Finite Group Databasebeta

← #8726613

Subgroups — #8726613

Order 512.

5208 conjugacy classes of subgroups.

The subgroup lattice has 1578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59813C212yesmaximal, complemented
2#59632C211yesmaximal, characteristic, complemented
3#59125C212yesmaximal, complemented
4#59101C212yesmaximal, complemented
5#59054C212yesmaximal, complemented
6#58295C214yesmaximal, complemented
7#57235C214yesmaximal, complemented
8#57120C214yesmaximal, complemented
9#53521C212yesmaximal, complemented
10#53137C211yesmaximal, characteristic, complemented
11#53088C212yesmaximal, complemented
12#52299C211yesmaximal, characteristic, complemented
13#47231C214yesmaximal, complemented
14#46548C212yesmaximal, complemented
15#45244C211yesmaximal, characteristic, complemented
16#45033C214yesmaximal, complemented
17#44884C212yesmaximal, complemented
18#43403C212yesmaximal, complemented
19#42908C211yesmaximal, characteristic, complemented
20#42643C212yesmaximal, complemented
21#41827C214yesmaximal, complemented
22#41341C212yesmaximal, complemented
23#39961C212yesmaximal, complemented
24#39858C212yesmaximal, complemented
25#39721C211yesmaximal, characteristic, complemented
26#39246C212yesmaximal, complemented
27#38998C212yesmaximal, complemented
28#36066C211yesmaximal, characteristic, complemented
29#35886C212yesmaximal, complemented
30C2×#552C2212yes—
31C2×#550C2211yescharacteristic
32C2×#550C2212yes—
33C2×#548C2211yescharacteristic
34C2×#548C2212yes—
35C2×#548C2212yes—
36C2×#547C2212yes—
37C2×#537C2211yescharacteristic
38C2×#537C2212yes—
39C22×C4⋊Q8C2211yescharacteristic
40C2×#529C2212yes—
41#2854C2211yescharacteristic
42#2850C2212yes—
43#2838C2214yes—
44#2828C2214yes—
45#2826C2212yes—
46#2826C2214yes—
47#2825C2214yes—
48#2824C2212yes—
49#2817C2212yes—
50#2813C2214yes—
51#2813C2214yes—
52#2807C2212yes—
53#2801C2212yes—
54#2800C2214yes—
55#2780C2214yes—
56#2778C2214yes—
57#2778C2214yes—
58#2778C2214yes—
59#2760C2211yescharacteristic
60#2752C2212yes—
61#2752C2211yescharacteristic
62#2752C2212yes—
63#2749C2214yes—
64#2742C2211yescharacteristic
65#2742C2212yes—
66#2742C2212yes—
67#2740C2214yes—
68#2738C2214yes—
69#2731C2214yes—
70#2729C2214yes—
71#2723C2214yes—
72#2723C2214yes—
73#2720C2214yes—
74#2715C2214yes—
75#2714C2214yes—
76#2714C2214yes—
77#2711C2214yes—
78#2709C2214yes—
79#2709C2214yes—
80#2709C2214yes—
81#2709C2212yes—
82#2708C2214yes—
83#2703C2212yes—
84#2703C2214yes—
85#2703C2212yes—
86#2703C2212yes—
87#2703C2214yes—
88#2703C2214yes—
89#2701C2214yes—
90#2696C2214yes—
91#2694C2214yes—
92#2693C2214yes—
93#2688C2214yes—
94#2688C2214yes—
95#2686C2214yes—
96#2683C2212yes—
97#2682C2214yes—
98#2681C2214yes—
99#2676C2214yes—
100#2675C2211yescharacteristic
101#2675C2214yes—
102#2675C2212yes—
103#2674C2214yes—
104#2674C2214yes—
105#2673C2214yes—
106#2673C2214yes—
107#2673C2214yes—
108#2671C2214yes—
109#2671C2214yes—
110#2661C2214yes—
111#2661C2214yes—
112#2657C2212yes—
113#2657C2211yescharacteristic
114#2655C2214yes—
115#2654C2214yes—
116#2648C2214yes—
117#2645C2212yes—
118#2639C2212yes—
119#2635C2212yes—
120#2631C2214yes—
121#2624C2214yes—
122#2618C2212yes—
123#2616C2211yescharacteristic
124#2610C2214yes—
125#2602C2214yes—
126#2602C2214yes—
127#2598C2214yes—
128#2597C2214yes—
129#2591C2214yes—
130#2591C2212yes—
131#2587C2214yes—
132#2579C2212yes—
133#2577C2214yes—
134#2564C2212yes—
135#2559C2214yes—
136#2559C2214yes—
137#2557C2214yes—
138#2556C2214yes—
139#2555C2212yes—
140#2547C2212yes—
141#2545C2212yes—
142#2544C2212yes—
143#2542C2212yes—
144#2541C2212yes—
145#2541C2212yes—
146#2541C2214yes—
147#2541C2211yescharacteristic
148#2540C2212yes—
149#2540C2212yes—
150#2540C2214yes—
151#2540C2212yes—
152#2540C2211yescharacteristic
153#2535C2212yes—
154#2533C2214yes—
155#2530C2214yes—
156#2528C2214yes—
157#2526C2214yes—
158#2512C2214yes—
159#2509C2212yes—
160#2509C2214yes—
161#2503C2211yescharacteristic
162#2500C2214yes—
163#2491C2214yes—
164#2490C2212yes—
165#2490C2212yes—
166#2489C2212yes—
167#2487C2211yescharacteristic
168#2485C2212yes—
169#2479C2214yes—
170#2477C2214yes—
171#2476C2214yes—
172#2471C2214yes—
173#2467C2214yes—
174#2466C2214yes—
175#2464C2214yes—
176#2463C2212yes—
177#2460C2214yes—
178#2457C2214yes—
179#2457C2214yes—
180#2455C2212yes—
181#2453C2212yes—
182#2449C2214yes—
183#2448C2212yes—
184#2446C2212yes—
185#2445C2212yes—
186#2445C2214yes—
187#2445C2212yes—
188#2444C2214yes—
189#2443C2214yes—
190#2443C2214yes—
191#2441C2214yes—
192#2440C2214yes—
193#2436C2211yescharacteristic
194#2432C2212yes—
195#2432C2212yes—
196#2432C2212yes—
197#2431C2212yes—
198#2431C2212yes—
199#2429C2212yes—
200#2429C2212yes—
201#2429C2212yes—
202#2428C2214yes—
203#2428C2214yes—
204#2428C2212yes—
205#2428C2214yes—
206#2427C2212yes—
207#2426C2212yes—
208#2426C2212yes—
209#2421C2212yes—
210#2420C2212yes—
211#2417C2212yes—
212#2416C2214yes—
213#2416C2212yes—
214#2416C2212yes—
215#2416C2214yes—
216#2415C2212yes—
217#2415C2212yes—
218#2414C2212yes—
219#2409C2211yescharacteristic
220#2409C2212yes—
221#2409C2212yes—
222#2407C2212yes—
223#2407C2212yes—
224#2401C2212yes—
225#2401C2214yes—
226#2397C2211yescharacteristic
227#2397C2212yes—
228#2388C2212yes—
229#2388C2211yescharacteristic
230#2370C2212yes—
231#2366C2212yes—
232#2365C2212yes—
233#2363C2212yes—
234#2363C2214yes—
235#2363C2214yes—
236#2361C2212yes—
237#2360C2212yes—
238#2360C2212yes—
239#2359C2214yes—
240#2356C2212yes—
241D4×C4⋊C4C2214yes—
242#2345C2212yes—
243Q8×C22⋊C4C2211yescharacteristic
244#2339C2211yescharacteristic
245#2333C2214yes—
246#2328C2214yes—
247#2322C2214yes—
248#2322C2212yes—
249#2319C2214yes—
250C4×C22⋊Q8C2212yes—
251C4×#123C2211yescharacteristic
252C4×#123C2212yes—
253C4×#121C2212yes—
254C4×#121C2212yes—
255C4×#121C2212yes—
256C4×#121C2212yes—
257#2297C2212yes—
258#2276C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2312yes—
261C22×#41C2311yescharacteristic
262C22×#41C2312yes—
263C23×Q8C2311yescharacteristic
264C23×Q8C2311yescharacteristic
265#552—48no—
266#550—48no—
267#550—44no—
268#548—48no—
269#548—48no—
270#548—44no—
271#547—48no—
272#537—48no—
273#537—44no—
274C2×C4⋊Q8—44no—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2314yes—
277C2×C4⋊Q8C2312yes—
278C2×#127C2314yes—
279C2×#127C2312yes—
280C2×#127C2312yes—
281C2×#127C2314yes—
282C2×#127C2312yes—
283C2×#127C2311yescharacteristic
284#529—48no—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#125C2312yes—
288C2×#125C2314yes—
289C2×#124C2312yes—
290C2×#124C2314yes—
291C2×#124C2314yes—
292C2×#124C2312yes—
293C2×#124C2311yescharacteristic
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#123C2312yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2311yescharacteristic
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2311yescharacteristic
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×#121C2312yes—
319C2×#121C2312yes—
320C2×#121C2312yes—
321C2×#121C2314yes—
322C2×#121C2312yes—
323C2×#121C2314yes—
324C2×#121C2312yes—
325C2×#121C2311yescharacteristic
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×#121C2312yes—
330C2×#121C2312yes—
331C2×#121C2312yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2312yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2314yes—
340C2×#121C2312yes—
341C2×#121C2312yes—
342C2×#121C2314yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2314yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2314yes—
351C2×C4×D4C2314yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2314yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2311yescharacteristic
364C2×#117C2314yes—
365C2×#117C2314yes—
366C2×#117C2312yes—
367C22×C4⋊C4C2312yes—
368C22×C4⋊C4C2314yes—
369C22×C4⋊C4C2312yes—
370C22×C4⋊C4C2312yes—
371C22×C4⋊C4C2311yescharacteristic
372C22×C42C2312yes—
373C22×C42C2311yescharacteristic
374#401C2314yes—
375#401C2312yes—
376#400C2312yes—
377#400C2314yes—
378#400C2312yes—
379#400C2312yes—
380#400C2314yes—
381#400C2312yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2314yes—
386#400C2314yes—
387#400C2312yes—
388#400C2314yes—
389#400C2314yes—
390#400C2312yes—
391#399C2312yes—
392#399C2314yes—
393#399C2312yes—
394#399C2314yes—
395#399C2314yes—
396#399C2314yes—
397#399C2311yescharacteristic
398#399C2312yes—
399#399C2311yescharacteristic
400#399C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2312yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2312yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2312yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2312yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#395C2311yescharacteristic
435#395C2312yes—
436#395C2314yes—
437#395C2312yes—
438#395C2314yes—
439#395C2312yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2312yes—
459#394C2314yes—
460#394C2314yes—
461#394C2312yes—
462#394C2311yescharacteristic
463#394C2312yes—
464#394C2312yes—
465#394C2312yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#393C2311yescharacteristic
475#393C2314yes—
476#393C2312yes—
477#393C2314yes—
478#393C2314yes—
479#393C2312yes—
480#392C2311yescharacteristic
481#392C2314yes—
482#392C2314yes—
483#392C2314yes—
484#392C2314yes—
485#392C2311yescharacteristic
486#392C2312yes—
487#392C2314yes—
488#392C2314yes—
489#392C2314yes—
490#392C2312yes—
491#392C2314yes—
492#392C2314yes—
493#392C2314yes—
494#392C2311yescharacteristic
495#392C2314yes—
496#392C2312yes—
497#392C2312yes—
498#392C2312yes—
499#392C2312yes—
500#392C2312yes—
501#392C2312yes—
502#392C2312yes—
503#392C2314yes—
504#392C2312yes—
505#392C2314yes—
506#392C2314yes—
507#391C2312yes—
508#391C2312yes—
509#391C2312yes—
510#391C2314yes—
511#391C2312yes—
512#391C2312yes—
513#391C2312yes—
514#391C2312yes—
515#390C2314yes—
516#390C2314yes—
517#390C2314yes—
518#390C2314yes—
519#390C2314yes—
520#390C2314yes—
521#390C2314yes—
522#390C2312yes—
523#390C2312yes—
524#390C2312yes—
525#390C2314yes—
526#390C2314yes—
527#390C2312yes—
528#390C2314yes—
529#390C2314yes—
530#390C2314yes—
531#390C2312yes—
532#390C2314yes—
533#390C2312yes—
534#390C2312yes—
535#390C2312yes—
536#390C2312yes—
537#389C2314yes—
538#389C2314yes—
539#389C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2312yes—
546#389C2312yes—
547#389C2314yes—
548#389C2312yes—
549#389C2312yes—
550#389C2314yes—
551#389C2314yes—
552#389C2312yes—
553#389C2314yes—
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#388C2314yes—
558#388C2314yes—
559#388C2312yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2312yes—
570#388C2314yes—
571#388C2312yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2312yes—
578#388C2312yes—
579#388C2312yes—
580#388C2312yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2312yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2312yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2312yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2312yes—
608#387C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2312yes—
618#386C2314yes—
619#386C2312yes—
620#386C2312yes—
621#386C2312yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2311yescharacteristic
630#386C2314yes—
631#386C2312yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2312yes—
638#386C2314yes—
639#386C2314yes—
640#386C2312yes—
641#386C2312yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2312yes—
646#386C2314yes—
647#386C2312yes—
648#386C2312yes—
649#386C2312yes—
650#385C2314yes—
651#385C2312yes—
652#385C2312yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2311yescharacteristic
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2312yes—
668#384C2314yes—
669#383C2314yes—
670#382C2314yes—
671#382C2312yes—
672#381C2312yes—
673#381C2314yes—
674#381C2314yes—
675#381C2311yescharacteristic
676#381C2312yes—
677#380C2314yes—
678#380C2314yes—
679#380C2314yes—
680#380C2314yes—
681#380C2312yes—
682#380C2311yescharacteristic
683#380C2311yescharacteristic
684#380C2312yes—
685#380C2312yes—
686#380C2314yes—
687#380C2312yes—
688#380C2312yes—
689#380C2312yes—
690#380C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2311yescharacteristic
711C4×C22⋊C4C2311yescharacteristic
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2314yes—
719#376C2314yes—
720#376C2311yescharacteristic
721#376C2312yes—
722C2×#95C2312yes—
723C2×#41—24no—
724C2×#41—28no—
725C2×#41—44no—
726C2×#41—42no—
727C2×#41—44no—
728C2×#41—44no—
729C2×#41—44no—
730C2×#41—44no—
731C2×#41—44no—
732C2×#41—44no—
733C22×Q8—24no—
734C22×Q8—42no—
735C22×Q8—44no—
736C22×Q8—44no—
737C22×Q8C2411yescharacteristic
738C22×Q8C2412yes—
739C22×Q8C2411yescharacteristic
740C22×Q8C2412yes—
741C22×Q8C2411yescharacteristic
742C22×Q8C2412yes—
743C22×D4C2411yescharacteristic
744C22×D4C2412yes—
745C22×D4C2414yes—
746C22×D4C2412yes—
747C22×D4C2412yes—
748C22×D4C2412yes—
749C22×D4C2414yes—
750C22×D4C2414yes—
751C22×D4C2412yes—
752C22×D4C2411yescharacteristic
753C22×D4C2412yes—
754C22×D4C2414yes—
755C22×D4C2412yes—
756C22×D4C2411yescharacteristic
757C22×D4C2412yes—
758C22×D4C2414yes—
759C22×D4C2412yes—
760C22×D4C2411yescharacteristic
761C22×D4C2412yes—
762C22×D4C2414yes—
763C22×D4C2414yes—
764C22×D4C2414yes—
765C22×D4C2414yes—
766C22×D4C2412yes—
767C22×D4C2414yes—
768C23×C4C2412yes—
769C23×C4C2411yescharacteristic
770C23×C4C2412yes—
771C23×C4C2411yescharacteristic
772C23×C4C2411yescharacteristic
773C23×C4C2412yes—
774C23×C4C2411yescharacteristic
775C23×C4C2414yes—
776C23×C4C2414yes—
777C23×C4C2414yes—
778C23×C4C2412yes—
779C23×C4C2412yes—
780C23×C4C2412yes—
781C23×C4C2414yes—
782C23×C4C2414yes—
783C23×C4C2412yes—
784C23×C4C2412yes—
785C4⋊Q8—28no—
786C4⋊Q8—44no—
787C4⋊Q8—48no—
788#127—44no—
789#127—42no—
790#127—48no—
791#127—44no—
792#127—44no—
793#127—48no—
794#126—48no—
795#126—48no—
796#125—28no—
797#125—48no—
798#124—48no—
799#124—48no—
800#124—44no—
801#124—44no—
802#124—44no—
803#124—42no—
804#124—44no—
805#123—44no—
806#123—48no—
807#123—48no—
808#123—48no—
809#123—48no—
810#123—44no—
811#123—42no—
812#123—48no—
813#123—48no—
814C22⋊Q8—28no—
815C22⋊Q8—28no—
816C22⋊Q8—28no—
817C22⋊Q8—48no—
818C22⋊Q8—48no—
819C22⋊Q8—48no—
820C22⋊Q8—44no—
821C22⋊Q8—44no—
822C22⋊Q8—44no—
823C22⋊Q8—44no—
824C22⋊Q8—42no—
825C22⋊Q8—44no—
826C22⋊Q8—44no—
827#121—28no—
828#121—28no—
829#121—28no—
830#121—44no—
831#121—48no—
832#121—48no—
833#121—44no—
834#121—48no—
835#121—44no—
836#121—48no—
837#121—48no—
838#121—48no—
839#121—48no—
840#121—48no—
841#121—48no—
842#121—48no—
843#121—48no—
844#121—44no—
845#121—44no—
846#121—44no—
847#121—48no—
848#121—42no—
849#121—44no—
850#121—44no—
851#121—48no—
852C4×Q8—24no—
853C4×Q8—28no—
854C4×Q8—28no—
855C4×Q8—44no—
856C4×D4—48no—
857C4×D4—44no—
858C4×D4—48no—
859C4×D4—44no—
860C4×D4—48no—
861C4×D4—48no—
862C4×D4—44no—
863C4×D4—44no—
864C4×D4—42no—
865C4×D4—44no—
866C4×D4—44no—
867C4×D4—44no—
868C4×D4—42no—
869C4×D4—44no—
870C4×D4—44no—
871C4×D4—48no—
872C4×D4—48no—
873#117—48no—
874#117—44no—
875#117—48no—
876C2×C4⋊C4—28no—
877C2×C4⋊C4—44no—
878C2×C4⋊C4—44no—
879C2×C4⋊C4—42no—
880C2×C4⋊C4—48no—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2411yescharacteristic
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2411yescharacteristic
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2411yescharacteristic
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2411yescharacteristic
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2411yescharacteristic
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2414yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2412yes—
981C2×C22⋊C4C2414yes—
982C2×C22⋊C4C2414yes—
983C2×C22⋊C4C2411yescharacteristic
984C2×C22⋊C4C2412yes—
985C2×C22⋊C4C2412yes—
986C2×C22⋊C4C2414yes—
987C2×C22⋊C4C2412yes—
988C2×C22⋊C4C2412yes—
989C2×C22⋊C4C2414yes—
990C2×C22⋊C4C2414yes—
991C2×C22⋊C4C2412yes—
992C2×C42—44no—
993C2×C42—42no—
994C2×C42C2414yes—
995C2×C42C2411yescharacteristic
996C2×C42C2412yes—
997C2×C42C2414yes—
998C2×C42C2412yes—
999C2×C42C2412yes—
1000C2×C42C2412yes—
1001C2×C42C2412yes—
1002C2×C42C2414yes—
1003C2×C42C2412yes—
1004C2×C42C2414yes—
1005C2×C42C2414yes—
1006C2×C42C2414yes—
1007C2×C42C2412yes—
1008C2×C42C2414yes—
1009C2×C42C2412yes—
1010C2×C42C2412yes—
1011#95C2411yescharacteristic
1012#95C2414yes—
1013#95C2412yes—
1014#95C2411yescharacteristic
1015#95C2412yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2411yescharacteristic
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2411yescharacteristic
1037#95C2414yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2412yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2412yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2412yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2414yes—
1063#95C2414yes—
1064C24C2512yes—
1065C24C2512yes—
1066C24C2514yes—
1067C24C2512yes—
1068C24C2511yescharacteristic
1069C24C2511yescharacteristic
1070#41—88no—
1071#41—816no—
1072#41—88no—
1073#41—816no—
1074C2×Q8—24no—
1075C2×Q8—24no—
1076C2×Q8—24no—
1077C2×Q8—24no—
1078C2×Q8—22no—
1079C2×Q8—24no—
1080C2×Q8—24no—
1081C2×Q8—42no—
1082C2×Q8—41no—
1083C2×Q8—44no—
1084C2×Q8—44no—
1085C2×Q8—42no—
1086C2×Q8—88no—
1087C2×Q8—88no—
1088C2×Q8H(5,𝔽2)14yes—
1089C2×D4—28no—
1090C2×D4—24no—
1091C2×D4—24no—
1092C2×D4—22no—
1093C2×D4—24no—
1094C2×D4—28no—
1095C2×D4—24no—
1096C2×D4—24no—
1097C2×D4—24no—
1098C2×D4—24no—
1099C2×D4—22no—
1100C2×D4—28no—
1101C2×D4—28no—
1102C2×D4—24no—
1103C2×D4—28no—
1104C2×D4—24no—
1105C2×D4—44no—
1106C2×D4—42no—
1107C2×D4—42no—
1108C2×D4—42no—
1109C2×D4—42no—
1110C2×D4—41no—
1111C2×D4—42no—
1112C2×D4—44no—
1113C2×D4—41no—
1114C2×D4—42no—
1115C2×D4—42no—
1116C2×D4—44no—
1117C2×D4—42no—
1118C2×D4—44no—
1119C2×D4—42no—
1120C2×D4—42no—
1121C2×D4—42no—
1122C2×D4—41no—
1123C2×D4—44no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C2×D4—44no—
1129C2×D4—42no—
1130C2×D4—42no—
1131C2×D4—42no—
1132C2×D4—42no—
1133C2×D4—42no—
1134C2×D4—42no—
1135C2×D4—44no—
1136C2×D4—44no—
1137C2×D4—42no—
1138C2×D4—44no—
1139C2×D4—44no—
1140C2×D4—41no—
1141C2×D4—42no—
1142C2×D4—42no—
1143C2×D4—44no—
1144C2×D4—44no—
1145C2×D4—44no—
1146C2×D4—44no—
1147C2×D4—44no—
1148C2×D4—42no—
1149C2×D4—44no—
1150C2×D4—44no—
1151C2×D4—44no—
1152C2×D4—44no—
1153C2×D4—44no—
1154C2×D4—44no—
1155C2×D4—42no—
1156C2×D4—44no—
1157C2×D4—42no—
1158C2×D4—44no—
1159C22×C4—22no—
1160C22×C4—24no—
1161C22×C4—22no—
1162C22×C4—24no—
1163C22×C4—22no—
1164C22×C4—24no—
1165C22×C4—24no—
1166C22×C4—24no—
1167C22×C4—24no—
1168C22×C4—24no—
1169C22×C4—24no—
1170C22×C4—24no—
1171C22×C4—28no—
1172C22×C4—24no—
1173C22×C4—28no—
1174C22×C4—24no—
1175C22×C4—28no—
1176C22×C4—41no—
1177C22×C4—41no—
1178C22×C4—41no—
1179C22×C4—42no—
1180C22×C4—42no—
1181C22×C4—42no—
1182C22×C4—44no—
1183C22×C4—44no—
1184C22×C4—44no—
1185C22×C4—44no—
1186C22×C4—44no—
1187C22×C4—44no—
1188C22×C4—44no—
1189C22×C4—44no—
1190C22×C4—44no—
1191C22×C4—44no—
1192C22×C4—44no—
1193C22×C4—44no—
1194C22×C4—44no—
1195C22×C4—42no—
1196C22×C4—42no—
1197C22×C4—42no—
1198C22×C4—44no—
1199C22×C4—42no—
1200C22×C4—44no—
1201C22×C4—42no—
1202C22×C4—44no—
1203C22×C4C2512yes—
1204C22×C4C2512yes—
1205C22×C4C2512yes—
1206C22×C4C2511yescharacteristic
1207C22×C4C2511yescharacteristic
1208C22×C4C2512yes—
1209C22×C4C2514yes—
1210C22×C4C2512yes—
1211C22×C4C2512yes—
1212C22×C4C2514yes—
1213C22×C4C2512yes—
1214C22×C4C2512yes—
1215C22×C4C2514yes—
1216C22×C4C2511yescharacteristic
1217C22×C4C2514yes—
1218C22×C4C2511yescharacteristic
1219C22×C4C2512yes—
1220C22×C4C2512yes—
1221C22×C4C2512yes—
1222C22×C4C2512yes—
1223C22×C4C2514yes—
1224C22×C4C2512yes—
1225C22×C4C2511yescharacteristic
1226C4⋊C4—24no—
1227C4⋊C4—28no—
1228C4⋊C4—28no—
1229C4⋊C4—24no—
1230C4⋊C4—28no—
1231C4⋊C4—28no—
1232C4⋊C4—28no—
1233C4⋊C4—24no—
1234C4⋊C4—28no—
1235C4⋊C4—28no—
1236C4⋊C4—28no—
1237C4⋊C4—28no—
1238C4⋊C4—24no—
1239C4⋊C4—22no—
1240C4⋊C4—28no—
1241C4⋊C4—28no—
1242C4⋊C4—24no—
1243C4⋊C4—24no—
1244C4⋊C4—42no—
1245C4⋊C4—42no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—42no—
1251C4⋊C4—41no—
1252C4⋊C4—42no—
1253C4⋊C4—41no—
1254C4⋊C4—42no—
1255C4⋊C4—42no—
1256C4⋊C4—42no—
1257C4⋊C4—44no—
1258C4⋊C4—42no—
1259C4⋊C4—44no—
1260C4⋊C4—42no—
1261C4⋊C4—44no—
1262C4⋊C4—44no—
1263C4⋊C4—44no—
1264C4⋊C4—42no—
1265C4⋊C4—42no—
1266C4⋊C4—44no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4H(5,𝔽2)18yes—
1270C22⋊C4—22no—
1271C22⋊C4—24no—
1272C22⋊C4—28no—
1273C22⋊C4—28no—
1274C22⋊C4—28no—
1275C22⋊C4—28no—
1276C22⋊C4—28no—
1277C22⋊C4—28no—
1278C22⋊C4—24no—
1279C22⋊C4—28no—
1280C22⋊C4—24no—
1281C22⋊C4—24no—
1282C22⋊C4—28no—
1283C22⋊C4—41no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—42no—
1287C22⋊C4—42no—
1288C22⋊C4—42no—
1289C22⋊C4—42no—
1290C22⋊C4—44no—
1291C22⋊C4—42no—
1292C22⋊C4—42no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—42no—
1299C22⋊C4—42no—
1300C22⋊C4—41no—
1301C22⋊C4—42no—
1302C22⋊C4—42no—
1303C22⋊C4—42no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—42no—
1308C22⋊C4—42no—
1309C22⋊C4—44no—
1310C22⋊C4—42no—
1311C22⋊C4—44no—
1312C22⋊C4—41no—
1313C22⋊C4—44no—
1314C22⋊C4—42no—
1315C22⋊C4—42no—
1316C22⋊C4—44no—
1317C22⋊C4—42no—
1318C22⋊C4—42no—
1319C22⋊C4—44no—
1320C22⋊C4—44no—
1321C22⋊C4—42no—
1322C22⋊C4—44no—
1323C22⋊C4—44no—
1324C22⋊C4—44no—
1325C22⋊C4—44no—
1326C22⋊C4—44no—
1327C22⋊C4—42no—
1328C22⋊C4—44no—
1329C22⋊C4—42no—
1330C22⋊C4—42no—
1331C22⋊C4—44no—
1332C22⋊C4—44no—
1333C22⋊C4—44no—
1334C22⋊C4—42no—
1335C22⋊C4—42no—
1336C22⋊C4—44no—
1337C42—24no—
1338C42—24no—
1339C42—24no—
1340C42—28no—
1341C42—28no—
1342C42—24no—
1343C42—22no—
1344C42—24no—
1345C42—42no—
1346C42—42no—
1347C42—42no—
1348C42—44no—
1349C42—44no—
1350C42—44no—
1351C42—44no—
1352C42—42no—
1353C42—44no—
1354C23—22no—
1355C23—21no—
1356C23—22no—
1357C23—21no—
1358C23—22no—
1359C23—22no—
1360C23—22no—
1361C23—24no—
1362C23—24no—
1363C23—24no—
1364C23—22no—
1365C23—22no—
1366C23—22no—
1367C23—21no—
1368C23—22no—
1369C23—22no—
1370C23—24no—
1371C23—24no—
1372C23—22no—
1373C23—22no—
1374C23—24no—
1375C23—22no—
1376C23—24no—
1377C23—22no—
1378C23—21no—
1379C23—22no—
1380C23—22no—
1381C23—22no—
1382C23—24no—
1383C23—22no—
1384C23—22no—
1385C23—21no—
1386C23—24no—
1387C23—22no—
1388C23—22no—
1389C23#58512yes—
1390C23C2611yescharacteristic
1391Q8—28no—
1392Q8—44no—
1393Q8—48no—
1394Q8—84no—
1395Q8—84no—
1396Q8—82no—
1397D4—416no—
1398D4—44no—
1399D4—48no—
1400D4—88no—
1401D4—88no—
1402D4—84no—
1403D4—84no—
1404D4—88no—
1405D4—84no—
1406D4—84no—
1407D4—84no—
1408D4—82no—
1409D4—84no—
1410D4—84no—
1411D4—82no—
1412D4—88no—
1413D4—84no—
1414D4—82no—
1415D4—84no—
1416D4—88no—
1417D4—164no—
1418D4—164no—
1419D4—164no—
1420D4—164no—
1421D4—162no—
1422C2×C4—22no—
1423C2×C4—24no—
1424C2×C4—24no—
1425C2×C4—22no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—21no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—21no—
1437C2×C4—24no—
1438C2×C4—22no—
1439C2×C4—24no—
1440C2×C4—21no—
1441C2×C4—22no—
1442C2×C4—24no—
1443C2×C4—24no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—24no—
1447C2×C4—24no—
1448C2×C4—22no—
1449C2×C4—22no—
1450C2×C4—22no—
1451C2×C4—22no—
1452C2×C4—22no—
1453C2×C4—24no—
1454C2×C4—21no—
1455C2×C4—22no—
1456C2×C4—22no—
1457C2×C4—21no—
1458C2×C4—22no—
1459C2×C4—24no—
1460C2×C4—24no—
1461C2×C4—22no—
1462C2×C4—22no—
1463C2×C4—24no—
1464C2×C4—24no—
1465C2×C4—22no—
1466C2×C4—22no—
1467C2×C4—22no—
1468C2×C4—24no—
1469C2×C4—22no—
1470C2×C4—22no—
1471C2×C4—22no—
1472C2×C4—22no—
1473C2×C4—22no—
1474C2×C4—22no—
1475C2×C4—24no—
1476C2×C4—22no—
1477C2×C4—22no—
1478C2×C4—21no—
1479C2×C4—22no—
1480C2×C4—44no—
1481C2×C4—44no—
1482C2×C4—44no—
1483C2×C4—48no—
1484C2×C4—48no—
1485C2×C4—44no—
1486C2×C4—88no—
1487C2×C4—88no—
1488C2×C4—84no—
1489C2×C4—88no—
1490C2×C4—84no—
1491C2×C4—84no—
1492C2×C4—84no—
1493C2×C4—88no—
1494C2×C4—84no—
1495C2×C4—88no—
1496C2×C4—162no—
1497C2×C4C2×H(5,𝔽2)18yes—
1498C2×C4C2×H(5,𝔽2)14yes—
1499C2×C4C2×H(5,𝔽2)12yes—
1500C2×C4C2×H(5,𝔽2)14yes—
1501C2×C4#58514yes—
1502C22—24no—
1503C22—22no—
1504C22—41no—
1505C22—41no—
1506C22—42no—
1507C22—41no—
1508C22—42no—
1509C22—42no—
1510C22—44no—
1511C22—42no—
1512C22—42no—
1513C22—42no—
1514C22—44no—
1515C22—42no—
1516C22—42no—
1517C22—44no—
1518C22—42no—
1519C22—44no—
1520C22—44no—
1521C22—41no—
1522C22—42no—
1523C22—42no—
1524C22—42no—
1525C22—42no—
1526C22—41no—
1527C22—42no—
1528C22—44no—
1529C22—42no—
1530C22—44no—
1531C22—42no—
1532C22—44no—
1533C22—42no—
1534C22—42no—
1535C22—42no—
1536C22—44no—
1537C22—42no—
1538C22C22×H(5,𝔽2)12yes—
1539C22C22×H(5,𝔽2)11yescharacteristic
1540C22C2×#58511yescharacteristic
1541C22C2×#58512yes—
1542C222−1+611yescharacteristic
1543C4—24no—
1544C4—28no—
1545C4—24no—
1546C4—42no—
1547C4—41no—
1548C4—42no—
1549C4—41no—
1550C4—44no—
1551C4—42no—
1552C4—42no—
1553C4—42no—
1554C4—44no—
1555C4—42no—
1556C4—44no—
1557C4—41no—
1558C4—42no—
1559C4—42no—
1560C4—41no—
1561C4—42no—
1562C4—44no—
1563C4—42no—
1564C4—42no—
1565C4#354314yes—
1566C2—42no—
1567C2—82no—
1568C2—81no—
1569C2—82no—
1570C2—84no—
1571C2—82no—
1572C2C2×#354311yescharacteristic
1573C2#6291911yescharacteristic
1574C2#6292212yes—
1575C2#6301812yes—
1576C2#6302011yescharacteristic
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. #59813C2semidirect
2. #59632C2semidirect
3. #59125C2semidirect
4. #59101C2semidirect
5. #59054C2semidirect
6. #58295C2semidirect
7. #57235C2semidirect
8. #57120C2semidirect
9. #53521C2semidirect
10. #53137C2semidirect
11. #53088C2semidirect
12. #52299C2semidirect
13. #47231C2semidirect
14. #46548C2semidirect
15. #45244C2semidirect
16. #45033C2semidirect
17. #44884C2semidirect
18. #43403C2semidirect
19. #42908C2semidirect
20. #42643C2semidirect
21. #41827C2semidirect
22. #41341C2semidirect
23. #39961C2semidirect
24. #39858C2semidirect
25. #39721C2semidirect
26. #39246C2semidirect
27. #38998C2semidirect
28. #36066C2semidirect
29. #35886C2semidirect

Maximal subgroups

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

subgroupindex
#598132
#596322
#591252
#591012
#590542
#582952
#572352
#571202
#535212
#531372
#530882
#522992
#472312
#465482
#452442
#450332
#448842
#434032
#429082
#426432
#418272
#413412
#399612
#398582
#397212
#392462
#389982
#360662
#358862