Finite Group Databasebeta

← #8429476

Subgroups — #8429476

Order 512.

4675 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C211yesmaximal, characteristic, complemented
2#59321C212yesmaximal, complemented
3#59217C212yesmaximal, complemented
4#59052C212yesmaximal, complemented
5#55178C218yesmaximal, complemented
6#53067C214yesmaximal, complemented
7#53024C214yesmaximal, complemented
8#52959C214yesmaximal, complemented
9#42641C214yesmaximal, complemented
10#42577C214yesmaximal, complemented
11#42534C214yesmaximal, complemented
12#39737C212yesmaximal, complemented
13#39607C212yesmaximal, complemented
14#39606C212yesmaximal, complemented
15#39139C212yesmaximal, complemented
16#39127C212yesmaximal, complemented
17#39126C212yesmaximal, complemented
18#37643C212yesmaximal, complemented
19#37633C212yesmaximal, complemented
20#37620C212yesmaximal, complemented
21#36194C211yesmaximal, characteristic, complemented
22#36180C211yesmaximal, characteristic, complemented
23#36134C211yesmaximal, characteristic, complemented
24#34932C211yesmaximal, characteristic, complemented
25#34932C211yesmaximal, characteristic, complemented
26#34932C211yesmaximal, characteristic, complemented
27C2×#557C2212yes—
28C2×#554C2212yes—
29C2×#533C2212yes—
30C2×#529C2212yes—
31C2×#529C2212yes—
32C2×#529C2212yes—
33#2868C2211yescharacteristic
34#2857C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2845C2218yes—
38#2839C2218yes—
39#2837C2218yes—
40#2836C2218yes—
41#2827C2218yes—
42#2823C2218yes—
43#2814C2218yes—
44#2793C2218yes—
45#2791C2218yes—
46#2781C2218yes—
47#2772C2218yes—
48#2768C2218yes—
49#2755C2218yes—
50#2748C2218yes—
51#2747C2218yes—
52#2741C2218yes—
53#2732C2218yes—
54#2726C2214yes—
55#2725C2218yes—
56#2721C2218yes—
57#2711C2218yes—
58#2707C2218yes—
59#2704C2218yes—
60#2702C2218yes—
61#2694C2218yes—
62#2681C2218yes—
63#2649C2218yes—
64#2637C2218yes—
65#2629C2214yes—
66#2629C2214yes—
67#2629C2214yes—
68#2629C2214yes—
69#2629C2218yes—
70#2629C2214yes—
71#2629C2214yes—
72#2621C2214yes—
73#2620C2214yes—
74#2620C2214yes—
75#2618C2218yes—
76#2582C2212yes—
77#2571C2212yes—
78#2567C2212yes—
79#2565C2214yes—
80#2563C2212yes—
81#2562C2214yes—
82#2562C2214yes—
83#2553C2214yes—
84#2553C2214yes—
85#2553C2214yes—
86#2552C2211yescharacteristic
87#2552C2212yes—
88#2552C2214yes—
89#2552C2212yes—
90#2552C2214yes—
91#2552C2214yes—
92#2552C2212yes—
93#2552C2214yes—
94#2552C2212yes—
95#2552C2211yescharacteristic
96#2552C2211yescharacteristic
97#2547C2211yescharacteristic
98#2547C2211yescharacteristic
99#2547C2211yescharacteristic
100#2546C2212yes—
101#2545C2214yes—
102#2542C2212yes—
103#2542C2211yescharacteristic
104#2542C2211yescharacteristic
105#2542C2211yescharacteristic
106#2542C2214yes—
107#2538C2212yes—
108#2538C2212yes—
109#2538C2214yes—
110#2537C2214yes—
111#2537C2211yescharacteristic
112#2537C2211yescharacteristic
113#2537C2211yescharacteristic
114#2536C2214yes—
115#2511C2214yes—
116#2507C2214yes—
117#2506C2214yes—
118#2506C2214yes—
119#2502C2214yes—
120#2502C2214yes—
121#2497C2214yes—
122#2497C2214yes—
123#2497C2214yes—
124#2496C2212yes—
125#2496C2212yes—
126#2496C2212yes—
127#2492C2214yes—
128#2490C2214yes—
129#2489C2212yes—
130#2489C2212yes—
131#2489C2212yes—
132#2485C2214yes—
133#2485C2214yes—
134#2476C2218yes—
135#2473C2218yes—
136#2454C2214yes—
137#2453C2214yes—
138#2453C2214yes—
139#2448C2214yes—
140#2446C2214yes—
141#2442C2214yes—
142#2441C2214yes—
143#2441C2214yes—
144#2440C2214yes—
145#2440C2214yes—
146#2439C2214yes—
147#2429C2214yes—
148#2429C2214yes—
149#2427C2212yes—
150#2427C2212yes—
151#2427C2212yes—
152#2426C2214yes—
153#2423C2214yes—
154#2423C2218yes—
155#2423C2214yes—
156#2422C2212yes—
157#2422C2212yes—
158#2422C2212yes—
159#2417C2214yes—
160#2417C2214yes—
161#2416C2214yes—
162#2416C2214yes—
163#2395C2214yes—
164#2395C2214yes—
165#2395C2214yes—
166#2369C2212yes—
167#2365C2212yes—
168#2365C2212yes—
169#2363C2214yes—
170#2360C2214yes—
171#2355C2212yes—
172#2354C2212yes—
173#2354C2212yes—
174Q8×C4⋊C4C2212yes—
175Q8×C4⋊C4C2212yes—
176D4×C4⋊C4C2212yes—
177D4×C4⋊C4C2212yes—
178#2345C2214yes—
179#2324C2214yes—
180#2323C2214yes—
181#2323C2214yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190C4×#121C2212yes—
191#2285C2212yes—
192#2285C2212yes—
193#2285C2212yes—
194#2285C2212yes—
195C2×#384C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199#557—48no—
200#554—48no—
201#533—48no—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209#529—48no—
210#529—48no—
211#529—48no—
212C2×#126C2314yes—
213C2×#126C2314yes—
214C2×#126C2314yes—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#125C2312yes—
218C2×#125C2312yes—
219C2×#125C2312yes—
220C2×#125C2314yes—
221C2×#125C2318yes—
222C2×#125C2318yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#123C2314yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2314yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2312yes—
244C2×#121C2312yes—
245C2×#121C2312yes—
246C2×#121C2312yes—
247C2×#121C2318yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2311yescharacteristic
268C2×#117C2314yes—
269C2×#117C2314yes—
270C2×#117C2314yes—
271C2×#117C2314yes—
272C2×#117C2314yes—
273C22×C4⋊C4C2314yes—
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2314yes—
276C22×C42C2312yes—
277C22×C42C2312yes—
278C22×C42C2312yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2318yes—
287#399C2318yes—
288#399C2318yes—
289#399C2318yes—
290#399C2314yes—
291#399C2314yes—
292#399C2314yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2314yes—
306#398C2318yes—
307#398C2318yes—
308#398C2318yes—
309#398C2318yes—
310#398C2318yes—
311#398C2318yes—
312#398C2314yes—
313#398C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2318yes—
317#397C2314yes—
318#397C2318yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#396C2318yes—
326#396C2318yes—
327#396C2318yes—
328#396C2318yes—
329#396C2318yes—
330#396C2318yes—
331#396C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#396C2318yes—
336#396C2318yes—
337#395C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2314yes—
341#394C2318yes—
342#394C2314yes—
343#394C2318yes—
344#394C2314yes—
345#394C2318yes—
346#394C2314yes—
347#394C2314yes—
348#394C2314yes—
349#393C2318yes—
350#391C2312yes—
351#391C2312yes—
352#391C2312yes—
353#391C2312yes—
354#391C2314yes—
355#391C2314yes—
356#391C2312yes—
357#391C2314yes—
358#391C2314yes—
359#391C2314yes—
360#391C2318yes—
361#391C2312yes—
362#390C2314yes—
363#390C2312yes—
364#390C2318yes—
365#390C2314yes—
366#390C2312yes—
367#390C2318yes—
368#390C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2312yes—
380#389C2318yes—
381#389C2314yes—
382#389C2318yes—
383#389C2314yes—
384#389C2318yes—
385#389C2318yes—
386#389C2314yes—
387#389C2314yes—
388#389C2312yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2318yes—
393#389C2318yes—
394#389C2312yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2312yes—
399#389C2312yes—
400#389C2312yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#386C2318yes—
428#386C2318yes—
429#386C2314yes—
430#386C2314yes—
431#386C2314yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2314yes—
437#385C2314yes—
438#385C2314yes—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#384C2314yes—
443#384C2314yes—
444#384C2312yes—
445#384C2312yes—
446#384C2312yes—
447#384C2312yes—
448#384C2314yes—
449#384C2314yes—
450#384C2314yes—
451#384C2312yes—
452#384C2312yes—
453#384C2318yes—
454#384C2312yes—
455#384C2312yes—
456#384C2312yes—
457#384C2312yes—
458#382C2314yes—
459#382C2314yes—
460#382C2314yes—
461#382C2314yes—
462#382C2314yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2314yes—
473#380C2318yes—
474#380C2314yes—
475#380C2314yes—
476#380C2318yes—
477#380C2312yes—
478#380C2312yes—
479#380C2312yes—
480#380C2312yes—
481#380C2314yes—
482#380C2314yes—
483#380C2312yes—
484#380C2312yes—
485#380C2314yes—
486#380C2312yes—
487#380C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2312yes—
524C43C2311yescharacteristic
525C22×Q8C2412yes—
526C22×Q8C2412yes—
527C22×Q8C2412yes—
528C22×Q8C2414yes—
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2414yes—
533C22×D4C2414yes—
534C22×D4C2414yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2418yes—
545C4⋊Q8—24no—
546C4⋊Q8—28no—
547C4⋊Q8—24no—
548C4⋊Q8—24no—
549C4⋊Q8—44no—
550C4⋊Q8—48no—
551C4⋊Q8—82no—
552#126—48no—
553#126—48no—
554#126—48no—
555#125—44no—
556#125—44no—
557#125—44no—
558#125—48no—
559#125—48no—
560#125—48no—
561#125—416no—
562#125—88no—
563#124—44no—
564#124—44no—
565#124—44no—
566#123—48no—
567#123—48no—
568#123—48no—
569C22⋊Q8—28no—
570C22⋊Q8—28no—
571C22⋊Q8—416no—
572C22⋊Q8—48no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—44no—
577C22⋊Q8—48no—
578C22⋊Q8—48no—
579C22⋊Q8—48no—
580C22⋊Q8—84no—
581#121—28no—
582#121—28no—
583#121—44no—
584#121—44no—
585#121—44no—
586#121—44no—
587#121—88no—
588C4×Q8—28no—
589C4×Q8—28no—
590C4×Q8—28no—
591C4×Q8—48no—
592C4×Q8—48no—
593C4×Q8—48no—
594C4×Q8—48no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—24no—
602C4×D4—24no—
603C4×D4—42no—
604C4×D4—48no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4—48no—
608#117—48no—
609#117—48no—
610#117—48no—
611#117—48no—
612#117—84no—
613C2×C4⋊C4—48no—
614C2×C4⋊C4—48no—
615C2×C4⋊C4—84no—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2418yes—
708C2×C42—28no—
709C2×C42—28no—
710C2×C42—28no—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2418yes—
727C2×C42C2418yes—
728C2×C42C2418yes—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733#95C2414yes—
734#95C2412yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2414yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2418yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2418yes—
761#95C2418yes—
762#95C2414yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771C24C2512yes—
772C24C2512yes—
773C24C2512yes—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—28no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—44no—
785C2×Q8—44no—
786C2×D4—28no—
787C2×D4—28no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D42−1+414yes—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4C2511yescharacteristic
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2514yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2518yes—
849C22×C4C2512yes—
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2511yescharacteristic
853C22×C4C2512yes—
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C4⋊C4—24no—
858C4⋊C4—28no—
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—22no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—42no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—42no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—48no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—42no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C42−1+414yes—
917C22⋊C4—24no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—24no—
926C22⋊C4—24no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—42no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—48no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—24no—
953C42—24no—
954C42—24no—
955C42—28no—
956C42—28no—
957C42—28no—
958C42—24no—
959C42—24no—
960C42—24no—
961C42—22no—
962C42—22no—
963C42—22no—
964C42—48no—
965C42—48no—
966C42—48no—
967C42—41no—
968C42H(5,𝔽2)14yes—
969C42H(5,𝔽2)14yes—
970C422−1+414yes—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23C2×2−1+414yes—
992C23C2611yescharacteristic
993Q8—48no—
994Q8—48no—
995Q8—48no—
996Q8—88no—
997D4—28no—
998D4—44no—
999D4—44no—
1000D4—88no—
1001D4—88no—
1002D4—88no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—28no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—28no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—28no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—48no—
1062C2×C4—48no—
1063C2×C4—48no—
1064C2×C4—48no—
1065C2×C4—48no—
1066C2×C4—48no—
1067C2×C4—84no—
1068C2×C4—168no—
1069C2×C4C2×H(5,𝔽2)12yes—
1070C2×C4C2×H(5,𝔽2)12yes—
1071C2×C4C2×H(5,𝔽2)12yes—
1072C2×C4C2×H(5,𝔽2)12yes—
1073C2×C4C2×H(5,𝔽2)12yes—
1074C2×C4C2×H(5,𝔽2)12yes—
1075C2×C4C2×2−1+412yes—
1076C2×C4C2×2−1+414yes—
1077C2×C4C2×2−1+412yes—
1078C2×C4C2×2−1+412yes—
1079C2×C4C2×2−1+412yes—
1080C2×C4C2×2−1+412yes—
1081C2×C4#58512yes—
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22C22×H(5,𝔽2)11yescharacteristic
1104C22C22×H(5,𝔽2)11yescharacteristic
1105C22C22×2−1+411yescharacteristic
1106C22C22×2−1+411yescharacteristic
1107C22C22×2−1+411yescharacteristic
1108C22C2×#58511yescharacteristic
1109C22H(7,𝔽2)11yescharacteristic
1110C4—22no—
1111C4—22no—
1112C4—24no—
1113C4—22no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—44no—
1119C4—42no—
1120C4—42no—
1121C4—44no—
1122C4—44no—
1123C4—41no—
1124C4—42no—
1125C4—44no—
1126C4—44no—
1127C4—42no—
1128C4—44no—
1129C4—48no—
1130C4#354714yes—
1131C4#354814yes—
1132C4#355214yes—
1133C2—44no—
1134C2—82no—
1135C2—82no—
1136C2C2×#355211yescharacteristic
1137C2C2×#354711yescharacteristic
1138C2C2×#354811yescharacteristic
1139C2#6294411yescharacteristic
1140C2#6294511yescharacteristic
1141C2#6295511yescharacteristic
1142C2#6303211yescharacteristic
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. #59828C2semidirect
2. #59321C2semidirect
3. #59217C2semidirect
4. #59052C2semidirect
5. #55178C2semidirect
6. #53067C2semidirect
7. #53024C2semidirect
8. #52959C2semidirect
9. #42641C2semidirect
10. #42577C2semidirect
11. #42534C2semidirect
12. #39737C2semidirect
13. #39607C2semidirect
14. #39606C2semidirect
15. #39139C2semidirect
16. #39127C2semidirect
17. #39126C2semidirect
18. #37643C2semidirect
19. #37633C2semidirect
20. #37620C2semidirect
21. #36194C2semidirect
22. #36180C2semidirect
23. #36134C2semidirect
24. #34932C2semidirect
25. #34932C2semidirect
26. #34932C2semidirect

Maximal subgroups

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

subgroupindex
#598282
#593212
#592172
#590522
#551782
#530672
#530242
#529592
#426412
#425772
#425342
#397372
#396072
#396062
#391392
#391272
#391262
#376432
#376332
#376202
#361942
#361802
#361342
#349322