Finite Group Databasebeta

← #8093839

Subgroups — #8093839

Order 512.

4688 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52721C214yesmaximal, complemented
2#52450C214yesmaximal, complemented
3#52429C214yesmaximal, complemented
4#52377C214yesmaximal, complemented
5#52344C214yesmaximal, complemented
6#52318C214yesmaximal, complemented
7#46119C214yesmaximal, complemented
8#46033C214yesmaximal, complemented
9#45735C214yesmaximal, complemented
10#45561C214yesmaximal, complemented
11#45559C214yesmaximal, complemented
12#45463C214yesmaximal, complemented
13#35391C212yesmaximal, complemented
14#35370C212yesmaximal, complemented
15#35370C212yesmaximal, complemented
16#35010C212yesmaximal, complemented
17#34994C211yesmaximal, characteristic, complemented
18#34993C211yesmaximal, characteristic
19#34983C212yesmaximal
20C2×#2569C211yesmaximal, characteristic, complemented
21C2×#2450C212yesmaximal, complemented
22C2×#543C2211yescharacteristic
23C2×#534C2211yescharacteristic
24C22×C22⋊Q8C2212yes—
25C22×C4×D4C2212yes—
26#2855C2214yescomplemented
27#2853C2214yes—
28#2851C2214yescomplemented
29#2850C2214yes—
30#2849C2214yes—
31#2848C2214yescomplemented
32#2841C2214yescomplemented
33#2839C2214yescomplemented
34#2839C2214yescomplemented
35#2839C2214yescomplemented
36#2838C2214yescomplemented
37#2838C2214yescomplemented
38#2836C2214yescomplemented
39#2836C2214yescomplemented
40#2835C2214yescomplemented
41#2833C2214yescomplemented
42#2833C2214yescomplemented
43#2832C2214yescomplemented
44#2831C2214yescomplemented
45#2831C2214yescomplemented
46#2831C2214yescomplemented
47#2830C2214yescomplemented
48#2827C2214yescomplemented
49#2823C2214yescomplemented
50#2821C2214yescomplemented
51#2814C2214yescomplemented
52#2799C2214yescomplemented
53#2794C2214yescomplemented
54#2793C2214yescomplemented
55#2793C2214yescomplemented
56#2791C2214yescomplemented
57#2789C2214yescomplemented
58#2787C2214yescomplemented
59#2787C2214yescomplemented
60#2775C2214yescomplemented
61#2774C2214yescomplemented
62#2771C2214yescomplemented
63#2770C2214yescomplemented
64#2769C2214yescomplemented
65#2766C2214yescomplemented
66#2765C2214yescomplemented
67#2762C2214yescomplemented
68#2759C2214yescomplemented
69#2759C2214yescomplemented
70#2758C2214yescomplemented
71#2745C2214yescomplemented
72#2738C2214yescomplemented
73#2738C2214yescomplemented
74#2731C2214yescomplemented
75#2729C2214yescomplemented
76#2723C2214yescomplemented
77#2722C2214yescomplemented
78#2721C2214yescomplemented
79#2718C2214yescomplemented
80#2717C2214yescomplemented
81#2716C2214yescomplemented
82#2716C2214yescomplemented
83#2715C2214yescomplemented
84#2713C2214yescomplemented
85#2707C2214yescomplemented
86#2702C2214yescomplemented
87#2695C2214yescomplemented
88#2695C2214yescomplemented
89#2690C2214yescomplemented
90#2689C2214yescomplemented
91#2674C2214yescomplemented
92#2646C2214yescomplemented
93#2639C2214yes—
94#2627C2214yescomplemented
95#2626C2214yescomplemented
96#2623C2214yes—
97#2622C2214yes—
98#2583C2214yescomplemented
99#2583C2214yescomplemented
100#2579C2214yes—
101#2579C2214yes—
102#2569C2214yescomplemented
103#2569C2214yescomplemented
104#2569C2214yescomplemented
105#2569C2214yescomplemented
106#2564C2214yescomplemented
107#2564C2214yescomplemented
108#2549C2214yescomplemented
109#2549C2214yescomplemented
110#2549C2214yescomplemented
111#2549C2214yescomplemented
112#2510C2214yes—
113#2510C2214yes—
114#2510C2214yes—
115#2510C2214yes—
116#2510C2214yescomplemented
117#2510C2214yescomplemented
118#2510C2214yescomplemented
119#2510C2214yescomplemented
120#2505C2214yescomplemented
121#2505C2214yescomplemented
122#2502C2214yescomplemented
123#2493C2214yescomplemented
124#2493C2214yescomplemented
125#2493C2214yescomplemented
126#2493C2214yescomplemented
127#2488C2214yes—
128#2488C2214yes—
129#2487C2214yes—
130#2481C2214yes—
131#2481C2214yes—
132#2481C2214yes—
133#2481C2214yes—
134#2481C2214yescomplemented
135#2481C2214yescomplemented
136#2481C2214yescomplemented
137#2481C2214yescomplemented
138#2480C2214yescomplemented
139#2480C2214yescomplemented
140#2480C2214yescomplemented
141#2480C2214yescomplemented
142#2473C2214yescomplemented
143#2473C2214yescomplemented
144#2472C2214yes—
145#2472C2214yes—
146#2450C2214yes—
147#2450C2214yes—
148#2450C2214yes—
149#2450C2214yes—
150#2450C2214yescomplemented
151#2450C2214yescomplemented
152#2450C2214yescomplemented
153#2450C2214yescomplemented
154#2444C2214yes—
155#2444C2214yes—
156#2443C2214yes—
157#2443C2214yes—
158#2440C2214yescomplemented
159#2440C2214yescomplemented
160#2440C2214yescomplemented
161#2440C2214yescomplemented
162#2434C2214yescomplemented
163#2419C2214yes—
164#2419C2214yes—
165#2418C2214yes—
166#2418C2214yes—
167#2417C2214yescomplemented
168#2417C2214yescomplemented
169#2409C2214yes—
170C2×#400C2212yescomplemented
171C2×#400C2212yescomplemented
172C2×#398C2212yescomplemented
173C2×#398C2212yescomplemented
174C2×#396C2212yescomplemented
175C2×#393C2212yescomplemented
176#2383C2214yescomplemented
177#2381C2214yescomplemented
178#2378C2214yescomplemented
179#2376C2214yescomplemented
180#2315C2211yescharacteristic
181#2315C2212yes—
182#2315C2212yes—
183#2315C2211yescharacteristic
184#2308C2212yes—
185#2308C2212yes—
186#2308C2212yes—
187C2×#391C2212yescomplemented
188C2×#387C2212yescomplemented
189C2×#387C2212yescomplemented
190C2×#387C2212yescomplemented
191C2×#386C2212yes—
192C2×#386C2212yes—
193C2×#385C2212yes—
194C2×#385C2212yes—
195C2×#385C2212yes—
196C2×#385C2212yescomplemented
197C2×#380C2211yescharacteristic
198C2×#380C2212yes—
199C2×#380C2212yescomplemented
200#2273C2212yes—
201C2×C4×C22⋊C4C2211yescharacteristic
202C22×#95C2211yescharacteristic
203C23×Q8C2312yes—
204C23×D4C2312yes—
205C24×C4C2312yes—
206C24×C4C2311yescharacteristic
207C24×C4C2312yes—
208#543—44no—
209#534—44no—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×#126C2314yes—
213C2×#126C2314yes—
214C2×#126C2314yes—
215C2×#126C2314yes—
216C2×#125C2314yes—
217C2×#124C2314yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×C22⋊Q8—48no—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×#121C2314yes—
232C2×#120C2314yes—
233C2×C4×D4—48no—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2312yes—
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2312yes—
244C22×C4⋊C4C2312yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C22⋊C4C2311yescharacteristic
252C22×C22⋊C4C2312yes—
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2312yes—
255C22×C22⋊C4C2312yes—
256C22×C22⋊C4C2311yescharacteristic
257C22×C22⋊C4C2312yes—
258C22×C22⋊C4C2312yes—
259C22×C22⋊C4C2312yes—
260C22×C22⋊C4C2312yes—
261C22×C22⋊C4C2312yes—
262C22×C42C2312yes—
263C22×C42C2312yes—
264#401C2314yes—
265#401C2314yes—
266#401C2314yes—
267#401C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#399C2314yes—
299#399C2314yes—
300#399C2314yes—
301#399C2314yes—
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#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#390C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
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#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#386C2314yes—
465#386C2314yes—
466#386C2314yes—
467#386C2314yes—
468#386C2314yes—
469#386C2314yes—
470#386C2314yes—
471#386C2314yes—
472#386C2314yes—
473#386C2314yes—
474#386C2314yes—
475#386C2314yes—
476#386C2314yes—
477#386C2314yes—
478#386C2314yes—
479#386C2314yes—
480#386C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2314yes—
484#386C2314yes—
485#386C2314yes—
486#385C2314yes—
487#385C2314yes—
488#385C2314yes—
489#385C2314yes—
490#385C2314yes—
491#385C2314yes—
492#385C2314yes—
493#385C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2314yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#384C2314yes—
521#384C2314yes—
522#383C2314yes—
523#383C2314yes—
524#383C2314yes—
525#383C2314yes—
526#382C2314yes—
527#382C2314yes—
528#381C2314yes—
529#381C2314yes—
530#381C2314yes—
531#381C2314yes—
532#381C2314yes—
533#380C2314yes—
534#380C2314yes—
535#380C2314yes—
536#380C2314yes—
537#380C2314yes—
538#380C2314yes—
539#380C2314yes—
540#380C2314yes—
541#380C2314yes—
542#380C2314yes—
543#380C2314yes—
544#380C2314yes—
545#380C2314yes—
546#380C2314yes—
547#380C2314yes—
548#380C2314yes—
549#380C2314yes—
550#380C2314yes—
551#379C2314yes—
552#379C2314yes—
553#379C2314yes—
554C4×C22⋊C4C2314yes—
555C4×C22⋊C4C2314yes—
556C4×C22⋊C4C2314yes—
557C4×C22⋊C4C2314yes—
558C4×C22⋊C4C2314yes—
559C4×C22⋊C4C2314yes—
560C4×C22⋊C4C2314yes—
561C4×C22⋊C4C2314yes—
562C2×#95C2312yes—
563C2×#95C2312yes—
564C2×#95C2312yes—
565C2×#95C2312yes—
566C2×#95C2312yes—
567C2×#95C2312yes—
568C2×#95C2312yes—
569C2×#95C2312yes—
570C2×#95C2312yes—
571C2×#95C2311yescharacteristic
572C2×#95C2312yes—
573C2×#95C2312yes—
574C2×#95C2312yes—
575C2×#95C2311yescharacteristic
576C2×#95C2312yes—
577C2×#95C2312yes—
578C2×#95C2312yes—
579C2×#95C2312yes—
580C2×#95C2312yes—
581C2×#95C2312yes—
582C2×#95C2311yescharacteristic
583C2×#95C2311yescharacteristic
584C25C2412yes—
585C25C2411yescharacteristic
586C22×Q8—44no—
587C22×Q8—44no—
588C22×Q8—82no—
589C22×Q8C2414yes—
590C22×Q8C2414yes—
591C22×Q8C2414yes—
592C22×D4—28no—
593C22×D4—28no—
594C22×D4—28no—
595C22×D4C2414yes—
596C22×D4C2414yes—
597C22×D4C2414yes—
598C23×C4—28no—
599C23×C4—24no—
600C23×C4—44no—
601C23×C4—44no—
602C23×C4—44no—
603C23×C4—82no—
604C23×C4—82no—
605C23×C4—82no—
606C23×C4C2412yes—
607C23×C4C2412yes—
608C23×C4C2412yes—
609C23×C4C2412yes—
610C23×C4C2412yes—
611C23×C4C2412yes—
612C23×C4C2412yes—
613C23×C4C2412yes—
614C23×C4C2412yes—
615C23×C4C2412yes—
616C23×C4C2412yes—
617C23×C4C2412yes—
618C23×C4C2412yes—
619C23×C4C2412yes—
620C23×C4C2412yes—
621C23×C4C2412yes—
622C23×C4C2412yes—
623C23×C4C2412yes—
624C23×C4C2411yescharacteristic
625C23×C4C2412yes—
626C23×C4C2414yes—
627C23×C4C2411yescharacteristic
628C23×C4C2414yes—
629C4⋊Q8—48no—
630C4⋊Q8—84no—
631#126—48no—
632#126—84no—
633#126—84no—
634#126—84no—
635#125—84no—
636#124—84no—
637#123—48no—
638#123—48no—
639#123—84no—
640C22⋊Q8—48no—
641C22⋊Q8—48no—
642C22⋊Q8—48no—
643C22⋊Q8—48no—
644C22⋊Q8—48no—
645C22⋊Q8—48no—
646C22⋊Q8—48no—
647C22⋊Q8—48no—
648C22⋊Q8—84no—
649#121—48no—
650#120—48no—
651C4×D4—48no—
652C4×D4—48no—
653C4×D4—48no—
654C4×D4—48no—
655C2×C4⋊C4—44no—
656C2×C4⋊C4—44no—
657C2×C4⋊C4—44no—
658C2×C4⋊C4—44no—
659C2×C4⋊C4—44no—
660C2×C4⋊C4—44no—
661C2×C4⋊C4—44no—
662C2×C4⋊C4—82no—
663C2×C4⋊C4—82no—
664C2×C4⋊C4—82no—
665C2×C4⋊C4—82no—
666C2×C4⋊C4—82no—
667C2×C4⋊C4—82no—
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⋊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×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⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C22⋊C4—28no—
711C2×C22⋊C4—28no—
712C2×C22⋊C4—24no—
713C2×C22⋊C4—24no—
714C2×C22⋊C4—28no—
715C2×C22⋊C4—28no—
716C2×C22⋊C4—44no—
717C2×C22⋊C4—44no—
718C2×C22⋊C4—82no—
719C2×C22⋊C4—82no—
720C2×C22⋊C4—82no—
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×C42—44no—
756C2×C42—82no—
757C2×C42C2414yes—
758C2×C42C2414yes—
759C2×C42C2414yes—
760C2×C42C2414yes—
761C2×C42C2414yes—
762C2×C42C2414yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765#95C2411yescharacteristic
766#95C2412yes—
767#95C2412yes—
768#95C2412yes—
769#95C2411yescharacteristic
770#95C2412yes—
771#95C2412yes—
772#95C2412yes—
773#95C2411yescharacteristic
774#95C2411yescharacteristic
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—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831C24—24no—
832C24—24no—
833C24—24no—
834C24—42no—
835C24—42no—
836C24—42no—
837C24—42no—
838C24—42no—
839C24—42no—
840C24H(5,𝔽2)14yes—
841C242−1+414yes—
842C242−1+414yes—
843C24C2514yes—
844C24C2512yes—
845C24C2511yescharacteristic
846C2×Q8—28no—
847C2×Q8—44no—
848C2×Q8—44no—
849C2×Q8—44no—
850C2×Q8—44no—
851C2×Q8—44no—
852C2×Q8—44no—
853C2×Q8—44no—
854C2×Q8—44no—
855C2×Q8—816no—
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—28no—
859C2×D4—28no—
860C2×D4—28no—
861C2×D4—28no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—432no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—28no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—44no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—44no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—44no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—816no—
934C22×C4—88no—
935C22×C4—816no—
936C22×C4C2514yes—
937C22×C4C2512yes—
938C22×C4C2514yes—
939C22×C4C2511yescharacteristic
940C22×C4C2511yescharacteristic
941C22×C4C2514yes—
942C22×C4C2514yes—
943C22×C4C2514yes—
944C22×C4C2512yes—
945C22×C4C2512yes—
946C22×C4C2514yes—
947C22×C4C2514yes—
948C22×C4C2514yes—
949C22×C4C2514yes—
950C22×C4C2514yes—
951C22×C4C2512yes—
952C22×C4C2514yes—
953C22×C4C2512yes—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—28no—
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—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C22⋊C4—28no—
997C22⋊C4—28no—
998C22⋊C4—28no—
999C22⋊C4—28no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—28no—
1006C22⋊C4—28no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C42—44no—
1031C42—44no—
1032C42—44no—
1033C42—44no—
1034C42—44no—
1035C42—44no—
1036C42—44no—
1037C42—44no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—24no—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—48no—
1052C23—44no—
1053C23—44no—
1054C23—48no—
1055C23—48no—
1056C23—48no—
1057C23—48no—
1058C23—84no—
1059C23—84no—
1060C23—84no—
1061C23—84no—
1062C23#563116yes—
1063C23C2×H(5,𝔽2)12yes—
1064C23C2×H(5,𝔽2)14yes—
1065C23C2×2−1+414yes—
1066C23C2×2−1+412yes—
1067C23C2×2−1+414yes—
1068C23C2×2−1+412yes—
1069C23C2611yescharacteristic
1070Q8—88no—
1071Q8—88no—
1072Q8—164no—
1073D4—416no—
1074D4—416no—
1075D4—164no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—22no—
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—24no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—21no—
1094C2×C4—21no—
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—24no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—48no—
1128C2×C4—48no—
1129C2×C4—48no—
1130C2×C4—44no—
1131C2×C4—44no—
1132C2×C4—48no—
1133C2×C4—48no—
1134C2×C4—48no—
1135C2×C4—88no—
1136C2×C4—84no—
1137C2×C4—84no—
1138C2×C4—84no—
1139C2×C4—84no—
1140C2×C4—84no—
1141C2×C4—84no—
1142C2×C4—84no—
1143C2×C4—84no—
1144C2×C4—84no—
1145C2×C4—84no—
1146C2×C4—84no—
1147C2×C4—84no—
1148C2×C4—84no—
1149C2×C4—88no—
1150C2×C4#58514yes—
1151C22—24no—
1152C22—22no—
1153C22—22no—
1154C22—24no—
1155C22—24no—
1156C22—24no—
1157C22—24no—
1158C22—24no—
1159C22—24no—
1160C22—24no—
1161C22—416no—
1162C22—44no—
1163C22—44no—
1164C22—44no—
1165C22—44no—
1166C22—44no—
1167C22—44no—
1168C22—44no—
1169C22—816no—
1170C22C2×#56318yes—
1171C22C2×#56314yes—
1172C22C22×H(5,𝔽2)11yescharacteristic
1173C22C22×2−1+411yescharacteristic
1174C22C22×2−1+411yescharacteristic
1175C22C2×#58512yes—
1176C22H(7,𝔽2)12yes—
1177C4—24no—
1178C4—44no—
1179C4—42no—
1180C4—41no—
1181C4—41no—
1182C4—44no—
1183C4—44no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—44no—
1188C4—44no—
1189C4—44no—
1190C4—44no—
1191C4—44no—
1192C4—44no—
1193C4—44no—
1194C4—44no—
1195C2—28no—
1196C2—24no—
1197C2—84no—
1198C2C22×#56311yescharacteristic
1199C2#6282311yescharacteristic
1200C2#6286411yescharacteristic
1201C2#6290012yes—
1202C2#6290212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#534C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52721C2semidirect
2. #52450C2semidirect
3. #52429C2semidirect
4. #52377C2semidirect
5. #52344C2semidirect
6. #52318C2semidirect
7. #46119C2semidirect
8. #46033C2semidirect
9. #45735C2semidirect
10. #45561C2semidirect
11. #45559C2semidirect
12. #45463C2semidirect
13. #35391C2semidirect
14. #35370C2semidirect
15. #35370C2semidirect
16. #35010C2semidirect
17. #34994C2semidirect
20. C2×#2569C2semidirect
21. C2×#2450C2semidirect
26. #2855C22semidirect
28. #2851C22semidirect
31. #2848C22semidirect
32. #2841C22semidirect
33. #2839C22semidirect
34. #2839C22semidirect
35. #2839C22semidirect
36. #2838C22semidirect
37. #2838C22semidirect
38. #2836C22semidirect
39. #2836C22semidirect
40. #2835C22semidirect
41. #2833C22semidirect
42. #2833C22semidirect
43. #2832C22semidirect
44. #2831C22semidirect
45. #2831C22semidirect
46. #2831C22semidirect
47. #2830C22semidirect
48. #2827C22semidirect
49. #2823C22semidirect
50. #2821C22semidirect
51. #2814C22semidirect
52. #2799C22semidirect
53. #2794C22semidirect
54. #2793C22semidirect
55. #2793C22semidirect
56. #2791C22semidirect
57. #2789C22semidirect
58. #2787C22semidirect
59. #2787C22semidirect
60. #2775C22semidirect
61. #2774C22semidirect
62. #2771C22semidirect
63. #2770C22semidirect
64. #2769C22semidirect
65. #2766C22semidirect
66. #2765C22semidirect
67. #2762C22semidirect
68. #2759C22semidirect
69. #2759C22semidirect
70. #2758C22semidirect
71. #2745C22semidirect
72. #2738C22semidirect
73. #2738C22semidirect
74. #2731C22semidirect
75. #2729C22semidirect
76. #2723C22semidirect
77. #2722C22semidirect
78. #2721C22semidirect
79. #2718C22semidirect
80. #2717C22semidirect
81. #2716C22semidirect
82. #2716C22semidirect
83. #2715C22semidirect
84. #2713C22semidirect
85. #2707C22semidirect
86. #2702C22semidirect
87. #2695C22semidirect
88. #2695C22semidirect
89. #2690C22semidirect
90. #2689C22semidirect
91. #2674C22semidirect
92. #2646C22semidirect
94. #2627C22semidirect
95. #2626C22semidirect
98. #2583C22semidirect
99. #2583C22semidirect
102. #2569C22semidirect
103. #2569C22semidirect
104. #2569C22semidirect
105. #2569C22semidirect
106. #2564C22semidirect
107. #2564C22semidirect
108. #2549C22semidirect
109. #2549C22semidirect
110. #2549C22semidirect
111. #2549C22semidirect
116. #2510C22semidirect
117. #2510C22semidirect
118. #2510C22semidirect
119. #2510C22semidirect
120. #2505C22semidirect
121. #2505C22semidirect
122. #2502C22semidirect
123. #2493C22semidirect
124. #2493C22semidirect
125. #2493C22semidirect
126. #2493C22semidirect
134. #2481C22semidirect
135. #2481C22semidirect
136. #2481C22semidirect
137. #2481C22semidirect
138. #2480C22semidirect
139. #2480C22semidirect
140. #2480C22semidirect
141. #2480C22semidirect
142. #2473C22semidirect
143. #2473C22semidirect
150. #2450C22semidirect
151. #2450C22semidirect
152. #2450C22semidirect
153. #2450C22semidirect
158. #2440C22semidirect
159. #2440C22semidirect
160. #2440C22semidirect
161. #2440C22semidirect
162. #2434C22semidirect
167. #2417C22semidirect
168. #2417C22semidirect
170. C2×#400C22semidirect
171. C2×#400C22semidirect
172. C2×#398C22semidirect
173. C2×#398C22semidirect
174. C2×#396C22semidirect
175. C2×#393C22semidirect
176. #2383C22semidirect
177. #2381C22semidirect
178. #2378C22semidirect
179. #2376C22semidirect
187. C2×#391C22semidirect
188. C2×#387C22semidirect
189. C2×#387C22semidirect
190. C2×#387C22semidirect
196. C2×#385C22semidirect
199. C2×#380C22semidirect

Maximal subgroups

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

subgroupindex
#527212
#524502
#524292
#523772
#523442
#523182
#461192
#460332
#457352
#455612
#455592
#454632
#353912
#353702
#350102
#349942
#349932
#349832
C2×#25692
C2×#24502