Finite Group Databasebeta

← #7681615

Subgroups — #7681615

Order 512.

4644 conjugacy classes of subgroups.

The subgroup lattice has 1454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59365C214yesmaximal, complemented
2#59358C214yesmaximal, complemented
3#59355C214yesmaximal, complemented
4#59354C214yesmaximal, complemented
5#44851C214yesmaximal, complemented
6#44789C214yesmaximal, complemented
7#44471C214yesmaximal, complemented
8#43972C214yesmaximal, complemented
9#39758C211yesmaximal, characteristic, complemented
10#39629C211yesmaximal, characteristic, complemented
11#39045C212yesmaximal, complemented
12#39043C212yesmaximal, complemented
13#38972C211yesmaximal, characteristic, complemented
14#38970C211yesmaximal, characteristic, complemented
15#37939C212yesmaximal, complemented
16#37749C212yesmaximal, complemented
17#36539C211yesmaximal, characteristic, complemented
18#36509C211yesmaximal, characteristic, complemented
19#36195C211yesmaximal, characteristic, complemented
20#36151C211yesmaximal, characteristic, complemented
21#35646C212yesmaximal, complemented
22#35586C212yesmaximal, complemented
23#35344C211yesmaximal, characteristic, complemented
24#35270C212yesmaximal, complemented
25#34971C211yesmaximal, characteristic, complemented
26#34909C211yesmaximal, characteristic
27#34221C212yesmaximal, complemented
28#34197C211yesmaximal, characteristic, complemented
29#34192C211yesmaximal, characteristic, complemented
30#34123C211yesmaximal, characteristic, complemented
31C4×#536C211yesmaximal, characteristic, complemented
32C2×#536C2211yescharacteristic
33C2×#533C2212yes—
34C2×C4×#41C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37#2864C2211yescharacteristic
38#2864C2211yescharacteristic
39#2862C2211yescharacteristic
40#2862C2211yescharacteristic
41#2857C2212yes—
42#2855C2212yes—
43#2854C2212yes—
44#2850C2212yes—
45#2806C2214yes—
46#2805C2214yes—
47#2798C2214yes—
48#2776C2214yes—
49#2775C2214yes—
50#2774C2214yes—
51#2773C2214yes—
52#2766C2214yes—
53#2763C2214yes—
54#2762C2214yes—
55#2759C2214yes—
56#2747C2214yes—
57#2746C2214yes—
58#2745C2214yes—
59#2738C2214yes—
60#2737C2214yes—
61#2717C2214yes—
62#2706C2214yes—
63#2698C2214yes—
64#2696C2214yes—
65#2694C2214yes—
66#2692C2214yes—
67#2690C2214yes—
68#2687C2214yes—
69#2647C2212yes—
70#2645C2212yes—
71#2644C2212yes—
72#2640C2212yes—
73#2628C2212yes—
74#2628C2212yes—
75#2612C2214yes—
76#2607C2214yes—
77#2607C2214yes—
78#2605C2214yes—
79#2605C2214yes—
80#2605C2214yes—
81#2602C2214yes—
82#2600C2214yes—
83#2599C2212yes—
84#2599C2214yes—
85#2598C2212yes—
86#2594C2214yes—
87#2590C2214yes—
88#2581C2211yescharacteristic
89#2581C2211yescharacteristic
90#2581C2211yescharacteristic
91#2580C2211yescharacteristic
92#2578C2214yes—
93#2577C2214yes—
94#2576C2214yes—
95#2575C2214yes—
96#2575C2214yes—
97#2574C2214yes—
98#2574C2214yes—
99#2574C2214yes—
100#2572C2214yes—
101#2572C2214yes—
102#2557C2214yes—
103#2553C2214yes—
104#2536C2211yescharacteristic
105#2536C2211yescharacteristic
106#2536C2211yescharacteristic
107#2535C2211yescharacteristic
108#2532C2214yes—
109#2532C2214yes—
110#2532C2214yes—
111#2531C2214yes—
112#2530C2214yes—
113#2530C2214yes—
114#2529C2214yes—
115#2528C2214yes—
116#2528C2214yes—
117#2527C2214yes—
118#2527C2214yes—
119#2527C2214yes—
120#2527C2214yes—
121#2527C2214yes—
122#2525C2214yes—
123#2524C2214yes—
124#2524C2214yes—
125#2523C2214yes—
126#2521C2214yes—
127#2520C2214yes—
128#2520C2214yes—
129#2520C2214yes—
130#2517C2214yes—
131#2516C2214yes—
132#2515C2214yes—
133#2515C2214yes—
134#2515C2214yes—
135#2514C2214yes—
136#2514C2212yes—
137#2513C2212yes—
138#2510C2214yes—
139#2508C2212yes—
140#2507C2212yes—
141#2496C2212yes—
142#2494C2212yes—
143#2492C2212yes—
144#2491C2212yes—
145#2489C2214yes—
146#2488C2214yes—
147#2486C2212yes—
148#2485C2212yes—
149#2484C2212yes—
150#2477C2214yes—
151#2471C2214yes—
152#2468C2214yes—
153#2466C2214yes—
154#2465C2214yes—
155#2459C2214yes—
156#2458C2214yes—
157#2453C2214yes—
158#2451C2212yes—
159#2451C2212yes—
160#2450C2214yes—
161#2448C2212yes—
162#2447C2214yes—
163#2446C2212yes—
164#2429C2212yes—
165#2426C2212yes—
166#2421C2212yes—
167#2421C2212yes—
168#2419C2214yes—
169#2415C2214yes—
170#2409C2212yes—
171#2407C2212yes—
172#2406C2212yes—
173#2399C2212yes—
174#2398C2212yes—
175#2395C2212yes—
176#2388C2212yes—
177#2374C2214yes—
178#2373C2214yes—
179#2372C2214yes—
180#2371C2214yes—
181#2371C2214yes—
182#2368C2214yes—
183#2368C2214yes—
184#2362C2214yes—
185#2357C2211yescharacteristic
186#2357C2211yescharacteristic
187#2357C2212yes—
188#2357C2212yes—
189#2356C2212yes—
190#2356C2214yes—
191#2356C2211yescharacteristic
192#2356C2211yescharacteristic
193#2356C2212yes—
194#2356C2212yes—
195#2356C2214yes—
196#2353C2212yes—
197#2353C2212yes—
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2349C2212yes—
203#2346C2212yes—
204#2346C2214yes—
205#2346C2212yes—
206#2345C2212yes—
207#2345C2214yes—
208#2343C2212yes—
209#2343C2212yes—
210#2343C2214yes—
211#2343C2214yes—
212#2341C2212yes—
213Q8×C22⋊C4C2212yes—
214#2339C2212yes—
215#2331C2212yes—
216#2331C2212yes—
217#2331C2212yes—
218#2327C2211yescharacteristic
219#2327C2211yescharacteristic
220#2327C2212yes—
221#2326C2211yescharacteristic
222#2326C2211yescharacteristic
223#2323C2214yes—
224#2322C2214yes—
225#2320C2214yes—
226#2320C2212yes—
227#2320C2212yes—
228#2320C2212yes—
229#2319C2212yes—
230#2319C2214yes—
231#2317C2211yescharacteristic
232#2311C2211yescharacteristic
233#2310C2211yescharacteristic
234C4×C4⋊Q8C2211yescharacteristic
235C4×C4⋊Q8C2211yescharacteristic
236C4×#124C2211yescharacteristic
237C4×#124C2211yescharacteristic
238C4×C22⋊Q8C2212yes—
239C4×C22⋊Q8C2214yes—
240C4×C22⋊Q8C2212yes—
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×#123C2214yes—
245C4×#123C2214yes—
246C4×#121C2212yes—
247#2295C2211yescharacteristic
248#2295C2211yescharacteristic
249#2290C2212yes—
250#2290C2212yes—
251#2290C2214yes—
252#2283C2212yes—
253#2283C2211yescharacteristic
254#2283C2211yescharacteristic
255#2283C2212yes—
256#2283C2211yescharacteristic
257#2283C2212yes—
258#2283C2212yes—
259#2283C2212yes—
260#2283C2212yes—
261#2276C2212yes—
262#2276C2212yes—
263C42×D4C2211yescharacteristic
264C42×D4C2211yescharacteristic
265C4×#117C2211yescharacteristic
266C2×#376C2212yes—
267C22×#41C2311yescharacteristic
268C22×#41C2311yescharacteristic
269C23×Q8C2311yescharacteristic
270#536—28no—
271#533—216no—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2311yescharacteristic
276C2×#126C2314yes—
277C2×#125C2314yes—
278C2×#124C2311yescharacteristic
279C2×#124C2311yescharacteristic
280C2×#124C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×#121C2312yes—
291C4×#41—28no—
292C4×#41—28no—
293C2×C4×Q8—28no—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2314yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2311yescharacteristic
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×#117C2311yescharacteristic
321C2×#117C2311yescharacteristic
322C2×#117C2312yes—
323C2×#117C2312yes—
324C2×#117C2314yes—
325C2×#117C2311yescharacteristic
326C2×#117C2311yescharacteristic
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2312yes—
329C22×C42C2312yes—
330C22×C42C2312yes—
331C22×C42C2312yes—
332C22×C42C2312yes—
333C22×C42C2312yes—
334C22×C42C2311yescharacteristic
335#401C2314yes—
336#401C2314yes—
337#401C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2312yes—
346#400C2312yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2312yes—
358#399C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2312yes—
364#398C2312yes—
365#398C2314yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2312yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2312yes—
394#395C2312yes—
395#395C2312yes—
396#395C2314yes—
397#395C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2312yes—
402#394C2314yes—
403#394C2312yes—
404#394C2312yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2312yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#392C2312yes—
414#392C2314yes—
415#391C2311yescharacteristic
416#391C2311yescharacteristic
417#391C2311yescharacteristic
418#391C2311yescharacteristic
419#391C2311yescharacteristic
420#391C2314yes—
421#391C2311yescharacteristic
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#390C2312yes—
448#390C2312yes—
449#390C2314yes—
450#390C2314yes—
451#390C2312yes—
452#390C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2312yes—
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#388C2312yes—
508#388C2312yes—
509#388C2312yes—
510#388C2314yes—
511#387C2312yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
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#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#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2312yes—
559#387C2312yes—
560#387C2312yes—
561#387C2312yes—
562#387C2312yes—
563#387C2312yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#386C2314yes—
570#386C2312yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2312yes—
578#386C2312yes—
579#386C2312yes—
580#386C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2312yes—
589#385C2314yes—
590#385C2314yes—
591#385C2312yes—
592#385C2312yes—
593#385C2312yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#384C2311yescharacteristic
598#384C2311yescharacteristic
599#383C2312yes—
600#383C2314yes—
601#383C2314yes—
602#383C2314yes—
603#383C2314yes—
604#383C2312yes—
605#383C2314yes—
606#383C2311yescharacteristic
607#383C2311yescharacteristic
608#383C2312yes—
609#383C2312yes—
610#383C2312yes—
611#383C2312yes—
612#382C2311yescharacteristic
613#382C2311yescharacteristic
614#382C2312yes—
615#382C2314yes—
616#382C2314yes—
617#382C2312yes—
618#382C2314yes—
619#382C2312yes—
620#382C2312yes—
621#382C2311yescharacteristic
622#382C2311yescharacteristic
623#382C2311yescharacteristic
624#382C2311yescharacteristic
625#382C2312yes—
626#382C2312yes—
627#382C2314yes—
628#382C2312yes—
629#382C2312yes—
630#382C2312yes—
631#382C2314yes—
632#381C2314yes—
633#381C2312yes—
634#381C2314yes—
635#381C2314yes—
636#381C2314yes—
637#381C2312yes—
638#381C2312yes—
639#381C2312yes—
640#381C2312yes—
641#381C2312yes—
642#381C2311yescharacteristic
643#381C2311yescharacteristic
644#381C2314yes—
645#380C2314yes—
646#380C2312yes—
647#380C2314yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2314yes—
652#380C2312yes—
653#380C2314yes—
654#380C2312yes—
655#380C2312yes—
656#380C2314yes—
657#380C2314yes—
658#380C2312yes—
659#380C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716#376C2312yes—
717#376C2314yes—
718#376C2312yes—
719#376C2314yes—
720#376C2311yescharacteristic
721#376C2311yescharacteristic
722#376C2312yes—
723#376C2312yes—
724#376C2312yes—
725#376C2312yes—
726#376C2314yes—
727#376C2312yes—
728#376C2312yes—
729#376C2312yes—
730#376C2312yes—
731#376C2312yes—
732#376C2314yes—
733C2×#95C2312yes—
734C2×#95C2312yes—
735C2×#95C2312yes—
736C2×#95C2312yes—
737C43C2311yescharacteristic
738C43C2311yescharacteristic
739C2×#41—24no—
740C2×#41—24no—
741C2×#41—24no—
742C2×#41—44no—
743C2×#41—42no—
744C22×Q8—24no—
745C22×Q8—24no—
746C22×Q8—42no—
747C22×Q8C2411yescharacteristic
748C22×Q8C2412yes—
749C22×Q8C2411yescharacteristic
750C22×Q8C2411yescharacteristic
751C22×Q8C2411yescharacteristic
752C22×Q8C2414yes—
753C22×Q8C2414yes—
754C22×D4C2411yescharacteristic
755C22×D4C2411yescharacteristic
756C22×D4C2412yes—
757C22×D4C2412yes—
758C22×D4C2414yes—
759C23×C4C2412yes—
760C23×C4C2412yes—
761C23×C4C2412yes—
762C23×C4C2412yes—
763C23×C4C2412yes—
764C23×C4C2411yescharacteristic
765C23×C4C2412yes—
766C23×C4C2412yes—
767C23×C4C2412yes—
768C23×C4C2412yes—
769C23×C4C2412yes—
770C23×C4C2412yes—
771C23×C4C2412yes—
772C23×C4C2411yescharacteristic
773C23×C4C2411yescharacteristic
774C4⋊Q8—24no—
775C4⋊Q8—28no—
776C4⋊Q8—44no—
777C4⋊Q8#4118yescomplemented
778#126—48no—
779#125—216no—
780#124—24no—
781#124—24no—
782#124—48no—
783#123—216no—
784#123—48no—
785#123—48no—
786C22⋊Q8—28no—
787C22⋊Q8—28no—
788C22⋊Q8—216no—
789C22⋊Q8—216no—
790C22⋊Q8—48no—
791C22⋊Q8—44no—
792#121—44no—
793C4×Q8—28no—
794C4×Q8—28no—
795C4×Q8—216no—
796C4×Q8—28no—
797C4×Q8—24no—
798C4×Q8—24no—
799C4×Q8—28no—
800C4×Q8—24no—
801C4×Q8—24no—
802C4×Q8—24no—
803C4×Q8—24no—
804C4×Q8—24no—
805C4×Q8—24no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×D4—28no—
809C4×D4—28no—
810C4×D4—28no—
811C4×D4—28no—
812C4×D4—24no—
813C4×D4—24no—
814C4×D4—24no—
815C4×D4—24no—
816C4×D4—48no—
817C4×D4—44no—
818C4×D4—44no—
819#117—24no—
820#117—24no—
821#117—216no—
822#117—28no—
823#117—28no—
824#117—24no—
825#117—42no—
826C2×C4⋊C4—28no—
827C2×C4⋊C4—24no—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C42—28no—
915C2×C42—28no—
916C2×C42—28no—
917C2×C42—28no—
918C2×C42—44no—
919C2×C42#4118yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2411yescharacteristic
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2411yescharacteristic
973#95C2411yescharacteristic
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2411yescharacteristic
998#95C2412yes—
999#95C2411yescharacteristic
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042C24C2512yes—
1043C24C2511yescharacteristic
1044C24C2512yes—
1045#41—416no—
1046#41—416no—
1047C2×Q8—22no—
1048C2×Q8—22no—
1049C2×Q8—24no—
1050C2×Q8—22no—
1051C2×Q8—22no—
1052C2×Q8—24no—
1053C2×Q8—22no—
1054C2×Q8—28no—
1055C2×Q8—22no—
1056C2×Q8—22no—
1057C2×Q8—22no—
1058C2×Q8—42no—
1059C2×Q8—42no—
1060C2×Q8—44no—
1061C2×Q8—44no—
1062C2×Q8—44no—
1063C2×Q8—44no—
1064C2×Q8—44no—
1065C2×Q8—416no—
1066C2×Q8C2×#4114yes—
1067C2×Q8C2×#4114yes—
1068C2×D4—24no—
1069C2×D4—24no—
1070C2×D4—24no—
1071C2×D4—24no—
1072C2×D4—28no—
1073C2×D4—22no—
1074C2×D4—22no—
1075C2×D4—24no—
1076C2×D4—22no—
1077C2×D4—22no—
1078C2×D4—42no—
1079C2×D4—42no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C22×C4—22no—
1083C22×C4—22no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—24no—
1095C22×C4—24no—
1096C22×C4—24no—
1097C22×C4—24no—
1098C22×C4—24no—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—42no—
1105C22×C4—42no—
1106C22×C4—42no—
1107C22×C4—42no—
1108C22×C4—42no—
1109C22×C4—44no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—42no—
1115C22×C4—42no—
1116C22×C4—42no—
1117C22×C4—42no—
1118C22×C4—42no—
1119C22×C4C2×#4114yes—
1120C22×C4C2×#4114yes—
1121C22×C4C2×#4114yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2514yes—
1134C22×C4C2514yes—
1135C22×C4C2514yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2511yescharacteristic
1142C22×C4C2511yescharacteristic
1143C22×C4C2511yescharacteristic
1144C22×C4C2512yes—
1145C22×C4C2511yescharacteristic
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2511yescharacteristic
1149C22×C4C2511yescharacteristic
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—22no—
1154C4⋊C4—22no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—22no—
1160C4⋊C4—22no—
1161C4⋊C4—22no—
1162C4⋊C4—22no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—28no—
1167C4⋊C4—28no—
1168C4⋊C4—28no—
1169C4⋊C4—28no—
1170C4⋊C4—28no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—28no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4C2×#41116yes—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—28no—
1205C22⋊C4—24no—
1206C22⋊C4—24no—
1207C22⋊C4—28no—
1208C22⋊C4—28no—
1209C22⋊C4—24no—
1210C22⋊C4—24no—
1211C22⋊C4—24no—
1212C22⋊C4—24no—
1213C22⋊C4—28no—
1214C22⋊C4—28no—
1215C22⋊C4—24no—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—44no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C42—24no—
1237C42—24no—
1238C42—24no—
1239C42—24no—
1240C42—24no—
1241C42—24no—
1242C42—24no—
1243C42—24no—
1244C42—24no—
1245C42—24no—
1246C42—24no—
1247C42—24no—
1248C42—24no—
1249C42—28no—
1250C42—28no—
1251C42—22no—
1252C42—22no—
1253C42—24no—
1254C42—22no—
1255C42—42no—
1256C42—42no—
1257C42—42no—
1258C42—44no—
1259C42—42no—
1260C42—44no—
1261C42—44no—
1262C42—42no—
1263C42—42no—
1264C42—44no—
1265C42—44no—
1266C42—44no—
1267C42—44no—
1268C42—44no—
1269C42C2×#4114yes—
1270C42C2×#4114yes—
1271C42C2×#4114yes—
1272C42C2×#4114yes—
1273C42C2×#4114yes—
1274C23—22no—
1275C23—22no—
1276C23—21no—
1277C23—22no—
1278C23—21no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—24no—
1287C23—22no—
1288C23—24no—
1289C23C22×#4112yes—
1290C23#58514yes—
1291C23C2611yescharacteristic
1292Q8—28no—
1293Q8—28no—
1294Q8—48no—
1295Q8—44no—
1296Q8—44no—
1297Q8—88no—
1298Q8—164no—
1299D4—28no—
1300D4—48no—
1301D4—48no—
1302D4—44no—
1303D4—88no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—21no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—28no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—44no—
1371C2×C4—44no—
1372C2×C4—48no—
1373C2×C4—48no—
1374C2×C4—48no—
1375C2×C4—48no—
1376C2×C4—48no—
1377C2×C4—84no—
1378C2×C4—84no—
1379C2×C4—84no—
1380C2×C4—84no—
1381C2×C4—84no—
1382C2×C4—84no—
1383C2×C4—84no—
1384C2×C4C22×#4112yes—
1385C2×C4C22×#4112yes—
1386C2×C4C22×#4112yes—
1387C2×C4C22×#4112yes—
1388C2×C4C22×#4114yes—
1389C2×C4C22×#4114yes—
1390C2×C4C22×#4114yes—
1391C2×C4C22×#4112yes—
1392C2×C4C22×#4112yes—
1393C2×C4C22×#4112yes—
1394C2×C4#58512yes—
1395C22—24no—
1396C22—22no—
1397C22—24no—
1398C22—22no—
1399C22—24no—
1400C22—22no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—44no—
1408C22—42no—
1409C22—42no—
1410C22—44no—
1411C22—42no—
1412C22C23×#4111yescharacteristic
1413C22C23×#4111yescharacteristic
1414C22C2×#58512yes—
1415C22C2×#58511yescharacteristic
1416C222−1+612yes—
1417C4—24no—
1418C4—22no—
1419C4—22no—
1420C4—22no—
1421C4—22no—
1422C4—22no—
1423C4—24no—
1424C4—24no—
1425C4—42no—
1426C4—42no—
1427C4—42no—
1428C4—44no—
1429C4—44no—
1430C4—42no—
1431C4—42no—
1432C4—42no—
1433C4—42no—
1434C4—42no—
1435C4—42no—
1436C4—42no—
1437C4—42no—
1438C4—42no—
1439C4—44no—
1440C4—44no—
1441C4—42no—
1442C4—42no—
1443C4—42no—
1444C4#347514yes—
1445C2—44no—
1446C2—42no—
1447C2—82no—
1448C2C2×#347511yescharacteristic
1449C2#6281411yescharacteristic
1450C2#6286011yescharacteristic
1451C2#6294012yes—
1452C2#6300512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34909C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59365C2semidirect
2. #59358C2semidirect
3. #59355C2semidirect
4. #59354C2semidirect
5. #44851C2semidirect
6. #44789C2semidirect
7. #44471C2semidirect
8. #43972C2semidirect
9. #39758C2semidirect
10. #39629C2semidirect
11. #39045C2semidirect
12. #39043C2semidirect
13. #38972C2semidirect
14. #38970C2semidirect
15. #37939C2semidirect
16. #37749C2semidirect
17. #36539C2semidirect
18. #36509C2semidirect
19. #36195C2semidirect
20. #36151C2semidirect
21. #35646C2semidirect
22. #35586C2semidirect
23. #35344C2semidirect
24. #35270C2semidirect
25. #34971C2semidirect
27. #34221C2semidirect
28. #34197C2semidirect
29. #34192C2semidirect
30. #34123C2semidirect
31. C4×#536C2semidirect
777. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#593652
#593582
#593552
#593542
#448512
#447892
#444712
#439722
#397582
#396292
#390452
#390432
#389722
#389702
#379392
#377492
#365392
#365092
#361952
#361512
#356462
#355862
#353442
#352702
#349712
#349092
#342212
#341972
#341922
#341232
C4×#5362