Finite Group Databasebeta

← #8094871

Subgroups — #8094871

Order 512.

5470 conjugacy classes of subgroups.

The subgroup lattice has 1181 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53108C214yesmaximal, complemented
2#53057C214yesmaximal, complemented
3#52964C214yesmaximal, complemented
4#52959C214yesmaximal, complemented
5#52425C218yesmaximal, complemented
6#45675C214yesmaximal, complemented
7#45670C214yesmaximal, complemented
8#45486C214yesmaximal, complemented
9#45484C214yesmaximal, complemented
10#45445C218yesmaximal, complemented
11#35592C211yesmaximal, characteristic, complemented
12#35574C211yesmaximal, characteristic, complemented
13#35556C211yesmaximal, characteristic, complemented
14#35555C211yesmaximal, characteristic, complemented
15#35533C211yesmaximal, characteristic, complemented
16#35530C211yesmaximal, characteristic, complemented
17#35280C211yesmaximal, characteristic, complemented
18#35273C211yesmaximal, characteristic, complemented
19#35256C211yesmaximal, characteristic, complemented
20#35254C211yesmaximal, characteristic, complemented
21#35168C211yesmaximal, characteristic, complemented
22#35152C211yesmaximal, characteristic, complemented
23C2×#2542C211yesmaximal, characteristic, complemented
24#34745C211yesmaximal, characteristic, complemented
25#34744C211yesmaximal, characteristic, complemented
26C2×#562C2218yescomplemented
27C2×#537C2211yescharacteristic
28C2×#537C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C2×#533C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C22×C22⋊Q8C2214yes—
36C2×#520C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39C22×C4×D4C2211yescharacteristic
40#2857C2214yescomplemented
41#2857C2212yescomplemented
42#2856C2212yes—
43#2856C2212yescomplemented
44#2854C2214yes—
45#2850C2212yes—
46#2849C2214yes—
47#2847C2214yes—
48#2837C2218yescomplemented
49#2837C2218yescomplemented
50#2836C2218yescomplemented
51#2829C2218yescomplemented
52#2829C2218yescomplemented
53#2827C2218yescomplemented
54#2816C2218yescomplemented
55#2816C2218yescomplemented
56#2814C2218yescomplemented
57#2813C2218yescomplemented
58#2798C2218yescomplemented
59#2741C2218yescomplemented
60#2740C2218yescomplemented
61#2732C2218yescomplemented
62#2730C2218yescomplemented
63#2730C2218yescomplemented
64#2711C2218yescomplemented
65#2710C2218yescomplemented
66#2704C2218yescomplemented
67#2700C2218yescomplemented
68#2696C2218yescomplemented
69#2694C2218yescomplemented
70#2692C2218yescomplemented
71#2692C2218yescomplemented
72#2687C2218yescomplemented
73#2681C2218yescomplemented
74#2681C2218yescomplemented
75#2676C2218yescomplemented
76#2672C2218yescomplemented
77#2671C2218yescomplemented
78#2629C2214yescomplemented
79#2624C2214yes—
80#2622C2214yes—
81#2620C2212yes—
82#2620C2212yescomplemented
83#2620C2212yescomplemented
84#2619C2212yes—
85#2617C2214yes—
86#2592C2214yes—
87#2591C2214yes—
88#2582C2214yescomplemented
89#2579C2214yes—
90#2570C2214yescomplemented
91#2552C2214yescomplemented
92#2548C2212yes—
93#2548C2214yes—
94#2545C2212yes—
95#2544C2212yes—
96#2542C2214yes—
97#2542C2214yes—
98#2542C2214yes—
99#2542C2214yes—
100#2541C2212yes—
101#2538C2214yescomplemented
102#2538C2214yescomplemented
103#2537C2214yescomplemented
104#2507C2214yescomplemented
105#2506C2214yescomplemented
106#2502C2212yescomplemented
107#2501C2212yescomplemented
108#2500C2212yescomplemented
109#2499C2212yescomplemented
110#2492C2214yescomplemented
111#2492C2214yescomplemented
112#2491C2214yes—
113#2491C2214yescomplemented
114#2491C2214yescomplemented
115#2490C2214yes—
116#2473C2218yes—
117#2472C2218yes—
118#2454C2212yescomplemented
119#2453C2212yescomplemented
120#2452C2214yescomplemented
121#2452C2212yescomplemented
122#2451C2212yescomplemented
123#2451C2214yescomplemented
124#2450C2214yes—
125#2449C2214yes—
126#2448C2214yes—
127#2448C2212yescomplemented
128#2447C2214yes—
129#2447C2212yescomplemented
130#2446C2212yescomplemented
131#2445C2214yes—
132#2445C2214yes—
133#2445C2212yescomplemented
134#2444C2214yes—
135#2443C2214yes—
136#2443C2218yes—
137#2440C2214yescomplemented
138#2439C2214yescomplemented
139#2436C2214yes—
140#2428C2214yes—
141#2428C2214yes—
142#2428C2214yes—
143#2427C2214yes—
144#2427C2214yes—
145#2426C2214yes—
146#2424C2218yes—
147#2424C2218yes—
148#2423C2214yescomplemented
149#2422C2214yes—
150#2422C2214yescomplemented
151#2420C2214yes—
152#2418C2218yes—
153#2417C2218yes—
154#2416C2218yes—
155#2416C2214yes—
156#2414C2214yes—
157#2409C2214yes—
158#2396C2214yescomplemented
159#2395C2214yescomplemented
160C2×#399C2214yes—
161#2378C2218yescomplemented
162#2317C2211yescharacteristic
163#2317C2211yescharacteristic
164#2316C2211yescharacteristic
165#2316C2211yescharacteristic
166#2311C2211yescharacteristic
167#2311C2211yescharacteristic
168#2311C2211yescharacteristic
169#2311C2211yescharacteristic
170#2309C2211yescharacteristic
171C4×C22⋊Q8C2214yescomplemented
172C4×#123C2214yescomplemented
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2211yescharacteristic
177#2297C2211yescharacteristic
178#2296C2211yescharacteristic
179#2296C2211yescharacteristic
180#2296C2211yescharacteristic
181C2×#390C2211yescharacteristic
182C2×#390C2211yescharacteristic
183C2×#384C2211yescharacteristic
184C2×#384C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C22×#41C2311yescharacteristic
190C23×Q8C2312yes—
191C23×D4C2311yescharacteristic
192C24×C4C2312yes—
193#562—432no—
194#537—44no—
195#537—44no—
196#535—44no—
197#535—44no—
198#535—44no—
199#533—44no—
200#532—44no—
201C2×C4⋊Q8—44no—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2314yes—
205C2×C4⋊Q8C2314yes—
206C2×#127C2312yes—
207C2×#127C2311yescharacteristic
208C2×#127C2312yes—
209C2×#127C2312yes—
210C2×#125C2312yes—
211C2×#125C2318yes—
212C2×#124C2312yes—
213C2×#124C2312yes—
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#124C2318yes—
217C2×#124C2312yes—
218C2×#124C2318yes—
219C2×#123C2314yes—
220C2×#123C2318yes—
221C2×#123C2318yes—
222C2×#123C2318yes—
223C2×C22⋊Q8—416no—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2318yes—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2312yes—
236C2×#121C2318yes—
237C2×#121C2318yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2312yes—
241C2×#121C2314yes—
242C2×#121C2312yes—
243C2×#121C2312yes—
244C2×#121C2312yes—
245C2×#121C2312yes—
246C2×#121C2318yes—
247C2×#121C2314yes—
248C2×#121C2318yes—
249C2×#121C2314yes—
250C2×#121C2312yes—
251C2×#120C2314yes—
252C2×#120C2314yes—
253C2×#120C2314yes—
254#520—44no—
255C4×#41—44no—
256C4×#41—44no—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2312yes—
261C2×C4×D4—44no—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2312yes—
271C2×#117C2311yescharacteristic
272C2×#117C2311yescharacteristic
273C2×#117C2311yescharacteristic
274C2×#117C2311yescharacteristic
275C2×#117C2311yescharacteristic
276C2×#117C2312yes—
277C2×#117C2312yes—
278C2×#117C2312yes—
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2314yes—
285C22×C4⋊C4C2314yes—
286C22×C4⋊C4C2312yes—
287C22×C22⋊C4C2312yes—
288C22×C22⋊C4C2314yes—
289C22×C22⋊C4C2314yes—
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293C22×C42C2312yes—
294C22×C42C2312yes—
295#400C2318yes—
296#400C2314yes—
297#400C2318yes—
298#400C2314yes—
299#399C2314yes—
300#399C2314yes—
301#399C2318yes—
302#399C2318yes—
303#399C2318yes—
304#399C2318yes—
305#399C2318yes—
306#399C2318yes—
307#398C2318yes—
308#398C2318yes—
309#398C2318yes—
310#398C2318yes—
311#398C2318yes—
312#398C2318yes—
313#398C2318yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#397C2314yes—
318#397C2318yes—
319#397C2318yes—
320#397C2314yes—
321#397C2318yes—
322#397C2318yes—
323#397C2318yes—
324#397C2318yes—
325#397C2314yes—
326#396C2318yes—
327#396C2318yes—
328#396C2314yes—
329#396C2318yes—
330#396C2318yes—
331#396C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2314yes—
335#395C2314yes—
336#395C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2318yes—
350#394C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2314yes—
354#394C2314yes—
355#393C2314yes—
356#393C2318yes—
357#393C2318yes—
358#393C2318yes—
359#393C2318yes—
360#392C2318yes—
361#392C2318yes—
362#392C2318yes—
363#391C2312yes—
364#391C2312yes—
365#391C2312yes—
366#391C2312yes—
367#391C2318yes—
368#391C2312yes—
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2318yes—
372#391C2318yes—
373#391C2312yes—
374#391C2312yes—
375#391C2312yes—
376#391C2314yes—
377#390C2314yes—
378#390C2314yes—
379#390C2312yes—
380#390C2312yes—
381#390C2312yes—
382#390C2312yes—
383#390C2318yes—
384#390C2318yes—
385#390C2314yes—
386#390C2312yes—
387#390C2312yes—
388#390C2311yescharacteristic
389#390C2318yes—
390#390C2318yes—
391#390C2311yescharacteristic
392#390C2312yes—
393#390C2312yes—
394#390C2314yes—
395#390C2312yes—
396#390C2312yes—
397#390C2312yes—
398#390C2312yes—
399#389C2312yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2318yes—
407#389C2318yes—
408#389C2318yes—
409#389C2312yes—
410#389C2312yes—
411#389C2312yes—
412#389C2312yes—
413#389C2312yes—
414#389C2314yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2314yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2314yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2318yes—
433#387C2314yes—
434#386C2314yes—
435#386C2314yes—
436#386C2314yes—
437#386C2314yes—
438#386C2318yes—
439#386C2312yes—
440#386C2312yes—
441#386C2312yes—
442#386C2312yes—
443#386C2312yes—
444#386C2318yes—
445#386C2318yes—
446#386C2312yes—
447#386C2318yes—
448#386C2318yes—
449#386C2318yes—
450#386C2314yes—
451#386C2314yes—
452#386C2314yes—
453#385C2318yes—
454#385C2318yes—
455#385C2314yes—
456#385C2314yes—
457#385C2312yes—
458#385C2312yes—
459#385C2318yes—
460#385C2314yes—
461#385C2314yes—
462#385C2314yes—
463#385C2314yes—
464#385C2314yes—
465#384C2314yes—
466#384C2312yes—
467#384C2312yes—
468#384C2314yes—
469#384C2312yes—
470#384C2312yes—
471#384C2312yes—
472#384C2312yes—
473#382C2312yes—
474#382C2312yes—
475#381C2314yes—
476#381C2318yes—
477#380C2314yes—
478#380C2314yes—
479#380C2314yes—
480#380C2314yes—
481#380C2314yes—
482#380C2314yes—
483#380C2318yes—
484#380C2318yes—
485#380C2318yes—
486#380C2314yes—
487#379C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2312yes—
505C2×#95C2312yes—
506C25C2412yes—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—24no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C22×Q8—44no—
517C22×Q8—48no—
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2414yes—
522C22×Q8C2418yes—
523C22×D4—24no—
524C22×D4—24no—
525C22×D4—24no—
526C22×D4C2412yes—
527C22×D4C2412yes—
528C22×D4C2412yes—
529C22×D4C2412yes—
530C22×D4C2411yescharacteristic
531C22×D4C2412yes—
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2414yes—
535C22×D4C2414yes—
536C22×D4C2418yes—
537C22×D4C2418yes—
538C22×D4C2414yes—
539C22×D4C2414yes—
540C22×D4C2414yes—
541C23×C4—48no—
542C23×C4—44no—
543C23×C4C2411yescharacteristic
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2411yescharacteristic
552C23×C4C2412yes—
553C23×C4C2414yes—
554C23×C4C2414yes—
555C23×C4C2418yes—
556C23×C4C2414yes—
557C23×C4C2411yescharacteristic
558C4⋊Q8—48no—
559C4⋊Q8—48no—
560C4⋊Q8—44no—
561C4⋊Q8—42no—
562#127—42no—
563#127—44no—
564#127—44no—
565#127—44no—
566#125—44no—
567#125—416no—
568#124—42no—
569#124—42no—
570#124—44no—
571#124—44no—
572#124—44no—
573#124—416no—
574#124—416no—
575#123—216no—
576#123—416no—
577#123—416no—
578#123—416no—
579C22⋊Q8—232no—
580C22⋊Q8—216no—
581C22⋊Q8—48no—
582C22⋊Q8—416no—
583C22⋊Q8—416no—
584C22⋊Q8—416no—
585C22⋊Q8—416no—
586C22⋊Q8—44no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C22⋊Q8—44no—
590C22⋊Q8—416no—
591#121—416no—
592#121—416no—
593#121—416no—
594#121—44no—
595#121—44no—
596#121—48no—
597#121—48no—
598#121—44no—
599#121—44no—
600#121—44no—
601#121—44no—
602#121—416no—
603#121—48no—
604#121—48no—
605#121—48no—
606#120—48no—
607#120—48no—
608#120—48no—
609C4×Q8—48no—
610C4×Q8—44no—
611C4×Q8—44no—
612C4×Q8—44no—
613C4×D4—48no—
614C4×D4—48no—
615C4×D4—44no—
616C4×D4—44no—
617C4×D4—44no—
618C4×D4—48no—
619C4×D4—48no—
620C4×D4—48no—
621C4×D4—48no—
622#117—24no—
623#117—24no—
624#117—24no—
625#117—24no—
626#117—24no—
627#117—44no—
628#117—44no—
629#117—44no—
630C2×C4⋊C4—24no—
631C2×C4⋊C4—24no—
632C2×C4⋊C4—24no—
633C2×C4⋊C4—28no—
634C2×C4⋊C4—44no—
635C2×C4⋊C4—48no—
636C2×C4⋊C4—48no—
637C2×C4⋊C4—44no—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2411yescharacteristic
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⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
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⋊C4C2418yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C22⋊C4—48no—
679C2×C22⋊C4—48no—
680C2×C22⋊C4—44no—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2418yes—
720C2×C42—24no—
721C2×C42—24no—
722C2×C42—24no—
723C2×C42—44no—
724C2×C42—44no—
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2412yes—
728C2×C42C2411yescharacteristic
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2412yes—
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2414yes—
739C2×C42C2414yes—
740C2×C42C2414yes—
741C2×C42C2418yes—
742#95C2412yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771C24—24no—
772C24—24no—
773C24—24no—
774C24—44no—
775C24—44no—
776C24C2514yes—
777C24C2512yes—
778C24C2512yes—
779C24C2512yes—
780C24C2511yescharacteristic
781#41—416no—
782#41—416no—
783#41—416no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—22no—
787C2×Q8—22no—
788C2×Q8—22no—
789C2×Q8—22no—
790C2×Q8—28no—
791C2×Q8—216no—
792C2×Q8—22no—
793C2×Q8—22no—
794C2×Q8—22no—
795C2×Q8—44no—
796C2×Q8—48no—
797C2×Q8—48no—
798C2×Q8—44no—
799C2×Q8—816no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—22no—
811C2×D4—24no—
812C2×D4—22no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—28no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—44no—
828C2×D4—48no—
829C2×D4—48no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4—48no—
834C2×D4—48no—
835C2×D4—48no—
836C2×D4—48no—
837C2×D4—48no—
838C2×D4—48no—
839C2×D4—48no—
840C2×D4—48no—
841C2×D4—416no—
842C22×C4—22no—
843C22×C4—24no—
844C22×C4—22no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—24no—
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—28no—
862C22×C4—28no—
863C22×C4—216no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—48no—
878C22×C4—816no—
879C22×C4H(5,𝔽2)14yes—
880C22×C4H(5,𝔽2)14yes—
881C22×C42−1+414yes—
882C22×C4C2512yes—
883C22×C4C2514yes—
884C22×C4C2512yes—
885C22×C4C2512yes—
886C22×C4C2512yes—
887C22×C4C2512yes—
888C22×C4C2514yes—
889C22×C4C2514yes—
890C22×C4C2514yes—
891C22×C4C2512yes—
892C22×C4C2512yes—
893C22×C4C2514yes—
894C22×C4C2514yes—
895C22×C4C2512yes—
896C22×C4C2514yes—
897C22×C4C2512yes—
898C22×C4C2512yes—
899C22×C4C2512yes—
900C22×C4C2511yescharacteristic
901C22×C4C2511yescharacteristic
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—24no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—22no—
912C4⋊C4—216no—
913C4⋊C4—216no—
914C4⋊C4—22no—
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—28no—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—24no—
922C4⋊C4—44no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—48no—
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—48no—
938C4⋊C4—48no—
939C4⋊C4—48no—
940C4⋊C4—48no—
941C4⋊C4H(5,𝔽2)18yes—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—216no—
948C22⋊C4—216no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—48no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—48no—
977C22⋊C4—48no—
978C22⋊C4—48no—
979C22⋊C4—48no—
980C22⋊C4—48no—
981C42—22no—
982C42—22no—
983C42—22no—
984C42—22no—
985C42—24no—
986C42—24no—
987C42—24no—
988C42—24no—
989C42—24no—
990C42—24no—
991C42—24no—
992C42—24no—
993C42—24no—
994C42—44no—
995C42—44no—
996C42—44no—
997C42—48no—
998C23—22no—
999C23—22no—
1000C23—28no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—24no—
1008C23—24no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—28no—
1020C23—416no—
1021C23—48no—
1022C23—84no—
1023C23—84no—
1024C23—88no—
1025C23C2×H(5,𝔽2)12yes—
1026C23C2×H(5,𝔽2)12yes—
1027C23C2×2−1+412yes—
1028C23C2611yescharacteristic
1029Q8—44no—
1030Q8—44no—
1031Q8—44no—
1032Q8—88no—
1033Q8—816no—
1034D4—48no—
1035D4—48no—
1036D4—48no—
1037D4—48no—
1038D4—48no—
1039D4—44no—
1040D4—44no—
1041D4—44no—
1042D4—88no—
1043D4—164no—
1044D4—164no—
1045D4—164no—
1046D4—164no—
1047D4—168no—
1048D4—168no—
1049C2×C4—28no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—28no—
1070C2×C4—24no—
1071C2×C4—28no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—28no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—48no—
1097C2×C4—48no—
1098C2×C4—44no—
1099C2×C4—48no—
1100C2×C4—48no—
1101C2×C4—48no—
1102C2×C4—88no—
1103C2×C4—88no—
1104C2×C4—816no—
1105C2×C4—84no—
1106C2×C4—84no—
1107C2×C4—84no—
1108C2×C4—164no—
1109C2×C4#562116yescomplemented
1110C2×C4C2×H(5,𝔽2)14yes—
1111C2×C4C2×H(5,𝔽2)14yes—
1112C2×C4C2×H(5,𝔽2)14yes—
1113C2×C4C2×H(5,𝔽2)12yes—
1114C2×C4C2×H(5,𝔽2)12yes—
1115C2×C4C2×H(5,𝔽2)12yes—
1116C2×C4C2×H(5,𝔽2)12yes—
1117C2×C4C2×2−1+412yes—
1118C2×C4C2×2−1+412yes—
1119C22—22no—
1120C22—22no—
1121C22—24no—
1122C22—24no—
1123C22—44no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—44no—
1129C22—42no—
1130C22—42no—
1131C22—44no—
1132C22—44no—
1133C22—44no—
1134C22—48no—
1135C22—44no—
1136C22—44no—
1137C22—44no—
1138C22—48no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—44no—
1143C22—816no—
1144C22C2×#56214yes—
1145C22C22×H(5,𝔽2)11yescharacteristic
1146C22C22×H(5,𝔽2)12yes—
1147C22C22×H(5,𝔽2)11yescharacteristic
1148C22C22×2−1+411yescharacteristic
1149C222−1+612yes—
1150C4—24no—
1151C4—24no—
1152C4—24no—
1153C4—44no—
1154C4—44no—
1155C4—44no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—44no—
1160C4—42no—
1161C4—42no—
1162C4—44no—
1163C4—44no—
1164C4—44no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4C2×#56214yes—
1169C4C2×#56214yes—
1170C2—24no—
1171C2—82no—
1172C2—82no—
1173C2—82no—
1174C2—84no—
1175C2C22×#56211yescharacteristic
1176C2#6283211yescharacteristic
1177C2#6288711yescharacteristic
1178C2#6291312yes—
1179C2#6291412yes—
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. #53108C2semidirect
2. #53057C2semidirect
3. #52964C2semidirect
4. #52959C2semidirect
5. #52425C2semidirect
6. #45675C2semidirect
7. #45670C2semidirect
8. #45486C2semidirect
9. #45484C2semidirect
10. #45445C2semidirect
11. #35592C2semidirect
12. #35574C2semidirect
13. #35556C2semidirect
14. #35555C2semidirect
15. #35533C2semidirect
16. #35530C2semidirect
17. #35280C2semidirect
18. #35273C2semidirect
19. #35256C2semidirect
20. #35254C2semidirect
21. #35168C2semidirect
22. #35152C2semidirect
23. C2×#2542C2semidirect
24. #34745C2semidirect
25. #34744C2semidirect
26. C2×#562C22semidirect
40. #2857C22semidirect
41. #2857C22semidirect
43. #2856C22semidirect
48. #2837C22semidirect
49. #2837C22semidirect
50. #2836C22semidirect
51. #2829C22semidirect
52. #2829C22semidirect
53. #2827C22semidirect
54. #2816C22semidirect
55. #2816C22semidirect
56. #2814C22semidirect
57. #2813C22semidirect
58. #2798C22semidirect
59. #2741C22semidirect
60. #2740C22semidirect
61. #2732C22semidirect
62. #2730C22semidirect
63. #2730C22semidirect
64. #2711C22semidirect
65. #2710C22semidirect
66. #2704C22semidirect
67. #2700C22semidirect
68. #2696C22semidirect
69. #2694C22semidirect
70. #2692C22semidirect
71. #2692C22semidirect
72. #2687C22semidirect
73. #2681C22semidirect
74. #2681C22semidirect
75. #2676C22semidirect
76. #2672C22semidirect
77. #2671C22semidirect
78. #2629C22semidirect
82. #2620C22semidirect
83. #2620C22semidirect
88. #2582C22semidirect
90. #2570C22semidirect
91. #2552C22semidirect
101. #2538C22semidirect
102. #2538C22semidirect
103. #2537C22semidirect
104. #2507C22semidirect
105. #2506C22semidirect
106. #2502C22semidirect
107. #2501C22semidirect
108. #2500C22semidirect
109. #2499C22semidirect
110. #2492C22semidirect
111. #2492C22semidirect
113. #2491C22semidirect
114. #2491C22semidirect
118. #2454C22semidirect
119. #2453C22semidirect
120. #2452C22semidirect
121. #2452C22semidirect
122. #2451C22semidirect
123. #2451C22semidirect
127. #2448C22semidirect
129. #2447C22semidirect
130. #2446C22semidirect
133. #2445C22semidirect
137. #2440C22semidirect
138. #2439C22semidirect
148. #2423C22semidirect
150. #2422C22semidirect
158. #2396C22semidirect
159. #2395C22semidirect
161. #2378C22semidirect
171. C4×C22⋊Q8C22semidirect
172. C4×#123C22semidirect
1109. C2×C4#562semidirect

Maximal subgroups

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

subgroupindex
#531082
#530572
#529642
#529592
#524252
#456752
#456702
#454862
#454842
#454452
#355922
#355742
#355562
#355552
#355332
#355302
#352802
#352732
#352562
#352542
#351682
#351522
C2×#25422
#347452
#347442