Finite Group Databasebeta

← #7657718

Subgroups — #7657718

Order 512.

4550 conjugacy classes of subgroups.

The subgroup lattice has 1495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42216C214yesmaximal, complemented
2#42056C214yesmaximal, complemented
3#41970C214yesmaximal, complemented
4#41027C214yesmaximal, complemented
5#41011C214yesmaximal, complemented
6#40555C214yesmaximal, complemented
7#39188C211yesmaximal, characteristic, complemented
8#39185C211yesmaximal, characteristic, complemented
9#39059C212yesmaximal, complemented
10#39054C212yesmaximal, complemented
11#38972C211yesmaximal, characteristic, complemented
12#38969C211yesmaximal, characteristic, complemented
13#38216C212yesmaximal, complemented
14#38212C212yesmaximal, complemented
15#37592C212yesmaximal, complemented
16#37587C212yesmaximal, complemented
17#37554C211yesmaximal, characteristic, complemented
18#37553C211yesmaximal, characteristic, complemented
19#36536C211yesmaximal, characteristic, complemented
20#36498C211yesmaximal, characteristic, complemented
21#36394C211yesmaximal, characteristic, complemented
22#36370C211yesmaximal, characteristic, complemented
23#35755C214yesmaximal, complemented
24#35733C214yesmaximal, complemented
25#35339C211yesmaximal, characteristic, complemented
26#35290C212yesmaximal, complemented
27#34624C211yesmaximal, characteristic, complemented
28#34621C212yesmaximal, complemented
29#34229C211yesmaximal, characteristic, complemented
30#34226C211yesmaximal, characteristic, complemented
31#34151C211yesmaximal, characteristic, complemented
32C2×#532C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#529C2211yescharacteristic
35#2864C2211yescharacteristic
36#2864C2211yescharacteristic
37#2864C2211yescharacteristic
38#2864C2211yescharacteristic
39#2863C2212yes—
40#2860C2212yes—
41#2855C2212yes—
42#2854C2212yes—
43#2839C2214yes—
44#2836C2214yes—
45#2829C2214yes—
46#2828C2214yes—
47#2820C2212yes—
48#2819C2212yes—
49#2814C2212yes—
50#2813C2212yes—
51#2803C2214yes—
52#2796C2214yes—
53#2796C2214yes—
54#2795C2214yes—
55#2786C2214yes—
56#2783C2214yes—
57#2779C2214yes—
58#2777C2214yes—
59#2775C2214yes—
60#2773C2214yes—
61#2772C2214yes—
62#2757C2214yes—
63#2756C2214yes—
64#2753C2214yes—
65#2753C2214yes—
66#2751C2214yes—
67#2718C2214yes—
68#2714C2214yes—
69#2714C2214yes—
70#2711C2214yes—
71#2703C2214yes—
72#2701C2214yes—
73#2694C2214yes—
74#2691C2214yes—
75#2666C2214yes—
76#2664C2212yes—
77#2662C2214yes—
78#2662C2212yes—
79#2661C2214yes—
80#2661C2214yes—
81#2660C2211yescharacteristic
82#2657C2211yescharacteristic
83#2656C2212yes—
84#2651C2214yes—
85#2651C2214yes—
86#2650C2214yes—
87#2648C2214yes—
88#2648C2214yes—
89#2648C2214yes—
90#2647C2212yes—
91#2647C2212yes—
92#2644C2212yes—
93#2644C2212yes—
94#2641C2211yescharacteristic
95#2640C2211yescharacteristic
96#2639C2212yes—
97#2637C2214yes—
98#2636C2214yes—
99#2635C2214yes—
100#2634C2214yes—
101#2630C2214yes—
102#2630C2214yes—
103#2629C2212yes—
104#2628C2212yes—
105#2624C2212yes—
106#2624C2212yes—
107#2620C2211yescharacteristic
108#2620C2211yescharacteristic
109#2620C2212yes—
110#2619C2212yes—
111#2619C2211yescharacteristic
112#2619C2211yescharacteristic
113#2608C2214yes—
114#2602C2214yes—
115#2601C2214yes—
116#2600C2214yes—
117#2599C2214yes—
118#2598C2214yes—
119#2597C2214yes—
120#2581C2211yescharacteristic
121#2580C2211yescharacteristic
122#2580C2211yescharacteristic
123#2580C2211yescharacteristic
124#2578C2214yes—
125#2578C2214yes—
126#2578C2214yes—
127#2577C2214yes—
128#2577C2214yes—
129#2575C2214yes—
130#2574C2214yes—
131#2573C2214yes—
132#2572C2214yes—
133#2570C2214yes—
134#2570C2214yes—
135#2569C2214yes—
136#2569C2214yes—
137#2553C2214yes—
138#2536C2211yescharacteristic
139#2535C2211yescharacteristic
140#2535C2211yescharacteristic
141#2535C2211yescharacteristic
142#2535C2214yes—
143#2525C2214yes—
144#2524C2214yes—
145#2519C2214yes—
146#2518C2214yes—
147#2518C2214yes—
148#2518C2214yes—
149#2518C2214yes—
150#2517C2214yes—
151#2516C2214yes—
152#2516C2214yes—
153#2515C2214yes—
154#2508C2212yes—
155#2508C2212yes—
156#2507C2212yes—
157#2506C2212yes—
158#2500C2214yes—
159#2497C2212yes—
160#2496C2212yes—
161#2495C2212yes—
162#2495C2212yes—
163#2479C2214yes—
164#2476C2214yes—
165#2469C2214yes—
166#2468C2214yes—
167#2467C2214yes—
168#2466C2214yes—
169#2464C2214yes—
170#2464C2214yes—
171#2460C2214yes—
172#2458C2214yes—
173#2458C2214yes—
174#2457C2214yes—
175#2457C2214yes—
176#2457C2214yes—
177#2456C2214yes—
178#2448C2212yes—
179#2447C2212yes—
180#2445C2212yes—
181#2445C2212yes—
182#2444C2214yes—
183#2441C2214yes—
184#2430C2214yes—
185#2428C2212yes—
186#2428C2212yes—
187#2427C2212yes—
188#2426C2212yes—
189#2420C2214yes—
190#2419C2214yes—
191#2416C2212yes—
192#2416C2212yes—
193#2415C2212yes—
194#2414C2212yes—
195#2395C2214yes—
196#2395C2214yes—
197#2392C2214yes—
198#2392C2214yes—
199#2392C2214yes—
200#2388C2214yes—
201#2374C2212yes—
202#2374C2212yes—
203#2373C2212yes—
204#2373C2212yes—
205#2370C2212yes—
206#2367C2214yes—
207#2367C2212yes—
208#2364C2214yes—
209#2363C2212yes—
210#2363C2212yes—
211#2363C2212yes—
212#2362C2212yes—
213#2361C2212yes—
214#2360C2212yes—
215#2359C2214yes—
216#2359C2214yes—
217#2357C2211yescharacteristic
218#2357C2211yescharacteristic
219#2357C2211yescharacteristic
220#2356C2211yescharacteristic
221#2353C2214yes—
222#2351C2211yescharacteristic
223#2349C2211yescharacteristic
224#2349C2211yescharacteristic
225#2349C2211yescharacteristic
226#2346C2212yes—
227#2343C2214yes—
228#2343C2212yes—
229#2341C2212yes—
230#2339C2212yes—
231#2334C2214yes—
232#2324C2212yes—
233#2324C2214yes—
234#2323C2212yes—
235#2320C2212yes—
236#2319C2212yes—
237#2319C2212yes—
238#2318C2212yes—
239#2317C2212yes—
240#2316C2212yes—
241C4×C4⋊Q8C2212yes—
242C4×#127C2211yescharacteristic
243C4×#127C2211yescharacteristic
244C4×#127C2212yes—
245C4×#125C2212yes—
246C4×#124C2211yescharacteristic
247C4×#124C2211yescharacteristic
248C4×#124C2212yes—
249C4×#121C2212yes—
250C4×#121C2212yes—
251#2298C2212yes—
252#2295C2211yescharacteristic
253#2293C2211yescharacteristic
254#2293C2212yes—
255#2293C2212yes—
256#2293C2212yes—
257#2290C2212yes—
258#2285C2211yescharacteristic
259C2×#382C2211yescharacteristic
260#2275C2212yes—
261#2275C2212yes—
262C42×Q8C2211yescharacteristic
263C42×D4C2211yescharacteristic
264C4×#117C2211yescharacteristic
265C4×#117C2212yes—
266C4×#117C2211yescharacteristic
267C22×#41C2312yes—
268#532—28no—
269C2×C4⋊Q8C2311yescharacteristic
270C2×#127C2311yescharacteristic
271C2×#127C2311yescharacteristic
272C2×#127C2311yescharacteristic
273#529—28no—
274#529—28no—
275C2×#126C2312yes—
276C2×#126C2312yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#125C2311yescharacteristic
280C2×#125C2311yescharacteristic
281C2×#125C2314yes—
282C2×#124C2311yescharacteristic
283C2×#124C2312yes—
284C2×#124C2311yescharacteristic
285C2×#124C2311yescharacteristic
286C2×#124C2311yescharacteristic
287C2×#123C2312yes—
288C2×#123C2312yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2311yescharacteristic
294C2×C22⋊Q8C2312yes—
295C2×#121C2312yes—
296C2×#121C2311yescharacteristic
297C2×#121C2311yescharacteristic
298C2×#121C2311yescharacteristic
299C2×#121C2311yescharacteristic
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×#117C2312yes—
331C2×#117C2312yes—
332C2×#117C2311yescharacteristic
333C2×#117C2312yes—
334C2×#117C2311yescharacteristic
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2314yes—
338C2×#117C2314yes—
339C22×C4⋊C4C2312yes—
340C22×C42C2312yes—
341C22×C42C2311yescharacteristic
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#399C2312yes—
356#399C2312yes—
357#399C2314yes—
358#399C2312yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#397C2312yes—
376#397C2312yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2312yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#395C2314yes—
408#395C2312yes—
409#395C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2312yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#393C2314yes—
438#393C2312yes—
439#393C2312yes—
440#393C2314yes—
441#393C2312yes—
442#392C2314yes—
443#392C2312yes—
444#392C2312yes—
445#392C2314yes—
446#392C2314yes—
447#392C2314yes—
448#392C2314yes—
449#392C2314yes—
450#392C2314yes—
451#392C2314yes—
452#392C2314yes—
453#392C2312yes—
454#391C2314yes—
455#391C2311yescharacteristic
456#391C2312yes—
457#391C2311yescharacteristic
458#391C2312yes—
459#391C2312yes—
460#390C2314yes—
461#390C2311yescharacteristic
462#390C2314yes—
463#390C2311yescharacteristic
464#390C2314yes—
465#390C2312yes—
466#390C2312yes—
467#390C2311yescharacteristic
468#390C2311yescharacteristic
469#390C2314yes—
470#390C2312yes—
471#390C2314yes—
472#390C2314yes—
473#390C2314yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2314yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#390C2311yescharacteristic
482#390C2311yescharacteristic
483#390C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#388C2314yes—
513#388C2314yes—
514#388C2312yes—
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#388C2312yes—
530#388C2312yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2312yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2312yes—
548#388C2312yes—
549#388C2312yes—
550#388C2314yes—
551#388C2312yes—
552#388C2312yes—
553#388C2312yes—
554#388C2312yes—
555#388C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
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#387C2312yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#387C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2314yes—
593#387C2314yes—
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#386C2312yes—
609#386C2312yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2312yes—
627#385C2312yes—
628#384C2312yes—
629#384C2311yescharacteristic
630#384C2311yescharacteristic
631#384C2314yes—
632#383C2314yes—
633#383C2314yes—
634#383C2312yes—
635#383C2314yes—
636#383C2314yes—
637#382C2312yes—
638#382C2312yes—
639#382C2314yes—
640#382C2312yes—
641#382C2312yes—
642#382C2314yes—
643#382C2314yes—
644#382C2311yescharacteristic
645#382C2311yescharacteristic
646#382C2311yescharacteristic
647#382C2311yescharacteristic
648#382C2311yescharacteristic
649#382C2311yescharacteristic
650#382C2314yes—
651#381C2314yes—
652#381C2314yes—
653#381C2312yes—
654#381C2312yes—
655#381C2312yes—
656#381C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2314yes—
663#380C2312yes—
664#380C2312yes—
665#380C2314yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2311yescharacteristic
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2311yescharacteristic
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2312yes—
722#376C2311yescharacteristic
723#376C2312yes—
724#376C2312yes—
725#376C2311yescharacteristic
726#376C2311yescharacteristic
727#376C2311yescharacteristic
728C2×#95C2312yes—
729C2×#95C2312yes—
730C2×#95C2312yes—
731C2×#95C2312yes—
732C2×#95C2312yes—
733C43C2312yes—
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C43C2312yes—
737C2×#41—28no—
738C2×#41—84no—
739C22×Q8C2411yescharacteristic
740C22×Q8C2411yescharacteristic
741C22×Q8C2412yes—
742C22×D4C2411yescharacteristic
743C22×D4C2411yescharacteristic
744C22×D4C2411yescharacteristic
745C22×D4C2412yes—
746C22×D4C2411yescharacteristic
747C22×D4C2412yes—
748C22×D4C2412yes—
749C22×D4C2412yes—
750C22×D4C2412yes—
751C22×D4C2412yes—
752C22×D4C2414yes—
753C22×D4C2414yes—
754C22×D4C2414yes—
755C22×D4C2414yes—
756C22×D4C2414yes—
757C23×C4C2412yes—
758C23×C4C2411yescharacteristic
759C23×C4C2412yes—
760C23×C4C2414yes—
761C23×C4C2414yes—
762C23×C4C2412yes—
763C23×C4C2412yes—
764C23×C4C2412yes—
765C23×C4C2414yes—
766C23×C4C2414yes—
767C23×C4C2412yes—
768C23×C4C2411yescharacteristic
769C23×C4C2411yescharacteristic
770C4⋊Q8—24no—
771#127—24no—
772#127—42no—
773#127—42no—
774#126—28no—
775#126—28no—
776#126—84no—
777#126—84no—
778#125—24no—
779#125—24no—
780#125—84no—
781#124—24no—
782#124—24no—
783#124—28no—
784#124—42no—
785#124—42no—
786#123—28no—
787#123—28no—
788#123—48no—
789#123—84no—
790#123—84no—
791C22⋊Q8—24no—
792C22⋊Q8—24no—
793C22⋊Q8—44no—
794#121—24no—
795#121—24no—
796#121—24no—
797#121—24no—
798#121—28no—
799#121—48no—
800#121—44no—
801#121—44no—
802#121—44no—
803#121—84no—
804#121—84no—
805#121—84no—
806C4×Q8—24no—
807C4×Q8—24no—
808C4×Q8—44no—
809C4×Q8—44no—
810C4×Q8—84no—
811C4×D4—28no—
812C4×D4—28no—
813C4×D4—24no—
814C4×D4—24no—
815C4×D4—28no—
816C4×D4—24no—
817C4×D4—24no—
818C4×D4—48no—
819C4×D4—44no—
820C4×D4—44no—
821C4×D4—44no—
822C4×D4—48no—
823C4×D4—48no—
824C4×D4—44no—
825C4×D4—84no—
826C4×D4—84no—
827C4×D4—84no—
828C4×D4—84no—
829#117—28no—
830#117—28no—
831#117—42no—
832#117—44no—
833#117—42no—
834#117—48no—
835#117—44no—
836#117—44no—
837#117—84no—
838C2×C4⋊C4—44no—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
946C2×C22⋊C4C2412yes—
947C2×C42—44no—
948C2×C42#4118yes—
949C2×C42C2411yescharacteristic
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2412yes—
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958C2×C42C2411yescharacteristic
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2414yes—
962C2×C42C2412yes—
963C2×C42C2414yes—
964C2×C42C2412yes—
965C2×C42C2412yes—
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2414yes—
970C2×C42C2414yes—
971C2×C42C2412yes—
972C2×C42C2412yes—
973C2×C42C2414yes—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2411yescharacteristic
978C2×C42C2411yescharacteristic
979C2×C42C2411yescharacteristic
980C2×C42C2411yescharacteristic
981#95C2411yescharacteristic
982#95C2411yescharacteristic
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2411yescharacteristic
995#95C2412yes—
996#95C2411yescharacteristic
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045C24C2512yes—
1046C24C2512yes—
1047C24C2512yes—
1048C24C2512yes—
1049C24C2511yescharacteristic
1050#41—816no—
1051C2×Q8—22no—
1052C2×Q8—22no—
1053C2×Q8—24no—
1054C2×Q8—22no—
1055C2×Q8—22no—
1056C2×Q8—42no—
1057C2×Q8—44no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—24no—
1062C2×D4—22no—
1063C2×D4—22no—
1064C2×D4—24no—
1065C2×D4—22no—
1066C2×D4—22no—
1067C2×D4—24no—
1068C2×D4—22no—
1069C2×D4—22no—
1070C2×D4—22no—
1071C2×D4—22no—
1072C2×D4—22no—
1073C2×D4—22no—
1074C2×D4—44no—
1075C2×D4—42no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—44no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—42no—
1087C2×D4—42no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C22×C4—22no—
1098C22×C4—22no—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—24no—
1102C22×C4—24no—
1103C22×C4—24no—
1104C22×C4—24no—
1105C22×C4—28no—
1106C22×C4—24no—
1107C22×C4—28no—
1108C22×C4—42no—
1109C22×C4—42no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—42no—
1116C22×C4—42no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—42no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4C2×#4114yes—
1129C22×C4C2×#4114yes—
1130C22×C4C2×#4114yes—
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2514yes—
1141C22×C4C2514yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2514yes—
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2511yescharacteristic
1154C22×C4C2511yescharacteristic
1155C22×C4C2512yes—
1156C22×C4C2511yescharacteristic
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—22no—
1163C4⋊C4—22no—
1164C4⋊C4—22no—
1165C4⋊C4—22no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—22no—
1169C4⋊C4—22no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—42no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—42no—
1206C4⋊C4—44no—
1207C4⋊C4—42no—
1208C4⋊C4—44no—
1209C22⋊C4—24no—
1210C22⋊C4—24no—
1211C22⋊C4—24no—
1212C22⋊C4—24no—
1213C22⋊C4—24no—
1214C22⋊C4—24no—
1215C22⋊C4—24no—
1216C22⋊C4—24no—
1217C22⋊C4—24no—
1218C22⋊C4—24no—
1219C22⋊C4—24no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—28no—
1226C22⋊C4—44no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—42no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—42no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—42no—
1265C42—24no—
1266C42—24no—
1267C42—22no—
1268C42—24no—
1269C42—22no—
1270C42—24no—
1271C42—24no—
1272C42—28no—
1273C42—24no—
1274C42—22no—
1275C42—22no—
1276C42—42no—
1277C42—42no—
1278C42—42no—
1279C42—44no—
1280C42—42no—
1281C42—44no—
1282C42—42no—
1283C42—42no—
1284C42—42no—
1285C42—42no—
1286C42—42no—
1287C42—42no—
1288C42—44no—
1289C42—42no—
1290C42—44no—
1291C42—44no—
1292C42—42no—
1293C42C2×#4114yes—
1294C42C2×#4114yes—
1295C42C2×#4114yes—
1296C42C2×#4114yes—
1297C23—22no—
1298C23—21no—
1299C23—21no—
1300C23—22no—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23—22no—
1305C23—24no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23—24no—
1310C23—22no—
1311C23—24no—
1312C23—22no—
1313C23—22no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—22no—
1318C23—22no—
1319C23—24no—
1320C23—24no—
1321C23—24no—
1322C23—22no—
1323C23C22×#4112yes—
1324C23C2611yescharacteristic
1325Q8—44no—
1326Q8—48no—
1327Q8—44no—
1328D4—48no—
1329D4—44no—
1330D4—48no—
1331D4—48no—
1332D4—44no—
1333D4—44no—
1334D4—44no—
1335D4—84no—
1336D4—84no—
1337D4—84no—
1338D4—88no—
1339D4—88no—
1340D4—88no—
1341D4—88no—
1342D4—164no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—21no—
1346C2×C4—22no—
1347C2×C4—21no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—28no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—22no—
1399C2×C4—24no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—44no—
1406C2×C4—44no—
1407C2×C4—48no—
1408C2×C4—84no—
1409C2×C4—88no—
1410C2×C4—84no—
1411C2×C4—88no—
1412C2×C4—84no—
1413C2×C4—84no—
1414C2×C4—84no—
1415C2×C4—164no—
1416C2×C4—164no—
1417C2×C4C22×#4112yes—
1418C2×C4C22×#4112yes—
1419C2×C4C22×#4112yes—
1420C2×C4C22×#4112yes—
1421C2×C4C22×#4112yes—
1422C2×C4C22×#4112yes—
1423C2×C4#58514yes—
1424C2×C4#58512yes—
1425C2×C4#58512yes—
1426C22—22no—
1427C22—22no—
1428C22—22no—
1429C22—42no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—42no—
1437C22—42no—
1438C22—42no—
1439C22—44no—
1440C22—42no—
1441C22—42no—
1442C22—44no—
1443C22—44no—
1444C22—44no—
1445C22—42no—
1446C22—44no—
1447C22—42no—
1448C22—44no—
1449C22—42no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22C23×#4111yescharacteristic
1454C22C2×#58511yescharacteristic
1455C22C2×#58511yescharacteristic
1456C22C2×#58512yes—
1457C22H(7,𝔽2)12yes—
1458C4—22no—
1459C4—22no—
1460C4—22no—
1461C4—24no—
1462C4—22no—
1463C4—22no—
1464C4—42no—
1465C4—42no—
1466C4—42no—
1467C4—42no—
1468C4—42no—
1469C4—42no—
1470C4—42no—
1471C4—42no—
1472C4—42no—
1473C4—44no—
1474C4—44no—
1475C4—42no—
1476C4—42no—
1477C4—44no—
1478C4—42no—
1479C4—44no—
1480C4—42no—
1481C4—42no—
1482C4—42no—
1483C4#351214yes—
1484C2—42no—
1485C2—82no—
1486C2—82no—
1487C2—82no—
1488C2—82no—
1489C2#6268611yescharacteristic
1490C2C2×#351211yescharacteristic
1491C2#6285511yescharacteristic
1492C2#6293812yes—
1493C2#6294112yes—
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. #42216C2semidirect
2. #42056C2semidirect
3. #41970C2semidirect
4. #41027C2semidirect
5. #41011C2semidirect
6. #40555C2semidirect
7. #39188C2semidirect
8. #39185C2semidirect
9. #39059C2semidirect
10. #39054C2semidirect
11. #38972C2semidirect
12. #38969C2semidirect
13. #38216C2semidirect
14. #38212C2semidirect
15. #37592C2semidirect
16. #37587C2semidirect
17. #37554C2semidirect
18. #37553C2semidirect
19. #36536C2semidirect
20. #36498C2semidirect
21. #36394C2semidirect
22. #36370C2semidirect
23. #35755C2semidirect
24. #35733C2semidirect
25. #35339C2semidirect
26. #35290C2semidirect
27. #34624C2semidirect
28. #34621C2semidirect
29. #34229C2semidirect
30. #34226C2semidirect
31. #34151C2semidirect

Maximal subgroups

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

subgroupindex
#422162
#420562
#419702
#410272
#410112
#405552
#391882
#391852
#390592
#390542
#389722
#389692
#382162
#382122
#375922
#375872
#375542
#375532
#365362
#364982
#363942
#363702
#357552
#357332
#353392
#352902
#346242
#346212
#342292
#342262
#341512