Finite Group Databasebeta

← #7697444

Subgroups — #7697444

Order 512.

5388 conjugacy classes of subgroups.

The subgroup lattice has 1435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60047C211yesmaximal, characteristic, complemented
2#60042C212yesmaximal, complemented
3#59885C211yesmaximal, characteristic, complemented
4#59834C211yesmaximal, characteristic, complemented
5#59182C212yesmaximal, complemented
6#59135C212yesmaximal, complemented
7#52306C211yesmaximal, characteristic, complemented
8#52167C211yesmaximal, characteristic, complemented
9C2×#2734C211yesmaximal, characteristic, complemented
10#44707C212yesmaximal, complemented
11#44223C214yesmaximal, complemented
12#43857C214yesmaximal, complemented
13#43575C214yesmaximal, complemented
14#43488C212yesmaximal, complemented
15#43150C212yesmaximal, complemented
16#39742C212yesmaximal, complemented
17#39738C214yesmaximal, complemented
18#38832C214yesmaximal, complemented
19#38829C212yesmaximal, complemented
20#38823C212yesmaximal, complemented
21#38819C214yesmaximal, complemented
22#36396C211yesmaximal, characteristic, complemented
23#36122C212yesmaximal, complemented
24#35953C212yesmaximal, complemented
25#35929C214yesmaximal, complemented
26#34325C214yesmaximal, complemented
27#34323C212yesmaximal, complemented
28C2×#555C2212yes—
29C2×#553C2212yes—
30C2×#553C2214yes—
31C2×#553C2211yescharacteristic
32C2×#553C2212yes—
33C2×#548C2211yescharacteristic
34C2×#548C2212yes—
35C2×#532C2212yes—
36C22×C4⋊Q8C2212yes—
37#2861C2211yescharacteristic
38#2858C2212yes—
39#2857C2212yes—
40#2856C2212yes—
41#2856C2211yescharacteristic
42#2850C2211yescharacteristic
43#2809C2211yescharacteristic
44#2808C2212yes—
45#2785C2214yes—
46#2784C2214yes—
47#2781C2214yes—
48#2775C2214yes—
49#2775C2214yes—
50#2769C2212yes—
51#2756C2214yes—
52#2744C2214yes—
53#2737C2214yes—
54#2737C2214yes—
55#2734C2212yes—
56#2734C2214yes—
57#2734C2211yescharacteristic
58#2734C2211yescharacteristic
59#2734C2214yes—
60#2734C2212yes—
61#2734C2212yes—
62#2733C2211yescharacteristic
63#2731C2212yes—
64#2731C2212yes—
65#2731C2214yes—
66#2727C2212yes—
67#2727C2212yes—
68#2721C2214yes—
69#2721C2214yes—
70#2714C2214yes—
71#2714C2214yes—
72#2705C2214yes—
73#2705C2214yes—
74#2699C2212yes—
75#2694C2214yes—
76#2694C2214yes—
77#2686C2214yes—
78#2686C2214yes—
79#2682C2212yes—
80#2682C2212yes—
81#2673C2214yes—
82#2673C2214yes—
83#2664C2212yes—
84#2663C2214yes—
85#2662C2214yes—
86#2661C2212yes—
87#2656C2212yes—
88#2656C2214yes—
89#2612C2214yes—
90#2611C2212yes—
91#2610C2214yes—
92#2610C2214yes—
93#2610C2214yes—
94#2609C2212yes—
95#2604C2214yes—
96#2603C2212yes—
97#2593C2212yes—
98#2591C2214yes—
99#2591C2212yes—
100#2574C2214yes—
101#2574C2214yes—
102#2572C2212yes—
103#2565C2211yescharacteristic
104#2564C2214yes—
105#2563C2214yes—
106#2560C2214yes—
107#2557C2214yes—
108#2556C2214yes—
109#2556C2214yes—
110#2555C2214yes—
111#2555C2214yes—
112#2555C2214yes—
113#2554C2214yes—
114#2553C2214yes—
115#2545C2212yes—
116#2545C2212yes—
117#2544C2211yescharacteristic
118#2543C2214yes—
119#2543C2214yes—
120#2543C2214yes—
121#2543C2214yes—
122#2543C2212yes—
123#2532C2214yes—
124#2531C2214yes—
125#2529C2214yes—
126#2521C2214yes—
127#2521C2214yes—
128#2519C2214yes—
129#2504C2211yescharacteristic
130#2504C2212yes—
131#2499C2211yescharacteristic
132#2498C2212yes—
133#2491C2214yes—
134#2491C2214yes—
135#2491C2214yes—
136#2491C2214yes—
137#2479C2214yes—
138#2479C2214yes—
139#2476C2214yes—
140#2474C2214yes—
141#2474C2214yes—
142#2471C2214yes—
143#2471C2214yes—
144#2467C2214yes—
145#2467C2214yes—
146#2464C2214yes—
147#2461C2214yes—
148#2461C2214yes—
149#2459C2214yes—
150#2456C2214yes—
151#2456C2214yes—
152#2454C2214yes—
153#2452C2214yes—
154#2452C2214yes—
155#2441C2214yes—
156#2439C2214yes—
157#2439C2214yes—
158#2436C2212yes—
159#2436C2212yes—
160#2436C2211yescharacteristic
161#2436C2214yes—
162#2432C2212yes—
163#2432C2212yes—
164#2431C2211yescharacteristic
165#2430C2214yes—
166#2428C2214yes—
167#2416C2214yes—
168#2416C2214yes—
169#2416C2214yes—
170#2416C2214yes—
171#2416C2214yes—
172#2414C2214yes—
173#2396C2214yes—
174#2395C2212yes—
175#2392C2212yes—
176C2×#398C2212yes—
177#2388C2214yes—
178C2×#395C2214yes—
179#2374C2214yes—
180#2373C2214yes—
181#2373C2214yes—
182#2373C2214yes—
183#2372C2212yes—
184#2371C2214yes—
185#2370C2212yes—
186#2369C2212yes—
187#2364C2214yes—
188#2364C2214yes—
189#2364C2214yes—
190#2363C2212yes—
191#2361C2214yes—
192#2361C2212yes—
193#2361C2214yes—
194#2359C2214yes—
195#2359C2214yes—
196#2353C2214yes—
197#2353C2214yes—
198#2353C2214yes—
199#2352C2212yes—
200#2352C2214yes—
201#2352C2214yes—
202#2349C2212yes—
203#2346C2212yes—
204#2345C2212yes—
205#2343C2214yes—
206#2336C2214yes—
207#2335C2214yes—
208#2335C2214yes—
209#2334C2214yes—
210#2334C2214yes—
211#2333C2214yes—
212#2325C2214yes—
213#2325C2214yes—
214#2325C2214yes—
215C4×C4⋊Q8C2212yes—
216C4×#125C2212yes—
217C4×#126C2214yes—
218C4×#124C2211yescharacteristic
219C4×#123C2214yes—
220C4×#121C2212yes—
221C4×#121C2212yes—
222C4×#121C2214yes—
223#2298C2214yes—
224#2297C2211yescharacteristic
225#2296C2212yes—
226C2×#391C2211yescharacteristic
227#2293C2212yes—
228C2×#389C2212yes—
229#2290C2214yes—
230C2×#387C2214yes—
231#2275C2214yes—
232#2275C2212yes—
233C42×D4C2211yescharacteristic
234C42×D4C2212yes—
235C22×#41C2311yescharacteristic
236C22×#41C2312yes—
237C23×Q8C2311yescharacteristic
238C23×Q8C2312yes—
239#555—48no—
240#553—216no—
241#553—232no—
242#553—48no—
243#553—44no—
244#548—44no—
245#548—48no—
246#532—48no—
247C2×C4⋊Q8—48no—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2312yes—
252C2×C4⋊Q8C2314yes—
253C2×C4⋊Q8C2314yes—
254C2×#127C2312yes—
255C2×#127C2311yescharacteristic
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#126C2312yes—
260C2×#126C2314yes—
261C2×#125C2312yes—
262C2×#125C2314yes—
263C2×#125C2311yescharacteristic
264C2×#125C2312yes—
265C2×#124C2312yes—
266C2×#124C2311yescharacteristic
267C2×#124C2312yes—
268C2×#124C2312yes—
269C2×#124C2311yescharacteristic
270C2×#124C2312yes—
271C2×#124C2314yes—
272C2×#124C2314yes—
273C2×#124C2311yescharacteristic
274C2×#124C2312yes—
275C2×#124C2312yes—
276C2×#124C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2312yes—
281C2×#123C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2311yescharacteristic
285C2×C22⋊Q8C2312yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2312yes—
291C2×#121C2312yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2312yes—
295C2×#121C2311yescharacteristic
296C2×#121C2311yescharacteristic
297C2×#121C2311yescharacteristic
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2314yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2314yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×#117C2314yes—
329C2×#117C2312yes—
330C2×#117C2314yes—
331C2×#117C2314yes—
332C2×#117C2312yes—
333C2×#117C2311yescharacteristic
334C2×#117C2312yes—
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2311yescharacteristic
337C22×C4⋊C4C2314yes—
338C22×C4⋊C4C2314yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2312yes—
341C22×C42C2312yes—
342C22×C42C2312yes—
343C22×C42C2311yescharacteristic
344C22×C42C2311yescharacteristic
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2312yes—
349#399C2314yes—
350#399C2312yes—
351#399C2312yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2312yes—
360#398C2312yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#397C2314yes—
367#397C2312yes—
368#397C2312yes—
369#397C2312yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2312yes—
374#397C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#394C2314yes—
394#394C2312yes—
395#394C2312yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#392C2312yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2312yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2314yes—
438#391C2311yescharacteristic
439#391C2312yes—
440#391C2312yes—
441#391C2311yescharacteristic
442#391C2314yes—
443#391C2311yescharacteristic
444#390C2314yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2311yescharacteristic
451#390C2311yescharacteristic
452#390C2311yescharacteristic
453#390C2312yes—
454#390C2312yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2311yescharacteristic
460#390C2314yes—
461#390C2314yes—
462#390C2312yes—
463#390C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2314yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#384C2312yes—
591#384C2311yescharacteristic
592#383C2314yes—
593#383C2314yes—
594#382C2312yes—
595#382C2314yes—
596#382C2314yes—
597#382C2311yescharacteristic
598#382C2314yes—
599#382C2311yescharacteristic
600#381C2314yes—
601#381C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2314yes—
605#380C2314yes—
606#380C2314yes—
607#380C2314yes—
608#380C2314yes—
609#380C2312yes—
610#380C2314yes—
611#380C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2311yescharacteristic
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C22⋊C4C2312yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2312yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2312yes—
650C4×C22⋊C4C2311yescharacteristic
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2311yescharacteristic
654C4×C22⋊C4C2312yes—
655#376C2312yes—
656#376C2314yes—
657#376C2314yes—
658#376C2314yes—
659C2×#95C2314yes—
660C2×#95C2314yes—
661C2×#95C2312yes—
662C2×#95C2312yes—
663C2×#95C2314yes—
664C2×#95C2314yes—
665C43C2312yes—
666C43C2311yescharacteristic
667C2×#41—24no—
668C2×#41—42no—
669C2×#41—44no—
670C2×#41—44no—
671C2×#41—81no—
672C2×#41—82no—
673C22×Q8—24no—
674C22×Q8—42no—
675C22×Q8—44no—
676C22×Q8—44no—
677C22×Q8—81no—
678C22×Q8—82no—
679C22×Q8C2412yes—
680C22×Q8C2412yes—
681C22×Q8C2411yescharacteristic
682C22×Q8C2412yes—
683C22×Q8C2414yes—
684C22×Q8C2411yescharacteristic
685C22×D4C2411yescharacteristic
686C22×D4C2412yes—
687C22×D4C2412yes—
688C22×D4C2414yes—
689C22×D4C2412yes—
690C22×D4C2411yescharacteristic
691C22×D4C2414yes—
692C22×D4C2414yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2411yescharacteristic
696C22×D4C2412yes—
697C22×D4C2412yes—
698C22×D4C2412yes—
699C22×D4C2414yes—
700C22×D4C2414yes—
701C22×D4C2412yes—
702C23×C4C2411yescharacteristic
703C23×C4C2412yes—
704C23×C4C2411yescharacteristic
705C23×C4C2412yes—
706C23×C4C2414yes—
707C23×C4C2412yes—
708C23×C4C2412yes—
709C23×C4C2414yes—
710C23×C4C2414yes—
711C23×C4C2414yes—
712C23×C4C2412yes—
713C23×C4C2414yes—
714C23×C4C2414yes—
715C23×C4C2414yes—
716C23×C4C2412yes—
717C4⋊Q8—28no—
718C4⋊Q8—28no—
719C4⋊Q8—44no—
720C4⋊Q8—44no—
721C4⋊Q8—48no—
722C4⋊Q8—48no—
723#127—44no—
724#127—81no—
725#126—216no—
726#126—216no—
727#126—216no—
728#126—44no—
729#126—48no—
730#125—216no—
731#125—28no—
732#125—44no—
733#125—42no—
734#124—28no—
735#124—24no—
736#124—48no—
737#124—42no—
738#124—44no—
739#124—44no—
740#124—44no—
741#124—48no—
742#124—81no—
743#124—84no—
744#124—82no—
745#124—82no—
746#123—216no—
747#123—216no—
748#123—216no—
749#123—48no—
750#123—44no—
751C22⋊Q8—42no—
752C22⋊Q8—48no—
753C22⋊Q8—44no—
754C22⋊Q8—44no—
755#121—216no—
756#121—216no—
757#121—216no—
758#121—28no—
759#121—216no—
760#121—216no—
761#121—28no—
762#121—42no—
763#121—44no—
764#121—48no—
765#121—48no—
766#121—48no—
767#121—48no—
768#121—42no—
769#121—44no—
770#121—44no—
771#121—48no—
772#121—44no—
773#121—48no—
774#121—42no—
775#121—44no—
776#121—84no—
777C4×Q8—44no—
778C4×Q8—42no—
779C4×D4—216no—
780C4×D4—216no—
781C4×D4—216no—
782C4×D4—28no—
783C4×D4—216no—
784C4×D4—216no—
785C4×D4—28no—
786C4×D4—28no—
787C4×D4—216no—
788C4×D4—24no—
789C4×D4—28no—
790C4×D4—48no—
791C4×D4—44no—
792C4×D4—42no—
793C4×D4—48no—
794C4×D4—48no—
795C4×D4—82no—
796C4×D4—82no—
797#117—216no—
798#117—28no—
799#117—42no—
800#117—44no—
801#117—48no—
802#117—48no—
803#117—82no—
804C2×C4⋊C4—48no—
805C2×C4⋊C4—48no—
806C2×C4⋊C4—42no—
807C2×C4⋊C4—44no—
808C2×C4⋊C4—82no—
809C2×C4⋊C4#41116yescomplemented
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2411yescharacteristic
907C2×C42—44no—
908C2×C42—44no—
909C2×C42—81no—
910C2×C42—81no—
911C2×C42C2411yescharacteristic
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2411yescharacteristic
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2411yescharacteristic
936C2×C42C2414yes—
937#95C2412yes—
938#95C2414yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983C24C2512yes—
984C24C2514yes—
985C24C2511yescharacteristic
986C24C2512yes—
987C24C2511yescharacteristic
988#41—88no—
989#41—816no—
990C2×Q8—24no—
991C2×Q8—24no—
992C2×Q8—22no—
993C2×Q8—24no—
994C2×Q8—41no—
995C2×Q8—42no—
996C2×Q8—41no—
997C2×Q8—42no—
998C2×Q8—41no—
999C2×Q8—42no—
1000C2×Q8—42no—
1001C2×Q8—44no—
1002C2×Q8—41no—
1003C2×Q8—42no—
1004C2×Q8—42no—
1005C2×Q8—44no—
1006C2×Q8—44no—
1007C2×Q8—88no—
1008C2×Q8—816no—
1009C2×Q8H(5,𝔽2)14yes—
1010C2×D4—28no—
1011C2×D4—28no—
1012C2×D4—28no—
1013C2×D4—24no—
1014C2×D4—28no—
1015C2×D4—24no—
1016C2×D4—28no—
1017C2×D4—22no—
1018C2×D4—24no—
1019C2×D4—24no—
1020C2×D4—28no—
1021C2×D4—28no—
1022C2×D4—28no—
1023C2×D4—28no—
1024C2×D4—22no—
1025C2×D4—22no—
1026C2×D4—24no—
1027C2×D4—24no—
1028C2×D4—42no—
1029C2×D4—42no—
1030C2×D4—44no—
1031C2×D4—41no—
1032C2×D4—42no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—41no—
1037C2×D4—42no—
1038C2×D4—42no—
1039C2×D4—44no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C2×D4—41no—
1043C2×D4—42no—
1044C2×D4—42no—
1045C2×D4—41no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—44no—
1051C2×D4—42no—
1052C2×D4—44no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—44no—
1056C22×C4—22no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—28no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—22no—
1064C22×C4—22no—
1065C22×C4—24no—
1066C22×C4—22no—
1067C22×C4—28no—
1068C22×C4—28no—
1069C22×C4—28no—
1070C22×C4—28no—
1071C22×C4—24no—
1072C22×C4—28no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—41no—
1077C22×C4—41no—
1078C22×C4—42no—
1079C22×C4—42no—
1080C22×C4—44no—
1081C22×C4—42no—
1082C22×C4—42no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4C2×#41116yes—
1098C22×C4C2×#4118yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2514yes—
1103C22×C4C2514yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2514yes—
1107C22×C4C2514yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2511yescharacteristic
1111C22×C4C2514yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2514yes—
1116C22×C4C2514yes—
1117C22×C4C2512yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—28no—
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—24no—
1136C4⋊C4—28no—
1137C4⋊C4—22no—
1138C4⋊C4—24no—
1139C4⋊C4—41no—
1140C4⋊C4—42no—
1141C4⋊C4—41no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—41no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—41no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4C2×#41116yes—
1165C4⋊C4C2×#4118yes—
1166C4⋊C4C2×#4118yes—
1167C22⋊C4—24no—
1168C22⋊C4—28no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—28no—
1173C22⋊C4—28no—
1174C22⋊C4—28no—
1175C22⋊C4—28no—
1176C22⋊C4—28no—
1177C22⋊C4—28no—
1178C22⋊C4—24no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—28no—
1182C22⋊C4—28no—
1183C22⋊C4—28no—
1184C22⋊C4—28no—
1185C22⋊C4—24no—
1186C22⋊C4—28no—
1187C22⋊C4—22no—
1188C22⋊C4—24no—
1189C22⋊C4—28no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—42no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4H(5,𝔽2)14yes—
1218C42—28no—
1219C42—28no—
1220C42—28no—
1221C42—28no—
1222C42—24no—
1223C42—24no—
1224C42—24no—
1225C42—24no—
1226C42—22no—
1227C42—24no—
1228C42—28no—
1229C42—22no—
1230C42—24no—
1231C42—44no—
1232C42—44no—
1233C42—41no—
1234C42—42no—
1235C42—42no—
1236C42—41no—
1237C42—41no—
1238C42—42no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—42no—
1244C23—21no—
1245C23—21no—
1246C23—22no—
1247C23—24no—
1248C23—24no—
1249C23—24no—
1250C23—22no—
1251C23—24no—
1252C23—22no—
1253C23—24no—
1254C23—22no—
1255C23—24no—
1256C23—21no—
1257C23—22no—
1258C23—21no—
1259C23—22no—
1260C23—21no—
1261C23—22no—
1262C23—24no—
1263C23—22no—
1264C23—24no—
1265C23—24no—
1266C23—24no—
1267C23—24no—
1268C23—22no—
1269C23C22×#4114yes—
1270C23C2×H(5,𝔽2)12yes—
1271C23C2611yescharacteristic
1272Q8—44no—
1273Q8—48no—
1274Q8—84no—
1275Q8—84no—
1276Q8—82no—
1277Q8—88no—
1278D4—48no—
1279D4—48no—
1280D4—416no—
1281D4—44no—
1282D4—48no—
1283D4—88no—
1284D4—88no—
1285D4—88no—
1286D4—88no—
1287D4—82no—
1288D4—84no—
1289D4—84no—
1290D4—82no—
1291D4—84no—
1292D4—88no—
1293D4—162no—
1294D4—164no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—21no—
1298C2×C4—22no—
1299C2×C4—21no—
1300C2×C4—22no—
1301C2×C4—21no—
1302C2×C4—22no—
1303C2×C4—21no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—21no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—21no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—21no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—21no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—416no—
1348C2×C4—48no—
1349C2×C4—44no—
1350C2×C4—48no—
1351C2×C4—44no—
1352C2×C4—48no—
1353C2×C4—48no—
1354C2×C4—88no—
1355C2×C4—88no—
1356C2×C4—88no—
1357C2×C4—84no—
1358C2×C4—88no—
1359C2×C4—88no—
1360C2×C4—84no—
1361C2×C4—88no—
1362C2×C4C22×#4118yes—
1363C2×C4C22×#4114yes—
1364C2×C4C22×#4114yes—
1365C2×C4C22×#4118yes—
1366C2×C4C2×H(5,𝔽2)12yes—
1367C2×C4C2×H(5,𝔽2)14yes—
1368C2×C4C2×H(5,𝔽2)12yes—
1369C2×C4C2×H(5,𝔽2)12yes—
1370C22—24no—
1371C22—22no—
1372C22—24no—
1373C22—22no—
1374C22—44no—
1375C22—44no—
1376C22—44no—
1377C22—44no—
1378C22—42no—
1379C22—42no—
1380C22—44no—
1381C22—41no—
1382C22—42no—
1383C22—42no—
1384C22—44no—
1385C22—44no—
1386C22—44no—
1387C22—44no—
1388C22—42no—
1389C22—41no—
1390C22—44no—
1391C22—42no—
1392C22—42no—
1393C22—42no—
1394C22—44no—
1395C22—41no—
1396C22#348314yes—
1397C22C23×#4112yes—
1398C22C22×H(5,𝔽2)11yescharacteristic
1399C22C22×H(5,𝔽2)11yescharacteristic
1400C22H(7,𝔽2)11yescharacteristic
1401C222−1+612yes—
1402C4—28no—
1403C4—28no—
1404C4—22no—
1405C4—24no—
1406C4—24no—
1407C4—22no—
1408C4—24no—
1409C4—22no—
1410C4—44no—
1411C4—42no—
1412C4—42no—
1413C4—42no—
1414C4—42no—
1415C4—44no—
1416C4—41no—
1417C4—42no—
1418C4—44no—
1419C4—44no—
1420C4—42no—
1421C4—42no—
1422C4—44no—
1423C4—41no—
1424C2—24no—
1425C2—82no—
1426C2—82no—
1427C2—84no—
1428C2—81no—
1429C2C2×#348311yescharacteristic
1430C2#6285612yes—
1431C2#6289211yescharacteristic
1432C2#6298412yes—
1433C2#6306311yescharacteristic
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. #60047C2semidirect
2. #60042C2semidirect
3. #59885C2semidirect
4. #59834C2semidirect
5. #59182C2semidirect
6. #59135C2semidirect
7. #52306C2semidirect
8. #52167C2semidirect
9. C2×#2734C2semidirect
10. #44707C2semidirect
11. #44223C2semidirect
12. #43857C2semidirect
13. #43575C2semidirect
14. #43488C2semidirect
15. #43150C2semidirect
16. #39742C2semidirect
17. #39738C2semidirect
18. #38832C2semidirect
19. #38829C2semidirect
20. #38823C2semidirect
21. #38819C2semidirect
22. #36396C2semidirect
23. #36122C2semidirect
24. #35953C2semidirect
25. #35929C2semidirect
26. #34325C2semidirect
27. #34323C2semidirect
809. C2×C4⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
#600472
#600422
#598852
#598342
#591822
#591352
#523062
#521672
C2×#27342
#447072
#442232
#438572
#435752
#434882
#431502
#397422
#397382
#388322
#388292
#388232
#388192
#363962
#361222
#359532
#359292
#343252
#343232