Finite Group Databasebeta

← #7649991

Subgroups — #7649991

Order 512.

5468 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42946C214yesmaximal, complemented
2#42841C214yesmaximal, complemented
3#42576C214yesmaximal, complemented
4#42450C214yesmaximal, complemented
5#40844C218yesmaximal, complemented
6#40099C214yesmaximal, complemented
7#39938C214yesmaximal, complemented
8#39404C214yesmaximal, complemented
9#39348C214yesmaximal, complemented
10#37712C218yesmaximal, complemented
11#35563C211yesmaximal, characteristic
12#35558C211yesmaximal, characteristic, complemented
13#35555C211yesmaximal, characteristic, complemented
14#35540C211yesmaximal, characteristic, complemented
15#35532C211yesmaximal, characteristic, complemented
16#35529C211yesmaximal, characteristic, complemented
17#35286C211yesmaximal, characteristic, complemented
18#35254C211yesmaximal, characteristic, complemented
19#35224C211yesmaximal, characteristic, complemented
20#34814C211yesmaximal, characteristic, complemented
21C2×#2501C211yesmaximal, characteristic, complemented
22#34742C211yesmaximal, characteristic, complemented
23#34275C211yesmaximal, characteristic, complemented
24#34200C211yesmaximal, characteristic, complemented
25#34183C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#539C2218yescomplemented
28C2×#535C2211yescharacteristic
29C2×#525C2211yescharacteristic
30C22×#123C2214yes—
31C22×#121C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#518C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C23×C4⋊C4C2211yescharacteristic
37#2859C2214yescomplemented
38#2854C2214yescomplemented
39#2848C2214yes—
40#2838C2218yescomplemented
41#2827C2218yescomplemented
42#2807C2218yescomplemented
43#2777C2218yescomplemented
44#2746C2218yescomplemented
45#2743C2218yescomplemented
46#2724C2218yescomplemented
47#2723C2218yescomplemented
48#2721C2218yescomplemented
49#2720C2218yescomplemented
50#2718C2218yescomplemented
51#2708C2218yescomplemented
52#2706C2218yescomplemented
53#2694C2218yescomplemented
54#2694C2218yescomplemented
55#2693C2218yescomplemented
56#2681C2218yescomplemented
57#2680C2218yescomplemented
58#2667C2218yescomplemented
59#2663C2218yescomplemented
60#2654C2218yescomplemented
61#2647C2214yescomplemented
62#2633C2218yescomplemented
63#2630C2218yescomplemented
64#2627C2214yes—
65#2624C2214yescomplemented
66#2623C2218yescomplemented
67#2575C2218yescomplemented
68#2571C2214yescomplemented
69#2570C2214yescomplemented
70#2567C2212yescomplemented
71#2566C2212yescomplemented
72#2566C2212yescomplemented
73#2566C2212yescomplemented
74#2565C2212yescomplemented
75#2563C2212yescomplemented
76#2558C2218yescomplemented
77#2553C2218yescomplemented
78#2552C2214yescomplemented
79#2552C2214yescomplemented
80#2542C2212yescomplemented
81#2542C2212yescomplemented
82#2534C2214yes—
83#2513C2214yescomplemented
84#2513C2214yescomplemented
85#2512C2214yescomplemented
86#2512C2214yescomplemented
87#2507C2214yescomplemented
88#2506C2214yescomplemented
89#2501C2214yes—
90#2501C2214yes—
91#2501C2214yes—
92#2501C2214yes—
93#2497C2212yescomplemented
94#2496C2212yescomplemented
95#2495C2212yescomplemented
96#2494C2212yescomplemented
97#2493C2214yes—
98#2483C2214yes—
99#2480C2214yes—
100#2480C2218yes—
101#2473C2218yes—
102#2455C2218yescomplemented
103#2454C2214yescomplemented
104#2452C2214yescomplemented
105#2449C2218yes—
106#2449C2218yescomplemented
107#2448C2214yescomplemented
108#2445C2214yescomplemented
109#2443C2218yescomplemented
110#2442C2218yes—
111#2442C2214yescomplemented
112#2442C2214yescomplemented
113#2441C2214yescomplemented
114#2440C2214yescomplemented
115#2440C2214yescomplemented
116#2440C2214yescomplemented
117#2437C2218yes—
118#2428C2214yes—
119#2426C2214yes—
120#2423C2212yescomplemented
121#2422C2214yes—
122#2422C2214yes—
123#2422C2212yescomplemented
124#2421C2212yescomplemented
125#2420C2214yes—
126#2420C2214yes—
127#2420C2212yescomplemented
128#2419C2214yes—
129#2418C2214yes—
130#2418C2218yes—
131#2416C2214yes—
132#2414C2214yes—
133#2408C2214yes—
134#2405C2214yes—
135#2401C2214yescomplemented
136#2395C2214yescomplemented
137C2×#399C2214yes—
138#2363C2214yescomplemented
139#2361C2214yescomplemented
140#2361C2214yescomplemented
141#2360C2214yescomplemented
142#2358C2218yes—
143#2352C2214yescomplemented
144Q8×C4⋊C4C2214yescomplemented
145D4×C4⋊C4C2218yes—
146D4×C4⋊C4C2214yescomplemented
147D4×C4⋊C4C2214yescomplemented
148#2335C2218yescomplemented
149#2328C2212yescomplemented
150#2326C2212yescomplemented
151#2322C2214yes—
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2211yescharacteristic
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2317C2212yescomplemented
158#2317C2212yescomplemented
159#2316C2211yescharacteristic
160#2316C2211yescharacteristic
161#2311C2211yescharacteristic
162#2309C2211yescharacteristic
163#2309C2211yescharacteristic
164C4×#127C2212yescomplemented
165C4×#126C2214yescomplemented
166C4×#124C2212yescomplemented
167C4×#123C2214yescomplemented
168C4×#120C2214yes—
169#2297C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173C2×#390C2211yescharacteristic
174C2×#390C2211yescharacteristic
175#2285C2211yescharacteristic
176#2285C2211yescharacteristic
177#2285C2212yescomplemented
178C2×#384C2211yescharacteristic
179C2×#384C2211yescharacteristic
180C2×#384C2212yescomplemented
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183#2280C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×D4C2311yescharacteristic
189C23×D4C2312yes—
190C24×C4C2311yescharacteristic
191C24×C4C2312yes—
192#544—44no—
193#539—432no—
194#535—28no—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×#127C2312yes—
198C2×#126C2314yes—
199C2×#126C2318yes—
200C2×#125C2312yes—
201C2×#125C2312yes—
202C2×#125C2318yes—
203C2×#125C2318yes—
204C2×#124C2312yes—
205#525—28no—
206C2×#123—416no—
207C2×#123C2312yes—
208C2×#123C2318yes—
209C2×#123C2314yes—
210C2×#123C2318yes—
211C2×#123C2318yes—
212C2×#123C2318yes—
213C2×#123C2318yes—
214C2×#123C2318yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2318yes—
220C2×#121—44no—
221C2×#121C2314yes—
222C2×#121C2312yes—
223C2×#121C2318yes—
224C2×#121C2314yes—
225C2×#121C2314yes—
226C2×#120C2314yes—
227C2×#120C2312yes—
228#520—44no—
229#520—44no—
230#518—44no—
231C4×#41—28no—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2318yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2318yes—
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2312yes—
258C22×C4⋊C4—44no—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2318yes—
267C22×C4⋊C4C2314yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2314yes—
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2314yes—
272C22×C22⋊C4C2314yes—
273C22×C22⋊C4C2312yes—
274C22×C22⋊C4C2314yes—
275C22×C42C2312yes—
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278#401C2314yes—
279#400C2318yes—
280#400C2318yes—
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#399C2318yes—
294#399C2314yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2314yes—
303#398C2318yes—
304#397C2314yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2314yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#396C2318yes—
317#396C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2314yes—
321#396C2318yes—
322#395C2318yes—
323#395C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2314yes—
328#394C2318yes—
329#394C2314yes—
330#394C2318yes—
331#394C2318yes—
332#393C2318yes—
333#392C2318yes—
334#391C2311yescharacteristic
335#391C2312yes—
336#391C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2318yes—
339#390C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2312yes—
343#390C2314yes—
344#390C2314yes—
345#390C2314yes—
346#390C2311yescharacteristic
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2318yes—
351#390C2314yes—
352#390C2314yes—
353#389C2318yes—
354#389C2312yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2318yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2318yes—
366#389C2318yes—
367#389C2318yes—
368#389C2312yes—
369#389C2318yes—
370#389C2312yes—
371#389C2318yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2314yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2314yes—
396#387C2318yes—
397#387C2314yes—
398#386C2314yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2314yes—
405#386C2318yes—
406#386C2314yes—
407#385C2318yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2314yes—
413#385C2314yes—
414#385C2314yes—
415#385C2314yes—
416#385C2314yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2314yes—
424#385C2314yes—
425#385C2314yes—
426#385C2314yes—
427#384C2312yes—
428#384C2312yes—
429#384C2311yescharacteristic
430#384C2312yes—
431#384C2312yes—
432#384C2312yes—
433#384C2314yes—
434#384C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2312yes—
439#384C2318yes—
440#384C2311yescharacteristic
441#384C2312yes—
442#383C2314yes—
443#382C2311yescharacteristic
444#382C2312yes—
445#382C2312yes—
446#382C2311yescharacteristic
447#382C2312yes—
448#382C2312yes—
449#382C2318yes—
450#382C2312yes—
451#382C2312yes—
452#381C2318yes—
453#381C2312yes—
454#381C2314yes—
455#381C2312yes—
456#381C2312yes—
457#380C2318yes—
458#380C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2318yes—
462#380C2314yes—
463#380C2318yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467#380C2312yes—
468#380C2314yes—
469#380C2312yes—
470#380C2312yes—
471#379C2314yes—
472#379C2314yes—
473#379C2312yes—
474#379C2312yes—
475#379C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2318yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2318yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2312yes—
500#376C2312yes—
501C2×#95C2312yes—
502C43C2312yes—
503C25C2411yescharacteristic
504C25C2412yes—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41#4118yes—
508C22×Q8C2411yescharacteristic
509C22×Q8C2414yes—
510C22×D4—24no—
511C22×D4—24no—
512C22×D4—24no—
513C22×D4—44no—
514C22×D4—48no—
515C22×D4C2412yes—
516C22×D4C2412yes—
517C22×D4C2414yes—
518C22×D4C2412yes—
519C22×D4C2411yescharacteristic
520C22×D4C2418yes—
521C22×D4C2418yes—
522C23×C4—24no—
523C23×C4—24no—
524C23×C4—24no—
525C23×C4—44no—
526C23×C4—48no—
527C23×C4C2411yescharacteristic
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2414yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2418yes—
538C23×C4C2414yes—
539C23×C4C2414yes—
540C23×C4C2414yes—
541C23×C4C2414yes—
542C23×C4C2411yescharacteristic
543C4⋊Q8—44no—
544C4⋊Q8—44no—
545#127—28no—
546#126—216no—
547#126—416no—
548#125—416no—
549#125—44no—
550#125—44no—
551#125—416no—
552#124—28no—
553#123—28no—
554#123—232no—
555#123—216no—
556#123—416no—
557#123—416no—
558#123—416no—
559#123—416no—
560#123—416no—
561C22⋊Q8—28no—
562C22⋊Q8—416no—
563C22⋊Q8—48no—
564C22⋊Q8—416no—
565C22⋊Q8—416no—
566#121—28no—
567#121—216no—
568#121—416no—
569#121—48no—
570#121—48no—
571#120—28no—
572#120—216no—
573C4×Q8—28no—
574C4×Q8—44no—
575C4×Q8—44no—
576C4×D4—216no—
577C4×D4—28no—
578C4×D4—216no—
579C4×D4—416no—
580C4×D4—44no—
581C4×D4—44no—
582C4×D4—44no—
583C4×D4—44no—
584C4×D4—44no—
585C4×D4—44no—
586C4×D4—48no—
587C4×D4—48no—
588C4×D4—416no—
589#117—28no—
590#117—24no—
591#117—24no—
592#117—24no—
593#117—24no—
594#117—24no—
595#117—24no—
596#117—24no—
597#117—44no—
598#117—44no—
599C2×C4⋊C4—24no—
600C2×C4⋊C4—24no—
601C2×C4⋊C4—24no—
602C2×C4⋊C4—48no—
603C2×C4⋊C4—48no—
604C2×C4⋊C4—44no—
605C2×C4⋊C4—44no—
606C2×C4⋊C4—48no—
607C2×C4⋊C4—48no—
608C2×C4⋊C4—416no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C22⋊C4—28no—
656C2×C22⋊C4—48no—
657C2×C22⋊C4—48no—
658C2×C22⋊C4—48no—
659C2×C22⋊C4—44no—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2412yes—
697C2×C42—28no—
698C2×C42—24no—
699C2×C42—24no—
700C2×C42C2412yes—
701C2×C42C2411yescharacteristic
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2414yes—
709C2×C42C2412yes—
710C2×C42C2414yes—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2412yes—
714C2×C42C2411yescharacteristic
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2418yes—
718C2×C42C2414yes—
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2412yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
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—
752C24—24no—
753C24—22no—
754C24—22no—
755C24—22no—
756C24—24no—
757C24—24no—
758C24—24no—
759C24—42no—
760C24—44no—
761C24—44no—
762C24C2514yes—
763C24C2512yes—
764C24C2512yes—
765C24C2511yescharacteristic
766#41—232no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—48no—
770C2×Q8—44no—
771C2×Q8C2×#4114yes—
772C2×D4—24no—
773C2×D4—24no—
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—216no—
777C2×D4—216no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—22no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—22no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—44no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—416no—
792C2×D4—816no—
793C2×D4C2×#4118yes—
794C2×D4C2×#4114yes—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—28no—
798C22×C4—24no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—24no—
802C22×C4—22no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—216no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—28no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—42no—
817C22×C4—44no—
818C22×C4—42no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—48no—
822C22×C4—44no—
823C22×C4—48no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—48no—
828C22×C4—44no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—416no—
833C22×C4—816no—
834C22×C4C2×#4118yes—
835C22×C4C2×#4114yes—
836C22×C4H(5,𝔽2)14yes—
837C22×C42−1+414yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2512yes—
845C22×C4C2514yes—
846C22×C4C2512yes—
847C22×C4C2514yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—28no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—28no—
873C4⋊C4—216no—
874C4⋊C4—216no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—24no—
884C4⋊C4—48no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C22⋊C4—28no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—28no—
909C22⋊C4—24no—
910C22⋊C4—24no—
911C22⋊C4—24no—
912C22⋊C4—24no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—24no—
917C22⋊C4—28no—
918C22⋊C4—216no—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—216no—
922C22⋊C4—216no—
923C22⋊C4—28no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4H(5,𝔽2)18yes—
941C42—22no—
942C42—24no—
943C42—22no—
944C42—28no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—28no—
952C42—22no—
953C42—24no—
954C42—22no—
955C42—24no—
956C42—44no—
957C42—44no—
958C42—44no—
959C42—48no—
960C23—22no—
961C23—22no—
962C23—28no—
963C23—22no—
964C23—22no—
965C23—24no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—24no—
973C23—24no—
974C23—28no—
975C23—24no—
976C23—24no—
977C23—28no—
978C23—48no—
979C23—48no—
980C23—44no—
981C23—44no—
982C23—48no—
983C23—84no—
984C23—88no—
985C23—84no—
986C23—88no—
987C23C22×#4114yes—
988C23C22×#4112yes—
989C23C2×H(5,𝔽2)14yes—
990C23C2×H(5,𝔽2)12yes—
991C23C2×2−1+412yes—
992C23C2611yescharacteristic
993Q8—28no—
994Q8—164no—
995D4—216no—
996D4—28no—
997D4—416no—
998D4—48no—
999D4—48no—
1000D4—816no—
1001D4—816no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—216no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—28no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—28no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—28no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—48no—
1049C2×C4—416no—
1050C2×C4—48no—
1051C2×C4—44no—
1052C2×C4—48no—
1053C2×C4—48no—
1054C2×C4—84no—
1055C2×C4—816no—
1056C2×C4—84no—
1057C2×C4—84no—
1058C2×C4—164no—
1059C2×C4—164no—
1060C2×C4—164no—
1061C2×C4—164no—
1062C2×C4#539116yescomplemented
1063C2×C4C22×#4114yes—
1064C2×C4C22×#4112yes—
1065C2×C4C22×#4112yes—
1066C2×C4C2×H(5,𝔽2)14yes—
1067C2×C4C2×H(5,𝔽2)14yes—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4C2×H(5,𝔽2)12yes—
1070C2×C4C2×2−1+412yes—
1071C2×C4C2×2−1+412yes—
1072C22—24no—
1073C22—22no—
1074C22—22no—
1075C22—24no—
1076C22—28no—
1077C22—24no—
1078C22—24no—
1079C22—24no—
1080C22—24no—
1081C22—416no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—44no—
1087C22—42no—
1088C22—42no—
1089C22—48no—
1090C22—44no—
1091C22—44no—
1092C22—48no—
1093C22—44no—
1094C22—168no—
1095C22C2×#53914yes—
1096C22C23×#4111yescharacteristic
1097C22C22×H(5,𝔽2)12yes—
1098C22C22×H(5,𝔽2)11yescharacteristic
1099C22C22×2−1+411yescharacteristic
1100C222−1+612yes—
1101C4—24no—
1102C4—24no—
1103C4—24no—
1104C4—42no—
1105C4—44no—
1106C4—44no—
1107C4—44no—
1108C4—44no—
1109C4—44no—
1110C4—44no—
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—44no—
1118C4—42no—
1119C4—42no—
1120C4C2×#53914yes—
1121C4C2×#53914yes—
1122C2—24no—
1123C2—44no—
1124C2—44no—
1125C2—84no—
1126C2C22×#53911yescharacteristic
1127C2#6283211yescharacteristic
1128C2#6288711yescharacteristic
1129C2#6291512yes—
1130C2#6298512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35563C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42946C2semidirect
2. #42841C2semidirect
3. #42576C2semidirect
4. #42450C2semidirect
5. #40844C2semidirect
6. #40099C2semidirect
7. #39938C2semidirect
8. #39404C2semidirect
9. #39348C2semidirect
10. #37712C2semidirect
12. #35558C2semidirect
13. #35555C2semidirect
14. #35540C2semidirect
15. #35532C2semidirect
16. #35529C2semidirect
17. #35286C2semidirect
18. #35254C2semidirect
19. #35224C2semidirect
20. #34814C2semidirect
21. C2×#2501C2semidirect
22. #34742C2semidirect
23. #34275C2semidirect
24. #34200C2semidirect
25. #34183C2semidirect
27. C2×#539C22semidirect
37. #2859C22semidirect
38. #2854C22semidirect
40. #2838C22semidirect
41. #2827C22semidirect
42. #2807C22semidirect
43. #2777C22semidirect
44. #2746C22semidirect
45. #2743C22semidirect
46. #2724C22semidirect
47. #2723C22semidirect
48. #2721C22semidirect
49. #2720C22semidirect
50. #2718C22semidirect
51. #2708C22semidirect
52. #2706C22semidirect
53. #2694C22semidirect
54. #2694C22semidirect
55. #2693C22semidirect
56. #2681C22semidirect
57. #2680C22semidirect
58. #2667C22semidirect
59. #2663C22semidirect
60. #2654C22semidirect
61. #2647C22semidirect
62. #2633C22semidirect
63. #2630C22semidirect
65. #2624C22semidirect
66. #2623C22semidirect
67. #2575C22semidirect
68. #2571C22semidirect
69. #2570C22semidirect
70. #2567C22semidirect
71. #2566C22semidirect
72. #2566C22semidirect
73. #2566C22semidirect
74. #2565C22semidirect
75. #2563C22semidirect
76. #2558C22semidirect
77. #2553C22semidirect
78. #2552C22semidirect
79. #2552C22semidirect
80. #2542C22semidirect
81. #2542C22semidirect
83. #2513C22semidirect
84. #2513C22semidirect
85. #2512C22semidirect
86. #2512C22semidirect
87. #2507C22semidirect
88. #2506C22semidirect
93. #2497C22semidirect
94. #2496C22semidirect
95. #2495C22semidirect
96. #2494C22semidirect
102. #2455C22semidirect
103. #2454C22semidirect
104. #2452C22semidirect
106. #2449C22semidirect
107. #2448C22semidirect
108. #2445C22semidirect
109. #2443C22semidirect
111. #2442C22semidirect
112. #2442C22semidirect
113. #2441C22semidirect
114. #2440C22semidirect
115. #2440C22semidirect
116. #2440C22semidirect
120. #2423C22semidirect
123. #2422C22semidirect
124. #2421C22semidirect
127. #2420C22semidirect
135. #2401C22semidirect
136. #2395C22semidirect
138. #2363C22semidirect
139. #2361C22semidirect
140. #2361C22semidirect
141. #2360C22semidirect
143. #2352C22semidirect
144. Q8×C4⋊C4C22semidirect
146. D4×C4⋊C4C22semidirect
147. D4×C4⋊C4C22semidirect
148. #2335C22semidirect
149. #2328C22semidirect
150. #2326C22semidirect
157. #2317C22semidirect
158. #2317C22semidirect
164. C4×#127C22semidirect
165. C4×#126C22semidirect
166. C4×#124C22semidirect
167. C4×#123C22semidirect
177. #2285C22semidirect
180. C2×#384C22semidirect
1062. C2×C4#539semidirect

Maximal subgroups

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

subgroupindex
#429462
#428412
#425762
#424502
#408442
#400992
#399382
#394042
#393482
#377122
#355632
#355582
#355552
#355402
#355322
#355292
#352862
#352542
#352242
#348142
C2×#25012
#347422
#342752
#342002
#341832