Finite Group Databasebeta

← #7649992

Subgroups — #7649992

Order 512.

5446 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42925C214yesmaximal, complemented
2#42873C214yesmaximal, complemented
3#42551C214yesmaximal, complemented
4#42453C214yesmaximal, complemented
5#40697C218yesmaximal, complemented
6#40191C214yesmaximal, complemented
7#39915C214yesmaximal, complemented
8#39397C214yesmaximal, complemented
9#39348C214yesmaximal, complemented
10#37721C218yesmaximal, complemented
11#35574C211yesmaximal, characteristic, complemented
12#35574C211yesmaximal, characteristic, complemented
13#35557C211yesmaximal, characteristic, complemented
14#35555C211yesmaximal, characteristic, complemented
15#35533C211yesmaximal, characteristic
16#35531C211yesmaximal, characteristic, complemented
17#35266C211yesmaximal, characteristic, complemented
18#35254C211yesmaximal, characteristic, complemented
19#35152C211yesmaximal, characteristic, complemented
20C2×#2542C211yesmaximal, characteristic, complemented
21#34815C211yesmaximal, characteristic, complemented
22#34744C211yesmaximal, characteristic, complemented
23#34265C211yesmaximal, characteristic, complemented
24#34207C211yesmaximal, characteristic, complemented
25#34183C211yesmaximal, characteristic, complemented
26C2×#539C2218yescomplemented
27C2×#535C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#532C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2214yes—
32C2×#520C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×D4C2211yescharacteristic
37#2860C2214yes—
38#2854C2214yes—
39#2849C2214yes—
40#2837C2218yescomplemented
41#2827C2218yescomplemented
42#2796C2218yescomplemented
43#2796C2218yescomplemented
44#2773C2218yescomplemented
45#2740C2218yescomplemented
46#2732C2218yescomplemented
47#2728C2218yescomplemented
48#2721C2218yescomplemented
49#2720C2218yescomplemented
50#2718C2218yescomplemented
51#2711C2218yescomplemented
52#2705C2218yescomplemented
53#2696C2218yescomplemented
54#2689C2218yescomplemented
55#2687C2218yescomplemented
56#2681C2218yescomplemented
57#2680C2218yescomplemented
58#2663C2218yescomplemented
59#2654C2218yescomplemented
60#2651C2218yescomplemented
61#2644C2214yes—
62#2638C2218yescomplemented
63#2636C2218yescomplemented
64#2624C2214yes—
65#2623C2218yescomplemented
66#2622C2214yes—
67#2596C2218yescomplemented
68#2579C2214yes—
69#2579C2214yes—
70#2570C2214yescomplemented
71#2560C2218yescomplemented
72#2556C2218yescomplemented
73#2552C2214yescomplemented
74#2548C2212yes—
75#2545C2212yes—
76#2544C2212yes—
77#2542C2214yes—
78#2542C2214yes—
79#2542C2214yes—
80#2542C2214yes—
81#2541C2212yes—
82#2513C2214yes—
83#2512C2214yes—
84#2512C2214yescomplemented
85#2511C2214yescomplemented
86#2509C2212yescomplemented
87#2508C2212yescomplemented
88#2507C2214yescomplemented
89#2507C2212yescomplemented
90#2506C2212yescomplemented
91#2506C2214yescomplemented
92#2505C2214yes—
93#2504C2212yes—
94#2501C2212yes—
95#2500C2212yes—
96#2500C2212yes—
97#2497C2214yescomplemented
98#2496C2214yescomplemented
99#2481C2218yes—
100#2480C2218yes—
101#2473C2214yes—
102#2473C2218yes—
103#2463C2218yescomplemented
104#2452C2214yescomplemented
105#2452C2214yescomplemented
106#2451C2214yescomplemented
107#2451C2214yescomplemented
108#2449C2218yescomplemented
109#2448C2214yes—
110#2448C2214yes—
111#2448C2212yescomplemented
112#2447C2214yes—
113#2447C2212yescomplemented
114#2446C2212yescomplemented
115#2445C2214yes—
116#2445C2214yes—
117#2445C2214yes—
118#2445C2212yescomplemented
119#2444C2214yes—
120#2443C2214yes—
121#2443C2218yescomplemented
122#2440C2214yescomplemented
123#2440C2214yescomplemented
124#2439C2214yescomplemented
125#2439C2214yescomplemented
126#2424C2218yes—
127#2422C2214yes—
128#2420C2214yes—
129#2418C2218yes—
130#2418C2218yes—
131#2416C2214yes—
132#2414C2214yes—
133#2409C2214yes—
134#2409C2214yes—
135#2402C2214yescomplemented
136#2395C2214yescomplemented
137C2×#399C2214yes—
138#2367C2214yes—
139#2366C2214yes—
140#2363C2214yes—
141#2361C2218yes—
142#2361C2214yes—
143#2354C2214yescomplemented
144Q8×C4⋊C4C2214yescomplemented
145D4×C4⋊C4C2218yes—
146D4×C4⋊C4C2214yescomplemented
147D4×C4⋊C4C2214yescomplemented
148#2332C2218yescomplemented
149#2326C2212yescomplemented
150#2326C2212yescomplemented
151#2321C2214yes—
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2211yescharacteristic
155#2317C2212yescomplemented
156#2317C2212yescomplemented
157#2316C2211yescharacteristic
158#2316C2211yescharacteristic
159#2311C2211yescharacteristic
160#2311C2211yescharacteristic
161#2311C2211yescharacteristic
162#2309C2211yescharacteristic
163#2309C2211yescharacteristic
164C4×C4⋊Q8C2212yescomplemented
165C4×#127C2212yescomplemented
166C4×#125C2214yescomplemented
167C4×#123C2214yescomplemented
168C4×#120C2214yes—
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177C2×#390C2211yescharacteristic
178C2×#390C2211yescharacteristic
179#2285C2211yescharacteristic
180#2285C2212yescomplemented
181C2×#384C2211yescharacteristic
182C2×#384C2211yescharacteristic
183C2×#384C2212yescomplemented
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2312yes—
190C23×D4C2311yescharacteristic
191C24×C4C2312yes—
192#539—432no—
193#535—28no—
194#535—44no—
195#532—28no—
196C2×C4⋊Q8—44no—
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2314yes—
200C2×#127C2311yescharacteristic
201C2×#127C2312yes—
202C2×#127C2312yes—
203C2×#126C2318yes—
204C2×#126C2318yes—
205C2×#125C2314yes—
206C2×#125C2318yes—
207C2×#124C2311yescharacteristic
208C2×#124C2311yescharacteristic
209C2×#124C2312yes—
210C2×#124C2312yes—
211C2×#123C2314yes—
212C2×#123C2318yes—
213C2×#123C2318yes—
214C2×#123C2318yes—
215C2×C22⋊Q8—416no—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2318yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#121C2318yes—
227C2×#120C2314yes—
228C2×#120C2314yes—
229#520—44no—
230#520—44no—
231#520—44no—
232C4×#41—28no—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×D4—44no—
238C2×C4×D4C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2318yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2318yes—
250C2×C4×D4C2314yes—
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2312yes—
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2318yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2314yes—
272C22×C22⋊C4C2312yes—
273C22×C22⋊C4C2314yes—
274C22×C22⋊C4C2314yes—
275C22×C42C2312yes—
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279#400C2318yes—
280#400C2314yes—
281#400C2318yes—
282#400C2314yes—
283#400C2318yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#399C2318yes—
288#399C2318yes—
289#399C2318yes—
290#399C2318yes—
291#399C2318yes—
292#399C2318yes—
293#399C2314yes—
294#398C2314yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2318yes—
303#398C2314yes—
304#397C2318yes—
305#397C2314yes—
306#397C2318yes—
307#397C2318yes—
308#397C2314yes—
309#397C2318yes—
310#397C2318yes—
311#397C2318yes—
312#397C2314yes—
313#397C2318yes—
314#397C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2318yes—
318#396C2318yes—
319#396C2318yes—
320#395C2318yes—
321#395C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2314yes—
331#394C2314yes—
332#393C2318yes—
333#393C2318yes—
334#392C2318yes—
335#391C2318yes—
336#391C2312yes—
337#391C2312yes—
338#391C2312yes—
339#391C2318yes—
340#391C2312yes—
341#391C2312yes—
342#391C2312yes—
343#390C2318yes—
344#390C2312yes—
345#390C2312yes—
346#390C2318yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2312yes—
351#390C2312yes—
352#390C2312yes—
353#390C2318yes—
354#390C2312yes—
355#390C2312yes—
356#390C2312yes—
357#390C2312yes—
358#390C2312yes—
359#390C2314yes—
360#390C2312yes—
361#390C2312yes—
362#390C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2318yes—
366#389C2312yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2318yes—
375#389C2318yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2312yes—
382#389C2318yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#388C2314yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2314yes—
399#388C2318yes—
400#388C2318yes—
401#387C2318yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2314yes—
410#387C2318yes—
411#387C2314yes—
412#387C2318yes—
413#386C2318yes—
414#386C2314yes—
415#386C2314yes—
416#386C2314yes—
417#386C2318yes—
418#386C2312yes—
419#386C2312yes—
420#386C2312yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2312yes—
426#386C2314yes—
427#386C2314yes—
428#385C2318yes—
429#385C2318yes—
430#385C2314yes—
431#385C2314yes—
432#385C2314yes—
433#385C2318yes—
434#385C2312yes—
435#385C2312yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2312yes—
440#385C2318yes—
441#385C2318yes—
442#385C2312yes—
443#385C2314yes—
444#385C2314yes—
445#385C2314yes—
446#385C2314yes—
447#384C2312yes—
448#384C2314yes—
449#384C2312yes—
450#384C2312yes—
451#384C2312yes—
452#384C2312yes—
453#384C2312yes—
454#384C2318yes—
455#384C2314yes—
456#384C2312yes—
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#382C2314yes—
460#382C2312yes—
461#382C2312yes—
462#382C2312yes—
463#382C2311yescharacteristic
464#382C2311yescharacteristic
465#381C2318yes—
466#381C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2314yes—
473#380C2318yes—
474#379C2314yes—
475#379C2314yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2318yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C22⋊C4C2318yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500#376C2312yes—
501C2×#95C2312yes—
502C43C2312yes—
503C25C2412yes—
504C2×#41—24no—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41#4118yes—
510C22×Q8—44no—
511C22×Q8—48no—
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2418yes—
515C22×D4—24no—
516C22×D4—24no—
517C22×D4—24no—
518C22×D4C2412yes—
519C22×D4C2412yes—
520C22×D4C2412yes—
521C22×D4C2411yescharacteristic
522C22×D4C2414yes—
523C22×D4C2412yes—
524C22×D4C2411yescharacteristic
525C22×D4C2418yes—
526C22×D4C2414yes—
527C22×D4C2414yes—
528C23×C4—48no—
529C23×C4—44no—
530C23×C4C2411yescharacteristic
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2414yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2411yescharacteristic
539C23×C4C2412yes—
540C23×C4C2418yes—
541C23×C4C2414yes—
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2411yescharacteristic
545C4⋊Q8—24no—
546C4⋊Q8—48no—
547C4⋊Q8—48no—
548#127—24no—
549#127—28no—
550#127—44no—
551#126—416no—
552#126—416no—
553#125—216no—
554#125—416no—
555#124—24no—
556#124—28no—
557#124—24no—
558#124—44no—
559#123—216no—
560#123—416no—
561#123—416no—
562#123—416no—
563C22⋊Q8—232no—
564C22⋊Q8—416no—
565C22⋊Q8—416no—
566C22⋊Q8—416no—
567C22⋊Q8—416no—
568C22⋊Q8—416no—
569#121—216no—
570#121—216no—
571#121—416no—
572#121—44no—
573#121—44no—
574#120—216no—
575#120—48no—
576C4×Q8—28no—
577C4×Q8—44no—
578C4×Q8—44no—
579C4×Q8—44no—
580C4×D4—216no—
581C4×D4—28no—
582C4×D4—216no—
583C4×D4—48no—
584C4×D4—48no—
585C4×D4—44no—
586C4×D4—44no—
587C4×D4—44no—
588C4×D4—416no—
589C4×D4—416no—
590C4×D4—48no—
591C4×D4—48no—
592C4×D4—48no—
593#117—28no—
594#117—24no—
595#117—24no—
596#117—24no—
597#117—24no—
598#117—24no—
599#117—24no—
600#117—44no—
601#117—44no—
602#117—44no—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—28no—
607C2×C4⋊C4—44no—
608C2×C4⋊C4—44no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—48no—
611C2×C4⋊C4—48no—
612C2×C4⋊C4—416no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C22⋊C4—48no—
660C2×C22⋊C4—48no—
661C2×C22⋊C4—44no—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C42—28no—
696C2×C42—24no—
697C2×C42—24no—
698C2×C42—24no—
699C2×C42C2412yes—
700C2×C42C2411yescharacteristic
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2414yes—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2418yes—
719C2×C42C2414yes—
720#95C2412yes—
721#95C2412yes—
722#95C2412yes—
723#95C2412yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753C24—24no—
754C24—24no—
755C24—24no—
756C24—44no—
757C24—44no—
758C24C2514yes—
759C24C2512yes—
760C24C2512yes—
761C24C2511yescharacteristic
762#41—232no—
763#41—416no—
764C2×Q8—22no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—216no—
768C2×Q8—22no—
769C2×Q8—22no—
770C2×Q8—48no—
771C2×Q8—48no—
772C2×Q8—816no—
773C2×Q8C2×#4114yes—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—28no—
777C2×D4—24no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—216no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—28no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—22no—
793C2×D4—44no—
794C2×D4—48no—
795C2×D4—48no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—48no—
799C2×D4—48no—
800C2×D4—416no—
801C2×D4C2×#4118yes—
802C2×D4C2×#4114yes—
803C22×C4—22no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—28no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—22no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—28no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—216no—
821C22×C4—42no—
822C22×C4—44no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—816no—
837C22×C4C2×#4118yes—
838C22×C4C2×#4114yes—
839C22×C4H(5,𝔽2)14yes—
840C22×C42−1+414yes—
841C22×C4C2512yes—
842C22×C4C2512yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C4⋊C4—28no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—216no—
878C4⋊C4—28no—
879C4⋊C4—216no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—48no—
906C4⋊C4H(5,𝔽2)18yes—
907C22⋊C4—28no—
908C22⋊C4—24no—
909C22⋊C4—24no—
910C22⋊C4—28no—
911C22⋊C4—24no—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—28no—
916C22⋊C4—216no—
917C22⋊C4—216no—
918C22⋊C4—216no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C42—22no—
941C42—24no—
942C42—22no—
943C42—24no—
944C42—28no—
945C42—24no—
946C42—22no—
947C42—22no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—24no—
953C42—28no—
954C42—24no—
955C42—24no—
956C42—44no—
957C42—44no—
958C42—44no—
959C42—44no—
960C42—48no—
961C23—22no—
962C23—22no—
963C23—24no—
964C23—22no—
965C23—22no—
966C23—24no—
967C23—22no—
968C23—24no—
969C23—28no—
970C23—24no—
971C23—24no—
972C23—22no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—28no—
977C23—416no—
978C23—48no—
979C23—84no—
980C23—88no—
981C23—84no—
982C23C22×#4114yes—
983C23C22×#4112yes—
984C23C2×H(5,𝔽2)12yes—
985C23C2×2−1+412yes—
986C23C2611yescharacteristic
987Q8—28no—
988Q8—44no—
989Q8—816no—
990D4—216no—
991D4—28no—
992D4—416no—
993D4—48no—
994D4—48no—
995D4—48no—
996D4—44no—
997D4—816no—
998D4—164no—
999D4—164no—
1000C2×C4—28no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—216no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—28no—
1031C2×C4—28no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—48no—
1049C2×C4—416no—
1050C2×C4—48no—
1051C2×C4—44no—
1052C2×C4—48no—
1053C2×C4—816no—
1054C2×C4—84no—
1055C2×C4—84no—
1056C2×C4—84no—
1057C2×C4—164no—
1058C2×C4—164no—
1059C2×C4—164no—
1060C2×C4#539116yescomplemented
1061C2×C4C22×#4114yes—
1062C2×C4C22×#4112yes—
1063C2×C4C22×#4112yes—
1064C2×C4C2×H(5,𝔽2)14yes—
1065C2×C4C2×H(5,𝔽2)14yes—
1066C2×C4C2×H(5,𝔽2)14yes—
1067C2×C4C2×H(5,𝔽2)12yes—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4C2×2−1+412yes—
1070C2×C4C2×2−1+412yes—
1071C22—24no—
1072C22—22no—
1073C22—22no—
1074C22—24no—
1075C22—28no—
1076C22—24no—
1077C22—42no—
1078C22—42no—
1079C22—44no—
1080C22—44no—
1081C22—48no—
1082C22—44no—
1083C22—42no—
1084C22—42no—
1085C22—44no—
1086C22—44no—
1087C22—48no—
1088C22—42no—
1089C22—44no—
1090C22—816no—
1091C22C2×#53914yes—
1092C22C23×#4111yescharacteristic
1093C22C22×H(5,𝔽2)12yes—
1094C22C22×H(5,𝔽2)11yescharacteristic
1095C22C22×2−1+411yescharacteristic
1096C222−1+612yes—
1097C4—24no—
1098C4—24no—
1099C4—24no—
1100C4—24no—
1101C4—42no—
1102C4—44no—
1103C4—42no—
1104C4—44no—
1105C4—44no—
1106C4—44no—
1107C4—44no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—42no—
1113C4—44no—
1114C4—44no—
1115C4—42no—
1116C4C2×#53914yes—
1117C4C2×#53914yes—
1118C2—24no—
1119C2—44no—
1120C2—82no—
1121C2—84no—
1122C2C22×#53911yescharacteristic
1123C2#6283211yescharacteristic
1124C2#6288711yescharacteristic
1125C2#6291312yes—
1126C2#6298512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35533C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42925C2semidirect
2. #42873C2semidirect
3. #42551C2semidirect
4. #42453C2semidirect
5. #40697C2semidirect
6. #40191C2semidirect
7. #39915C2semidirect
8. #39397C2semidirect
9. #39348C2semidirect
10. #37721C2semidirect
11. #35574C2semidirect
12. #35574C2semidirect
13. #35557C2semidirect
14. #35555C2semidirect
16. #35531C2semidirect
17. #35266C2semidirect
18. #35254C2semidirect
19. #35152C2semidirect
20. C2×#2542C2semidirect
21. #34815C2semidirect
22. #34744C2semidirect
23. #34265C2semidirect
24. #34207C2semidirect
25. #34183C2semidirect
26. C2×#539C22semidirect
40. #2837C22semidirect
41. #2827C22semidirect
42. #2796C22semidirect
43. #2796C22semidirect
44. #2773C22semidirect
45. #2740C22semidirect
46. #2732C22semidirect
47. #2728C22semidirect
48. #2721C22semidirect
49. #2720C22semidirect
50. #2718C22semidirect
51. #2711C22semidirect
52. #2705C22semidirect
53. #2696C22semidirect
54. #2689C22semidirect
55. #2687C22semidirect
56. #2681C22semidirect
57. #2680C22semidirect
58. #2663C22semidirect
59. #2654C22semidirect
60. #2651C22semidirect
62. #2638C22semidirect
63. #2636C22semidirect
65. #2623C22semidirect
67. #2596C22semidirect
70. #2570C22semidirect
71. #2560C22semidirect
72. #2556C22semidirect
73. #2552C22semidirect
84. #2512C22semidirect
85. #2511C22semidirect
86. #2509C22semidirect
87. #2508C22semidirect
88. #2507C22semidirect
89. #2507C22semidirect
90. #2506C22semidirect
91. #2506C22semidirect
97. #2497C22semidirect
98. #2496C22semidirect
103. #2463C22semidirect
104. #2452C22semidirect
105. #2452C22semidirect
106. #2451C22semidirect
107. #2451C22semidirect
108. #2449C22semidirect
111. #2448C22semidirect
113. #2447C22semidirect
114. #2446C22semidirect
118. #2445C22semidirect
121. #2443C22semidirect
122. #2440C22semidirect
123. #2440C22semidirect
124. #2439C22semidirect
125. #2439C22semidirect
135. #2402C22semidirect
136. #2395C22semidirect
143. #2354C22semidirect
144. Q8×C4⋊C4C22semidirect
146. D4×C4⋊C4C22semidirect
147. D4×C4⋊C4C22semidirect
148. #2332C22semidirect
149. #2326C22semidirect
150. #2326C22semidirect
155. #2317C22semidirect
156. #2317C22semidirect
164. C4×C4⋊Q8C22semidirect
165. C4×#127C22semidirect
166. C4×#125C22semidirect
167. C4×#123C22semidirect
180. #2285C22semidirect
183. C2×#384C22semidirect
1060. C2×C4#539semidirect

Maximal subgroups

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

subgroupindex
#429252
#428732
#425512
#424532
#406972
#401912
#399152
#393972
#393482
#377212
#355742
#355572
#355552
#355332
#355312
#352662
#352542
#351522
C2×#25422
#348152
#347442
#342652
#342072
#341832