Finite Group Databasebeta

← #7736611

Subgroups — #7736611

Order 512.

4874 conjugacy classes of subgroups.

The subgroup lattice has 1510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59902C212yesmaximal, complemented
2#59549C212yesmaximal, complemented
3#59145C212yesmaximal, complemented
4#59064C212yesmaximal, complemented
5#50927C214yesmaximal, complemented
6#50709C214yesmaximal, complemented
7#45428C211yesmaximal, characteristic, complemented
8#45421C211yesmaximal, characteristic, complemented
9#45344C211yesmaximal, characteristic, complemented
10#45221C211yesmaximal, characteristic, complemented
11#45151C211yesmaximal, characteristic, complemented
12#45137C211yesmaximal, characteristic, complemented
13#45070C211yesmaximal, characteristic, complemented
14#45041C211yesmaximal, characteristic, complemented
15#44349C214yesmaximal, complemented
16#44207C214yesmaximal, complemented
17#40025C212yesmaximal, complemented
18#40023C212yesmaximal, complemented
19#39920C214yesmaximal, complemented
20#36789C214yesmaximal, complemented
21#36527C212yesmaximal, complemented
22#36522C214yesmaximal, complemented
23#36469C212yesmaximal, complemented
24#35420C214yesmaximal, complemented
25#35211C211yesmaximal, characteristic, complemented
26#35191C211yesmaximal, characteristic, complemented
27#34966C211yesmaximal, characteristic, complemented
28#34937C211yesmaximal, characteristic, complemented
29#34402C211yesmaximal, characteristic, complemented
30#34224C211yesmaximal, characteristic, complemented
31#34123C211yesmaximal, characteristic, complemented
32C2×#559C2212yes—
33C2×#559C2212yes—
34C2×#532C2211yescharacteristic
35C2×#532C2212yes—
36C2×#529C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2861C2212yes—
39#2858C2212yes—
40#2854C2214yes—
41#2852C2214yes—
42#2852C2214yes—
43#2800C2214yes—
44#2793C2214yes—
45#2786C2214yes—
46#2780C2214yes—
47#2778C2214yes—
48#2776C2214yes—
49#2775C2214yes—
50#2772C2214yes—
51#2770C2214yes—
52#2766C2214yes—
53#2761C2214yes—
54#2749C2214yes—
55#2749C2214yes—
56#2747C2214yes—
57#2744C2214yes—
58#2739C2214yes—
59#2737C2214yes—
60#2737C2214yes—
61#2729C2214yes—
62#2723C2214yes—
63#2717C2214yes—
64#2717C2214yes—
65#2708C2214yes—
66#2708C2214yes—
67#2707C2214yes—
68#2706C2214yes—
69#2703C2214yes—
70#2703C2214yes—
71#2691C2214yes—
72#2688C2214yes—
73#2676C2214yes—
74#2672C2214yes—
75#2661C2212yes—
76#2661C2212yes—
77#2651C2214yes—
78#2650C2214yes—
79#2630C2214yes—
80#2609C2214yes—
81#2606C2214yes—
82#2606C2212yes—
83#2605C2212yes—
84#2603C2214yes—
85#2603C2212yes—
86#2603C2212yes—
87#2602C2214yes—
88#2602C2214yes—
89#2600C2214yes—
90#2597C2214yes—
91#2595C2214yes—
92#2595C2214yes—
93#2592C2212yes—
94#2592C2212yes—
95#2592C2212yes—
96#2585C2214yes—
97#2581C2212yes—
98#2576C2214yes—
99#2576C2214yes—
100#2576C2214yes—
101#2574C2214yes—
102#2574C2214yes—
103#2570C2212yes—
104#2569C2214yes—
105#2568C2212yes—
106#2566C2211yescharacteristic
107#2565C2211yescharacteristic
108#2558C2214yes—
109#2557C2214yes—
110#2557C2214yes—
111#2550C2212yes—
112#2548C2211yescharacteristic
113#2548C2211yescharacteristic
114#2547C2211yescharacteristic
115#2547C2211yescharacteristic
116#2547C2212yes—
117#2547C2212yes—
118#2546C2212yes—
119#2546C2211yescharacteristic
120#2546C2211yescharacteristic
121#2545C2212yes—
122#2545C2212yes—
123#2545C2211yescharacteristic
124#2544C2212yes—
125#2544C2211yescharacteristic
126#2544C2212yes—
127#2543C2214yes—
128#2543C2212yes—
129#2543C2212yes—
130#2541C2212yes—
131#2541C2211yescharacteristic
132#2541C2211yescharacteristic
133#2538C2212yes—
134#2531C2214yes—
135#2531C2214yes—
136#2531C2214yes—
137#2530C2214yes—
138#2530C2214yes—
139#2530C2214yes—
140#2529C2214yes—
141#2529C2214yes—
142#2526C2214yes—
143#2526C2214yes—
144#2518C2214yes—
145#2517C2214yes—
146#2514C2212yes—
147#2513C2212yes—
148#2512C2212yes—
149#2511C2212yes—
150#2500C2211yescharacteristic
151#2499C2211yescharacteristic
152#2491C2214yes—
153#2488C2214yes—
154#2466C2214yes—
155#2464C2214yes—
156#2464C2214yes—
157#2463C2214yes—
158#2461C2214yes—
159#2459C2214yes—
160#2457C2214yes—
161#2457C2214yes—
162#2456C2214yes—
163#2448C2212yes—
164#2447C2212yes—
165#2447C2212yes—
166#2447C2212yes—
167#2447C2214yes—
168#2446C2212yes—
169#2446C2212yes—
170#2445C2212yes—
171#2445C2212yes—
172#2444C2214yes—
173#2442C2212yes—
174#2440C2212yes—
175#2438C2212yes—
176#2438C2212yes—
177#2432C2212yes—
178#2432C2211yescharacteristic
179#2431C2211yescharacteristic
180#2431C2212yes—
181#2427C2214yes—
182#2425C2214yes—
183#2425C2214yes—
184#2422C2214yes—
185#2420C2214yes—
186#2419C2214yes—
187#2419C2214yes—
188#2419C2214yes—
189#2419C2214yes—
190#2416C2214yes—
191#2414C2214yes—
192#2402C2211yescharacteristic
193#2402C2211yescharacteristic
194#2399C2211yescharacteristic
195#2399C2211yescharacteristic
196#2392C2212yes—
197#2392C2212yes—
198#2377C2214yes—
199#2373C2214yes—
200#2373C2214yes—
201#2370C2212yes—
202#2367C2212yes—
203#2367C2212yes—
204#2367C2212yes—
205#2367C2212yes—
206#2366C2212yes—
207#2366C2212yes—
208#2365C2212yes—
209#2364C2214yes—
210#2357C2211yescharacteristic
211#2357C2212yes—
212#2356C2211yescharacteristic
213#2356C2211yescharacteristic
214#2356C2211yescharacteristic
215#2355C2212yes—
216#2353C2212yes—
217#2353C2214yes—
218#2353C2212yes—
219#2353C2214yes—
220#2351C2211yescharacteristic
221#2349C2211yescharacteristic
222#2349C2211yescharacteristic
223#2349C2211yescharacteristic
224#2349C2214yes—
225#2347C2212yes—
226#2346C2212yes—
227#2343C2212yes—
228#2343C2214yes—
229#2341C2212yes—
230#2339C2212yes—
231#2339C2212yes—
232#2335C2214yes—
233#2333C2214yes—
234#2332C2214yes—
235#2328C2211yescharacteristic
236#2328C2211yescharacteristic
237#2328C2211yescharacteristic
238#2327C2211yescharacteristic
239#2327C2211yescharacteristic
240#2327C2211yescharacteristic
241#2326C2211yescharacteristic
242#2326C2211yescharacteristic
243#2324C2214yes—
244#2322C2214yes—
245#2318C2214yes—
246#2318C2212yes—
247C4×C4⋊Q8C2212yes—
248C4×#125C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×#123C2214yes—
253C4×#121C2212yes—
254C4×#121C2214yes—
255C4×#121C2214yes—
256#2297C2212yes—
257#2295C2212yes—
258#2290C2214yes—
259#2283C2211yescharacteristic
260#2283C2212yes—
261#2283C2211yescharacteristic
262#2275C2212yes—
263C42×D4C2212yes—
264C4×#117C2211yescharacteristic
265C2×C4×C4⋊C4C2211yescharacteristic
266C2×#376C2212yes—
267C22×#41C2311yescharacteristic
268C22×#41C2312yes—
269#559—48no—
270#559—48no—
271#532—28no—
272#532—48no—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×#127C2311yescharacteristic
279C2×#127C2311yescharacteristic
280C2×#127C2312yes—
281C2×#127C2312yes—
282#529—28no—
283C2×#126C2312yes—
284C2×#126C2314yes—
285C2×#125C2311yescharacteristic
286C2×#125C2312yes—
287C2×#124C2311yescharacteristic
288C2×#124C2311yescharacteristic
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2311yescharacteristic
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2314yes—
296C2×#124C2314yes—
297C2×#123C2312yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×C22⋊Q8C2311yescharacteristic
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×#121C2312yes—
309C2×#121C2312yes—
310C2×#121C2311yescharacteristic
311C2×#121C2314yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C4×#41—28no—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2311yescharacteristic
349C2×#117C2312yes—
350C22×C4⋊C4C2312yes—
351C22×C42C2312yes—
352C22×C42C2314yes—
353C22×C42C2312yes—
354C22×C42C2311yescharacteristic
355#401C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2312yes—
361#400C2312yes—
362#400C2314yes—
363#400C2314yes—
364#400C2312yes—
365#400C2312yes—
366#400C2314yes—
367#400C2314yes—
368#399C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2314yes—
376#398C2312yes—
377#398C2314yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2314yes—
383#398C2312yes—
384#398C2314yes—
385#398C2312yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2314yes—
398#397C2312yes—
399#397C2312yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#395C2312yes—
418#395C2314yes—
419#395C2312yes—
420#395C2312yes—
421#395C2312yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2312yes—
433#394C2312yes—
434#394C2314yes—
435#394C2312yes—
436#394C2312yes—
437#394C2314yes—
438#394C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2312yes—
446#392C2312yes—
447#392C2312yes—
448#392C2312yes—
449#392C2314yes—
450#392C2314yes—
451#391C2312yes—
452#391C2312yes—
453#391C2311yescharacteristic
454#391C2311yescharacteristic
455#391C2314yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2311yescharacteristic
462#391C2311yescharacteristic
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#390C2311yescharacteristic
470#390C2311yescharacteristic
471#390C2314yes—
472#390C2314yes—
473#390C2314yes—
474#390C2311yescharacteristic
475#390C2312yes—
476#390C2312yes—
477#390C2311yescharacteristic
478#390C2314yes—
479#390C2314yes—
480#390C2314yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2314yes—
485#390C2314yes—
486#390C2314yes—
487#390C2314yes—
488#390C2312yes—
489#390C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2312yes—
556#387C2312yes—
557#387C2312yes—
558#387C2312yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#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#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2312yes—
623#385C2314yes—
624#385C2314yes—
625#385C2312yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2312yes—
630#385C2312yes—
631#384C2312yes—
632#384C2311yescharacteristic
633#384C2311yescharacteristic
634#383C2312yes—
635#383C2312yes—
636#383C2312yes—
637#383C2314yes—
638#383C2312yes—
639#383C2312yes—
640#382C2312yes—
641#382C2311yescharacteristic
642#382C2311yescharacteristic
643#382C2314yes—
644#382C2312yes—
645#382C2312yes—
646#382C2314yes—
647#382C2314yes—
648#382C2311yescharacteristic
649#382C2311yescharacteristic
650#381C2314yes—
651#381C2312yes—
652#381C2314yes—
653#381C2314yes—
654#381C2312yes—
655#381C2314yes—
656#381C2312yes—
657#381C2314yes—
658#381C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2312yes—
664#380C2314yes—
665#380C2314yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2314yes—
670#380C2314yes—
671#380C2312yes—
672#380C2312yes—
673#380C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C4⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2311yescharacteristic
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2311yescharacteristic
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2311yescharacteristic
721C4×C22⋊C4C2311yescharacteristic
722#376C2311yescharacteristic
723#376C2311yescharacteristic
724#376C2314yes—
725#376C2312yes—
726#376C2311yescharacteristic
727#376C2312yes—
728#376C2311yescharacteristic
729#376C2312yes—
730#376C2312yes—
731#376C2314yes—
732C2×#95C2312yes—
733C2×#95C2311yescharacteristic
734C2×#95C2314yes—
735C2×#95C2314yes—
736C2×#95C2312yes—
737C2×#95C2312yes—
738C2×#95C2311yescharacteristic
739C43C2312yes—
740C2×#41—24no—
741C2×#41—24no—
742C2×#41—28no—
743C2×#41—42no—
744C2×#41—44no—
745C2×#41—44no—
746C22×Q8C2411yescharacteristic
747C22×Q8C2411yescharacteristic
748C22×Q8C2412yes—
749C22×Q8C2412yes—
750C22×Q8C2412yes—
751C22×D4C2411yescharacteristic
752C22×D4C2412yes—
753C22×D4C2414yes—
754C22×D4C2412yes—
755C22×D4C2411yescharacteristic
756C22×D4C2412yes—
757C22×D4C2414yes—
758C22×D4C2412yes—
759C22×D4C2412yes—
760C22×D4C2414yes—
761C22×D4C2414yes—
762C22×D4C2414yes—
763C22×D4C2414yes—
764C23×C4C2412yes—
765C23×C4C2411yescharacteristic
766C23×C4C2412yes—
767C23×C4C2412yes—
768C23×C4C2414yes—
769C23×C4C2414yes—
770C23×C4C2414yes—
771C23×C4C2412yes—
772C23×C4C2412yes—
773C23×C4C2412yes—
774C23×C4C2414yes—
775C23×C4C2414yes—
776C23×C4C2414yes—
777C23×C4C2411yescharacteristic
778C23×C4C2411yescharacteristic
779C4⋊Q8—24no—
780C4⋊Q8—42no—
781C4⋊Q8—44no—
782C4⋊Q8—44no—
783C4⋊Q8—44no—
784#127—28no—
785#127—24no—
786#127—24no—
787#127—44no—
788#126—28no—
789#126—48no—
790#125—24no—
791#125—44no—
792#124—28no—
793#124—24no—
794#124—24no—
795#124—28no—
796#124—42no—
797#124—44no—
798#124—44no—
799#124—44no—
800#124—48no—
801#124—48no—
802#123—28no—
803#123—48no—
804#123—48no—
805#123—48no—
806#123—48no—
807#123—48no—
808#123—48no—
809C22⋊Q8—24no—
810C22⋊Q8—44no—
811C22⋊Q8—44no—
812C22⋊Q8—48no—
813#121—24no—
814#121—28no—
815#121—28no—
816#121—48no—
817#121—48no—
818#121—48no—
819#121—48no—
820#121—48no—
821#121—48no—
822C4×Q8—24no—
823C4×Q8—24no—
824C4×Q8—24no—
825C4×Q8—44no—
826C4×Q8—44no—
827C4×Q8—44no—
828C4×Q8—44no—
829C4×Q8—44no—
830C4×D4—28no—
831C4×D4—28no—
832C4×D4—28no—
833C4×D4—28no—
834C4×D4—24no—
835C4×D4—24no—
836C4×D4—24no—
837C4×D4—28no—
838C4×D4—28no—
839C4×D4—48no—
840C4×D4—44no—
841C4×D4—44no—
842C4×D4—44no—
843C4×D4—44no—
844C4×D4—48no—
845C4×D4—48no—
846C4×D4—48no—
847C4×D4—48no—
848C4×D4—48no—
849C4×D4—48no—
850#117—24no—
851#117—28no—
852#117—28no—
853#117—44no—
854C2×C4⋊C4—44no—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C42—28no—
958C2×C42—44no—
959C2×C42—48no—
960C2×C42#4118yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2414yes—
971C2×C42C2412yes—
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2412yes—
978C2×C42C2414yes—
979C2×C42C2414yes—
980C2×C42C2414yes—
981C2×C42C2414yes—
982C2×C42C2414yes—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2414yes—
986C2×C42C2414yes—
987C2×C42C2411yescharacteristic
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991#95C2411yescharacteristic
992#95C2412yes—
993#95C2411yescharacteristic
994#95C2411yescharacteristic
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2411yescharacteristic
1005#95C2412yes—
1006#95C2414yes—
1007#95C2411yescharacteristic
1008#95C2411yescharacteristic
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2411yescharacteristic
1015#95C2411yescharacteristic
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2414yes—
1045#95C2412yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061C24C2512yes—
1062C24C2514yes—
1063C24C2511yescharacteristic
1064C24C2512yes—
1065#41—416no—
1066#41—816no—
1067C2×Q8—22no—
1068C2×Q8—22no—
1069C2×Q8—24no—
1070C2×Q8—22no—
1071C2×Q8—24no—
1072C2×Q8—22no—
1073C2×Q8—24no—
1074C2×Q8—22no—
1075C2×Q8—22no—
1076C2×Q8—24no—
1077C2×Q8—42no—
1078C2×Q8—42no—
1079C2×Q8—42no—
1080C2×Q8—42no—
1081C2×Q8—42no—
1082C2×D4—24no—
1083C2×D4—24no—
1084C2×D4—28no—
1085C2×D4—24no—
1086C2×D4—28no—
1087C2×D4—28no—
1088C2×D4—28no—
1089C2×D4—22no—
1090C2×D4—22no—
1091C2×D4—24no—
1092C2×D4—24no—
1093C2×D4—24no—
1094C2×D4—22no—
1095C2×D4—24no—
1096C2×D4—22no—
1097C2×D4—24no—
1098C2×D4—28no—
1099C2×D4—22no—
1100C2×D4—28no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—42no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4H(5,𝔽2)14yes—
1118C22×C4—22no—
1119C22×C4—22no—
1120C22×C4—24no—
1121C22×C4—28no—
1122C22×C4—24no—
1123C22×C4—24no—
1124C22×C4—24no—
1125C22×C4—24no—
1126C22×C4—28no—
1127C22×C4—28no—
1128C22×C4—24no—
1129C22×C4—44no—
1130C22×C4—42no—
1131C22×C4—42no—
1132C22×C4—42no—
1133C22×C4—42no—
1134C22×C4—42no—
1135C22×C4—44no—
1136C22×C4—42no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—42no—
1143C22×C4—42no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4—44no—
1155C22×C4C2×#4114yes—
1156C22×C4C2×#4114yes—
1157C22×C4C2×#4114yes—
1158C22×C4C2514yes—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2514yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2514yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2512yes—
1173C22×C4C2512yes—
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2511yescharacteristic
1178C22×C4C2511yescharacteristic
1179C22×C4C2511yescharacteristic
1180C22×C4C2511yescharacteristic
1181C22×C4C2511yescharacteristic
1182C22×C4C2512yes—
1183C22×C4C2512yes—
1184C22×C4C2511yescharacteristic
1185C4⋊C4—22no—
1186C4⋊C4—22no—
1187C4⋊C4—24no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—22no—
1194C4⋊C4—24no—
1195C4⋊C4—22no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—28no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—42no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4—42no—
1214C4⋊C4—42no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—44no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C4⋊C4—42no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—42no—
1230C4⋊C4—42no—
1231C4⋊C4—42no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—42no—
1236C4⋊C4—42no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C22⋊C4—24no—
1240C22⋊C4—24no—
1241C22⋊C4—28no—
1242C22⋊C4—28no—
1243C22⋊C4—28no—
1244C22⋊C4—28no—
1245C22⋊C4—24no—
1246C22⋊C4—24no—
1247C22⋊C4—24no—
1248C22⋊C4—24no—
1249C22⋊C4—28no—
1250C22⋊C4—28no—
1251C22⋊C4—24no—
1252C22⋊C4—24no—
1253C22⋊C4—24no—
1254C22⋊C4—28no—
1255C22⋊C4—28no—
1256C22⋊C4—28no—
1257C22⋊C4—42no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—42no—
1277C22⋊C4—42no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C42—24no—
1288C42—24no—
1289C42—24no—
1290C42—24no—
1291C42—24no—
1292C42—24no—
1293C42—24no—
1294C42—22no—
1295C42—22no—
1296C42—24no—
1297C42—28no—
1298C42—22no—
1299C42—24no—
1300C42—22no—
1301C42—44no—
1302C42—44no—
1303C42—42no—
1304C42—42no—
1305C42—42no—
1306C42—44no—
1307C42—44no—
1308C42—44no—
1309C42—44no—
1310C42—44no—
1311C42—42no—
1312C42—42no—
1313C42C2×#4114yes—
1314C42C2×#4114yes—
1315C42C2×#4114yes—
1316C42C2×#4114yes—
1317C23—22no—
1318C23—21no—
1319C23—22no—
1320C23—22no—
1321C23—22no—
1322C23—24no—
1323C23—24no—
1324C23—21no—
1325C23—22no—
1326C23—24no—
1327C23—22no—
1328C23—24no—
1329C23—24no—
1330C23—24no—
1331C23—24no—
1332C23—24no—
1333C23—24no—
1334C23—24no—
1335C23—22no—
1336C23—24no—
1337C23C22×#4112yes—
1338C23C2×H(5,𝔽2)14yes—
1339C23C2611yescharacteristic
1340Q8—44no—
1341Q8—44no—
1342Q8—48no—
1343Q8—84no—
1344Q8—84no—
1345D4—28no—
1346D4—416no—
1347D4—48no—
1348D4—48no—
1349D4—44no—
1350D4—48no—
1351D4—88no—
1352D4—84no—
1353D4—84no—
1354D4—88no—
1355D4—88no—
1356D4—88no—
1357D4—164no—
1358C2×C4—22no—
1359C2×C4—21no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—28no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—24no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—24no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—44no—
1423C2×C4—44no—
1424C2×C4—48no—
1425C2×C4—48no—
1426C2×C4—84no—
1427C2×C4—88no—
1428C2×C4—84no—
1429C2×C4—84no—
1430C2×C4—88no—
1431C2×C4—88no—
1432C2×C4—84no—
1433C2×C4—164no—
1434C2×C4—164no—
1435C2×C4—164no—
1436C2×C4C22×#4112yes—
1437C2×C4C22×#4112yes—
1438C2×C4C22×#4112yes—
1439C2×C4C22×#4112yes—
1440C2×C4C22×#4112yes—
1441C2×C4C22×#4112yes—
1442C2×C4C2×H(5,𝔽2)12yes—
1443C2×C4#58514yes—
1444C2×C4#58514yes—
1445C2×C4#58512yes—
1446C22—28no—
1447C22—22no—
1448C22—24no—
1449C22—22no—
1450C22—22no—
1451C22—42no—
1452C22—44no—
1453C22—42no—
1454C22—42no—
1455C22—42no—
1456C22—44no—
1457C22—44no—
1458C22—44no—
1459C22—44no—
1460C22—44no—
1461C22—44no—
1462C22—44no—
1463C22—42no—
1464C22—42no—
1465C22—42no—
1466C22—44no—
1467C22—44no—
1468C22C23×#4111yescharacteristic
1469C22C22×H(5,𝔽2)11yescharacteristic
1470C22C2×#58512yes—
1471C22C2×#58512yes—
1472C22C2×#58511yescharacteristic
1473C4—24no—
1474C4—24no—
1475C4—22no—
1476C4—22no—
1477C4—22no—
1478C4—22no—
1479C4—22no—
1480C4—42no—
1481C4—42no—
1482C4—44no—
1483C4—42no—
1484C4—42no—
1485C4—42no—
1486C4—42no—
1487C4—42no—
1488C4—42no—
1489C4—44no—
1490C4—42no—
1491C4—42no—
1492C4—42no—
1493C4—44no—
1494C4—42no—
1495C4—42no—
1496C4—42no—
1497C4—42no—
1498C4—42no—
1499C4#349414yes—
1500C2—44no—
1501C2—42no—
1502C2—82no—
1503C2—84no—
1504C2C2×#349411yescharacteristic
1505C2#6281511yescharacteristic
1506C2#6281511yescharacteristic
1507C2#6301812yes—
1508C2#6303012yes—
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. #59902C2semidirect
2. #59549C2semidirect
3. #59145C2semidirect
4. #59064C2semidirect
5. #50927C2semidirect
6. #50709C2semidirect
7. #45428C2semidirect
8. #45421C2semidirect
9. #45344C2semidirect
10. #45221C2semidirect
11. #45151C2semidirect
12. #45137C2semidirect
13. #45070C2semidirect
14. #45041C2semidirect
15. #44349C2semidirect
16. #44207C2semidirect
17. #40025C2semidirect
18. #40023C2semidirect
19. #39920C2semidirect
20. #36789C2semidirect
21. #36527C2semidirect
22. #36522C2semidirect
23. #36469C2semidirect
24. #35420C2semidirect
25. #35211C2semidirect
26. #35191C2semidirect
27. #34966C2semidirect
28. #34937C2semidirect
29. #34402C2semidirect
30. #34224C2semidirect
31. #34123C2semidirect

Maximal subgroups

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

subgroupindex
#599022
#595492
#591452
#590642
#509272
#507092
#454282
#454212
#453442
#452212
#451512
#451372
#450702
#450412
#443492
#442072
#400252
#400232
#399202
#367892
#365272
#365222
#364692
#354202
#352112
#351912
#349662
#349372
#344022
#342242
#341232