Finite Group Databasebeta

← #7652679

Subgroups — #7652679

Order 512.

4940 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42659C214yesmaximal, complemented
2#42596C214yesmaximal, complemented
3#42588C214yesmaximal, complemented
4#42472C214yesmaximal, complemented
5#40786C218yesmaximal, complemented
6#40050C214yesmaximal, complemented
7#39925C214yesmaximal, complemented
8#39736C214yesmaximal, complemented
9#39251C214yesmaximal, complemented
10#38535C218yesmaximal, complemented
11#35649C211yesmaximal, characteristic, complemented
12#35640C211yesmaximal, characteristic, complemented
13#35618C211yesmaximal, characteristic, complemented
14#35558C211yesmaximal, characteristic, complemented
15#35556C211yesmaximal, characteristic, complemented
16#35532C211yesmaximal, characteristic, complemented
17#35264C211yesmaximal, characteristic, complemented
18#35256C211yesmaximal, characteristic
19#35152C211yesmaximal, characteristic, complemented
20C2×#2566C211yesmaximal, characteristic, complemented
21#34816C211yesmaximal, characteristic, complemented
22#34745C211yesmaximal, characteristic, complemented
23#34265C211yesmaximal, characteristic, complemented
24#34215C211yesmaximal, characteristic, complemented
25#34188C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C22×#125C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35#2861C2212yes—
36#2858C2212yes—
37#2856C2212yes—
38#2850C2212yes—
39#2849C2214yes—
40#2831C2218yescomplemented
41#2829C2218yescomplemented
42#2796C2218yescomplemented
43#2795C2218yescomplemented
44#2793C2218yescomplemented
45#2772C2218yescomplemented
46#2765C2218yescomplemented
47#2763C2218yescomplemented
48#2761C2218yescomplemented
49#2761C2218yescomplemented
50#2757C2218yescomplemented
51#2730C2218yescomplemented
52#2717C2218yescomplemented
53#2710C2218yescomplemented
54#2702C2218yescomplemented
55#2700C2218yescomplemented
56#2691C2218yescomplemented
57#2691C2218yescomplemented
58#2653C2218yescomplemented
59#2651C2218yescomplemented
60#2651C2218yescomplemented
61#2650C2218yescomplemented
62#2641C2212yes—
63#2640C2212yes—
64#2638C2218yescomplemented
65#2622C2214yes—
66#2620C2212yes—
67#2620C2218yescomplemented
68#2619C2212yes—
69#2592C2214yes—
70#2591C2214yes—
71#2583C2214yes—
72#2567C2212yescomplemented
73#2566C2214yes—
74#2566C2214yes—
75#2566C2214yes—
76#2566C2214yes—
77#2566C2212yescomplemented
78#2565C2212yescomplemented
79#2552C2214yescomplemented
80#2552C2214yescomplemented
81#2550C2214yescomplemented
82#2550C2214yescomplemented
83#2548C2214yes—
84#2542C2212yescomplemented
85#2515C2218yescomplemented
86#2514C2212yescomplemented
87#2513C2214yes—
88#2513C2214yes—
89#2513C2212yescomplemented
90#2512C2214yes—
91#2512C2214yes—
92#2512C2212yescomplemented
93#2512C2218yescomplemented
94#2511C2212yescomplemented
95#2510C2214yes—
96#2504C2214yes—
97#2504C2212yescomplemented
98#2503C2212yescomplemented
99#2502C2214yes—
100#2500C2212yescomplemented
101#2499C2212yescomplemented
102#2491C2214yes—
103#2491C2214yes—
104#2490C2214yes—
105#2490C2214yes—
106#2490C2214yescomplemented
107#2490C2214yescomplemented
108#2489C2214yescomplemented
109#2489C2214yescomplemented
110#2481C2214yes—
111#2480C2218yes—
112#2474C2218yescomplemented
113#2472C2218yes—
114#2472C2218yes—
115#2470C2218yescomplemented
116#2461C2218yescomplemented
117#2454C2212yescomplemented
118#2453C2212yescomplemented
119#2452C2212yescomplemented
120#2451C2212yescomplemented
121#2450C2214yes—
122#2449C2214yes—
123#2449C2218yes—
124#2447C2214yes—
125#2447C2218yescomplemented
126#2445C2214yes—
127#2444C2218yes—
128#2441C2214yescomplemented
129#2440C2214yescomplemented
130#2428C2214yes—
131#2426C2214yes—
132#2424C2218yes—
133#2422C2214yes—
134#2421C2214yescomplemented
135#2420C2214yes—
136#2420C2214yescomplemented
137#2401C2214yescomplemented
138#2396C2214yescomplemented
139C2×#396C2214yes—
140#2368C2218yes—
141#2367C2214yes—
142#2366C2214yes—
143#2363C2214yes—
144#2361C2214yes—
145#2355C2214yescomplemented
146#2355C2214yescomplemented
147#2355C2214yescomplemented
148#2354C2214yescomplemented
149#2352C2218yes—
150#2334C2218yescomplemented
151#2331C2214yescomplemented
152#2324C2218yescomplemented
153#2321C2214yes—
154#2317C2211yescharacteristic
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2314C2214yescomplemented
158#2311C2211yescharacteristic
159#2311C2211yescharacteristic
160#2311C2211yescharacteristic
161#2309C2211yescharacteristic
162#2309C2211yescharacteristic
163C4×#125C2214yescomplemented
164C4×#126C2214yescomplemented
165C4×C22⋊Q8C2214yescomplemented
166C4×#120C2214yes—
167#2297C2211yescharacteristic
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175C2×#390C2211yescharacteristic
176C2×#390C2211yescharacteristic
177C2×#385C2214yes—
178#2285C2211yescharacteristic
179#2285C2214yescomplemented
180C2×#384C2211yescharacteristic
181C2×#382C2211yescharacteristic
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×D4C2311yescharacteristic
190C24×C4C2312yes—
191#544—44no—
192#537—44no—
193#535—28no—
194#535—44no—
195#533—28no—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×#127C2312yes—
200C2×#127C2312yes—
201C2×#126C2314yes—
202C2×#126C2318yes—
203C2×#125—44no—
204C2×#125C2312yes—
205C2×#125C2312yes—
206C2×#125C2314yes—
207C2×#125C2314yes—
208C2×#125C2312yes—
209C2×#124C2312yes—
210C2×#124C2312yes—
211C2×#124C2318yes—
212C2×#124C2318yes—
213C2×#123C2318yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2318yes—
220C2×#121C2314yes—
221C2×#121C2318yes—
222C2×#121C2314yes—
223C2×#121C2312yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#121C2312yes—
227C2×#120C2314yes—
228C2×#120C2314yes—
229#520—44no—
230C4×#41—28no—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×D4—44no—
235C2×C4×D4C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2318yes—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2312yes—
247C2×#117C2311yescharacteristic
248C2×#117C2312yes—
249C2×#117C2318yes—
250C2×#117C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2314yes—
259C22×C22⋊C4C2312yes—
260C22×C22⋊C4C2314yes—
261C22×C22⋊C4C2314yes—
262C22×C42C2312yes—
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266#401C2314yes—
267#400C2314yes—
268#400C2318yes—
269#400C2318yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#399C2318yes—
274#399C2314yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2314yes—
280#398C2314yes—
281#397C2314yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2314yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2314yes—
295#396C2318yes—
296#396C2318yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2314yes—
301#396C2318yes—
302#396C2314yes—
303#396C2318yes—
304#396C2314yes—
305#395C2318yes—
306#395C2314yes—
307#395C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#393C2318yes—
319#393C2318yes—
320#393C2314yes—
321#392C2318yes—
322#391C2311yescharacteristic
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2311yescharacteristic
327#391C2318yes—
328#391C2318yes—
329#391C2312yes—
330#391C2311yescharacteristic
331#391C2312yes—
332#391C2311yescharacteristic
333#391C2318yes—
334#391C2312yes—
335#391C2314yes—
336#390C2314yes—
337#390C2312yes—
338#390C2312yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2314yes—
347#390C2311yescharacteristic
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2318yes—
352#390C2318yes—
353#390C2318yes—
354#390C2318yes—
355#390C2318yes—
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2312yes—
359#390C2311yescharacteristic
360#390C2312yes—
361#390C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2318yes—
365#389C2314yes—
366#389C2318yes—
367#389C2318yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2314yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2318yes—
405#387C2314yes—
406#386C2314yes—
407#386C2314yes—
408#386C2314yes—
409#386C2312yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2312yes—
414#386C2312yes—
415#386C2318yes—
416#386C2318yes—
417#386C2314yes—
418#386C2314yes—
419#386C2314yes—
420#386C2312yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2314yes—
427#385C2314yes—
428#385C2314yes—
429#385C2312yes—
430#385C2312yes—
431#385C2312yes—
432#385C2318yes—
433#385C2318yes—
434#385C2312yes—
435#385C2314yes—
436#385C2314yes—
437#385C2314yes—
438#384C2312yes—
439#384C2312yes—
440#384C2314yes—
441#384C2312yes—
442#384C2312yes—
443#384C2312yes—
444#384C2318yes—
445#384C2312yes—
446#383C2314yes—
447#382C2312yes—
448#382C2312yes—
449#382C2312yes—
450#382C2314yes—
451#382C2312yes—
452#382C2312yes—
453#382C2312yes—
454#382C2318yes—
455#382C2318yes—
456#381C2318yes—
457#381C2318yes—
458#380C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2318yes—
464#379C2314yes—
465#379C2314yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2312yes—
497#376C2312yes—
498C2×#95C2314yes—
499C2×#95C2312yes—
500C43C2312yes—
501C25C2412yes—
502C2×#41—24no—
503C2×#41—24no—
504C2×#41—24no—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2414yes—
511C22×Q8C2414yes—
512C22×D4—24no—
513C22×D4—24no—
514C22×D4—24no—
515C22×D4C2412yes—
516C22×D4C2412yes—
517C22×D4C2412yes—
518C22×D4C2412yes—
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2418yes—
522C22×D4C2414yes—
523C22×D4C2414yes—
524C22×D4C2414yes—
525C23×C4—44no—
526C23×C4—84no—
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2414yes—
531C23×C4C2412yes—
532C23×C4C2411yescharacteristic
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2411yescharacteristic
537C23×C4C2414yes—
538C23×C4C2418yes—
539C23×C4C2411yescharacteristic
540C4⋊Q8—28no—
541C4⋊Q8—44no—
542C4⋊Q8—44no—
543#127—28no—
544#127—44no—
545#126—416no—
546#126—48no—
547#125—28no—
548#125—48no—
549#125—48no—
550#125—44no—
551#125—44no—
552#124—28no—
553#124—44no—
554#124—88no—
555#124—88no—
556#123—88no—
557C22⋊Q8—216no—
558C22⋊Q8—48no—
559C22⋊Q8—48no—
560C22⋊Q8—44no—
561C22⋊Q8—44no—
562C22⋊Q8—88no—
563#121—216no—
564#121—416no—
565#121—44no—
566#121—44no—
567#121—44no—
568#121—44no—
569#121—48no—
570#120—216no—
571#120—48no—
572C4×Q8—28no—
573C4×Q8—216no—
574C4×Q8—44no—
575C4×D4—28no—
576C4×D4—216no—
577C4×D4—48no—
578C4×D4—48no—
579C4×D4—44no—
580C4×D4—48no—
581C4×D4—88no—
582#117—24no—
583#117—24no—
584#117—24no—
585#117—24no—
586#117—24no—
587#117—28no—
588#117—44no—
589#117—88no—
590#117#4118yes—
591C2×C4⋊C4—24no—
592C2×C4⋊C4—24no—
593C2×C4⋊C4—24no—
594C2×C4⋊C4—44no—
595C2×C4⋊C4—44no—
596C2×C4⋊C4—44no—
597C2×C4⋊C4—44no—
598C2×C4⋊C4—84no—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2412yes—
641C2×C22⋊C4—48no—
642C2×C22⋊C4—44no—
643C2×C22⋊C4—84no—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2412yes—
679C2×C42—24no—
680C2×C42—24no—
681C2×C42—24no—
682C2×C42—28no—
683C2×C42C2411yescharacteristic
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2412yes—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2414yes—
698C2×C42C2418yes—
699C2×C42C2418yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2418yes—
703C2×C42C2412yes—
704#95C2412yes—
705#95C2418yes—
706#95C2412yes—
707#95C2412yes—
708#95C2412yes—
709#95C2418yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2418yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739C24—24no—
740C24—24no—
741C24—24no—
742C24—44no—
743C24—44no—
744C24C2514yes—
745C24C2512yes—
746C24C2512yes—
747C24C2511yescharacteristic
748#41—416no—
749#41—416no—
750C2×Q8—22no—
751C2×Q8—22no—
752C2×Q8—28no—
753C2×Q8—22no—
754C2×Q8—22no—
755C2×Q8—22no—
756C2×Q8—22no—
757C2×Q8—44no—
758C2×Q8—44no—
759C2×Q8—44no—
760C2×Q8—48no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—24no—
764C2×D4—24no—
765C2×D4—24no—
766C2×D4—24no—
767C2×D4—22no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—22no—
771C2×D4—216no—
772C2×D4—24no—
773C2×D4—22no—
774C2×D4—24no—
775C2×D4—22no—
776C2×D4—24no—
777C2×D4—24no—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—48no—
786C2×D4—48no—
787C2×D4—48no—
788C2×D4—416no—
789C22×C4—24no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—28no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—28no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—44no—
808C22×C4—42no—
809C22×C4—44no—
810C22×C4—42no—
811C22×C4—44no—
812C22×C4—42no—
813C22×C4—44no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—44no—
818C22×C4—48no—
819C22×C4—816no—
820C22×C4C2×#4114yes—
821C22×C4H(5,𝔽2)14yes—
822C22×C42−1+414yes—
823C22×C4C2512yes—
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2514yes—
831C22×C4C2512yes—
832C22×C4C2514yes—
833C22×C4C2512yes—
834C22×C4C2512yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C4⋊C4—28no—
845C4⋊C4—24no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—44no—
868C4⋊C4—48no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—48no—
882C4⋊C4—44no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4C2×#4118yes—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—28no—
892C22⋊C4—216no—
893C22⋊C4—216no—
894C22⋊C4—28no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—44no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—44no—
903C22⋊C4—48no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—48no—
912C22⋊C4—44no—
913C22⋊C4—48no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4C2×#4118yes—
921C42—22no—
922C42—22no—
923C42—24no—
924C42—28no—
925C42—24no—
926C42—22no—
927C42—22no—
928C42—24no—
929C42—24no—
930C42—24no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—24no—
935C42—44no—
936C42—48no—
937C42—48no—
938C42—44no—
939C42—48no—
940C42—44no—
941C42C2×#4118yes—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—24no—
946C23—22no—
947C23—22no—
948C23—24no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—24no—
953C23—28no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—28no—
959C23—416no—
960C23—48no—
961C23—84no—
962C23—88no—
963C23—84no—
964C23C22×#4112yes—
965C23C2×H(5,𝔽2)12yes—
966C23C2×2−1+412yes—
967C23C2611yescharacteristic
968Q8—44no—
969Q8—44no—
970Q8—88no—
971Q8—164no—
972D4—48no—
973D4—48no—
974D4—48no—
975D4—48no—
976D4—44no—
977D4—44no—
978D4—816no—
979D4—164no—
980D4—164no—
981D4—164no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—28no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—28no—
1022C2×C4—28no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—416no—
1031C2×C4—48no—
1032C2×C4—44no—
1033C2×C4—44no—
1034C2×C4—48no—
1035C2×C4—48no—
1036C2×C4—84no—
1037C2×C4—84no—
1038C2×C4—84no—
1039C2×C4—84no—
1040C2×C4—816no—
1041C2×C4—164no—
1042C2×C4#542116yes—
1043C2×C4C22×#4118yes—
1044C2×C4C22×#4112yes—
1045C2×C4C22×#4112yes—
1046C2×C4C2×H(5,𝔽2)12yes—
1047C2×C4C2×H(5,𝔽2)12yes—
1048C2×C4C2×2−1+412yes—
1049C2×C4C2×2−1+412yes—
1050C2×C4#58514yes—
1051C22—24no—
1052C22—22no—
1053C22—22no—
1054C22—24no—
1055C22—44no—
1056C22—44no—
1057C22—48no—
1058C22—42no—
1059C22—42no—
1060C22—44no—
1061C22—44no—
1062C22—42no—
1063C22—42no—
1064C22—44no—
1065C22—44no—
1066C22—48no—
1067C22—42no—
1068C22—42no—
1069C22—44no—
1070C22—816no—
1071C22C2×#54214yes—
1072C22C23×#4111yescharacteristic
1073C22C22×H(5,𝔽2)11yescharacteristic
1074C22C22×2−1+411yescharacteristic
1075C22C2×#58512yes—
1076C22H(7,𝔽2)12yes—
1077C4—24no—
1078C4—28no—
1079C4—42no—
1080C4—42no—
1081C4—42no—
1082C4—44no—
1083C4—42no—
1084C4—42no—
1085C4—44no—
1086C4—42no—
1087C4—42no—
1088C4—44no—
1089C4—44no—
1090C4—42no—
1091C4—42no—
1092C4—44no—
1093C4—44no—
1094C4—42no—
1095C4—42no—
1096C4C2×#54214yes—
1097C4C2×#54214yes—
1098C2—24no—
1099C2—82no—
1100C2—82no—
1101C2—84no—
1102C2C22×#54211yescharacteristic
1103C2#6283611yescharacteristic
1104C2#6287611yescharacteristic
1105C2#6292612yes—
1106C2#6300812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35256C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42659C2semidirect
2. #42596C2semidirect
3. #42588C2semidirect
4. #42472C2semidirect
5. #40786C2semidirect
6. #40050C2semidirect
7. #39925C2semidirect
8. #39736C2semidirect
9. #39251C2semidirect
10. #38535C2semidirect
11. #35649C2semidirect
12. #35640C2semidirect
13. #35618C2semidirect
14. #35558C2semidirect
15. #35556C2semidirect
16. #35532C2semidirect
17. #35264C2semidirect
19. #35152C2semidirect
20. C2×#2566C2semidirect
21. #34816C2semidirect
22. #34745C2semidirect
23. #34265C2semidirect
24. #34215C2semidirect
25. #34188C2semidirect
40. #2831C22semidirect
41. #2829C22semidirect
42. #2796C22semidirect
43. #2795C22semidirect
44. #2793C22semidirect
45. #2772C22semidirect
46. #2765C22semidirect
47. #2763C22semidirect
48. #2761C22semidirect
49. #2761C22semidirect
50. #2757C22semidirect
51. #2730C22semidirect
52. #2717C22semidirect
53. #2710C22semidirect
54. #2702C22semidirect
55. #2700C22semidirect
56. #2691C22semidirect
57. #2691C22semidirect
58. #2653C22semidirect
59. #2651C22semidirect
60. #2651C22semidirect
61. #2650C22semidirect
64. #2638C22semidirect
67. #2620C22semidirect
72. #2567C22semidirect
77. #2566C22semidirect
78. #2565C22semidirect
79. #2552C22semidirect
80. #2552C22semidirect
81. #2550C22semidirect
82. #2550C22semidirect
84. #2542C22semidirect
85. #2515C22semidirect
86. #2514C22semidirect
89. #2513C22semidirect
92. #2512C22semidirect
93. #2512C22semidirect
94. #2511C22semidirect
97. #2504C22semidirect
98. #2503C22semidirect
100. #2500C22semidirect
101. #2499C22semidirect
106. #2490C22semidirect
107. #2490C22semidirect
108. #2489C22semidirect
109. #2489C22semidirect
112. #2474C22semidirect
115. #2470C22semidirect
116. #2461C22semidirect
117. #2454C22semidirect
118. #2453C22semidirect
119. #2452C22semidirect
120. #2451C22semidirect
125. #2447C22semidirect
128. #2441C22semidirect
129. #2440C22semidirect
134. #2421C22semidirect
136. #2420C22semidirect
137. #2401C22semidirect
138. #2396C22semidirect
145. #2355C22semidirect
146. #2355C22semidirect
147. #2355C22semidirect
148. #2354C22semidirect
150. #2334C22semidirect
151. #2331C22semidirect
152. #2324C22semidirect
157. #2314C22semidirect
163. C4×#125C22semidirect
164. C4×#126C22semidirect
165. C4×C22⋊Q8C22semidirect
179. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#426592
#425962
#425882
#424722
#407862
#400502
#399252
#397362
#392512
#385352
#356492
#356402
#356182
#355582
#355562
#355322
#352642
#352562
#351522
C2×#25662
#348162
#347452
#342652
#342152
#341882