Finite Group Databasebeta

← #7674363

Subgroups — #7674363

Order 512.

4708 conjugacy classes of subgroups.

The subgroup lattice has 1466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45434C211yesmaximal, characteristic, complemented
2#45431C211yesmaximal, characteristic, complemented
3#45428C211yesmaximal, characteristic, complemented
4#45421C211yesmaximal, characteristic, complemented
5#45306C211yesmaximal, characteristic, complemented
6#45299C211yesmaximal, characteristic, complemented
7#45148C212yesmaximal, complemented
8#45147C212yesmaximal, complemented
9#45146C212yesmaximal, complemented
10#45083C211yesmaximal, characteristic, complemented
11#45070C211yesmaximal, characteristic, complemented
12#44995C212yesmaximal, complemented
13#40255C214yesmaximal, complemented
14#40228C214yesmaximal, complemented
15#38655C214yesmaximal, complemented
16#38644C214yesmaximal, complemented
17#38000C214yesmaximal, complemented
18#37994C214yesmaximal, complemented
19#37921C214yesmaximal, complemented
20#37915C214yesmaximal, complemented
21#35615C212yesmaximal, complemented
22#35610C212yesmaximal, complemented
23#35249C211yesmaximal, characteristic, complemented
24#35206C212yesmaximal, complemented
25#35190C211yesmaximal, characteristic
26#34644C211yesmaximal, characteristic, complemented
27#34329C212yesmaximal, complemented
28#34195C211yesmaximal, characteristic, complemented
29#34192C211yesmaximal, characteristic, complemented
30C4×#536C211yesmaximal, characteristic, complemented
31#34086C211yesmaximal, characteristic, complemented
32C2×#559C2212yes—
33C2×#536C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37#2855C2214yes—
38#2854C2214yes—
39#2851C2214yes—
40#2850C2214yes—
41#2777C2214yes—
42#2768C2214yes—
43#2767C2214yes—
44#2764C2214yes—
45#2762C2214yes—
46#2761C2214yes—
47#2759C2214yes—
48#2758C2214yes—
49#2758C2214yes—
50#2757C2214yes—
51#2749C2214yes—
52#2746C2214yes—
53#2743C2214yes—
54#2740C2214yes—
55#2740C2214yes—
56#2738C2214yes—
57#2738C2214yes—
58#2737C2214yes—
59#2737C2214yes—
60#2707C2214yes—
61#2706C2214yes—
62#2706C2214yes—
63#2704C2214yes—
64#2700C2214yes—
65#2696C2214yes—
66#2693C2214yes—
67#2693C2214yes—
68#2691C2214yes—
69#2690C2214yes—
70#2687C2214yes—
71#2687C2214yes—
72#2672C2214yes—
73#2667C2212yes—
74#2667C2212yes—
75#2666C2212yes—
76#2666C2212yes—
77#2666C2212yes—
78#2666C2212yes—
79#2665C2212yes—
80#2665C2212yes—
81#2652C2214yes—
82#2652C2214yes—
83#2635C2212yes—
84#2635C2212yes—
85#2632C2212yes—
86#2632C2212yes—
87#2612C2214yes—
88#2611C2214yes—
89#2605C2214yes—
90#2603C2214yes—
91#2598C2212yes—
92#2598C2212yes—
93#2597C2214yes—
94#2592C2212yes—
95#2592C2212yes—
96#2589C2214yes—
97#2589C2214yes—
98#2587C2214yes—
99#2582C2212yes—
100#2580C2214yes—
101#2578C2214yes—
102#2576C2214yes—
103#2572C2214yes—
104#2571C2212yes—
105#2568C2212yes—
106#2568C2211yescharacteristic
107#2567C2211yescharacteristic
108#2567C2211yescharacteristic
109#2564C2214yes—
110#2558C2214yes—
111#2557C2214yes—
112#2556C2214yes—
113#2556C2214yes—
114#2553C2214yes—
115#2552C2212yes—
116#2552C2212yes—
117#2549C2214yes—
118#2548C2211yescharacteristic
119#2548C2211yescharacteristic
120#2548C2211yescharacteristic
121#2547C2212yes—
122#2545C2212yes—
123#2544C2212yes—
124#2542C2211yescharacteristic
125#2541C2211yescharacteristic
126#2538C2212yes—
127#2538C2212yes—
128#2533C2214yes—
129#2532C2214yes—
130#2532C2214yes—
131#2531C2214yes—
132#2531C2214yes—
133#2529C2214yes—
134#2528C2214yes—
135#2526C2214yes—
136#2526C2214yes—
137#2525C2214yes—
138#2519C2214yes—
139#2519C2214yes—
140#2518C2214yes—
141#2518C2214yes—
142#2515C2214yes—
143#2515C2214yes—
144#2514C2212yes—
145#2513C2212yes—
146#2512C2212yes—
147#2511C2212yes—
148#2511C2212yes—
149#2511C2212yes—
150#2510C2214yes—
151#2501C2212yes—
152#2500C2212yes—
153#2498C2214yes—
154#2495C2214yes—
155#2489C2214yes—
156#2488C2214yes—
157#2488C2214yes—
158#2478C2214yes—
159#2477C2214yes—
160#2475C2214yes—
161#2471C2214yes—
162#2470C2214yes—
163#2461C2214yes—
164#2457C2214yes—
165#2457C2214yes—
166#2450C2214yes—
167#2448C2212yes—
168#2447C2212yes—
169#2447C2212yes—
170#2447C2212yes—
171#2446C2212yes—
172#2445C2212yes—
173#2444C2214yes—
174#2438C2214yes—
175#2436C2212yes—
176#2431C2212yes—
177#2425C2214yes—
178#2407C2214yes—
179#2406C2212yes—
180#2406C2212yes—
181#2402C2211yescharacteristic
182#2402C2211yescharacteristic
183#2399C2211yescharacteristic
184#2399C2211yescharacteristic
185#2396C2212yes—
186#2396C2212yes—
187#2374C2214yes—
188#2372C2214yes—
189#2367C2212yes—
190#2367C2212yes—
191#2366C2212yes—
192#2359C2214yes—
193#2357C2212yes—
194#2356C2211yescharacteristic
195#2356C2212yes—
196#2356C2211yescharacteristic
197#2356C2212yes—
198#2356C2211yescharacteristic
199#2356C2211yescharacteristic
200#2356C2212yes—
201#2355C2212yes—
202#2354C2212yes—
203#2353C2214yes—
204#2353C2212yes—
205#2353C2212yes—
206#2351C2211yescharacteristic
207#2351C2211yescharacteristic
208#2349C2211yescharacteristic
209#2349C2211yescharacteristic
210#2347C2212yes—
211#2345C2214yes—
212#2345C2212yes—
213#2343C2214yes—
214Q8×C22⋊C4C2212yes—
215#2339C2212yes—
216#2337C2214yes—
217#2337C2214yes—
218#2335C2214yes—
219#2333C2214yes—
220#2331C2211yescharacteristic
221#2331C2211yescharacteristic
222#2328C2211yescharacteristic
223#2328C2212yes—
224#2328C2211yescharacteristic
225#2327C2211yescharacteristic
226#2327C2211yescharacteristic
227#2326C2211yescharacteristic
228#2326C2212yes—
229#2326C2212yes—
230#2326C2212yes—
231#2326C2211yescharacteristic
232#2324C2212yes—
233#2324C2212yes—
234#2323C2214yes—
235#2322C2214yes—
236#2320C2212yes—
237#2320C2214yes—
238#2320C2212yes—
239#2318C2214yes—
240#2317C2211yescharacteristic
241#2311C2211yescharacteristic
242#2310C2211yescharacteristic
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×#124C2211yescharacteristic
246C4×#124C2211yescharacteristic
247C4×C22⋊Q8C2214yes—
248C4×#123C2214yes—
249C4×#123C2214yes—
250#2297C2214yes—
251#2295C2212yes—
252#2295C2212yes—
253#2293C2212yes—
254#2290C2214yes—
255#2290C2214yes—
256#2283C2212yes—
257#2283C2211yescharacteristic
258#2283C2211yescharacteristic
259#2283C2211yescharacteristic
260#2283C2212yes—
261#2283C2212yes—
262C2×#383C2212yes—
263#2276C2212yes—
264#2275C2212yes—
265C42×D4C2212yes—
266C4×#117C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2312yes—
269C23×Q8C2311yescharacteristic
270#559—216no—
271#536—28no—
272#532—28no—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×#127C2311yescharacteristic
277C2×#127C2312yes—
278C2×#126C2314yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#124C2312yes—
282C2×#124C2311yescharacteristic
283C2×#124C2312yes—
284C2×#124C2314yes—
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#124C2311yescharacteristic
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2314yes—
301C4×#41—28no—
302C2×C4×Q8—28no—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×#117C2311yescharacteristic
328C2×#117C2311yescharacteristic
329C2×#117C2312yes—
330C2×#117C2311yescharacteristic
331C2×#117C2314yes—
332C2×#117C2314yes—
333C22×C4⋊C4C2311yescharacteristic
334C22×C4⋊C4C2312yes—
335C22×C42C2312yes—
336C22×C42C2312yes—
337C22×C42C2314yes—
338C22×C42C2311yescharacteristic
339#401C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2312yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2312yes—
356#400C2312yes—
357#400C2312yes—
358#400C2312yes—
359#400C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2312yes—
364#399C2312yes—
365#399C2312yes—
366#399C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2314yes—
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2312yes—
404#396C2312yes—
405#396C2312yes—
406#396C2312yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#395C2312yes—
412#395C2312yes—
413#395C2312yes—
414#395C2312yes—
415#395C2312yes—
416#395C2312yes—
417#395C2312yes—
418#395C2312yes—
419#395C2312yes—
420#395C2312yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2312yes—
425#394C2312yes—
426#394C2312yes—
427#394C2312yes—
428#394C2312yes—
429#394C2312yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#393C2314yes—
434#393C2312yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2312yes—
439#392C2312yes—
440#392C2312yes—
441#392C2314yes—
442#392C2314yes—
443#391C2311yescharacteristic
444#391C2311yescharacteristic
445#391C2311yescharacteristic
446#391C2311yescharacteristic
447#391C2314yes—
448#391C2311yescharacteristic
449#391C2311yescharacteristic
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2312yes—
460#391C2312yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2312yes—
465#391C2312yes—
466#391C2314yes—
467#391C2312yes—
468#391C2312yes—
469#390C2311yescharacteristic
470#390C2311yescharacteristic
471#390C2312yes—
472#390C2312yes—
473#390C2314yes—
474#390C2314yes—
475#390C2314yes—
476#390C2314yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2314yes—
483#390C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2312yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
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#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2312yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
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#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#384C2311yescharacteristic
620#384C2311yescharacteristic
621#384C2312yes—
622#384C2312yes—
623#384C2312yes—
624#383C2314yes—
625#383C2314yes—
626#383C2314yes—
627#383C2312yes—
628#383C2314yes—
629#383C2311yescharacteristic
630#383C2311yescharacteristic
631#383C2314yes—
632#383C2312yes—
633#383C2312yes—
634#383C2312yes—
635#383C2312yes—
636#383C2311yescharacteristic
637#383C2311yescharacteristic
638#382C2312yes—
639#382C2314yes—
640#382C2311yescharacteristic
641#382C2314yes—
642#382C2311yescharacteristic
643#382C2314yes—
644#382C2312yes—
645#382C2314yes—
646#382C2312yes—
647#382C2311yescharacteristic
648#382C2311yescharacteristic
649#382C2312yes—
650#382C2312yes—
651#381C2314yes—
652#381C2314yes—
653#381C2312yes—
654#381C2314yes—
655#381C2314yes—
656#381C2314yes—
657#381C2311yescharacteristic
658#381C2311yescharacteristic
659#381C2314yes—
660#381C2311yescharacteristic
661#381C2311yescharacteristic
662#380C2314yes—
663#380C2314yes—
664#380C2312yes—
665#380C2314yes—
666#380C2312yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2312yes—
672#380C2314yes—
673#380C2312yes—
674#380C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2314yes—
722#376C2312yes—
723#376C2312yes—
724#376C2314yes—
725#376C2311yescharacteristic
726#376C2311yescharacteristic
727#376C2312yes—
728#376C2312yes—
729#376C2312yes—
730#376C2312yes—
731#376C2312yes—
732#376C2314yes—
733C2×#95C2314yes—
734C2×#95C2314yes—
735C2×#95C2312yes—
736C2×#95C2312yes—
737C43C2311yescharacteristic
738C43C2311yescharacteristic
739C2×#41—24no—
740C2×#41—24no—
741C2×#41—28no—
742C2×#41—42no—
743C2×#41—84no—
744C22×Q8—24no—
745C22×Q8—24no—
746C22×Q8—42no—
747C22×Q8C2411yescharacteristic
748C22×Q8C2411yescharacteristic
749C22×Q8C2412yes—
750C22×Q8C2411yescharacteristic
751C22×Q8C2412yes—
752C22×Q8C2412yes—
753C22×Q8C2412yes—
754C22×D4C2412yes—
755C22×D4C2412yes—
756C22×D4C2411yescharacteristic
757C22×D4C2414yes—
758C22×D4C2414yes—
759C22×D4C2412yes—
760C22×D4C2414yes—
761C22×D4C2412yes—
762C23×C4C2412yes—
763C23×C4C2412yes—
764C23×C4C2411yescharacteristic
765C23×C4C2412yes—
766C23×C4C2414yes—
767C23×C4C2414yes—
768C23×C4C2412yes—
769C23×C4C2414yes—
770C23×C4C2412yes—
771C23×C4C2414yes—
772C23×C4C2414yes—
773C23×C4C2411yescharacteristic
774C23×C4C2411yescharacteristic
775C4⋊Q8—24no—
776C4⋊Q8—24no—
777C4⋊Q8—24no—
778#127—28no—
779#127—24no—
780#126—84no—
781#125—84no—
782#125—84no—
783#124—28no—
784#124—24no—
785#124—216no—
786#124—28no—
787#124—44no—
788#124—44no—
789#124#4118yescomplemented
790#123—216no—
791#123—216no—
792#123—216no—
793#123—84no—
794#123—84no—
795#123—84no—
796C22⋊Q8—216no—
797C22⋊Q8—84no—
798C22⋊Q8—84no—
799C22⋊Q8—84no—
800#121—28no—
801#121—28no—
802#121—84no—
803C4×Q8—28no—
804C4×Q8—28no—
805C4×Q8—28no—
806C4×Q8—24no—
807C4×Q8—24no—
808C4×Q8—24no—
809C4×Q8—24no—
810C4×Q8—24no—
811C4×Q8—24no—
812C4×Q8—28no—
813C4×Q8—44no—
814C4×Q8—44no—
815C4×D4—28no—
816C4×D4—28no—
817C4×D4—28no—
818C4×D4—216no—
819C4×D4—24no—
820C4×D4—24no—
821C4×D4—28no—
822C4×D4—28no—
823C4×D4—28no—
824C4×D4—44no—
825C4×D4—44no—
826C4×D4—84no—
827#117—24no—
828#117—28no—
829#117—24no—
830#117—42no—
831#117—84no—
832#117—84no—
833C2×C4⋊C4—28no—
834C2×C4⋊C4—24no—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C42—28no—
933C2×C42—28no—
934C2×C42—84no—
935C2×C42#4118yes—
936C2×C42C2412yes—
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2414yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2414yes—
962C2×C42C2414yes—
963C2×C42C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968#95C2412yes—
969#95C2412yes—
970#95C2411yescharacteristic
971#95C2411yescharacteristic
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2411yescharacteristic
984#95C2411yescharacteristic
985#95C2412yes—
986#95C2412yes—
987#95C2411yescharacteristic
988#95C2411yescharacteristic
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2411yescharacteristic
1028#95C2411yescharacteristic
1029#95C2414yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046C24C2514yes—
1047C24C2511yescharacteristic
1048C24C2512yes—
1049#41—416no—
1050#41—816no—
1051C2×Q8—22no—
1052C2×Q8—24no—
1053C2×Q8—22no—
1054C2×Q8—22no—
1055C2×Q8—24no—
1056C2×Q8—22no—
1057C2×Q8—22no—
1058C2×Q8—24no—
1059C2×Q8—24no—
1060C2×Q8—22no—
1061C2×Q8—22no—
1062C2×Q8—22no—
1063C2×Q8—42no—
1064C2×Q8—42no—
1065C2×Q8—42no—
1066C2×Q8—42no—
1067C2×Q8—44no—
1068C2×Q8—42no—
1069C2×Q8—42no—
1070C2×Q8—416no—
1071C2×Q8C2×#4114yes—
1072C2×D4—24no—
1073C2×D4—24no—
1074C2×D4—28no—
1075C2×D4—28no—
1076C2×D4—28no—
1077C2×D4—22no—
1078C2×D4—24no—
1079C2×D4—24no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—22no—
1083C2×D4—24no—
1084C2×D4—42no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4C2×#4114yes—
1094C22×C4—22no—
1095C22×C4—22no—
1096C22×C4—24no—
1097C22×C4—24no—
1098C22×C4—24no—
1099C22×C4—28no—
1100C22×C4—24no—
1101C22×C4—28no—
1102C22×C4—24no—
1103C22×C4—24no—
1104C22×C4—24no—
1105C22×C4—28no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—42no—
1109C22×C4—42no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4C2×#4114yes—
1126C22×C4C2×#4114yes—
1127C22×C4C2×#4114yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2514yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2514yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2511yescharacteristic
1149C22×C4C2511yescharacteristic
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2512yes—
1154C22×C4C2512yes—
1155C22×C4C2511yescharacteristic
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—22no—
1160C4⋊C4—22no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—22no—
1164C4⋊C4—22no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—28no—
1174C4⋊C4—24no—
1175C4⋊C4—28no—
1176C4⋊C4—28no—
1177C4⋊C4—24no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—42no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
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—44no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—42no—
1213C22⋊C4—24no—
1214C22⋊C4—28no—
1215C22⋊C4—28no—
1216C22⋊C4—24no—
1217C22⋊C4—24no—
1218C22⋊C4—24no—
1219C22⋊C4—28no—
1220C22⋊C4—28no—
1221C22⋊C4—28no—
1222C22⋊C4—28no—
1223C22⋊C4—28no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
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—44no—
1244C22⋊C4—42no—
1245C22⋊C4—44no—
1246C22⋊C4—42no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4C2×#41116yes—
1253C42—24no—
1254C42—24no—
1255C42—24no—
1256C42—24no—
1257C42—24no—
1258C42—24no—
1259C42—24no—
1260C42—22no—
1261C42—28no—
1262C42—24no—
1263C42—24no—
1264C42—22no—
1265C42—22no—
1266C42—24no—
1267C42—24no—
1268C42—42no—
1269C42—44no—
1270C42—44no—
1271C42—44no—
1272C42—42no—
1273C42—42no—
1274C42—44no—
1275C42—44no—
1276C42—42no—
1277C42—44no—
1278C42—44no—
1279C42—44no—
1280C42C2×#4114yes—
1281C42C2×#4114yes—
1282C42C2×#4114yes—
1283C42C2×#4114yes—
1284C42C2×#4114yes—
1285C23—21no—
1286C23—22no—
1287C23—21no—
1288C23—22no—
1289C23—24no—
1290C23—22no—
1291C23—22no—
1292C23—24no—
1293C23—24no—
1294C23—24no—
1295C23—24no—
1296C23—24no—
1297C23—24no—
1298C23—24no—
1299C23—24no—
1300C23C22×#4114yes—
1301C23C22×#4112yes—
1302C23C2611yescharacteristic
1303Q8—28no—
1304Q8—48no—
1305Q8—44no—
1306Q8—44no—
1307Q8—84no—
1308Q8—84no—
1309Q8—84no—
1310D4—28no—
1311D4—48no—
1312D4—48no—
1313D4—84no—
1314D4—84no—
1315D4—88no—
1316D4—88no—
1317D4—88no—
1318C2×C4—22no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—28no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—44no—
1386C2×C4—44no—
1387C2×C4—48no—
1388C2×C4—48no—
1389C2×C4—416no—
1390C2×C4—84no—
1391C2×C4—88no—
1392C2×C4—84no—
1393C2×C4—84no—
1394C2×C4—88no—
1395C2×C4—88no—
1396C2×C4—164no—
1397C2×C4C22×#4112yes—
1398C2×C4C22×#4112yes—
1399C2×C4C22×#4112yes—
1400C2×C4C22×#4112yes—
1401C2×C4C22×#4114yes—
1402C2×C4C22×#4112yes—
1403C2×C4C22×#4114yes—
1404C2×C4C22×#4112yes—
1405C2×C4C22×#4112yes—
1406C2×C4#58512yes—
1407C22—22no—
1408C22—28no—
1409C22—22no—
1410C22—22no—
1411C22—24no—
1412C22—42no—
1413C22—42no—
1414C22—42no—
1415C22—44no—
1416C22—42no—
1417C22—44no—
1418C22—44no—
1419C22—44no—
1420C22—44no—
1421C22—44no—
1422C22—44no—
1423C22—44no—
1424C22C23×#4111yescharacteristic
1425C22C23×#4111yescharacteristic
1426C22C2×#58511yescharacteristic
1427C22H(7,𝔽2)12yes—
1428C222−1+612yes—
1429C4—22no—
1430C4—22no—
1431C4—24no—
1432C4—22no—
1433C4—22no—
1434C4—22no—
1435C4—24no—
1436C4—44no—
1437C4—42no—
1438C4—42no—
1439C4—42no—
1440C4—42no—
1441C4—44no—
1442C4—42no—
1443C4—42no—
1444C4—42no—
1445C4—42no—
1446C4—42no—
1447C4—42no—
1448C4—42no—
1449C4—42no—
1450C4—44no—
1451C4—42no—
1452C4—42no—
1453C4—42no—
1454C4—42no—
1455C4—42no—
1456C4#347514yes—
1457C2—42no—
1458C2—44no—
1459C2—84no—
1460C2C2×#347511yescharacteristic
1461C2#6285511yescharacteristic
1462C2#6285712yes—
1463C2#6286011yescharacteristic
1464C2#6288412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35190C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45434C2semidirect
2. #45431C2semidirect
3. #45428C2semidirect
4. #45421C2semidirect
5. #45306C2semidirect
6. #45299C2semidirect
7. #45148C2semidirect
8. #45147C2semidirect
9. #45146C2semidirect
10. #45083C2semidirect
11. #45070C2semidirect
12. #44995C2semidirect
13. #40255C2semidirect
14. #40228C2semidirect
15. #38655C2semidirect
16. #38644C2semidirect
17. #38000C2semidirect
18. #37994C2semidirect
19. #37921C2semidirect
20. #37915C2semidirect
21. #35615C2semidirect
22. #35610C2semidirect
23. #35249C2semidirect
24. #35206C2semidirect
26. #34644C2semidirect
27. #34329C2semidirect
28. #34195C2semidirect
29. #34192C2semidirect
30. C4×#536C2semidirect
31. #34086C2semidirect
789. #124#41semidirect

Maximal subgroups

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

subgroupindex
#454342
#454312
#454282
#454212
#453062
#452992
#451482
#451472
#451462
#450832
#450702
#449952
#402552
#402282
#386552
#386442
#380002
#379942
#379212
#379152
#356152
#356102
#352492
#352062
#351902
#346442
#343292
#341952
#341922
C4×#5362
#340862