Finite Group Databasebeta

← #7648458

Subgroups — #7648458

Order 512.

4948 conjugacy classes of subgroups.

The subgroup lattice has 1550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41767C214yesmaximal, complemented
2#41643C214yesmaximal, complemented
3#41138C214yesmaximal, complemented
4#40966C214yesmaximal, complemented
5#40314C214yesmaximal, complemented
6#40260C214yesmaximal, complemented
7#38714C214yesmaximal, complemented
8#38676C214yesmaximal, complemented
9#37572C212yesmaximal, complemented
10#37559C211yesmaximal, characteristic, complemented
11#37554C211yesmaximal, characteristic, complemented
12#37432C211yesmaximal, characteristic, complemented
13#37397C211yesmaximal, characteristic, complemented
14#37361C212yesmaximal, complemented
15#37346C212yesmaximal, complemented
16#37322C211yesmaximal, characteristic, complemented
17#37319C211yesmaximal, characteristic, complemented
18#35601C212yesmaximal, complemented
19#35539C212yesmaximal, complemented
20#35331C211yesmaximal, characteristic, complemented
21#35324C211yesmaximal, characteristic, complemented
22#35296C211yesmaximal, characteristic, complemented
23#35293C211yesmaximal, characteristic, complemented
24#35278C211yesmaximal, characteristic, complemented
25#35169C212yesmaximal, complemented
26#35132C211yesmaximal, characteristic, complemented
27#35109C212yesmaximal, complemented
28#34918C212yesmaximal, complemented
29#34208C211yesmaximal, characteristic, complemented
30#34151C211yesmaximal, characteristic, complemented
31#34086C211yesmaximal, characteristic, complemented
32C2×#542C2212yes—
33C2×#540C2212yes—
34C2×#532C2211yescharacteristic
35C2×#532C2211yescharacteristic
36C2×#529C2211yescharacteristic
37C2×#520C2212yes—
38#2867C2211yescharacteristic
39#2864C2211yescharacteristic
40#2864C2211yescharacteristic
41#2862C2211yescharacteristic
42#2862C2211yescharacteristic
43#2859C2211yescharacteristic
44#2858C2211yescharacteristic
45#2858C2211yescharacteristic
46#2856C2212yes—
47#2855C2212yes—
48#2854C2212yes—
49#2854C2214yes—
50#2850C2212yes—
51#2850C2214yes—
52#2837C2214yes—
53#2832C2214yes—
54#2820C2212yes—
55#2819C2212yes—
56#2816C2212yes—
57#2815C2212yes—
58#2798C2214yes—
59#2797C2214yes—
60#2797C2214yes—
61#2786C2214yes—
62#2786C2214yes—
63#2784C2214yes—
64#2781C2214yes—
65#2778C2214yes—
66#2778C2214yes—
67#2773C2214yes—
68#2767C2214yes—
69#2755C2214yes—
70#2753C2214yes—
71#2752C2214yes—
72#2751C2214yes—
73#2750C2214yes—
74#2740C2214yes—
75#2730C2214yes—
76#2712C2214yes—
77#2709C2214yes—
78#2709C2214yes—
79#2708C2214yes—
80#2708C2214yes—
81#2703C2214yes—
82#2700C2214yes—
83#2696C2214yes—
84#2688C2214yes—
85#2688C2214yes—
86#2686C2214yes—
87#2676C2214yes—
88#2673C2214yes—
89#2673C2214yes—
90#2666C2214yes—
91#2663C2214yes—
92#2663C2214yes—
93#2661C2212yes—
94#2661C2212yes—
95#2661C2214yes—
96#2656C2212yes—
97#2653C2214yes—
98#2653C2214yes—
99#2651C2214yes—
100#2649C2214yes—
101#2645C2212yes—
102#2644C2212yes—
103#2641C2212yes—
104#2640C2212yes—
105#2639C2212yes—
106#2636C2212yes—
107#2636C2212yes—
108#2635C2214yes—
109#2633C2212yes—
110#2631C2212yes—
111#2628C2211yescharacteristic
112#2628C2211yescharacteristic
113#2621C2211yescharacteristic
114#2621C2211yescharacteristic
115#2619C2211yescharacteristic
116#2619C2214yes—
117#2619C2211yescharacteristic
118#2619C2211yescharacteristic
119#2619C2211yescharacteristic
120#2612C2214yes—
121#2610C2214yes—
122#2603C2214yes—
123#2603C2212yes—
124#2603C2212yes—
125#2602C2214yes—
126#2601C2214yes—
127#2597C2214yes—
128#2595C2214yes—
129#2595C2214yes—
130#2592C2212yes—
131#2591C2214yes—
132#2588C2214yes—
133#2580C2212yes—
134#2575C2214yes—
135#2570C2212yes—
136#2560C2214yes—
137#2560C2214yes—
138#2559C2214yes—
139#2557C2214yes—
140#2557C2214yes—
141#2557C2214yes—
142#2557C2214yes—
143#2555C2214yes—
144#2553C2214yes—
145#2550C2212yes—
146#2544C2212yes—
147#2544C2214yes—
148#2544C2212yes—
149#2540C2212yes—
150#2540C2214yes—
151#2535C2212yes—
152#2528C2214yes—
153#2527C2214yes—
154#2516C2214yes—
155#2516C2214yes—
156#2513C2212yes—
157#2511C2212yes—
158#2491C2212yes—
159#2489C2212yes—
160#2477C2214yes—
161#2476C2214yes—
162#2476C2214yes—
163#2474C2214yes—
164#2471C2214yes—
165#2471C2214yes—
166#2470C2214yes—
167#2470C2214yes—
168#2464C2214yes—
169#2464C2214yes—
170#2463C2214yes—
171#2458C2214yes—
172#2457C2214yes—
173#2456C2214yes—
174#2453C2212yes—
175#2452C2212yes—
176#2449C2214yes—
177#2448C2212yes—
178#2447C2212yes—
179#2445C2214yes—
180#2445C2212yes—
181#2445C2214yes—
182#2445C2212yes—
183#2443C2214yes—
184#2442C2212yes—
185#2440C2212yes—
186#2438C2214yes—
187#2431C2212yes—
188#2431C2214yes—
189#2431C2212yes—
190#2430C2212yes—
191#2430C2212yes—
192#2428C2214yes—
193#2428C2212yes—
194#2428C2212yes—
195#2428C2214yes—
196#2427C2212yes—
197#2426C2212yes—
198#2423C2212yes—
199#2420C2212yes—
200#2416C2212yes—
201#2416C2212yes—
202#2414C2214yes—
203#2413C2214yes—
204#2407C2212yes—
205#2407C2212yes—
206#2398C2214yes—
207#2395C2214yes—
208#2374C2212yes—
209#2374C2212yes—
210#2373C2212yes—
211#2373C2212yes—
212#2370C2212yes—
213#2367C2212yes—
214#2364C2214yes—
215#2364C2214yes—
216#2363C2212yes—
217#2362C2212yes—
218#2352C2214yes—
219#2352C2214yes—
220#2337C2214yes—
221#2333C2214yes—
222#2333C2214yes—
223#2333C2214yes—
224#2331C2211yescharacteristic
225#2331C2211yescharacteristic
226#2329C2214yes—
227#2328C2211yescharacteristic
228#2328C2211yescharacteristic
229#2328C2214yes—
230#2328C2211yescharacteristic
231#2328C2211yescharacteristic
232#2327C2211yescharacteristic
233#2327C2211yescharacteristic
234#2324C2212yes—
235#2324C2212yes—
236#2324C2212yes—
237#2323C2212yes—
238#2311C2212yes—
239C4×#127C2212yes—
240C4×#124C2212yes—
241C4×#124C2212yes—
242C4×#124C2212yes—
243C4×#123C2214yes—
244#2298C2211yescharacteristic
245#2298C2211yescharacteristic
246#2297C2214yes—
247#2295C2212yes—
248#2295C2211yescharacteristic
249#2293C2211yescharacteristic
250#2293C2212yes—
251#2293C2212yes—
252#2293C2211yescharacteristic
253#2293C2211yescharacteristic
254#2290C2214yes—
255#2290C2214yes—
256#2290C2211yescharacteristic
257#2290C2211yescharacteristic
258#2283C2211yescharacteristic
259C2×#382C2211yescharacteristic
260C42×Q8C2211yescharacteristic
261C42×D4C2211yescharacteristic
262C42×D4C2212yes—
263C4×#117C2211yescharacteristic
264C4×#117C2211yescharacteristic
265C4×#117C2211yescharacteristic
266C4×#117C2211yescharacteristic
267C22×#41C2312yes—
268C22×#41C2312yes—
269#542—48no—
270#540—48no—
271#532—28no—
272#532—28no—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×#127C2311yescharacteristic
277C2×#127C2311yescharacteristic
278C2×#127C2312yes—
279C2×#127C2314yes—
280C2×#127C2312yes—
281C2×#127C2314yes—
282#529—28no—
283C2×#126C2311yescharacteristic
284C2×#126C2311yescharacteristic
285C2×#126C2314yes—
286C2×#125C2311yescharacteristic
287C2×#125C2312yes—
288C2×#124C2311yescharacteristic
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2314yes—
294C2×#124C2314yes—
295C2×#124C2314yes—
296C2×#123C2311yescharacteristic
297C2×#123C2311yescharacteristic
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×C22⋊Q8C2311yescharacteristic
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2314yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2312yes—
313C2×#121C2311yescharacteristic
314C2×#121C2312yes—
315C2×#121C2312yes—
316C2×#121C2314yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×#121C2312yes—
320C2×#121C2314yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2314yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×#121C2314yes—
327#520—48no—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2314yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2314yes—
348C2×#117C2311yescharacteristic
349C2×#117C2311yescharacteristic
350C2×#117C2311yescharacteristic
351C2×#117C2311yescharacteristic
352C2×#117C2311yescharacteristic
353C2×#117C2311yescharacteristic
354C2×#117C2314yes—
355C2×#117C2312yes—
356C2×#117C2314yes—
357C2×#117C2314yes—
358C22×C4⋊C4C2312yes—
359C22×C4⋊C4C2314yes—
360C22×C42C2311yescharacteristic
361C22×C42C2311yescharacteristic
362C22×C42C2314yes—
363C22×C42C2311yescharacteristic
364#401C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2312yes—
372#400C2314yes—
373#400C2314yes—
374#400C2312yes—
375#400C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2312yes—
379#399C2314yes—
380#399C2312yes—
381#399C2314yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2312yes—
407#397C2312yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#395C2312yes—
417#395C2312yes—
418#395C2314yes—
419#395C2314yes—
420#394C2312yes—
421#394C2312yes—
422#394C2312yes—
423#394C2314yes—
424#394C2312yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2312yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2312yes—
440#394C2312yes—
441#394C2314yes—
442#394C2312yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2312yes—
455#393C2312yes—
456#393C2314yes—
457#393C2314yes—
458#392C2312yes—
459#392C2312yes—
460#392C2314yes—
461#392C2314yes—
462#392C2312yes—
463#392C2314yes—
464#392C2312yes—
465#392C2314yes—
466#392C2312yes—
467#392C2312yes—
468#392C2312yes—
469#392C2312yes—
470#392C2314yes—
471#392C2314yes—
472#392C2314yes—
473#392C2314yes—
474#392C2314yes—
475#392C2314yes—
476#391C2314yes—
477#391C2314yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2314yes—
483#391C2314yes—
484#391C2314yes—
485#391C2314yes—
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#390C2314yes—
490#390C2314yes—
491#390C2312yes—
492#390C2312yes—
493#390C2314yes—
494#390C2314yes—
495#390C2312yes—
496#390C2312yes—
497#390C2312yes—
498#390C2312yes—
499#390C2314yes—
500#390C2314yes—
501#390C2314yes—
502#390C2312yes—
503#390C2312yes—
504#390C2314yes—
505#390C2314yes—
506#390C2314yes—
507#390C2314yes—
508#390C2314yes—
509#390C2312yes—
510#390C2312yes—
511#390C2314yes—
512#390C2312yes—
513#390C2312yes—
514#390C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
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#388C2314yes—
547#388C2312yes—
548#388C2314yes—
549#388C2314yes—
550#388C2312yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2312yes—
560#388C2312yes—
561#388C2314yes—
562#388C2314yes—
563#388C2312yes—
564#388C2314yes—
565#388C2312yes—
566#388C2312yes—
567#388C2312yes—
568#388C2312yes—
569#388C2312yes—
570#388C2312yes—
571#388C2314yes—
572#388C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2314yes—
601#387C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2312yes—
638#386C2312yes—
639#386C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2312yes—
652#385C2312yes—
653#385C2314yes—
654#384C2312yes—
655#383C2312yes—
656#382C2312yes—
657#382C2312yes—
658#382C2312yes—
659#382C2314yes—
660#382C2311yescharacteristic
661#382C2311yescharacteristic
662#382C2311yescharacteristic
663#382C2311yescharacteristic
664#382C2314yes—
665#382C2312yes—
666#381C2312yes—
667#381C2314yes—
668#381C2314yes—
669#381C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2314yes—
676#380C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2311yescharacteristic
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
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⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2311yescharacteristic
720C4×C22⋊C4C2311yescharacteristic
721C4×C22⋊C4C2311yescharacteristic
722C4×C22⋊C4C2311yescharacteristic
723C4×C22⋊C4C2311yescharacteristic
724C4×C22⋊C4C2311yescharacteristic
725#376C2311yescharacteristic
726#376C2311yescharacteristic
727#376C2312yes—
728#376C2312yes—
729#376C2314yes—
730#376C2311yescharacteristic
731#376C2311yescharacteristic
732C2×#95C2312yes—
733C2×#95C2312yes—
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C43C2311yescharacteristic
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C2×#41—28no—
741C2×#41—28no—
742C2×#41—44no—
743C2×#41—44no—
744C2×#41—84no—
745C22×Q8C2412yes—
746C22×Q8C2411yescharacteristic
747C22×Q8C2412yes—
748C22×Q8C2414yes—
749C22×D4C2412yes—
750C22×D4C2412yes—
751C22×D4C2411yescharacteristic
752C22×D4C2414yes—
753C22×D4C2411yescharacteristic
754C22×D4C2411yescharacteristic
755C22×D4C2414yes—
756C22×D4C2414yes—
757C22×D4C2412yes—
758C22×D4C2412yes—
759C22×D4C2412yes—
760C22×D4C2414yes—
761C22×D4C2412yes—
762C22×D4C2414yes—
763C22×D4C2414yes—
764C22×D4C2414yes—
765C22×D4C2414yes—
766C22×D4C2414yes—
767C22×D4C2414yes—
768C23×C4C2411yescharacteristic
769C23×C4C2411yescharacteristic
770C23×C4C2411yescharacteristic
771C23×C4C2414yes—
772C23×C4C2414yes—
773C23×C4C2414yes—
774C23×C4C2414yes—
775C23×C4C2412yes—
776C23×C4C2414yes—
777C23×C4C2414yes—
778C23×C4C2414yes—
779C23×C4C2412yes—
780C23×C4C2411yescharacteristic
781C23×C4C2411yescharacteristic
782C4⋊Q8—24no—
783C4⋊Q8—24no—
784C4⋊Q8—44no—
785#127—24no—
786#127—24no—
787#127—44no—
788#127—48no—
789#127—44no—
790#127—84no—
791#126—24no—
792#126—24no—
793#126—48no—
794#125—24no—
795#125—44no—
796#124—24no—
797#124—28no—
798#124—28no—
799#124—48no—
800#124—44no—
801#124—44no—
802#124—84no—
803#124—84no—
804#123—24no—
805#123—24no—
806#123—48no—
807#123—48no—
808#123—48no—
809#123—48no—
810#123—84no—
811#123—84no—
812C22⋊Q8—24no—
813C22⋊Q8—48no—
814C22⋊Q8—48no—
815C22⋊Q8—44no—
816C22⋊Q8—44no—
817C22⋊Q8—84no—
818#121—24no—
819#121—28no—
820#121—28no—
821#121—28no—
822#121—28no—
823#121—48no—
824#121—48no—
825#121—48no—
826#121—44no—
827#121—48no—
828#121—44no—
829#121—44no—
830#121—44no—
831#121—84no—
832#121—84no—
833#121—84no—
834#121—84no—
835C4×Q8—24no—
836C4×Q8—28no—
837C4×Q8—44no—
838C4×Q8—44no—
839C4×D4—24no—
840C4×D4—24no—
841C4×D4—24no—
842C4×D4—28no—
843C4×D4—28no—
844C4×D4—28no—
845C4×D4—28no—
846C4×D4—28no—
847C4×D4—28no—
848C4×D4—48no—
849C4×D4—44no—
850C4×D4—48no—
851C4×D4—44no—
852C4×D4—44no—
853C4×D4—48no—
854C4×D4—84no—
855#117—24no—
856#117—24no—
857#117—24no—
858#117—24no—
859#117—24no—
860#117—42no—
861#117—44no—
862#117—48no—
863#117—84no—
864#117—84no—
865C2×C4⋊C4—48no—
866C2×C4⋊C4—44no—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2411yescharacteristic
917C2×C22⋊C4C2411yescharacteristic
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2411yescharacteristic
921C2×C22⋊C4C2411yescharacteristic
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2411yescharacteristic
929C2×C22⋊C4C2411yescharacteristic
930C2×C22⋊C4C2411yescharacteristic
931C2×C22⋊C4C2411yescharacteristic
932C2×C22⋊C4C2411yescharacteristic
933C2×C22⋊C4C2411yescharacteristic
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C42—42no—
975C2×C42—42no—
976C2×C42—84no—
977C2×C42#4118yes—
978C2×C42C2411yescharacteristic
979C2×C42C2411yescharacteristic
980C2×C42C2414yes—
981C2×C42C2411yescharacteristic
982C2×C42C2411yescharacteristic
983C2×C42C2411yescharacteristic
984C2×C42C2411yescharacteristic
985C2×C42C2412yes—
986C2×C42C2411yescharacteristic
987C2×C42C2412yes—
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2412yes—
991C2×C42C2412yes—
992C2×C42C2414yes—
993C2×C42C2412yes—
994C2×C42C2414yes—
995C2×C42C2414yes—
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2412yes—
999C2×C42C2412yes—
1000C2×C42C2412yes—
1001C2×C42C2414yes—
1002C2×C42C2412yes—
1003C2×C42C2412yes—
1004C2×C42C2412yes—
1005C2×C42C2412yes—
1006C2×C42C2411yescharacteristic
1007C2×C42C2411yescharacteristic
1008C2×C42C2411yescharacteristic
1009C2×C42C2411yescharacteristic
1010C2×C42C2411yescharacteristic
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2412yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2414yes—
1064#95C2414yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2414yes—
1068#95C2414yes—
1069C24C2511yescharacteristic
1070C24C2511yescharacteristic
1071C24C2514yes—
1072C24C2514yes—
1073C24C2511yescharacteristic
1074#41—432no—
1075#41—816no—
1076C2×Q8—22no—
1077C2×Q8—24no—
1078C2×Q8—24no—
1079C2×Q8—24no—
1080C2×Q8—24no—
1081C2×Q8—42no—
1082C2×Q8—44no—
1083C2×Q8—44no—
1084C2×Q8—44no—
1085C2×Q8—44no—
1086C2×D4—28no—
1087C2×D4—22no—
1088C2×D4—22no—
1089C2×D4—28no—
1090C2×D4—22no—
1091C2×D4—24no—
1092C2×D4—24no—
1093C2×D4—24no—
1094C2×D4—24no—
1095C2×D4—24no—
1096C2×D4—24no—
1097C2×D4—24no—
1098C2×D4—24no—
1099C2×D4—24no—
1100C2×D4—24no—
1101C2×D4—28no—
1102C2×D4—28no—
1103C2×D4—44no—
1104C2×D4—42no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—42no—
1108C2×D4—42no—
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×D4—44no—
1118C2×D4—44no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C2×D4—44no—
1129C2×D4—44no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—44no—
1135C2×D4—44no—
1136C22×C4—22no—
1137C22×C4—22no—
1138C22×C4—22no—
1139C22×C4—22no—
1140C22×C4—28no—
1141C22×C4—28no—
1142C22×C4—22no—
1143C22×C4—22no—
1144C22×C4—22no—
1145C22×C4—22no—
1146C22×C4—28no—
1147C22×C4—28no—
1148C22×C4—24no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—42no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4—42no—
1155C22×C4—42no—
1156C22×C4—42no—
1157C22×C4—44no—
1158C22×C4—44no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—44no—
1163C22×C4—42no—
1164C22×C4—42no—
1165C22×C4—44no—
1166C22×C4—42no—
1167C22×C4—44no—
1168C22×C4—44no—
1169C22×C4—44no—
1170C22×C4—44no—
1171C22×C4—44no—
1172C22×C4—44no—
1173C22×C4C2×#4114yes—
1174C22×C4C2×#4114yes—
1175C22×C4C2×#4114yes—
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2511yescharacteristic
1179C22×C4C2511yescharacteristic
1180C22×C4C2512yes—
1181C22×C4C2514yes—
1182C22×C4C2514yes—
1183C22×C4C2514yes—
1184C22×C4C2514yes—
1185C22×C4C2512yes—
1186C22×C4C2514yes—
1187C22×C4C2514yes—
1188C22×C4C2512yes—
1189C22×C4C2512yes—
1190C22×C4C2511yescharacteristic
1191C22×C4C2511yescharacteristic
1192C22×C4C2511yescharacteristic
1193C22×C4C2511yescharacteristic
1194C22×C4C2511yescharacteristic
1195C22×C4C2511yescharacteristic
1196C22×C4C2511yescharacteristic
1197C22×C4C2511yescharacteristic
1198C22×C4C2511yescharacteristic
1199C22×C4C2512yes—
1200C22×C4C2512yes—
1201C22×C4C2511yescharacteristic
1202C4⋊C4—22no—
1203C4⋊C4—22no—
1204C4⋊C4—22no—
1205C4⋊C4—22no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—22no—
1211C4⋊C4—22no—
1212C4⋊C4—22no—
1213C4⋊C4—22no—
1214C4⋊C4—22no—
1215C4⋊C4—22no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—24no—
1219C4⋊C4—28no—
1220C4⋊C4—24no—
1221C4⋊C4—24no—
1222C4⋊C4—24no—
1223C4⋊C4—24no—
1224C4⋊C4—24no—
1225C4⋊C4—28no—
1226C4⋊C4—24no—
1227C4⋊C4—28no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—42no—
1231C4⋊C4—42no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—42no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—42no—
1246C4⋊C4—44no—
1247C4⋊C4—42no—
1248C22⋊C4—22no—
1249C22⋊C4—22no—
1250C22⋊C4—22no—
1251C22⋊C4—22no—
1252C22⋊C4—22no—
1253C22⋊C4—22no—
1254C22⋊C4—28no—
1255C22⋊C4—28no—
1256C22⋊C4—28no—
1257C22⋊C4—28no—
1258C22⋊C4—22no—
1259C22⋊C4—22no—
1260C22⋊C4—22no—
1261C22⋊C4—22no—
1262C22⋊C4—24no—
1263C22⋊C4—24no—
1264C22⋊C4—24no—
1265C22⋊C4—28no—
1266C22⋊C4—28no—
1267C22⋊C4—24no—
1268C22⋊C4—24no—
1269C22⋊C4—42no—
1270C22⋊C4—42no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—42no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—42no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—42no—
1308C22⋊C4—44no—
1309C42—22no—
1310C42—22no—
1311C42—22no—
1312C42—22no—
1313C42—22no—
1314C42—28no—
1315C42—22no—
1316C42—22no—
1317C42—22no—
1318C42—22no—
1319C42—24no—
1320C42—24no—
1321C42—42no—
1322C42—42no—
1323C42—42no—
1324C42—44no—
1325C42—44no—
1326C42—44no—
1327C42—42no—
1328C42—44no—
1329C42—42no—
1330C42—42no—
1331C42—42no—
1332C42—42no—
1333C42—42no—
1334C42—42no—
1335C42—42no—
1336C42—42no—
1337C42C2×#4114yes—
1338C42C2×#4114yes—
1339C42C2×#4114yes—
1340C42C2×#4114yes—
1341C42H(5,𝔽2)14yes—
1342C23—21no—
1343C23—22no—
1344C23—21no—
1345C23—22no—
1346C23—21no—
1347C23—21no—
1348C23—24no—
1349C23—24no—
1350C23—21no—
1351C23—21no—
1352C23—24no—
1353C23—24no—
1354C23—22no—
1355C23—21no—
1356C23—24no—
1357C23—24no—
1358C23—24no—
1359C23—24no—
1360C23—22no—
1361C23—24no—
1362C23—24no—
1363C23—21no—
1364C23—24no—
1365C23—24no—
1366C23—24no—
1367C23—22no—
1368C23—22no—
1369C23—24no—
1370C23C22×#4112yes—
1371C23C2611yescharacteristic
1372Q8—44no—
1373Q8—48no—
1374Q8—84no—
1375Q8—164no—
1376D4—44no—
1377D4—416no—
1378D4—48no—
1379D4—48no—
1380D4—84no—
1381D4—84no—
1382D4—84no—
1383D4—88no—
1384D4—88no—
1385D4—84no—
1386D4—82no—
1387D4—82no—
1388D4—88no—
1389D4—164no—
1390D4—164no—
1391D4—164no—
1392D4—164no—
1393D4—164no—
1394D4—164no—
1395C2×C4—21no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—21no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—28no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—24no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—24no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—24no—
1419C2×C4—24no—
1420C2×C4—24no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—21no—
1429C2×C4—22no—
1430C2×C4—21no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—24no—
1437C2×C4—24no—
1438C2×C4—24no—
1439C2×C4—24no—
1440C2×C4—24no—
1441C2×C4—24no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—24no—
1445C2×C4—24no—
1446C2×C4—24no—
1447C2×C4—22no—
1448C2×C4—22no—
1449C2×C4—22no—
1450C2×C4—22no—
1451C2×C4—22no—
1452C2×C4—22no—
1453C2×C4—24no—
1454C2×C4—24no—
1455C2×C4—24no—
1456C2×C4—44no—
1457C2×C4—44no—
1458C2×C4—416no—
1459C2×C4—416no—
1460C2×C4—44no—
1461C2×C4—44no—
1462C2×C4—84no—
1463C2×C4—88no—
1464C2×C4—88no—
1465C2×C4—84no—
1466C2×C4—88no—
1467C2×C4—164no—
1468C2×C4—164no—
1469C2×C4C22×#4112yes—
1470C2×C4C22×#4112yes—
1471C2×C4C22×#4112yes—
1472C2×C4C22×#4112yes—
1473C2×C4C22×#4112yes—
1474C2×C4C22×#4112yes—
1475C2×C4C2×H(5,𝔽2)14yes—
1476C2×C4C2×H(5,𝔽2)12yes—
1477C2×C4#58514yes—
1478C2×C4#58512yes—
1479C22—22no—
1480C22—22no—
1481C22—22no—
1482C22—42no—
1483C22—42no—
1484C22—41no—
1485C22—41no—
1486C22—44no—
1487C22—44no—
1488C22—44no—
1489C22—44no—
1490C22—41no—
1491C22—41no—
1492C22—44no—
1493C22—41no—
1494C22—41no—
1495C22—44no—
1496C22—44no—
1497C22—42no—
1498C22—42no—
1499C22—44no—
1500C22—44no—
1501C22—44no—
1502C22—44no—
1503C22—44no—
1504C22—42no—
1505C22—42no—
1506C22—44no—
1507C22—44no—
1508C22C23×#4111yescharacteristic
1509C22C22×H(5,𝔽2)11yescharacteristic
1510C22C2×#58512yes—
1511C22C2×#58511yescharacteristic
1512C22H(7,𝔽2)12yes—
1513C4—22no—
1514C4—22no—
1515C4—22no—
1516C4—22no—
1517C4—22no—
1518C4—24no—
1519C4—24no—
1520C4—41no—
1521C4—41no—
1522C4—44no—
1523C4—41no—
1524C4—41no—
1525C4—41no—
1526C4—41no—
1527C4—44no—
1528C4—42no—
1529C4—42no—
1530C4—42no—
1531C4—44no—
1532C4—44no—
1533C4—44no—
1534C4—42no—
1535C4—44no—
1536C4—42no—
1537C4—42no—
1538C4#346014yes—
1539C2—42no—
1540C2—81no—
1541C2—81no—
1542C2—84no—
1543C2—84no—
1544C2C2×#346011yescharacteristic
1545C2#6281511yescharacteristic
1546C2#6285511yescharacteristic
1547C2#6294112yes—
1548C2#6296112yes—
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. #41767C2semidirect
2. #41643C2semidirect
3. #41138C2semidirect
4. #40966C2semidirect
5. #40314C2semidirect
6. #40260C2semidirect
7. #38714C2semidirect
8. #38676C2semidirect
9. #37572C2semidirect
10. #37559C2semidirect
11. #37554C2semidirect
12. #37432C2semidirect
13. #37397C2semidirect
14. #37361C2semidirect
15. #37346C2semidirect
16. #37322C2semidirect
17. #37319C2semidirect
18. #35601C2semidirect
19. #35539C2semidirect
20. #35331C2semidirect
21. #35324C2semidirect
22. #35296C2semidirect
23. #35293C2semidirect
24. #35278C2semidirect
25. #35169C2semidirect
26. #35132C2semidirect
27. #35109C2semidirect
28. #34918C2semidirect
29. #34208C2semidirect
30. #34151C2semidirect
31. #34086C2semidirect

Maximal subgroups

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

subgroupindex
#417672
#416432
#411382
#409662
#403142
#402602
#387142
#386762
#375722
#375592
#375542
#374322
#373972
#373612
#373462
#373222
#373192
#356012
#355392
#353312
#353242
#352962
#352932
#352782
#351692
#351322
#351092
#349182
#342082
#341512
#340862