Finite Group Databasebeta

← #7642900

Subgroups — #7642900

Order 512.

5378 conjugacy classes of subgroups.

The subgroup lattice has 1193 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39767C212yesmaximal, complemented
2#39759C212yesmaximal, complemented
3#39639C212yesmaximal, complemented
4#39631C212yesmaximal, complemented
5#39512C212yesmaximal, complemented
6#39504C212yesmaximal, complemented
7#39384C212yesmaximal, complemented
8#39376C212yesmaximal, complemented
9#39199C214yesmaximal, complemented
10#39190C214yesmaximal, complemented
11#38982C214yesmaximal, complemented
12#38973C214yesmaximal, complemented
13#37141C214yesmaximal, complemented
14#37139C214yesmaximal, complemented
15#36625C211yesmaximal, characteristic, complemented
16#36624C211yesmaximal, characteristic
17#35545C212yesmaximal, complemented
18#35543C212yesmaximal, complemented
19#35519C212yesmaximal, complemented
20#35517C212yesmaximal, complemented
21#35227C212yesmaximal, complemented
22#34997C214yesmaximal, complemented
23#34989C214yesmaximal, complemented
24#34200C212yesmaximal, complemented
25C22×#389C211yesmaximal, characteristic, complemented
26C2×#539C2214yes—
27C2×#533C2211yescharacteristic
28C2×#532C2211yescharacteristic
29C2×#525C2212yes—
30C2×#520C2212yes—
31C23×C4⋊C4C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C4⋊C4C2212yes—
34C23×C42C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2857C2211yescharacteristic
39#2857C2211yescharacteristic
40#2857C2211yescharacteristic
41#2856C2211yescharacteristic
42#2856C2211yescharacteristic
43#2855C2212yes—
44#2855C2212yes—
45#2854C2212yes—
46#2854C2212yes—
47#2851C2212yes—
48#2851C2212yes—
49#2850C2212yes—
50#2850C2212yes—
51#2849C2218yes—
52#2848C2212yes—
53#2848C2212yes—
54#2847C2212yes—
55#2847C2212yes—
56#2810C2214yescomplemented
57#2809C2214yescomplemented
58#2808C2214yescomplemented
59#2807C2218yescomplemented
60#2805C2214yescomplemented
61#2802C2218yescomplemented
62#2798C2218yescomplemented
63#2796C2218yescomplemented
64#2787C2218yescomplemented
65#2783C2218yescomplemented
66#2777C2218yescomplemented
67#2776C2218yescomplemented
68#2773C2218yescomplemented
69#2771C2218yescomplemented
70#2732C2214yescomplemented
71#2727C2214yescomplemented
72#2726C2214yescomplemented
73#2724C2214yescomplemented
74#2694C2218yescomplemented
75#2689C2218yescomplemented
76#2646C2214yes—
77#2643C2218yes—
78#2639C2214yes—
79#2627C2214yes—
80#2623C2218yes—
81#2623C2218yes—
82#2618C2214yes—
83#2582C2214yescomplemented
84#2581C2214yescomplemented
85#2580C2214yescomplemented
86#2571C2214yescomplemented
87#2570C2214yescomplemented
88#2570C2214yescomplemented
89#2552C2214yescomplemented
90#2538C2214yescomplemented
91#2514C2214yescomplemented
92#2513C2214yescomplemented
93#2512C2214yescomplemented
94#2511C2214yescomplemented
95#2510C2218yes—
96#2509C2214yescomplemented
97#2508C2214yescomplemented
98#2507C2214yescomplemented
99#2506C2214yescomplemented
100#2505C2218yes—
101#2504C2214yes—
102#2503C2214yes—
103#2502C2214yes—
104#2501C2214yes—
105#2497C2214yescomplemented
106#2496C2214yescomplemented
107#2495C2214yescomplemented
108#2494C2214yescomplemented
109#2493C2218yes—
110#2488C2218yes—
111#2487C2214yes—
112#2487C2214yes—
113#2487C2214yescomplemented
114#2486C2214yes—
115#2486C2214yes—
116#2486C2214yescomplemented
117#2485C2214yescomplemented
118#2485C2214yescomplemented
119#2481C2218yes—
120#2481C2218yes—
121#2473C2218yes—
122#2473C2218yes—
123#2450C2218yes—
124#2449C2218yes—
125#2449C2218yes—
126#2448C2214yescomplemented
127#2447C2214yescomplemented
128#2446C2214yescomplemented
129#2445C2214yescomplemented
130#2444C2218yes—
131#2443C2218yes—
132#2443C2218yes—
133#2442C2214yescomplemented
134#2441C2214yescomplemented
135#2440C2214yescomplemented
136#2439C2214yescomplemented
137#2425C2218yes—
138#2419C2218yes—
139#2361C2214yes—
140#2361C2214yes—
141#2360C2214yes—
142#2360C2214yes—
143#2352C2214yes—
144#2352C2214yes—
145D4×C4⋊C4C2214yes—
146D4×C4⋊C4C2214yes—
147#2329C2214yes—
148#2325C2214yes—
149#2322C2218yes—
150#2322C2218yes—
151#2318C2218yes—
152#2317C2212yes—
153#2317C2212yes—
154#2317C2212yes—
155#2313C2214yes—
156#2311C2212yes—
157#2311C2212yes—
158#2311C2212yes—
159C4×C22⋊Q8C2212yes—
160C4×C22⋊Q8C2212yes—
161C4×C22⋊Q8C2212yes—
162C4×C22⋊Q8C2212yes—
163C4×#121C2212yes—
164C4×#121C2212yes—
165C4×#121C2212yes—
166C4×#121C2212yes—
167C4×#120C2218yes—
168#2297C2212yes—
169#2296C2212yes—
170C2×#389C2212yes—
171C2×#389C2212yes—
172C2×#389C2212yes—
173C2×#389C2212yes—
174C2×#389C2212yes—
175C2×#389C2212yes—
176C2×#389C2212yes—
177C2×#389C2212yes—
178C2×#389C2212yes—
179C2×#389C2212yes—
180C2×#389C2212yes—
181C2×#389C2212yes—
182#2285C2211yescharacteristic
183#2285C2211yescharacteristic
184#2280C2212yes—
185#2274C2212yes—
186C22×#95C2212yes—
187C22×#41C2312yes—
188C24×C4C2311yescharacteristic
189C24×C4C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2312yes—
192C24×C4C2312yes—
193#539—416no—
194#533—44no—
195#532—44no—
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2311yescharacteristic
199C2×#127C2311yescharacteristic
200C2×#126C2318yes—
201C2×#125C2312yes—
202C2×#125C2318yes—
203C2×#124C2312yes—
204#525—216no—
205C2×#123C2314yes—
206C2×#123C2318yes—
207C2×#123C2318yes—
208C2×#123C2318yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2312yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2318yes—
218C2×#121C2312yes—
219C2×#121C2312yes—
220C2×#121C2312yes—
221C2×#121C2312yes—
222C2×#121C2312yes—
223C2×#121C2312yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#120C2314yes—
227#520—48no—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2318yes—
234C2×C4×D4C2318yes—
235C2×C4×D4C2318yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×#117C2312yes—
240C2×#117C2312yes—
241C2×#117C2312yes—
242C2×#117C2314yes—
243C22×C4⋊C4—28no—
244C22×C4⋊C4—44no—
245C22×C4⋊C4—48no—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2314yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2314yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2314yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C42—44no—
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278#401C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#399C2318yes—
291#399C2318yes—
292#399C2318yes—
293#399C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#396C2318yes—
312#396C2318yes—
313#396C2318yes—
314#395C2318yes—
315#394C2318yes—
316#394C2318yes—
317#393C2318yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2312yes—
322#391C2312yes—
323#391C2318yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#390C2314yes—
329#390C2314yes—
330#390C2314yes—
331#390C2312yes—
332#390C2312yes—
333#390C2312yes—
334#390C2312yes—
335#390C2312yes—
336#390C2312yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2318yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2318yes—
347#389C2318yes—
348#389C2318yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2314yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#386C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2314yes—
408#386C2318yes—
409#386C2314yes—
410#386C2318yes—
411#386C2318yes—
412#386C2314yes—
413#386C2314yes—
414#386C2314yes—
415#386C2314yes—
416#386C2318yes—
417#386C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#385C2318yes—
423#385C2314yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2314yes—
431#385C2314yes—
432#385C2314yes—
433#385C2314yes—
434#385C2318yes—
435#385C2318yes—
436#384C2311yescharacteristic
437#384C2314yes—
438#384C2314yes—
439#384C2314yes—
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#383C2318yes—
444#382C2312yes—
445#382C2314yes—
446#382C2314yes—
447#382C2318yes—
448#382C2314yes—
449#382C2312yes—
450#381C2318yes—
451#381C2318yes—
452#381C2314yes—
453#381C2318yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457#380C2314yes—
458#380C2314yes—
459#380C2314yes—
460#380C2312yes—
461#380C2312yes—
462#380C2318yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2312yes—
475#380C2312yes—
476#380C2312yes—
477#379C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C2×#95C2314yes—
496C2×#95C2314yes—
497C2×#95C2314yes—
498C2×#95C2314yes—
499C2×#95C2314yes—
500C2×#95C2314yes—
501C25C2411yescharacteristic
502C2×#41—28no—
503C2×#41—28no—
504C2×#41—28no—
505C22×Q8C2412yes—
506C22×Q8C2412yes—
507C22×Q8C2412yes—
508C22×D4C2414yes—
509C22×D4C2414yes—
510C22×D4C2414yes—
511C22×D4C2412yes—
512C22×D4C2412yes—
513C22×D4C2412yes—
514C23×C4—24no—
515C23×C4—24no—
516C23×C4—28no—
517C23×C4—24no—
518C23×C4—24no—
519C23×C4—44no—
520C23×C4—42no—
521C23×C4—42no—
522C23×C4—44no—
523C23×C4—42no—
524C23×C4—42no—
525C23×C4—44no—
526C23×C4—44no—
527C23×C4—44no—
528C23×C4#4118yes—
529C23×C4C2414yes—
530C23×C4C2414yes—
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2411yescharacteristic
543C23×C4C2411yescharacteristic
544C23×C4C2414yes—
545C23×C4C2414yes—
546C23×C4C2414yes—
547C23×C4C2414yes—
548C23×C4C2414yes—
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2418yes—
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555C4⋊Q8—42no—
556C4⋊Q8—42no—
557C4⋊Q8—42no—
558#127—42no—
559#126—416no—
560#125—44no—
561#125—416no—
562#124—44no—
563#123—216no—
564#123—416no—
565#123—416no—
566#123—416no—
567C22⋊Q8—28no—
568C22⋊Q8—28no—
569C22⋊Q8—28no—
570C22⋊Q8—28no—
571C22⋊Q8—44no—
572C22⋊Q8—44no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575C22⋊Q8—416no—
576#121—28no—
577#121—28no—
578#121—28no—
579#121—28no—
580#121—44no—
581#121—44no—
582#121—44no—
583#121—44no—
584#120—216no—
585C4×Q8—44no—
586C4×Q8—44no—
587C4×Q8—48no—
588C4×D4—216no—
589C4×D4—216no—
590C4×D4—48no—
591C4×D4—44no—
592C4×D4—44no—
593C4×D4—416no—
594C4×D4—416no—
595C4×D4—416no—
596#117—28no—
597#117—28no—
598#117—28no—
599#117—48no—
600C2×C4⋊C4—28no—
601C2×C4⋊C4—28no—
602C2×C4⋊C4—28no—
603C2×C4⋊C4—28no—
604C2×C4⋊C4—28no—
605C2×C4⋊C4—28no—
606C2×C4⋊C4—28no—
607C2×C4⋊C4—216no—
608C2×C4⋊C4—44no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—44no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4—48no—
613C2×C4⋊C4—48no—
614C2×C4⋊C4—48no—
615C2×C4⋊C4—48no—
616C2×C4⋊C4—48no—
617C2×C4⋊C4—44no—
618C2×C4⋊C4—48no—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C42—24no—
689C2×C42—24no—
690C2×C42—42no—
691C2×C42—42no—
692C2×C42—42no—
693C2×C42—42no—
694C2×C42—42no—
695C2×C42—42no—
696C2×C42—42no—
697C2×C42—42no—
698C2×C42—42no—
699C2×C42—42no—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2418yes—
712C2×C42C2418yes—
713C2×C42C2418yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2414yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756C24—22no—
757C24—22no—
758C24—22no—
759C24—22no—
760C24—22no—
761C24—22no—
762C24C2×#4114yes—
763C24C2514yes—
764C24C2511yescharacteristic
765C24C2511yescharacteristic
766C24C2511yescharacteristic
767#41—432no—
768C2×Q8—24no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×D4—28no—
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—28no—
781C2×D4—28no—
782C2×D4—28no—
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—28no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—42no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—42no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—232no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—28no—
807C22×C4—28no—
808C22×C4—28no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—28no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—28no—
824C22×C4—28no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—28no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—28no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—41no—
842C22×C4—41no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—41no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—416no—
865C22×C4—416no—
866C22×C4—432no—
867C22×C4—816no—
868C22×C4C2×#4114yes—
869C22×C4C2×#4114yes—
870C22×C4C2×#4114yes—
871C22×C4C2×#4114yes—
872C22×C4C2×#4114yes—
873C22×C4C2×#4114yes—
874C22×C4H(5,𝔽2)14yes—
875C22×C4H(5,𝔽2)14yes—
876C22×C42−1+414yes—
877C22×C42−1+414yes—
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C22×C4C2514yes—
881C22×C4C2514yes—
882C22×C4C2514yes—
883C22×C4C2514yes—
884C22×C4C2514yes—
885C22×C4C2518yes—
886C22×C4C2518yes—
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C22×C4C2514yes—
890C22×C4C2514yes—
891C22×C4C2511yescharacteristic
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—216no—
910C4⋊C4—216no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—28no—
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—28no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—48no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—48no—
941C4⋊C4—48no—
942C4⋊C4—48no—
943C4⋊C4—48no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—28no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—48no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—48no—
967C22⋊C4—48no—
968C42—28no—
969C42—22no—
970C42—22no—
971C42—22no—
972C42—22no—
973C42—22no—
974C42—22no—
975C42—22no—
976C42—22no—
977C42—28no—
978C42—28no—
979C42—41no—
980C42—41no—
981C42—41no—
982C42—41no—
983C42—41no—
984C42—41no—
985C42—41no—
986C42—41no—
987C42—48no—
988C42—48no—
989C42—48no—
990C23—28no—
991C23—28no—
992C23—28no—
993C23—28no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—28no—
1007C23—28no—
1008C23—28no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23C22×#4112yes—
1017C23C22×#4112yes—
1018C23C22×#4112yes—
1019C23C2×H(5,𝔽2)12yes—
1020C23C2×H(5,𝔽2)12yes—
1021C23C2×2−1+412yes—
1022C23C2×2−1+412yes—
1023C23#58512yes—
1024C23#58512yes—
1025C23C2611yescharacteristic
1026Q8—48no—
1027Q8—84no—
1028Q8—84no—
1029D4—416no—
1030D4—416no—
1031D4—416no—
1032D4—48no—
1033D4—84no—
1034D4—84no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—28no—
1048C2×C4—28no—
1049C2×C4—28no—
1050C2×C4—28no—
1051C2×C4—28no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—28no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—28no—
1066C2×C4—28no—
1067C2×C4—24no—
1068C2×C4—28no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—28no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—28no—
1088C2×C4—24no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—44no—
1092C2×C4—44no—
1093C2×C4—44no—
1094C2×C4—44no—
1095C2×C4—44no—
1096C2×C4—44no—
1097C2×C4—44no—
1098C2×C4—44no—
1099C2×C4—44no—
1100C2×C4—44no—
1101C2×C4—416no—
1102C2×C4—416no—
1103C2×C4—44no—
1104C2×C4—44no—
1105C2×C4—416no—
1106C2×C4—416no—
1107C2×C4—88no—
1108C2×C4—88no—
1109C2×C4—88no—
1110C2×C4—168no—
1111C2×C4#539116yescomplemented
1112C2×C4C22×#4112yes—
1113C2×C4C22×#4112yes—
1114C2×C4C22×#4112yes—
1115C2×C4C22×#4112yes—
1116C2×C4C2×H(5,𝔽2)12yes—
1117C2×C4C2×H(5,𝔽2)12yes—
1118C2×C4C2×H(5,𝔽2)12yes—
1119C2×C4C2×H(5,𝔽2)12yes—
1120C2×C4C2×2−1+412yes—
1121C2×C4C2×2−1+412yes—
1122C2×C4C2×2−1+412yes—
1123C2×C4C2×2−1+412yes—
1124C22—232no—
1125C22—22no—
1126C22—22no—
1127C22—22no—
1128C22—22no—
1129C22—22no—
1130C22—22no—
1131C22—22no—
1132C22—22no—
1133C22—22no—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—22no—
1139C22—22no—
1140C22—22no—
1141C22—22no—
1142C22—22no—
1143C22—44no—
1144C22—44no—
1145C22—44no—
1146C22—44no—
1147C22—44no—
1148C22—44no—
1149C22—44no—
1150C22C2×#53914yes—
1151C22#350614yes—
1152C22#350714yes—
1153C22C23×#4111yescharacteristic
1154C22C22×H(5,𝔽2)11yescharacteristic
1155C22C22×H(5,𝔽2)11yescharacteristic
1156C22C22×2−1+411yescharacteristic
1157C22C22×2−1+411yescharacteristic
1158C22C2×#58511yescharacteristic
1159C22C2×#58511yescharacteristic
1160C4—22no—
1161C4—22no—
1162C4—22no—
1163C4—22no—
1164C4—22no—
1165C4—22no—
1166C4—48no—
1167C4—44no—
1168C4—44no—
1169C4—41no—
1170C4—41no—
1171C4—48no—
1172C4—44no—
1173C4—41no—
1174C4—41no—
1175C4—44no—
1176C4—44no—
1177C4—44no—
1178C4—44no—
1179C4C2×#53914yes—
1180C4C2×#53914yes—
1181C2—24no—
1182C2—24no—
1183C2—24no—
1184C2—84no—
1185C2C22×#53911yescharacteristic
1186C2C2×#350611yescharacteristic
1187C2C2×#350711yescharacteristic
1188C2#6281811yescharacteristic
1189C2#6281911yescharacteristic
1190C2#6282511yescharacteristic
1191C2#6283311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36624C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39767C2semidirect
2. #39759C2semidirect
3. #39639C2semidirect
4. #39631C2semidirect
5. #39512C2semidirect
6. #39504C2semidirect
7. #39384C2semidirect
8. #39376C2semidirect
9. #39199C2semidirect
10. #39190C2semidirect
11. #38982C2semidirect
12. #38973C2semidirect
13. #37141C2semidirect
14. #37139C2semidirect
15. #36625C2semidirect
17. #35545C2semidirect
18. #35543C2semidirect
19. #35519C2semidirect
20. #35517C2semidirect
21. #35227C2semidirect
22. #34997C2semidirect
23. #34989C2semidirect
24. #34200C2semidirect
25. C22×#389C2semidirect
56. #2810C22semidirect
57. #2809C22semidirect
58. #2808C22semidirect
59. #2807C22semidirect
60. #2805C22semidirect
61. #2802C22semidirect
62. #2798C22semidirect
63. #2796C22semidirect
64. #2787C22semidirect
65. #2783C22semidirect
66. #2777C22semidirect
67. #2776C22semidirect
68. #2773C22semidirect
69. #2771C22semidirect
70. #2732C22semidirect
71. #2727C22semidirect
72. #2726C22semidirect
73. #2724C22semidirect
74. #2694C22semidirect
75. #2689C22semidirect
83. #2582C22semidirect
84. #2581C22semidirect
85. #2580C22semidirect
86. #2571C22semidirect
87. #2570C22semidirect
88. #2570C22semidirect
89. #2552C22semidirect
90. #2538C22semidirect
91. #2514C22semidirect
92. #2513C22semidirect
93. #2512C22semidirect
94. #2511C22semidirect
96. #2509C22semidirect
97. #2508C22semidirect
98. #2507C22semidirect
99. #2506C22semidirect
105. #2497C22semidirect
106. #2496C22semidirect
107. #2495C22semidirect
108. #2494C22semidirect
113. #2487C22semidirect
116. #2486C22semidirect
117. #2485C22semidirect
118. #2485C22semidirect
126. #2448C22semidirect
127. #2447C22semidirect
128. #2446C22semidirect
129. #2445C22semidirect
133. #2442C22semidirect
134. #2441C22semidirect
135. #2440C22semidirect
136. #2439C22semidirect
1111. C2×C4#539semidirect

Maximal subgroups

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

subgroupindex
#397672
#397592
#396392
#396312
#395122
#395042
#393842
#393762
#391992
#391902
#389822
#389732
#371412
#371392
#366252
#366242
#355452
#355432
#355192
#355172
#352272
#349972
#349892
#342002
C22×#3892