes—
551C4×C4⋊C4C2314yes—
552C4×C4⋊C4C2312yes—
553C4×C4⋊C4C2312yes—
554C4×C4⋊C4C2312yes—
555C4×C4⋊C4C2312yes—
556C4×C4⋊C4C2314yes—
557C4×C4⋊C4C2312yes—
558C4×C4⋊C4C2312yes—
559C4×C4⋊C4C2314yes—
560C4×C4⋊C4C2314yes—
561C4×C22⋊C4C2312yes—
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—
571C4×C22⋊C4C2314yes—
572C4×C22⋊C4C2314yes—
573C4×C22⋊C4C2312yes—
574C4×C22⋊C4C2314yes—
575C4×C22⋊C4C2314yes—
576#376C2312yes—
577#376C2314yes—
578C2×#95C2314yes—
579C2×#95C2314yes—
580C2×#95C2314yes—
581C2×#95C2314yes—
582C2×#95C2314yes—
583C43C2312yes—
584C2×#41—28no—
585C2×#41—44no—
586C2×#41—44no—
587C22×Q8C2412yes—
588C22×Q8C2412yes—
589C22×D4C2414yes—
590C22×D4C2414yes—
591C22×D4C2412yes—
592C22×D4C2412yes—
593C22×D4C2414yes—
594C22×D4C2414yes—
595C22×D4C2414yes—
596C22×D4C2414yes—
597C22×D4C2414yes—
598C22×D4C2414yes—
599C23×C4C2411yescharacteristic
600C23×C4C2414yes—
601C23×C4C2414yes—
602C23×C4C2414yes—
603C23×C4C2414yes—
604C23×C4C2414yes—
605C23×C4C2414yes—
606C23×C4C2414yes—
607C23×C4C2414yes—
608C23×C4C2414yes—
609C23×C4C2412yes—
610C4⋊Q8—24no—
611#127—24no—
612#126—216no—
613#126—48no—
614#126—48no—
615#126—84no—
616#125—28no—
617#125—48no—
618#124—28no—
619#124—28no—
620#123—216no—
621#123—48no—
622#123—48no—
623#123—84no—
624#123—84no—
625#123—84no—
626C22⋊Q8—28no—
627#121—28no—
628#121—216no—
629#121—48no—
630#121—48no—
631#121—48no—
632#121—48no—
633#121—48no—
634#121—48no—
635#121—84no—
636#121—84no—
637#121—84no—
638#121—84no—
639C4×Q8—28no—
640C4×Q8—44no—
641C4×Q8—44no—
642C4×Q8—82no—
643C4×Q8—82no—
644C4×D4—216no—
645C4×D4—216no—
646C4×D4—216no—
647C4×D4—28no—
648C4×D4—216no—
649C4×D4—44no—
650C4×D4—44no—
651C4×D4—48no—
652C4×D4—48no—
653C4×D4—48no—
654C4×D4—84no—
655C4×D4—82no—
656C4×D4—82no—
657#117—24no—
658#117—216no—
659#117—48no—
660#117—48no—
661#117—42no—
662#117—84no—
663C2×C4⋊C4—48no—
664C2×C4⋊C4—44no—
665C2×C4⋊C4—48no—
666C2×C4⋊C4—84no—
667C2×C4⋊C4—82no—
668C2×C4⋊C4—82no—
669C2×C4⋊C4—84no—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C22⋊C4C2411yescharacteristic
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2411yescharacteristic
760C2×C42#4118yes—
761C2×C42C2414yes—
762C2×C42C2412yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2414yes—
767C2×C42C2414yes—
768C2×C42C2412yes—
769C2×C42C2412yes—
770C2×C42C2412yes—
771C2×C42C2414yes—
772C2×C42C2414yes—
773C2×C42C2412yes—
774C2×C42C2412yes—
775C2×C42C2414yes—
776C2×C42C2411yescharacteristic
777C2×C42C2412yes—
778C2×C42C2411yescharacteristic
779#95C2412yes—
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#95C2412yes—
799#95C2414yes—
800#95C2414yes—
801#95C2412yes—
802#95C2412yes—
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—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829C24C2514yes—
830C24C2514yes—
831C24C2511yescharacteristic
832#41—432no—
833C2×Q8—24no—
834C2×Q8—24no—
835C2×Q8—42no—
836C2×Q8—42no—
837C2×Q8—42no—
838C2×Q8—42no—
839C2×D4—28no—
840C2×D4—28no—
841C2×D4—28no—
842C2×D4—28no—
843C2×D4—28no—
844C2×D4—28no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—28no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—28no—
872C22×C4—28no—
873C22×C4—28no—
874C22×C4—28no—
875C22×C4—28no—
876C22×C4—28no—
877C22×C4—28no—
878C22×C4—44no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4C2×#4114yes—
901C22×C4C2×#4118yes—
902C22×C4C2512yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2514yes—
908C22×C4C2514yes—
909C22×C4C2512yes—
910C22×C4C2512yes—
911C22×C4C2514yes—
912C22×C4C2514yes—
913C22×C4C2514yes—
914C22×C4C2514yes—
915C22×C4C2512yes—
916C22×C4C2512yes—
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C22×C4C2512yes—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—28no—
923C4⋊C4—24no—
924C4⋊C4—28no—
925C4⋊C4—24no—
926C4⋊C4—28no—
927C4⋊C4—24no—
928C4⋊C4—28no—
929C4⋊C4—28no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—44no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—41no—
955C4⋊C4—41no—
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—
966C22⋊C4—28no—
967C22⋊C4—22no—
968C22⋊C4—24no—
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—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
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—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4H(5,𝔽2)14yes—
1010C42—28no—
1011C42—24no—
1012C42—28no—
1013C42—28no—
1014C42—42no—
1015C42—42no—
1016C42—44no—
1017C42—42no—
1018C42—44no—
1019C42—44no—
1020C42—44no—
1021C42—44no—
1022C42—42no—
1023C42—42no—
1024C42—44no—
1025C42C2×#4114yes—
1026C42C2×#4118yes—
1027C42C2×#4114yes—
1028C23—22no—
1029C23—22no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—24no—
1034C23—24no—
1035C23—24no—
1036C23—24no—
1037C23—24no—
1038C23—24no—
1039C23—24no—
1040C23—24no—
1041C23—24no—
1042C23—24no—
1043C23—24no—
1044C23C22×#4112yes—
1045C23C2×H(5,𝔽2)12yes—
1046C23#58512yes—
1047C23C2611yescharacteristic
1048Q8—48no—
1049Q8—48no—
1050D4—48no—
1051D4—48no—
1052D4—416no—
1053D4—416no—
1054D4—88no—
1055D4—88no—
1056D4—88no—
1057D4—164no—
1058D4—164no—
1059D4—164no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—28no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
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—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—48no—
1111C2×C4—416no—
1112C2×C4—88no—
1113C2×C4—88no—
1114C2×C4—88no—
1115C2×C4—88no—
1116C2×C4—88no—
1117C2×C4—88no—
1118C2×C4—164no—
1119C2×C4—164no—
1120C2×C4C22×#4114yes—
1121C2×C4C22×#4114yes—
1122C2×C4C22×#4112yes—
1123C2×C4C22×#4112yes—
1124C2×C4C2×H(5,𝔽2)14yes—
1125C22—24no—
1126C22—22no—
1127C22—22no—
1128C22—24no—
1129C22—44no—
1130C22—44no—
1131C22—44no—
1132C22—44no—
1133C22—44no—
1134C22—44no—
1135C22—44no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22#346014yes—
1144C22C23×#4111yescharacteristic
1145C22C22×H(5,𝔽2)11yescharacteristic
1146C22C2×#58511yescharacteristic
1147C22H(7,𝔽2)12yes—
1148C222−1+612yes—
1149C4—24no—
1150C4—24no—
1151C4—24no—
1152C4—22no—
1153C4—22no—
1154C4—44no—
1155C4—44no—
1156C4—44no—
1157C4—44no—
1158C4—42no—
1159C4—44no—
1160C4—44no—
1161C4—42no—
1162C4—42no—
1163C4—44no—
1164C4—44no—
1165C4—44no—
1166C4—44no—
1167C2—24no—
1168C2—84no—
1169C2—84no—
1170C2C2×#346011yescharacteristic
1171C2#6285612yes—
1172C2#6304912yes—
1173C2#6305511yescharacteristic
1174C2#6306811yescharacteristic
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. #42343C2semidirect
2. #42051C2semidirect
3. #42024C2semidirect
4. #41663C2semidirect
5. #41653C2semidirect
6. #40999C2semidirect
7. #40985C2semidirect
8. #40669C2semidirect
9. #40667C2semidirect
10. #37610C2semidirect
11. #37608C2semidirect
12. #37604C2semidirect
13. #37600C2semidirect
14. #37554C2semidirect
15. #36695C2semidirect
16. C2×#2845C2semidirect
17. #35953C2semidirect
18. #35859C2semidirect
19. #35807C2semidirect
20. #34229C2semidirect
21. #34208C2semidirect

Maximal subgroups

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

subgroupindex
#423432
#420512
#420242
#416632
#416532
#409992
#409852
#406692
#406672
#376102
#376082
#376042
#376002
#375542
#366952
C2×#28452
#359532
#358592
#358072
#342292
#342082