Finite Group Databasebeta

← #8751457

Subgroups — #8751457

Order 512.

4553 conjugacy classes of subgroups.

The subgroup lattice has 1438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59842C212yesmaximal, complemented
2#59841C211yesmaximal, characteristic, complemented
3#57703C214yesmaximal, complemented
4#57475C214yesmaximal, complemented
5#56558C212yesmaximal, complemented
6#56374C214yesmaximal, complemented
7#56117C214yesmaximal, complemented
8#53100C211yesmaximal, characteristic, complemented
9#53088C212yesmaximal, complemented
10#52643C212yesmaximal, complemented
11#52463C214yesmaximal, complemented
12#47806C212yesmaximal, complemented
13#45369C211yesmaximal, characteristic, complemented
14#45220C212yesmaximal, complemented
15#44987C212yesmaximal, complemented
16#44962C212yesmaximal, complemented
17#44896C212yesmaximal, complemented
18#42980C212yesmaximal, complemented
19#42842C212yesmaximal, complemented
20#42809C211yesmaximal, characteristic, complemented
21#42641C212yesmaximal, complemented
22#42519C212yesmaximal, complemented
23#42441C212yesmaximal, complemented
24#42177C214yesmaximal, complemented
25#39513C212yesmaximal, complemented
26#39488C211yesmaximal, characteristic, complemented
27#36698C211yesmaximal, characteristic, complemented
28#35956C211yesmaximal, characteristic, complemented
29#35919C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×Q82C2211yescharacteristic
32C2×#556C2211yescharacteristic
33C2×#555C2212yes—
34C2×#552C2214yes—
35C2×#547C2211yescharacteristic
36C2×#542C2212yes—
37#2868C2211yescharacteristic
38#2844C2211yescharacteristic
39#2839C2214yes—
40#2838C2212yes—
41#2838C2212yes—
42#2837C2214yes—
43#2836C2212yes—
44#2836C2212yes—
45#2833C2212yes—
46#2833C2212yes—
47#2830C2211yescharacteristic
48#2830C2211yescharacteristic
49#2829C2214yes—
50#2828C2214yes—
51#2826C2214yes—
52#2825C2214yes—
53#2824C2214yes—
54#2822C2211yescharacteristic
55#2822C2212yes—
56#2821C2212yes—
57#2820C2212yes—
58#2814C2214yes—
59#2813C2214yes—
60#2799C2212yes—
61#2797C2214yes—
62#2793C2214yes—
63#2793C2214yes—
64#2793C2214yes—
65#2793C2214yes—
66#2793C2214yes—
67#2789C2212yes—
68#2787C2214yes—
69#2786C2214yes—
70#2785C2212yes—
71#2784C2214yes—
72#2784C2214yes—
73#2784C2212yes—
74#2782C2214yes—
75#2781C2214yes—
76#2779C2214yes—
77#2778C2214yes—
78#2778C2214yes—
79#2770C2214yes—
80#2761C2214yes—
81#2751C2214yes—
82#2748C2214yes—
83#2747C2214yes—
84#2747C2214yes—
85#2741C2214yes—
86#2731C2214yes—
87#2731C2212yes—
88#2729C2214yes—
89#2722C2214yes—
90#2718C2214yes—
91#2718C2214yes—
92#2716C2214yes—
93#2716C2214yes—
94#2715C2214yes—
95#2713C2214yes—
96#2712C2214yes—
97#2711C2214yes—
98#2710C2214yes—
99#2707C2214yes—
100#2705C2214yes—
101#2703C2214yes—
102#2702C2214yes—
103#2699C2212yes—
104#2696C2214yes—
105#2695C2214yes—
106#2695C2214yes—
107#2695C2214yes—
108#2693C2214yes—
109#2693C2214yes—
110#2677C2214yes—
111#2676C2214yes—
112#2674C2214yes—
113#2672C2214yes—
114#2662C2212yes—
115#2662C2214yes—
116#2657C2211yescharacteristic
117#2655C2214yes—
118#2653C2214yes—
119#2649C2214yes—
120#2648C2214yes—
121#2645C2212yes—
122#2640C2211yescharacteristic
123#2637C2212yes—
124#2630C2214yes—
125#2630C2214yes—
126#2629C2214yes—
127#2629C2214yes—
128#2621C2212yes—
129#2620C2212yes—
130#2620C2212yes—
131#2618C2214yes—
132#2610C2212yes—
133#2609C2212yes—
134#2609C2214yes—
135#2609C2212yes—
136#2603C2212yes—
137#2601C2214yes—
138#2599C2212yes—
139#2595C2214yes—
140#2593C2212yes—
141#2592C2211yescharacteristic
142#2592C2212yes—
143#2592C2211yescharacteristic
144#2588C2214yes—
145#2582C2212yes—
146#2579C2214yes—
147#2578C2214yes—
148#2575C2214yes—
149#2574C2214yes—
150#2568C2211yescharacteristic
151#2557C2214yes—
152#2554C2214yes—
153#2548C2212yes—
154#2548C2211yescharacteristic
155#2547C2212yes—
156#2547C2212yes—
157#2546C2211yescharacteristic
158#2545C2214yes—
159#2545C2212yes—
160#2545C2212yes—
161#2545C2212yes—
162#2545C2212yes—
163#2544C2212yes—
164#2542C2211yescharacteristic
165#2528C2214yes—
166#2527C2214yes—
167#2522C2214yes—
168#2512C2212yes—
169#2512C2212yes—
170#2511C2212yes—
171#2506C2212yes—
172#2506C2212yes—
173#2502C2212yes—
174#2502C2212yes—
175#2500C2212yes—
176#2497C2214yes—
177#2497C2214yes—
178#2492C2212yes—
179#2491C2212yes—
180#2481C2214yes—
181#2481C2214yes—
182#2479C2214yes—
183#2477C2214yes—
184#2476C2214yes—
185#2476C2214yes—
186#2475C2214yes—
187#2474C2214yes—
188#2469C2214yes—
189#2467C2214yes—
190#2464C2214yes—
191#2461C2214yes—
192#2460C2214yes—
193#2460C2214yes—
194#2459C2214yes—
195#2458C2214yes—
196#2458C2214yes—
197#2453C2214yes—
198#2452C2212yes—
199#2452C2212yes—
200#2451C2212yes—
201#2451C2212yes—
202#2448C2212yes—
203#2446C2212yes—
204#2446C2212yes—
205#2446C2212yes—
206#2446C2212yes—
207#2445C2212yes—
208#2445C2212yes—
209#2442C2214yes—
210#2432C2212yes—
211#2432C2212yes—
212#2431C2212yes—
213#2431C2212yes—
214#2429C2212yes—
215#2429C2212yes—
216#2429C2214yes—
217#2428C2212yes—
218#2427C2212yes—
219#2427C2212yes—
220#2427C2212yes—
221#2426C2212yes—
222#2423C2212yes—
223#2417C2214yes—
224#2417C2214yes—
225#2416C2212yes—
226#2401C2212yes—
227#2401C2212yes—
228#2399C2211yescharacteristic
229#2399C2211yescharacteristic
230#2396C2212yes—
231#2396C2214yes—
232#2396C2212yes—
233#2395C2212yes—
234#2392C2212yes—
235#2367C2212yes—
236#2366C2212yes—
237#2365C2212yes—
238#2365C2212yes—
239#2365C2212yes—
240#2361C2212yes—
241#2360C2212yes—
242#2360C2212yes—
243#2355C2212yes—
244#2354C2212yes—
245D4×C4⋊C4C2212yes—
246#2344C2212yes—
247#2341C2212yes—
248#2326C2212yes—
249#2323C2212yes—
250#2320C2211yescharacteristic
251#2317C2212yes—
252#2314C2214yes—
253#2311C2212yes—
254C4×#125C2212yes—
255C4×#124C2211yescharacteristic
256#2293C2211yescharacteristic
257#2293C2212yes—
258#2276C2211yescharacteristic
259C22×#41C2312yes—
260#559—44no—
261Q82—44no—
262#556—44no—
263#555—48no—
264#552—416no—
265#547—44no—
266#542—48no—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2314yes—
275C2×C4⋊Q8C2312yes—
276C2×#127C2312yes—
277C2×#127C2311yescharacteristic
278C2×#126C2312yes—
279C2×#126C2314yes—
280C2×#126C2312yes—
281C2×#126C2314yes—
282C2×#126C2314yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#124C2311yescharacteristic
287C2×#124C2312yes—
288C2×#124C2311yescharacteristic
289C2×#124C2311yescharacteristic
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2314yes—
295C2×#124C2314yes—
296C2×#124C2312yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×#121C2312yes—
310C2×#121C2314yes—
311C2×#121C2312yes—
312C2×#121C2314yes—
313C2×#121C2312yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2314yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2311yescharacteristic
333C2×#117C2314yes—
334C2×#117C2312yes—
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2314yes—
338C2×#117C2314yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2314yes—
342#401C2314yes—
343#401C2312yes—
344#401C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2312yes—
350#400C2312yes—
351#400C2312yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2312yes—
356#400C2312yes—
357#400C2312yes—
358#400C2314yes—
359#400C2314yes—
360#400C2312yes—
361#400C2312yes—
362#400C2312yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#399C2312yes—
369#399C2312yes—
370#399C2314yes—
371#399C2314yes—
372#399C2314yes—
373#399C2312yes—
374#398C2311yescharacteristic
375#398C2312yes—
376#398C2311yescharacteristic
377#398C2314yes—
378#398C2311yescharacteristic
379#398C2314yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2311yescharacteristic
387#398C2312yes—
388#398C2312yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#398C2312yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#397C2312yes—
403#397C2312yes—
404#397C2312yes—
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2312yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2312yes—
414#397C2312yes—
415#397C2312yes—
416#397C2312yes—
417#397C2312yes—
418#397C2312yes—
419#397C2314yes—
420#397C2312yes—
421#397C2314yes—
422#397C2312yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#396C2312yes—
427#396C2312yes—
428#396C2312yes—
429#396C2312yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2312yes—
436#396C2312yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#395C2312yes—
451#395C2312yes—
452#395C2314yes—
453#395C2312yes—
454#395C2311yescharacteristic
455#395C2311yescharacteristic
456#395C2314yes—
457#395C2311yescharacteristic
458#395C2311yescharacteristic
459#395C2312yes—
460#394C2312yes—
461#394C2312yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2312yes—
481#394C2312yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#393C2314yes—
486#393C2312yes—
487#393C2312yes—
488#393C2314yes—
489#393C2312yes—
490#393C2312yes—
491#393C2314yes—
492#393C2314yes—
493#393C2314yes—
494#393C2314yes—
495#392C2314yes—
496#392C2312yes—
497#392C2314yes—
498#392C2314yes—
499#392C2314yes—
500#392C2314yes—
501#392C2312yes—
502#392C2314yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#391C2314yes—
509#391C2312yes—
510#391C2311yescharacteristic
511#391C2312yes—
512#391C2312yes—
513#391C2314yes—
514#391C2314yes—
515#391C2312yes—
516#391C2312yes—
517#391C2312yes—
518#391C2312yes—
519#391C2314yes—
520#391C2314yes—
521#390C2312yes—
522#390C2312yes—
523#390C2314yes—
524#390C2314yes—
525#390C2311yescharacteristic
526#390C2312yes—
527#390C2312yes—
528#390C2312yes—
529#390C2314yes—
530#390C2314yes—
531#390C2312yes—
532#390C2314yes—
533#390C2312yes—
534#390C2312yes—
535#390C2314yes—
536#390C2312yes—
537#390C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2312yes—
543#389C2312yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2312yes—
555#389C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2312yes—
570#388C2312yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#384C2312yes—
660#384C2312yes—
661#384C2312yes—
662#384C2312yes—
663#384C2314yes—
664#384C2312yes—
665#383C2312yes—
666#382C2312yes—
667#382C2312yes—
668#382C2311yescharacteristic
669#382C2314yes—
670#382C2312yes—
671#381C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2314yes—
676#380C2314yes—
677#380C2312yes—
678#380C2314yes—
679#380C2314yes—
680#380C2314yes—
681#380C2314yes—
682#380C2314yes—
683#380C2314yes—
684#380C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2312yes—
715#376C2311yescharacteristic
716#376C2312yes—
717#376C2311yescharacteristic
718C43C2311yescharacteristic
719C2×#41—44no—
720C2×#41—44no—
721C2×#41—44no—
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2411yescharacteristic
729C22×Q8C2412yes—
730C22×D4C2412yes—
731C22×D4C2411yescharacteristic
732C22×D4C2411yescharacteristic
733C22×D4C2414yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C22×D4C2414yes—
737C22×D4C2412yes—
738C22×D4C2414yes—
739C22×D4C2414yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2414yes—
747C4⋊Q8—28no—
748C4⋊Q8—42no—
749C4⋊Q8—44no—
750C4⋊Q8—44no—
751C4⋊Q8—42no—
752C4⋊Q8—42no—
753C4⋊Q8—44no—
754C4⋊Q8—44no—
755C4⋊Q8—48no—
756#127—44no—
757#127—42no—
758#126—48no—
759#126—44no—
760#126—44no—
761#126—48no—
762#126—48no—
763#125—28no—
764#125—48no—
765#125—48no—
766#124—24no—
767#124—48no—
768#124—44no—
769#124—44no—
770#124—44no—
771#124—44no—
772#124—42no—
773#124—42no—
774#124—44no—
775#124—48no—
776#124—44no—
777#123—48no—
778#123—48no—
779#123—48no—
780#123—48no—
781#123—48no—
782C22⋊Q8—28no—
783C22⋊Q8—48no—
784C22⋊Q8—48no—
785C22⋊Q8—44no—
786C22⋊Q8—44no—
787C22⋊Q8—44no—
788C22⋊Q8—48no—
789#121—44no—
790#121—48no—
791#121—48no—
792#121—44no—
793#121—44no—
794C4×Q8—24no—
795C4×Q8—24no—
796C4×Q8—42no—
797C4×Q8—42no—
798C4×Q8—42no—
799C4×Q8—48no—
800C4×Q8—44no—
801C4×Q8—44no—
802C4×Q8—44no—
803C4×Q8—44no—
804C4×Q8—44no—
805C4×D4—28no—
806C4×D4—24no—
807C4×D4—44no—
808C4×D4—44no—
809C4×D4—42no—
810C4×D4—44no—
811C4×D4—48no—
812C4×D4—48no—
813#117—28no—
814#117—216no—
815#117—44no—
816#117—44no—
817#117—48no—
818#117—48no—
819C2×C4⋊C4—44no—
820C2×C4⋊C4—44no—
821C2×C4⋊C4—48no—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C42C2412yes—
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2411yescharacteristic
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2414yes—
950C2×C42C2412yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2411yescharacteristic
957C2×C42C2412yes—
958C2×C42C2411yescharacteristic
959#95C2411yescharacteristic
960#95C2412yes—
961#95C2414yes—
962#95C2412yes—
963#95C2411yescharacteristic
964#95C2411yescharacteristic
965#95C2411yescharacteristic
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026C24C2512yes—
1027C24C2512yes—
1028C24C2514yes—
1029#41—816no—
1030C2×Q8—22no—
1031C2×Q8—22no—
1032C2×Q8—24no—
1033C2×Q8—28no—
1034C2×Q8—22no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—41no—
1040C2×Q8—42no—
1041C2×Q8—41no—
1042C2×Q8—44no—
1043C2×Q8—41no—
1044C2×Q8—41no—
1045C2×Q8—44no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—42no—
1049C2×Q8—42no—
1050C2×D4—24no—
1051C2×D4—22no—
1052C2×D4—22no—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—41no—
1057C2×D4—44no—
1058C2×D4—44no—
1059C2×D4—42no—
1060C2×D4—44no—
1061C2×D4—44no—
1062C2×D4—44no—
1063C2×D4—41no—
1064C2×D4—44no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—42no—
1071C2×D4—44no—
1072C2×D4—42no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—42no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—28no—
1084C22×C4—28no—
1085C22×C4—42no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2511yescharacteristic
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2514yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2514yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C22×C4C2514yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2514yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2511yescharacteristic
1124C22×C4C2511yescharacteristic
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—28no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—41no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—41no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—41no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—41no—
1172C4⋊C4—41no—
1173C4⋊C4—41no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4H(5,𝔽2)14yes—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—28no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—28no—
1194C22⋊C4—24no—
1195C22⋊C4—28no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—42no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C42—24no—
1240C42—28no—
1241C42—24no—
1242C42—24no—
1243C42—24no—
1244C42—24no—
1245C42—22no—
1246C42—22no—
1247C42—22no—
1248C42—24no—
1249C42—24no—
1250C42—24no—
1251C42—42no—
1252C42—41no—
1253C42—42no—
1254C42—44no—
1255C42—42no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C42H(5,𝔽2)14yes—
1262C23—22no—
1263C23—22no—
1264C23—24no—
1265C23—22no—
1266C23—24no—
1267C23—22no—
1268C23—24no—
1269C23—22no—
1270C23—22no—
1271C23—24no—
1272C23—24no—
1273C23—22no—
1274C23—24no—
1275C23—22no—
1276C23—22no—
1277C23—24no—
1278C23—22no—
1279C23—24no—
1280C23—24no—
1281C23C2611yescharacteristic
1282Q8—44no—
1283Q8—44no—
1284Q8—44no—
1285Q8—48no—
1286Q8—82no—
1287Q8—88no—
1288Q8—82no—
1289Q8—162no—
1290D4—48no—
1291D4—44no—
1292D4—82no—
1293D4—84no—
1294D4—88no—
1295D4—88no—
1296D4—88no—
1297D4—164no—
1298D4—162no—
1299D4—164no—
1300C2×C4—21no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—21no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—48no—
1368C2×C4—48no—
1369C2×C4—88no—
1370C2×C4—88no—
1371C2×C4—88no—
1372C2×C4—88no—
1373C2×C4—88no—
1374C2×C4C2×H(5,𝔽2)14yes—
1375C2×C4C2×H(5,𝔽2)12yes—
1376C2×C4C2×H(5,𝔽2)14yes—
1377C2×C4C2×H(5,𝔽2)12yes—
1378C2×C4#58514yes—
1379C22—42no—
1380C22—42no—
1381C22—44no—
1382C22—44no—
1383C22—42no—
1384C22—42no—
1385C22—44no—
1386C22—44no—
1387C22—44no—
1388C22—42no—
1389C22—42no—
1390C22—42no—
1391C22—44no—
1392C22—42no—
1393C22—44no—
1394C22—42no—
1395C22—42no—
1396C22—44no—
1397C22—44no—
1398C22C22×H(5,𝔽2)11yescharacteristic
1399C22C22×H(5,𝔽2)11yescharacteristic
1400C22C2×#58512yes—
1401C222−1+612yes—
1402C222−1+611yescharacteristic
1403C4—22no—
1404C4—24no—
1405C4—24no—
1406C4—42no—
1407C4—44no—
1408C4—42no—
1409C4—42no—
1410C4—41no—
1411C4—41no—
1412C4—41no—
1413C4—42no—
1414C4—42no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—42no—
1419C4—41no—
1420C4—44no—
1421C4—42no—
1422C4—41no—
1423C4—44no—
1424C4—44no—
1425C4—42no—
1426C4—44no—
1427C4—42no—
1428C4#355114yes—
1429C2—82no—
1430C2—82no—
1431C2—84no—
1432C2C2×#355111yescharacteristic
1433C2#6291411yescharacteristic
1434C2#6296012yes—
1435C2#6304411yescharacteristic
1436C2#6306212yes—
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. #59842C2semidirect
2. #59841C2semidirect
3. #57703C2semidirect
4. #57475C2semidirect
5. #56558C2semidirect
6. #56374C2semidirect
7. #56117C2semidirect
8. #53100C2semidirect
9. #53088C2semidirect
10. #52643C2semidirect
11. #52463C2semidirect
12. #47806C2semidirect
13. #45369C2semidirect
14. #45220C2semidirect
15. #44987C2semidirect
16. #44962C2semidirect
17. #44896C2semidirect
18. #42980C2semidirect
19. #42842C2semidirect
20. #42809C2semidirect
21. #42641C2semidirect
22. #42519C2semidirect
23. #42441C2semidirect
24. #42177C2semidirect
25. #39513C2semidirect
26. #39488C2semidirect
27. #36698C2semidirect
28. #35956C2semidirect
29. #35919C2semidirect

Maximal subgroups

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

subgroupindex
#598422
#598412
#577032
#574752
#565582
#563742
#561172
#531002
#530882
#526432
#524632
#478062
#453692
#452202
#449872
#449622
#448962
#429802
#428422
#428092
#426412
#425192
#424412
#421772
#395132
#394882
#366982
#359562
#359192