Finite Group Databasebeta

← #8459228

Subgroups — #8459228

Order 512.

3949 conjugacy classes of subgroups.

The subgroup lattice has 1525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59924C211yesmaximal, characteristic, complemented
2#59673C211yesmaximal, characteristic, complemented
3#59464C211yesmaximal, characteristic, complemented
4#57711C214yesmaximal, complemented
5#56857C214yesmaximal, complemented
6#55871C214yesmaximal, complemented
7#53142C212yesmaximal, complemented
8#52998C212yesmaximal
9#50556C214yesmaximal, complemented
10#46343C212yesmaximal
11#45618C212yesmaximal, complemented
12#45407C212yesmaximal
13#45065C212yesmaximal, complemented
14#42782C212yesmaximal, complemented
15#42670C212yesmaximal, complemented
16#42600C212yesmaximal, complemented
17#42470C212yesmaximal, complemented
18#39974C212yesmaximal, complemented
19#39642C211yesmaximal, characteristic, complemented
20#39515C211yesmaximal, characteristic
21#39514C211yesmaximal, characteristic
22#39157C212yesmaximal, complemented
23#38986C211yesmaximal, characteristic, complemented
24#38237C212yesmaximal
25#37985C212yesmaximal, complemented
26#37631C211yesmaximal, characteristic
27#37404C212yesmaximal, complemented
28#37311C212yesmaximal, complemented
29#36598C211yesmaximal, characteristic, complemented
30#36286C211yesmaximal, characteristic, complemented
31#36175C211yesmaximal, characteristic
32#35185C211yesmaximal, characteristic
33#35177C211yesmaximal, characteristic
34#34951C211yesmaximal, characteristic, complemented
35#34893C211yesmaximal, characteristic
36#2868C2211yescharacteristic
37#2864C2212yes—
38#2863C2212yes—
39#2862C2211yescharacteristic
40#2862C2211yescharacteristic
41#2860C2212yes—
42#2857C2212yes—
43#2855C2212yes—
44#2851C2212yes—
45#2838C2214yes—
46#2838C2214yes—
47#2836C2214yes—
48#2835C2214yes—
49#2833C2214yes—
50#2833C2214yes—
51#2831C2214yes—
52#2831C2214yes—
53#2811C2214yes—
54#2805C2214yes—
55#2802C2214yes—
56#2799C2214yes—
57#2798C2214yes—
58#2798C2214yes—
59#2794C2214yes—
60#2794C2214yes—
61#2793C2214yes—
62#2792C2214yes—
63#2791C2214yes—
64#2789C2214yes—
65#2789C2214yes—
66#2788C2214yes—
67#2776C2214yes—
68#2776C2214yes—
69#2775C2214yes—
70#2774C2214yes—
71#2771C2214yes—
72#2768C2214yes—
73#2764C2214yes—
74#2762C2214yes—
75#2762C2214yes—
76#2762C2214yes—
77#2762C2214yes—
78#2759C2214yes—
79#2759C2214yes—
80#2758C2214yes—
81#2758C2214yes—
82#2758C2214yes—
83#2758C2214yes—
84#2758C2214yes—
85#2755C2214yes—
86#2754C2214yes—
87#2745C2214yes—
88#2729C2214yes—
89#2721C2214yes—
90#2720C2214yes—
91#2716C2214yes—
92#2716C2214yes—
93#2716C2214yes—
94#2716C2214yes—
95#2713C2214yes—
96#2713C2214yes—
97#2713C2214yes—
98#2713C2214yes—
99#2698C2214yes—
100#2689C2214yes—
101#2689C2214yes—
102#2666C2214yes—
103#2665C2214yes—
104#2655C2214yes—
105#2655C2214yes—
106#2650C2214yes—
107#2650C2214yes—
108#2647C2212yes—
109#2645C2212yes—
110#2645C2214yes—
111#2645C2212yes—
112#2640C2212yes—
113#2634C2214yes—
114#2629C2212yes—
115#2628C2212yes—
116#2628C2212yes—
117#2625C2212yes—
118#2612C2214yes—
119#2605C2214yes—
120#2605C2214yes—
121#2604C2214yes—
122#2592C2212yes—
123#2589C2212yes—
124#2588C2214yes—
125#2588C2214yes—
126#2587C2212yes—
127#2585C2212yes—
128#2585C2212yes—
129#2584C2211yescharacteristic
130#2582C2212yes—
131#2582C2211yescharacteristic
132#2581C2214yes—
133#2581C2212yes—
134#2581C2212yes—
135#2580C2211yescharacteristic
136#2575C2214yes—
137#2571C2211yescharacteristic
138#2571C2212yes—
139#2571C2212yes—
140#2570C2212yes—
141#2570C2212yes—
142#2570C2212yes—
143#2570C2212yes—
144#2570C2212yes—
145#2570C2212yes—
146#2568C2212yes—
147#2568C2212yes—
148#2568C2211yescharacteristic
149#2568C2211yescharacteristic
150#2567C2212yes—
151#2567C2212yes—
152#2567C2212yes—
153#2567C2214yes—
154#2567C2212yes—
155#2567C2211yescharacteristic
156#2567C2211yescharacteristic
157#2566C2211yescharacteristic
158#2563C2211yescharacteristic
159#2563C2211yescharacteristic
160#2552C2211yescharacteristic
161#2552C2212yes—
162#2552C2212yes—
163#2551C2212yes—
164#2551C2212yes—
165#2551C2211yescharacteristic
166#2551C2211yescharacteristic
167#2550C2212yes—
168#2550C2212yes—
169#2550C2211yescharacteristic
170#2550C2212yes—
171#2547C2211yescharacteristic
172#2546C2211yescharacteristic
173#2538C2211yescharacteristic
174#2533C2214yes—
175#2527C2214yes—
176#2527C2214yes—
177#2525C2214yes—
178#2523C2214yes—
179#2522C2212yes—
180#2519C2214yes—
181#2514C2212yes—
182#2514C2212yes—
183#2514C2212yes—
184#2514C2212yes—
185#2514C2212yes—
186#2513C2212yes—
187#2512C2212yes—
188#2512C2212yes—
189#2511C2212yes—
190#2511C2212yes—
191#2511C2212yes—
192#2511C2212yes—
193#2511C2212yes—
194#2511C2212yes—
195#2509C2212yes—
196#2509C2212yes—
197#2509C2211yescharacteristic
198#2509C2212yes—
199#2509C2212yes—
200#2509C2212yes—
201#2509C2211yescharacteristic
202#2509C2211yescharacteristic
203#2508C2212yes—
204#2508C2212yes—
205#2508C2212yes—
206#2507C2211yescharacteristic
207#2506C2212yes—
208#2506C2212yes—
209#2497C2212yes—
210#2496C2212yes—
211#2496C2212yes—
212#2496C2214yes—
213#2496C2212yes—
214#2495C2212yes—
215#2495C2212yes—
216#2494C2212yes—
217#2494C2212yes—
218#2494C2212yes—
219#2492C2212yes—
220#2492C2212yes—
221#2489C2214yes—
222#2469C2214yes—
223#2469C2214yes—
224#2465C2212yes—
225#2465C2214yes—
226#2454C2211yescharacteristic
227#2453C2212yes—
228#2453C2212yes—
229#2453C2211yescharacteristic
230#2453C2211yescharacteristic
231#2452C2212yes—
232#2452C2211yescharacteristic
233#2451C2212yes—
234#2451C2212yes—
235#2451C2212yes—
236#2448C2212yes—
237#2448C2212yes—
238#2447C2212yes—
239#2446C2214yes—
240#2446C2212yes—
241#2446C2212yes—
242#2446C2212yes—
243#2421C2212yes—
244#2402C2212yes—
245#2402C2212yes—
246#2396C2212yes—
247#2396C2212yes—
248#2383C2214yes—
249#2369C2212yes—
250#2369C2212yes—
251#2369C2211yescharacteristic
252#2369C2211yescharacteristic
253#2369C2212yes—
254#2369C2211yescharacteristic
255#2369C2211yescharacteristic
256#2367C2212yes—
257#2365C2212yes—
258#2365C2212yes—
259#2365C2211yescharacteristic
260#2365C2211yescharacteristic
261#2365C2212yes—
262#2356C2212yes—
263#2356C2212yes—
264#2355C2212yes—
265#2355C2212yes—
266#2355C2212yes—
267#2351C2212yes—
268#2331C2212yes—
269#2330C2212yes—
270#2330C2214yes—
271#2323C2212yes—
272#2320C2212yes—
273#2319C2212yes—
274#2314C2212yes—
275#2314C2212yes—
276#2314C2212yes—
277C4×C4⋊Q8C2212yes—
278C4×C4⋊Q8C2211yescharacteristic
279C4×C4⋊Q8C2211yescharacteristic
280C4×C4⋊Q8C2211yescharacteristic
281C4×C4⋊Q8C2211yescharacteristic
282C4×C4⋊Q8C2211yescharacteristic
283C4×#125C2211yescharacteristic
284C4×#125C2211yescharacteristic
285C4×#125C2211yescharacteristic
286C4×#125C2211yescharacteristic
287C4×C22⋊Q8C2212yes—
288#2296C2212yes—
289#2295C2212yes—
290#2295C2212yes—
291#2295C2211yescharacteristic
292#2295C2211yescharacteristic
293#2293C2211yescharacteristic
294#2293C2211yescharacteristic
295#2283C2212yes—
296C42×Q8C2211yescharacteristic
297C42×Q8C2211yescharacteristic
298C42×D4C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×C4⋊Q8C2311yescharacteristic
301C2×C4⋊Q8C2311yescharacteristic
302C2×C4⋊Q8C2311yescharacteristic
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2312yes—
305C2×C4⋊Q8C2312yes—
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2314yes—
311C2×C4⋊Q8C2312yes—
312C2×#126C2314yes—
313C2×#126C2314yes—
314C2×#126C2314yes—
315C2×#125C2311yescharacteristic
316C2×#125C2311yescharacteristic
317C2×#125C2311yescharacteristic
318C2×#125C2311yescharacteristic
319C2×#125C2314yes—
320C2×#125C2314yes—
321C2×#124C2312yes—
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2314yes—
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2311yescharacteristic
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2314yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2311yescharacteristic
342C2×#117C2312yes—
343C2×#117C2312yes—
344C22×C42C2312yes—
345#401C2314yes—
346#401C2314yes—
347#401C2314yes—
348#401C2314yes—
349#401C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2312yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2312yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2312yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2312yes—
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2312yes—
384#400C2312yes—
385#400C2314yes—
386#400C2314yes—
387#400C2314yes—
388#400C2312yes—
389#400C2314yes—
390#400C2314yes—
391#400C2312yes—
392#400C2314yes—
393#400C2314yes—
394#400C2312yes—
395#399C2314yes—
396#399C2312yes—
397#399C2314yes—
398#399C2312yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2312yes—
406#398C2314yes—
407#398C2314yes—
408#398C2312yes—
409#398C2314yes—
410#398C2314yes—
411#398C2312yes—
412#398C2314yes—
413#398C2312yes—
414#398C2312yes—
415#398C2312yes—
416#398C2312yes—
417#398C2312yes—
418#398C2312yes—
419#398C2312yes—
420#398C2314yes—
421#398C2312yes—
422#398C2314yes—
423#398C2312yes—
424#398C2314yes—
425#398C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#396C2312yes—
439#396C2312yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2312yes—
445#396C2312yes—
446#395C2314yes—
447#395C2314yes—
448#395C2314yes—
449#395C2314yes—
450#395C2314yes—
451#395C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2312yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#395C2312yes—
463#393C2314yes—
464#393C2314yes—
465#393C2314yes—
466#393C2314yes—
467#393C2314yes—
468#393C2312yes—
469#393C2312yes—
470#393C2314yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2314yes—
479#391C2312yes—
480#391C2312yes—
481#391C2314yes—
482#391C2314yes—
483#391C2314yes—
484#391C2314yes—
485#391C2314yes—
486#391C2314yes—
487#391C2312yes—
488#391C2312yes—
489#391C2314yes—
490#391C2311yescharacteristic
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2314yes—
495#391C2311yescharacteristic
496#391C2312yes—
497#391C2312yes—
498#391C2314yes—
499#391C2312yes—
500#391C2314yes—
501#391C2312yes—
502#391C2314yes—
503#391C2312yes—
504#391C2314yes—
505#391C2312yes—
506#391C2311yescharacteristic
507#391C2311yescharacteristic
508#391C2314yes—
509#391C2312yes—
510#391C2314yes—
511#391C2312yes—
512#391C2312yes—
513#391C2314yes—
514#391C2314yes—
515#391C2312yes—
516#391C2312yes—
517#391C2314yes—
518#391C2312yes—
519#390C2312yes—
520#390C2312yes—
521#390C2311yescharacteristic
522#390C2311yescharacteristic
523#390C2312yes—
524#390C2311yescharacteristic
525#390C2311yescharacteristic
526#389C2311yescharacteristic
527#389C2311yescharacteristic
528#389C2311yescharacteristic
529#389C2311yescharacteristic
530#389C2311yescharacteristic
531#389C2311yescharacteristic
532#389C2311yescharacteristic
533#389C2311yescharacteristic
534#389C2312yes—
535#389C2311yescharacteristic
536#389C2312yes—
537#389C2311yescharacteristic
538#389C2312yes—
539#389C2312yes—
540#389C2311yescharacteristic
541#389C2311yescharacteristic
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2314yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2314yes—
564#389C2311yescharacteristic
565#389C2311yescharacteristic
566#389C2311yescharacteristic
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2311yescharacteristic
572#389C2312yes—
573#389C2314yes—
574#389C2314yes—
575#389C2312yes—
576#389C2314yes—
577#389C2311yescharacteristic
578#389C2314yes—
579#389C2312yes—
580#389C2314yes—
581#389C2312yes—
582#389C2312yes—
583#389C2312yes—
584#389C2314yes—
585#389C2314yes—
586#389C2314yes—
587#389C2312yes—
588#389C2312yes—
589#389C2314yes—
590#389C2314yes—
591#389C2314yes—
592#389C2312yes—
593#389C2311yescharacteristic
594#389C2312yes—
595#389C2312yes—
596#389C2312yes—
597#389C2311yescharacteristic
598#389C2311yescharacteristic
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2312yes—
611#388C2314yes—
612#388C2312yes—
613#388C2312yes—
614#388C2312yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
623#387C2312yes—
624#387C2312yes—
625#387C2312yes—
626#387C2312yes—
627#387C2312yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2312yes—
659#387C2312yes—
660#387C2312yes—
661#387C2312yes—
662#387C2312yes—
663#387C2312yes—
664#387C2312yes—
665#387C2312yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2314yes—
684#387C2314yes—
685#387C2312yes—
686#387C2312yes—
687#385C2312yes—
688#385C2312yes—
689#385C2312yes—
690#385C2314yes—
691#385C2314yes—
692#385C2312yes—
693#385C2312yes—
694#385C2314yes—
695#385C2312yes—
696#384C2311yescharacteristic
697#384C2311yescharacteristic
698#384C2311yescharacteristic
699#384C2312yes—
700#384C2314yes—
701#384C2314yes—
702#384C2312yes—
703#384C2312yes—
704#384C2312yes—
705#384C2312yes—
706#384C2312yes—
707#384C2312yes—
708#383C2314yes—
709#383C2314yes—
710#383C2314yes—
711#383C2314yes—
712#383C2314yes—
713#383C2314yes—
714#382C2311yescharacteristic
715#382C2311yescharacteristic
716#382C2311yescharacteristic
717#382C2311yescharacteristic
718#382C2312yes—
719#382C2312yes—
720#382C2312yes—
721#382C2312yes—
722#382C2314yes—
723#382C2312yes—
724#382C2312yes—
725#382C2312yes—
726#382C2312yes—
727#382C2312yes—
728#382C2314yes—
729#382C2314yes—
730#382C2314yes—
731#381C2314yes—
732#381C2314yes—
733#380C2312yes—
734#380C2312yes—
735#380C2312yes—
736#380C2312yes—
737#380C2312yes—
738#380C2312yes—
739#380C2314yes—
740#380C2312yes—
741#380C2312yes—
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2311yescharacteristic
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2314yes—
785C4×C4⋊C4C2314yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2314yes—
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2311yescharacteristic
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802#376C2312yes—
803#376C2314yes—
804#376C2312yes—
805#376C2314yes—
806C43C2311yescharacteristic
807C43C2311yescharacteristic
808C43C2311yescharacteristic
809C43C2312yes—
810C22×Q8C2411yescharacteristic
811C22×Q8C2412yes—
812C22×Q8C2411yescharacteristic
813C22×Q8C2412yes—
814C22×Q8C2412yes—
815C22×Q8C2412yes—
816C22×Q8C2412yes—
817C22×Q8C2414yes—
818C22×Q8C2414yes—
819C22×D4C2411yescharacteristic
820C23×C4C2412yes—
821C23×C4C2412yes—
822C23×C4C2412yes—
823C4⋊Q8—24no—
824C4⋊Q8—24no—
825C4⋊Q8—24no—
826C4⋊Q8—24no—
827C4⋊Q8—24no—
828C4⋊Q8—44no—
829C4⋊Q8—44no—
830C4⋊Q8—44no—
831C4⋊Q8—44no—
832C4⋊Q8—44no—
833C4⋊Q8—44no—
834C4⋊Q8—84no—
835C4⋊Q8—82no—
836#126—48no—
837#126—84no—
838#126—84no—
839#125—24no—
840#125—42no—
841#125—42no—
842#125—42no—
843#125—48no—
844#125—84no—
845#124—44no—
846C22⋊Q8—44no—
847C22⋊Q8—44no—
848C22⋊Q8—84no—
849C4×Q8—28no—
850C4×Q8—24no—
851C4×Q8—24no—
852C4×Q8—24no—
853C4×Q8—44no—
854C4×Q8—42no—
855C4×Q8—44no—
856C4×Q8—42no—
857C4×Q8—44no—
858C4×Q8—44no—
859C4×Q8—42no—
860C4×Q8—82no—
861C4×Q8—84no—
862C4×Q8—82no—
863C4×D4—24no—
864C4×D4—24no—
865C4×D4—42no—
866#117—28no—
867#117—44no—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2411yescharacteristic
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2411yescharacteristic
916C2×C4⋊C4C2411yescharacteristic
917C2×C4⋊C4C2411yescharacteristic
918C2×C4⋊C4C2411yescharacteristic
919C2×C4⋊C4C2411yescharacteristic
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2411yescharacteristic
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2414yes—
979C2×C42—44no—
980C2×C42C2411yescharacteristic
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2411yescharacteristic
984C2×C42C2411yescharacteristic
985C2×C42C2411yescharacteristic
986C2×C42C2411yescharacteristic
987C2×C42C2411yescharacteristic
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2411yescharacteristic
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2411yescharacteristic
995C2×C42C2411yescharacteristic
996C2×C42C2412yes—
997C2×C42C2414yes—
998C2×C42C2411yescharacteristic
999C2×C42C2411yescharacteristic
1000C2×C42C2411yescharacteristic
1001C2×C42C2411yescharacteristic
1002C2×C42C2411yescharacteristic
1003C2×C42C2414yes—
1004C2×C42C2414yes—
1005C2×C42C2414yes—
1006C2×C42C2414yes—
1007C2×C42C2411yescharacteristic
1008C2×C42C2411yescharacteristic
1009C2×C42C2412yes—
1010C2×C42C2414yes—
1011C2×C42C2414yes—
1012C2×C42C2414yes—
1013C2×C42C2412yes—
1014C2×C42C2414yes—
1015C2×C42C2411yescharacteristic
1016C2×C42C2412yes—
1017C2×C42C2412yes—
1018C2×C42C2412yes—
1019C2×C42C2411yescharacteristic
1020C2×C42C2411yescharacteristic
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2411yescharacteristic
1047#95C2411yescharacteristic
1048#95C2411yescharacteristic
1049#95C2411yescharacteristic
1050#95C2411yescharacteristic
1051#95C2412yes—
1052#95C2411yescharacteristic
1053#95C2412yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2414yes—
1057#95C2412yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2414yes—
1066#95C2412yes—
1067#95C2414yes—
1068#95C2414yes—
1069#95C2412yes—
1070#95C2412yes—
1071#95C2412yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2412yes—
1075#95C2414yes—
1076#95C2414yes—
1077#95C2414yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2412yes—
1081#95C2412yes—
1082#95C2414yes—
1083#95C2414yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2412yes—
1089#95C2414yes—
1090#95C2412yes—
1091#95C2414yes—
1092#95C2412yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2412yes—
1096#95C2412yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2412yes—
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119C24C2512yes—
1120C2×Q8—22no—
1121C2×Q8—24no—
1122C2×Q8—22no—
1123C2×Q8—22no—
1124C2×Q8—24no—
1125C2×Q8—24no—
1126C2×Q8—24no—
1127C2×Q8—24no—
1128C2×Q8—24no—
1129C2×Q8—24no—
1130C2×Q8—22no—
1131C2×Q8—22no—
1132C2×Q8—41no—
1133C2×Q8—42no—
1134C2×Q8—42no—
1135C2×Q8—42no—
1136C2×Q8—42no—
1137C2×Q8—44no—
1138C2×Q8—42no—
1139C2×Q8—42no—
1140C2×Q8—42no—
1141C2×Q8—42no—
1142C2×Q8—44no—
1143C2×Q8—44no—
1144C2×Q8—44no—
1145C2×Q8—44no—
1146C2×Q8—44no—
1147C2×D4—22no—
1148C2×D4—22no—
1149C2×D4—22no—
1150C22×C4—24no—
1151C22×C4—24no—
1152C22×C4—24no—
1153C22×C4—24no—
1154C22×C4—42no—
1155C22×C4—42no—
1156C22×C4—42no—
1157C22×C4—42no—
1158C22×C4—42no—
1159C22×C4C2512yes—
1160C22×C4C2514yes—
1161C22×C4C2512yes—
1162C22×C4C2511yescharacteristic
1163C22×C4C2511yescharacteristic
1164C22×C4C2512yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2512yes—
1167C22×C4C2511yescharacteristic
1168C22×C4C2511yescharacteristic
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2512yes—
1173C22×C4C2511yescharacteristic
1174C22×C4C2512yes—
1175C22×C4C2514yes—
1176C22×C4C2514yes—
1177C22×C4C2512yes—
1178C22×C4C2511yescharacteristic
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2512yes—
1182C22×C4C2512yes—
1183C22×C4C2514yes—
1184C22×C4C2511yescharacteristic
1185C22×C4C2511yescharacteristic
1186C22×C4C2511yescharacteristic
1187C22×C4C2511yescharacteristic
1188C22×C4C2512yes—
1189C22×C4C2511yescharacteristic
1190C22×C4C2511yescharacteristic
1191C22×C4C2511yescharacteristic
1192C22×C4C2511yescharacteristic
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—22no—
1196C4⋊C4—22no—
1197C4⋊C4—22no—
1198C4⋊C4—22no—
1199C4⋊C4—22no—
1200C4⋊C4—28no—
1201C4⋊C4—24no—
1202C4⋊C4—22no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—22no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—22no—
1211C4⋊C4—22no—
1212C4⋊C4—22no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—22no—
1219C4⋊C4—22no—
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—24no—
1223C4⋊C4—24no—
1224C4⋊C4—24no—
1225C4⋊C4—24no—
1226C4⋊C4—28no—
1227C4⋊C4—22no—
1228C4⋊C4—22no—
1229C4⋊C4—22no—
1230C4⋊C4—24no—
1231C4⋊C4—42no—
1232C4⋊C4—42no—
1233C4⋊C4—41no—
1234C4⋊C4—42no—
1235C4⋊C4—42no—
1236C4⋊C4—41no—
1237C4⋊C4—41no—
1238C4⋊C4—42no—
1239C4⋊C4—42no—
1240C4⋊C4—42no—
1241C4⋊C4—41no—
1242C4⋊C4—42no—
1243C4⋊C4—44no—
1244C4⋊C4—41no—
1245C4⋊C4—44no—
1246C4⋊C4—42no—
1247C4⋊C4—42no—
1248C4⋊C4—42no—
1249C4⋊C4—42no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—42no—
1254C4⋊C4—44no—
1255C4⋊C4—42no—
1256C4⋊C4—44no—
1257C4⋊C4—44no—
1258C4⋊C4—42no—
1259C4⋊C4—42no—
1260C4⋊C4—42no—
1261C4⋊C4—42no—
1262C4⋊C4—42no—
1263C4⋊C4—42no—
1264C4⋊C4—44no—
1265C4⋊C4—44no—
1266C4⋊C4—42no—
1267C4⋊C4—42no—
1268C4⋊C4—44no—
1269C4⋊C4—44no—
1270C4⋊C4—44no—
1271C4⋊C4—44no—
1272C4⋊C4—42no—
1273C4⋊C4—44no—
1274C4⋊C4—44no—
1275C4⋊C4—44no—
1276C4⋊C4—44no—
1277C4⋊C4—44no—
1278C4⋊C4—44no—
1279C4⋊C4—44no—
1280C4⋊C4—42no—
1281C4⋊C4—42no—
1282C4⋊C4—42no—
1283C4⋊C4—42no—
1284C4⋊C42−1+414yes—
1285C22⋊C4—24no—
1286C22⋊C4—24no—
1287C22⋊C4—24no—
1288C22⋊C4—24no—
1289C22⋊C4—24no—
1290C22⋊C4—42no—
1291C22⋊C4—42no—
1292C22⋊C4—42no—
1293C22⋊C4—42no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—42no—
1302C22⋊C4—44no—
1303C22⋊C4—42no—
1304C42—24no—
1305C42—22no—
1306C42—22no—
1307C42—24no—
1308C42—28no—
1309C42—24no—
1310C42—22no—
1311C42—24no—
1312C42—22no—
1313C42—22no—
1314C42—22no—
1315C42—24no—
1316C42—22no—
1317C42—24no—
1318C42—22no—
1319C42—22no—
1320C42—22no—
1321C42—22no—
1322C42—24no—
1323C42—24no—
1324C42—22no—
1325C42—42no—
1326C42—42no—
1327C42—44no—
1328C42—41no—
1329C42—41no—
1330C42—42no—
1331C42—44no—
1332C42—41no—
1333C42—41no—
1334C42—44no—
1335C42—44no—
1336C42—44no—
1337C42—44no—
1338C42—44no—
1339C42—44no—
1340C42—42no—
1341C42—42no—
1342C42—41no—
1343C422−1+414yes—
1344C422−1+414yes—
1345C23—22no—
1346C23—22no—
1347C23—22no—
1348C23—22no—
1349C23—22no—
1350C23—22no—
1351C23—22no—
1352C23C2611yescharacteristic
1353Q8—44no—
1354Q8—44no—
1355Q8—48no—
1356Q8—84no—
1357Q8—84no—
1358Q8—84no—
1359Q8—84no—
1360Q8—88no—
1361Q8—164no—
1362D4—44no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—22no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—22no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—22no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—22no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—24no—
1398C2×C4—24no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—22no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—24no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—21no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—21no—
1430C2×C4—24no—
1431C2×C4—21no—
1432C2×C4—22no—
1433C2×C4—24no—
1434C2×C4—24no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—22no—
1442C2×C4—24no—
1443C2×C4—22no—
1444C2×C4—22no—
1445C2×C4—24no—
1446C2×C4—22no—
1447C2×C4—21no—
1448C2×C4—22no—
1449C2×C4—24no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—22no—
1453C2×C4—22no—
1454C2×C4—48no—
1455C2×C4—84no—
1456C2×C4—84no—
1457C2×C4C2×2−1+412yes—
1458C2×C4C2×2−1+414yes—
1459C2×C4C2×2−1+412yes—
1460C2×C4C2×2−1+412yes—
1461C2×C4C2×2−1+412yes—
1462C2×C4C2×2−1+412yes—
1463C2×C4C2×2−1+412yes—
1464C2×C4C2×2−1+412yes—
1465C2×C4#58512yes—
1466C2×C4#58512yes—
1467C2×C4#58512yes—
1468C22—42no—
1469C22—42no—
1470C22—42no—
1471C22—42no—
1472C22—42no—
1473C22—42no—
1474C22—42no—
1475C22C22×2−1+411yescharacteristic
1476C22C22×2−1+411yescharacteristic
1477C22C22×2−1+411yescharacteristic
1478C22C2×#58511yescharacteristic
1479C22C2×#58511yescharacteristic
1480C22C2×#58511yescharacteristic
1481C22H(7,𝔽2)11yescharacteristic
1482C4—24no—
1483C4—22no—
1484C4—22no—
1485C4—22no—
1486C4—22no—
1487C4—42no—
1488C4—42no—
1489C4—44no—
1490C4—41no—
1491C4—42no—
1492C4—41no—
1493C4—42no—
1494C4—41no—
1495C4—42no—
1496C4—41no—
1497C4—42no—
1498C4—42no—
1499C4—41no—
1500C4—41no—
1501C4—41no—
1502C4—42no—
1503C4—42no—
1504C4—42no—
1505C4—44no—
1506C4—42no—
1507C4—42no—
1508C4—41no—
1509C4—42no—
1510C4—41no—
1511C4—42no—
1512C4—44no—
1513C4—44no—
1514C4#355514yes—
1515C4#355514yes—
1516C2—82no—
1517C2C2×#355511yescharacteristic
1518C2C2×#355511yescharacteristic
1519C2#6283111yescharacteristic
1520C2#6293811yescharacteristic
1521C2#6294311yescharacteristic
1522C2#6296211yescharacteristic
1523C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59924C2semidirect
2. #59673C2semidirect
3. #59464C2semidirect
4. #57711C2semidirect
5. #56857C2semidirect
6. #55871C2semidirect
7. #53142C2semidirect
9. #50556C2semidirect
11. #45618C2semidirect
13. #45065C2semidirect
14. #42782C2semidirect
15. #42670C2semidirect
16. #42600C2semidirect
17. #42470C2semidirect
18. #39974C2semidirect
19. #39642C2semidirect
22. #39157C2semidirect
23. #38986C2semidirect
25. #37985C2semidirect
27. #37404C2semidirect
28. #37311C2semidirect
29. #36598C2semidirect
30. #36286C2semidirect
34. #34951C2semidirect

Maximal subgroups

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

subgroupindex
#599242
#596732
#594642
#577112
#568572
#558712
#531422
#529982
#505562
#463432
#456182
#454072
#450652
#427822
#426702
#426002
#424702
#399742
#396422
#395152
#395142
#391572
#389862
#382372
#379852
#376312
#374042
#373112
#365982
#362862
#361752
#351852
#351772
#349512
#348932