Finite Group Databasebeta

← #8700360

Subgroups — #8700360

Order 512.

4514 conjugacy classes of subgroups.

The subgroup lattice has 1472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59811C212yesmaximal, complemented
2#59629C212yesmaximal, complemented
3#59277C212yesmaximal, complemented
4#59234C212yesmaximal, complemented
5#58963C212yesmaximal, complemented
6#57411C214yesmaximal, complemented
7#54678C212yesmaximal, complemented
8#54100C214yesmaximal, complemented
9#52292C211yesmaximal, characteristic, complemented
10#51878C214yesmaximal, complemented
11#50323C214yesmaximal, complemented
12#48428C214yesmaximal, complemented
13#45601C212yesmaximal, complemented
14#45493C211yesmaximal, characteristic, complemented
15#45433C211yesmaximal, characteristic, complemented
16#45345C211yesmaximal, characteristic, complemented
17#45098C212yesmaximal, complemented
18#45040C212yesmaximal, complemented
19#42914C211yesmaximal, characteristic, complemented
20#42894C212yesmaximal, complemented
21#42763C212yesmaximal, complemented
22#42679C211yesmaximal, characteristic, complemented
23#40007C212yesmaximal, complemented
24#39737C212yesmaximal, complemented
25#39657C212yesmaximal, complemented
26#37100C212yesmaximal, complemented
27#36879C214yesmaximal, complemented
28#36517C211yesmaximal, characteristic, complemented
29#36439C212yesmaximal, complemented
30C2×#556C2212yes—
31C2×#553C2211yescharacteristic
32C2×#547C2211yescharacteristic, complemented
33C2×#544C2211yescharacteristic, complemented
34C22×#117C2211yescharacteristic
35#2857C2212yescomplemented
36#2854C2212yes—
37#2852C2214yes—
38#2848C2212yes—
39#2847C2211yescharacteristic
40#2842C2212yes—
41#2831C2214yes—
42#2829C2214yes—
43#2824C2214yes—
44#2821C2212yescomplemented
45#2813C2212yescomplemented
46#2808C2214yes—
47#2807C2211yescharacteristic
48#2807C2212yes—
49#2804C2214yes—
50#2800C2214yescomplemented
51#2798C2214yescomplemented
52#2796C2212yes—
53#2794C2212yescomplemented
54#2793C2214yes—
55#2790C2214yes—
56#2786C2214yescomplemented
57#2782C2214yes—
58#2780C2214yes—
59#2780C2212yes—
60#2778C2212yes—
61#2775C2214yes—
62#2775C2214yescomplemented
63#2772C2214yes—
64#2772C2214yescomplemented
65#2771C2212yes—
66#2767C2214yescomplemented
67#2759C2214yescomplemented
68#2755C2214yescomplemented
69#2755C2214yescomplemented
70#2754C2214yes—
71#2754C2214yescomplemented
72#2753C2214yes—
73#2752C2212yes—
74#2748C2212yes—
75#2746C2212yes—
76#2742C2214yes—
77#2741C2214yes—
78#2741C2214yescomplemented
79#2741C2214yescomplemented
80#2740C2214yescomplemented
81#2735C2211yescharacteristic
82#2733C2214yes—
83#2731C2214yes—
84#2730C2214yes—
85#2730C2214yes—
86#2729C2214yescomplemented
87#2725C2214yes—
88#2718C2214yescomplemented
89#2715C2214yes—
90#2715C2214yes—
91#2712C2214yes—
92#2712C2212yescomplemented
93#2706C2214yes—
94#2703C2214yes—
95#2703C2214yes—
96#2702C2214yescomplemented
97#2700C2214yes—
98#2696C2214yescomplemented
99#2695C2214yescomplemented
100#2693C2211yescharacteristic
101#2692C2214yes—
102#2688C2212yes—
103#2684C2214yes—
104#2681C2214yes—
105#2680C2214yescomplemented
106#2678C2212yes—
107#2676C2214yes—
108#2670C2214yes—
109#2668C2211yescharacteristic
110#2665C2214yescomplemented
111#2664C2212yescomplemented
112#2662C2214yescomplemented
113#2655C2214yescomplemented
114#2654C2214yes—
115#2649C2214yes—
116#2648C2214yes—
117#2642C2211yescharacteristic, complemented
118#2635C2212yes—
119#2633C2212yes—
120#2624C2211yescharacteristic, complemented
121#2623C2212yescomplemented
122#2620C2214yes—
123#2607C2212yes—
124#2607C2212yes—
125#2601C2214yes—
126#2599C2214yes—
127#2589C2214yescomplemented
128#2589C2214yescomplemented
129#2582C2212yescomplemented
130#2573C2214yescomplemented
131#2565C2212yescomplemented
132#2563C2212yes—
133#2562C2212yes—
134#2562C2211yescharacteristic, complemented
135#2560C2214yes—
136#2559C2214yescomplemented
137#2557C2214yes—
138#2557C2214yes—
139#2557C2214yes—
140#2554C2214yes—
141#2553C2214yes—
142#2552C2212yescomplemented
143#2551C2212yescomplemented
144#2547C2212yes—
145#2547C2212yescomplemented
146#2545C2214yes—
147#2542C2211yescharacteristic
148#2542C2212yes—
149#2539C2212yes—
150#2538C2212yes—
151#2534C2212yes—
152#2522C2214yescomplemented
153#2520C2214yescomplemented
154#2519C2214yescomplemented
155#2517C2212yescomplemented
156#2517C2214yescomplemented
157#2513C2214yes—
158#2513C2212yescomplemented
159#2512C2212yescomplemented
160#2511C2214yescomplemented
161#2511C2212yescomplemented
162#2511C2214yescomplemented
163#2501C2211yescharacteristic
164#2501C2211yescharacteristic, complemented
165#2499C2212yes—
166#2497C2212yes—
167#2497C2212yescomplemented
168#2495C2214yescomplemented
169#2492C2212yes—
170#2492C2212yes—
171#2492C2214yes—
172#2492C2212yescomplemented
173#2492C2212yescomplemented
174#2492C2214yescomplemented
175#2491C2212yes—
176#2491C2212yes—
177#2491C2214yes—
178#2490C2212yes—
179#2489C2212yes—
180#2487C2211yescharacteristic
181#2487C2212yes—
182#2486C2211yescharacteristic
183#2485C2212yes—
184#2485C2212yescomplemented
185#2481C2214yes—
186#2480C2214yes—
187#2479C2214yes—
188#2479C2214yescomplemented
189#2478C2214yes—
190#2474C2214yes—
191#2474C2214yes—
192#2474C2214yescomplemented
193#2472C2214yes—
194#2471C2214yes—
195#2471C2214yes—
196#2469C2214yescomplemented
197#2458C2214yes—
198#2458C2214yescomplemented
199#2452C2212yescomplemented
200#2451C2212yescomplemented
201#2448C2214yes—
202#2446C2212yescomplemented
203#2446C2214yescomplemented
204#2441C2212yes—
205#2441C2212yescomplemented
206#2440C2212yes—
207#2439C2212yes—
208#2429C2212yes—
209#2423C2212yes—
210#2421C2214yescomplemented
211#2417C2212yes—
212#2417C2212yes—
213#2415C2212yes—
214#2415C2212yescomplemented
215#2414C2212yes—
216#2407C2212yes—
217#2407C2212yes—
218#2407C2212yes—
219#2407C2212yescomplemented
220#2401C2212yes—
221#2397C2211yescharacteristic
222#2395C2211yescharacteristic
223#2392C2212yes—
224#2379C2214yes—
225#2375C2212yes—
226#2374C2214yes—
227#2369C2212yescomplemented
228#2369C2214yescomplemented
229#2365C2212yescomplemented
230#2363C2212yes—
231#2362C2212yes—
232#2360C2212yes—
233#2360C2214yescomplemented
234#2355C2212yescomplemented
235#2354C2212yes—
236#2354C2212yes—
237#2352C2212yes—
238#2352C2212yescomplemented
239#2347C2212yes—
240#2347C2211yescharacteristic, complemented
241#2345C2211yescharacteristic
242#2341C2212yescomplemented
243#2335C2214yes—
244#2335C2214yescomplemented
245#2331C2212yescomplemented
246#2323C2214yescomplemented
247#2323C2212yescomplemented
248#2319C2211yescharacteristic, complemented
249C4×C22⋊Q8C2214yes—
250C4×C22⋊Q8C2212yescomplemented
251C4×#123C2212yes—
252C4×#123C2212yes—
253C4×#121C2212yes—
254C4×#121C2212yes—
255C4×#120C2212yes—
256C4×#120C2211yescharacteristic
257#2297C2212yescomplemented
258#2285C2212yescomplemented
259C22×#41C2312yes—
260C24×C4C2311yescharacteristic
261#556—48no—
262#553—44no—
263#547—44no—
264#544—44no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×#126C2314yes—
272C2×#126C2312yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#125C2312yes—
276C2×#125C2311yescharacteristic
277C2×#125C2312yes—
278C2×#124C2314yes—
279C2×#124C2314yes—
280C2×#124C2314yes—
281C2×#124C2314yes—
282C2×#124C2314yes—
283C2×#123C2312yes—
284C2×#123C2312yes—
285C2×#123C2314yes—
286C2×#123C2312yes—
287C2×#123C2314yes—
288C2×#123C2312yes—
289C2×#123C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×#121C2312yes—
300C2×#121C2311yescharacteristic
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2311yescharacteristic
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#120C2311yescharacteristic
307C2×#120C2312yes—
308C2×#120C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2314yes—
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2312yes—
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×#117—44no—
323C2×#117C2312yes—
324C2×#117C2311yescharacteristic
325C2×#117C2311yescharacteristic
326C2×#117C2314yes—
327C2×#117C2312yes—
328C2×#117C2312yes—
329C2×#117C2314yes—
330C22×C4⋊C4C2311yescharacteristic
331C22×C4⋊C4C2311yescharacteristic
332C22×C4⋊C4C2311yescharacteristic
333C22×C4⋊C4C2312yes—
334C22×C22⋊C4C2312yes—
335C22×C42C2312yes—
336C22×C42C2312yes—
337#401C2312yes—
338#400C2314yes—
339#400C2312yes—
340#400C2311yescharacteristic
341#400C2312yes—
342#400C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2312yes—
357#400C2314yes—
358#399C2312yes—
359#399C2312yes—
360#399C2312yes—
361#399C2312yes—
362#399C2314yes—
363#399C2312yes—
364#399C2311yescharacteristic
365#399C2311yescharacteristic
366#399C2311yescharacteristic
367#399C2312yes—
368#399C2312yes—
369#399C2314yes—
370#399C2314yes—
371#399C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2311yescharacteristic
378#398C2314yes—
379#398C2312yes—
380#398C2312yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2312yes—
397#397C2311yescharacteristic
398#397C2312yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2312yes—
403#397C2314yes—
404#397C2312yes—
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2312yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2312yes—
420#396C2312yes—
421#396C2312yes—
422#396C2314yes—
423#396C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#394C2312yes—
429#394C2314yes—
430#394C2312yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2312yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2312yes—
444#394C2312yes—
445#394C2314yes—
446#394C2314yes—
447#393C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2314yes—
455#393C2314yes—
456#393C2314yes—
457#392C2314yes—
458#392C2311yescharacteristic
459#392C2314yes—
460#392C2312yes—
461#392C2314yes—
462#392C2312yes—
463#392C2311yescharacteristic
464#392C2314yes—
465#392C2314yes—
466#391C2314yes—
467#391C2312yes—
468#391C2312yes—
469#391C2314yes—
470#391C2314yes—
471#391C2312yes—
472#391C2314yes—
473#391C2314yes—
474#391C2314yes—
475#391C2314yes—
476#391C2314yes—
477#391C2314yes—
478#391C2314yes—
479#391C2312yes—
480#391C2312yes—
481#391C2314yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2314yes—
486#390C2314yes—
487#390C2314yes—
488#390C2314yes—
489#390C2312yes—
490#390C2314yes—
491#390C2312yes—
492#390C2312yes—
493#390C2314yes—
494#390C2314yes—
495#390C2314yes—
496#390C2314yes—
497#390C2314yes—
498#390C2312yes—
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
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#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2312yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2312yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2312yes—
565#388C2312yes—
566#388C2312yes—
567#388C2312yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
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#387C2312yes—
599#387C2312yes—
600#386C2314yes—
601#386C2312yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2312yes—
606#386C2312yes—
607#386C2314yes—
608#386C2311yescharacteristic
609#386C2312yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2312yes—
614#386C2314yes—
615#386C2314yes—
616#386C2312yes—
617#386C2312yes—
618#386C2314yes—
619#386C2312yes—
620#386C2312yes—
621#386C2312yes—
622#386C2312yes—
623#386C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2314yes—
635#385C2312yes—
636#385C2314yes—
637#385C2312yes—
638#385C2312yes—
639#385C2311yescharacteristic
640#385C2312yes—
641#385C2312yes—
642#384C2312yes—
643#384C2312yes—
644#384C2312yes—
645#384C2314yes—
646#384C2312yes—
647#383C2312yes—
648#383C2314yes—
649#382C2314yes—
650#382C2312yes—
651#382C2314yes—
652#382C2314yes—
653#382C2314yes—
654#381C2312yes—
655#381C2312yes—
656#381C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2311yescharacteristic
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2314yes—
669#380C2314yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673#380C2312yes—
674#380C2311yescharacteristic
675#380C2314yes—
676#380C2312yes—
677#380C2314yes—
678#379C2311yescharacteristic
679#379C2314yes—
680#379C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2311yescharacteristic
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2311yescharacteristic
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716#376C2311yescharacteristic
717C25C2411yescharacteristic
718C2×#41—44no—
719C2×#41—44no—
720C2×#41—44no—
721C22×Q8C2412yes—
722C22×Q8C2414yes—
723C22×Q8C2414yes—
724C22×Q8C2414yes—
725C22×D4C2411yescharacteristic
726C22×D4C2411yescharacteristic
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C22×D4C2414yes—
737C23×C4—42no—
738C23×C4—44no—
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2414yes—
750C23×C4C2412yes—
751C23×C4C2411yescharacteristic
752C4⋊Q8—28no—
753C4⋊Q8—44no—
754C4⋊Q8—44no—
755C4⋊Q8—44no—
756C4⋊Q8—42no—
757C4⋊Q8—48no—
758#126—44no—
759#126—48no—
760#126—48no—
761#126—84no—
762#125—44no—
763#125—44no—
764#125—42no—
765#124—48no—
766#124—48no—
767#124—84no—
768#124—84no—
769#124—84no—
770#123—28no—
771#123—28no—
772#123—48no—
773#123—48no—
774#123—44no—
775#123—82no—
776#123—82no—
777C22⋊Q8—28no—
778C22⋊Q8—48no—
779C22⋊Q8—48no—
780C22⋊Q8—48no—
781C22⋊Q8—44no—
782C22⋊Q8—48no—
783C22⋊Q8—44no—
784C22⋊Q8—44no—
785C22⋊Q8—44no—
786#121—44no—
787#121—44no—
788#121—44no—
789#121—44no—
790#121—44no—
791#121—42no—
792#121—42no—
793#120—24no—
794#120—44no—
795#120—82no—
796C4×Q8—44no—
797C4×Q8—48no—
798C4×Q8—44no—
799C4×Q8—84no—
800C4×D4—24no—
801C4×D4—44no—
802C4×D4—44no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—42no—
806C4×D4—44no—
807C4×D4—42no—
808C4×D4—44no—
809#117—28no—
810#117—24no—
811#117—42no—
812#117—48no—
813#117—44no—
814#117—44no—
815#117—84no—
816C2×C4⋊C4—24no—
817C2×C4⋊C4—42no—
818C2×C4⋊C4—42no—
819C2×C4⋊C4—44no—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C22⋊C4—44no—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2411yescharacteristic
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2411yescharacteristic
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2411yescharacteristic
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2411yescharacteristic
937C2×C42—44no—
938C2×C42—44no—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2411yescharacteristic
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2412yes—
958C2×C42C2412yes—
959#95C2411yescharacteristic
960#95C2411yescharacteristic
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2411yescharacteristic
969#95C2412yes—
970#95C2411yescharacteristic
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022C24—22no—
1023C24—41no—
1024C24—42no—
1025C24—42no—
1026C24—41no—
1027C24C2512yes—
1028C24C2512yes—
1029C24C2511yescharacteristic
1030C24C2512yes—
1031C24C2511yescharacteristic
1032#41—816no—
1033C2×Q8—24no—
1034C2×Q8—28no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—28no—
1038C2×Q8—44no—
1039C2×Q8—44no—
1040C2×Q8—44no—
1041C2×Q8—44no—
1042C2×Q8—44no—
1043C2×Q8—44no—
1044C2×Q8—44no—
1045C2×D4—22no—
1046C2×D4—24no—
1047C2×D4—24no—
1048C2×D4—22no—
1049C2×D4—24no—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—41no—
1053C2×D4—42no—
1054C2×D4—41no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—44no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—41no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—42no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C22×C4—24no—
1079C22×C4—22no—
1080C22×C4—22no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—24no—
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—41no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4—42no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—44no—
1103C22×C4—42no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—42no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—42no—
1110C22×C4—44no—
1111C22×C4—416no—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2514yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2514yes—
1120C22×C4C2511yescharacteristic
1121C22×C4C2511yescharacteristic
1122C22×C4C2514yes—
1123C22×C4C2514yes—
1124C22×C4C2514yes—
1125C22×C4C2511yescharacteristic
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2514yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2511yescharacteristic
1136C4⋊C4—22no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—22no—
1142C4⋊C4—28no—
1143C4⋊C4—24no—
1144C4⋊C4—28no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—28no—
1151C4⋊C4—28no—
1152C4⋊C4—24no—
1153C4⋊C4—41no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—41no—
1158C4⋊C4—41no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—41no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4H(5,𝔽2)14yes—
1192C22⋊C4—24no—
1193C22⋊C4—28no—
1194C22⋊C4—24no—
1195C22⋊C4—24no—
1196C22⋊C4—28no—
1197C22⋊C4—24no—
1198C22⋊C4—24no—
1199C22⋊C4—28no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—28no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—41no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—41no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—41no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—42no—
1247C22⋊C4—44no—
1248C22⋊C4—42no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C42−1+414yes—
1252C42—28no—
1253C42—24no—
1254C42—24no—
1255C42—22no—
1256C42—24no—
1257C42—24no—
1258C42—24no—
1259C42—42no—
1260C42—42no—
1261C42—44no—
1262C42—44no—
1263C42—44no—
1264C42—44no—
1265C42—44no—
1266C42—44no—
1267C42—42no—
1268C42—44no—
1269C42—44no—
1270C42—44no—
1271C42—44no—
1272C23—21no—
1273C23—22no—
1274C23—22no—
1275C23—21no—
1276C23—22no—
1277C23—22no—
1278C23—21no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23—21no—
1284C23—24no—
1285C23—22no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—24no—
1295C23—22no—
1296C23—22no—
1297C23—21no—
1298C23—22no—
1299C23—22no—
1300C23—44no—
1301C23—84no—
1302C23—82no—
1303C23—82no—
1304C23—84no—
1305C23C2×2−1+412yes—
1306C23C2611yescharacteristic
1307Q8—48no—
1308Q8—88no—
1309Q8—88no—
1310Q8—164no—
1311D4—44no—
1312D4—84no—
1313D4—84no—
1314D4—84no—
1315D4—82no—
1316D4—84no—
1317D4—82no—
1318D4—84no—
1319D4—84no—
1320D4—88no—
1321D4—162no—
1322D4—164no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—21no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—21no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—21no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—21no—
1341C2×C4—22no—
1342C2×C4—21no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—21no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—48no—
1385C2×C4—44no—
1386C2×C4—48no—
1387C2×C4—44no—
1388C2×C4—44no—
1389C2×C4—48no—
1390C2×C4—48no—
1391C2×C4—84no—
1392C2×C4—84no—
1393C2×C4—84no—
1394C2×C4—84no—
1395C2×C4—88no—
1396C2×C4—162no—
1397C2×C4C2×H(5,𝔽2)14yes—
1398C2×C4C2×H(5,𝔽2)12yes—
1399C2×C4C2×2−1+414yes—
1400C2×C4#58514yes—
1401C2×C4#58514yes—
1402C22—24no—
1403C22—22no—
1404C22—41no—
1405C22—41no—
1406C22—42no—
1407C22—42no—
1408C22—42no—
1409C22—41no—
1410C22—42no—
1411C22—42no—
1412C22—41no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—42no—
1418C22—44no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—44no—
1427C22—41no—
1428C22—42no—
1429C22—42no—
1430C22—42no—
1431C22—88no—
1432C22C22×H(5,𝔽2)11yescharacteristic
1433C22C22×2−1+411yescharacteristic
1434C22C2×#58512yes—
1435C22C2×#58512yes—
1436C22H(7,𝔽2)11yescharacteristic
1437C4—24no—
1438C4—24no—
1439C4—24no—
1440C4—41no—
1441C4—42no—
1442C4—41no—
1443C4—42no—
1444C4—44no—
1445C4—41no—
1446C4—42no—
1447C4—44no—
1448C4—42no—
1449C4—42no—
1450C4—42no—
1451C4—42no—
1452C4—42no—
1453C4—44no—
1454C4—44no—
1455C4—44no—
1456C4—42no—
1457C4—44no—
1458C4—41no—
1459C4—42no—
1460C4#354014yes—
1461C2—42no—
1462C2—82no—
1463C2—81no—
1464C2—82no—
1465C2—82no—
1466C2C2×#354011yescharacteristic
1467C2#6290812yes—
1468C2#6291711yescharacteristic
1469C2#6302111yescharacteristic
1470C2#6302512yes—
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. #59811C2semidirect
2. #59629C2semidirect
3. #59277C2semidirect
4. #59234C2semidirect
5. #58963C2semidirect
6. #57411C2semidirect
7. #54678C2semidirect
8. #54100C2semidirect
9. #52292C2semidirect
10. #51878C2semidirect
11. #50323C2semidirect
12. #48428C2semidirect
13. #45601C2semidirect
14. #45493C2semidirect
15. #45433C2semidirect
16. #45345C2semidirect
17. #45098C2semidirect
18. #45040C2semidirect
19. #42914C2semidirect
20. #42894C2semidirect
21. #42763C2semidirect
22. #42679C2semidirect
23. #40007C2semidirect
24. #39737C2semidirect
25. #39657C2semidirect
26. #37100C2semidirect
27. #36879C2semidirect
28. #36517C2semidirect
29. #36439C2semidirect
32. C2×#547C22semidirect
33. C2×#544C22semidirect
35. #2857C22semidirect
44. #2821C22semidirect
45. #2813C22semidirect
50. #2800C22semidirect
51. #2798C22semidirect
53. #2794C22semidirect
56. #2786C22semidirect
62. #2775C22semidirect
64. #2772C22semidirect
66. #2767C22semidirect
67. #2759C22semidirect
68. #2755C22semidirect
69. #2755C22semidirect
71. #2754C22semidirect
78. #2741C22semidirect
79. #2741C22semidirect
80. #2740C22semidirect
86. #2729C22semidirect
88. #2718C22semidirect
92. #2712C22semidirect
96. #2702C22semidirect
98. #2696C22semidirect
99. #2695C22semidirect
105. #2680C22semidirect
110. #2665C22semidirect
111. #2664C22semidirect
112. #2662C22semidirect
113. #2655C22semidirect
117. #2642C22semidirect
120. #2624C22semidirect
121. #2623C22semidirect
127. #2589C22semidirect
128. #2589C22semidirect
129. #2582C22semidirect
130. #2573C22semidirect
131. #2565C22semidirect
134. #2562C22semidirect
136. #2559C22semidirect
142. #2552C22semidirect
143. #2551C22semidirect
145. #2547C22semidirect
152. #2522C22semidirect
153. #2520C22semidirect
154. #2519C22semidirect
155. #2517C22semidirect
156. #2517C22semidirect
158. #2513C22semidirect
159. #2512C22semidirect
160. #2511C22semidirect
161. #2511C22semidirect
162. #2511C22semidirect
164. #2501C22semidirect
167. #2497C22semidirect
168. #2495C22semidirect
172. #2492C22semidirect
173. #2492C22semidirect
174. #2492C22semidirect
184. #2485C22semidirect
188. #2479C22semidirect
192. #2474C22semidirect
196. #2469C22semidirect
198. #2458C22semidirect
199. #2452C22semidirect
200. #2451C22semidirect
202. #2446C22semidirect
203. #2446C22semidirect
205. #2441C22semidirect
210. #2421C22semidirect
214. #2415C22semidirect
219. #2407C22semidirect
227. #2369C22semidirect
228. #2369C22semidirect
229. #2365C22semidirect
233. #2360C22semidirect
234. #2355C22semidirect
238. #2352C22semidirect
240. #2347C22semidirect
242. #2341C22semidirect
244. #2335C22semidirect
245. #2331C22semidirect
246. #2323C22semidirect
247. #2323C22semidirect
248. #2319C22semidirect
250. C4×C22⋊Q8C22semidirect
257. #2297C22semidirect
258. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#598112
#596292
#592772
#592342
#589632
#574112
#546782
#541002
#522922
#518782
#503232
#484282
#456012
#454932
#454332
#453452
#450982
#450402
#429142
#428942
#427632
#426792
#400072
#397372
#396572
#371002
#368792
#365172
#364392