Finite Group Databasebeta

← #8094802

Subgroups — #8094802

Order 512.

5492 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53115C214yesmaximal, complemented
2#53016C214yesmaximal, complemented
3#52992C214yesmaximal, complemented
4#52976C214yesmaximal, complemented
5#52547C218yesmaximal, complemented
6#46104C214yesmaximal, complemented
7#45995C214yesmaximal, complemented
8#45625C214yesmaximal, complemented
9#45486C214yesmaximal, complemented
10#45454C218yesmaximal, complemented
11#35563C211yesmaximal, characteristic, complemented
12#35541C211yesmaximal, characteristic, complemented
13#35532C211yesmaximal, characteristic, complemented
14#35530C211yesmaximal, characteristic, complemented
15#35515C211yesmaximal, characteristic, complemented
16#35514C211yesmaximal, characteristic, complemented
17#35286C211yesmaximal, characteristic, complemented
18#35280C211yesmaximal, characteristic, complemented
19#35264C211yesmaximal, characteristic, complemented
20#35256C211yesmaximal, characteristic, complemented
21#35224C211yesmaximal, characteristic, complemented
22#35223C211yesmaximal, characteristic, complemented
23#34813C211yesmaximal, characteristic, complemented
24C2×#2501C211yesmaximal, characteristic, complemented
25#34742C211yesmaximal, characteristic, complemented
26C2×#562C2218yescomplemented
27C2×#544C2211yescharacteristic
28C2×#537C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C2×#525C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×#123C2214yes—
35C22×#121C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#518C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39C23×C4⋊C4C2211yescharacteristic
40#2861C2212yescomplemented
41#2859C2214yescomplemented
42#2858C2212yescomplemented
43#2857C2214yescomplemented
44#2856C2212yescomplemented
45#2850C2212yescomplemented
46#2848C2214yes—
47#2847C2214yes—
48#2841C2218yescomplemented
49#2837C2218yescomplemented
50#2837C2218yescomplemented
51#2836C2218yescomplemented
52#2827C2218yescomplemented
53#2826C2218yescomplemented
54#2820C2218yescomplemented
55#2816C2218yescomplemented
56#2814C2218yescomplemented
57#2813C2218yescomplemented
58#2768C2218yescomplemented
59#2754C2218yescomplemented
60#2743C2218yescomplemented
61#2732C2218yescomplemented
62#2710C2218yescomplemented
63#2708C2218yescomplemented
64#2706C2218yescomplemented
65#2706C2218yescomplemented
66#2706C2218yescomplemented
67#2701C2218yescomplemented
68#2696C2218yescomplemented
69#2694C2218yescomplemented
70#2694C2218yescomplemented
71#2692C2218yescomplemented
72#2687C2218yescomplemented
73#2682C2218yescomplemented
74#2681C2218yescomplemented
75#2672C2218yescomplemented
76#2672C2218yescomplemented
77#2671C2218yescomplemented
78#2647C2214yescomplemented
79#2641C2212yescomplemented
80#2640C2212yescomplemented
81#2629C2214yescomplemented
82#2627C2214yes—
83#2620C2212yescomplemented
84#2619C2212yescomplemented
85#2618C2214yes—
86#2582C2214yescomplemented
87#2580C2214yescomplemented
88#2571C2214yescomplemented
89#2567C2212yescomplemented
90#2566C2212yescomplemented
91#2565C2212yescomplemented
92#2552C2214yescomplemented
93#2542C2212yescomplemented
94#2538C2214yescomplemented
95#2538C2214yescomplemented
96#2537C2214yes—
97#2535C2214yes—
98#2534C2214yes—
99#2502C2212yescomplemented
100#2501C2214yes—
101#2501C2214yes—
102#2501C2214yes—
103#2501C2214yes—
104#2501C2212yescomplemented
105#2500C2212yescomplemented
106#2499C2212yescomplemented
107#2492C2212yescomplemented
108#2491C2214yescomplemented
109#2491C2212yescomplemented
110#2490C2214yescomplemented
111#2490C2212yescomplemented
112#2489C2212yescomplemented
113#2488C2214yes—
114#2472C2218yes—
115#2472C2214yes—
116#2454C2214yescomplemented
117#2452C2214yescomplemented
118#2449C2218yes—
119#2447C2214yescomplemented
120#2445C2214yescomplemented
121#2443C2218yes—
122#2442C2218yes—
123#2442C2214yescomplemented
124#2442C2214yescomplemented
125#2441C2214yescomplemented
126#2440C2214yescomplemented
127#2440C2214yescomplemented
128#2440C2214yescomplemented
129#2437C2218yes—
130#2428C2214yes—
131#2428C2214yes—
132#2428C2214yescomplemented
133#2427C2214yes—
134#2426C2214yes—
135#2426C2214yescomplemented
136#2424C2218yes—
137#2423C2212yescomplemented
138#2423C2214yescomplemented
139#2422C2214yescomplemented
140#2422C2212yescomplemented
141#2422C2214yescomplemented
142#2421C2212yescomplemented
143#2420C2214yescomplemented
144#2420C2212yescomplemented
145#2419C2214yes—
146#2418C2214yes—
147#2417C2218yes—
148#2417C2214yescomplemented
149#2417C2214yescomplemented
150#2416C2214yes—
151#2416C2214yescomplemented
152#2416C2214yescomplemented
153#2414C2214yes—
154#2412C2214yes—
155#2412C2218yes—
156#2410C2214yes—
157#2408C2214yes—
158#2398C2214yescomplemented
159#2395C2214yescomplemented
160C2×#399C2214yes—
161#2376C2218yescomplemented
162#2317C2211yescharacteristic
163#2317C2211yescharacteristic
164#2317C2211yescharacteristic
165#2316C2211yescharacteristic
166#2316C2211yescharacteristic
167#2316C2211yescharacteristic
168#2311C2211yescharacteristic
169#2311C2211yescharacteristic
170#2311C2211yescharacteristic
171#2309C2211yescharacteristic
172C4×#124C2214yescomplemented
173C4×#123C2214yescomplemented
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2211yescharacteristic
177#2296C2211yescharacteristic
178C2×#390C2211yescharacteristic
179C2×#390C2211yescharacteristic
180#2285C2211yescharacteristic
181C2×#384C2211yescharacteristic
182C2×#384C2211yescharacteristic
183#2280C2211yescharacteristic
184#2280C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×D4C2311yescharacteristic
190C23×D4C2312yes—
191C24×C4C2311yescharacteristic
192C24×C4C2312yes—
193#562—432no—
194#544—44no—
195#537—44no—
196#535—44no—
197#535—44no—
198#533—44no—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×#127C2312yes—
203C2×#127C2312yes—
204C2×#125C2318yes—
205C2×#125C2312yes—
206C2×#125C2312yes—
207C2×#125C2312yes—
208C2×#124C2314yes—
209C2×#124C2318yes—
210C2×#124C2312yes—
211C2×#124C2312yes—
212#525—44no—
213#525—44no—
214C2×#123—416no—
215C2×#123C2318yes—
216C2×#123C2314yes—
217C2×#123C2312yes—
218C2×#123C2312yes—
219C2×#123C2318yes—
220C2×#123C2318yes—
221C2×#123C2318yes—
222C2×#123C2318yes—
223C2×#123C2318yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2318yes—
234C2×#121—44no—
235C2×#121C2318yes—
236C2×#121C2314yes—
237C2×#121C2318yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2318yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2318yes—
245C2×#121C2312yes—
246C2×#121C2312yes—
247C2×#121C2314yes—
248C2×#121C2312yes—
249C2×#120C2312yes—
250C2×#120C2312yes—
251C2×#120C2314yes—
252C2×#120C2314yes—
253#520—44no—
254#518—44no—
255C4×#41—44no—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C2×#117C2311yescharacteristic
271C2×#117C2311yescharacteristic
272C2×#117C2311yescharacteristic
273C2×#117C2312yes—
274C2×#117C2312yes—
275C22×C4⋊C4—44no—
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2312yes—
280C22×C4⋊C4C2314yes—
281C22×C4⋊C4C2314yes—
282C22×C4⋊C4C2314yes—
283C22×C4⋊C4C2314yes—
284C22×C4⋊C4C2312yes—
285C22×C22⋊C4C2312yes—
286C22×C22⋊C4C2312yes—
287C22×C22⋊C4C2314yes—
288C22×C22⋊C4C2314yes—
289C22×C22⋊C4C2314yes—
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292C22×C42C2312yes—
293#400C2318yes—
294#400C2318yes—
295#400C2318yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#399C2318yes—
300#399C2318yes—
301#399C2318yes—
302#399C2318yes—
303#399C2318yes—
304#399C2318yes—
305#399C2318yes—
306#399C2314yes—
307#398C2318yes—
308#398C2318yes—
309#398C2318yes—
310#398C2318yes—
311#398C2318yes—
312#398C2318yes—
313#398C2318yes—
314#398C2314yes—
315#398C2318yes—
316#398C2318yes—
317#397C2314yes—
318#397C2318yes—
319#397C2314yes—
320#397C2314yes—
321#397C2318yes—
322#397C2318yes—
323#397C2318yes—
324#397C2318yes—
325#397C2314yes—
326#397C2314yes—
327#396C2318yes—
328#396C2318yes—
329#396C2318yes—
330#396C2318yes—
331#396C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#396C2318yes—
336#395C2318yes—
337#395C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2314yes—
349#394C2314yes—
350#394C2314yes—
351#394C2314yes—
352#394C2318yes—
353#394C2318yes—
354#393C2314yes—
355#393C2318yes—
356#393C2318yes—
357#393C2314yes—
358#392C2318yes—
359#392C2318yes—
360#392C2318yes—
361#391C2311yescharacteristic
362#391C2312yes—
363#391C2312yes—
364#391C2312yes—
365#391C2311yescharacteristic
366#391C2318yes—
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2312yes—
370#391C2314yes—
371#390C2312yes—
372#390C2312yes—
373#390C2314yes—
374#390C2311yescharacteristic
375#390C2312yes—
376#390C2312yes—
377#390C2312yes—
378#390C2314yes—
379#390C2312yes—
380#390C2311yescharacteristic
381#390C2318yes—
382#390C2311yescharacteristic
383#390C2312yes—
384#390C2318yes—
385#390C2312yes—
386#390C2318yes—
387#390C2312yes—
388#390C2311yescharacteristic
389#390C2312yes—
390#390C2314yes—
391#390C2314yes—
392#389C2318yes—
393#389C2314yes—
394#389C2314yes—
395#389C2318yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2312yes—
404#389C2318yes—
405#389C2318yes—
406#389C2312yes—
407#388C2318yes—
408#388C2314yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#387C2318yes—
419#387C2314yes—
420#387C2318yes—
421#387C2314yes—
422#386C2314yes—
423#386C2314yes—
424#386C2314yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2314yes—
433#386C2314yes—
434#386C2314yes—
435#386C2314yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2314yes—
440#385C2314yes—
441#385C2314yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2318yes—
446#385C2314yes—
447#385C2314yes—
448#384C2312yes—
449#384C2312yes—
450#384C2312yes—
451#384C2314yes—
452#384C2312yes—
453#384C2312yes—
454#384C2314yes—
455#384C2312yes—
456#384C2312yes—
457#384C2312yes—
458#382C2314yes—
459#382C2312yes—
460#382C2312yes—
461#382C2318yes—
462#382C2312yes—
463#382C2312yes—
464#381C2314yes—
465#381C2318yes—
466#381C2312yes—
467#381C2312yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2318yes—
475#380C2318yes—
476#380C2318yes—
477#380C2318yes—
478#380C2318yes—
479#380C2314yes—
480#380C2312yes—
481#380C2312yes—
482#380C2312yes—
483#380C2312yes—
484#379C2314yes—
485#379C2312yes—
486#379C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2312yes—
503#376C2312yes—
504C2×#95C2312yes—
505C43C2312yes—
506C25C2411yescharacteristic
507C25C2412yes—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—24no—
513C2×#41—24no—
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2414yes—
517C22×Q8C2414yes—
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—24no—
521C22×D4—44no—
522C22×D4—48no—
523C22×D4C2412yes—
524C22×D4C2412yes—
525C22×D4C2412yes—
526C22×D4C2412yes—
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2414yes—
530C22×D4C2414yes—
531C22×D4C2418yes—
532C22×D4C2414yes—
533C22×D4C2418yes—
534C22×D4C2414yes—
535C22×D4C2414yes—
536C23×C4—24no—
537C23×C4—24no—
538C23×C4—24no—
539C23×C4—44no—
540C23×C4—48no—
541C23×C4C2411yescharacteristic
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2418yes—
552C23×C4C2414yes—
553C23×C4C2418yes—
554C23×C4C2414yes—
555C23×C4C2411yescharacteristic
556C4⋊Q8—44no—
557C4⋊Q8—44no—
558C4⋊Q8—44no—
559#127—44no—
560#127—44no—
561#125—44no—
562#125—44no—
563#125—44no—
564#125—416no—
565#124—216no—
566#124—416no—
567#124—44no—
568#124—44no—
569#123—232no—
570#123—216no—
571#123—416no—
572#123—416no—
573#123—416no—
574#123—416no—
575#123—416no—
576#123—44no—
577#123—44no—
578C22⋊Q8—48no—
579C22⋊Q8—48no—
580C22⋊Q8—416no—
581C22⋊Q8—416no—
582C22⋊Q8—416no—
583C22⋊Q8—44no—
584C22⋊Q8—44no—
585C22⋊Q8—44no—
586C22⋊Q8—44no—
587C22⋊Q8—416no—
588#121—416no—
589#121—416no—
590#121—416no—
591#121—48no—
592#121—48no—
593#121—44no—
594#121—44no—
595#121—48no—
596#121—44no—
597#121—44no—
598#121—44no—
599#121—44no—
600#121—48no—
601#121—416no—
602#120—44no—
603#120—44no—
604#120—48no—
605#120—48no—
606C4×Q8—48no—
607C4×Q8—44no—
608C4×Q8—44no—
609C4×D4—44no—
610C4×D4—48no—
611C4×D4—48no—
612C4×D4—44no—
613C4×D4—48no—
614C4×D4—48no—
615C4×D4—48no—
616C4×D4—48no—
617#117—24no—
618#117—24no—
619#117—24no—
620#117—24no—
621#117—24no—
622#117—24no—
623#117—44no—
624#117—44no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4—24no—
627C2×C4⋊C4—24no—
628C2×C4⋊C4—48no—
629C2×C4⋊C4—48no—
630C2×C4⋊C4—44no—
631C2×C4⋊C4—48no—
632C2×C4⋊C4—48no—
633C2×C4⋊C4—44no—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C22⋊C4—28no—
675C2×C22⋊C4—48no—
676C2×C22⋊C4—48no—
677C2×C22⋊C4—48no—
678C2×C22⋊C4—44no—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2412yes—
721C2×C42—24no—
722C2×C42—24no—
723C2×C42—44no—
724C2×C42C2412yes—
725C2×C42C2411yescharacteristic
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2414yes—
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2412yes—
737C2×C42C2414yes—
738C2×C42C2414yes—
739C2×C42C2414yes—
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2412yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769C24—24no—
770C24—22no—
771C24—22no—
772C24—22no—
773C24—24no—
774C24—24no—
775C24—24no—
776C24—42no—
777C24—44no—
778C24—44no—
779C24C2514yes—
780C24C2512yes—
781C24C2512yes—
782C24C2512yes—
783C24C2511yescharacteristic
784#41—416no—
785#41—416no—
786C2×Q8—22no—
787C2×Q8—22no—
788C2×Q8—22no—
789C2×Q8—22no—
790C2×Q8—28no—
791C2×Q8—22no—
792C2×Q8—22no—
793C2×Q8—44no—
794C2×Q8—44no—
795C2×Q8—48no—
796C2×Q8—44no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—216no—
806C2×D4—24no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—22no—
813C2×D4—22no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—44no—
819C2×D4—44no—
820C2×D4—48no—
821C2×D4—48no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—48no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—44no—
828C2×D4—48no—
829C2×D4—48no—
830C2×D4—48no—
831C2×D4—48no—
832C2×D4—48no—
833C2×D4—416no—
834C2×D4—816no—
835C22×C4—24no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—24no—
839C22×C4—22no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—216no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—28no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—48no—
865C22×C4—44no—
866C22×C4—48no—
867C22×C4—44no—
868C22×C4—48no—
869C22×C4—44no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—416no—
874C22×C4—816no—
875C22×C4H(5,𝔽2)14yes—
876C22×C4H(5,𝔽2)14yes—
877C22×C42−1+414yes—
878C22×C4C2512yes—
879C22×C4C2512yes—
880C22×C4C2512yes—
881C22×C4C2512yes—
882C22×C4C2512yes—
883C22×C4C2512yes—
884C22×C4C2514yes—
885C22×C4C2514yes—
886C22×C4C2514yes—
887C22×C4C2514yes—
888C22×C4C2512yes—
889C22×C4C2512yes—
890C22×C4C2512yes—
891C22×C4C2514yes—
892C22×C4C2514yes—
893C22×C4C2514yes—
894C22×C4C2512yes—
895C22×C4C2512yes—
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—22no—
905C4⋊C4—216no—
906C4⋊C4—216no—
907C4⋊C4—22no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—24no—
914C4⋊C4—28no—
915C4⋊C4—28no—
916C4⋊C4—48no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—48no—
932C4⋊C4—48no—
933C4⋊C4—48no—
934C4⋊C4—48no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—216no—
950C22⋊C4—216no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—48no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—48no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—48no—
976C22⋊C4—48no—
977C22⋊C4—48no—
978C22⋊C4—48no—
979C22⋊C4H(5,𝔽2)18yes—
980C42—22no—
981C42—22no—
982C42—24no—
983C42—24no—
984C42—24no—
985C42—24no—
986C42—24no—
987C42—24no—
988C42—24no—
989C42—28no—
990C42—22no—
991C42—24no—
992C42—22no—
993C42—44no—
994C42—44no—
995C42—44no—
996C23—22no—
997C23—22no—
998C23—28no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—28no—
1006C23—24no—
1007C23—24no—
1008C23—22no—
1009C23—22no—
1010C23—24no—
1011C23—24no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—28no—
1020C23—48no—
1021C23—48no—
1022C23—44no—
1023C23—44no—
1024C23—48no—
1025C23—84no—
1026C23—84no—
1027C23—88no—
1028C23—88no—
1029C23C2×H(5,𝔽2)14yes—
1030C23C2×H(5,𝔽2)12yes—
1031C23C2×H(5,𝔽2)12yes—
1032C23C2×2−1+412yes—
1033C23C2611yescharacteristic
1034Q8—44no—
1035Q8—44no—
1036Q8—88no—
1037Q8—164no—
1038D4—48no—
1039D4—48no—
1040D4—48no—
1041D4—48no—
1042D4—44no—
1043D4—44no—
1044D4—88no—
1045D4—88no—
1046D4—816no—
1047D4—164no—
1048D4—164no—
1049D4—164no—
1050D4—168no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—28no—
1074C2×C4—28no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—28no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—48no—
1097C2×C4—48no—
1098C2×C4—44no—
1099C2×C4—48no—
1100C2×C4—48no—
1101C2×C4—48no—
1102C2×C4—48no—
1103C2×C4—88no—
1104C2×C4—84no—
1105C2×C4—816no—
1106C2×C4—84no—
1107C2×C4—84no—
1108C2×C4—164no—
1109C2×C4—168no—
1110C2×C4#562116yescomplemented
1111C2×C4C2×H(5,𝔽2)14yes—
1112C2×C4C2×H(5,𝔽2)14yes—
1113C2×C4C2×H(5,𝔽2)12yes—
1114C2×C4C2×H(5,𝔽2)12yes—
1115C2×C4C2×H(5,𝔽2)12yes—
1116C2×C4C2×H(5,𝔽2)12yes—
1117C2×C4C2×2−1+412yes—
1118C2×C4C2×2−1+412yes—
1119C22—22no—
1120C22—22no—
1121C22—24no—
1122C22—24no—
1123C22—24no—
1124C22—24no—
1125C22—24no—
1126C22—416no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—44no—
1133C22—42no—
1134C22—42no—
1135C22—44no—
1136C22—42no—
1137C22—44no—
1138C22—48no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—48no—
1143C22—42no—
1144C22—42no—
1145C22—44no—
1146C22—168no—
1147C22C2×#56214yes—
1148C22C22×H(5,𝔽2)11yescharacteristic
1149C22C22×H(5,𝔽2)12yes—
1150C22C22×H(5,𝔽2)11yescharacteristic
1151C22C22×2−1+411yescharacteristic
1152C222−1+612yes—
1153C4—24no—
1154C4—24no—
1155C4—44no—
1156C4—44no—
1157C4—44no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—44no—
1164C4—44no—
1165C4—44no—
1166C4—44no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4C2×#56214yes—
1172C4C2×#56214yes—
1173C2—24no—
1174C2—44no—
1175C2—82no—
1176C2—82no—
1177C2—84no—
1178C2C22×#56211yescharacteristic
1179C2#6283211yescharacteristic
1180C2#6288711yescharacteristic
1181C2#6291412yes—
1182C2#6291512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53115C2semidirect
2. #53016C2semidirect
3. #52992C2semidirect
4. #52976C2semidirect
5. #52547C2semidirect
6. #46104C2semidirect
7. #45995C2semidirect
8. #45625C2semidirect
9. #45486C2semidirect
10. #45454C2semidirect
11. #35563C2semidirect
12. #35541C2semidirect
13. #35532C2semidirect
14. #35530C2semidirect
15. #35515C2semidirect
16. #35514C2semidirect
17. #35286C2semidirect
18. #35280C2semidirect
19. #35264C2semidirect
20. #35256C2semidirect
21. #35224C2semidirect
22. #35223C2semidirect
23. #34813C2semidirect
24. C2×#2501C2semidirect
25. #34742C2semidirect
26. C2×#562C22semidirect
40. #2861C22semidirect
41. #2859C22semidirect
42. #2858C22semidirect
43. #2857C22semidirect
44. #2856C22semidirect
45. #2850C22semidirect
48. #2841C22semidirect
49. #2837C22semidirect
50. #2837C22semidirect
51. #2836C22semidirect
52. #2827C22semidirect
53. #2826C22semidirect
54. #2820C22semidirect
55. #2816C22semidirect
56. #2814C22semidirect
57. #2813C22semidirect
58. #2768C22semidirect
59. #2754C22semidirect
60. #2743C22semidirect
61. #2732C22semidirect
62. #2710C22semidirect
63. #2708C22semidirect
64. #2706C22semidirect
65. #2706C22semidirect
66. #2706C22semidirect
67. #2701C22semidirect
68. #2696C22semidirect
69. #2694C22semidirect
70. #2694C22semidirect
71. #2692C22semidirect
72. #2687C22semidirect
73. #2682C22semidirect
74. #2681C22semidirect
75. #2672C22semidirect
76. #2672C22semidirect
77. #2671C22semidirect
78. #2647C22semidirect
79. #2641C22semidirect
80. #2640C22semidirect
81. #2629C22semidirect
83. #2620C22semidirect
84. #2619C22semidirect
86. #2582C22semidirect
87. #2580C22semidirect
88. #2571C22semidirect
89. #2567C22semidirect
90. #2566C22semidirect
91. #2565C22semidirect
92. #2552C22semidirect
93. #2542C22semidirect
94. #2538C22semidirect
95. #2538C22semidirect
99. #2502C22semidirect
104. #2501C22semidirect
105. #2500C22semidirect
106. #2499C22semidirect
107. #2492C22semidirect
108. #2491C22semidirect
109. #2491C22semidirect
110. #2490C22semidirect
111. #2490C22semidirect
112. #2489C22semidirect
116. #2454C22semidirect
117. #2452C22semidirect
119. #2447C22semidirect
120. #2445C22semidirect
123. #2442C22semidirect
124. #2442C22semidirect
125. #2441C22semidirect
126. #2440C22semidirect
127. #2440C22semidirect
128. #2440C22semidirect
132. #2428C22semidirect
135. #2426C22semidirect
137. #2423C22semidirect
138. #2423C22semidirect
139. #2422C22semidirect
140. #2422C22semidirect
141. #2422C22semidirect
142. #2421C22semidirect
143. #2420C22semidirect
144. #2420C22semidirect
148. #2417C22semidirect
149. #2417C22semidirect
151. #2416C22semidirect
152. #2416C22semidirect
158. #2398C22semidirect
159. #2395C22semidirect
161. #2376C22semidirect
172. C4×#124C22semidirect
173. C4×#123C22semidirect
1110. C2×C4#562semidirect

Maximal subgroups

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

subgroupindex
#531152
#530162
#529922
#529762
#525472
#461042
#459952
#456252
#454862
#454542
#355632
#355412
#355322
#355302
#355152
#355142
#352862
#352802
#352642
#352562
#352242
#352232
#348132
C2×#25012
#347422