Finite Group Databasebeta

← #7898105

Subgroups — #7898105

Order 512.

4873 conjugacy classes of subgroups.

The subgroup lattice has 1506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59815C211yesmaximal, characteristic, complemented
2#59275C212yesmaximal, complemented
3#52273C211yesmaximal, characteristic, complemented
4#50591C214yesmaximal, complemented
5#50043C214yesmaximal, complemented
6#49188C214yesmaximal, complemented
7#46766C214yesmaximal, complemented
8#46288C212yesmaximal, complemented
9#45176C212yesmaximal, complemented
10#45042C212yesmaximal, complemented
11#44935C212yesmaximal, complemented
12#43622C214yesmaximal, complemented
13#42691C212yesmaximal, complemented
14#42547C212yesmaximal, complemented
15#41495C214yesmaximal, complemented
16#39757C211yesmaximal, characteristic, complemented
17#39611C211yesmaximal, characteristic, complemented
18#39580C212yesmaximal, complemented
19#38997C212yesmaximal, complemented
20#38802C212yesmaximal, complemented
21#38092C212yesmaximal, complemented
22#37953C212yesmaximal, complemented
23#37155C212yesmaximal, complemented
24#36468C211yesmaximal, characteristic, complemented
25#36042C212yesmaximal, complemented
26#35551C212yesmaximal, complemented
27#35206C211yesmaximal, characteristic, complemented
28#34477C212yesmaximal, complemented
29#34330C211yesmaximal, characteristic, complemented
30C2×#554C2212yes—
31C2×#553C2212yes—
32C2×#550C2211yescharacteristic
33C2×#550C2212yes—
34C2×#547C2212yes—
35#2859C2211yescharacteristic
36#2855C2212yes—
37#2854C2212yes—
38#2851C2212yes—
39#2850C2212yes—
40#2831C2214yes—
41#2826C2214yes—
42#2810C2212yes—
43#2810C2212yes—
44#2808C2211yescharacteristic
45#2808C2211yescharacteristic
46#2805C2212yes—
47#2805C2212yes—
48#2804C2211yescharacteristic
49#2796C2212yes—
50#2796C2212yes—
51#2794C2212yes—
52#2784C2214yes—
53#2782C2214yes—
54#2781C2214yes—
55#2775C2214yes—
56#2767C2214yes—
57#2761C2214yes—
58#2758C2214yes—
59#2756C2214yes—
60#2753C2214yes—
61#2752C2214yes—
62#2751C2212yes—
63#2751C2212yes—
64#2750C2214yes—
65#2750C2214yes—
66#2749C2214yes—
67#2743C2214yes—
68#2743C2214yes—
69#2743C2214yes—
70#2739C2214yes—
71#2737C2214yes—
72#2732C2212yes—
73#2732C2212yes—
74#2730C2214yes—
75#2724C2211yescharacteristic
76#2709C2212yes—
77#2702C2214yes—
78#2696C2214yes—
79#2696C2214yes—
80#2693C2214yes—
81#2693C2214yes—
82#2688C2214yes—
83#2688C2214yes—
84#2688C2214yes—
85#2688C2214yes—
86#2688C2214yes—
87#2683C2212yes—
88#2683C2212yes—
89#2682C2212yes—
90#2682C2212yes—
91#2681C2214yes—
92#2676C2214yes—
93#2676C2214yes—
94#2673C2214yes—
95#2673C2214yes—
96#2665C2214yes—
97#2660C2212yes—
98#2652C2214yes—
99#2650C2214yes—
100#2648C2214yes—
101#2642C2212yes—
102#2639C2214yes—
103#2639C2214yes—
104#2635C2214yes—
105#2620C2212yes—
106#2610C2214yes—
107#2609C2214yes—
108#2602C2214yes—
109#2600C2214yes—
110#2591C2214yes—
111#2581C2212yes—
112#2577C2214yes—
113#2575C2214yes—
114#2568C2211yescharacteristic
115#2566C2212yes—
116#2566C2212yes—
117#2562C2212yes—
118#2559C2214yes—
119#2558C2214yes—
120#2552C2211yescharacteristic
121#2547C2211yescharacteristic
122#2542C2212yes—
123#2541C2212yes—
124#2538C2212yes—
125#2538C2211yescharacteristic
126#2537C2211yescharacteristic
127#2537C2211yescharacteristic
128#2537C2212yes—
129#2535C2212yes—
130#2533C2214yes—
131#2533C2214yes—
132#2529C2214yes—
133#2518C2214yes—
134#2516C2214yes—
135#2515C2214yes—
136#2515C2214yes—
137#2511C2212yes—
138#2511C2212yes—
139#2511C2212yes—
140#2505C2214yes—
141#2505C2214yes—
142#2503C2214yes—
143#2503C2212yes—
144#2499C2212yes—
145#2497C2212yes—
146#2496C2212yes—
147#2495C2212yes—
148#2495C2212yes—
149#2492C2212yes—
150#2492C2212yes—
151#2491C2212yes—
152#2490C2212yes—
153#2489C2212yes—
154#2489C2212yes—
155#2489C2212yes—
156#2488C2214yes—
157#2488C2214yes—
158#2488C2214yes—
159#2488C2214yes—
160#2488C2214yes—
161#2481C2214yes—
162#2481C2214yes—
163#2481C2214yes—
164#2477C2214yes—
165#2476C2214yes—
166#2474C2214yes—
167#2471C2214yes—
168#2470C2214yes—
169#2463C2214yes—
170#2460C2214yes—
171#2457C2214yes—
172#2457C2214yes—
173#2457C2214yes—
174#2456C2214yes—
175#2450C2214yes—
176#2449C2214yes—
177#2449C2214yes—
178#2447C2212yes—
179#2445C2214yes—
180#2444C2214yes—
181#2444C2214yes—
182#2444C2214yes—
183#2442C2212yes—
184#2439C2212yes—
185#2431C2212yes—
186#2431C2212yes—
187#2430C2214yes—
188#2430C2214yes—
189#2428C2212yes—
190#2428C2212yes—
191#2428C2212yes—
192#2427C2214yes—
193#2425C2214yes—
194#2422C2212yes—
195#2422C2212yes—
196#2419C2214yes—
197#2416C2214yes—
198#2416C2214yes—
199#2407C2212yes—
200#2407C2212yes—
201#2398C2212yes—
202#2398C2212yes—
203#2395C2212yes—
204C2×#400C2214yes—
205#2380C2214yes—
206#2377C2214yes—
207#2368C2214yes—
208#2366C2212yes—
209#2366C2211yescharacteristic
210#2364C2214yes—
211#2364C2214yes—
212#2363C2212yes—
213#2363C2212yes—
214#2361C2212yes—
215#2357C2212yes—
216#2356C2212yes—
217#2355C2211yescharacteristic
218#2354C2211yescharacteristic
219#2354C2211yescharacteristic
220#2353C2214yes—
221#2352C2212yes—
222D4×C4⋊C4C2212yes—
223D4×C4⋊C4C2211yescharacteristic
224#2339C2212yes—
225#2339C2212yes—
226#2339C2212yes—
227#2339C2212yes—
228#2339C2212yes—
229#2333C2214yes—
230#2333C2214yes—
231#2330C2212yes—
232#2328C2212yes—
233#2328C2214yes—
234#2328C2212yes—
235#2326C2212yes—
236#2325C2214yes—
237#2324C2212yes—
238#2320C2212yes—
239#2318C2214yes—
240#2318C2214yes—
241#2314C2212yes—
242#2311C2212yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×#127C2211yescharacteristic
245C4×#127C2211yescharacteristic
246C4×#123C2212yes—
247C4×#121C2212yes—
248C4×#121C2212yes—
249C4×#121C2212yes—
250#2297C2212yes—
251#2297C2212yes—
252#2295C2211yescharacteristic
253#2295C2211yescharacteristic
254#2290C2212yes—
255#2290C2212yes—
256#2285C2212yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2312yes—
261C22×#41C2312yes—
262#554—48no—
263#553—48no—
264#550—28no—
265#550—216no—
266#547—48no—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×#127C2312yes—
270C2×#127C2314yes—
271C2×#127C2311yescharacteristic
272C2×#127C2311yescharacteristic
273C2×#126C2314yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#124C2312yes—
278C2×#124C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2312yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×#121C2312yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2312yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2312yes—
332C2×#117C2312yes—
333C2×#117C2312yes—
334C2×#117C2312yes—
335C2×#117C2314yes—
336C22×C4⋊C4C2312yes—
337C22×C4⋊C4C2314yes—
338C22×C4⋊C4C2314yes—
339C22×C42C2312yes—
340C22×C42C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2312yes—
360#400C2314yes—
361#400C2314yes—
362#400C2312yes—
363#400C2312yes—
364#400C2312yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2314yes—
376#397C2312yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2312yes—
386#397C2314yes—
387#397C2312yes—
388#397C2314yes—
389#397C2312yes—
390#397C2314yes—
391#397C2312yes—
392#397C2312yes—
393#397C2312yes—
394#397C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2312yes—
415#394C2312yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2312yes—
422#394C2314yes—
423#394C2314yes—
424#394C2312yes—
425#394C2312yes—
426#394C2312yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#393C2312yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2312yes—
436#393C2312yes—
437#393C2312yes—
438#392C2314yes—
439#392C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2311yescharacteristic
457#391C2312yes—
458#391C2311yescharacteristic
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2311yescharacteristic
463#391C2311yescharacteristic
464#390C2312yes—
465#390C2312yes—
466#390C2311yescharacteristic
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2311yescharacteristic
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2314yes—
475#390C2312yes—
476#390C2312yes—
477#390C2314yes—
478#390C2312yes—
479#390C2314yes—
480#390C2312yes—
481#390C2314yes—
482#390C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2311yescharacteristic
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2311yescharacteristic
500#389C2311yescharacteristic
501#389C2311yescharacteristic
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2312yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2312yes—
527#388C2314yes—
528#388C2312yes—
529#388C2314yes—
530#388C2312yes—
531#388C2312yes—
532#388C2312yes—
533#387C2314yes—
534#387C2314yes—
535#387C2312yes—
536#387C2312yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2312yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2312yes—
556#387C2312yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2312yes—
562#387C2312yes—
563#387C2314yes—
564#387C2312yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2312yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2312yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2312yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2312yes—
609#386C2312yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2312yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2312yes—
625#385C2314yes—
626#385C2314yes—
627#385C2312yes—
628#385C2312yes—
629#385C2312yes—
630#384C2311yescharacteristic
631#384C2311yescharacteristic
632#384C2311yescharacteristic
633#384C2311yescharacteristic
634#384C2312yes—
635#384C2312yes—
636#384C2311yescharacteristic
637#383C2314yes—
638#383C2314yes—
639#383C2314yes—
640#382C2312yes—
641#382C2312yes—
642#382C2314yes—
643#382C2314yes—
644#382C2314yes—
645#382C2312yes—
646#382C2312yes—
647#382C2314yes—
648#381C2314yes—
649#381C2314yes—
650#381C2314yes—
651#381C2314yes—
652#381C2314yes—
653#381C2314yes—
654#381C2314yes—
655#381C2314yes—
656#381C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2314yes—
662#380C2314yes—
663#380C2312yes—
664#380C2312yes—
665#380C2314yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673#380C2314yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708#376C2312yes—
709#376C2312yes—
710#376C2314yes—
711C2×#95C2314yes—
712C2×#95C2314yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C2×#41—28no—
718C2×#41—28no—
719C2×#41—28no—
720C2×#41—44no—
721C2×#41—44no—
722C2×#41—44no—
723C2×#41—44no—
724C2×#41—82no—
725C2×#41—82no—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2411yescharacteristic
729C22×Q8C2414yes—
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2414yes—
736C22×D4C2411yescharacteristic
737C22×D4C2414yes—
738C22×D4C2412yes—
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2414yes—
743C22×D4C2414yes—
744C22×D4C2412yes—
745C22×D4C2412yes—
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2412yes—
754C23×C4C2414yes—
755C23×C4C2414yes—
756C23×C4C2414yes—
757C23×C4C2414yes—
758C23×C4C2412yes—
759C23×C4C2414yes—
760C23×C4C2412yes—
761C4⋊Q8—24no—
762C4⋊Q8—44no—
763#127—28no—
764#127—216no—
765#127—42no—
766#127#4118yes—
767#126—48no—
768#125—28no—
769#125—44no—
770#125—82no—
771#124—44no—
772#124—84no—
773#123—48no—
774#123—48no—
775#123—48no—
776#123—44no—
777#123—84no—
778#123—84no—
779C22⋊Q8—48no—
780C22⋊Q8—48no—
781C22⋊Q8—48no—
782C22⋊Q8—48no—
783C22⋊Q8—44no—
784C22⋊Q8—44no—
785C22⋊Q8—84no—
786C22⋊Q8—82no—
787#121—28no—
788#121—28no—
789#121—28no—
790#121—216no—
791#121—216no—
792#121—216no—
793#121—48no—
794#121—44no—
795#121—48no—
796#121—44no—
797#121—44no—
798#121—84no—
799#121—82no—
800#121—84no—
801#121—84no—
802C4×Q8—28no—
803C4×Q8—24no—
804C4×Q8—24no—
805C4×D4—28no—
806C4×D4—216no—
807C4×D4—24no—
808C4×D4—28no—
809C4×D4—28no—
810C4×D4—28no—
811C4×D4—24no—
812C4×D4—44no—
813C4×D4—44no—
814C4×D4—42no—
815C4×D4—44no—
816C4×D4—44no—
817C4×D4—42no—
818C4×D4—42no—
819C4×D4—48no—
820C4×D4—48no—
821C4×D4—82no—
822C4×D4—82no—
823C4×D4—84no—
824C4×D4—84no—
825C4×D4—82no—
826#117—44no—
827#117—44no—
828#117—82no—
829#117—84no—
830C2×C4⋊C4—48no—
831C2×C4⋊C4—44no—
832C2×C4⋊C4—48no—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C42—44no—
941C2×C42—82no—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2411yescharacteristic
945C2×C42C2412yes—
946C2×C42C2411yescharacteristic
947C2×C42C2412yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2411yescharacteristic
953C2×C42C2414yes—
954C2×C42C2412yes—
955C2×C42C2412yes—
956C2×C42C2414yes—
957C2×C42C2412yes—
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2411yescharacteristic
963C2×C42C2411yescharacteristic
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029C24C2512yes—
1030C24C2512yes—
1031C24C2512yes—
1032C24C2514yes—
1033#41—816no—
1034#41—816no—
1035#41—816no—
1036C2×Q8—22no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—22no—
1040C2×Q8—24no—
1041C2×Q8—41no—
1042C2×Q8—41no—
1043C2×Q8—41no—
1044C2×Q8—41no—
1045C2×Q8—44no—
1046C2×Q8—44no—
1047C2×Q8—44no—
1048C2×D4—28no—
1049C2×D4—28no—
1050C2×D4—28no—
1051C2×D4—28no—
1052C2×D4—28no—
1053C2×D4—28no—
1054C2×D4—22no—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—22no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—22no—
1061C2×D4—22no—
1062C2×D4—22no—
1063C2×D4—41no—
1064C2×D4—42no—
1065C2×D4—41no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—42no—
1069C2×D4—44no—
1070C2×D4—41no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—41no—
1078C2×D4—42no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—44no—
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×D4C2×#4118yes—
1094C2×D4C2×#4118yes—
1095C2×D4C2×#4118yes—
1096C22×C4—28no—
1097C22×C4—28no—
1098C22×C4—28no—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—24no—
1102C22×C4—24no—
1103C22×C4—24no—
1104C22×C4—24no—
1105C22×C4—24no—
1106C22×C4—28no—
1107C22×C4—24no—
1108C22×C4—24no—
1109C22×C4—42no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—42no—
1113C22×C4—42no—
1114C22×C4—42no—
1115C22×C4—42no—
1116C22×C4—42no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—42no—
1121C22×C4—44no—
1122C22×C4—42no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—42no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—42no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4C2512yes—
1142C22×C4C2514yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2512yes—
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2514yes—
1154C22×C4C2512yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2514yes—
1157C22×C4C2512yes—
1158C22×C4C2514yes—
1159C22×C4C2514yes—
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C22×C4C2511yescharacteristic
1163C22×C4C2511yescharacteristic
1164C22×C4C2511yescharacteristic
1165C22×C4C2511yescharacteristic
1166C4⋊C4—24no—
1167C4⋊C4—22no—
1168C4⋊C4—22no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—28no—
1172C4⋊C4—22no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—28no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—28no—
1181C4⋊C4—22no—
1182C4⋊C4—24no—
1183C4⋊C4—22no—
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—41no—
1193C4⋊C4—42no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—41no—
1198C4⋊C4—42no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—41no—
1202C4⋊C4—41no—
1203C4⋊C4—42no—
1204C4⋊C4—41no—
1205C4⋊C4—42no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—42no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—42no—
1214C4⋊C4—42no—
1215C4⋊C4—42no—
1216C4⋊C4—44no—
1217C4⋊C4—41no—
1218C22⋊C4—28no—
1219C22⋊C4—28no—
1220C22⋊C4—28no—
1221C22⋊C4—24no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—24no—
1226C22⋊C4—28no—
1227C22⋊C4—24no—
1228C22⋊C4—28no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—42no—
1232C22⋊C4—44no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—42no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—42no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—42no—
1259C22⋊C4—42no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—42no—
1266C22⋊C4—42no—
1267C22⋊C4—42no—
1268C22⋊C4—42no—
1269C22⋊C4—42no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—42no—
1273C42—28no—
1274C42—24no—
1275C42—24no—
1276C42—24no—
1277C42—24no—
1278C42—22no—
1279C42—22no—
1280C42—42no—
1281C42—42no—
1282C42—41no—
1283C42—42no—
1284C42—42no—
1285C42—42no—
1286C42—41no—
1287C42—44no—
1288C42—44no—
1289C42—44no—
1290C42—44no—
1291C42—41no—
1292C42—44no—
1293C42C2×#4114yes—
1294C42H(5,𝔽2)14yes—
1295C23—24no—
1296C23—24no—
1297C23—24no—
1298C23—24no—
1299C23—24no—
1300C23—24no—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23—22no—
1310C23—22no—
1311C23—22no—
1312C23—22no—
1313C23—22no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—22no—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23—22no—
1322C23C22×#4118yes—
1323C23C2611yescharacteristic
1324Q8—44no—
1325Q8—48no—
1326Q8—82no—
1327Q8—164no—
1328D4—216no—
1329D4—48no—
1330D4—48no—
1331D4—44no—
1332D4—44no—
1333D4—84no—
1334D4—82no—
1335D4—84no—
1336D4—88no—
1337D4—88no—
1338D4—88no—
1339D4—88no—
1340D4—88no—
1341D4—88no—
1342D4—88no—
1343D4—164no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—24no—
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—24no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—21no—
1393C2×C4—24no—
1394C2×C4—24no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—21no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—24no—
1411C2×C4—48no—
1412C2×C4—48no—
1413C2×C4—48no—
1414C2×C4—48no—
1415C2×C4—84no—
1416C2×C4—84no—
1417C2×C4—88no—
1418C2×C4—88no—
1419C2×C4—88no—
1420C2×C4—88no—
1421C2×C4—88no—
1422C2×C4—84no—
1423C2×C4—164no—
1424C2×C4—164no—
1425C2×C4—164no—
1426C2×C4C22×#4112yes—
1427C2×C4C22×#4112yes—
1428C2×C4C22×#4112yes—
1429C2×C4C2×H(5,𝔽2)12yes—
1430C2×C4C2×H(5,𝔽2)12yes—
1431C2×C4C2×H(5,𝔽2)12yes—
1432C2×C4#58512yes—
1433C2×C4#58512yes—
1434C22—28no—
1435C22—28no—
1436C22—28no—
1437C22—44no—
1438C22—44no—
1439C22—44no—
1440C22—44no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—42no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22—42no—
1454C22—42no—
1455C22—42no—
1456C22—42no—
1457C22—42no—
1458C22—42no—
1459C22—42no—
1460C22—42no—
1461C22—42no—
1462C22C23×#4111yescharacteristic
1463C22C22×H(5,𝔽2)11yescharacteristic
1464C22C2×#58511yescharacteristic
1465C22C2×#58511yescharacteristic
1466C22H(7,𝔽2)11yescharacteristic
1467C22H(7,𝔽2)11yescharacteristic
1468C222−1+611yescharacteristic
1469C4—22no—
1470C4—22no—
1471C4—22no—
1472C4—22no—
1473C4—22no—
1474C4—42no—
1475C4—42no—
1476C4—42no—
1477C4—44no—
1478C4—41no—
1479C4—42no—
1480C4—42no—
1481C4—42no—
1482C4—42no—
1483C4—44no—
1484C4—42no—
1485C4—42no—
1486C4—44no—
1487C4—42no—
1488C4—42no—
1489C4—42no—
1490C4—44no—
1491C4—42no—
1492C4—44no—
1493C4#351414yes—
1494C2—48no—
1495C2—82no—
1496C2—82no—
1497C2—82no—
1498C2C2×#351411yescharacteristic
1499C2#6284611yescharacteristic
1500C2#6287811yescharacteristic
1501C2#6290811yescharacteristic
1502C2#6295511yescharacteristic
1503C2#6299111yescharacteristic
1504C2#6304711yescharacteristic
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. #59815C2semidirect
2. #59275C2semidirect
3. #52273C2semidirect
4. #50591C2semidirect
5. #50043C2semidirect
6. #49188C2semidirect
7. #46766C2semidirect
8. #46288C2semidirect
9. #45176C2semidirect
10. #45042C2semidirect
11. #44935C2semidirect
12. #43622C2semidirect
13. #42691C2semidirect
14. #42547C2semidirect
15. #41495C2semidirect
16. #39757C2semidirect
17. #39611C2semidirect
18. #39580C2semidirect
19. #38997C2semidirect
20. #38802C2semidirect
21. #38092C2semidirect
22. #37953C2semidirect
23. #37155C2semidirect
24. #36468C2semidirect
25. #36042C2semidirect
26. #35551C2semidirect
27. #35206C2semidirect
28. #34477C2semidirect
29. #34330C2semidirect

Maximal subgroups

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

subgroupindex
#598152
#592752
#522732
#505912
#500432
#491882
#467662
#462882
#451762
#450422
#449352
#436222
#426912
#425472
#414952
#397572
#396112
#395802
#389972
#388022
#380922
#379532
#371552
#364682
#360422
#355512
#352062
#344772
#343302