Finite Group Databasebeta

← #7652522

Subgroups — #7652522

Order 512.

6544 conjugacy classes of subgroups.

The subgroup lattice has 1513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3516C212yesmaximal, complemented
2#42980C211yesmaximal, characteristic, complemented
3#42952C211yesmaximal, characteristic, complemented
4#42884C212yesmaximal, complemented
5#42883C211yesmaximal, characteristic, complemented
6#42810C212yesmaximal, complemented
7#42807C211yesmaximal, characteristic, complemented
8#42393C214yesmaximal, complemented
9#42389C214yesmaximal, complemented
10#42302C214yesmaximal, complemented
11#42301C214yesmaximal, complemented
12#39962C212yesmaximal, complemented
13#39954C212yesmaximal, complemented
14#39848C214yesmaximal, complemented
15#39173C212yesmaximal, complemented
16#39166C212yesmaximal, complemented
17#39118C214yesmaximal, complemented
18#38384C214yesmaximal, complemented
19#38379C214yesmaximal, complemented
20#35625C212yesmaximal, complemented
21#35569C212yesmaximal, complemented
22#35525C212yesmaximal, complemented
23#35331C211yesmaximal, characteristic, complemented
24#35244C212yesmaximal, complemented
25#34880C211yesmaximal, characteristic, complemented
26#34708C212yesmaximal, complemented
27#34254C211yesmaximal, characteristic, complemented
28#3516—232no—
29C2×#557C2212yes—
30C2×#556C2212yes—
31C2×#556C2214yes—
32C2×#554C2212yes—
33C2×#554C2214yes—
34C2×#553C2212yes—
35C2×#553C2214yes—
36C2×#552C2212yes—
37C2×#552C2214yes—
38C2×D4×Q8C2212yes—
39C2×#548C2212yes—
40C2×#548C2212yes—
41C2×#542C2212yes—
42C2×#542C2214yes—
43C2×#541C2212yes—
44C2×#541C2214yes—
45C2×#529C2212yes—
46C2×#529C2212yes—
47C2×#529C2214yes—
48C2×#529C2214yes—
49C2×#520C2212yes—
50C2×#519C2211yescharacteristic
51C22×C4×Q8C2212yes—
52#2862C2211yescharacteristic
53#2858C2211yescharacteristic
54#2852C2214yes—
55#2851C2214yes—
56#2850C2212yes—
57#2823C2212yes—
58#2822C2212yes—
59#2821C2214yes—
60#2820C2214yes—
61#2817C2212yes—
62#2815C2212yes—
63#2734C2212yes—
64#2733C2212yes—
65#2731C2214yes—
66#2730C2214yes—
67#2730C2214yes—
68#2729C2214yes—
69#2729C2214yes—
70#2728C2212yes—
71#2728C2212yes—
72#2728C2214yes—
73#2723C2214yes—
74#2722C2212yes—
75#2721C2214yes—
76#2721C2214yes—
77#2714C2214yes—
78#2695C2214yes—
79#2695C2214yes—
80#2693C2214yes—
81#2693C2212yes—
82#2693C2212yes—
83#2692C2214yes—
84#2692C2214yes—
85#2692C2214yes—
86#2691C2214yes—
87#2690C2214yes—
88#2690C2214yes—
89#2690C2214yes—
90#2690C2214yes—
91#2690C2214yes—
92#2690C2214yes—
93#2676C2214yes—
94#2676C2214yes—
95#2676C2214yes—
96#2675C2212yes—
97#2671C2214yes—
98#2671C2214yes—
99#2664C2214yes—
100#2662C2214yes—
101#2642C2214yes—
102#2640C2212yes—
103#2639C2214yes—
104#2638C2214yes—
105#2637C2214yes—
106#2637C2214yes—
107#2636C2214yes—
108#2635C2214yes—
109#2634C2214yes—
110#2633C2214yes—
111#2631C2214yes—
112#2629C2214yes—
113#2628C2214yes—
114#2621C2211yescharacteristic
115#2619C2211yescharacteristic
116#2611C2214yes—
117#2610C2214yes—
118#2609C2214yes—
119#2609C2212yes—
120#2603C2214yes—
121#2603C2214yes—
122#2601C2214yes—
123#2601C2214yes—
124#2600C2212yes—
125#2600C2212yes—
126#2599C2214yes—
127#2598C2214yes—
128#2598C2214yes—
129#2592C2212yes—
130#2567C2212yes—
131#2565C2214yes—
132#2564C2214yes—
133#2562C2214yes—
134#2562C2214yes—
135#2560C2214yes—
136#2560C2214yes—
137#2560C2214yes—
138#2557C2214yes—
139#2557C2214yes—
140#2557C2214yes—
141#2556C2214yes—
142#2556C2212yes—
143#2555C2212yes—
144#2555C2214yes—
145#2554C2212yes—
146#2553C2212yes—
147#2547C2212yes—
148#2547C2214yes—
149#2543C2214yes—
150#2540C2212yes—
151#2537C2212yes—
152#2535C2214yes—
153#2535C2214yes—
154#2521C2212yes—
155#2521C2214yes—
156#2519C2212yes—
157#2512C2214yes—
158#2481C2214yes—
159#2481C2214yes—
160#2481C2214yes—
161#2481C2214yes—
162#2473C2214yes—
163#2473C2214yes—
164#2469C2214yes—
165#2469C2214yes—
166#2467C2214yes—
167#2467C2214yes—
168#2464C2212yes—
169#2462C2214yes—
170#2461C2212yes—
171#2461C2214yes—
172#2460C2214yes—
173#2458C2214yes—
174#2456C2214yes—
175#2454C2212yes—
176#2454C2212yes—
177#2453C2212yes—
178#2453C2212yes—
179#2448C2212yes—
180#2448C2212yes—
181#2446C2212yes—
182#2446C2212yes—
183#2443C2214yes—
184#2443C2214yes—
185#2442C2212yes—
186#2442C2212yes—
187#2442C2212yes—
188#2442C2212yes—
189#2436C2212yes—
190#2434C2212yes—
191#2432C2212yes—
192#2431C2212yes—
193#2429C2212yes—
194#2428C2212yes—
195#2427C2212yes—
196#2426C2212yes—
197#2422C2214yes—
198#2421C2212yes—
199#2421C2212yes—
200#2421C2212yes—
201#2421C2212yes—
202#2417C2212yes—
203#2417C2212yes—
204#2417C2212yes—
205#2416C2212yes—
206#2416C2212yes—
207#2416C2212yes—
208#2415C2212yes—
209#2414C2212yes—
210#2409C2212yes—
211#2409C2212yes—
212#2407C2212yes—
213#2407C2212yes—
214#2399C2211yescharacteristic
215#2398C2214yes—
216#2397C2211yescharacteristic
217#2396C2214yes—
218#2392C2211yescharacteristic
219#2392C2211yescharacteristic
220#2356C2214yes—
221#2355C2214yes—
222#2343C2214yes—
223#2343C2214yes—
224#2328C2211yescharacteristic
225#2327C2211yescharacteristic
226#2326C2214yes—
227#2325C2214yes—
228#2324C2214yes—
229#2324C2214yes—
230#2324C2212yes—
231#2323C2212yes—
232#2320C2212yes—
233#2320C2212yes—
234#2317C2211yescharacteristic
235#2310C2211yescharacteristic
236C4×#124C2212yes—
237C4×#124C2212yes—
238C4×C22⋊Q8C2212yes—
239C4×#121C2212yes—
240C4×#121C2214yes—
241C4×#121C2212yes—
242#2296C2211yescharacteristic
243#2295C2212yes—
244#2295C2212yes—
245C2×#391C2211yescharacteristic
246#2293C2211yescharacteristic
247#2290C2212yes—
248#2290C2214yes—
249#2274C2211yescharacteristic
250C42×D4C2211yescharacteristic
251C4×#117C2211yescharacteristic
252C22×#41C2312yes—
253C23×Q8C2312yes—
254C23×Q8C2311yescharacteristic
255#557—216no—
256#556—232no—
257#556—216no—
258#554—232no—
259#554—216no—
260#553—232no—
261#553—216no—
262#552—232no—
263#552—216no—
264D4×Q8—216no—
265#548—216no—
266#548—216no—
267#542—216no—
268#542—232no—
269#541—216no—
270#541—232no—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2314yes—
275C2×C4⋊Q8C2311yescharacteristic
276C2×#127C2311yescharacteristic
277#529—216no—
278#529—232no—
279#529—216no—
280#529—232no—
281C2×#126C2314yes—
282C2×#126C2314yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#126C2314yes—
288C2×#126C2312yes—
289C2×#126C2314yes—
290C2×#126C2312yes—
291C2×#125C2314yes—
292C2×#125C2314yes—
293C2×#125C2314yes—
294C2×#125C2314yes—
295C2×#125C2312yes—
296C2×#125C2314yes—
297C2×#125C2312yes—
298C2×#125C2314yes—
299C2×#125C2312yes—
300C2×#124C2314yes—
301C2×#124C2312yes—
302C2×#124C2312yes—
303C2×#124C2314yes—
304C2×#124C2312yes—
305C2×#124C2314yes—
306C2×#124C2314yes—
307C2×#124C2312yes—
308C2×#124C2312yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×#123C2312yes—
312C2×#123C2314yes—
313C2×#123C2312yes—
314C2×#123C2314yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2312yes—
330C2×#121C2312yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2312yes—
334C2×#121C2314yes—
335C2×#121C2312yes—
336C2×#121C2312yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2314yes—
340C2×#121C2312yes—
341C2×#121C2312yes—
342C2×#121C2314yes—
343#520—216no—
344#519D4116yescomplemented
345C2×C4×Q8—216no—
346C2×C4×Q8C2314yes—
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2314yes—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2314yes—
353C2×C4×Q8C2312yes—
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2314yes—
357C2×C4×D4C2314yes—
358C2×C4×D4C2314yes—
359C2×C4×D4C2314yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2314yes—
363C2×C4×D4C2314yes—
364C2×C4×D4C2314yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2314yes—
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2312yes—
373C2×C4×D4C2314yes—
374C2×C4×D4C2312yes—
375C2×#117C2312yes—
376C2×#117C2314yes—
377C2×#117C2314yes—
378C2×#117C2314yes—
379C2×#117C2314yes—
380C2×#117C2311yescharacteristic
381C2×#117C2311yescharacteristic
382C2×#117C2311yescharacteristic
383C2×#117C2314yes—
384C2×#117C2311yescharacteristic
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2314yes—
387C22×C4⋊C4C2312yes—
388C22×C4⋊C4C2314yes—
389C22×C4⋊C4C2311yescharacteristic
390C22×C42C2314yes—
391C22×C42C2312yes—
392C22×C42C2311yescharacteristic
393#400C2314yes—
394#400C2314yes—
395#400C2314yes—
396#400C2314yes—
397#400C2314yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#399C2314yes—
406#399C2312yes—
407#399C2314yes—
408#399C2314yes—
409#399C2314yes—
410#399C2314yes—
411#399C2312yes—
412#398C2312yes—
413#398C2312yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2311yescharacteristic
422#398C2314yes—
423#398C2314yes—
424#398C2311yescharacteristic
425#398C2312yes—
426#398C2314yes—
427#398C2314yes—
428#398C2312yes—
429#398C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2311yescharacteristic
434#397C2312yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2311yescharacteristic
441#397C2314yes—
442#397C2314yes—
443#397C2312yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2312yes—
456#396C2314yes—
457#396C2312yes—
458#396C2314yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#395C2312yes—
463#395C2314yes—
464#395C2314yes—
465#395C2312yes—
466#395C2314yes—
467#394C2312yes—
468#394C2312yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2311yescharacteristic
481#394C2314yes—
482#394C2312yes—
483#394C2312yes—
484#394C2311yescharacteristic
485#393C2314yes—
486#393C2314yes—
487#393C2314yes—
488#393C2314yes—
489#393C2314yes—
490#393C2314yes—
491#393C2314yes—
492#392C2314yes—
493#392C2314yes—
494#392C2311yescharacteristic
495#392C2312yes—
496#392C2314yes—
497#392C2312yes—
498#392C2312yes—
499#392C2314yes—
500#392C2314yes—
501#392C2314yes—
502#392C2311yescharacteristic
503#392C2312yes—
504#392C2314yes—
505#391C2314yes—
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2312yes—
510#391C2312yes—
511#391C2312yes—
512#391C2312yes—
513#391C2312yes—
514#391C2312yes—
515#391C2312yes—
516#391C2312yes—
517#391C2314yes—
518#391C2312yes—
519#391C2312yes—
520#391C2312yes—
521#390C2314yes—
522#390C2314yes—
523#390C2314yes—
524#390C2314yes—
525#390C2312yes—
526#390C2312yes—
527#390C2314yes—
528#390C2314yes—
529#390C2312yes—
530#390C2312yes—
531#390C2312yes—
532#390C2312yes—
533#390C2314yes—
534#390C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2312yes—
547#389C2314yes—
548#389C2312yes—
549#389C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2312yes—
558#388C2312yes—
559#388C2314yes—
560#388C2314yes—
561#388C2312yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2312yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2312yes—
575#388C2312yes—
576#388C2314yes—
577#388C2312yes—
578#388C2312yes—
579#388C2314yes—
580#388C2312yes—
581#388C2312yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#387C2312yes—
605#387C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2312yes—
617#386C2314yes—
618#386C2314yes—
619#386C2312yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2312yes—
630#386C2314yes—
631#386C2312yes—
632#385C2314yes—
633#385C2314yes—
634#385C2312yes—
635#385C2312yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2312yes—
646#385C2314yes—
647#385C2314yes—
648#385C2312yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#384C2314yes—
654#384C2312yes—
655#383C2314yes—
656#383C2314yes—
657#382C2314yes—
658#382C2312yes—
659#382C2312yes—
660#382C2314yes—
661#382C2311yescharacteristic
662#382C2311yescharacteristic
663#382C2312yes—
664#381C2312yes—
665#381C2312yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2312yes—
674#380C2314yes—
675#380C2312yes—
676#380C2312yes—
677#380C2314yes—
678#380C2314yes—
679#380C2312yes—
680#380C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707#376C2311yescharacteristic
708#376C2311yescharacteristic
709#376C2314yes—
710#376C2314yes—
711C2×#95C2314yes—
712C43C2311yescharacteristic
713C43C2311yescharacteristic
714C2×#41—28no—
715C2×#41—44no—
716C2×#41—44no—
717C22×Q8—28no—
718C22×Q8—42no—
719C22×Q8—42no—
720C22×Q8—44no—
721C22×Q8—44no—
722C22×Q8C2×D418yes—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×Q8C2414yes—
727C22×Q8C2412yes—
728C22×Q8C2412yes—
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2414yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2414yes—
736C22×D4C2412yes—
737C22×D4C2414yes—
738C22×D4C2412yes—
739C22×D4C2411yescharacteristic
740C22×D4C2412yes—
741C22×D4C2414yes—
742C22×D4C2412yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2411yescharacteristic
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C23×C4C2414yes—
752C23×C4C2414yes—
753C23×C4C2414yes—
754C23×C4C2412yes—
755C23×C4C2412yes—
756C23×C4C2412yes—
757C4⋊Q8—28no—
758C4⋊Q8—216no—
759C4⋊Q8—216no—
760C4⋊Q8—28no—
761C4⋊Q8—42no—
762#127—42no—
763#126—216no—
764#126—216no—
765#126—216no—
766#126—216no—
767#126—28no—
768#126—216no—
769#126—28no—
770#126—216no—
771#126—216no—
772#126—216no—
773#125—216no—
774#125—28no—
775#125—28no—
776#125—216no—
777#125—28no—
778#125—216no—
779#125—216no—
780#125—216no—
781#125—216no—
782#124—28no—
783#124—216no—
784#124—28no—
785#124—216no—
786#124—216no—
787#124—28no—
788#124—44no—
789#124—48no—
790#124—44no—
791#123—216no—
792#123—28no—
793#123—28no—
794#123—216no—
795#123—216no—
796#123—216no—
797C22⋊Q8—28no—
798C22⋊Q8—216no—
799C22⋊Q8—28no—
800C22⋊Q8—216no—
801C22⋊Q8—28no—
802C22⋊Q8—216no—
803C22⋊Q8—216no—
804C22⋊Q8—28no—
805C22⋊Q8—28no—
806C22⋊Q8—216no—
807C22⋊Q8—216no—
808C22⋊Q8—216no—
809C22⋊Q8—216no—
810C22⋊Q8—44no—
811C22⋊Q8—44no—
812#121—28no—
813#121—216no—
814#121—28no—
815#121—216no—
816#121—216no—
817#121—28no—
818#121—44no—
819#121—48no—
820#121—48no—
821#121—48no—
822#121—48no—
823#121—44no—
824#121—44no—
825C4×Q8—28no—
826C4×Q8—28no—
827C4×Q8—28no—
828C4×Q8—216no—
829C4×Q8—28no—
830C4×Q8—216no—
831C4×Q8—216no—
832C4×Q8—28no—
833C4×Q8C2×D4116yes—
834C4×Q8C2×D4132yes—
835C4×Q8C2×D4116yes—
836C4×D4—28no—
837C4×D4—216no—
838C4×D4—28no—
839C4×D4—216no—
840C4×D4—28no—
841C4×D4—216no—
842C4×D4—28no—
843C4×D4—216no—
844C4×D4—216no—
845C4×D4—28no—
846C4×D4—216no—
847C4×D4—216no—
848C4×D4—216no—
849C4×D4—44no—
850C4×D4—42no—
851C4×D4—42no—
852C4×D4—44no—
853C4×D4—48no—
854#117—28no—
855#117—216no—
856#117—216no—
857#117—216no—
858#117—216no—
859#117—42no—
860#117—42no—
861#117C2×D418yes—
862#117C2×D4132yes—
863#117C2×D418yes—
864C2×C4⋊C4—28no—
865C2×C4⋊C4—216no—
866C2×C4⋊C4—28no—
867C2×C4⋊C4—216no—
868C2×C4⋊C4—42no—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2411yescharacteristic
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2411yescharacteristic
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2411yescharacteristic
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2411yescharacteristic
949C2×C22⋊C4C2411yescharacteristic
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2412yes—
979C2×C42—28no—
980C2×C42—216no—
981C2×C42—42no—
982C2×C42C2412yes—
983C2×C42C2414yes—
984C2×C42C2412yes—
985C2×C42C2414yes—
986C2×C42C2411yescharacteristic
987C2×C42C2411yescharacteristic
988C2×C42C2411yescharacteristic
989C2×C42C2412yes—
990C2×C42C2414yes—
991C2×C42C2414yes—
992C2×C42C2412yes—
993C2×C42C2411yescharacteristic
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2414yes—
997C2×C42C2412yes—
998C2×C42C2414yes—
999C2×C42C2412yes—
1000C2×C42C2412yes—
1001C2×C42C2412yes—
1002C2×C42C2411yescharacteristic
1003C2×C42C2414yes—
1004C2×C42C2412yes—
1005C2×C42C2414yes—
1006C2×C42C2411yescharacteristic
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2411yescharacteristic
1023#95C2411yescharacteristic
1024#95C2414yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2411yescharacteristic
1041#95C2412yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2412yes—
1048#95C2411yescharacteristic
1049#95C2414yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2414yes—
1060#95C2414yes—
1061C24C2512yes—
1062C24C2514yes—
1063C24C2511yescharacteristic
1064C24C2512yes—
1065#41—432no—
1066C2×Q8—28no—
1067C2×Q8—24no—
1068C2×Q8—28no—
1069C2×Q8—24no—
1070C2×Q8—24no—
1071C2×Q8—24no—
1072C2×Q8—24no—
1073C2×Q8—24no—
1074C2×Q8—42no—
1075C2×Q8—42no—
1076C2×Q8—44no—
1077C2×Q8—44no—
1078C2×Q8—42no—
1079C2×Q8—44no—
1080C2×Q8—42no—
1081C2×Q8—44no—
1082C2×Q8—416no—
1083C2×Q8—432no—
1084C2×Q8C22×D418yes—
1085C2×Q8C22×D418yes—
1086C2×D4—24no—
1087C2×D4—24no—
1088C2×D4—28no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—24no—
1092C2×D4—28no—
1093C2×D4—28no—
1094C2×D4—24no—
1095C2×D4—28no—
1096C2×D4—24no—
1097C2×D4—28no—
1098C2×D4—24no—
1099C2×D4—24no—
1100C2×D4—24no—
1101C2×D4—41no—
1102C2×D4—42no—
1103C2×D4—44no—
1104C2×D4—42no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—42no—
1108C2×D4—41no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—42no—
1112C2×D4—44no—
1113C2×D4—42no—
1114C2×D4—42no—
1115C2×D4—42no—
1116C2×D4—44no—
1117C2×D4—44no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—42no—
1121C2×D4—42no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C22×C4—22no—
1125C22×C4—22no—
1126C22×C4—24no—
1127C22×C4—24no—
1128C22×C4—28no—
1129C22×C4—24no—
1130C22×C4—28no—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—24no—
1135C22×C4—24no—
1136C22×C4—24no—
1137C22×C4—28no—
1138C22×C4—28no—
1139C22×C4—28no—
1140C22×C4—28no—
1141C22×C4—42no—
1142C22×C4—42no—
1143C22×C4—42no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—42no—
1149C22×C4—44no—
1150C22×C4—42no—
1151C22×C4—44no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4—42no—
1155C22×C4—42no—
1156C22×C4—44no—
1157C22×C4—44no—
1158C22×C4—44no—
1159C22×C4—44no—
1160C22×C4—42no—
1161C22×C4—42no—
1162C22×C4—44no—
1163C22×C4C22×D414yes—
1164C22×C4C22×D418yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2511yescharacteristic
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2514yes—
1170C22×C4C2511yescharacteristic
1171C22×C4C2514yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2514yes—
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2514yes—
1177C22×C4C2512yes—
1178C22×C4C2514yes—
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2512yes—
1182C22×C4C2514yes—
1183C22×C4C2512yes—
1184C22×C4C2512yes—
1185C22×C4C2514yes—
1186C22×C4C2511yescharacteristic
1187C22×C4C2511yescharacteristic
1188C4⋊C4—24no—
1189C4⋊C4—28no—
1190C4⋊C4—28no—
1191C4⋊C4—24no—
1192C4⋊C4—28no—
1193C4⋊C4—24no—
1194C4⋊C4—28no—
1195C4⋊C4—28no—
1196C4⋊C4—28no—
1197C4⋊C4—24no—
1198C4⋊C4—28no—
1199C4⋊C4—24no—
1200C4⋊C4—28no—
1201C4⋊C4—28no—
1202C4⋊C4—28no—
1203C4⋊C4—28no—
1204C4⋊C4—24no—
1205C4⋊C4—28no—
1206C4⋊C4—24no—
1207C4⋊C4—28no—
1208C4⋊C4—28no—
1209C4⋊C4—28no—
1210C4⋊C4—28no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—28no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—42no—
1218C4⋊C4—44no—
1219C4⋊C4—42no—
1220C4⋊C4—42no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—42no—
1226C4⋊C4—41no—
1227C4⋊C4—41no—
1228C4⋊C4—42no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—42no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—42no—
1238C4⋊C4—42no—
1239C4⋊C4C22×D418yes—
1240C4⋊C4C22×D4116yes—
1241C4⋊C4C22×D4116yes—
1242C4⋊C4C22×D418yes—
1243C22⋊C4—24no—
1244C22⋊C4—28no—
1245C22⋊C4—24no—
1246C22⋊C4—24no—
1247C22⋊C4—28no—
1248C22⋊C4—28no—
1249C22⋊C4—24no—
1250C22⋊C4—28no—
1251C22⋊C4—24no—
1252C22⋊C4—24no—
1253C22⋊C4—28no—
1254C22⋊C4—24no—
1255C22⋊C4—28no—
1256C22⋊C4—28no—
1257C22⋊C4—28no—
1258C22⋊C4—28no—
1259C22⋊C4—28no—
1260C22⋊C4—24no—
1261C22⋊C4—24no—
1262C22⋊C4—28no—
1263C22⋊C4—28no—
1264C22⋊C4—28no—
1265C22⋊C4—28no—
1266C22⋊C4—24no—
1267C22⋊C4—44no—
1268C22⋊C4—42no—
1269C22⋊C4—42no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—41no—
1273C22⋊C4—41no—
1274C22⋊C4—42no—
1275C22⋊C4—42no—
1276C22⋊C4—42no—
1277C22⋊C4—42no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—44no—
1281C22⋊C4—42no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—42no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—42no—
1296C22⋊C4C22×D418yes—
1297C22⋊C4C22×D418yes—
1298C42—24no—
1299C42—28no—
1300C42—28no—
1301C42—24no—
1302C42—24no—
1303C42—28no—
1304C42—28no—
1305C42—24no—
1306C42—22no—
1307C42—22no—
1308C42—22no—
1309C42—22no—
1310C42—42no—
1311C42—42no—
1312C42—42no—
1313C42—42no—
1314C42—42no—
1315C42—44no—
1316C42—42no—
1317C42—44no—
1318C42C22×D414yes—
1319C42C22×D4116yes—
1320C42C22×D418yes—
1321C42C22×D4116yes—
1322C42C22×D414yes—
1323C23—22no—
1324C23—22no—
1325C23—21no—
1326C23—21no—
1327C23—22no—
1328C23—22no—
1329C23—22no—
1330C23—22no—
1331C23—22no—
1332C23—22no—
1333C23—24no—
1334C23—22no—
1335C23—22no—
1336C23—22no—
1337C23—24no—
1338C23—24no—
1339C23—24no—
1340C23—22no—
1341C23—22no—
1342C23—24no—
1343C23—24no—
1344C23—22no—
1345C23—24no—
1346C23—22no—
1347C23C23×D412yes—
1348C23#58514yes—
1349C23C2611yescharacteristic
1350Q8—216no—
1351Q8—48no—
1352Q8—416no—
1353Q8—48no—
1354Q8—84no—
1355Q8—88no—
1356D4—416no—
1357D4—48no—
1358D4—416no—
1359D4—48no—
1360D4—44no—
1361D4—48no—
1362D4—88no—
1363D4—84no—
1364D4—88no—
1365D4—84no—
1366D4—82no—
1367D4—162no—
1368D4—162no—
1369D4—164no—
1370C2×C4—21no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—21no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—28no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—24no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—22no—
1397C2×C4—24no—
1398C2×C4—24no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—24no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—24no—
1412C2×C4—24no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—24no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—48no—
1429C2×C4—48no—
1430C2×C4—416no—
1431C2×C4—416no—
1432C2×C4—48no—
1433C2×C4—48no—
1434C2×C4—88no—
1435C2×C4—84no—
1436C2×C4—88no—
1437C2×C4—88no—
1438C2×C4—88no—
1439C2×C4—84no—
1440C2×C4—162no—
1441C2×C4C23×D414yes—
1442C2×C4C23×D418yes—
1443C2×C4C23×D418yes—
1444C2×C4C23×D414yes—
1445C2×C4C23×D412yes—
1446C2×C4C23×D412yes—
1447C2×C4#58512yes—
1448C2×C4#58512yes—
1449C22—24no—
1450C22—24no—
1451C22—24no—
1452C22—22no—
1453C22—24no—
1454C22—42no—
1455C22—41no—
1456C22—41no—
1457C22—42no—
1458C22—42no—
1459C22—42no—
1460C22—42no—
1461C22—44no—
1462C22—42no—
1463C22—42no—
1464C22—44no—
1465C22—44no—
1466C22—42no—
1467C22—42no—
1468C22—44no—
1469C22—44no—
1470C22—42no—
1471C22—42no—
1472C22—44no—
1473C22—42no—
1474C22—44no—
1475C22C24×D411yescharacteristic
1476C22C2×#58512yes—
1477C22C2×#58511yescharacteristic
1478C22C2×#58511yescharacteristic
1479C222−1+612yes—
1480C4—24no—
1481C4—28no—
1482C4—24no—
1483C4—22no—
1484C4—28no—
1485C4—42no—
1486C4—42no—
1487C4—44no—
1488C4—44no—
1489C4—42no—
1490C4—42no—
1491C4—44no—
1492C4—41no—
1493C4—41no—
1494C4—41no—
1495C4—41no—
1496C4—42no—
1497C4—42no—
1498C4—44no—
1499C4—42no—
1500C4—42no—
1501C4—44no—
1502C4#344914yes—
1503C2—44no—
1504C2—42no—
1505C2—84no—
1506C2—82no—
1507C2C2×#344911yescharacteristic
1508C2#6282911yescharacteristic
1509C2#6289111yescharacteristic
1510C2#6297112yes—
1511C2#6300212yes—
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. C2×#3516C2semidirect
2. #42980C2semidirect
3. #42952C2semidirect
4. #42884C2semidirect
5. #42883C2semidirect
6. #42810C2semidirect
7. #42807C2semidirect
8. #42393C2semidirect
9. #42389C2semidirect
10. #42302C2semidirect
11. #42301C2semidirect
12. #39962C2semidirect
13. #39954C2semidirect
14. #39848C2semidirect
15. #39173C2semidirect
16. #39166C2semidirect
17. #39118C2semidirect
18. #38384C2semidirect
19. #38379C2semidirect
20. #35625C2semidirect
21. #35569C2semidirect
22. #35525C2semidirect
23. #35331C2semidirect
24. #35244C2semidirect
25. #34880C2semidirect
26. #34708C2semidirect
27. #34254C2semidirect
344. #519D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35162
#429802
#429522
#428842
#428832
#428102
#428072
#423932
#423892
#423022
#423012
#399622
#399542
#398482
#391732
#391662
#391182
#383842
#383792
#356252
#355692
#355252
#353312
#352442
#348802
#347082
#342542