Finite Group Databasebeta

← #7653566

Subgroups — #7653566

Order 512.

4800 conjugacy classes of subgroups.

The subgroup lattice has 1494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41103C214yesmaximal, complemented
2#41091C214yesmaximal, complemented
3#40569C214yesmaximal, complemented
4#40263C214yesmaximal, complemented
5#39693C212yesmaximal, complemented
6#39630C211yesmaximal, characteristic, complemented
7#39372C211yesmaximal, characteristic, complemented
8#39281C212yesmaximal, complemented
9#39186C211yesmaximal, characteristic, complemented
10#38971C211yesmaximal, characteristic, complemented
11#38663C214yesmaximal, complemented
12#38404C214yesmaximal, complemented
13#38274C212yesmaximal, complemented
14#37798C212yesmaximal, complemented
15#37553C211yesmaximal, characteristic, complemented
16#37510C212yesmaximal, complemented
17#36574C211yesmaximal, characteristic, complemented
18#36539C211yesmaximal, characteristic, complemented
19#36370C211yesmaximal, characteristic, complemented
20#36353C214yesmaximal, complemented
21#36135C211yesmaximal, characteristic, complemented
22#35721C214yesmaximal, complemented
23#35210C211yesmaximal, characteristic, complemented
24#35202C211yesmaximal, characteristic, complemented
25#35156C212yesmaximal, complemented
26#35047C212yesmaximal, complemented
27#34910C211yesmaximal, characteristic, complemented
28#34724C212yesmaximal, complemented
29#34224C211yesmaximal, characteristic, complemented
30#34153C211yesmaximal, characteristic, complemented
31C4⋊C4×#41C211yesmaximal, characteristic, complemented
32C2×#540C2212yes—
33C2×#529C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#529C2212yes—
36C2×C4×#41C2211yescharacteristic
37C2×C4×#41C2212yes—
38#2864C2211yescharacteristic
39#2864C2211yescharacteristic
40#2860C2212yes—
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2859C2212yes—
44#2854C2214yes—
45#2854C2212yes—
46#2853C2214yes—
47#2852C2214yes—
48#2851C2212yes—
49#2834C2214yes—
50#2827C2214yes—
51#2814C2212yes—
52#2813C2212yes—
53#2807C2214yes—
54#2802C2214yes—
55#2802C2214yes—
56#2801C2214yes—
57#2800C2214yes—
58#2791C2214yes—
59#2790C2214yes—
60#2790C2214yes—
61#2790C2214yes—
62#2788C2214yes—
63#2787C2214yes—
64#2781C2214yes—
65#2771C2214yes—
66#2765C2214yes—
67#2745C2214yes—
68#2725C2214yes—
69#2724C2214yes—
70#2718C2214yes—
71#2718C2214yes—
72#2708C2214yes—
73#2707C2214yes—
74#2701C2214yes—
75#2695C2214yes—
76#2682C2214yes—
77#2667C2214yes—
78#2664C2212yes—
79#2662C2212yes—
80#2655C2214yes—
81#2654C2214yes—
82#2652C2214yes—
83#2649C2214yes—
84#2649C2214yes—
85#2647C2212yes—
86#2645C2212yes—
87#2638C2212yes—
88#2636C2214yes—
89#2635C2214yes—
90#2635C2212yes—
91#2630C2214yes—
92#2630C2214yes—
93#2629C2212yes—
94#2629C2212yes—
95#2625C2212yes—
96#2620C2212yes—
97#2611C2212yes—
98#2610C2212yes—
99#2606C2214yes—
100#2602C2214yes—
101#2602C2214yes—
102#2602C2214yes—
103#2601C2214yes—
104#2601C2214yes—
105#2596C2214yes—
106#2594C2214yes—
107#2594C2214yes—
108#2594C2214yes—
109#2593C2214yes—
110#2590C2214yes—
111#2587C2214yes—
112#2587C2214yes—
113#2587C2214yes—
114#2585C2214yes—
115#2584C2214yes—
116#2581C2211yescharacteristic
117#2581C2211yescharacteristic
118#2580C2211yescharacteristic
119#2580C2211yescharacteristic
120#2576C2214yes—
121#2566C2211yescharacteristic
122#2565C2211yescharacteristic
123#2558C2214yes—
124#2558C2214yes—
125#2558C2214yes—
126#2553C2214yes—
127#2552C2212yes—
128#2552C2212yes—
129#2545C2211yescharacteristic
130#2544C2211yescharacteristic
131#2536C2211yescharacteristic
132#2536C2211yescharacteristic
133#2535C2211yescharacteristic
134#2535C2211yescharacteristic
135#2530C2214yes—
136#2529C2214yes—
137#2525C2214yes—
138#2522C2214yes—
139#2509C2214yes—
140#2509C2212yes—
141#2508C2214yes—
142#2507C2214yes—
143#2507C2212yes—
144#2505C2214yes—
145#2500C2211yescharacteristic
146#2499C2211yescharacteristic
147#2497C2212yes—
148#2494C2212yes—
149#2493C2214yes—
150#2485C2212yes—
151#2479C2214yes—
152#2478C2214yes—
153#2478C2214yes—
154#2476C2214yes—
155#2475C2214yes—
156#2473C2214yes—
157#2470C2214yes—
158#2470C2214yes—
159#2470C2214yes—
160#2468C2214yes—
161#2466C2214yes—
162#2460C2214yes—
163#2458C2214yes—
164#2456C2214yes—
165#2455C2214yes—
166#2455C2214yes—
167#2455C2214yes—
168#2455C2214yes—
169#2454C2212yes—
170#2453C2212yes—
171#2453C2212yes—
172#2453C2212yes—
173#2447C2212yes—
174#2445C2212yes—
175#2443C2214yes—
176#2441C2212yes—
177#2441C2214yes—
178#2441C2212yes—
179#2432C2211yescharacteristic
180#2431C2211yescharacteristic
181#2429C2212yes—
182#2426C2212yes—
183#2425C2214yes—
184#2425C2214yes—
185#2423C2212yes—
186#2422C2212yes—
187#2422C2214yes—
188#2422C2212yes—
189#2422C2212yes—
190#2415C2212yes—
191#2414C2212yes—
192#2413C2214yes—
193#2413C2214yes—
194#2407C2212yes—
195#2395C2214yes—
196#2392C2214yes—
197#2392C2214yes—
198#2374C2214yes—
199#2373C2212yes—
200#2373C2212yes—
201#2373C2214yes—
202#2370C2214yes—
203#2370C2212yes—
204#2370C2212yes—
205#2367C2212yes—
206#2367C2212yes—
207#2361C2212yes—
208#2360C2212yes—
209#2359C2214yes—
210#2359C2214yes—
211#2359C2212yes—
212#2359C2212yes—
213#2357C2211yescharacteristic
214#2356C2211yescharacteristic
215#2351C2211yescharacteristic
216#2351C2211yescharacteristic
217#2351C2211yescharacteristic
218Q8×C4⋊C4C2212yes—
219#2349C2211yescharacteristic
220#2349C2211yescharacteristic
221#2349C2212yes—
222#2349C2212yes—
223#2349C2211yescharacteristic
224D4×C4⋊C4C2212yes—
225D4×C4⋊C4C2214yes—
226#2347C2212yes—
227#2343C2212yes—
228#2335C2214yes—
229#2334C2214yes—
230#2330C2214yes—
231#2326C2212yes—
232#2324C2212yes—
233#2323C2212yes—
234#2323C2212yes—
235#2322C2214yes—
236#2319C2212yes—
237#2318C2212yes—
238C4×C4⋊Q8C2211yescharacteristic
239C4×C4⋊Q8C2212yes—
240C4×#127C2211yescharacteristic
241C4×#124C2211yescharacteristic
242C4×#124C2211yescharacteristic
243C4×C22⋊Q8C2212yes—
244C4×C22⋊Q8C2212yes—
245C4×#123C2214yes—
246C4×#121C2212yes—
247#2298C2212yes—
248#2296C2214yes—
249#2296C2214yes—
250#2296C2212yes—
251#2296C2212yes—
252#2295C2211yescharacteristic
253#2293C2212yes—
254#2293C2211yescharacteristic
255#2290C2214yes—
256#2290C2212yes—
257#2285C2212yes—
258#2285C2211yescharacteristic
259#2283C2211yescharacteristic
260#2275C2212yes—
261C42×Q8C2211yescharacteristic
262C42×D4C2211yescharacteristic
263C42×D4C2212yes—
264C4×#117C2211yescharacteristic
265C2×C4×C4⋊C4C2212yes—
266C2×C4×C4⋊C4C2211yescharacteristic
267C22×#41C2311yescharacteristic
268#540—48no—
269C2×C4⋊Q8C2311yescharacteristic
270C2×#127C2311yescharacteristic
271#529—28no—
272#529—28no—
273#529—48no—
274C2×#126C2312yes—
275C2×#126C2312yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2311yescharacteristic
279C2×#125C2311yescharacteristic
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#124C2311yescharacteristic
285C2×#124C2311yescharacteristic
286C2×#124C2311yescharacteristic
287C2×#124C2311yescharacteristic
288C2×#123C2312yes—
289C2×#123C2312yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2311yescharacteristic
300C2×C22⋊Q8C2311yescharacteristic
301C2×C22⋊Q8C2312yes—
302C2×#121C2312yes—
303C2×#121C2311yescharacteristic
304C2×#121C2311yescharacteristic
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C4×#41—28no—
309C4×#41—48no—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×#117C2312yes—
338C2×#117C2312yes—
339C2×#117C2312yes—
340C2×#117C2311yescharacteristic
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2314yes—
344C2×#117C2314yes—
345C2×#117C2312yes—
346C2×#117C2314yes—
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2314yes—
349C22×C42C2312yes—
350C22×C42C2312yes—
351C22×C42C2314yes—
352C22×C42C2312yes—
353C22×C42C2311yescharacteristic
354#401C2314yes—
355#401C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#399C2314yes—
371#399C2314yes—
372#399C2312yes—
373#399C2312yes—
374#399C2314yes—
375#399C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2312yes—
403#397C2314yes—
404#397C2312yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#395C2312yes—
425#395C2312yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2312yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2312yes—
443#393C2312yes—
444#393C2312yes—
445#392C2312yes—
446#392C2314yes—
447#392C2314yes—
448#392C2312yes—
449#392C2314yes—
450#391C2311yescharacteristic
451#391C2312yes—
452#391C2312yes—
453#391C2311yescharacteristic
454#391C2311yescharacteristic
455#391C2312yes—
456#391C2312yes—
457#391C2311yescharacteristic
458#390C2311yescharacteristic
459#390C2314yes—
460#390C2311yescharacteristic
461#390C2311yescharacteristic
462#390C2312yes—
463#390C2314yes—
464#390C2312yes—
465#390C2314yes—
466#390C2314yes—
467#390C2311yescharacteristic
468#390C2312yes—
469#390C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2312yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2312yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
553#388C2312yes—
554#388C2312yes—
555#388C2312yes—
556#388C2312yes—
557#388C2312yes—
558#388C2314yes—
559#388C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2312yes—
589#387C2314yes—
590#387C2314yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#386C2312yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2312yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2312yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2312yes—
621#385C2312yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2312yes—
635#385C2312yes—
636#385C2314yes—
637#385C2314yes—
638#384C2311yescharacteristic
639#384C2311yescharacteristic
640#384C2312yes—
641#384C2312yes—
642#384C2314yes—
643#384C2312yes—
644#384C2314yes—
645#383C2312yes—
646#383C2312yes—
647#382C2311yescharacteristic
648#382C2311yescharacteristic
649#382C2312yes—
650#382C2312yes—
651#382C2311yescharacteristic
652#382C2311yescharacteristic
653#382C2311yescharacteristic
654#382C2311yescharacteristic
655#382C2314yes—
656#382C2312yes—
657#381C2312yes—
658#381C2314yes—
659#381C2312yes—
660#381C2314yes—
661#380C2312yes—
662#380C2314yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2314yes—
667#380C2312yes—
668#380C2314yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2312yes—
673#380C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2311yescharacteristic
727C4×C22⋊C4C2311yescharacteristic
728#376C2312yes—
729#376C2312yes—
730#376C2312yes—
731#376C2312yes—
732C2×#95C2311yescharacteristic
733C2×#95C2312yes—
734C2×#95C2312yes—
735C2×#95C2311yescharacteristic
736C2×#95C2312yes—
737C43C2311yescharacteristic
738C43C2312yes—
739C43C2311yescharacteristic
740C2×#41—24no—
741C2×#41—24no—
742C2×#41—24no—
743C22×Q8C2411yescharacteristic
744C22×Q8C2411yescharacteristic
745C22×Q8C2411yescharacteristic
746C22×D4C2412yes—
747C22×D4C2411yescharacteristic
748C22×D4C2411yescharacteristic
749C22×D4C2412yes—
750C22×D4C2412yes—
751C22×D4C2411yescharacteristic
752C22×D4C2414yes—
753C22×D4C2414yes—
754C22×D4C2414yes—
755C23×C4C2412yes—
756C23×C4C2412yes—
757C23×C4C2414yes—
758C23×C4C2411yescharacteristic
759C23×C4C2412yes—
760C23×C4C2412yes—
761C23×C4C2414yes—
762C23×C4C2412yes—
763C23×C4C2412yes—
764C23×C4C2412yes—
765C23×C4C2412yes—
766C23×C4C2414yes—
767C23×C4C2412yes—
768C23×C4C2411yescharacteristic
769C23×C4C2411yescharacteristic
770C4⋊Q8—24no—
771#127—24no—
772#126—28no—
773#126—28no—
774#126—48no—
775#126—48no—
776#125—24no—
777#125—24no—
778#125—48no—
779#125—44no—
780#125—44no—
781#125—48no—
782#124—24no—
783#124—24no—
784#124—24no—
785#124—24no—
786#123—28no—
787#123—28no—
788#123—48no—
789#123—48no—
790#123—48no—
791#123—48no—
792#123—48no—
793#123—48no—
794#123—48no—
795#123—48no—
796C22⋊Q8—28no—
797C22⋊Q8—24no—
798C22⋊Q8—24no—
799C22⋊Q8—44no—
800#121—28no—
801#121—24no—
802#121—24no—
803#121—48no—
804#121—44no—
805#121—48no—
806C4×Q8—24no—
807C4×Q8—24no—
808C4×Q8—24no—
809C4×Q8—24no—
810C4×Q8—44no—
811C4×Q8—44no—
812C4×Q8—44no—
813C4×Q8—44no—
814C4×D4—28no—
815C4×D4—28no—
816C4×D4—28no—
817C4×D4—28no—
818C4×D4—28no—
819C4×D4—28no—
820C4×D4—24no—
821C4×D4—24no—
822C4×D4—24no—
823C4×D4—24no—
824C4×D4—44no—
825C4×D4—48no—
826C4×D4—44no—
827C4×D4—44no—
828C4×D4—44no—
829C4×D4—48no—
830C4×D4—48no—
831C4×D4—48no—
832C4×D4—48no—
833#117—24no—
834#117—28no—
835#117—28no—
836#117—28no—
837#117—44no—
838#117—48no—
839#117—44no—
840#117—48no—
841#117—48no—
842#117—44no—
843C2×C4⋊C4—44no—
844C2×C4⋊C4—48no—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C42—28no—
956C2×C42—44no—
957C2×C42—44no—
958C2×C42—48no—
959C2×C42#4118yes—
960C2×C42C2412yes—
961C2×C42C2411yescharacteristic
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2412yes—
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2414yes—
978C2×C42C2414yes—
979C2×C42C2412yes—
980C2×C42C2414yes—
981C2×C42C2414yes—
982C2×C42C2414yes—
983C2×C42C2412yes—
984C2×C42C2414yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2414yes—
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2411yescharacteristic
993C2×C42C2411yescharacteristic
994#95C2411yescharacteristic
995#95C2411yescharacteristic
996#95C2411yescharacteristic
997#95C2411yescharacteristic
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058C24C2512yes—
1059C24C2512yes—
1060C24C2511yescharacteristic
1061C24C2512yes—
1062#41—232no—
1063C2×Q8—22no—
1064C2×Q8—22no—
1065C2×Q8—22no—
1066C2×Q8—22no—
1067C2×Q8—22no—
1068C2×Q8—22no—
1069C2×Q8—42no—
1070C2×Q82−1+414yes—
1071C2×D4—24no—
1072C2×D4—24no—
1073C2×D4—24no—
1074C2×D4—24no—
1075C2×D4—28no—
1076C2×D4—28no—
1077C2×D4—22no—
1078C2×D4—22no—
1079C2×D4—22no—
1080C2×D4—22no—
1081C2×D4—24no—
1082C2×D4—22no—
1083C2×D4—22no—
1084C2×D4—42no—
1085C2×D4—42no—
1086C2×D4—42no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4H(5,𝔽2)14yes—
1096C22×C4—24no—
1097C22×C4—24no—
1098C22×C4—22no—
1099C22×C4—24no—
1100C22×C4—22no—
1101C22×C4—28no—
1102C22×C4—28no—
1103C22×C4—24no—
1104C22×C4—24no—
1105C22×C4—24no—
1106C22×C4—24no—
1107C22×C4—28no—
1108C22×C4—24no—
1109C22×C4—24no—
1110C22×C4—24no—
1111C22×C4—24no—
1112C22×C4—42no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—42no—
1116C22×C4—42no—
1117C22×C4—42no—
1118C22×C4—42no—
1119C22×C4—42no—
1120C22×C4—42no—
1121C22×C4—44no—
1122C22×C4—42no—
1123C22×C4—42no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—42no—
1127C22×C4—42no—
1128C22×C4—42no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4C2×#4114yes—
1134C22×C4C2×#4114yes—
1135C22×C4C2×#4114yes—
1136C22×C4C2512yes—
1137C22×C4C2514yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2512yes—
1151C22×C4C2514yes—
1152C22×C4C2514yes—
1153C22×C4C2514yes—
1154C22×C4C2511yescharacteristic
1155C22×C4C2511yescharacteristic
1156C22×C4C2511yescharacteristic
1157C22×C4C2511yescharacteristic
1158C22×C4C2511yescharacteristic
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2512yes—
1162C22×C4C2511yescharacteristic
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—22no—
1166C4⋊C4—22no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—22no—
1172C4⋊C4—22no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—22no—
1176C4⋊C4—22no—
1177C4⋊C4—24no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—28no—
1184C4⋊C4—28no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—28no—
1188C4⋊C4—24no—
1189C4⋊C4—28no—
1190C4⋊C4—28no—
1191C4⋊C4—24no—
1192C4⋊C4—28no—
1193C4⋊C4—42no—
1194C4⋊C4—42no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—42no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—42no—
1206C4⋊C4—42no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—42no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C22⋊C4—24no—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—28no—
1231C22⋊C4—28no—
1232C22⋊C4—28no—
1233C22⋊C4—28no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—24no—
1237C22⋊C4—24no—
1238C22⋊C4—24no—
1239C22⋊C4—24no—
1240C22⋊C4—24no—
1241C22⋊C4—24no—
1242C22⋊C4—24no—
1243C22⋊C4—24no—
1244C22⋊C4—28no—
1245C22⋊C4—28no—
1246C22⋊C4—24no—
1247C22⋊C4—28no—
1248C22⋊C4—24no—
1249C22⋊C4—28no—
1250C22⋊C4—24no—
1251C22⋊C4—24no—
1252C22⋊C4—28no—
1253C22⋊C4—44no—
1254C22⋊C4—42no—
1255C22⋊C4—44no—
1256C22⋊C4—42no—
1257C22⋊C4—42no—
1258C22⋊C4—42no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C42—24no—
1274C42—24no—
1275C42—24no—
1276C42—24no—
1277C42—24no—
1278C42—24no—
1279C42—22no—
1280C42—24no—
1281C42—22no—
1282C42—22no—
1283C42—22no—
1284C42—24no—
1285C42—24no—
1286C42—24no—
1287C42—24no—
1288C42—42no—
1289C42—42no—
1290C42—42no—
1291C42—44no—
1292C42—44no—
1293C42—44no—
1294C42—42no—
1295C42—44no—
1296C42—42no—
1297C42—44no—
1298C42—42no—
1299C42—44no—
1300C42—42no—
1301C42—42no—
1302C42—44no—
1303C42C2×#4114yes—
1304C42C2×#4114yes—
1305C42C2×#4114yes—
1306C42C2×#4114yes—
1307C23—22no—
1308C23—21no—
1309C23—21no—
1310C23—22no—
1311C23—24no—
1312C23—22no—
1313C23—24no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—22no—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23—24no—
1322C23—22no—
1323C23—22no—
1324C23—22no—
1325C23—24no—
1326C23—22no—
1327C23C22×#4112yes—
1328C23C2×H(5,𝔽2)14yes—
1329C23C2611yescharacteristic
1330Q8—28no—
1331Q8—44no—
1332Q8—44no—
1333D4—216no—
1334D4—28no—
1335D4—44no—
1336D4—48no—
1337D4—48no—
1338D4—44no—
1339D4—88no—
1340D4—88no—
1341D4—164no—
1342C2×C4—216no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—21no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—21no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—28no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—24no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—24no—
1400C2×C4—24no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—24no—
1404C2×C4—24no—
1405C2×C4—22no—
1406C2×C4—44no—
1407C2×C4—44no—
1408C2×C4—416no—
1409C2×C4—48no—
1410C2×C4—48no—
1411C2×C4—84no—
1412C2×C4—84no—
1413C2×C4—84no—
1414C2×C4—84no—
1415C2×C4—88no—
1416C2×C4—84no—
1417C2×C4—84no—
1418C2×C4—164no—
1419C2×C4C22×#4112yes—
1420C2×C4C22×#4112yes—
1421C2×C4C22×#4112yes—
1422C2×C4C22×#4112yes—
1423C2×C4C22×#4112yes—
1424C2×C4C22×#4112yes—
1425C2×C4C2×H(5,𝔽2)12yes—
1426C2×C4C2×2−1+414yes—
1427C2×C4C2×2−1+412yes—
1428C2×C4#58514yes—
1429C2×C4#58514yes—
1430C22—28no—
1431C22—22no—
1432C22—24no—
1433C22—22no—
1434C22—22no—
1435C22—42no—
1436C22—44no—
1437C22—42no—
1438C22—42no—
1439C22—42no—
1440C22—42no—
1441C22—42no—
1442C22—44no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—42no—
1447C22—44no—
1448C22—42no—
1449C22—42no—
1450C22—42no—
1451C22—42no—
1452C22C23×#4111yescharacteristic
1453C22C22×H(5,𝔽2)11yescharacteristic
1454C22C22×2−1+411yescharacteristic
1455C22C2×#58512yes—
1456C22C2×#58512yes—
1457C4—24no—
1458C4—22no—
1459C4—24no—
1460C4—24no—
1461C4—22no—
1462C4—22no—
1463C4—22no—
1464C4—22no—
1465C4—44no—
1466C4—42no—
1467C4—42no—
1468C4—42no—
1469C4—42no—
1470C4—44no—
1471C4—44no—
1472C4—42no—
1473C4—42no—
1474C4—42no—
1475C4—42no—
1476C4—44no—
1477C4—42no—
1478C4—42no—
1479C4—42no—
1480C4—42no—
1481C4—42no—
1482C4—42no—
1483C4#349214yes—
1484C2—44no—
1485C2—42no—
1486C2—82no—
1487C2—82no—
1488C2#6268611yescharacteristic
1489C2C2×#349211yescharacteristic
1490C2#6281511yescharacteristic
1491C2#6301812yes—
1492C2#6303312yes—
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. #41103C2semidirect
2. #41091C2semidirect
3. #40569C2semidirect
4. #40263C2semidirect
5. #39693C2semidirect
6. #39630C2semidirect
7. #39372C2semidirect
8. #39281C2semidirect
9. #39186C2semidirect
10. #38971C2semidirect
11. #38663C2semidirect
12. #38404C2semidirect
13. #38274C2semidirect
14. #37798C2semidirect
15. #37553C2semidirect
16. #37510C2semidirect
17. #36574C2semidirect
18. #36539C2semidirect
19. #36370C2semidirect
20. #36353C2semidirect
21. #36135C2semidirect
22. #35721C2semidirect
23. #35210C2semidirect
24. #35202C2semidirect
25. #35156C2semidirect
26. #35047C2semidirect
27. #34910C2semidirect
28. #34724C2semidirect
29. #34224C2semidirect
30. #34153C2semidirect
31. C4⋊C4×#41C2semidirect

Maximal subgroups

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

subgroupindex
#411032
#410912
#405692
#402632
#396932
#396302
#393722
#392812
#391862
#389712
#386632
#384042
#382742
#377982
#375532
#375102
#365742
#365392
#363702
#363532
#361352
#357212
#352102
#352022
#351562
#350472
#349102
#347242
#342242
#341532
C4⋊C4×#412