Finite Group Databasebeta

← #7673854

Subgroups — #7673854

Order 512.

4698 conjugacy classes of subgroups.

The subgroup lattice has 1422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44565C214yesmaximal, complemented
2#44563C214yesmaximal, complemented
3#43735C214yesmaximal, complemented
4#43733C214yesmaximal, complemented
5#39757C211yesmaximal, characteristic, complemented
6#39634C211yesmaximal, characteristic, complemented
7#39506C211yesmaximal, characteristic, complemented
8#39372C211yesmaximal, characteristic, complemented
9#39260C212yesmaximal, complemented
10#39040C212yesmaximal, complemented
11#38296C214yesmaximal, complemented
12#38292C214yesmaximal, complemented
13#38224C212yesmaximal, complemented
14#38204C212yesmaximal, complemented
15#38179C214yesmaximal, complemented
16#38175C214yesmaximal, complemented
17#37883C211yesmaximal, characteristic, complemented
18#37882C211yesmaximal, characteristic, complemented
19#37700C211yesmaximal, characteristic, complemented
20#37700C211yesmaximal, characteristic, complemented
21#35548C212yesmaximal, complemented
22#35521C212yesmaximal, complemented
23#35336C211yesmaximal, characteristic, complemented
24#35321C211yesmaximal, characteristic, complemented
25#35203C212yesmaximal, complemented
26#34629C211yesmaximal, characteristic, complemented
27#34280C211yesmaximal, characteristic, complemented
28#34260C212yesmaximal, complemented
29#34207C211yesmaximal, characteristic, complemented
30C4×#540C211yesmaximal, characteristic, complemented
31#34081C211yesmaximal, characteristic, complemented
32C2×#540C2211yescharacteristic
33C2×#540C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×#529C2211yescharacteristic
36C2×#520C2212yes—
37#2863C2212yes—
38#2859C2211yescharacteristic
39#2859C2211yescharacteristic
40#2855C2212yes—
41#2853C2214yes—
42#2851C2211yescharacteristic
43#2851C2211yescharacteristic
44#2851C2214yes—
45#2810C2214yes—
46#2805C2214yes—
47#2794C2214yes—
48#2793C2214yes—
49#2791C2214yes—
50#2786C2214yes—
51#2783C2214yes—
52#2783C2214yes—
53#2780C2214yes—
54#2780C2214yes—
55#2770C2214yes—
56#2765C2214yes—
57#2750C2214yes—
58#2750C2214yes—
59#2749C2214yes—
60#2749C2214yes—
61#2747C2214yes—
62#2746C2214yes—
63#2744C2214yes—
64#2744C2214yes—
65#2743C2214yes—
66#2740C2214yes—
67#2738C2214yes—
68#2724C2214yes—
69#2721C2214yes—
70#2708C2214yes—
71#2708C2214yes—
72#2693C2214yes—
73#2690C2214yes—
74#2688C2214yes—
75#2688C2214yes—
76#2682C2214yes—
77#2655C2214yes—
78#2652C2214yes—
79#2652C2214yes—
80#2649C2214yes—
81#2647C2212yes—
82#2647C2211yescharacteristic
83#2647C2211yescharacteristic
84#2645C2212yes—
85#2642C2211yescharacteristic
86#2642C2211yescharacteristic
87#2629C2212yes—
88#2629C2211yescharacteristic
89#2629C2211yescharacteristic
90#2625C2212yes—
91#2621C2211yescharacteristic
92#2621C2211yescharacteristic
93#2609C2214yes—
94#2603C2214yes—
95#2590C2214yes—
96#2590C2214yes—
97#2587C2214yes—
98#2587C2214yes—
99#2585C2214yes—
100#2581C2212yes—
101#2579C2214yes—
102#2578C2214yes—
103#2576C2214yes—
104#2575C2214yes—
105#2573C2214yes—
106#2573C2214yes—
107#2569C2214yes—
108#2558C2214yes—
109#2553C2214yes—
110#2538C2212yes—
111#2538C2212yes—
112#2535C2212yes—
113#2533C2214yes—
114#2533C2214yes—
115#2531C2214yes—
116#2530C2214yes—
117#2530C2214yes—
118#2524C2214yes—
119#2517C2214yes—
120#2515C2214yes—
121#2515C2214yes—
122#2513C2214yes—
123#2511C2212yes—
124#2511C2212yes—
125#2508C2214yes—
126#2507C2212yes—
127#2506C2212yes—
128#2505C2214yes—
129#2505C2214yes—
130#2498C2214yes—
131#2497C2212yes—
132#2496C2212yes—
133#2495C2214yes—
134#2493C2214yes—
135#2489C2212yes—
136#2489C2212yes—
137#2487C2214yes—
138#2487C2212yes—
139#2486C2212yes—
140#2484C2214yes—
141#2481C2214yes—
142#2481C2214yes—
143#2481C2214yes—
144#2475C2214yes—
145#2475C2214yes—
146#2473C2214yes—
147#2471C2214yes—
148#2471C2214yes—
149#2466C2214yes—
150#2466C2214yes—
151#2461C2214yes—
152#2457C2214yes—
153#2457C2214yes—
154#2456C2214yes—
155#2454C2212yes—
156#2454C2212yes—
157#2449C2214yes—
158#2447C2212yes—
159#2447C2212yes—
160#2444C2214yes—
161#2444C2214yes—
162#2438C2214yes—
163#2427C2212yes—
164#2427C2212yes—
165#2425C2214yes—
166#2425C2214yes—
167#2422C2212yes—
168#2422C2212yes—
169#2419C2214yes—
170#2419C2214yes—
171#2419C2214yes—
172#2419C2214yes—
173#2417C2214yes—
174#2413C2214yes—
175#2407C2212yes—
176#2407C2212yes—
177#2402C2214yes—
178#2401C2214yes—
179#2374C2214yes—
180#2364C2214yes—
181#2363C2214yes—
182#2361C2214yes—
183#2361C2214yes—
184#2359C2214yes—
185#2356C2212yes—
186#2355C2212yes—
187#2354C2214yes—
188#2353C2214yes—
189#2352C2214yes—
190#2349C2212yes—
191D4×C4⋊C4C2214yes—
192D4×C4⋊C4C2212yes—
193#2345C2212yes—
194#2344C2212yes—
195#2343C2214yes—
196#2343C2214yes—
197#2339C2212yes—
198#2339C2212yes—
199#2337C2212yes—
200#2336C2212yes—
201#2335C2212yes—
202#2335C2212yes—
203#2335C2214yes—
204#2334C2212yes—
205#2334C2212yes—
206#2333C2214yes—
207#2333C2212yes—
208#2332C2212yes—
209#2330C2212yes—
210#2330C2211yescharacteristic
211#2330C2211yescharacteristic
212#2328C2211yescharacteristic
213#2328C2211yescharacteristic
214#2326C2212yes—
215#2326C2212yes—
216#2324C2212yes—
217#2324C2212yes—
218#2323C2212yes—
219#2320C2212yes—
220#2319C2212yes—
221#2318C2214yes—
222#2314C2212yes—
223#2314C2211yescharacteristic
224#2314C2211yescharacteristic
225#2313C2214yes—
226#2311C2212yes—
227C4×C4⋊Q8C2211yescharacteristic
228C4×C4⋊Q8C2211yescharacteristic
229C4×#127C2211yescharacteristic
230C4×#127C2211yescharacteristic
231C4×#125C2211yescharacteristic
232C4×#125C2211yescharacteristic
233C4×C22⋊Q8C2212yes—
234C4×#123C2214yes—
235C4×#121C2214yes—
236C4×#121C2212yes—
237C4×#121C2212yes—
238#2298C2211yescharacteristic
239#2298C2211yescharacteristic
240#2295C2211yescharacteristic
241#2295C2211yescharacteristic
242#2295C2212yes—
243#2293C2211yescharacteristic
244#2293C2211yescharacteristic
245#2293C2212yes—
246#2290C2211yescharacteristic
247#2290C2211yescharacteristic
248#2290C2211yescharacteristic
249#2290C2211yescharacteristic
250#2290C2214yes—
251C2×#387C2214yes—
252C2×#384C2211yescharacteristic
253#2283C2211yescharacteristic
254#2275C2212yes—
255C42×D4C2212yes—
256C4×#117C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C4×#117C2211yescharacteristic
259C22×#41C2312yes—
260#540—28no—
261#540—28no—
262#532—28no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×#127C2311yescharacteristic
265#529—28no—
266C2×#126C2311yescharacteristic
267C2×#126C2311yescharacteristic
268C2×#126C2314yes—
269C2×#125C2311yescharacteristic
270C2×#125C2311yescharacteristic
271C2×#125C2311yescharacteristic
272C2×#125C2312yes—
273C2×#125C2314yes—
274C2×#124C2312yes—
275C2×#124C2311yescharacteristic
276C2×#123C2311yescharacteristic
277C2×#123C2311yescharacteristic
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×C22⋊Q8C2311yescharacteristic
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×#121C2311yescharacteristic
290C2×#121C2314yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293#520—216no—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×#117C2311yescharacteristic
314C2×#117C2311yescharacteristic
315C2×#117C2311yescharacteristic
316C2×#117C2314yes—
317C2×#117C2311yescharacteristic
318C2×#117C2311yescharacteristic
319C2×#117C2314yes—
320C2×#117C2314yes—
321C2×#117C2311yescharacteristic
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2314yes—
324C22×C4⋊C4C2314yes—
325C22×C4⋊C4C2314yes—
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328C22×C42C2311yescharacteristic
329C22×C42C2314yes—
330#401C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#395C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#392C2314yes—
408#392C2314yes—
409#392C2314yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#390C2312yes—
421#390C2312yes—
422#390C2314yes—
423#390C2314yes—
424#390C2312yes—
425#390C2312yes—
426#390C2314yes—
427#390C2314yes—
428#390C2312yes—
429#390C2312yes—
430#390C2314yes—
431#389C2312yes—
432#389C2312yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2314yes—
440#389C2312yes—
441#389C2312yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
446#389C2312yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2312yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2312yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2312yes—
478#388C2312yes—
479#388C2312yes—
480#388C2312yes—
481#388C2312yes—
482#388C2312yes—
483#388C2312yes—
484#388C2312yes—
485#388C2314yes—
486#388C2312yes—
487#388C2312yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2312yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2312yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2312yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2312yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2312yes—
528#387C2312yes—
529#387C2312yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2314yes—
535#387C2314yes—
536#387C2312yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2312yes—
561#386C2312yes—
562#386C2312yes—
563#386C2312yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2312yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2312yes—
587#385C2312yes—
588#385C2312yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#384C2311yescharacteristic
599#384C2311yescharacteristic
600#384C2312yes—
601#384C2312yes—
602#384C2312yes—
603#384C2314yes—
604#383C2314yes—
605#383C2314yes—
606#383C2314yes—
607#383C2312yes—
608#382C2311yescharacteristic
609#382C2311yescharacteristic
610#382C2312yes—
611#382C2314yes—
612#382C2314yes—
613#382C2314yes—
614#382C2312yes—
615#382C2314yes—
616#381C2314yes—
617#381C2314yes—
618#381C2314yes—
619#381C2314yes—
620#381C2314yes—
621#381C2314yes—
622#381C2314yes—
623#381C2314yes—
624#381C2312yes—
625#380C2314yes—
626#380C2314yes—
627#380C2314yes—
628#380C2314yes—
629#380C2314yes—
630#380C2314yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2314yes—
636#380C2312yes—
637#380C2312yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2312yes—
642#380C2314yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2311yescharacteristic
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2311yescharacteristic
684C4×C22⋊C4C2311yescharacteristic
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2311yescharacteristic
687C4×C22⋊C4C2311yescharacteristic
688C4×C22⋊C4C2311yescharacteristic
689C4×C22⋊C4C2311yescharacteristic
690C4×C22⋊C4C2314yes—
691#376C2311yescharacteristic
692#376C2311yescharacteristic
693#376C2311yescharacteristic
694#376C2311yescharacteristic
695#376C2311yescharacteristic
696#376C2311yescharacteristic
697#376C2314yes—
698#376C2314yes—
699C2×#95C2314yes—
700C2×#95C2314yes—
701C2×#95C2314yes—
702C2×#95C2314yes—
703C43C2311yescharacteristic
704C43C2311yescharacteristic
705C43C2311yescharacteristic
706C43C2311yescharacteristic
707C2×#41—28no—
708C2×#41—28no—
709C2×#41—44no—
710C22×Q8C2412yes—
711C22×Q8C2411yescharacteristic
712C22×D4C2414yes—
713C22×D4C2412yes—
714C22×D4C2414yes—
715C22×D4C2414yes—
716C22×D4C2411yescharacteristic
717C22×D4C2411yescharacteristic
718C22×D4C2411yescharacteristic
719C22×D4C2414yes—
720C23×C4C2411yescharacteristic
721C23×C4C2411yescharacteristic
722C23×C4C2414yes—
723C23×C4C2411yescharacteristic
724C23×C4C2414yes—
725C23×C4C2414yes—
726C23×C4C2412yes—
727C23×C4C2414yes—
728C23×C4C2414yes—
729C23×C4C2411yescharacteristic
730C23×C4C2414yes—
731C23×C4C2411yescharacteristic
732C23×C4C2414yes—
733C23×C4C2414yes—
734C23×C4C2412yes—
735C4⋊Q8—24no—
736#127#4118yes—
737#126—24no—
738#126—24no—
739#126—84no—
740#125—24no—
741#125—24no—
742#125—24no—
743#125—44no—
744#125—84no—
745#124—28no—
746#124—24no—
747#123—216no—
748#123—216no—
749#123—24no—
750#123—24no—
751#123—84no—
752#123—84no—
753#123—84no—
754C22⋊Q8—24no—
755C22⋊Q8—44no—
756C22⋊Q8—44no—
757C22⋊Q8—84no—
758#121—216no—
759#121—216no—
760#121—216no—
761#121—28no—
762#121—28no—
763#121—24no—
764C4×Q8—28no—
765C4×Q8—28no—
766C4×Q8—24no—
767C4×D4—216no—
768C4×D4—28no—
769C4×D4—28no—
770C4×D4—24no—
771C4×D4—24no—
772C4×D4—216no—
773C4×D4—216no—
774C4×D4—28no—
775C4×D4—28no—
776C4×D4—24no—
777C4×D4—44no—
778C4×D4—44no—
779C4×D4—84no—
780C4×D4—84no—
781C4×D4—84no—
782C4×D4—84no—
783#117—216no—
784#117—24no—
785#117—24no—
786#117—24no—
787#117—42no—
788#117—42no—
789#117—84no—
790#117—84no—
791#117#4118yes—
792C2×C4⋊C4—28no—
793C2×C4⋊C4—216no—
794C2×C4⋊C4—84no—
795C2×C4⋊C4—84no—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2411yescharacteristic
857C2×C22⋊C4C2411yescharacteristic
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2411yescharacteristic
863C2×C22⋊C4C2411yescharacteristic
864C2×C22⋊C4C2411yescharacteristic
865C2×C22⋊C4C2411yescharacteristic
866C2×C22⋊C4C2411yescharacteristic
867C2×C22⋊C4C2411yescharacteristic
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2411yescharacteristic
897C2×C22⋊C4C2411yescharacteristic
898C2×C42—24no—
899C2×C42—24no—
900C2×C42—42no—
901C2×C42—84no—
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911C2×C42C2412yes—
912C2×C42C2411yescharacteristic
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2412yes—
931C2×C42C2411yescharacteristic
932C2×C42C2411yescharacteristic
933C2×C42C2411yescharacteristic
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002C24C2511yescharacteristic
1003C24C2511yescharacteristic
1004C24C2514yes—
1005C24C2511yescharacteristic
1006#41—432no—
1007C2×Q8—24no—
1008C2×Q8—24no—
1009C2×Q8—22no—
1010C2×Q8—24no—
1011C2×Q8—42no—
1012C2×D4—28no—
1013C2×D4—28no—
1014C2×D4—22no—
1015C2×D4—22no—
1016C2×D4—28no—
1017C2×D4—28no—
1018C2×D4—24no—
1019C2×D4—22no—
1020C2×D4—24no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—42no—
1027C2×D4—42no—
1028C2×D4—42no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4C2×#4118yes—
1032C2×D4C2×#41116yes—
1033C22×C4—22no—
1034C22×C4—22no—
1035C22×C4—28no—
1036C22×C4—28no—
1037C22×C4—28no—
1038C22×C4—28no—
1039C22×C4—22no—
1040C22×C4—24no—
1041C22×C4—28no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—22no—
1049C22×C4—28no—
1050C22×C4—28no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—44no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4C2×#4114yes—
1076C22×C4C2512yes—
1077C22×C4C2511yescharacteristic
1078C22×C4C2511yescharacteristic
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2514yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2511yescharacteristic
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C22×C4C2511yescharacteristic
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C4⋊C4—28no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—22no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—22no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—28no—
1115C4⋊C4—22no—
1116C4⋊C4—22no—
1117C4⋊C4—22no—
1118C4⋊C4—22no—
1119C4⋊C4—22no—
1120C4⋊C4—22no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4C2×#4114yes—
1158C4⋊C4C2×#4114yes—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—22no—
1164C22⋊C4—22no—
1165C22⋊C4—28no—
1166C22⋊C4—28no—
1167C22⋊C4—28no—
1168C22⋊C4—28no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—22no—
1172C22⋊C4—22no—
1173C22⋊C4—22no—
1174C22⋊C4—22no—
1175C22⋊C4—22no—
1176C22⋊C4—22no—
1177C22⋊C4—44no—
1178C22⋊C4—42no—
1179C22⋊C4—42no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—42no—
1183C22⋊C4—42no—
1184C22⋊C4—42no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4C2×#4114yes—
1204C22⋊C4C2×#4114yes—
1205C42—24no—
1206C42—22no—
1207C42—22no—
1208C42—22no—
1209C42—22no—
1210C42—22no—
1211C42—22no—
1212C42—28no—
1213C42—28no—
1214C42—22no—
1215C42—22no—
1216C42—22no—
1217C42—22no—
1218C42—22no—
1219C42—42no—
1220C42—42no—
1221C42—44no—
1222C42—44no—
1223C42—44no—
1224C42—42no—
1225C42—44no—
1226C42—42no—
1227C42—42no—
1228C42—42no—
1229C42—44no—
1230C42—42no—
1231C42—42no—
1232C42—42no—
1233C42—44no—
1234C42C2×#4114yes—
1235C42C2×#4114yes—
1236C42C2×#4114yes—
1237C23—24no—
1238C23—21no—
1239C23—21no—
1240C23—24no—
1241C23—24no—
1242C23—22no—
1243C23—24no—
1244C23—22no—
1245C23—24no—
1246C23—24no—
1247C23—21no—
1248C23—21no—
1249C23—21no—
1250C23—21no—
1251C23—21no—
1252C23—21no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23C22×#4118yes—
1258C23C22×#4112yes—
1259C23C2611yescharacteristic
1260Q8—48no—
1261Q8—82no—
1262D4—216no—
1263D4—416no—
1264D4—416no—
1265D4—82no—
1266D4—88no—
1267D4—88no—
1268D4—82no—
1269D4—82no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—28no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—24no—
1284C2×C4—21no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—21no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—21no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—416no—
1336C2×C4—48no—
1337C2×C4—44no—
1338C2×C4—44no—
1339C2×C4—88no—
1340C2×C4—82no—
1341C2×C4—88no—
1342C2×C4—82no—
1343C2×C4—88no—
1344C2×C4—88no—
1345C2×C4—88no—
1346C2×C4—88no—
1347C2×C4—84no—
1348C2×C4—164no—
1349C2×C4C22×#4112yes—
1350C2×C4C22×#4112yes—
1351C2×C4C22×#4114yes—
1352C2×C4C22×#4112yes—
1353C2×C4C22×#4112yes—
1354C2×C4C22×#4112yes—
1355C2×C4C22×#4112yes—
1356C2×C4C22×#4112yes—
1357C2×C4#58512yes—
1358C22—28no—
1359C22—28no—
1360C22—22no—
1361C22—22no—
1362C22—22no—
1363C22—28no—
1364C22—42no—
1365C22—44no—
1366C22—44no—
1367C22—44no—
1368C22—42no—
1369C22—44no—
1370C22—42no—
1371C22—42no—
1372C22—41no—
1373C22—41no—
1374C22—41no—
1375C22—41no—
1376C22—42no—
1377C22—42no—
1378C22—41no—
1379C22—41no—
1380C22C23×#4111yescharacteristic
1381C22C23×#4111yescharacteristic
1382C22C2×#58511yescharacteristic
1383C22H(7,𝔽2)12yes—
1384C222−1+612yes—
1385C4—24no—
1386C4—22no—
1387C4—22no—
1388C4—22no—
1389C4—22no—
1390C4—22no—
1391C4—42no—
1392C4—42no—
1393C4—42no—
1394C4—44no—
1395C4—44no—
1396C4—44no—
1397C4—44no—
1398C4—41no—
1399C4—41no—
1400C4—41no—
1401C4—41no—
1402C4—42no—
1403C4—42no—
1404C4—44no—
1405C4—42no—
1406C4—42no—
1407C4—44no—
1408C4—41no—
1409C4—41no—
1410C4—44no—
1411C4#347514yes—
1412C2—48no—
1413C2—42no—
1414C2—81no—
1415C2—81no—
1416C2C2×#347511yescharacteristic
1417C2#6284712yes—
1418C2#6285811yescharacteristic
1419C2#6286111yescharacteristic
1420C2#6288412yes—
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. #44565C2semidirect
2. #44563C2semidirect
3. #43735C2semidirect
4. #43733C2semidirect
5. #39757C2semidirect
6. #39634C2semidirect
7. #39506C2semidirect
8. #39372C2semidirect
9. #39260C2semidirect
10. #39040C2semidirect
11. #38296C2semidirect
12. #38292C2semidirect
13. #38224C2semidirect
14. #38204C2semidirect
15. #38179C2semidirect
16. #38175C2semidirect
17. #37883C2semidirect
18. #37882C2semidirect
19. #37700C2semidirect
20. #37700C2semidirect
21. #35548C2semidirect
22. #35521C2semidirect
23. #35336C2semidirect
24. #35321C2semidirect
25. #35203C2semidirect
26. #34629C2semidirect
27. #34280C2semidirect
28. #34260C2semidirect
29. #34207C2semidirect
30. C4×#540C2semidirect
31. #34081C2semidirect

Maximal subgroups

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

subgroupindex
#445652
#445632
#437352
#437332
#397572
#396342
#395062
#393722
#392602
#390402
#382962
#382922
#382242
#382042
#381792
#381752
#378832
#378822
#377002
#355482
#355212
#353362
#353212
#352032
#346292
#342802
#342602
#342072
C4×#5402
#340812