Finite Group Databasebeta

← #7655296

Subgroups — #7655296

Order 512.

4724 conjugacy classes of subgroups.

The subgroup lattice has 1139 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42935C214yesmaximal, complemented
2#42226C218yesmaximal, complemented
3#39737C212yesmaximal, complemented
4#39607C212yesmaximal, complemented
5#39547C214yesmaximal, complemented
6#39479C212yesmaximal, complemented
7#39417C214yesmaximal, complemented
8#39353C212yesmaximal, complemented
9#38205C214yesmaximal, complemented
10#38203C214yesmaximal, complemented
11#37643C211yesmaximal, characteristic, complemented
12#37627C212yesmaximal, complemented
13#36481C212yesmaximal, complemented
14#36459C212yesmaximal, complemented
15#36315C212yesmaximal, complemented
16#36287C212yesmaximal, complemented
17#36026C214yesmaximal, complemented
18#35316C211yesmaximal, characteristic, complemented
19#35279C211yesmaximal, characteristic, complemented
20#35209C212yesmaximal, complemented
21#35184C212yesmaximal, complemented
22#34976C211yesmaximal, characteristic
23#34951C212yesmaximal, complemented
24#34216C211yesmaximal, characteristic, complemented
25#34129C211yesmaximal, characteristic, complemented
26#34129C211yesmaximal, characteristic, complemented
27C2×#541C2214yes—
28C2×#536C2212yes—
29C22×C4⋊Q8C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32#2863C2214yes—
33#2861C2214yes—
34#2860C2214yes—
35#2859C2214yes—
36#2857C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2845C2214yes—
41#2837C2218yes—
42#2772C2218yes—
43#2755C2218yes—
44#2754C2218yes—
45#2741C2218yes—
46#2740C2218yes—
47#2739C2218yes—
48#2722C2218yes—
49#2719C2218yes—
50#2707C2218yes—
51#2705C2218yes—
52#2704C2218yes—
53#2702C2218yes—
54#2664C2218yes—
55#2654C2218yes—
56#2651C2218yes—
57#2629C2214yes—
58#2629C2214yes—
59#2629C2214yes—
60#2629C2214yes—
61#2628C2214yes—
62#2625C2214yes—
63#2624C2214yes—
64#2621C2214yes—
65#2620C2214yes—
66#2612C2218yes—
67#2609C2214yes—
68#2606C2218yes—
69#2585C2218yes—
70#2582C2211yescharacteristic
71#2568C2212yes—
72#2567C2212yes—
73#2563C2212yes—
74#2562C2214yes—
75#2560C2218yes—
76#2558C2218yes—
77#2556C2218yes—
78#2554C2218yes—
79#2552C2212yes—
80#2552C2212yes—
81#2552C2212yes—
82#2552C2212yes—
83#2552C2212yes—
84#2552C2212yes—
85#2552C2214yes—
86#2547C2212yes—
87#2547C2212yes—
88#2546C2212yes—
89#2546C2212yes—
90#2542C2212yes—
91#2538C2211yescharacteristic
92#2538C2211yescharacteristic
93#2537C2211yescharacteristic
94#2532C2218yes—
95#2531C2218yes—
96#2529C2218yes—
97#2526C2218yes—
98#2525C2218yes—
99#2522C2218yes—
100#2519C2218yes—
101#2515C2218yes—
102#2512C2214yes—
103#2511C2214yes—
104#2509C2214yes—
105#2507C2214yes—
106#2506C2214yes—
107#2506C2214yes—
108#2497C2214yes—
109#2497C2214yes—
110#2497C2214yes—
111#2496C2214yes—
112#2496C2214yes—
113#2495C2214yes—
114#2490C2214yes—
115#2489C2214yes—
116#2487C2214yes—
117#2486C2214yes—
118#2486C2214yes—
119#2485C2214yes—
120#2485C2214yes—
121#2485C2212yes—
122#2485C2212yes—
123#2453C2214yes—
124#2453C2214yes—
125#2448C2214yes—
126#2446C2214yes—
127#2441C2214yes—
128#2441C2214yes—
129#2429C2214yes—
130#2426C2214yes—
131#2423C2214yes—
132#2423C2214yes—
133#2409C2214yes—
134#2407C2212yes—
135#2407C2212yes—
136#2402C2218yes—
137#2392C2214yes—
138#2370C2214yes—
139#2369C2212yes—
140#2369C2212yes—
141#2365C2212yes—
142#2365C2212yes—
143#2354C2211yescharacteristic
144#2354C2211yescharacteristic
145#2354C2211yescharacteristic
146#2354C2212yes—
147#2354C2212yes—
148#2354C2212yes—
149#2354C2212yes—
150#2354C2211yescharacteristic
151#2354C2214yes—
152Q8×C4⋊C4C2211yescharacteristic
153Q8×C4⋊C4C2211yescharacteristic
154Q8×C4⋊C4C2211yescharacteristic
155Q8×C4⋊C4C2211yescharacteristic
156#2347C2214yes—
157#2346C2212yes—
158#2346C2212yes—
159#2346C2214yes—
160#2346C2214yes—
161#2346C2214yes—
162#2345C2214yes—
163#2341C2212yes—
164#2341C2212yes—
165Q8×C22⋊C4C2214yes—
166#2331C2214yes—
167#2323C2214yes—
168#2323C2214yes—
169#2317C2212yes—
170#2316C2212yes—
171#2314C2214yes—
172#2311C2212yes—
173#2310C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2214yes—
176C4×C4⋊Q8C2212yes—
177C4×#125C2214yes—
178C4×C22⋊Q8C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×#121C2212yes—
181C4×#121C2212yes—
182#2295C2214yes—
183#2295C2214yes—
184#2293C2214yes—
185#2293C2214yes—
186#2293C2212yes—
187#2293C2212yes—
188#2285C2211yescharacteristic
189#2285C2211yescharacteristic
190#2285C2211yescharacteristic
191#2285C2212yes—
192#2285C2212yes—
193#2274C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2212yes—
196C4×#117C2211yescharacteristic
197C4×#117C2212yes—
198C4×#117C2212yes—
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C23×Q8C2312yes—
202#541—416no—
203#536—48no—
204C2×C4⋊Q8—28no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×#126C2318yes—
211C2×#126C2318yes—
212C2×#125C2314yes—
213C2×#125C2314yes—
214C2×#125C2318yes—
215C2×#125C2314yes—
216C2×#125C2318yes—
217C2×#124C2314yes—
218C2×#123C2318yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×#121C2312yes—
226C2×#121C2312yes—
227C4×#41—28no—
228C4×#41—28no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2312yes—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2314yes—
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2312yes—
254C2×#117C2311yescharacteristic
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2314yes—
258C2×#117C2311yescharacteristic
259C2×#117C2312yes—
260C2×#117C2314yes—
261C2×#117C2312yes—
262C2×#117C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C42C2312yes—
266C22×C42C2312yes—
267C22×C42C2311yescharacteristic
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#399C2318yes—
276#399C2318yes—
277#399C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2314yes—
298#397C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2314yes—
302#396C2314yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#395C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2314yes—
311#394C2318yes—
312#394C2314yes—
313#394C2314yes—
314#393C2318yes—
315#392C2314yes—
316#391C2318yes—
317#391C2312yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2312yes—
328#391C2318yes—
329#390C2318yes—
330#390C2314yes—
331#390C2312yes—
332#390C2312yes—
333#390C2312yes—
334#390C2312yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2312yes—
340#390C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2318yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2318yes—
356#389C2314yes—
357#389C2314yes—
358#389C2318yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2312yes—
364#389C2314yes—
365#389C2312yes—
366#389C2314yes—
367#389C2312yes—
368#389C2312yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2318yes—
375#389C2312yes—
376#389C2314yes—
377#389C2314yes—
378#388C2314yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2314yes—
388#388C2314yes—
389#388C2318yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#388C2314yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2314yes—
403#388C2314yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2314yes—
417#387C2318yes—
418#387C2318yes—
419#387C2314yes—
420#386C2314yes—
421#386C2318yes—
422#386C2314yes—
423#385C2318yes—
424#385C2314yes—
425#385C2314yes—
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2314yes—
429#384C2314yes—
430#384C2314yes—
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2312yes—
439#384C2314yes—
440#383C2318yes—
441#382C2314yes—
442#382C2312yes—
443#382C2312yes—
444#382C2312yes—
445#382C2314yes—
446#382C2314yes—
447#382C2318yes—
448#381C2318yes—
449#380C2312yes—
450#380C2312yes—
451#380C2314yes—
452#380C2314yes—
453#380C2314yes—
454#380C2314yes—
455#380C2314yes—
456#380C2312yes—
457#380C2314yes—
458#380C2318yes—
459#380C2312yes—
460#380C2314yes—
461#380C2312yes—
462#380C2312yes—
463#380C2312yes—
464#380C2314yes—
465#380C2314yes—
466#380C2312yes—
467#380C2314yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517#376C2312yes—
518#376C2314yes—
519#376C2314yes—
520#376C2318yes—
521C43C2314yes—
522C43C2312yes—
523C43C2314yes—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41—42no—
529C2×#41—42no—
530C22×Q8—28no—
531C22×Q8—44no—
532C22×Q8—44no—
533C22×Q8C2414yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2411yescharacteristic
536C22×Q8C2414yes—
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2414yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2414yes—
552C4⋊Q8—216no—
553C4⋊Q8—28no—
554C4⋊Q8—28no—
555C4⋊Q8—28no—
556C4⋊Q8—28no—
557#126—416no—
558#126—416no—
559#125—48no—
560#125—48no—
561#125—48no—
562#125—416no—
563#125—416no—
564#124—48no—
565#123—416no—
566C22⋊Q8—28no—
567C22⋊Q8—28no—
568C22⋊Q8—48no—
569C22⋊Q8—48no—
570C22⋊Q8—48no—
571C22⋊Q8—48no—
572#121—44no—
573#121—44no—
574C4×Q8—28no—
575C4×Q8—28no—
576C4×Q8—24no—
577C4×Q8—24no—
578C4×Q8—24no—
579C4×Q8—24no—
580C4×Q8—44no—
581C4×Q8—48no—
582C4×Q8—44no—
583C4×Q8—48no—
584C4×D4—28no—
585C4×D4—28no—
586C4×D4—28no—
587C4×D4—28no—
588C4×D4—24no—
589C4×D4—24no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—48no—
593#117—24no—
594#117—24no—
595#117—24no—
596#117—28no—
597#117—28no—
598#117—28no—
599#117—28no—
600#117—48no—
601#117—44no—
602#117—44no—
603#117—44no—
604#117—48no—
605#117—42no—
606#117—44no—
607#117—44no—
608C2×C4⋊C4—28no—
609C2×C4⋊C4—28no—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2411yescharacteristic
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C42—28no—
697C2×C42—28no—
698C2×C42#4118yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2414yes—
707C2×C42C2412yes—
708C2×C42C2414yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2414yes—
715C2×C42C2412yes—
716C2×C42C2414yes—
717C2×C42C2412yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2418yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2418yes—
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728#95C2412yes—
729#95C2412yes—
730#95C2414yes—
731#95C2412yes—
732#95C2412yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2414yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766C24C2512yes—
767C24C2512yes—
768C24C2511yescharacteristic
769#41—416no—
770#41—416no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—28no—
774C2×Q8—28no—
775C2×Q8—28no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—28no—
779C2×Q8—44no—
780C2×Q8—44no—
781C2×Q8—816no—
782C2×Q8H(5,𝔽2)14yes—
783C2×Q82−1+414yes—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—24no—
789C2×D4—22no—
790C2×D4—24no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—28no—
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—42no—
823C22×C4—42no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4C2×#4114yes—
827C22×C4C2×#4114yes—
828C22×C4C2×#4114yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2514yes—
833C22×C4C2518yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2514yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2511yescharacteristic
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—24no—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—216no—
869C4⋊C4—216no—
870C4⋊C4—22no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—28no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C42−1+414yes—
909C22⋊C4—24no—
910C22⋊C4—24no—
911C22⋊C4—24no—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—28no—
916C22⋊C4—24no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—42no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C42—24no—
939C42—24no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—28no—
946C42—28no—
947C42—24no—
948C42—28no—
949C42—28no—
950C42—28no—
951C42—24no—
952C42—24no—
953C42—28no—
954C42—28no—
955C42—24no—
956C42—42no—
957C42—44no—
958C42—44no—
959C42—44no—
960C42—48no—
961C42—44no—
962C42—48no—
963C42C2×#4114yes—
964C42C2×#4114yes—
965C42C2×#4114yes—
966C42C2×#4114yes—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
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—
987C23C22×#4112yes—
988C23C2611yescharacteristic
989Q8—28no—
990Q8—28no—
991Q8—416no—
992Q8—88no—
993D4—48no—
994D4—48no—
995D4—44no—
996D4—44no—
997D4—88no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—28no—
1011C2×C4—28no—
1012C2×C4—28no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—28no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—28no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—28no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—48no—
1056C2×C4—48no—
1057C2×C4—48no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—88no—
1062C2×C4C22×#4112yes—
1063C2×C4C22×#4112yes—
1064C2×C4C22×#4112yes—
1065C2×C4C22×#4112yes—
1066C2×C4C22×#4112yes—
1067C2×C4C22×#4112yes—
1068C2×C4C2×H(5,𝔽2)14yes—
1069C2×C4C2×H(5,𝔽2)12yes—
1070C2×C4C2×2−1+414yes—
1071C2×C4C2×2−1+414yes—
1072C2×C4C2×2−1+412yes—
1073C2×C4C2×2−1+412yes—
1074C2×C4#58512yes—
1075C2×C4#58512yes—
1076C2×C4#58512yes—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—41no—
1081C22—41no—
1082C22—41no—
1083C22—41no—
1084C22—42no—
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—
1098C22C23×#4111yescharacteristic
1099C22C22×H(5,𝔽2)11yescharacteristic
1100C22C22×2−1+411yescharacteristic
1101C22C22×2−1+411yescharacteristic
1102C22C2×#58511yescharacteristic
1103C22C2×#58511yescharacteristic
1104C22C2×#58511yescharacteristic
1105C4—24no—
1106C4—22no—
1107C4—24no—
1108C4—22no—
1109C4—24no—
1110C4—22no—
1111C4—42no—
1112C4—44no—
1113C4—44no—
1114C4—42no—
1115C4—42no—
1116C4—44no—
1117C4—44no—
1118C4—44no—
1119C4—44no—
1120C4—42no—
1121C4—48no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4#346114yes—
1126C4#349414yes—
1127C4#349514yes—
1128C2—42no—
1129C2—82no—
1130C2—82no—
1131C2C2×#346111yescharacteristic
1132C2C2×#349411yescharacteristic
1133C2C2×#349511yescharacteristic
1134C2#6303111yescharacteristic
1135C2#6303211yescharacteristic
1136C2#6303911yescharacteristic
1137C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34976C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42935C2semidirect
2. #42226C2semidirect
3. #39737C2semidirect
4. #39607C2semidirect
5. #39547C2semidirect
6. #39479C2semidirect
7. #39417C2semidirect
8. #39353C2semidirect
9. #38205C2semidirect
10. #38203C2semidirect
11. #37643C2semidirect
12. #37627C2semidirect
13. #36481C2semidirect
14. #36459C2semidirect
15. #36315C2semidirect
16. #36287C2semidirect
17. #36026C2semidirect
18. #35316C2semidirect
19. #35279C2semidirect
20. #35209C2semidirect
21. #35184C2semidirect
23. #34951C2semidirect
24. #34216C2semidirect
25. #34129C2semidirect
26. #34129C2semidirect

Maximal subgroups

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

subgroupindex
#429352
#422262
#397372
#396072
#395472
#394792
#394172
#393532
#382052
#382032
#376432
#376272
#364812
#364592
#363152
#362872
#360262
#353162
#352792
#352092
#351842
#349762
#349512
#342162
#341292