Finite Group Databasebeta

← #8429499

Subgroups — #8429499

Order 512.

4677 conjugacy classes of subgroups.

The subgroup lattice has 1137 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59212C212yesmaximal, complemented
3#59134C212yesmaximal, complemented
4#59036C212yesmaximal, complemented
5#55188C218yesmaximal, complemented
6#53120C214yesmaximal, complemented
7#53058C214yesmaximal, complemented
8#53022C214yesmaximal, complemented
9#42866C214yesmaximal, complemented
10#42630C214yesmaximal, complemented
11#42513C214yesmaximal, complemented
12#39734C212yesmaximal, complemented
13#39606C212yesmaximal, complemented
14#39136C212yesmaximal, complemented
15#39124C212yesmaximal, complemented
16#38940C212yesmaximal, complemented
17#38933C212yesmaximal, complemented
18#37633C212yesmaximal, complemented
19#37624C212yesmaximal, complemented
20#37615C212yesmaximal, complemented
21#36188C211yesmaximal, characteristic, complemented
22#36134C211yesmaximal, characteristic, complemented
23D4×C4⋊Q8C211yesmaximal, characteristic, complemented
24#34943C211yesmaximal, characteristic, complemented
25#34932C211yesmaximal, characteristic, complemented
26#34932C211yesmaximal, characteristic, complemented
27C2×#556C2212yes—
28C2×D4×Q8C2212yes—
29C2×#533C2212yes—
30C22×C4⋊Q8C2212yes—
31C2×#529C2212yes—
32C2×#529C2212yes—
33#2868C2211yescharacteristic
34#2857C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2841C2218yes—
38#2838C2218yes—
39#2831C2218yes—
40#2830C2218yes—
41#2826C2218yes—
42#2821C2218yes—
43#2814C2218yes—
44#2805C2214yes—
45#2786C2218yes—
46#2778C2218yes—
47#2775C2218yes—
48#2774C2218yes—
49#2768C2218yes—
50#2766C2218yes—
51#2766C2218yes—
52#2757C2218yes—
53#2748C2218yes—
54#2747C2218yes—
55#2738C2218yes—
56#2737C2218yes—
57#2727C2218yes—
58#2723C2218yes—
59#2716C2218yes—
60#2705C2218yes—
61#2696C2218yes—
62#2692C2218yes—
63#2666C2218yes—
64#2660C2214yes—
65#2652C2218yes—
66#2647C2214yes—
67#2640C2214yes—
68#2637C2218yes—
69#2629C2214yes—
70#2629C2214yes—
71#2628C2214yes—
72#2623C2218yes—
73#2621C2214yes—
74#2621C2214yes—
75#2620C2214yes—
76#2595C2218yes—
77#2581C2214yes—
78#2572C2214yes—
79#2571C2211yescharacteristic
80#2571C2212yes—
81#2570C2214yes—
82#2568C2212yes—
83#2568C2212yes—
84#2567C2212yes—
85#2565C2214yes—
86#2563C2211yescharacteristic
87#2563C2214yes—
88#2563C2211yescharacteristic
89#2553C2214yes—
90#2553C2214yes—
91#2552C2211yescharacteristic
92#2552C2212yes—
93#2552C2211yescharacteristic
94#2551C2212yes—
95#2551C2212yes—
96#2550C2214yes—
97#2547C2212yes—
98#2547C2211yescharacteristic
99#2547C2212yes—
100#2547C2211yescharacteristic
101#2546C2212yes—
102#2545C2214yes—
103#2542C2212yes—
104#2542C2211yescharacteristic
105#2542C2211yescharacteristic
106#2540C2214yes—
107#2538C2214yes—
108#2538C2212yes—
109#2538C2214yes—
110#2537C2211yescharacteristic
111#2537C2211yescharacteristic
112#2537C2211yescharacteristic
113#2535C2214yes—
114#2514C2214yes—
115#2511C2214yes—
116#2509C2214yes—
117#2507C2214yes—
118#2504C2214yes—
119#2502C2214yes—
120#2499C2214yes—
121#2496C2212yes—
122#2496C2212yes—
123#2496C2214yes—
124#2496C2214yes—
125#2495C2214yes—
126#2495C2212yes—
127#2495C2212yes—
128#2494C2214yes—
129#2494C2214yes—
130#2492C2214yes—
131#2489C2212yes—
132#2489C2214yes—
133#2489C2212yes—
134#2485C2214yes—
135#2485C2214yes—
136#2481C2218yes—
137#2465C2218yes—
138#2454C2214yes—
139#2446C2214yes—
140#2441C2214yes—
141#2441C2214yes—
142#2440C2214yes—
143#2440C2214yes—
144#2439C2214yes—
145#2439C2214yes—
146#2436C2214yes—
147#2434C2214yes—
148#2429C2214yes—
149#2427C2212yes—
150#2427C2212yes—
151#2426C2214yes—
152#2423C2214yes—
153#2423C2214yes—
154#2423C2214yes—
155#2422C2212yes—
156#2422C2212yes—
157#2420C2212yes—
158#2420C2212yes—
159#2417C2214yes—
160#2414C2214yes—
161#2409C2214yes—
162#2409C2214yes—
163#2398C2214yes—
164#2395C2214yes—
165#2395C2214yes—
166#2365C2212yes—
167#2365C2212yes—
168#2365C2212yes—
169#2365C2212yes—
170#2363C2214yes—
171#2355C2212yes—
172#2354C2212yes—
173#2352C2214yes—
174Q8×C4⋊C4C2212yes—
175Q8×C4⋊C4C2212yes—
176D4×C4⋊C4C2212yes—
177D4×C4⋊C4C2212yes—
178Q8×C22⋊C4C2214yes—
179#2324C2214yes—
180#2323C2214yes—
181#2320C2214yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×#121C2212yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190C4×#121C2212yes—
191#2285C2212yes—
192#2285C2212yes—
193#2285C2212yes—
194#2283C2212yes—
195#2283C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C23×Q8C2314yes—
200#556—48no—
201D4×Q8—48no—
202#533—48no—
203C2×C4⋊Q8—48no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214#529—48no—
215#529—48no—
216C2×#126C2314yes—
217C2×#126C2314yes—
218C2×#126C2318yes—
219C2×#125C2312yes—
220C2×#125C2314yes—
221C2×#125C2312yes—
222C2×#124C2314yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#123C2314yes—
226C2×#123C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2318yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×#117C2314yes—
264C2×#117C2314yes—
265C2×#117C2314yes—
266C2×#117C2314yes—
267C22×C4⋊C4C2314yes—
268C22×C4⋊C4C2314yes—
269C22×C42C2312yes—
270C22×C42C2312yes—
271C22×C42C2312yes—
272#401C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2314yes—
278#400C2318yes—
279#400C2314yes—
280#400C2318yes—
281#400C2314yes—
282#400C2314yes—
283#400C2318yes—
284#399C2314yes—
285#399C2318yes—
286#399C2318yes—
287#399C2318yes—
288#399C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2314yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2314yes—
306#397C2314yes—
307#397C2314yes—
308#397C2314yes—
309#397C2318yes—
310#397C2318yes—
311#397C2318yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#396C2318yes—
317#396C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#396C2318yes—
322#396C2318yes—
323#395C2318yes—
324#395C2318yes—
325#395C2318yes—
326#395C2318yes—
327#395C2318yes—
328#394C2314yes—
329#394C2314yes—
330#394C2314yes—
331#394C2318yes—
332#394C2314yes—
333#394C2318yes—
334#394C2314yes—
335#394C2314yes—
336#393C2318yes—
337#393C2314yes—
338#393C2314yes—
339#393C2318yes—
340#393C2318yes—
341#393C2318yes—
342#392C2318yes—
343#391C2312yes—
344#391C2312yes—
345#391C2312yes—
346#391C2314yes—
347#391C2314yes—
348#391C2314yes—
349#391C2314yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2318yes—
354#391C2312yes—
355#391C2312yes—
356#391C2318yes—
357#391C2314yes—
358#390C2318yes—
359#390C2312yes—
360#390C2312yes—
361#390C2312yes—
362#390C2318yes—
363#390C2318yes—
364#390C2314yes—
365#390C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2312yes—
377#389C2314yes—
378#389C2312yes—
379#389C2312yes—
380#389C2314yes—
381#389C2318yes—
382#389C2318yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2318yes—
389#389C2314yes—
390#389C2312yes—
391#389C2312yes—
392#389C2318yes—
393#389C2312yes—
394#388C2314yes—
395#388C2314yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2314yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2314yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2314yes—
419#387C2314yes—
420#386C2318yes—
421#386C2318yes—
422#386C2314yes—
423#386C2314yes—
424#386C2318yes—
425#386C2318yes—
426#386C2314yes—
427#386C2314yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2314yes—
433#385C2314yes—
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2314yes—
438#384C2312yes—
439#384C2312yes—
440#384C2312yes—
441#384C2312yes—
442#384C2314yes—
443#384C2312yes—
444#384C2312yes—
445#384C2312yes—
446#384C2312yes—
447#383C2314yes—
448#383C2314yes—
449#383C2318yes—
450#382C2312yes—
451#382C2318yes—
452#382C2312yes—
453#382C2314yes—
454#382C2314yes—
455#382C2312yes—
456#382C2314yes—
457#382C2312yes—
458#382C2314yes—
459#382C2314yes—
460#381C2314yes—
461#381C2314yes—
462#380C2312yes—
463#380C2312yes—
464#380C2314yes—
465#380C2312yes—
466#380C2314yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#380C2314yes—
472#380C2314yes—
473#380C2318yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2312yes—
479#380C2312yes—
480#380C2314yes—
481#380C2312yes—
482#380C2312yes—
483#380C2312yes—
484#380C2314yes—
485#380C2312yes—
486#380C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2311yescharacteristic
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2312yes—
523#376C2314yes—
524C43C2311yescharacteristic
525C22×Q8—48no—
526C22×Q8—48no—
527C22×Q8—48no—
528C22×Q8C2412yes—
529C22×Q8C2414yes—
530C22×Q8C2412yes—
531C22×Q8C2412yes—
532C22×Q8C2418yes—
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2414yes—
537C22×D4C2414yes—
538C22×D4C2414yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2418yes—
549C4⋊Q8—24no—
550C4⋊Q8—28no—
551C4⋊Q8—24no—
552C4⋊Q8—28no—
553C4⋊Q8—24no—
554C4⋊Q8—48no—
555C4⋊Q8—48no—
556C4⋊Q8—48no—
557C4⋊Q8—48no—
558C4⋊Q8—44no—
559#126—48no—
560#126—48no—
561#126—416no—
562#125—44no—
563#125—44no—
564#125—48no—
565#124—44no—
566#124—44no—
567#124—48no—
568#123—48no—
569#123—48no—
570C22⋊Q8—416no—
571C22⋊Q8—44no—
572C22⋊Q8—44no—
573C22⋊Q8—48no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—48no—
577C22⋊Q8—48no—
578C22⋊Q8—48no—
579C22⋊Q8—48no—
580#121—28no—
581#121—28no—
582#121—44no—
583#121—44no—
584#121—44no—
585#121—44no—
586C4×Q8—28no—
587C4×Q8—28no—
588C4×Q8—44no—
589C4×Q8—48no—
590C4×Q8—48no—
591C4×Q8—48no—
592C4×Q8—48no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—42no—
601C4×D4—42no—
602C4×D4—48no—
603C4×D4—48no—
604C4×D4—48no—
605C4×D4—48no—
606#117—48no—
607#117—48no—
608#117—48no—
609#117—48no—
610C2×C4⋊C4—48no—
611C2×C4⋊C4—48no—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C42—28no—
698C2×C42—28no—
699C2×C42—28no—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2411yescharacteristic
705C2×C42C2414yes—
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2418yes—
716C2×C42C2418yes—
717C2×C42C2418yes—
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2412yes—
728#95C2412yes—
729#95C2412yes—
730#95C2412yes—
731#95C2412yes—
732#95C2412yes—
733#95C2412yes—
734#95C2412yes—
735#95C2412yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2414yes—
757#95C2418yes—
758#95C2414yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766C24C2512yes—
767C24C2512yes—
768C24C2512yes—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—24no—
772C2×Q8—28no—
773C2×Q8—28no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—28no—
778C2×Q8—24no—
779C2×Q8—42no—
780C2×Q8—42no—
781C2×Q8—48no—
782C2×Q8—48no—
783C2×Q8—48no—
784C2×Q8—832no—
785C2×D4—28no—
786C2×D4—28no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D42−1+414yes—
803C22×C4—24no—
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—42no—
826C22×C4—48no—
827C22×C4—48no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—48no—
833C22×C4C2512yes—
834C22×C4C2512yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2511yescharacteristic
838C22×C4C2514yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2512yes—
848C22×C4C2518yes—
849C22×C4C2512yes—
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2511yescharacteristic
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—24no—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—28no—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—42no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C22⋊C4—24no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—24no—
916C22⋊C4—24no—
917C22⋊C4—24no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—28no—
948C42—28no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—22no—
953C42—22no—
954C42—28no—
955C42—22no—
956C42—41no—
957C42—48no—
958C42—48no—
959C42—48no—
960C42H(5,𝔽2)14yes—
961C42H(5,𝔽2)14yes—
962C422−1+414yes—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23C2×2−1+414yes—
984C23C2611yescharacteristic
985Q8—48no—
986Q8—416no—
987Q8—48no—
988Q8—48no—
989Q8—816no—
990D4—28no—
991D4—44no—
992D4—44no—
993D4—88no—
994D4—88no—
995D4—88no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—28no—
1015C2×C4—28no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—28no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—48no—
1054C2×C4—48no—
1055C2×C4—48no—
1056C2×C4—48no—
1057C2×C4—48no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—84no—
1061C2×C4—84no—
1062C2×C4—816no—
1063C2×C4C2×H(5,𝔽2)12yes—
1064C2×C4C2×H(5,𝔽2)12yes—
1065C2×C4C2×H(5,𝔽2)12yes—
1066C2×C4C2×H(5,𝔽2)12yes—
1067C2×C4C2×H(5,𝔽2)12yes—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4C2×2−1+412yes—
1070C2×C4C2×2−1+412yes—
1071C2×C4C2×2−1+412yes—
1072C2×C4C2×2−1+412yes—
1073C2×C4#58512yes—
1074C2×C4#58512yes—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22C22×H(5,𝔽2)11yescharacteristic
1097C22C22×H(5,𝔽2)11yescharacteristic
1098C22C22×2−1+411yescharacteristic
1099C22C22×2−1+411yescharacteristic
1100C22C2×#58511yescharacteristic
1101C22C2×#58511yescharacteristic
1102C222−1+611yescharacteristic
1103C4—22no—
1104C4—22no—
1105C4—22no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—44no—
1111C4—48no—
1112C4—42no—
1113C4—42no—
1114C4—44no—
1115C4—41no—
1116C4—44no—
1117C4—42no—
1118C4—44no—
1119C4—44no—
1120C4—42no—
1121C4—44no—
1122C4—42no—
1123C4#354614yes—
1124C4#354714yes—
1125C4#355214yes—
1126C2—44no—
1127C2—82no—
1128C2—82no—
1129C2C2×#355211yescharacteristic
1130C2C2×#354611yescharacteristic
1131C2C2×#354711yescharacteristic
1132C2#6292511yescharacteristic
1133C2#6294211yescharacteristic
1134C2#6295911yescharacteristic
1135C2#6302511yescharacteristic
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. #59870C2semidirect
2. #59212C2semidirect
3. #59134C2semidirect
4. #59036C2semidirect
5. #55188C2semidirect
6. #53120C2semidirect
7. #53058C2semidirect
8. #53022C2semidirect
9. #42866C2semidirect
10. #42630C2semidirect
11. #42513C2semidirect
12. #39734C2semidirect
13. #39606C2semidirect
14. #39136C2semidirect
15. #39124C2semidirect
16. #38940C2semidirect
17. #38933C2semidirect
18. #37633C2semidirect
19. #37624C2semidirect
20. #37615C2semidirect
21. #36188C2semidirect
22. #36134C2semidirect
23. D4×C4⋊Q8C2semidirect
24. #34943C2semidirect
25. #34932C2semidirect
26. #34932C2semidirect

Maximal subgroups

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

subgroupindex
#598702
#592122
#591342
#590362
#551882
#531202
#530582
#530222
#428662
#426302
#425132
#397342
#396062
#391362
#391242
#389402
#389332
#376332
#376242
#376152
#361882
#361342
D4×C4⋊Q82
#349432
#349322