Finite Group Databasebeta

← #8094471

Subgroups — #8094471

Order 512.

5989 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53103C212yesmaximal, complemented
2#53098C214yesmaximal, complemented
3#53014C214yesmaximal, complemented
4#53007C212yesmaximal, complemented
5#52993C212yesmaximal, complemented
6#52966C212yesmaximal, complemented
7#52586C214yesmaximal, complemented
8#52549C214yesmaximal, complemented
9#46342C212yesmaximal, complemented
10#46339C214yesmaximal, complemented
11#46328C212yesmaximal, complemented
12#45623C214yesmaximal, complemented
13#45622C212yesmaximal, complemented
14#45478C212yesmaximal, complemented
15#45473C214yesmaximal, complemented
16#45455C214yesmaximal, complemented
17#35564C212yesmaximal, complemented
18#35518C212yesmaximal, complemented
19#35516C212yesmaximal, complemented
20#35267C212yesmaximal, complemented
21#35251C212yesmaximal, complemented
22#35223C212yesmaximal, complemented
23#34936C211yesmaximal, characteristic, complemented
24C2×#2486C211yesmaximal, characteristic, complemented
25#34736C211yesmaximal, characteristic, complemented
26C23×#41C2211yescharacteristic
27C2×#560C2214yes—
28C2×#537C2212yes—
29C2×#537C2212yes—
30C2×#532C2211yescharacteristic, complemented
31C2×#525C2212yes—
32C2×#525C2212yes—
33C2×#525C2212yescomplemented
34C22×#123C2212yes—
35C2×#520C2212yescomplemented
36C22×C4×D4C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic, complemented
38#2863C2214yescomplemented
39#2860C2214yescomplemented
40#2848C2214yescomplemented
41#2847C2214yescomplemented
42#2847C2218yescomplemented
43#2841C2214yescomplemented
44#2841C2218yescomplemented
45#2837C2218yescomplemented
46#2834C2214yescomplemented
47#2830C2214yescomplemented
48#2829C2218yescomplemented
49#2829C2218yescomplemented
50#2827C2218yescomplemented
51#2825C2218yescomplemented
52#2823C2214yescomplemented
53#2815C2214yescomplemented
54#2813C2218yescomplemented
55#2812C2214yescomplemented
56#2792C2214yescomplemented
57#2790C2218yescomplemented
58#2780C2218yescomplemented
59#2760C2214yescomplemented
60#2757C2218yescomplemented
61#2756C2218yescomplemented
62#2752C2214yescomplemented
63#2749C2218yescomplemented
64#2746C2218yescomplemented
65#2737C2218yescomplemented
66#2735C2214yescomplemented
67#2709C2214yes—
68#2705C2218yescomplemented
69#2703C2218yescomplemented
70#2699C2218yescomplemented
71#2699C2214yescomplemented
72#2697C2214yes—
73#2697C2218yescomplemented
74#2693C2218yes—
75#2693C2214yescomplemented
76#2691C2218yescomplemented
77#2688C2218yescomplemented
78#2678C2218yes—
79#2673C2218yescomplemented
80#2645C2214yescomplemented
81#2644C2214yescomplemented
82#2618C2218yescomplemented
83#2616C2214yescomplemented
84#2615C2214yescomplemented
85#2543C2218yescomplemented
86#2542C2211yescharacteristic
87#2542C2211yescharacteristic, complemented
88#2541C2211yescharacteristic
89#2541C2211yescharacteristic, complemented
90#2540C2212yes—
91#2540C2212yescomplemented
92#2539C2212yes—
93#2539C2212yescomplemented
94#2538C2214yescomplemented
95#2537C2214yescomplemented
96#2536C2214yescomplemented
97#2535C2214yescomplemented
98#2510C2218yescomplemented
99#2501C2212yescomplemented
100#2497C2214yescomplemented
101#2496C2214yescomplemented
102#2495C2214yescomplemented
103#2494C2214yescomplemented
104#2487C2214yescomplemented
105#2486C2212yes—
106#2486C2212yes—
107#2486C2212yes—
108#2486C2212yes—
109#2486C2214yescomplemented
110#2486C2212yescomplemented
111#2486C2212yescomplemented
112#2486C2212yescomplemented
113#2486C2212yescomplemented
114#2485C2214yescomplemented
115#2485C2214yescomplemented
116#2481C2218yescomplemented
117#2433C2212yes—
118#2430C2218yes—
119#2429C2214yescomplemented
120#2428C2214yescomplemented
121#2427C2214yescomplemented
122#2426C2214yescomplemented
123#2425C2218yescomplemented
124#2424C2218yescomplemented
125#2423C2214yescomplemented
126#2422C2214yescomplemented
127#2421C2214yescomplemented
128#2420C2214yescomplemented
129#2419C2218yescomplemented
130#2418C2218yes—
131#2417C2214yescomplemented
132#2417C2214yescomplemented
133#2417C2214yescomplemented
134#2417C2214yescomplemented
135#2417C2214yescomplemented
136#2417C2214yescomplemented
137#2416C2214yescomplemented
138#2416C2214yescomplemented
139#2416C2214yescomplemented
140#2416C2214yescomplemented
141#2416C2218yescomplemented
142#2416C2214yescomplemented
143#2416C2214yescomplemented
144#2415C2214yescomplemented
145#2415C2214yescomplemented
146#2414C2214yescomplemented
147#2414C2214yescomplemented
148#2410C2218yes—
149#2409C2211yescharacteristic
150#2409C2211yescharacteristic
151#2409C2214yescomplemented
152#2408C2211yescharacteristic
153#2408C2211yescharacteristic
154#2408C2214yescomplemented
155#2407C2212yes—
156#2407C2212yes—
157#2407C2214yescomplemented
158#2407C2214yescomplemented
159#2406C2212yes—
160#2405C2212yes—
161#2404C2212yes—
162#2403C2212yes—
163#2397C2212yes—
164#2397C2212yescomplemented
165C2×#398C2212yescomplemented
166C2×#397C2212yes—
167#2388C2212yes—
168#2388C2212yes—
169#2377C2218yescomplemented
170#2376C2214yes—
171#2317C2212yescomplemented
172#2316C2212yescomplemented
173#2311C2212yes—
174#2311C2212yes—
175#2311C2212yescomplemented
176C4×#127C2212yes—
177C4×#127C2212yescomplemented
178C4×#120C2212yes—
179C4×#120C2212yes—
180#2297C2212yes—
181C2×#389C2212yescomplemented
182#2280C2211yescharacteristic
183C2×#381C2212yescomplemented
184C2×#380C2212yes—
185C2×#380C2211yescharacteristic, complemented
186C4×#117C2211yescharacteristic, complemented
187C22×#41—44no—
188C22×#41—48no—
189C22×#41C2312yes—
190C22×#41C2312yes—
191C22×#41C2312yes—
192C22×#41C2312yes—
193C22×#41C2312yes—
194C23×Q8C2311yescharacteristic
195C23×D4C2311yescharacteristic
196C23×D4C2312yes—
197C23×D4C2311yescharacteristic
198C24×C4C2311yescharacteristic
199C24×C4C2311yescharacteristic
200C24×C4C2312yes—
201C24×C4C2312yes—
202#560—416no—
203#537—48no—
204#537—48no—
205#532—44no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×#127C2312yes—
208C2×#127C2312yes—
209C2×#127C2311yescharacteristic
210C2×#126C2318yes—
211C2×#124C2312yes—
212#525—48no—
213#525—48no—
214#525—48no—
215C2×#123—48no—
216C2×#123C2314yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×#123C2314yes—
223C2×#123C2318yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×#121C2312yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C2×#121C2318yes—
238C2×#121C2318yes—
239C2×#121C2318yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2318yes—
246C2×#121C2312yes—
247C2×#121C2312yes—
248C2×#121C2312yes—
249C2×#121C2318yes—
250C2×#121C2318yes—
251C2×#121C2312yes—
252C2×#120C2312yes—
253C2×#120C2314yes—
254C2×#120C2314yes—
255C2×#120C2318yes—
256C2×#120C2312yes—
257C2×#120C2314yes—
258#520—48no—
259C2×C4×Q8C2314yes—
260C2×C4×D4—44no—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2312yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2312yes—
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2311yescharacteristic
277C2×C4×D4C2318yes—
278C2×C4×D4C2314yes—
279C2×#117C2312yes—
280C2×#117C2312yes—
281C2×#117C2314yes—
282C22×C4⋊C4—44no—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2314yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2314yes—
293C22×C22⋊C4C2311yescharacteristic
294C22×C22⋊C4C2314yes—
295C22×C22⋊C4C2311yescharacteristic
296C22×C22⋊C4C2312yes—
297C22×C42C2311yescharacteristic
298#401C2318yes—
299#400C2318yes—
300#400C2318yes—
301#400C2318yes—
302#400C2318yes—
303#399C2314yes—
304#399C2314yes—
305#399C2318yes—
306#399C2312yes—
307#399C2312yes—
308#399C2312yes—
309#399C2312yes—
310#398C2314yes—
311#398C2318yes—
312#398C2314yes—
313#398C2318yes—
314#398C2314yes—
315#398C2318yes—
316#398C2318yes—
317#398C2318yes—
318#398C2314yes—
319#397C2314yes—
320#397C2318yes—
321#397C2318yes—
322#397C2318yes—
323#397C2318yes—
324#397C2314yes—
325#397C2318yes—
326#397C2318yes—
327#397C2314yes—
328#397C2318yes—
329#397C2318yes—
330#397C2314yes—
331#396C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#396C2318yes—
336#396C2318yes—
337#396C2318yes—
338#396C2318yes—
339#396C2318yes—
340#395C2312yes—
341#395C2312yes—
342#395C2318yes—
343#394C2312yes—
344#394C2318yes—
345#394C2314yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2312yes—
350#394C2314yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#394C2318yes—
358#394C2318yes—
359#394C2318yes—
360#393C2318yes—
361#393C2312yes—
362#393C2312yes—
363#392C2312yes—
364#392C2318yes—
365#392C2318yes—
366#392C2318yes—
367#392C2318yes—
368#392C2314yes—
369#392C2314yes—
370#392C2312yes—
371#392C2312yes—
372#392C2314yes—
373#392C2312yes—
374#392C2312yes—
375#392C2312yes—
376#392C2314yes—
377#392C2318yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2312yes—
382#391C2312yes—
383#390C2312yes—
384#390C2312yes—
385#390C2314yes—
386#390C2314yes—
387#390C2314yes—
388#390C2314yes—
389#390C2312yes—
390#390C2312yes—
391#390C2314yes—
392#390C2314yes—
393#390C2314yes—
394#390C2318yes—
395#390C2312yes—
396#390C2318yes—
397#390C2312yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2318yes—
405#389C2314yes—
406#389C2318yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2312yes—
438#386C2314yes—
439#386C2318yes—
440#386C2318yes—
441#386C2314yes—
442#386C2312yes—
443#386C2314yes—
444#386C2314yes—
445#385C2314yes—
446#385C2318yes—
447#385C2318yes—
448#385C2312yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2312yes—
453#385C2314yes—
454#384C2312yes—
455#384C2312yes—
456#384C2314yes—
457#383C2318yes—
458#382C2314yes—
459#381C2318yes—
460#381C2314yes—
461#381C2314yes—
462#381C2312yes—
463#381C2314yes—
464#381C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2318yes—
472#380C2318yes—
473#380C2318yes—
474#380C2318yes—
475#380C2314yes—
476#380C2318yes—
477#380C2314yes—
478#380C2312yes—
479#380C2314yes—
480#380C2311yescharacteristic
481#380C2311yescharacteristic
482#380C2314yes—
483#380C2312yes—
484#380C2312yes—
485#380C2312yes—
486#380C2312yes—
487#379C2318yes—
488#379C2312yes—
489#379C2312yes—
490#379C2312yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2312yes—
500#376C2312yes—
501C2×#95C2312yes—
502C2×#95C2314yes—
503C2×#95C2314yes—
504C43C2312yes—
505C25C2411yescharacteristic
506C25C2411yescharacteristic
507C25C2412yes—
508C2×#41—28no—
509C2×#41—28no—
510C2×#41—28no—
511C2×#41—28no—
512C2×#41—28no—
513C2×#41—28no—
514C2×#41—44no—
515C2×#41—48no—
516C2×#41—44no—
517C2×#41—48no—
518C2×#41—44no—
519C2×#41—44no—
520C2×#41—44no—
521C2×#41—464no—
522C22×Q8—42no—
523C22×Q8—44no—
524C22×Q8C2412yes—
525C22×Q8C2412yes—
526C22×Q8C2412yes—
527C22×D4—24no—
528C22×D4—42no—
529C22×D4—44no—
530C22×D4—42no—
531C22×D4—42no—
532C22×D4—48no—
533C22×D4—44no—
534C22×D4C2414yes—
535C22×D4C2412yes—
536C22×D4C2414yes—
537C22×D4C2412yes—
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2414yes—
542C22×D4C2414yes—
543C22×D4C2414yes—
544C22×D4C2414yes—
545C22×D4C2414yes—
546C22×D4C2412yes—
547C22×D4C2414yes—
548C22×D4C2412yes—
549C22×D4C2418yes—
550C22×D4C2418yes—
551C22×D4C2414yes—
552C22×D4C2412yes—
553C22×D4C2411yescharacteristic
554C23×C4—24no—
555C23×C4—24no—
556C23×C4—28no—
557C23×C4—28no—
558C23×C4—44no—
559C23×C4—48no—
560C23×C4—44no—
561C23×C4—44no—
562C23×C4—44no—
563C23×C4C2411yescharacteristic
564C23×C4C2411yescharacteristic
565C23×C4C2411yescharacteristic
566C23×C4C2411yescharacteristic
567C23×C4C2411yescharacteristic
568C23×C4C2411yescharacteristic
569C23×C4C2414yes—
570C23×C4C2411yescharacteristic
571C23×C4C2411yescharacteristic
572C23×C4C2411yescharacteristic
573C23×C4C2411yescharacteristic
574C23×C4C2414yes—
575C23×C4C2411yescharacteristic
576C23×C4C2414yes—
577C23×C4C2411yescharacteristic
578C23×C4C2414yes—
579C23×C4C2414yes—
580C23×C4C2414yes—
581C23×C4C2418yes—
582C23×C4C2412yes—
583C23×C4C2414yes—
584C23×C4C2411yescharacteristic
585C4⋊Q8—42no—
586#127—28no—
587#127—42no—
588#127—44no—
589#126—416no—
590#124—44no—
591#123—216no—
592#123—48no—
593#123—416no—
594#123—48no—
595#123—48no—
596#123—48no—
597#123—48no—
598#123—48no—
599C22⋊Q8—44no—
600C22⋊Q8—44no—
601C22⋊Q8—44no—
602C22⋊Q8—44no—
603C22⋊Q8—44no—
604C22⋊Q8—44no—
605C22⋊Q8—48no—
606C22⋊Q8—48no—
607C22⋊Q8—48no—
608C22⋊Q8—48no—
609#121—416no—
610#121—416no—
611#121—44no—
612#121—44no—
613#121—44no—
614#121—44no—
615#121—44no—
616#121—44no—
617#121—48no—
618#121—48no—
619#121—48no—
620#121—48no—
621#121—416no—
622#121—44no—
623#121—44no—
624#121—416no—
625#121—416no—
626#121—416no—
627#120—28no—
628#120—48no—
629#120—48no—
630#120—48no—
631#120—416no—
632#120—44no—
633C4×Q8—48no—
634C4×D4—48no—
635C4×D4—42no—
636C4×D4—42no—
637C4×D4—42no—
638C4×D4—42no—
639C4×D4—42no—
640C4×D4—42no—
641C4×D4—42no—
642C4×D4—42no—
643C4×D4—48no—
644C4×D4—48no—
645C4×D4—48no—
646C4×D4—48no—
647C4×D4—48no—
648C4×D4—48no—
649C4×D4—44no—
650C4×D4—44no—
651C4×D4—416no—
652#117—28no—
653#117—28no—
654#117—48no—
655C2×C4⋊C4—28no—
656C2×C4⋊C4—28no—
657C2×C4⋊C4—44no—
658C2×C4⋊C4—44no—
659C2×C4⋊C4—44no—
660C2×C4⋊C4—44no—
661C2×C4⋊C4—48no—
662C2×C4⋊C4—48no—
663C2×C4⋊C4—44no—
664C2×C4⋊C4—42no—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2418yes—
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⋊C4C2418yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2418yes—
693C2×C4⋊C4C2418yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2418yes—
696C2×C22⋊C4—48no—
697C2×C22⋊C4—44no—
698C2×C22⋊C4—42no—
699C2×C22⋊C4—42no—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2411yescharacteristic
707C2×C22⋊C4C2411yescharacteristic
708C2×C22⋊C4C2411yescharacteristic
709C2×C22⋊C4C2411yescharacteristic
710C2×C22⋊C4C2411yescharacteristic
711C2×C22⋊C4C2411yescharacteristic
712C2×C22⋊C4C2411yescharacteristic
713C2×C22⋊C4C2411yescharacteristic
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2418yes—
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⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2412yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2418yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2418yes—
740C2×C22⋊C4C2418yes—
741C2×C22⋊C4C2418yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2418yes—
746C2×C42—24no—
747C2×C42C2414yes—
748C2×C42C2414yes—
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2412yes—
754C2×C42C2418yes—
755C2×C42C2412yes—
756C2×C42C2414yes—
757#95C2414yes—
758#95C2418yes—
759#95C2418yes—
760#95C2414yes—
761#95C2418yes—
762#95C2418yes—
763#95C2414yes—
764#95C2412yes—
765#95C2412yes—
766#95C2414yes—
767#95C2412yes—
768#95C2414yes—
769#95C2412yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783C24—22no—
784C24—22no—
785C24—22no—
786C24—22no—
787C24—24no—
788C24—22no—
789C24—24no—
790C24—24no—
791C24—42no—
792C24—42no—
793C24—44no—
794C24—41no—
795C24—42no—
796C24—42no—
797C24—44no—
798C24C2514yes—
799C24C2511yescharacteristic
800C24C2514yes—
801C24C2511yescharacteristic
802C24C2511yescharacteristic
803C24C2511yescharacteristic
804C24C2511yescharacteristic
805#41—432no—
806#41—432no—
807#41—432no—
808#41—432no—
809#41—432no—
810C2×Q8—24no—
811C2×Q8—24no—
812C2×Q8—24no—
813C2×Q8—24no—
814C2×Q8—24no—
815C2×Q8—24no—
816C2×Q8—42no—
817C2×Q8—44no—
818C2×Q8—416no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—28no—
823C2×D4—28no—
824C2×D4—28no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—28no—
830C2×D4—28no—
831C2×D4—28no—
832C2×D4—28no—
833C2×D4—28no—
834C2×D4—24no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—22no—
841C2×D4—24no—
842C2×D4—41no—
843C2×D4—41no—
844C2×D4—41no—
845C2×D4—41no—
846C2×D4—41no—
847C2×D4—41no—
848C2×D4—42no—
849C2×D4—44no—
850C2×D4—44no—
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—48no—
871C2×D4—48no—
872C2×D4—48no—
873C2×D4—48no—
874C2×D4—48no—
875C2×D4—48no—
876C2×D4—416no—
877C2×D4—432no—
878C2×D4—416no—
879C2×D4H(5,𝔽2)14yes—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—22no—
886C22×C4—28no—
887C22×C4—28no—
888C22×C4—28no—
889C22×C4—28no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—28no—
896C22×C4—24no—
897C22×C4—24no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—28no—
901C22×C4—28no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—24no—
905C22×C4—22no—
906C22×C4—24no—
907C22×C4—22no—
908C22×C4—28no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—28no—
912C22×C4—28no—
913C22×C4—42no—
914C22×C4—44no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4—41no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4—44no—
926C22×C4—42no—
927C22×C4—44no—
928C22×C4—48no—
929C22×C4—48no—
930C22×C4—48no—
931C22×C4—432no—
932C22×C4—416no—
933C22×C4—416no—
934C22×C4—816no—
935C22×C4H(5,𝔽2)14yes—
936C22×C4H(5,𝔽2)18yes—
937C22×C4C2511yescharacteristic
938C22×C4C2511yescharacteristic
939C22×C4C2514yes—
940C22×C4C2511yescharacteristic
941C22×C4C2511yescharacteristic
942C22×C4C2514yes—
943C22×C4C2514yes—
944C22×C4C2514yes—
945C22×C4C2518yes—
946C22×C4C2518yes—
947C22×C4C2514yes—
948C22×C4C2511yescharacteristic
949C22×C4C2514yes—
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C22×C4C2511yescharacteristic
955C4⋊C4—28no—
956C4⋊C4—28no—
957C4⋊C4—28no—
958C4⋊C4—28no—
959C4⋊C4—24no—
960C4⋊C4—216no—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—48no—
971C4⋊C4—48no—
972C4⋊C4—48no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—48no—
982C4⋊C4—48no—
983C4⋊C4—48no—
984C4⋊C4—48no—
985C4⋊C4—48no—
986C22⋊C4—216no—
987C22⋊C4—28no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—24no—
991C22⋊C4—28no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—44no—
1001C22⋊C4—48no—
1002C22⋊C4—44no—
1003C22⋊C4—48no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—48no—
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—42no—
1022C22⋊C4—44no—
1023C22⋊C4—48no—
1024C22⋊C4—48no—
1025C22⋊C4—48no—
1026C22⋊C4—48no—
1027C22⋊C4—48no—
1028C22⋊C4—48no—
1029C22⋊C4—48no—
1030C22⋊C4—48no—
1031C22⋊C4—48no—
1032C42—22no—
1033C42—22no—
1034C42—22no—
1035C42—22no—
1036C42—28no—
1037C42—28no—
1038C42—24no—
1039C42—44no—
1040C42—48no—
1041C42—42no—
1042C23—21no—
1043C23—21no—
1044C23—22no—
1045C23—28no—
1046C23—22no—
1047C23—22no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—22no—
1053C23—21no—
1054C23—21no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—24no—
1059C23—21no—
1060C23—24no—
1061C23—24no—
1062C23—24no—
1063C23—21no—
1064C23—22no—
1065C23—24no—
1066C23—24no—
1067C23—24no—
1068C23—24no—
1069C23—24no—
1070C23—24no—
1071C23—21no—
1072C23—24no—
1073C23—22no—
1074C23—24no—
1075C23—24no—
1076C23—24no—
1077C23—48no—
1078C23—48no—
1079C23—44no—
1080C23—48no—
1081C23—44no—
1082C23—44no—
1083C23—48no—
1084C23—44no—
1085C23—82no—
1086C23—84no—
1087C23—84no—
1088C23—88no—
1089C23—84no—
1090C23—88no—
1091C23C2×H(5,𝔽2)12yes—
1092C23C2×H(5,𝔽2)12yes—
1093C23C2×H(5,𝔽2)14yes—
1094C23C2×H(5,𝔽2)12yes—
1095C23#58512yes—
1096C23C2611yescharacteristic
1097Q8—48no—
1098Q8—48no—
1099Q8—48no—
1100D4—44no—
1101D4—44no—
1102D4—44no—
1103D4—44no—
1104D4—48no—
1105D4—416no—
1106D4—416no—
1107D4—416no—
1108D4—48no—
1109D4—48no—
1110D4—84no—
1111D4—88no—
1112D4—88no—
1113D4—88no—
1114D4—88no—
1115D4—88no—
1116D4—84no—
1117D4—88no—
1118D4—168no—
1119D4—168no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—28no—
1132C2×C4—28no—
1133C2×C4—24no—
1134C2×C4—28no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—28no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—21no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—21no—
1153C2×C4—28no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—28no—
1161C2×C4—44no—
1162C2×C4—48no—
1163C2×C4—416no—
1164C2×C4—44no—
1165C2×C4—44no—
1166C2×C4—44no—
1167C2×C4—44no—
1168C2×C4—44no—
1169C2×C4—44no—
1170C2×C4—44no—
1171C2×C4—44no—
1172C2×C4—44no—
1173C2×C4—44no—
1174C2×C4—416no—
1175C2×C4—416no—
1176C2×C4—82no—
1177C2×C4—88no—
1178C2×C4—88no—
1179C2×C4—88no—
1180C2×C4—88no—
1181C2×C4—168no—
1182C2×C4#560116yescomplemented
1183C2×C4C2×H(5,𝔽2)12yes—
1184C2×C4C2×H(5,𝔽2)12yes—
1185C2×C4C2×H(5,𝔽2)12yes—
1186C2×C4C2×H(5,𝔽2)14yes—
1187C2×C4C2×H(5,𝔽2)14yes—
1188C22—22no—
1189C22—22no—
1190C22—24no—
1191C22—24no—
1192C22—22no—
1193C22—22no—
1194C22—22no—
1195C22—24no—
1196C22—24no—
1197C22—24no—
1198C22—416no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—44no—
1210C22—44no—
1211C22—44no—
1212C22—41no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—42no—
1219C22—42no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—41no—
1226C22—44no—
1227C22—88no—
1228C22—816no—
1229C22C2×#56014yes—
1230C22C22×H(5,𝔽2)11yescharacteristic
1231C22C22×H(5,𝔽2)11yescharacteristic
1232C22C22×H(5,𝔽2)12yes—
1233C22C2×#58511yescharacteristic
1234C222−1+612yes—
1235C4—22no—
1236C4—41no—
1237C4—48no—
1238C4—41no—
1239C4—41no—
1240C4—48no—
1241C4—44no—
1242C4—44no—
1243C4—44no—
1244C4—44no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—44no—
1250C4—44no—
1251C4C2×#56014yes—
1252C4C2×#56014yes—
1253C2—24no—
1254C2—42no—
1255C2—42no—
1256C2—42no—
1257C2—84no—
1258C2—81no—
1259C2—84no—
1260C2C22×#56011yescharacteristic
1261C2#6281811yescharacteristic
1262C2#6288611yescharacteristic
1263C2#6291412yes—
1264C2#6292712yes—
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. #53103C2semidirect
2. #53098C2semidirect
3. #53014C2semidirect
4. #53007C2semidirect
5. #52993C2semidirect
6. #52966C2semidirect
7. #52586C2semidirect
8. #52549C2semidirect
9. #46342C2semidirect
10. #46339C2semidirect
11. #46328C2semidirect
12. #45623C2semidirect
13. #45622C2semidirect
14. #45478C2semidirect
15. #45473C2semidirect
16. #45455C2semidirect
17. #35564C2semidirect
18. #35518C2semidirect
19. #35516C2semidirect
20. #35267C2semidirect
21. #35251C2semidirect
22. #35223C2semidirect
23. #34936C2semidirect
24. C2×#2486C2semidirect
25. #34736C2semidirect
30. C2×#532C22semidirect
33. C2×#525C22semidirect
35. C2×#520C22semidirect
37. C23×C4⋊C4C22semidirect
38. #2863C22semidirect
39. #2860C22semidirect
40. #2848C22semidirect
41. #2847C22semidirect
42. #2847C22semidirect
43. #2841C22semidirect
44. #2841C22semidirect
45. #2837C22semidirect
46. #2834C22semidirect
47. #2830C22semidirect
48. #2829C22semidirect
49. #2829C22semidirect
50. #2827C22semidirect
51. #2825C22semidirect
52. #2823C22semidirect
53. #2815C22semidirect
54. #2813C22semidirect
55. #2812C22semidirect
56. #2792C22semidirect
57. #2790C22semidirect
58. #2780C22semidirect
59. #2760C22semidirect
60. #2757C22semidirect
61. #2756C22semidirect
62. #2752C22semidirect
63. #2749C22semidirect
64. #2746C22semidirect
65. #2737C22semidirect
66. #2735C22semidirect
68. #2705C22semidirect
69. #2703C22semidirect
70. #2699C22semidirect
71. #2699C22semidirect
73. #2697C22semidirect
75. #2693C22semidirect
76. #2691C22semidirect
77. #2688C22semidirect
79. #2673C22semidirect
80. #2645C22semidirect
81. #2644C22semidirect
82. #2618C22semidirect
83. #2616C22semidirect
84. #2615C22semidirect
85. #2543C22semidirect
87. #2542C22semidirect
89. #2541C22semidirect
91. #2540C22semidirect
93. #2539C22semidirect
94. #2538C22semidirect
95. #2537C22semidirect
96. #2536C22semidirect
97. #2535C22semidirect
98. #2510C22semidirect
99. #2501C22semidirect
100. #2497C22semidirect
101. #2496C22semidirect
102. #2495C22semidirect
103. #2494C22semidirect
104. #2487C22semidirect
109. #2486C22semidirect
110. #2486C22semidirect
111. #2486C22semidirect
112. #2486C22semidirect
113. #2486C22semidirect
114. #2485C22semidirect
115. #2485C22semidirect
116. #2481C22semidirect
119. #2429C22semidirect
120. #2428C22semidirect
121. #2427C22semidirect
122. #2426C22semidirect
123. #2425C22semidirect
124. #2424C22semidirect
125. #2423C22semidirect
126. #2422C22semidirect
127. #2421C22semidirect
128. #2420C22semidirect
129. #2419C22semidirect
131. #2417C22semidirect
132. #2417C22semidirect
133. #2417C22semidirect
134. #2417C22semidirect
135. #2417C22semidirect
136. #2417C22semidirect
137. #2416C22semidirect
138. #2416C22semidirect
139. #2416C22semidirect
140. #2416C22semidirect
141. #2416C22semidirect
142. #2416C22semidirect
143. #2416C22semidirect
144. #2415C22semidirect
145. #2415C22semidirect
146. #2414C22semidirect
147. #2414C22semidirect
151. #2409C22semidirect
154. #2408C22semidirect
157. #2407C22semidirect
158. #2407C22semidirect
164. #2397C22semidirect
165. C2×#398C22semidirect
169. #2377C22semidirect
171. #2317C22semidirect
172. #2316C22semidirect
175. #2311C22semidirect
177. C4×#127C22semidirect
181. C2×#389C22semidirect
183. C2×#381C22semidirect
185. C2×#380C22semidirect
186. C4×#117C22semidirect
1182. C2×C4#560semidirect

Maximal subgroups

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

subgroupindex
#531032
#530982
#530142
#530072
#529932
#529662
#525862
#525492
#463422
#463392
#463282
#456232
#456222
#454782
#454732
#454552
#355642
#355182
#355162
#352672
#352512
#352232
#349362
C2×#24862
#347362