Finite Group Databasebeta

← #7717613

Subgroups — #7717613

Order 512.

4432 conjugacy classes of subgroups.

The subgroup lattice has 1177 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51239C214yesmaximal, complemented
2#51238C214yesmaximal, complemented
3#51237C214yesmaximal, complemented
4#51236C214yesmaximal, complemented
5#44808C214yesmaximal, complemented
6#44805C214yesmaximal, complemented
7#44331C214yesmaximal, complemented
8#44185C214yesmaximal, complemented
9#39184C214yesmaximal, complemented
10#38211C214yesmaximal, complemented
11#38209C214yesmaximal, complemented
12#36979C211yesmaximal, characteristic, complemented
13#36978C211yesmaximal, characteristic, complemented
14#36728C211yesmaximal, characteristic, complemented
15#36727C211yesmaximal, characteristic
16#36336C214yesmaximal, complemented
17#35302C212yesmaximal, complemented
18#35181C211yesmaximal, characteristic, complemented
19#35042C212yesmaximal, complemented
20#35034C212yesmaximal, complemented
21#34594C211yesmaximal, characteristic, complemented
22#34401C212yesmaximal, complemented
23C2×#2347C211yesmaximal, characteristic, complemented
24C2×#529C2212yes—
25C22×#117C2211yescharacteristic
26#2855C2212yes—
27#2854C2212yes—
28#2852C2214yes—
29#2852C2214yes—
30#2851C2214yes—
31#2848C2212yes—
32#2847C2212yes—
33#2803C2214yes—
34#2802C2214yescomplemented
35#2801C2214yes—
36#2801C2214yescomplemented
37#2800C2214yes—
38#2800C2214yes—
39#2800C2214yes—
40#2795C2214yes—
41#2793C2214yes—
42#2790C2214yescomplemented
43#2779C2214yes—
44#2777C2214yescomplemented
45#2777C2214yescomplemented
46#2776C2214yescomplemented
47#2772C2214yes—
48#2772C2214yes—
49#2772C2214yescomplemented
50#2769C2214yescomplemented
51#2766C2214yescomplemented
52#2762C2214yescomplemented
53#2761C2214yes—
54#2758C2214yescomplemented
55#2757C2214yes—
56#2756C2214yescomplemented
57#2753C2214yes—
58#2753C2214yes—
59#2749C2214yescomplemented
60#2748C2214yes—
61#2747C2214yes—
62#2741C2214yes—
63#2738C2214yescomplemented
64#2725C2214yes—
65#2725C2214yescomplemented
66#2722C2214yes—
67#2718C2214yescomplemented
68#2711C2214yes—
69#2704C2214yes—
70#2703C2214yes—
71#2690C2214yes—
72#2671C2214yes—
73#2664C2214yescomplemented
74#2662C2214yescomplemented
75#2659C2211yescharacteristic
76#2656C2211yescharacteristic
77#2646C2211yescharacteristic
78#2646C2211yescharacteristic
79#2646C2212yes—
80#2639C2212yes—
81#2629C2212yes—
82#2629C2212yes—
83#2623C2214yes—
84#2622C2214yes—
85#2620C2212yes—
86#2620C2212yes—
87#2618C2214yes—
88#2609C2214yes—
89#2609C2214yes—
90#2606C2214yescomplemented
91#2606C2214yescomplemented
92#2601C2214yes—
93#2601C2214yes—
94#2601C2214yes—
95#2601C2214yescomplemented
96#2597C2214yescomplemented
97#2596C2214yescomplemented
98#2590C2214yescomplemented
99#2590C2214yescomplemented
100#2589C2214yescomplemented
101#2587C2214yescomplemented
102#2579C2214yes—
103#2578C2214yes—
104#2577C2214yes—
105#2577C2214yescomplemented
106#2575C2214yescomplemented
107#2571C2214yescomplemented
108#2570C2214yescomplemented
109#2570C2214yescomplemented
110#2560C2214yes—
111#2559C2214yes—
112#2559C2214yes—
113#2558C2214yescomplemented
114#2552C2214yescomplemented
115#2534C2214yes—
116#2533C2214yescomplemented
117#2532C2214yescomplemented
118#2531C2214yes—
119#2531C2214yes—
120#2530C2214yes—
121#2529C2214yes—
122#2529C2214yes—
123#2529C2214yescomplemented
124#2529C2214yescomplemented
125#2526C2214yes—
126#2525C2214yes—
127#2525C2214yes—
128#2524C2214yescomplemented
129#2522C2214yescomplemented
130#2519C2214yescomplemented
131#2518C2214yes—
132#2518C2214yes—
133#2518C2214yescomplemented
134#2516C2214yes—
135#2515C2214yescomplemented
136#2512C2214yes—
137#2510C2214yes—
138#2507C2214yescomplemented
139#2505C2214yes—
140#2500C2214yes—
141#2493C2214yes—
142#2480C2214yes—
143#2479C2214yescomplemented
144#2478C2214yescomplemented
145#2477C2214yes—
146#2476C2214yes—
147#2475C2214yescomplemented
148#2473C2214yes—
149#2470C2214yescomplemented
150#2468C2214yescomplemented
151#2467C2214yes—
152#2444C2214yes—
153#2444C2214yes—
154#2443C2214yes—
155#2441C2214yescomplemented
156#2425C2214yes—
157#2424C2214yes—
158#2413C2214yes—
159#2411C2214yes—
160#2396C2214yescomplemented
161#2392C2214yescomplemented
162#2383C2214yescomplemented
163#2383C2214yescomplemented
164#2373C2214yescomplemented
165#2371C2214yescomplemented
166#2359C2214yes—
167#2359C2214yes—
168#2359C2214yescomplemented
169#2353C2214yes—
170#2349C2214yes—
171#2347C2214yes—
172#2347C2214yes—
173#2347C2214yes—
174#2347C2214yes—
175#2347C2214yescomplemented
176#2343C2214yescomplemented
177#2343C2214yescomplemented
178#2337C2214yescomplemented
179#2336C2214yescomplemented
180#2329C2212yes—
181#2329C2212yes—
182#2325C2212yes—
183#2325C2212yes—
184#2324C2212yes—
185#2324C2212yes—
186#2323C2212yes—
187#2323C2212yes—
188#2322C2214yes—
189#2321C2214yes—
190#2320C2214yescomplemented
191#2318C2214yescomplemented
192#2317C2214yes—
193C4×#121C2214yes—
194C2×#389C2212yes—
195#2290C2214yes—
196#2290C2214yes—
197C2×#388C2212yes—
198C2×#388C2212yes—
199#2285C2212yes—
200C2×#383C2211yescharacteristic
201C2×#383C2211yescharacteristic
202C2×#380C2211yescharacteristic
203C2×C4×C4⋊C4C2211yescharacteristic
204C2×C4×C4⋊C4C2211yescharacteristic
205C2×C4×C4⋊C4C2212yes—
206C2×C4×C22⋊C4C2211yescharacteristic
207C24×C4C2311yescharacteristic
208#529—216no—
209C2×#126C2314yes—
210C2×#126C2314yes—
211C2×#126C2314yes—
212C2×#126C2314yes—
213C2×#125C2312yes—
214C2×#125C2314yes—
215C2×#125C2314yes—
216C2×#124C2312yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×#121C2312yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#121C2314yes—
227C2×#121C2314yes—
228C2×#120C2314yes—
229C2×C4×Q8C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×#117—28no—
236C2×#117C2312yes—
237C2×#117C2312yes—
238C2×#117C2314yes—
239C2×#117C2312yes—
240C2×#117C2312yes—
241C2×#117C2314yes—
242C2×#117C2314yes—
243C2×#117C2314yes—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C22⋊C4C2311yescharacteristic
250C22×C22⋊C4C2311yescharacteristic
251C22×C22⋊C4C2312yes—
252C22×C22⋊C4C2312yes—
253C22×C42C2311yescharacteristic
254C22×C42C2312yes—
255C22×C42C2312yes—
256C22×C42C2312yes—
257C22×C42C2311yescharacteristic
258#401C2314yes—
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#399C2314yes—
275#399C2314yes—
276#399C2314yes—
277#399C2314yes—
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#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#397C2314yes—
311#396C2314yes—
312#396C2314yes—
313#396C2314yes—
314#396C2314yes—
315#396C2314yes—
316#396C2314yes—
317#396C2314yes—
318#396C2314yes—
319#396C2314yes—
320#396C2314yes—
321#396C2314yes—
322#396C2314yes—
323#396C2314yes—
324#396C2314yes—
325#396C2314yes—
326#395C2314yes—
327#394C2314yes—
328#394C2314yes—
329#394C2314yes—
330#394C2314yes—
331#394C2314yes—
332#394C2314yes—
333#394C2314yes—
334#394C2314yes—
335#394C2314yes—
336#394C2314yes—
337#394C2314yes—
338#394C2314yes—
339#394C2314yes—
340#394C2314yes—
341#394C2314yes—
342#394C2314yes—
343#393C2314yes—
344#392C2314yes—
345#392C2314yes—
346#391C2314yes—
347#391C2314yes—
348#391C2312yes—
349#391C2312yes—
350#390C2314yes—
351#390C2314yes—
352#390C2312yes—
353#390C2312yes—
354#390C2314yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2312yes—
371#389C2314yes—
372#389C2312yes—
373#389C2312yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
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#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
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#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#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#386C2314yes—
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#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#385C2314yes—
513#385C2314yes—
514#384C2314yes—
515#384C2314yes—
516#384C2312yes—
517#384C2312yes—
518#383C2314yes—
519#383C2314yes—
520#383C2314yes—
521#383C2314yes—
522#383C2314yes—
523#383C2314yes—
524#383C2314yes—
525#383C2314yes—
526#382C2314yes—
527#382C2314yes—
528#382C2314yes—
529#382C2314yes—
530#382C2314yes—
531#382C2314yes—
532#381C2314yes—
533#381C2314yes—
534#381C2314yes—
535#380C2314yes—
536#380C2312yes—
537#380C2312yes—
538#380C2312yes—
539#380C2314yes—
540#380C2312yes—
541#380C2312yes—
542#380C2312yes—
543#380C2314yes—
544#380C2314yes—
545#380C2314yes—
546#380C2314yes—
547#379C2314yes—
548C4×C4⋊C4C2314yes—
549C4×C4⋊C4C2312yes—
550C4×C4⋊C4C2312yes—
551C4×C4⋊C4C2314yes—
552C4×C4⋊C4C2314yes—
553C4×C4⋊C4C2314yes—
554C4×C4⋊C4C2314yes—
555C4×C4⋊C4C2314yes—
556C4×C4⋊C4C2314yes—
557C4×C4⋊C4C2314yes—
558C4×C4⋊C4C2314yes—
559C4×C4⋊C4C2314yes—
560C4×C4⋊C4C2314yes—
561C4×C4⋊C4C2314yes—
562C4×C4⋊C4C2314yes—
563C4×C4⋊C4C2314yes—
564C4×C4⋊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⋊C4C2314yes—
574C4×C22⋊C4C2314yes—
575C4×C22⋊C4C2314yes—
576#376C2314yes—
577#376C2314yes—
578#376C2314yes—
579C2×#95C2314yes—
580C2×#95C2311yescharacteristic
581C2×#95C2311yescharacteristic
582C2×#95C2312yes—
583C2×#95C2312yes—
584C2×#95C2311yescharacteristic
585C2×#95C2311yescharacteristic
586C2×#95C2312yes—
587C2×#95C2312yes—
588C25C2411yescharacteristic
589C22×Q8C2412yes—
590C22×D4C2414yes—
591C22×D4C2412yes—
592C22×D4C2414yes—
593C22×D4C2414yes—
594C22×D4C2414yes—
595C23×C4—24no—
596C23×C4—44no—
597C23×C4C2411yescharacteristic
598C23×C4C2411yescharacteristic
599C23×C4C2412yes—
600C23×C4C2412yes—
601C23×C4C2411yescharacteristic
602C23×C4C2412yes—
603C23×C4C2412yes—
604C23×C4C2412yes—
605C23×C4C2411yescharacteristic
606C23×C4C2412yes—
607C23×C4C2414yes—
608C23×C4C2414yes—
609C23×C4C2414yes—
610C23×C4C2411yescharacteristic
611C23×C4C2411yescharacteristic
612#126—216no—
613#126—48no—
614#126—84no—
615#126—84no—
616#125—28no—
617#125—48no—
618#125—84no—
619#124—28no—
620#123—216no—
621#123—48no—
622#123—48no—
623C22⋊Q8—28no—
624C22⋊Q8—44no—
625C22⋊Q8—44no—
626#121—28no—
627#121—44no—
628#121—44no—
629#121—48no—
630#121—84no—
631#120—48no—
632C4×Q8—28no—
633C4×D4—216no—
634C4×D4—28no—
635C4×D4—48no—
636C4×D4—48no—
637C4×D4—84no—
638#117—28no—
639#117—28no—
640#117—28no—
641#117—28no—
642#117—216no—
643#117—48no—
644#117—48no—
645#117—84no—
646C2×C4⋊C4—24no—
647C2×C4⋊C4—24no—
648C2×C4⋊C4—44no—
649C2×C4⋊C4—44no—
650C2×C4⋊C4—44no—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C22⋊C4—24no—
699C2×C22⋊C4—24no—
700C2×C22⋊C4—44no—
701C2×C22⋊C4—82no—
702C2×C22⋊C4C2411yescharacteristic
703C2×C22⋊C4C2411yescharacteristic
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2411yescharacteristic
707C2×C22⋊C4C2411yescharacteristic
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×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×C42—24no—
744C2×C42—44no—
745C2×C42—82no—
746C2×C42—82no—
747C2×C42#4118yes—
748C2×C42C2412yes—
749C2×C42C2412yes—
750C2×C42C2414yes—
751C2×C42C2414yes—
752C2×C42C2414yes—
753C2×C42C2414yes—
754C2×C42C2414yes—
755C2×C42C2414yes—
756C2×C42C2414yes—
757C2×C42C2414yes—
758C2×C42C2414yes—
759C2×C42C2414yes—
760C2×C42C2414yes—
761C2×C42C2414yes—
762C2×C42C2414yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2412yes—
766C2×C42C2412yes—
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—
821C24—22no—
822C24—24no—
823C24—41no—
824C24—42no—
825C24—41no—
826C24C2511yescharacteristic
827C24C2511yescharacteristic
828C24C2514yes—
829C24C2511yescharacteristic
830C2×Q8—24no—
831C2×Q8—42no—
832C2×Q8—42no—
833C2×D4—28no—
834C2×D4—28no—
835C2×D4—28no—
836C2×D4—24no—
837C2×D4—44no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—44no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—44no—
846C2×D4—44no—
847C2×D4—44no—
848C22×C4—22no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—28no—
863C22×C4—42no—
864C22×C4—41no—
865C22×C4—42no—
866C22×C4—41no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—41no—
871C22×C4—41no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—42no—
885C22×C4—44no—
886C22×C4—416no—
887C22×C4C2×#4114yes—
888C22×C4C2×#4114yes—
889C22×C4C2×#4114yes—
890C22×C4C2514yes—
891C22×C4C2514yes—
892C22×C4C2514yes—
893C22×C4C2512yes—
894C22×C4C2514yes—
895C22×C4C2514yes—
896C22×C4C2514yes—
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C22×C4C2514yes—
900C22×C4C2514yes—
901C22×C4C2514yes—
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2511yescharacteristic
905C22×C4C2512yes—
906C22×C4C2512yes—
907C22×C4C2511yescharacteristic
908C22×C4C2512yes—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—28no—
914C4⋊C4—28no—
915C4⋊C4—24no—
916C4⋊C4—28no—
917C4⋊C4—24no—
918C4⋊C4—28no—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
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—42no—
939C4⋊C4—42no—
940C4⋊C4—44no—
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—44no—
955C4⋊C4—44no—
956C22⋊C4—28no—
957C22⋊C4—28no—
958C22⋊C4—28no—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—28no—
968C22⋊C4—28no—
969C22⋊C4—28no—
970C22⋊C4—28no—
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—
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—
997C42—24no—
998C42—24no—
999C42—28no—
1000C42—28no—
1001C42—44no—
1002C42—44no—
1003C42—44no—
1004C42—44no—
1005C42—44no—
1006C42—44no—
1007C42—44no—
1008C42—44no—
1009C42—44no—
1010C42—44no—
1011C42—44no—
1012C42—44no—
1013C42—44no—
1014C42C2×#4118yes—
1015C42C2×#4118yes—
1016C23—22no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—24no—
1022C23—24no—
1023C23—24no—
1024C23—22no—
1025C23—22no—
1026C23—24no—
1027C23—24no—
1028C23—22no—
1029C23—22no—
1030C23—21no—
1031C23—24no—
1032C23—21no—
1033C23—21no—
1034C23—24no—
1035C23—21no—
1036C23—44no—
1037C23—44no—
1038C23—44no—
1039C23—84no—
1040C23—84no—
1041C23C22×#4112yes—
1042C23#58514yes—
1043C23C2611yescharacteristic
1044Q8—84no—
1045D4—416no—
1046D4—84no—
1047D4—88no—
1048D4—164no—
1049D4—164no—
1050C2×C4—28no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—28no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
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—22no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—22no—
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—22no—
1102C2×C4—44no—
1103C2×C4—44no—
1104C2×C4—48no—
1105C2×C4—48no—
1106C2×C4—44no—
1107C2×C4—48no—
1108C2×C4—44no—
1109C2×C4—88no—
1110C2×C4—84no—
1111C2×C4—84no—
1112C2×C4—84no—
1113C2×C4—88no—
1114C2×C4—88no—
1115C2×C4C22×#4112yes—
1116C2×C4C22×#4114yes—
1117C2×C4C22×#4114yes—
1118C2×C4C22×#4112yes—
1119C2×C4#58514yes—
1120C22—22no—
1121C22—22no—
1122C22—24no—
1123C22—24no—
1124C22—44no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—44no—
1130C22—44no—
1131C22—41no—
1132C22—41no—
1133C22—44no—
1134C22—42no—
1135C22—44no—
1136C22—42no—
1137C22—44no—
1138C22—44no—
1139C22—42no—
1140C22—42no—
1141C22—88no—
1142C22#351214yes—
1143C22C23×#4111yescharacteristic
1144C22C2×#58512yes—
1145C22C2×#58512yes—
1146C22H(7,𝔽2)11yescharacteristic
1147C222−1+611yescharacteristic
1148C4—24no—
1149C4—24no—
1150C4—24no—
1151C4—22no—
1152C4—22no—
1153C4—41no—
1154C4—41no—
1155C4—44no—
1156C4—44no—
1157C4—42no—
1158C4—44no—
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4—44no—
1164C4—44no—
1165C4—44no—
1166C4—44no—
1167C2—24no—
1168C2—84no—
1169C2—81no—
1170C2—81no—
1171C2C2×#351211yescharacteristic
1172C2#6281411yescharacteristic
1173C2#6285611yescharacteristic
1174C2#6291112yes—
1175C2#6293512yes—
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. #51239C2semidirect
2. #51238C2semidirect
3. #51237C2semidirect
4. #51236C2semidirect
5. #44808C2semidirect
6. #44805C2semidirect
7. #44331C2semidirect
8. #44185C2semidirect
9. #39184C2semidirect
10. #38211C2semidirect
11. #38209C2semidirect
12. #36979C2semidirect
13. #36978C2semidirect
14. #36728C2semidirect
16. #36336C2semidirect
17. #35302C2semidirect
18. #35181C2semidirect
19. #35042C2semidirect
20. #35034C2semidirect
21. #34594C2semidirect
22. #34401C2semidirect
23. C2×#2347C2semidirect
34. #2802C22semidirect
36. #2801C22semidirect
42. #2790C22semidirect
44. #2777C22semidirect
45. #2777C22semidirect
46. #2776C22semidirect
49. #2772C22semidirect
50. #2769C22semidirect
51. #2766C22semidirect
52. #2762C22semidirect
54. #2758C22semidirect
56. #2756C22semidirect
59. #2749C22semidirect
63. #2738C22semidirect
65. #2725C22semidirect
67. #2718C22semidirect
73. #2664C22semidirect
74. #2662C22semidirect
90. #2606C22semidirect
91. #2606C22semidirect
95. #2601C22semidirect
96. #2597C22semidirect
97. #2596C22semidirect
98. #2590C22semidirect
99. #2590C22semidirect
100. #2589C22semidirect
101. #2587C22semidirect
105. #2577C22semidirect
106. #2575C22semidirect
107. #2571C22semidirect
108. #2570C22semidirect
109. #2570C22semidirect
113. #2558C22semidirect
114. #2552C22semidirect
116. #2533C22semidirect
117. #2532C22semidirect
123. #2529C22semidirect
124. #2529C22semidirect
128. #2524C22semidirect
129. #2522C22semidirect
130. #2519C22semidirect
133. #2518C22semidirect
135. #2515C22semidirect
138. #2507C22semidirect
143. #2479C22semidirect
144. #2478C22semidirect
147. #2475C22semidirect
149. #2470C22semidirect
150. #2468C22semidirect
155. #2441C22semidirect
160. #2396C22semidirect
161. #2392C22semidirect
162. #2383C22semidirect
163. #2383C22semidirect
164. #2373C22semidirect
165. #2371C22semidirect
168. #2359C22semidirect
175. #2347C22semidirect
176. #2343C22semidirect
177. #2343C22semidirect
178. #2337C22semidirect
179. #2336C22semidirect
190. #2320C22semidirect
191. #2318C22semidirect

Maximal subgroups

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

subgroupindex
#512392
#512382
#512372
#512362
#448082
#448052
#443312
#441852
#391842
#382112
#382092
#369792
#369782
#367282
#367272
#363362
#353022
#351812
#350422
#350342
#345942
#344012
C2×#23472