Finite Group Databasebeta

← #7656268

Subgroups — #7656268

Order 512.

5497 conjugacy classes of subgroups.

The subgroup lattice has 1414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42862C213yesmaximal, complemented
2#42860C213yesmaximal, complemented
3#42838C213yesmaximal, complemented
4#42834C213yesmaximal, complemented
5#42520C213yesmaximal, complemented
6#42504C213yesmaximal, complemented
7#42448C213yesmaximal, complemented
8#42446C213yesmaximal, complemented
9#40221C213yesmaximal, complemented
10#40194C213yesmaximal, complemented
11#39790C213yesmaximal, complemented
12#39654C213yesmaximal, complemented
13#37512C213yesmaximal, complemented
14#37500C213yesmaximal, complemented
15#36583C211yesmaximal, characteristic, complemented
16Q8×#126C211yesmaximal, characteristic, complemented
17#36483C211yesmaximal, characteristic, complemented
18#36434C211yesmaximal, characteristic, complemented
19#35996C211yesmaximal, characteristic, complemented
20#35910C211yesmaximal, characteristic, complemented
21#35898C211yesmaximal, characteristic, complemented
22#35831C211yesmaximal, characteristic, complemented
23#35786C211yesmaximal, characteristic, complemented
24#35771C211yesmaximal, characteristic, complemented
25#35757C211yesmaximal, characteristic, complemented
26#35687C211yesmaximal, characteristic, complemented
27#35044C213yesmaximal, complemented
28#34589C213yesmaximal, complemented
29#34294C211yesmaximal, characteristic, complemented
30#34257C211yesmaximal, characteristic, complemented
31C4×D4×Q8C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×#519C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45#2863C2213yes—
46#2858C2213yes—
47#2854C2213yes—
48#2850C2213yes—
49#2831C2216yes—
50#2829C2216yes—
51#2827C2216yes—
52#2826C2216yes—
53#2806C2216yes—
54#2803C2216yes—
55#2800C2216yes—
56#2788C2216yes—
57#2781C2216yes—
58#2780C2216yes—
59#2780C2216yes—
60#2768C2216yes—
61#2751C2216yes—
62#2750C2216yes—
63#2745C2216yes—
64#2715C2216yes—
65#2710C2216yes—
66#2708C2216yes—
67#2695C2216yes—
68#2682C2216yes—
69#2666C2213yes—
70#2665C2213yes—
71#2662C2213yes—
72#2661C2213yes—
73#2653C2213yes—
74#2653C2213yes—
75#2652C2216yes—
76#2651C2213yes—
77#2650C2213yes—
78#2649C2213yes—
79#2649C2216yes—
80#2648C2213yes—
81#2648C2213yes—
82#2648C2213yes—
83#2648C2216yes—
84#2644C2213yes—
85#2642C2213yes—
86#2636C2216yes—
87#2636C2211yescharacteristic
88#2635C2213yes—
89#2631C2213yes—
90#2630C2213yes—
91#2630C2216yes—
92#2629C2213yes—
93#2625C2213yes—
94#2620C2213yes—
95#2620C2213yes—
96#2616C2213yes—
97#2615C2213yes—
98#2597C2216yes—
99#2597C2216yes—
100#2587C2216yes—
101#2582C2213yes—
102#2574C2216yes—
103#2568C2213yes—
104#2565C2213yes—
105#2562C2213yes—
106#2557C2216yes—
107#2554C2216yes—
108#2548C2213yes—
109#2547C2213yes—
110#2545C2213yes—
111#2545C2213yes—
112#2544C2213yes—
113#2538C2213yes—
114#2537C2213yes—
115#2536C2213yes—
116#2513C2213yes—
117#2512C2213yes—
118#2512C2213yes—
119#2511C2213yes—
120#2511C2213yes—
121#2511C2213yes—
122#2502C2213yes—
123#2501C2213yes—
124#2497C2213yes—
125#2497C2213yes—
126#2497C2213yes—
127#2497C2213yes—
128#2496C2213yes—
129#2494C2213yes—
130#2492C2213yes—
131#2492C2213yes—
132#2490C2213yes—
133#2490C2213yes—
134#2490C2213yes—
135#2490C2213yes—
136#2489C2213yes—
137#2489C2213yes—
138#2486C2213yes—
139#2486C2213yes—
140#2459C2216yes—
141#2456C2216yes—
142#2453C2213yes—
143#2451C2213yes—
144#2448C2213yes—
145#2448C2213yes—
146#2447C2213yes—
147#2447C2213yes—
148#2441C2213yes—
149#2439C2213yes—
150#2436C2213yes—
151#2434C2213yes—
152#2432C2213yes—
153#2432C2213yes—
154#2431C2213yes—
155#2431C2213yes—
156#2429C2213yes—
157#2429C2213yes—
158#2428C2213yes—
159#2427C2213yes—
160#2426C2213yes—
161#2426C2213yes—
162#2423C2213yes—
163#2423C2213yes—
164#2422C2213yes—
165#2422C2213yes—
166#2417C2213yes—
167#2417C2213yes—
168#2416C2213yes—
169#2416C2213yes—
170#2415C2213yes—
171#2414C2213yes—
172#2409C2213yes—
173#2409C2213yes—
174#2407C2213yes—
175#2407C2213yes—
176#2407C2213yes—
177#2407C2213yes—
178#2401C2213yes—
179#2398C2213yes—
180#2396C2213yes—
181#2395C2213yes—
182#2392C2213yes—
183#2392C2213yes—
184#2388C2213yes—
185#2388C2213yes—
186#2367C2213yes—
187#2365C2213yes—
188#2361C2213yes—
189#2360C2213yes—
190#2360C2213yes—
191#2360C2213yes—
192#2351C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198D4×C4⋊C4C2213yes—
199D4×C4⋊C4C2213yes—
200#2341C2213yes—
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2213yes—
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208Q8×C22⋊C4C2213yes—
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2213yes—
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218#2337C2216yes—
219#2333C2216yes—
220#2326C2213yes—
221#2323C2213yes—
222#2311C2213yes—
223#2311C2213yes—
224C4×C4⋊Q8C2213yes—
225C4×#126C2213yes—
226C4×#124C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×C22⋊Q8C2213yes—
229C4×#123C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232#2297C2213yes—
233#2297C2213yes—
234#2290C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C2×2−1+4—28no—
239C2×2−1+4—44no—
240C2×2−1+4—44no—
241C22×#41C2311yescharacteristic
242C22×#41C2311yescharacteristic
243C22×#41C2313yes—
244C22×#41C2313yes—
245C22×#41C2313yes—
246C23×Q8C2311yescharacteristic
247C23×Q8C2311yescharacteristic
248C23×Q8C2311yescharacteristic
249C23×Q8C2313yes—
250#557—44no—
251#550—44no—
252D4×Q8—28no—
253D4×Q8—44no—
254#548—28no—
255#548—44no—
256#548—44no—
257#548—44no—
258C2×C4⋊Q8C2313yes—
259C2×C4⋊Q8C2313yes—
260C2×C4⋊Q8C2313yes—
261C2×#127C2313yes—
262C2×#126C2311yescharacteristic
263C2×#126C2316yes—
264C2×#125C2313yes—
265C2×#125C2313yes—
266C2×#124C2313yes—
267C2×#124C2313yes—
268C2×#124C2313yes—
269C2×#124C2313yes—
270C2×#124C2313yes—
271C2×#124C2316yes—
272C2×#123C2313yes—
273C2×#123C2316yes—
274C2×#123C2316yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2313yes—
277C2×C22⋊Q8C2313yes—
278C2×C22⋊Q8C2313yes—
279C2×C22⋊Q8C2313yes—
280C2×C22⋊Q8C2313yes—
281C2×C22⋊Q8C2313yes—
282C2×C22⋊Q8C2313yes—
283C2×#121C2313yes—
284C2×#121C2316yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#121C2313yes—
289C2×#121C2313yes—
290C2×#121C2313yes—
291#520—44no—
292#519—44no—
293C2×C4×Q8—44no—
294C2×C4×Q8—44no—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2313yes—
306C2×C4×Q8C2313yes—
307C2×C4×Q8C2313yes—
308C2×C4×Q8C2313yes—
309C2×C4×Q8C2313yes—
310C2×C4×Q8C2313yes—
311C2×C4×Q8C2313yes—
312C2×C4×D4C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×C4×D4C2313yes—
321C2×C4×D4C2313yes—
322C2×C4×D4C2313yes—
323C2×C4×D4C2316yes—
324C2×#117C2313yes—
325C2×#117C2313yes—
326C2×#117C2313yes—
327C22×C4⋊C4C2313yes—
328C22×C4⋊C4C2313yes—
329C22×C4⋊C4C2313yes—
330C22×C42C2313yes—
331C22×C42C2313yes—
332#401C2313yes—
333#400C2316yes—
334#400C2313yes—
335#400C2316yes—
336#400C2316yes—
337#400C2316yes—
338#400C2313yes—
339#400C2316yes—
340#400C2316yes—
341#400C2313yes—
342#400C2313yes—
343#400C2311yescharacteristic
344#400C2313yes—
345#400C2313yes—
346#399C2313yes—
347#399C2316yes—
348#399C2316yes—
349#399C2311yescharacteristic
350#398C2313yes—
351#398C2316yes—
352#398C2316yes—
353#398C2316yes—
354#398C2316yes—
355#398C2316yes—
356#398C2313yes—
357#398C2313yes—
358#398C2313yes—
359#398C2313yes—
360#397C2316yes—
361#397C2316yes—
362#397C2313yes—
363#397C2316yes—
364#397C2316yes—
365#397C2313yes—
366#397C2316yes—
367#397C2313yes—
368#397C2316yes—
369#397C2316yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#397C2313yes—
374#397C2313yes—
375#397C2313yes—
376#397C2313yes—
377#396C2316yes—
378#396C2316yes—
379#396C2316yes—
380#396C2316yes—
381#396C2316yes—
382#396C2316yes—
383#396C2316yes—
384#396C2316yes—
385#396C2313yes—
386#396C2313yes—
387#396C2313yes—
388#396C2311yescharacteristic
389#396C2311yescharacteristic
390#396C2313yes—
391#396C2313yes—
392#395C2316yes—
393#395C2313yes—
394#395C2313yes—
395#395C2313yes—
396#394C2313yes—
397#394C2313yes—
398#394C2316yes—
399#394C2316yes—
400#394C2316yes—
401#394C2313yes—
402#394C2316yes—
403#394C2313yes—
404#394C2316yes—
405#394C2316yes—
406#394C2316yes—
407#394C2316yes—
408#394C2313yes—
409#394C2313yes—
410#394C2311yescharacteristic
411#394C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2311yescharacteristic
415#394C2311yescharacteristic
416#394C2313yes—
417#394C2313yes—
418#394C2313yes—
419#394C2313yes—
420#393C2316yes—
421#393C2313yes—
422#393C2313yes—
423#393C2313yes—
424#393C2313yes—
425#393C2313yes—
426#392C2316yes—
427#392C2316yes—
428#392C2313yes—
429#392C2313yes—
430#392C2313yes—
431#392C2313yes—
432#392C2313yes—
433#392C2311yescharacteristic
434#392C2313yes—
435#392C2313yes—
436#391C2313yes—
437#391C2313yes—
438#391C2313yes—
439#391C2313yes—
440#391C2313yes—
441#391C2313yes—
442#391C2316yes—
443#391C2316yes—
444#391C2313yes—
445#391C2313yes—
446#391C2313yes—
447#391C2313yes—
448#391C2313yes—
449#391C2316yes—
450#391C2313yes—
451#391C2313yes—
452#391C2313yes—
453#391C2313yes—
454#391C2313yes—
455#391C2313yes—
456#391C2313yes—
457#391C2313yes—
458#390C2313yes—
459#390C2316yes—
460#390C2313yes—
461#390C2313yes—
462#390C2313yes—
463#390C2316yes—
464#390C2316yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2313yes—
472#390C2313yes—
473#390C2313yes—
474#390C2313yes—
475#390C2316yes—
476#390C2313yes—
477#390C2313yes—
478#389C2316yes—
479#389C2316yes—
480#389C2316yes—
481#389C2313yes—
482#389C2316yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2316yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2313yes—
496#388C2313yes—
497#388C2313yes—
498#388C2313yes—
499#388C2316yes—
500#388C2316yes—
501#388C2316yes—
502#388C2313yes—
503#388C2316yes—
504#388C2316yes—
505#388C2313yes—
506#388C2313yes—
507#388C2316yes—
508#388C2316yes—
509#388C2316yes—
510#388C2316yes—
511#388C2316yes—
512#388C2313yes—
513#388C2313yes—
514#388C2316yes—
515#388C2316yes—
516#388C2313yes—
517#388C2313yes—
518#388C2313yes—
519#388C2313yes—
520#388C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2313yes—
528#387C2316yes—
529#387C2316yes—
530#387C2313yes—
531#387C2313yes—
532#387C2316yes—
533#387C2316yes—
534#387C2316yes—
535#387C2313yes—
536#386C2316yes—
537#386C2313yes—
538#386C2313yes—
539#386C2313yes—
540#386C2313yes—
541#386C2313yes—
542#386C2316yes—
543#386C2316yes—
544#386C2316yes—
545#386C2316yes—
546#386C2316yes—
547#386C2316yes—
548#386C2313yes—
549#386C2313yes—
550#386C2311yescharacteristic
551#386C2311yescharacteristic
552#386C2316yes—
553#385C2316yes—
554#385C2313yes—
555#385C2316yes—
556#385C2316yes—
557#385C2316yes—
558#385C2316yes—
559#385C2316yes—
560#385C2316yes—
561#385C2316yes—
562#385C2316yes—
563#385C2316yes—
564#385C2311yescharacteristic
565#385C2311yescharacteristic
566#384C2313yes—
567#384C2313yes—
568#384C2313yes—
569#384C2313yes—
570#384C2313yes—
571#383C2313yes—
572#382C2313yes—
573#382C2316yes—
574#382C2311yescharacteristic
575#381C2316yes—
576#381C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2316yes—
585#380C2316yes—
586#380C2316yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2316yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2316yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2316yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2313yes—
629C4×C22⋊C4C2313yes—
630C4×C22⋊C4C2313yes—
631#376C2313yes—
632C43C2313yes—
6332−1+4—464no—
634C2×#41—24no—
635C2×#41—212no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C2×#41—24no—
641C2×#41—212no—
642C2×#41—212no—
643C2×#41—46no—
644C2×#41—46no—
645C2×#41—46no—
646C2×#41—46no—
647C2×#41—46no—
648C2×#41—46no—
649C22×Q8—24no—
650C22×Q8—24no—
651C22×Q8—24no—
652C22×Q8—212no—
653C22×Q8—24no—
654C22×Q8—24no—
655C22×Q8—24no—
656C22×Q8—24no—
657C22×Q8—24no—
658C22×Q8—46no—
659C22×Q8—46no—
660C22×Q8#4118yes—
661C22×Q8C2413yes—
662C22×Q8C2413yes—
663C22×Q8C2413yes—
664C22×Q8C2413yes—
665C22×Q8C2413yes—
666C22×Q8C2411yescharacteristic
667C22×D4C2411yescharacteristic
668C22×D4C2413yes—
669C22×D4C2413yes—
670C22×D4C2411yescharacteristic
671C22×D4C2413yes—
672C22×D4C2413yes—
673C22×D4C2413yes—
674C22×D4C2413yes—
675C22×D4C2411yescharacteristic
676C22×D4C2413yes—
677C22×D4C2413yes—
678C22×D4C2413yes—
679C22×D4C2416yes—
680C23×C4C2413yes—
681C23×C4C2413yes—
682C23×C4C2413yes—
683C23×C4C2413yes—
684C23×C4C2413yes—
685C23×C4C2413yes—
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2416yes—
689C23×C4C2413yes—
690C23×C4C2416yes—
691C4⋊Q8—212no—
692C4⋊Q8—46no—
693C4⋊Q8—46no—
694#127—46no—
695#126—24no—
696#126—86no—
697#125—46no—
698#125—46no—
699#124—212no—
700#124—212no—
701#124—46no—
702#124—46no—
703#124—46no—
704#124—86no—
705#123—46no—
706#123—86no—
707#123—86no—
708C22⋊Q8—212no—
709C22⋊Q8—212no—
710C22⋊Q8—212no—
711C22⋊Q8—46no—
712C22⋊Q8—46no—
713C22⋊Q8—46no—
714C22⋊Q8—46no—
715C22⋊Q8—46no—
716#121—212no—
717#121—412no—
718#121—46no—
719#121—46no—
720#121—46no—
721#121—46no—
722#121—46no—
723#121—46no—
724C4×Q8—24no—
725C4×Q8—24no—
726C4×Q8—24no—
727C4×Q8—24no—
728C4×Q8—24no—
729C4×Q8—24no—
730C4×Q8—24no—
731C4×Q8—24no—
732C4×Q8—24no—
733C4×Q8—24no—
734C4×Q8—46no—
735C4×Q8—46no—
736C4×Q8—46no—
737C4×Q8—46no—
738C4×Q8—46no—
739C4×Q8—46no—
740C4×Q8—46no—
741C4×D4—212no—
742C4×D4—212no—
743C4×D4—24no—
744C4×D4—46no—
745C4×D4—46no—
746C4×D4—46no—
747C4×D4—46no—
748C4×D4—46no—
749C4×D4—46no—
750C4×D4—46no—
751C4×D4—46no—
752C4×D4—86no—
753#117—46no—
754#117—46no—
755#117—46no—
756C2×C4⋊C4—46no—
757C2×C4⋊C4—46no—
758C2×C4⋊C4—46no—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2416yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2416yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2416yes—
794C2×C4⋊C4C2416yes—
795C2×C4⋊C4C2416yes—
796C2×C4⋊C4C2416yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2416yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2413yes—
804C2×C4⋊C4C2416yes—
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2411yescharacteristic
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2411yescharacteristic
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2411yescharacteristic
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2411yescharacteristic
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2411yescharacteristic
826C2×C22⋊C4C2411yescharacteristic
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2416yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2416yes—
839C2×C22⋊C4C2416yes—
840C2×C22⋊C4C2416yes—
841C2×C22⋊C4C2416yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2416yes—
848C2×C22⋊C4C2416yes—
849C2×C22⋊C4C2416yes—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2416yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2411yescharacteristic
855C2×C22⋊C4C2413yes—
856C2×C22⋊C4C2411yescharacteristic
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2413yes—
861C2×C42—46no—
862C2×C42—46no—
863C2×C42C2413yes—
864C2×C42C2413yes—
865C2×C42C2413yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2413yes—
872C2×C42C2413yes—
873C2×C42C2416yes—
874C2×C42C2416yes—
875C2×C42C2413yes—
876C2×C42C2413yes—
877C2×C42C2413yes—
878C2×C42C2413yes—
879C2×C42C2413yes—
880C2×C42C2413yes—
881C2×C42C2413yes—
882C2×C42C2411yescharacteristic
883#95C2411yescharacteristic
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2413yes—
892#95C2411yescharacteristic
893#95C2413yes—
894#95C2411yescharacteristic
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2416yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2416yes—
910#95C2413yes—
911#95C2413yes—
912#95C2416yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2416yes—
922#95C2411yescharacteristic
923#95C2416yes—
924#95C2416yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2413yes—
931#95C2413yes—
932#95C2413yes—
933#95C2416yes—
934#95C2416yes—
935#95C2416yes—
936#95C2416yes—
937C24C2513yes—
938C24C2511yescharacteristic
939C24C2513yes—
940C24C2511yescharacteristic
941C24C2511yescharacteristic
942#41—448no—
943#41—448no—
944#41—448no—
945#41—416no—
946#41—416no—
947C2×Q8—232no—
948C2×Q8—26no—
949C2×Q8—26no—
950C2×Q8—26no—
951C2×Q8—26no—
952C2×Q8—26no—
953C2×Q8—26no—
954C2×Q8—26no—
955C2×Q8—26no—
956C2×Q8—26no—
957C2×Q8—26no—
958C2×Q8—43no—
959C2×Q8—43no—
960C2×Q8—43no—
961C2×Q8—43no—
962C2×Q8—448no—
963C2×Q8—416no—
964C2×Q8—416no—
965C2×Q8C2×#41112yes—
966C2×Q8C2×#4114yes—
967C2×Q8H(5,𝔽2)14yes—
968C2×Q8H(5,𝔽2)14yes—
969C2×D4—22no—
970C2×D4—22no—
971C2×D4—26no—
972C2×D4—22no—
973C2×D4—26no—
974C2×D4—22no—
975C2×D4—26no—
976C2×D4—26no—
977C2×D4—26no—
978C2×D4—26no—
979C2×D4—26no—
980C2×D4—26no—
981C2×D4—26no—
982C2×D4—26no—
983C2×D4—26no—
984C2×D4—22no—
985C2×D4—26no—
986C2×D4—41no—
987C2×D4—43no—
988C2×D4—41no—
989C2×D4—43no—
990C2×D4—43no—
991C2×D4—43no—
992C2×D4—41no—
993C2×D4—43no—
994C2×D4—41no—
995C2×D4—43no—
996C2×D4—43no—
997C2×D4—43no—
998C2×D4—43no—
999C2×D4—43no—
1000C2×D4—43no—
1001C2×D4—43no—
1002C2×D4—43no—
1003C2×D4—43no—
1004C2×D4—43no—
1005C2×D4—46no—
1006C2×D4—46no—
1007C2×D4—46no—
1008C22×C4—26no—
1009C22×C4—26no—
1010C22×C4—26no—
1011C22×C4—26no—
1012C22×C4—26no—
1013C22×C4—212no—
1014C22×C4—26no—
1015C22×C4—26no—
1016C22×C4—26no—
1017C22×C4—26no—
1018C22×C4—26no—
1019C22×C4—26no—
1020C22×C4—26no—
1021C22×C4—26no—
1022C22×C4—26no—
1023C22×C4—26no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—41no—
1030C22×C4—46no—
1031C22×C4—46no—
1032C22×C4—43no—
1033C22×C4—43no—
1034C22×C4—43no—
1035C22×C4—43no—
1036C22×C4—43no—
1037C22×C4—46no—
1038C22×C4—46no—
1039C22×C4—46no—
1040C22×C4C2×#41112yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2513yes—
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2513yes—
1048C22×C4C2513yes—
1049C22×C4C2513yes—
1050C22×C4C2513yes—
1051C22×C4C2513yes—
1052C22×C4C2513yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2513yes—
1055C22×C4C2513yes—
1056C22×C4C2513yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2511yescharacteristic
1059C22×C4C2513yes—
1060C22×C4C2513yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2513yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C22×C4C2513yes—
1067C4⋊C4—26no—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—26no—
1071C4⋊C4—212no—
1072C4⋊C4—26no—
1073C4⋊C4—26no—
1074C4⋊C4—26no—
1075C4⋊C4—26no—
1076C4⋊C4—26no—
1077C4⋊C4—26no—
1078C4⋊C4—26no—
1079C4⋊C4—26no—
1080C4⋊C4—22no—
1081C4⋊C4—22no—
1082C4⋊C4—22no—
1083C4⋊C4—22no—
1084C4⋊C4—43no—
1085C4⋊C4—46no—
1086C4⋊C4—46no—
1087C4⋊C4—46no—
1088C4⋊C4—43no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4—43no—
1094C4⋊C4—41no—
1095C4⋊C4—43no—
1096C4⋊C4—43no—
1097C4⋊C4—43no—
1098C4⋊C4—43no—
1099C4⋊C4—46no—
1100C4⋊C4—41no—
1101C4⋊C4—43no—
1102C4⋊C4—43no—
1103C4⋊C4—46no—
1104C4⋊C4—43no—
1105C4⋊C4—46no—
1106C4⋊C4—43no—
1107C4⋊C4—43no—
1108C4⋊C4—46no—
1109C4⋊C4—46no—
1110C4⋊C4—46no—
1111C4⋊C4—43no—
1112C4⋊C4—43no—
1113C22⋊C4—22no—
1114C22⋊C4—26no—
1115C22⋊C4—26no—
1116C22⋊C4—22no—
1117C22⋊C4—26no—
1118C22⋊C4—26no—
1119C22⋊C4—212no—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—26no—
1123C22⋊C4—26no—
1124C22⋊C4—26no—
1125C22⋊C4—26no—
1126C22⋊C4—22no—
1127C22⋊C4—22no—
1128C22⋊C4—22no—
1129C22⋊C4—43no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—41no—
1133C22⋊C4—43no—
1134C22⋊C4—41no—
1135C22⋊C4—43no—
1136C22⋊C4—41no—
1137C22⋊C4—43no—
1138C22⋊C4—43no—
1139C22⋊C4—43no—
1140C22⋊C4—43no—
1141C22⋊C4—41no—
1142C22⋊C4—41no—
1143C22⋊C4—41no—
1144C22⋊C4—43no—
1145C22⋊C4—43no—
1146C22⋊C4—43no—
1147C22⋊C4—43no—
1148C22⋊C4—43no—
1149C22⋊C4—43no—
1150C22⋊C4—43no—
1151C22⋊C4—43no—
1152C22⋊C4—46no—
1153C22⋊C4—43no—
1154C22⋊C4—43no—
1155C22⋊C4—46no—
1156C22⋊C4—46no—
1157C22⋊C4—46no—
1158C22⋊C4—46no—
1159C22⋊C4—43no—
1160C22⋊C4—43no—
1161C22⋊C4—43no—
1162C22⋊C4—43no—
1163C22⋊C4—43no—
1164C22⋊C4—46no—
1165C22⋊C4—46no—
1166C22⋊C4—46no—
1167C22⋊C4—46no—
1168C22⋊C4—43no—
1169C42—26no—
1170C42—26no—
1171C42—26no—
1172C42—26no—
1173C42—26no—
1174C42—26no—
1175C42—26no—
1176C42—26no—
1177C42—26no—
1178C42—26no—
1179C42—43no—
1180C42—43no—
1181C42—43no—
1182C42—43no—
1183C42—43no—
1184C42—46no—
1185C42—43no—
1186C42—46no—
1187C42—43no—
1188C422−1+414yescomplemented
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—21no—
1198C23—21no—
1199C23—21no—
1200C23—21no—
1201C23—23no—
1202C23—21no—
1203C23—23no—
1204C23—23no—
1205C23—23no—
1206C23—21no—
1207C23—23no—
1208C23—21no—
1209C23—23no—
1210C23—21no—
1211C23—23no—
1212C23—23no—
1213C23—23no—
1214C23—21no—
1215C23—23no—
1216C23—23no—
1217C23—21no—
1218C23—23no—
1219C23—21no—
1220C23—23no—
1221C23—23no—
1222C23C22×#4112yes—
1223C23#58512yes—
1224C23C2611yescharacteristic
1225Q8—224no—
1226Q8—412no—
1227Q8—412no—
1228Q8—412no—
1229Q8—86no—
1230Q8#538116yes—
1231D4—28no—
1232D4—412no—
1233D4—412no—
1234D4—44no—
1235D4—44no—
1236D4—412no—
1237D4—412no—
1238D4—412no—
1239D4—86no—
1240D4—86no—
1241D4—86no—
1242D4—86no—
1243D4—166no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—224no—
1253C2×C4—21no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—21no—
1257C2×C4—23no—
1258C2×C4—21no—
1259C2×C4—23no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—23no—
1271C2×C4—23no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—21no—
1276C2×C4—23no—
1277C2×C4—21no—
1278C2×C4—23no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—23no—
1282C2×C4—23no—
1283C2×C4—23no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—23no—
1290C2×C4—23no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—23no—
1294C2×C4—21no—
1295C2×C4—23no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—23no—
1299C2×C4—23no—
1300C2×C4—23no—
1301C2×C4—23no—
1302C2×C4—23no—
1303C2×C4—23no—
1304C2×C4—21no—
1305C2×C4—23no—
1306C2×C4—23no—
1307C2×C4—23no—
1308C2×C4—23no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—23no—
1314C2×C4—21no—
1315C2×C4—23no—
1316C2×C4—44no—
1317C2×C4—44no—
1318C2×C4—424no—
1319C2×C4—412no—
1320C2×C4—412no—
1321C2×C4—412no—
1322C2×C4—412no—
1323C2×C4—86no—
1324C2×C4—86no—
1325C2×C4—166no—
1326C2×C4C22×#4116yes—
1327C2×C4C22×#4116yes—
1328C2×C4C2×H(5,𝔽2)16yes—
1329C2×C4C2×H(5,𝔽2)16yes—
1330C2×C4C2×2−1+412yes—
1331C2×C4C2×2−1+412yes—
1332C2×C4C2×2−1+412yes—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—22no—
1337C22—22no—
1338C22—22no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—43no—
1348C22—41no—
1349C22—43no—
1350C22—43no—
1351C22—43no—
1352C22—41no—
1353C22—43no—
1354C22—41no—
1355C22—43no—
1356C22—43no—
1357C22—43no—
1358C22—41no—
1359C22—43no—
1360C22—43no—
1361C22—41no—
1362C22—41no—
1363C22—43no—
1364C22—43no—
1365C22—43no—
1366C22—41no—
1367C22—43no—
1368C22C23×#4111yescharacteristic
1369C22C22×H(5,𝔽2)11yescharacteristic
1370C22C22×H(5,𝔽2)11yescharacteristic
1371C22C22×2−1+411yescharacteristic
1372C22C2×#58511yescharacteristic
1373C22H(7,𝔽2)11yescharacteristic
1374C222−1+611yescharacteristic
1375C4—22no—
1376C4—22no—
1377C4—22no—
1378C4—26no—
1379C4—41no—
1380C4—43no—
1381C4—43no—
1382C4—43no—
1383C4—43no—
1384C4—43no—
1385C4—43no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—43no—
1391C4—43no—
1392C4—41no—
1393C4—41no—
1394C4—43no—
1395C4—43no—
1396C4—41no—
1397C4—41no—
1398C4—43no—
1399C4—43no—
1400C4C2×#538112yes—
1401C2—42no—
1402C2—42no—
1403C2—83no—
1404C2—81no—
1405C2—83no—
1406C2C22×#53811yescharacteristic
1407C2#6278811yescharacteristic
1408C2#6285111yescharacteristic
1409C2#6289911yescharacteristic
1410C2#6291311yescharacteristic
1411C2#6291711yescharacteristic
1412C2#6291911yescharacteristic
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. #42862C2semidirect
2. #42860C2semidirect
3. #42838C2semidirect
4. #42834C2semidirect
5. #42520C2semidirect
6. #42504C2semidirect
7. #42448C2semidirect
8. #42446C2semidirect
9. #40221C2semidirect
10. #40194C2semidirect
11. #39790C2semidirect
12. #39654C2semidirect
13. #37512C2semidirect
14. #37500C2semidirect
15. #36583C2semidirect
16. Q8×#126C2semidirect
17. #36483C2semidirect
18. #36434C2semidirect
19. #35996C2semidirect
20. #35910C2semidirect
21. #35898C2semidirect
22. #35831C2semidirect
23. #35786C2semidirect
24. #35771C2semidirect
25. #35757C2semidirect
26. #35687C2semidirect
27. #35044C2semidirect
28. #34589C2semidirect
29. #34294C2semidirect
30. #34257C2semidirect
31. C4×D4×Q8C2semidirect
1188. C422−1+4semidirect

Maximal subgroups

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

subgroupindex
#428622
#428602
#428382
#428342
#425202
#425042
#424482
#424462
#402212
#401942
#397902
#396542
#375122
#375002
#365832
Q8×#1262
#364832
#364342
#359962
#359102
#358982
#358312
#357862
#357712
#357572
#356872
#350442
#345892
#342942
#342572
C4×D4×Q82