Finite Group Databasebeta

← #7717544

Subgroups — #7717544

Order 512.

4486 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#50931C214yesmaximal, complemented
2#50930C214yesmaximal, complemented
3#50929C214yesmaximal, complemented
4#50928C214yesmaximal, complemented
5#44811C214yesmaximal, complemented
6#44806C214yesmaximal, complemented
7#44349C214yesmaximal, complemented
8#44163C214yesmaximal, complemented
9#39051C214yesmaximal, complemented
10#39049C214yesmaximal, complemented
11#38968C214yesmaximal, complemented
12#36977C211yesmaximal, characteristic, complemented
13#36976C211yesmaximal, characteristic, complemented
14#36732C211yesmaximal, characteristic, complemented
15#36731C211yesmaximal, characteristic
16#36520C214yesmaximal, complemented
17#35302C212yesmaximal, complemented
18#35181C211yesmaximal, characteristic, complemented
19#35099C212yesmaximal, complemented
20#34997C212yesmaximal, complemented
21#34594C211yesmaximal, characteristic, complemented
22#34401C212yesmaximal, complemented
23C2×#2343C211yesmaximal, characteristic, complemented
24C2×#529C2212yes—
25C22×#117C2211yescharacteristic
26#2855C2212yes—
27#2854C2212yes—
28#2853C2214yes—
29#2851C2214yes—
30#2849C2214yes—
31#2848C2212yes—
32#2847C2212yes—
33#2795C2214yescomplemented
34#2793C2214yescomplemented
35#2790C2214yes—
36#2783C2214yescomplemented
37#2780C2214yes—
38#2779C2214yescomplemented
39#2777C2214yescomplemented
40#2776C2214yescomplemented
41#2773C2214yescomplemented
42#2772C2214yescomplemented
43#2772C2214yescomplemented
44#2768C2214yescomplemented
45#2766C2214yescomplemented
46#2766C2214yescomplemented
47#2766C2214yescomplemented
48#2765C2214yes—
49#2765C2214yescomplemented
50#2762C2214yescomplemented
51#2761C2214yes—
52#2761C2214yescomplemented
53#2757C2214yes—
54#2755C2214yescomplemented
55#2753C2214yes—
56#2753C2214yescomplemented
57#2744C2214yes—
58#2743C2214yes—
59#2740C2214yes—
60#2739C2214yes—
61#2739C2214yescomplemented
62#2739C2214yescomplemented
63#2719C2214yescomplemented
64#2719C2214yescomplemented
65#2718C2214yes—
66#2707C2214yescomplemented
67#2706C2214yescomplemented
68#2701C2214yes—
69#2699C2214yes—
70#2698C2214yes—
71#2689C2214yes—
72#2688C2214yes—
73#2664C2214yescomplemented
74#2662C2214yescomplemented
75#2659C2211yescharacteristic
76#2656C2211yescharacteristic
77#2646C2212yes—
78#2646C2211yescharacteristic
79#2646C2211yescharacteristic
80#2643C2214yes—
81#2643C2214yes—
82#2639C2212yes—
83#2629C2212yes—
84#2629C2212yes—
85#2620C2212yes—
86#2620C2212yes—
87#2618C2214yes—
88#2609C2214yes—
89#2609C2214yes—
90#2608C2214yes—
91#2608C2214yescomplemented
92#2602C2214yes—
93#2602C2214yes—
94#2601C2214yes—
95#2601C2214yes—
96#2594C2214yescomplemented
97#2590C2214yescomplemented
98#2587C2214yes—
99#2587C2214yes—
100#2579C2214yes—
101#2578C2214yes—
102#2576C2214yes—
103#2576C2214yes—
104#2576C2214yes—
105#2576C2214yescomplemented
106#2571C2214yescomplemented
107#2570C2214yescomplemented
108#2570C2214yescomplemented
109#2570C2214yescomplemented
110#2566C2214yes—
111#2559C2214yes—
112#2558C2214yes—
113#2558C2214yes—
114#2552C2214yescomplemented
115#2534C2214yes—
116#2533C2214yescomplemented
117#2532C2214yescomplemented
118#2531C2214yescomplemented
119#2530C2214yescomplemented
120#2530C2214yescomplemented
121#2529C2214yescomplemented
122#2528C2214yescomplemented
123#2528C2214yescomplemented
124#2527C2214yescomplemented
125#2526C2214yescomplemented
126#2524C2214yescomplemented
127#2518C2214yes—
128#2518C2214yescomplemented
129#2517C2214yescomplemented
130#2515C2214yes—
131#2515C2214yes—
132#2515C2214yescomplemented
133#2515C2214yescomplemented
134#2510C2214yes—
135#2505C2214yes—
136#2505C2214yes—
137#2497C2214yescomplemented
138#2493C2214yes—
139#2493C2214yes—
140#2493C2214yescomplemented
141#2488C2214yes—
142#2480C2214yes—
143#2473C2214yes—
144#2466C2214yes—
145#2460C2214yes—
146#2460C2214yescomplemented
147#2457C2214yes—
148#2450C2214yes—
149#2444C2214yes—
150#2444C2214yes—
151#2443C2214yes—
152#2425C2214yes—
153#2425C2214yes—
154#2424C2214yes—
155#2422C2214yes—
156#2419C2214yes—
157#2419C2214yescomplemented
158#2413C2214yes—
159#2411C2214yes—
160#2396C2214yescomplemented
161#2392C2214yescomplemented
162#2383C2214yescomplemented
163#2383C2214yescomplemented
164#2374C2214yes—
165#2373C2214yes—
166#2364C2214yes—
167#2359C2214yes—
168#2359C2214yes—
169#2353C2214yes—
170#2353C2214yes—
171#2349C2214yes—
172#2347C2214yescomplemented
173#2343C2214yes—
174#2343C2214yes—
175#2343C2214yes—
176#2343C2214yes—
177#2343C2214yescomplemented
178#2337C2214yescomplemented
179#2336C2214yescomplemented
180#2329C2212yes—
181#2329C2212yes—
182#2325C2212yes—
183#2325C2212yes—
184#2324C2212yes—
185#2324C2212yes—
186#2323C2212yes—
187#2323C2212yes—
188#2320C2214yescomplemented
189#2318C2214yes—
190#2318C2214yes—
191#2318C2214yescomplemented
192#2317C2214yes—
193C4×#123C2214yes—
194C4×#121C2214yes—
195C4×#120C2214yes—
196C2×#387C2212yes—
197C2×#387C2212yes—
198C2×#385C2212yes—
199#2285C2212yes—
200C2×#383C2211yescharacteristic
201C2×#382C2211yescharacteristic
202C2×#381C2211yescharacteristic
203C2×C4×C4⋊C4C2211yescharacteristic
204C2×C4×C22⋊C4C2212yes—
205C2×#376C2211yescharacteristic
206C22×#95C2211yescharacteristic
207C24×C4C2311yescharacteristic
208C24×C4C2312yes—
209#529—216no—
210C2×#126C2314yes—
211C2×#126C2314yes—
212C2×#125C2312yes—
213C2×#125C2314yes—
214C2×#125C2314yes—
215C2×#124C2312yes—
216C2×#123C2314yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#121C2312yes—
227C2×#121C2314yes—
228C2×#121C2314yes—
229C2×#120C2314yes—
230C2×C4×Q8C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×#117—28no—
239C2×#117C2312yes—
240C2×#117C2312yes—
241C2×#117C2312yes—
242C2×#117C2312yes—
243C2×#117C2314yes—
244C2×#117C2314yes—
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C22⋊C4C2311yescharacteristic
250C22×C22⋊C4C2311yescharacteristic
251C22×C22⋊C4C2312yes—
252C22×C42C2311yescharacteristic
253C22×C42C2312yes—
254C22×C42C2312yes—
255C22×C42C2311yescharacteristic
256#401C2314yes—
257#401C2314yes—
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#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
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#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#396C2314yes—
327#396C2314yes—
328#395C2314yes—
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#393C2314yes—
342#392C2314yes—
343#392C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2312yes—
347#391C2312yes—
348#390C2314yes—
349#390C2314yes—
350#390C2312yes—
351#390C2312yes—
352#390C2314yes—
353#390C2314yes—
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#389C2314yes—
367#389C2312yes—
368#389C2312yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
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#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
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#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
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#386C2314yes—
475#386C2314yes—
476#386C2314yes—
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#385C2314yes—
497#385C2314yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#384C2314yes—
505#384C2314yes—
506#384C2312yes—
507#384C2312yes—
508#383C2314yes—
509#383C2314yes—
510#383C2314yes—
511#383C2314yes—
512#383C2314yes—
513#383C2314yes—
514#382C2314yes—
515#382C2314yes—
516#382C2314yes—
517#382C2314yes—
518#382C2314yes—
519#382C2314yes—
520#382C2314yes—
521#382C2314yes—
522#382C2314yes—
523#382C2314yes—
524#381C2314yes—
525#381C2314yes—
526#381C2314yes—
527#381C2314yes—
528#381C2314yes—
529#381C2314yes—
530#381C2314yes—
531#381C2314yes—
532#381C2314yes—
533#380C2314yes—
534#380C2314yes—
535#380C2314yes—
536#380C2312yes—
537#380C2312yes—
538#380C2314yes—
539#380C2312yes—
540#380C2312yes—
541#380C2312yes—
542#380C2312yes—
543#380C2314yes—
544#380C2314yes—
545#379C2314yes—
546C4×C4⋊C4C2314yes—
547C4×C4⋊C4C2312yes—
548C4×C4⋊C4C2312yes—
549C4×C4⋊C4C2314yes—
550C4×C4⋊C4C2314yes—
551C4×C4⋊C4C2314yes—
552C4×C4⋊C4C2314yes—
553C4×C4⋊C4C2314yes—
554C4×C4⋊C4C2314yes—
555C4×C4⋊C4C2314yes—
556C4×C4⋊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—
571C4×C22⋊C4C2314yes—
572#376C2314yes—
573#376C2314yes—
574#376C2314yes—
575C2×#95C2312yes—
576C2×#95C2312yes—
577C2×#95C2314yes—
578C2×#95C2311yescharacteristic
579C2×#95C2311yescharacteristic
580C2×#95C2314yes—
581C2×#95C2314yes—
582C2×#95C2312yes—
583C2×#95C2312yes—
584C2×#95C2311yescharacteristic
585C2×#95C2311yescharacteristic
586C2×#95C2312yes—
587C2×#95C2312yes—
588C25C2411yescharacteristic
589C22×Q8C2412yes—
590C22×D4C2414yes—
591C22×D4C2414yes—
592C22×D4C2414yes—
593C22×D4C2412yes—
594C22×D4C2414yes—
595C23×C4—24no—
596C23×C4—44no—
597C23×C4—44no—
598C23×C4—44no—
599C23×C4—82no—
600C23×C4C2411yescharacteristic
601C23×C4C2412yes—
602C23×C4C2412yes—
603C23×C4C2411yescharacteristic
604C23×C4C2411yescharacteristic
605C23×C4C2412yes—
606C23×C4C2412yes—
607C23×C4C2411yescharacteristic
608C23×C4C2412yes—
609C23×C4C2412yes—
610C23×C4C2414yes—
611C23×C4C2414yes—
612C23×C4C2414yes—
613C23×C4C2414yes—
614C23×C4C2414yes—
615C23×C4C2411yescharacteristic
616C23×C4C2411yescharacteristic
617#126—216no—
618#126—48no—
619#125—28no—
620#125—84no—
621#125—84no—
622#124—28no—
623#123—216no—
624#123—48no—
625#123—48no—
626#123—84no—
627#123—84no—
628C22⋊Q8—28no—
629C22⋊Q8—44no—
630C22⋊Q8—44no—
631#121—28no—
632#121—48no—
633#121—44no—
634#121—44no—
635#121—48no—
636#120—48no—
637C4×Q8—28no—
638C4×D4—216no—
639C4×D4—28no—
640C4×D4—48no—
641C4×D4—48no—
642C4×D4—48no—
643C4×D4—84no—
644C4×D4—84no—
645#117—28no—
646#117—28no—
647#117—28no—
648#117—28no—
649#117—216no—
650#117—48no—
651C2×C4⋊C4—24no—
652C2×C4⋊C4—24no—
653C2×C4⋊C4—44no—
654C2×C4⋊C4—82no—
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
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⋊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⋊C4C2414yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C22⋊C4—24no—
703C2×C22⋊C4—24no—
704C2×C22⋊C4—44no—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2412yes—
707C2×C22⋊C4C2412yes—
708C2×C22⋊C4C2412yes—
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×C42—24no—
743C2×C42—44no—
744C2×C42—82no—
745C2×C42#4118yes—
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×C42C2414yes—
761C2×C42C2412yes—
762C2×C42C2412yes—
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—
821C24—22no—
822C24—24no—
823C24—24no—
824C24—41no—
825C24—41no—
826C24C2514yes—
827C24C2512yes—
828C24C2511yescharacteristic
829C2×Q8—24no—
830C2×Q8—42no—
831C2×Q8—42no—
832C2×D4—28no—
833C2×D4—28no—
834C2×D4—28no—
835C2×D4—28no—
836C2×D4—28no—
837C2×D4—24no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—44no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—44no—
845C2×D4—44no—
846C2×D4—44no—
847C22×C4—24no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—28no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—28no—
862C22×C4—41no—
863C22×C4—42no—
864C22×C4—41no—
865C22×C4—42no—
866C22×C4—42no—
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—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—42no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—42no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—416no—
892C22×C4—816no—
893C22×C4C2×#4114yes—
894C22×C4C2×#4114yes—
895C22×C4C2×#4114yes—
896C22×C4C2514yes—
897C22×C4C2514yes—
898C22×C4C2514yes—
899C22×C4C2511yescharacteristic
900C22×C4C2511yescharacteristic
901C22×C4C2514yes—
902C22×C4C2512yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2514yes—
906C22×C4C2511yescharacteristic
907C22×C4C2511yescharacteristic
908C22×C4C2514yes—
909C22×C4C2514yes—
910C22×C4C2514yes—
911C22×C4C2514yes—
912C22×C4C2511yescharacteristic
913C22×C4C2512yes—
914C22×C4C2512yes—
915C22×C4C2511yescharacteristic
916C4⋊C4—22no—
917C4⋊C4—22no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—28no—
923C4⋊C4—28no—
924C4⋊C4—24no—
925C4⋊C4—28no—
926C4⋊C4—24no—
927C4⋊C4—28no—
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—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—44no—
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—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—28no—
968C22⋊C4—28no—
969C22⋊C4—24no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—24no—
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—
1000C42—24no—
1001C42—24no—
1002C42—28no—
1003C42—44no—
1004C42—44no—
1005C42—44no—
1006C42—44no—
1007C42—44no—
1008C42—44no—
1009C42—44no—
1010C42—44no—
1011C42—44no—
1012C42—44no—
1013C42—44no—
1014C42—44no—
1015C42C2×#4118yes—
1016C42C2×#4118yes—
1017C23—22no—
1018C23—21no—
1019C23—21no—
1020C23—28no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—24no—
1034C23—48no—
1035C23—48no—
1036C23—44no—
1037C23—44no—
1038C23C22×#4112yes—
1039C23#58514yes—
1040C23#58514yes—
1041C23C2611yescharacteristic
1042Q8—84no—
1043D4—416no—
1044D4—84no—
1045D4—88no—
1046D4—88no—
1047D4—88no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—28no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—22no—
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—24no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—21no—
1095C2×C4—24no—
1096C2×C4—21no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—21no—
1101C2×C4—24no—
1102C2×C4—21no—
1103C2×C4—44no—
1104C2×C4—44no—
1105C2×C4—48no—
1106C2×C4—48no—
1107C2×C4—44no—
1108C2×C4—44no—
1109C2×C4—48no—
1110C2×C4—44no—
1111C2×C4—88no—
1112C2×C4—84no—
1113C2×C4—84no—
1114C2×C4—88no—
1115C2×C4—84no—
1116C2×C4—88no—
1117C2×C4—164no—
1118C2×C4—164no—
1119C2×C4C22×#4112yes—
1120C2×C4C22×#4114yes—
1121C2×C4C22×#4114yes—
1122C2×C4C22×#4112yes—
1123C22—22no—
1124C22—22no—
1125C22—24no—
1126C22—24no—
1127C22—24no—
1128C22—24no—
1129C22—24no—
1130C22—416no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—44no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22#351214yes—
1143C22C23×#4111yescharacteristic
1144C22C2×#58512yes—
1145C22C2×#58512yes—
1146C22H(7,𝔽2)11yescharacteristic
1147C222−1+611yescharacteristic
1148C4—24no—
1149C4—24no—
1150C4—22no—
1151C4—22no—
1152C4—42no—
1153C4—44no—
1154C4—41no—
1155C4—41no—
1156C4—44no—
1157C4—41no—
1158C4—41no—
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4—44no—
1164C4—44no—
1165C4—44no—
1166C4—44no—
1167C4—44no—
1168C2—24no—
1169C2—44no—
1170C2—84no—
1171C2C2×#351211yescharacteristic
1172C2#6281411yescharacteristic
1173C2#6285611yescharacteristic
1174C2#6290912yes—
1175C2#6293312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36731C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #50931C2semidirect
2. #50930C2semidirect
3. #50929C2semidirect
4. #50928C2semidirect
5. #44811C2semidirect
6. #44806C2semidirect
7. #44349C2semidirect
8. #44163C2semidirect
9. #39051C2semidirect
10. #39049C2semidirect
11. #38968C2semidirect
12. #36977C2semidirect
13. #36976C2semidirect
14. #36732C2semidirect
16. #36520C2semidirect
17. #35302C2semidirect
18. #35181C2semidirect
19. #35099C2semidirect
20. #34997C2semidirect
21. #34594C2semidirect
22. #34401C2semidirect
23. C2×#2343C2semidirect
33. #2795C22semidirect
34. #2793C22semidirect
36. #2783C22semidirect
38. #2779C22semidirect
39. #2777C22semidirect
40. #2776C22semidirect
41. #2773C22semidirect
42. #2772C22semidirect
43. #2772C22semidirect
44. #2768C22semidirect
45. #2766C22semidirect
46. #2766C22semidirect
47. #2766C22semidirect
49. #2765C22semidirect
50. #2762C22semidirect
52. #2761C22semidirect
54. #2755C22semidirect
56. #2753C22semidirect
61. #2739C22semidirect
62. #2739C22semidirect
63. #2719C22semidirect
64. #2719C22semidirect
66. #2707C22semidirect
67. #2706C22semidirect
73. #2664C22semidirect
74. #2662C22semidirect
91. #2608C22semidirect
96. #2594C22semidirect
97. #2590C22semidirect
105. #2576C22semidirect
106. #2571C22semidirect
107. #2570C22semidirect
108. #2570C22semidirect
109. #2570C22semidirect
114. #2552C22semidirect
116. #2533C22semidirect
117. #2532C22semidirect
118. #2531C22semidirect
119. #2530C22semidirect
120. #2530C22semidirect
121. #2529C22semidirect
122. #2528C22semidirect
123. #2528C22semidirect
124. #2527C22semidirect
125. #2526C22semidirect
126. #2524C22semidirect
128. #2518C22semidirect
129. #2517C22semidirect
132. #2515C22semidirect
133. #2515C22semidirect
137. #2497C22semidirect
140. #2493C22semidirect
146. #2460C22semidirect
157. #2419C22semidirect
160. #2396C22semidirect
161. #2392C22semidirect
162. #2383C22semidirect
163. #2383C22semidirect
172. #2347C22semidirect
177. #2343C22semidirect
178. #2337C22semidirect
179. #2336C22semidirect
188. #2320C22semidirect
191. #2318C22semidirect

Maximal subgroups

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

subgroupindex
#509312
#509302
#509292
#509282
#448112
#448062
#443492
#441632
#390512
#390492
#389682
#369772
#369762
#367322
#367312
#365202
#353022
#351812
#350992
#349972
#345942
#344012
C2×#23432