Finite Group Databasebeta

← #7647341

Subgroups — #7647341

Order 512.

7458 conjugacy classes of subgroups.

The subgroup lattice has 1373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3483C211yesmaximal, characteristic, complemented
2C2×#3460C211yesmaximal, characteristic, complemented
3#42985C212yesmaximal, complemented
4#42969C212yesmaximal, complemented
5#42965C212yesmaximal, complemented
6#42963C212yesmaximal, complemented
7#41949C214yesmaximal, complemented
8#41945C214yesmaximal, complemented
9#39469C212yesmaximal, complemented
10#39341C212yesmaximal, complemented
11#39138C212yesmaximal, complemented
12#39125C212yesmaximal, complemented
13#37845C214yesmaximal, complemented
14#37657C214yesmaximal, complemented
15#37618C212yesmaximal, complemented
16#37554C212yesmaximal, complemented
17#37235C218yesmaximal, complemented
18#35571C214yesmaximal, complemented
19#35328C212yesmaximal, complemented
20#35292C211yesmaximal, characteristic, complemented
21#35237C211yesmaximal, characteristic, complemented
22#35210C212yesmaximal, complemented
23#35195C214yesmaximal, complemented
24#34935C211yesmaximal, characteristic, complemented
25#34909C211yesmaximal, characteristic, complemented
26#34191C211yesmaximal, characteristic, complemented
27#3483—216no—
28C2×Q82C2211yescharacteristic, complemented
29C2×#555C2212yes—
30C2×#555C2212yes—
31C2×#555C2211yescharacteristic, complemented
32C2×#555C2214yescomplemented
33C2×#550C2212yes—
34C2×#550C2212yes—
35C2×#550C2211yescharacteristic, complemented
36C2×#550C2211yescharacteristic, complemented
37#3460—216no—
38C2×#544C2211yescharacteristic
39C2×#542C2212yes—
40C2×#542C2212yes—
41C2×#540C2212yes—
42C2×#540C2212yes—
43C2×#538C2214yes—
44C2×#537C2211yescharacteristic
45C2×#537C2214yescomplemented
46C2×#535C2211yescharacteristic
47C2×#535C2211yescharacteristic
48C2×#532C2212yes—
49C2×#532C2212yes—
50C2×#532C2214yes—
51C2×#532C2211yescharacteristic
52C2×#532C2212yescomplemented
53C2×#532C2212yescomplemented
54C2×#529C2212yes—
55C2×#529C2212yes—
56C2×#525C2214yes—
57C2×#525C2212yes—
58C2×C4×#41C2211yescharacteristic
59C2×C4×#41C2211yescharacteristic
60C2×C4×#41C2211yescharacteristic
61C2×C4×#41C2212yescomplemented
62C2×C4×#41C2212yescomplemented
63C22×C4×D4C2211yescharacteristic
64#2857C2212yescomplemented
65#2856C2212yescomplemented
66#2852C2218yescomplemented
67#2850C2218yescomplemented
68#2847C2214yes—
69#2820C2214yescomplemented
70#2819C2214yes—
71#2815C2214yes—
72#2815C2214yescomplemented
73#2716C2218yescomplemented
74#2714C2218yescomplemented
75#2712C2218yescomplemented
76#2700C2218yes—
77#2688C2218yes—
78#2681C2218yes—
79#2676C2218yescomplemented
80#2676C2218yescomplemented
81#2675C2218yescomplemented
82#2674C2218yescomplemented
83#2673C2218yes—
84#2673C2218yescomplemented
85#2670C2218yes—
86#2669C2218yes—
87#2669C2218yes—
88#2668C2218yes—
89#2657C2214yes—
90#2656C2214yes—
91#2640C2214yescomplemented
92#2639C2214yescomplemented
93#2638C2214yescomplemented
94#2636C2218yescomplemented
95#2635C2214yes—
96#2631C2214yes—
97#2631C2218yescomplemented
98#2628C2214yescomplemented
99#2624C2212yes—
100#2621C2214yescomplemented
101#2619C2214yes—
102#2619C2214yescomplemented
103#2615C2212yes—
104#2615C2214yescomplemented
105#2615C2214yescomplemented
106#2611C2214yescomplemented
107#2610C2214yes—
108#2602C2218yescomplemented
109#2600C2214yes—
110#2599C2212yescomplemented
111#2598C2212yescomplemented
112#2592C2212yescomplemented
113#2581C2211yescharacteristic, complemented
114#2580C2211yescharacteristic, complemented
115#2580C2212yescomplemented
116#2563C2212yes—
117#2557C2218yescomplemented
118#2555C2218yescomplemented
119#2550C2214yescomplemented
120#2547C2214yescomplemented
121#2543C2214yes—
122#2543C2218yescomplemented
123#2543C2214yescomplemented
124#2541C2212yes—
125#2541C2214yes—
126#2541C2214yes—
127#2541C2214yescomplemented
128#2540C2212yescomplemented
129#2538C2212yes—
130#2537C2212yes—
131#2536C2212yes—
132#2536C2211yescharacteristic, complemented
133#2536C2214yescomplemented
134#2535C2212yes—
135#2535C2212yes—
136#2535C2212yes—
137#2535C2214yescomplemented
138#2535C2212yescomplemented
139#2535C2214yescomplemented
140#2535C2211yescharacteristic, complemented
141#2534C2214yes—
142#2504C2212yes—
143#2491C2214yes—
144#2490C2214yescomplemented
145#2486C2212yes—
146#2485C2212yes—
147#2485C2214yescomplemented
148#2477C2218yescomplemented
149#2471C2218yescomplemented
150#2464C2218yescomplemented
151#2463C2218yescomplemented
152#2456C2218yescomplemented
153#2452C2214yescomplemented
154#2448C2214yes—
155#2439C2214yescomplemented
156#2433C2212yes—
157#2431C2214yes—
158#2431C2218yescomplemented
159#2430C2218yescomplemented
160#2428C2214yes—
161#2428C2214yes—
162#2428C2218yescomplemented
163#2428C2214yescomplemented
164#2421C2214yescomplemented
165#2416C2214yescomplemented
166#2416C2214yescomplemented
167#2414C2214yes—
168#2414C2214yes—
169#2408C2212yes—
170#2407C2212yes—
171#2407C2214yes—
172#2407C2214yescomplemented
173#2407C2214yescomplemented
174#2404C2214yes—
175#2395C2212yes—
176#2392C2214yes—
177#2388C2212yes—
178#2355C2212yescomplemented
179#2352C2214yes—
180D4×C4⋊C4C2212yescomplemented
181#2346C2212yes—
182#2343C2214yescomplemented
183#2339C2212yes—
184#2328C2214yes—
185#2324C2214yescomplemented
186#2324C2214yescomplemented
187#2323C2214yescomplemented
188#2320C2212yescomplemented
189#2318C2214yes—
190#2311C2214yescomplemented
191C4×C22⋊Q8C2212yescomplemented
192C4×#121C2214yes—
193C4×#121C2212yescomplemented
194#2290C2214yescomplemented
195#2285C2211yescharacteristic
196#2283C2211yescharacteristic
197#2283C2212yescomplemented
198C2×#382C2212yescomplemented
199#2280C2212yes—
200#2275C2212yescomplemented
201C22×#41C2311yescharacteristic
202C22×#41C2312yes—
203C22×#41C2314yes—
204C22×#41C2311yescharacteristic
205C22×#41C2312yes—
206C22×#41C2312yes—
207C22×#41C2314yes—
208C22×#41C2311yescharacteristic
209C23×D4C2311yescharacteristic
210C24×C4C2312yes—
211Q82—28no—
212#555—216no—
213#555—28no—
214#555—216no—
215#555—232no—
216#550—216no—
217#550—28no—
218#550—216no—
219#550—28no—
220#544—28no—
221#542—216no—
222#542—216no—
223#540—216no—
224#540—216no—
225#538—232no—
226#537—28no—
227#537—416no—
228#535—28no—
229#535—28no—
230#532—216no—
231#532—232no—
232#532—216no—
233#532—216no—
234#532—28no—
235#532—216no—
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×#127C2311yescharacteristic
243C2×#127C2312yes—
244C2×#127C2312yes—
245C2×#127C2314yes—
246C2×#127C2312yes—
247C2×#127C2312yes—
248C2×#127C2314yes—
249C2×#127C2318yes—
250#529—216no—
251#529—216no—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#124C2312yes—
257C2×#124C2314yes—
258C2×#124C2312yes—
259C2×#124C2314yes—
260C2×#124C2314yes—
261C2×#124C2312yes—
262C2×#124C2314yes—
263C2×#124C2314yes—
264C2×#124C2314yes—
265C2×#124C2318yes—
266#525—232no—
267#525—48no—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2318yes—
280C2×C22⋊Q8C2314yes—
281C2×#121C2312yes—
282C2×#121C2312yes—
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#121C2312yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2314yes—
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2314yes—
306C2×#121C2318yes—
307C2×#121C2314yes—
308C2×#121C2312yes—
309C2×#121C2314yes—
310C2×#121C2314yes—
311C2×#121C2318yes—
312C2×#121C2318yes—
313C2×#121C2314yes—
314C2×#121C2318yes—
315C2×#121C2318yes—
316C2×#120C2314yes—
317C2×#120C2314yes—
318C2×#120C2314yes—
319C2×#120C2318yes—
320C4×#41—216no—
321C4×#41—28no—
322C4×#41—28no—
323C4×#41—216no—
324C4×#41D4116yescomplemented
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2311yescharacteristic
333C2×C4×D4—28no—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2311yescharacteristic
351C2×C4×D4C2311yescharacteristic
352C2×C4×D4C2312yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2314yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2314yes—
358C2×C4×D4C2318yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2311yescharacteristic
361C2×C4×D4C2312yes—
362C2×C4×D4C2311yescharacteristic
363C2×#117C2312yes—
364C2×#117C2314yes—
365C2×#117C2312yes—
366C2×#117C2312yes—
367C2×#117C2314yes—
368C2×#117C2311yescharacteristic
369C2×#117C2311yescharacteristic
370C2×#117C2312yes—
371C2×#117C2314yes—
372C2×#117C2312yes—
373C2×#117C2312yes—
374C2×#117C2311yescharacteristic
375C22×C4⋊C4C2311yescharacteristic
376C22×C4⋊C4C2314yes—
377C22×C22⋊C4C2312yes—
378C22×C42C2314yes—
379C22×C42C2312yes—
380C22×C42C2312yes—
381C22×C42C2311yescharacteristic
382C22×C42C2312yes—
383#400C2312yes—
384#400C2318yes—
385#399C2312yes—
386#399C2314yes—
387#399C2318yes—
388#398C2312yes—
389#398C2314yes—
390#398C2318yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2312yes—
395#397C2314yes—
396#397C2318yes—
397#397C2314yes—
398#397C2318yes—
399#397C2318yes—
400#397C2318yes—
401#396C2318yes—
402#396C2318yes—
403#396C2318yes—
404#395C2318yes—
405#395C2312yes—
406#394C2318yes—
407#394C2318yes—
408#394C2318yes—
409#394C2312yes—
410#394C2314yes—
411#394C2314yes—
412#394C2318yes—
413#394C2318yes—
414#394C2314yes—
415#394C2318yes—
416#394C2318yes—
417#394C2318yes—
418#394C2318yes—
419#393C2318yes—
420#393C2312yes—
421#393C2314yes—
422#393C2318yes—
423#393C2318yes—
424#393C2318yes—
425#392C2314yes—
426#392C2318yes—
427#392C2314yes—
428#392C2312yes—
429#392C2314yes—
430#392C2318yes—
431#392C2314yes—
432#392C2314yes—
433#392C2318yes—
434#392C2318yes—
435#392C2318yes—
436#392C2318yes—
437#392C2318yes—
438#392C2318yes—
439#392C2318yes—
440#392C2318yes—
441#392C2318yes—
442#392C2318yes—
443#392C2318yes—
444#392C2318yes—
445#391C2318yes—
446#391C2314yes—
447#391C2312yes—
448#391C2314yes—
449#391C2318yes—
450#390C2314yes—
451#390C2318yes—
452#390C2314yes—
453#390C2314yes—
454#390C2318yes—
455#390C2318yes—
456#390C2312yes—
457#390C2314yes—
458#390C2314yes—
459#390C2318yes—
460#390C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2318yes—
464#389C2312yes—
465#389C2314yes—
466#389C2312yes—
467#389C2314yes—
468#388C2318yes—
469#388C2318yes—
470#388C2318yes—
471#388C2318yes—
472#388C2318yes—
473#388C2314yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2314yes—
479#388C2314yes—
480#387C2318yes—
481#387C2318yes—
482#387C2318yes—
483#387C2314yes—
484#387C2318yes—
485#387C2314yes—
486#387C2314yes—
487#386C2318yes—
488#386C2318yes—
489#386C2318yes—
490#386C2318yes—
491#386C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2318yes—
499#386C2318yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2318yes—
504#386C2318yes—
505#386C2318yes—
506#385C2318yes—
507#385C2318yes—
508#385C2318yes—
509#385C2314yes—
510#385C2318yes—
511#385C2314yes—
512#385C2314yes—
513#384C2312yes—
514#383C2314yes—
515#383C2312yes—
516#382C2314yes—
517#382C2314yes—
518#382C2314yes—
519#382C2311yescharacteristic
520#382C2312yes—
521#382C2311yescharacteristic
522#382C2314yes—
523#381C2312yes—
524#381C2314yes—
525#381C2314yes—
526#380C2314yes—
527#380C2314yes—
528#380C2312yes—
529#380C2314yes—
530#380C2314yes—
531#380C2312yes—
532#380C2314yes—
533#380C2312yes—
534#380C2312yes—
535#380C2314yes—
536#380C2312yes—
537#380C2314yes—
538#380C2314yes—
539#379C2314yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2312yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2312yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2314yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2312yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2318yes—
551C4×C22⋊C4C2314yes—
552#376C2312yes—
553#376C2314yes—
554C2×#95C2314yes—
555C2×#95C2314yes—
556C25C2412yes—
557C2×#41—28no—
558C2×#41—24no—
559C2×#41—28no—
560C2×#41—24no—
561C2×#41—24no—
562C2×#41—28no—
563C2×#41—216no—
564C2×#41—28no—
565C2×#41—216no—
566C2×#41—44no—
567C2×#41—48no—
568C2×#41—48no—
569C2×#41—42no—
570C2×#41—44no—
571C2×#41—44no—
572C2×#41—48no—
573C2×#41—84no—
574C2×#41—88no—
575C2×#41C2×D418yes—
576C22×Q8C2411yescharacteristic
577C22×Q8C2411yescharacteristic
578C22×Q8C2411yescharacteristic
579C22×Q8C2414yes—
580C22×Q8C2412yes—
581C22×Q8C2414yes—
582C22×D4—24no—
583C22×D4—44no—
584C22×D4C2412yes—
585C22×D4C2411yescharacteristic
586C22×D4C2412yes—
587C22×D4C2412yes—
588C22×D4C2412yes—
589C22×D4C2414yes—
590C22×D4C2411yescharacteristic
591C22×D4C2412yes—
592C22×D4C2412yes—
593C22×D4C2411yescharacteristic
594C22×D4C2414yes—
595C22×D4C2414yes—
596C22×D4C2414yes—
597C22×D4C2414yes—
598C22×D4C2414yes—
599C22×D4C2414yes—
600C22×D4C2414yes—
601C22×D4C2414yes—
602C22×D4C2414yes—
603C22×D4C2412yes—
604C22×D4C2414yes—
605C22×D4C2418yes—
606C22×D4C2414yes—
607C22×D4C2418yes—
608C22×D4C2418yes—
609C22×D4C2418yes—
610C22×D4C2412yes—
611C23×C4—28no—
612C23×C4—44no—
613C23×C4—44no—
614C23×C4C2412yes—
615C23×C4C2414yes—
616C23×C4C2412yes—
617C23×C4C2412yes—
618C23×C4C2412yes—
619C23×C4C2414yes—
620C23×C4C2412yes—
621C23×C4C2411yescharacteristic
622C23×C4C2411yescharacteristic
623C23×C4C2412yes—
624C23×C4C2414yes—
625C23×C4C2414yes—
626C23×C4C2414yes—
627C23×C4C2412yes—
628C23×C4C2412yes—
629C23×C4C2418yes—
630C23×C4C2411yescharacteristic
631C23×C4C2412yes—
632C23×C4C2412yes—
633C4⋊Q8—28no—
634C4⋊Q8—28no—
635C4⋊Q8—216no—
636C4⋊Q8—28no—
637C4⋊Q8—24no—
638C4⋊Q8—28no—
639#127—28no—
640#127—28no—
641#127—216no—
642#127—28no—
643#127—24no—
644#127—28no—
645#127—48no—
646#127—88no—
647#126—216no—
648#126—216no—
649#125—28no—
650#125—28no—
651#124—28no—
652#124—216no—
653#124—216no—
654#124—216no—
655#124—216no—
656#124—28no—
657#124—216no—
658#124—28no—
659#124—216no—
660#124—88no—
661#123—216no—
662#123—216no—
663#123—216no—
664#123—216no—
665#123—48no—
666C22⋊Q8—28no—
667C22⋊Q8—216no—
668C22⋊Q8—28no—
669C22⋊Q8—28no—
670C22⋊Q8—216no—
671C22⋊Q8—216no—
672C22⋊Q8—416no—
673C22⋊Q8—84no—
674#121—216no—
675#121—28no—
676#121—28no—
677#121—216no—
678#121—28no—
679#121—28no—
680#121—28no—
681#121—216no—
682#121—28no—
683#121—28no—
684#121—28no—
685#121—28no—
686#121—216no—
687#121—28no—
688#121—28no—
689#121—28no—
690#121—216no—
691#121—216no—
692#121—216no—
693#121—216no—
694#121—216no—
695#121—216no—
696#121—416no—
697#121—416no—
698#121—416no—
699#121—48no—
700#121—48no—
701#121—48no—
702#121—44no—
703#121—48no—
704#121—48no—
705#121—48no—
706#121—88no—
707#121—84no—
708#121—88no—
709#120—216no—
710#120—216no—
711#120—48no—
712#120—88no—
713C4×Q8—28no—
714C4×Q8—24no—
715C4×Q8—24no—
716C4×Q8—24no—
717C4×Q8—24no—
718C4×Q8—28no—
719C4×Q8C2×D418yes—
720C4×Q8C2×D418yes—
721C4×D4—28no—
722C4×D4—28no—
723C4×D4—216no—
724C4×D4—28no—
725C4×D4—28no—
726C4×D4—216no—
727C4×D4—216no—
728C4×D4—28no—
729C4×D4—216no—
730C4×D4—28no—
731C4×D4—28no—
732C4×D4—28no—
733C4×D4—28no—
734C4×D4—28no—
735C4×D4—216no—
736C4×D4—24no—
737C4×D4—28no—
738C4×D4—24no—
739C4×D4—24no—
740C4×D4—24no—
741C4×D4—28no—
742C4×D4—216no—
743C4×D4—48no—
744C4×D4—48no—
745C4×D4—416no—
746C4×D4C2×D4116yes—
747C4×D4C2×D4116yes—
748C4×D4C2×D418yes—
749C4×D4C2×D418yes—
750#117—24no—
751#117—24no—
752#117—28no—
753#117—28no—
754#117—216no—
755#117—28no—
756#117—28no—
757#117—216no—
758#117—216no—
759#117—44no—
760#117C2×D418yes—
761#117C2×D4116yes—
762C2×C4⋊C4—24no—
763C2×C4⋊C4—48no—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2418yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2418yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2418yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2412yes—
797C2×C22⋊C4—28no—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2418yes—
822C2×C22⋊C4C2418yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2418yes—
827C2×C22⋊C4C2418yes—
828C2×C22⋊C4C2418yes—
829C2×C22⋊C4C2418yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2418yes—
832C2×C22⋊C4C2418yes—
833C2×C22⋊C4C2418yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2418yes—
836C2×C22⋊C4C2418yes—
837C2×C22⋊C4C2418yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C42—28no—
843C2×C42—216no—
844C2×C42—28no—
845C2×C42C2×D418yes—
846C2×C42C2×D4116yes—
847C2×C42C2412yes—
848C2×C42C2414yes—
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2412yes—
856C2×C42C2414yes—
857C2×C42C2418yes—
858C2×C42C2411yescharacteristic
859C2×C42C2412yes—
860C2×C42C2411yescharacteristic
861C2×C42C2412yes—
862C2×C42C2411yescharacteristic
863C2×C42C2411yescharacteristic
864C2×C42C2412yes—
865#95C2412yes—
866#95C2412yes—
867#95C2414yes—
868#95C2414yes—
869#95C2418yes—
870#95C2418yes—
871#95C2412yes—
872#95C2414yes—
873#95C2412yes—
874#95C2418yes—
875#95C2418yes—
876#95C2418yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2418yes—
884#95C2414yes—
885#95C2418yes—
886#95C2418yes—
887#95C2418yes—
888#95C2418yes—
889C24—24no—
890C24—44no—
891C24—42no—
892C24—44no—
893C24—42no—
894C24C2514yes—
895C24C2512yes—
896C24C2512yes—
897C24C2514yes—
898C24C2511yescharacteristic
899C24C2512yes—
900#41—416no—
901#41—416no—
902#41—432no—
903#41—416no—
904#41—432no—
905#41—832no—
906#41—816no—
907#41—832no—
908C2×Q8—22no—
909C2×Q8—22no—
910C2×Q8—28no—
911C2×Q8—24no—
912C2×Q8—28no—
913C2×Q8—24no—
914C2×Q8—22no—
915C2×Q8—42no—
916C2×Q8—44no—
917C2×Q8—44no—
918C2×Q8—48no—
919C2×Q8—44no—
920C2×Q8C22×D414yes—
921C2×Q8H(5,𝔽2)14yes—
922C2×D4—24no—
923C2×D4—24no—
924C2×D4—28no—
925C2×D4—28no—
926C2×D4—28no—
927C2×D4—28no—
928C2×D4—28no—
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—24no—
932C2×D4—24no—
933C2×D4—28no—
934C2×D4—22no—
935C2×D4—24no—
936C2×D4—22no—
937C2×D4—24no—
938C2×D4—28no—
939C2×D4—28no—
940C2×D4—24no—
941C2×D4—28no—
942C2×D4—24no—
943C2×D4—28no—
944C2×D4—22no—
945C2×D4—24no—
946C2×D4—24no—
947C2×D4—24no—
948C2×D4—22no—
949C2×D4—24no—
950C2×D4—28no—
951C2×D4—24no—
952C2×D4—44no—
953C2×D4—42no—
954C2×D4—44no—
955C2×D4—42no—
956C2×D4—44no—
957C2×D4—48no—
958C2×D4—42no—
959C2×D4—42no—
960C2×D4—416no—
961C2×D4—48no—
962C2×D4—44no—
963C2×D4—48no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—48no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—48no—
972C2×D4—44no—
973C2×D4—48no—
974C2×D4—48no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—48no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—48no—
983C2×D4—48no—
984C2×D4—48no—
985C2×D4—48no—
986C2×D4—48no—
987C2×D4—48no—
988C2×D4—48no—
989C2×D4—48no—
990C2×D4—48no—
991C2×D4C22×D414yes—
992C2×D4C22×D418yes—
993C22×C4—24no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—24no—
1000C22×C4—28no—
1001C22×C4—28no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—28no—
1006C22×C4—24no—
1007C22×C4—28no—
1008C22×C4—24no—
1009C22×C4—28no—
1010C22×C4—24no—
1011C22×C4—28no—
1012C22×C4—24no—
1013C22×C4—28no—
1014C22×C4—24no—
1015C22×C4—28no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—28no—
1019C22×C4—42no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—48no—
1023C22×C4—44no—
1024C22×C4—42no—
1025C22×C4—48no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—44no—
1032C22×C4—42no—
1033C22×C4—48no—
1034C22×C4—48no—
1035C22×C4—48no—
1036C22×C4—816no—
1037C22×C4C22×D414yes—
1038C22×C4C22×D414yes—
1039C22×C4C22×D418yes—
1040C22×C4C22×D414yes—
1041C22×C4C22×D418yes—
1042C22×C4C22×D418yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2518yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2514yes—
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2511yescharacteristic
1055C22×C4C2512yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2512yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—22no—
1067C4⋊C4—22no—
1068C4⋊C4—24no—
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—22no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—22no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—216no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—24no—
1087C4⋊C4—48no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—48no—
1092C4⋊C4C22×D414yes—
1093C4⋊C4C22×D418yes—
1094C4⋊C4C22×D414yes—
1095C4⋊C4C22×D418yes—
1096C22⋊C4—24no—
1097C22⋊C4—24no—
1098C22⋊C4—28no—
1099C22⋊C4—28no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—24no—
1103C22⋊C4—24no—
1104C22⋊C4—28no—
1105C22⋊C4—24no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—24no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—216no—
1117C22⋊C4—28no—
1118C22⋊C4—44no—
1119C22⋊C4—48no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—48no—
1123C22⋊C4—44no—
1124C22⋊C4—48no—
1125C22⋊C4—48no—
1126C22⋊C4—48no—
1127C22⋊C4—48no—
1128C22⋊C4—48no—
1129C22⋊C4—44no—
1130C22⋊C4—48no—
1131C22⋊C4—48no—
1132C22⋊C4—48no—
1133C22⋊C4—44no—
1134C22⋊C4—48no—
1135C22⋊C4—48no—
1136C22⋊C4—44no—
1137C22⋊C4C22×D418yes—
1138C22⋊C4C22×D418yes—
1139C22⋊C4C22×D418yes—
1140C42—24no—
1141C42—24no—
1142C42—28no—
1143C42—24no—
1144C42—24no—
1145C42—28no—
1146C42—24no—
1147C42—24no—
1148C42—28no—
1149C42—44no—
1150C42—48no—
1151C42C22×D414yes—
1152C42C22×D414yes—
1153C42C22×D418yes—
1154C42C22×D414yes—
1155C42C22×D414yes—
1156C42C22×D418yes—
1157C42C22×D418yes—
1158C23—21no—
1159C23—22no—
1160C23—24no—
1161C23—21no—
1162C23—22no—
1163C23—22no—
1164C23—22no—
1165C23—24no—
1166C23—24no—
1167C23—24no—
1168C23—22no—
1169C23—22no—
1170C23—24no—
1171C23—22no—
1172C23—22no—
1173C23—24no—
1174C23—22no—
1175C23—22no—
1176C23—24no—
1177C23—24no—
1178C23—24no—
1179C23—28no—
1180C23—24no—
1181C23—22no—
1182C23—22no—
1183C23—24no—
1184C23—22no—
1185C23—24no—
1186C23—24no—
1187C23—24no—
1188C23—28no—
1189C23—22no—
1190C23—48no—
1191C23—84no—
1192C23—84no—
1193C23—88no—
1194C23—88no—
1195C23C23×D412yes—
1196C23C23×D414yes—
1197C23C2611yescharacteristic
1198Q8—28no—
1199Q8—28no—
1200Q8—44no—
1201Q8—88no—
1202Q8—84no—
1203Q8—88no—
1204D4—28no—
1205D4—48no—
1206D4—48no—
1207D4—416no—
1208D4—48no—
1209D4—44no—
1210D4—416no—
1211D4—48no—
1212D4—48no—
1213D4—48no—
1214D4—44no—
1215D4—48no—
1216D4—88no—
1217D4—88no—
1218D4—84no—
1219D4—88no—
1220D4—88no—
1221D4—88no—
1222D4—88no—
1223D4—88no—
1224D4—88no—
1225D4—88no—
1226D4—816no—
1227D4—88no—
1228D4—168no—
1229D4—168no—
1230D4—168no—
1231C2×C4—22no—
1232C2×C4—21no—
1233C2×C4—22no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—28no—
1243C2×C4—28no—
1244C2×C4—216no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—28no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—28no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—28no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—28no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—48no—
1273C2×C4—44no—
1274C2×C4—48no—
1275C2×C4—48no—
1276C2×C4—416no—
1277C2×C4—416no—
1278C2×C4—416no—
1279C2×C4—48no—
1280C2×C4—48no—
1281C2×C4—48no—
1282C2×C4—416no—
1283C2×C4—48no—
1284C2×C4—84no—
1285C2×C4—88no—
1286C2×C4—84no—
1287C2×C4—168no—
1288C2×C4C23×D412yes—
1289C2×C4C23×D412yes—
1290C2×C4C23×D414yes—
1291C2×C4C23×D412yes—
1292C2×C4C23×D414yes—
1293C2×C4C23×D412yes—
1294C2×C4C23×D414yes—
1295C2×C4C23×D412yes—
1296C2×C4C23×D412yes—
1297C2×C4C2×H(5,𝔽2)14yes—
1298C2×C4C2×H(5,𝔽2)12yes—
1299C2×C4#58514yes—
1300C2×C4#58512yes—
1301C22—22no—
1302C22—24no—
1303C22—24no—
1304C22—22no—
1305C22—22no—
1306C22—24no—
1307C22—44no—
1308C22—42no—
1309C22—44no—
1310C22—42no—
1311C22—44no—
1312C22—42no—
1313C22—44no—
1314C22—42no—
1315C22—42no—
1316C22—44no—
1317C22—42no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22—42no—
1322C22—48no—
1323C22—44no—
1324C22—42no—
1325C22—42no—
1326C22—44no—
1327C22—44no—
1328C22—48no—
1329C22—42no—
1330C22—44no—
1331C22—44no—
1332C22—42no—
1333C22—42no—
1334C22—44no—
1335C22—816no—
1336C22C24×D411yescharacteristic
1337C22C22×H(5,𝔽2)11yescharacteristic
1338C22C2×#58511yescharacteristic
1339C22C2×#58512yes—
1340C22H(7,𝔽2)12yes—
1341C4—22no—
1342C4—24no—
1343C4—24no—
1344C4—22no—
1345C4—22no—
1346C4—24no—
1347C4—22no—
1348C4—24no—
1349C4—44no—
1350C4—42no—
1351C4—44no—
1352C4—42no—
1353C4—42no—
1354C4—44no—
1355C4—48no—
1356C4—44no—
1357C4—42no—
1358C4—42no—
1359C4#344914yes—
1360C4#348814yes—
1361C2—44no—
1362C2—42no—
1363C2—82no—
1364C2—84no—
1365C2—82no—
1366C2—84no—
1367C2C2×#344911yescharacteristic
1368C2C2×#348811yescharacteristic
1369C2#6285211yescharacteristic
1370C2#6292312yes—
1371C2#6293712yes—
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. C2×#3483C2semidirect
2. C2×#3460C2semidirect
3. #42985C2semidirect
4. #42969C2semidirect
5. #42965C2semidirect
6. #42963C2semidirect
7. #41949C2semidirect
8. #41945C2semidirect
9. #39469C2semidirect
10. #39341C2semidirect
11. #39138C2semidirect
12. #39125C2semidirect
13. #37845C2semidirect
14. #37657C2semidirect
15. #37618C2semidirect
16. #37554C2semidirect
17. #37235C2semidirect
18. #35571C2semidirect
19. #35328C2semidirect
20. #35292C2semidirect
21. #35237C2semidirect
22. #35210C2semidirect
23. #35195C2semidirect
24. #34935C2semidirect
25. #34909C2semidirect
26. #34191C2semidirect
28. C2×Q82C22semidirect
31. C2×#555C22semidirect
32. C2×#555C22semidirect
35. C2×#550C22semidirect
36. C2×#550C22semidirect
45. C2×#537C22semidirect
52. C2×#532C22semidirect
53. C2×#532C22semidirect
61. C2×C4×#41C22semidirect
62. C2×C4×#41C22semidirect
64. #2857C22semidirect
65. #2856C22semidirect
66. #2852C22semidirect
67. #2850C22semidirect
69. #2820C22semidirect
72. #2815C22semidirect
73. #2716C22semidirect
74. #2714C22semidirect
75. #2712C22semidirect
79. #2676C22semidirect
80. #2676C22semidirect
81. #2675C22semidirect
82. #2674C22semidirect
84. #2673C22semidirect
91. #2640C22semidirect
92. #2639C22semidirect
93. #2638C22semidirect
94. #2636C22semidirect
97. #2631C22semidirect
98. #2628C22semidirect
100. #2621C22semidirect
102. #2619C22semidirect
104. #2615C22semidirect
105. #2615C22semidirect
106. #2611C22semidirect
108. #2602C22semidirect
110. #2599C22semidirect
111. #2598C22semidirect
112. #2592C22semidirect
113. #2581C22semidirect
114. #2580C22semidirect
115. #2580C22semidirect
117. #2557C22semidirect
118. #2555C22semidirect
119. #2550C22semidirect
120. #2547C22semidirect
122. #2543C22semidirect
123. #2543C22semidirect
127. #2541C22semidirect
128. #2540C22semidirect
132. #2536C22semidirect
133. #2536C22semidirect
137. #2535C22semidirect
138. #2535C22semidirect
139. #2535C22semidirect
140. #2535C22semidirect
144. #2490C22semidirect
147. #2485C22semidirect
148. #2477C22semidirect
149. #2471C22semidirect
150. #2464C22semidirect
151. #2463C22semidirect
152. #2456C22semidirect
153. #2452C22semidirect
155. #2439C22semidirect
158. #2431C22semidirect
159. #2430C22semidirect
162. #2428C22semidirect
163. #2428C22semidirect
164. #2421C22semidirect
165. #2416C22semidirect
166. #2416C22semidirect
172. #2407C22semidirect
173. #2407C22semidirect
178. #2355C22semidirect
180. D4×C4⋊C4C22semidirect
182. #2343C22semidirect
185. #2324C22semidirect
186. #2324C22semidirect
187. #2323C22semidirect
188. #2320C22semidirect
190. #2311C22semidirect
191. C4×C22⋊Q8C22semidirect
193. C4×#121C22semidirect
194. #2290C22semidirect
197. #2283C22semidirect
198. C2×#382C22semidirect
200. #2275C22semidirect
324. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34832
C2×#34602
#429852
#429692
#429652
#429632
#419492
#419452
#394692
#393412
#391382
#391252
#378452
#376572
#376182
#375542
#372352
#355712
#353282
#352922
#352372
#352102
#351952
#349352
#349092
#341912