Finite Group Databasebeta

← #7642204

Subgroups — #7642204

Order 512.

4518 conjugacy classes of subgroups.

The subgroup lattice has 1445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37410C212yesmaximal, complemented
2#37372C212yesmaximal, complemented
3#37371C212yesmaximal, complemented
4#37367C212yesmaximal, complemented
5#37345C212yesmaximal, complemented
6#37340C212yesmaximal, complemented
7#37334C212yesmaximal, complemented
8#37330C212yesmaximal, complemented
9#37201C214yesmaximal, complemented
10#37199C214yesmaximal, complemented
11#37025C212yesmaximal, complemented
12#37022C212yesmaximal, complemented
13#36993C214yesmaximal, complemented
14#36836C212yesmaximal, complemented
15#36833C212yesmaximal, complemented
16#36784C214yesmaximal, complemented
17#36735C214yesmaximal, complemented
18#36733C214yesmaximal, complemented
19#35299C212yesmaximal, complemented
20#35296C212yesmaximal, complemented
21#35236C211yesmaximal, characteristic, complemented
22#35233C211yesmaximal, characteristic, complemented
23#35212C211yesmaximal, characteristic, complemented
24#35194C212yesmaximal, complemented
25#35193C212yesmaximal, complemented
26#35192C211yesmaximal, characteristic, complemented
27#34084C211yesmaximal, characteristic, complemented
28#34081C211yesmaximal, characteristic, complemented
29#34058C211yesmaximal, characteristic, complemented
30C2×#529C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33#2865C2214yescomplemented
34#2864C2212yescomplemented
35#2864C2212yescomplemented
36#2863C2212yescomplemented
37#2862C2212yescomplemented
38#2861C2214yescomplemented
39#2860C2212yes—
40#2860C2214yescomplemented
41#2858C2212yes—
42#2857C2212yescomplemented
43#2854C2212yes—
44#2854C2212yescomplemented
45#2853C2214yescomplemented
46#2850C2212yes—
47#2850C2214yescomplemented
48#2849C2214yes—
49#2848C2212yes—
50#2847C2212yes—
51#2808C2214yes—
52#2805C2214yescomplemented
53#2803C2214yes—
54#2803C2214yescomplemented
55#2801C2214yescomplemented
56#2800C2214yes—
57#2800C2214yescomplemented
58#2798C2214yescomplemented
59#2798C2214yescomplemented
60#2797C2214yes—
61#2783C2214yescomplemented
62#2779C2214yescomplemented
63#2776C2214yescomplemented
64#2773C2214yescomplemented
65#2772C2214yescomplemented
66#2772C2214yescomplemented
67#2771C2214yescomplemented
68#2757C2214yescomplemented
69#2753C2214yescomplemented
70#2753C2214yescomplemented
71#2747C2214yescomplemented
72#2745C2214yes—
73#2745C2214yescomplemented
74#2744C2214yes—
75#2743C2214yescomplemented
76#2742C2214yescomplemented
77#2741C2214yescomplemented
78#2740C2214yes—
79#2739C2214yescomplemented
80#2737C2214yes—
81#2737C2214yescomplemented
82#2736C2214yes—
83#2735C2214yes—
84#2733C2214yes—
85#2732C2214yescomplemented
86#2731C2214yescomplemented
87#2731C2214yescomplemented
88#2725C2214yescomplemented
89#2717C2214yescomplemented
90#2714C2214yes—
91#2710C2214yes—
92#2710C2214yes—
93#2707C2214yes—
94#2703C2214yescomplemented
95#2701C2214yescomplemented
96#2700C2214yescomplemented
97#2698C2214yescomplemented
98#2697C2214yes—
99#2696C2214yes—
100#2694C2214yescomplemented
101#2693C2214yes—
102#2692C2214yescomplemented
103#2690C2214yescomplemented
104#2688C2214yescomplemented
105#2687C2214yes—
106#2686C2214yescomplemented
107#2685C2214yes—
108#2684C2214yes—
109#2684C2214yes—
110#2678C2214yes—
111#2674C2214yescomplemented
112#2674C2214yescomplemented
113#2672C2214yescomplemented
114#2670C2214yes—
115#2665C2214yes—
116#2663C2212yes—
117#2661C2212yes—
118#2653C2214yescomplemented
119#2651C2214yescomplemented
120#2650C2214yescomplemented
121#2648C2214yescomplemented
122#2647C2212yescomplemented
123#2644C2212yes—
124#2644C2212yescomplemented
125#2640C2212yes—
126#2636C2212yes—
127#2636C2214yes—
128#2636C2212yes—
129#2628C2212yescomplemented
130#2625C2212yescomplemented
131#2624C2212yes—
132#2619C2212yes—
133#2611C2212yescomplemented
134#2610C2212yescomplemented
135#2605C2212yescomplemented
136#2605C2212yescomplemented
137#2602C2214yes—
138#2598C2212yes—
139#2598C2212yes—
140#2597C2214yescomplemented
141#2596C2214yescomplemented
142#2595C2214yescomplemented
143#2595C2214yescomplemented
144#2592C2211yescharacteristic, complemented
145#2589C2214yescomplemented
146#2589C2214yescomplemented
147#2584C2211yescharacteristic, complemented
148#2578C2214yescomplemented
149#2576C2214yescomplemented
150#2571C2212yescomplemented
151#2566C2212yes—
152#2562C2212yes—
153#2562C2211yescharacteristic, complemented
154#2560C2214yescomplemented
155#2557C2214yescomplemented
156#2557C2214yescomplemented
157#2557C2214yescomplemented
158#2551C2212yescomplemented
159#2544C2212yes—
160#2540C2212yes—
161#2540C2211yescharacteristic, complemented
162#2538C2212yes—
163#2537C2212yes—
164#2534C2214yes—
165#2532C2214yescomplemented
166#2531C2214yescomplemented
167#2513C2212yes—
168#2513C2212yes—
169#2508C2212yescomplemented
170#2506C2212yescomplemented
171#2503C2211yescharacteristic
172#2501C2211yescharacteristic
173#2497C2212yescomplemented
174#2494C2212yescomplemented
175#2491C2212yes—
176#2491C2212yes—
177#2487C2212yes—
178#2478C2214yescomplemented
179#2477C2214yescomplemented
180#2477C2214yescomplemented
181#2476C2214yescomplemented
182#2475C2214yescomplemented
183#2474C2214yescomplemented
184#2474C2214yescomplemented
185#2474C2214yescomplemented
186#2471C2214yescomplemented
187#2471C2214yescomplemented
188#2452C2212yescomplemented
189#2451C2212yescomplemented
190#2448C2212yes—
191#2445C2212yes—
192#2439C2212yes—
193#2439C2214yes—
194#2439C2212yes—
195#2435C2211yescharacteristic
196#2433C2211yescharacteristic
197#2428C2212yes—
198#2426C2212yes—
199#2421C2212yescomplemented
200#2420C2212yescomplemented
201#2415C2212yes—
202#2414C2212yes—
203#2411C2214yes—
204#2408C2212yes—
205#2337C2211yescharacteristic, complemented
206#2337C2211yescharacteristic, complemented
207#2336C2211yescharacteristic, complemented
208#2336C2211yescharacteristic, complemented
209#2335C2212yes—
210#2335C2212yes—
211#2335C2214yes—
212#2334C2212yescomplemented
213#2334C2212yescomplemented
214#2334C2214yescomplemented
215#2333C2212yes—
216#2332C2212yes—
217#2331C2212yescomplemented
218#2331C2212yescomplemented
219#2330C2212yescomplemented
220#2328C2212yes—
221#2326C2212yes—
222#2326C2212yescomplemented
223#2324C2212yes—
224#2324C2212yes—
225#2324C2212yes—
226#2324C2212yescomplemented
227#2323C2212yes—
228#2323C2212yescomplemented
229#2319C2212yes—
230#2319C2212yes—
231#2319C2212yes—
232#2319C2212yes—
233#2316C2212yes—
234#2312C2212yes—
235#2312C2212yes—
236#2309C2212yes—
237#2298C2212yescomplemented
238#2298C2212yescomplemented
239#2296C2212yescomplemented
240#2295C2212yescomplemented
241#2295C2211yescharacteristic, complemented
242#2293C2214yes—
243#2293C2212yes—
244#2293C2212yes—
245#2293C2212yes—
246#2293C2212yes—
247#2293C2211yescharacteristic, complemented
248#2290C2212yes—
249#2290C2212yes—
250#2290C2212yescomplemented
251#2285C2211yescharacteristic
252#2283C2211yescharacteristic
253#2280C2214yes—
254C42×Q8C2211yescharacteristic, complemented
255C42×D4C2211yescharacteristic, complemented
256C4×#117C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C4×#117C2212yescomplemented
259C23×D4C2311yescharacteristic
260C24×C4C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2314yes—
264C2×#127C2312yes—
265#529—28no—
266#529—28no—
267C2×#126C2312yes—
268C2×#126C2312yes—
269C2×#126C2314yes—
270C2×#125C2311yescharacteristic
271C2×#125C2311yescharacteristic
272C2×#125C2314yes—
273C2×#124C2311yescharacteristic
274C2×#124C2311yescharacteristic
275C2×#124C2312yes—
276C2×#124C2314yes—
277C2×#124C2314yes—
278C2×#124C2314yes—
279C2×#124C2314yes—
280C2×#123C2312yes—
281C2×#123C2312yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×C22⋊Q8C2311yescharacteristic
287C2×C22⋊Q8C2311yescharacteristic
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×#121C2311yescharacteristic
293C2×#121C2311yescharacteristic
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#120C2314yes—
300C2×#120C2314yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2312yes—
304C2×C4×D4—28no—
305C2×C4×D4C2312yes—
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×#117C2312yes—
315C2×#117C2312yes—
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2312yes—
320C2×#117C2312yes—
321C2×#117C2314yes—
322C2×#117C2314yes—
323C22×C4⋊C4C2311yescharacteristic
324C22×C22⋊C4C2312yes—
325C22×C42C2312yes—
326C22×C42C2312yes—
327C22×C42C2311yescharacteristic
328#401C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2312yes—
339#400C2312yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2312yes—
346#399C2312yes—
347#399C2312yes—
348#399C2314yes—
349#399C2314yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2312yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#395C2312yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2312yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2312yes—
401#394C2312yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2312yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#392C2312yes—
425#392C2312yes—
426#392C2314yes—
427#392C2312yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2312yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#390C2314yes—
446#390C2312yes—
447#390C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2314yes—
451#390C2314yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2314yes—
456#390C2312yes—
457#390C2312yes—
458#390C2314yes—
459#390C2312yes—
460#390C2314yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2312yes—
477#389C2314yes—
478#389C2312yes—
479#389C2314yes—
480#389C2312yes—
481#389C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
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#388C2312yes—
522#388C2312yes—
523#388C2312yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2312yes—
533#388C2312yes—
534#388C2312yes—
535#388C2312yes—
536#388C2312yes—
537#388C2312yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2312yes—
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#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2312yes—
604#386C2312yes—
605#386C2312yes—
606#386C2312yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2312yes—
625#385C2312yes—
626#385C2312yes—
627#385C2312yes—
628#385C2314yes—
629#385C2314yes—
630#384C2312yes—
631#384C2312yes—
632#383C2314yes—
633#383C2311yescharacteristic
634#383C2311yescharacteristic
635#382C2312yes—
636#382C2312yes—
637#382C2312yes—
638#382C2314yes—
639#382C2314yes—
640#382C2311yescharacteristic
641#382C2312yes—
642#382C2311yescharacteristic
643#381C2314yes—
644#381C2314yes—
645#381C2314yes—
646#381C2312yes—
647#381C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2312yes—
651#380C2312yes—
652#380C2314yes—
653#380C2314yes—
654#380C2314yes—
655#380C2314yes—
656#380C2314yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#379C2314yes—
663#379C2314yes—
664#379C2314yes—
665#379C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2311yescharacteristic
689C4×C22⋊C4C2311yescharacteristic
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2311yescharacteristic
704C4×C22⋊C4C2311yescharacteristic
705#376C2312yes—
706#376C2312yes—
707#376C2312yes—
708#376C2312yes—
709#376C2312yes—
710C43C2312yes—
711C43C2312yes—
712C43C2312yes—
713C43C2311yescharacteristic
714C43C2311yescharacteristic
715C25C2412yes—
716C22×Q8C2411yescharacteristic
717C22×Q8C2411yescharacteristic
718C22×Q8C2414yes—
719C22×Q8C2414yes—
720C22×D4—24no—
721C22×D4—44no—
722C22×D4C2411yescharacteristic
723C22×D4C2412yes—
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2412yes—
727C22×D4C2411yescharacteristic
728C22×D4C2414yes—
729C22×D4C2414yes—
730C22×D4C2414yes—
731C22×D4C2414yes—
732C22×D4C2414yes—
733C23×C4—28no—
734C23×C4—84no—
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2412yes—
738C23×C4C2414yes—
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2411yescharacteristic
745C23×C4C2411yescharacteristic
746C4⋊Q8—44no—
747C4⋊Q8—44no—
748C4⋊Q8—84no—
749#127—44no—
750#126—28no—
751#126—28no—
752#126—84no—
753#125—24no—
754#125—24no—
755#125—84no—
756#124—24no—
757#124—24no—
758#124—44no—
759#124—84no—
760#124—84no—
761#124—84no—
762#124—84no—
763#123—28no—
764#123—28no—
765#123—84no—
766#123—84no—
767#123—84no—
768#123—84no—
769C22⋊Q8—24no—
770C22⋊Q8—24no—
771C22⋊Q8—44no—
772C22⋊Q8—84no—
773C22⋊Q8—84no—
774C22⋊Q8—84no—
775#121—24no—
776#121—24no—
777#121—44no—
778#121—44no—
779#121—44no—
780#121—84no—
781#121—84no—
782#120—84no—
783#120—84no—
784C4×Q8—24no—
785C4×Q8—24no—
786C4×Q8—44no—
787C4×D4—28no—
788C4×D4—28no—
789C4×D4—28no—
790C4×D4—28no—
791C4×D4—28no—
792C4×D4—28no—
793C4×D4—24no—
794C4×D4—24no—
795C4×D4—44no—
796#117—28no—
797#117—28no—
798#117—44no—
799#117—44no—
800#117—44no—
801#117—82no—
802#117—84no—
803#117—82no—
804#117—84no—
805C2×C4⋊C4—24no—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C22⋊C4—28no—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C42—44no—
915C2×C42—82no—
916C2×C42#4118yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2414yes—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2411yescharacteristic
973#95C2411yescharacteristic
974#95C2411yescharacteristic
975#95C2411yescharacteristic
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012C24—24no—
1013C24—44no—
1014C24—42no—
1015C24—44no—
1016C24—42no—
1017C24C2514yes—
1018C24C2512yes—
1019C24C2512yes—
1020C24C2511yescharacteristic
1021C2×Q8—22no—
1022C2×Q8—22no—
1023C2×Q8—24no—
1024C2×Q8—42no—
1025C2×Q8—44no—
1026C2×Q8—44no—
1027C2×Q8—44no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8—44no—
1031C2×D4—24no—
1032C2×D4—24no—
1033C2×D4—24no—
1034C2×D4—24no—
1035C2×D4—22no—
1036C2×D4—22no—
1037C2×D4—24no—
1038C2×D4—24no—
1039C2×D4—24no—
1040C2×D4—44no—
1041C2×D4—416no—
1042C2×D4—42no—
1043C2×D4—44no—
1044C2×D4—42no—
1045C2×D4—42no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—44no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—44no—
1056C2×D4—44no—
1057C2×D4—44no—
1058C2×D4—44no—
1059C2×D4—44no—
1060C2×D4—44no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—28no—
1066C22×C4—24no—
1067C22×C4—24no—
1068C22×C4—28no—
1069C22×C4—42no—
1070C22×C4—41no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—42no—
1074C22×C4—41no—
1075C22×C4—42no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—42no—
1083C22×C4—44no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—44no—
1087C22×C4—42no—
1088C22×C4—816no—
1089C22×C4C2×#4114yes—
1090C22×C4C2×#4114yes—
1091C22×C4C2×#4114yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2514yes—
1103C22×C4C2514yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2514yes—
1107C22×C4C2514yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2511yescharacteristic
1116C22×C4C2511yescharacteristic
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—22no—
1124C4⋊C4—22no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—22no—
1128C4⋊C4—22no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—24no—
1174C22⋊C4—24no—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—42no—
1182C22⋊C4—44no—
1183C22⋊C4—42no—
1184C22⋊C4—42no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C42—24no—
1225C42—24no—
1226C42—24no—
1227C42—24no—
1228C42—24no—
1229C42—24no—
1230C42—42no—
1231C42—42no—
1232C42—41no—
1233C42—42no—
1234C42—44no—
1235C42—42no—
1236C42—41no—
1237C42—41no—
1238C42—42no—
1239C42—44no—
1240C42—41no—
1241C42—42no—
1242C42—42no—
1243C42—42no—
1244C42—44no—
1245C42—44no—
1246C42—42no—
1247C42—42no—
1248C42—44no—
1249C42—42no—
1250C42—42no—
1251C42C2×#4114yes—
1252C42C2×#4114yes—
1253C42C2×#4114yes—
1254C42C2×#4114yes—
1255C23—22no—
1256C23—21no—
1257C23—22no—
1258C23—21no—
1259C23—22no—
1260C23—22no—
1261C23—24no—
1262C23—22no—
1263C23—24no—
1264C23—24no—
1265C23—24no—
1266C23—22no—
1267C23—24no—
1268C23—22no—
1269C23—24no—
1270C23—22no—
1271C23—24no—
1272C23—24no—
1273C23—22no—
1274C23—22no—
1275C23—24no—
1276C23—22no—
1277C23—22no—
1278C23—48no—
1279C23—84no—
1280C23—84no—
1281C23—88no—
1282C23—88no—
1283C23C22×#4112yes—
1284C23C2611yescharacteristic
1285Q8—44no—
1286Q8—82no—
1287Q8—164no—
1288Q8—164no—
1289D4—48no—
1290D4—44no—
1291D4—48no—
1292D4—82no—
1293D4—84no—
1294D4—84no—
1295D4—164no—
1296D4—164no—
1297D4—164no—
1298D4—164no—
1299D4—164no—
1300C2×C4—22no—
1301C2×C4—21no—
1302C2×C4—22no—
1303C2×C4—21no—
1304C2×C4—22no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—28no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—44no—
1364C2×C4—44no—
1365C2×C4—48no—
1366C2×C4—416no—
1367C2×C4—48no—
1368C2×C4—88no—
1369C2×C4—84no—
1370C2×C4—84no—
1371C2×C4—84no—
1372C2×C4—88no—
1373C2×C4C22×#4112yes—
1374C2×C4C22×#4112yes—
1375C2×C4C22×#4112yes—
1376C2×C4C22×#4112yes—
1377C2×C4C22×#4112yes—
1378C2×C4C22×#4112yes—
1379C2×C4#58514yes—
1380C22—22no—
1381C22—22no—
1382C22—22no—
1383C22—42no—
1384C22—42no—
1385C22—44no—
1386C22—42no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—44no—
1391C22—42no—
1392C22—44no—
1393C22—44no—
1394C22—42no—
1395C22—44no—
1396C22—42no—
1397C22—44no—
1398C22—42no—
1399C22—44no—
1400C22—44no—
1401C22—42no—
1402C22—44no—
1403C22—42no—
1404C22—816no—
1405C22C23×#4111yescharacteristic
1406C22C2×#58512yes—
1407C22H(7,𝔽2)12yes—
1408C22H(7,𝔽2)11yescharacteristic
1409C222−1+611yescharacteristic
1410C4—22no—
1411C4—22no—
1412C4—22no—
1413C4—22no—
1414C4—22no—
1415C4—44no—
1416C4—42no—
1417C4—42no—
1418C4—42no—
1419C4—42no—
1420C4—42no—
1421C4—42no—
1422C4—42no—
1423C4—44no—
1424C4—42no—
1425C4—42no—
1426C4—42no—
1427C4—44no—
1428C4—42no—
1429C4—42no—
1430C4—44no—
1431C4—44no—
1432C4—42no—
1433C4—42no—
1434C4#345514yes—
1435C2—42no—
1436C2—82no—
1437C2—82no—
1438C2—84no—
1439C2C2×#345511yescharacteristic
1440C2#6285511yescharacteristic
1441C2#6285611yescharacteristic
1442C2#6288212yes—
1443C2#6288512yes—
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. #37410C2semidirect
2. #37372C2semidirect
3. #37371C2semidirect
4. #37367C2semidirect
5. #37345C2semidirect
6. #37340C2semidirect
7. #37334C2semidirect
8. #37330C2semidirect
9. #37201C2semidirect
10. #37199C2semidirect
11. #37025C2semidirect
12. #37022C2semidirect
13. #36993C2semidirect
14. #36836C2semidirect
15. #36833C2semidirect
16. #36784C2semidirect
17. #36735C2semidirect
18. #36733C2semidirect
19. #35299C2semidirect
20. #35296C2semidirect
21. #35236C2semidirect
22. #35233C2semidirect
23. #35212C2semidirect
24. #35194C2semidirect
25. #35193C2semidirect
26. #35192C2semidirect
27. #34084C2semidirect
28. #34081C2semidirect
29. #34058C2semidirect
33. #2865C22semidirect
34. #2864C22semidirect
35. #2864C22semidirect
36. #2863C22semidirect
37. #2862C22semidirect
38. #2861C22semidirect
40. #2860C22semidirect
42. #2857C22semidirect
44. #2854C22semidirect
45. #2853C22semidirect
47. #2850C22semidirect
52. #2805C22semidirect
54. #2803C22semidirect
55. #2801C22semidirect
57. #2800C22semidirect
58. #2798C22semidirect
59. #2798C22semidirect
61. #2783C22semidirect
62. #2779C22semidirect
63. #2776C22semidirect
64. #2773C22semidirect
65. #2772C22semidirect
66. #2772C22semidirect
67. #2771C22semidirect
68. #2757C22semidirect
69. #2753C22semidirect
70. #2753C22semidirect
71. #2747C22semidirect
73. #2745C22semidirect
75. #2743C22semidirect
76. #2742C22semidirect
77. #2741C22semidirect
79. #2739C22semidirect
81. #2737C22semidirect
85. #2732C22semidirect
86. #2731C22semidirect
87. #2731C22semidirect
88. #2725C22semidirect
89. #2717C22semidirect
94. #2703C22semidirect
95. #2701C22semidirect
96. #2700C22semidirect
97. #2698C22semidirect
100. #2694C22semidirect
102. #2692C22semidirect
103. #2690C22semidirect
104. #2688C22semidirect
106. #2686C22semidirect
111. #2674C22semidirect
112. #2674C22semidirect
113. #2672C22semidirect
118. #2653C22semidirect
119. #2651C22semidirect
120. #2650C22semidirect
121. #2648C22semidirect
122. #2647C22semidirect
124. #2644C22semidirect
129. #2628C22semidirect
130. #2625C22semidirect
133. #2611C22semidirect
134. #2610C22semidirect
135. #2605C22semidirect
136. #2605C22semidirect
140. #2597C22semidirect
141. #2596C22semidirect
142. #2595C22semidirect
143. #2595C22semidirect
144. #2592C22semidirect
145. #2589C22semidirect
146. #2589C22semidirect
147. #2584C22semidirect
148. #2578C22semidirect
149. #2576C22semidirect
150. #2571C22semidirect
153. #2562C22semidirect
154. #2560C22semidirect
155. #2557C22semidirect
156. #2557C22semidirect
157. #2557C22semidirect
158. #2551C22semidirect
161. #2540C22semidirect
165. #2532C22semidirect
166. #2531C22semidirect
169. #2508C22semidirect
170. #2506C22semidirect
173. #2497C22semidirect
174. #2494C22semidirect
178. #2478C22semidirect
179. #2477C22semidirect
180. #2477C22semidirect
181. #2476C22semidirect
182. #2475C22semidirect
183. #2474C22semidirect
184. #2474C22semidirect
185. #2474C22semidirect
186. #2471C22semidirect
187. #2471C22semidirect
188. #2452C22semidirect
189. #2451C22semidirect
199. #2421C22semidirect
200. #2420C22semidirect
205. #2337C22semidirect
206. #2337C22semidirect
207. #2336C22semidirect
208. #2336C22semidirect
212. #2334C22semidirect
213. #2334C22semidirect
214. #2334C22semidirect
217. #2331C22semidirect
218. #2331C22semidirect
219. #2330C22semidirect
222. #2326C22semidirect
226. #2324C22semidirect
228. #2323C22semidirect
237. #2298C22semidirect
238. #2298C22semidirect
239. #2296C22semidirect
240. #2295C22semidirect
241. #2295C22semidirect
247. #2293C22semidirect
250. #2290C22semidirect
254. C42×Q8C22semidirect
255. C42×D4C22semidirect
258. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#374102
#373722
#373712
#373672
#373452
#373402
#373342
#373302
#372012
#371992
#370252
#370222
#369932
#368362
#368332
#367842
#367352
#367332
#352992
#352962
#352362
#352332
#352122
#351942
#351932
#351922
#340842
#340812
#340582