Finite Group Databasebeta

← #7658956

Subgroups — #7658956

Order 512.

7088 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic, complemented
2C2×#3514C211yesmaximal, characteristic, complemented
3#42951C214yesmaximal, complemented
4#42876C212yesmaximal, complemented
5#42875C212yesmaximal, complemented
6#42431C212yesmaximal, complemented
7#42430C212yesmaximal, complemented
8#42152C214yesmaximal, complemented
9#41995C218yesmaximal, complemented
10#41955C214yesmaximal, complemented
11#40501C214yesmaximal, complemented
12#40500C214yesmaximal, complemented
13#37639C211yesmaximal, characteristic, complemented
14#37606C212yesmaximal, complemented
15#37554C211yesmaximal, characteristic, complemented
16#37554C211yesmaximal, characteristic, complemented
17#37541C212yesmaximal, complemented
18#37536C212yesmaximal, complemented
19#36687C212yesmaximal, complemented
20#36684C211yesmaximal, characteristic, complemented
21#36019C212yesmaximal, complemented
22#35844C212yesmaximal, complemented
23#35830C214yesmaximal, complemented
24#35741C212yesmaximal, complemented
25#35730C212yesmaximal, complemented
26#34189C211yesmaximal, characteristic, complemented
27#3517—216no—
28#3514—216no—
29C2×#559C2211yescharacteristic
30C2×#557C2211yescharacteristic, complemented
31C2×#556C2211yescharacteristic
32C2×#555C2212yes—
33C2×#553C2214yescomplemented
34C2×#553C2212yescomplemented
35C2×#551C2214yes—
36C2×#550C2211yescharacteristic
37C2×#550C2212yes—
38C2×#550C2212yescomplemented
39C2×#550C2211yescharacteristic, complemented
40C2×D4×Q8C2211yescharacteristic
41C2×#548C2212yes—
42C2×#547C2211yescharacteristic
43C2×#547C2212yescomplemented
44C2×#546C2212yes—
45C2×#546C2212yes—
46C2×D42C2211yescharacteristic
47C2×#542C2212yes—
48C2×#540C2212yes—
49C2×#540C2214yescomplemented
50C2×#538C2214yes—
51C2×#532C2211yescharacteristic
52C2×#532C2211yescharacteristic, complemented
53C2×#532C2212yescomplemented
54C2×#529C2211yescharacteristic
55C2×#529C2212yes—
56C2×#529C2211yescharacteristic, complemented
57C2×#529C2212yescomplemented
58C22×#124C2212yes—
59C2×#520C2212yescomplemented
60C2×#518C2212yes—
61C2×C4×#41C2211yescharacteristic
62#2823C2214yescomplemented
63#2822C2211yescharacteristic, complemented
64#2821C2214yescomplemented
65#2820C2211yescharacteristic
66#2820C2211yescharacteristic, complemented
67#2820C2212yescomplemented
68#2820C2212yescomplemented
69#2819C2211yescharacteristic
70#2819C2212yes—
71#2819C2212yescomplemented
72#2819C2212yescomplemented
73#2819C2212yescomplemented
74#2818C2214yescomplemented
75#2816C2214yescomplemented
76#2815C2214yes—
77#2814C2212yescomplemented
78#2814C2212yescomplemented
79#2813C2212yes—
80#2813C2218yescomplemented
81#2813C2212yescomplemented
82#2694C2218yescomplemented
83#2690C2218yescomplemented
84#2688C2218yescomplemented
85#2687C2218yescomplemented
86#2678C2218yes—
87#2676C2218yescomplemented
88#2673C2218yescomplemented
89#2673C2218yescomplemented
90#2672C2218yescomplemented
91#2669C2218yes—
92#2669C2218yescomplemented
93#2668C2218yescomplemented
94#2663C2214yescomplemented
95#2662C2218yescomplemented
96#2661C2214yes—
97#2657C2214yescomplemented
98#2656C2212yes—
99#2656C2212yescomplemented
100#2640C2214yescomplemented
101#2639C2212yescomplemented
102#2639C2212yescomplemented
103#2638C2214yescomplemented
104#2636C2214yescomplemented
105#2636C2214yescomplemented
106#2635C2214yescomplemented
107#2632C2214yescomplemented
108#2631C2214yes—
109#2631C2214yescomplemented
110#2631C2214yescomplemented
111#2630C2218yescomplemented
112#2628C2212yescomplemented
113#2628C2212yescomplemented
114#2619C2212yes—
115#2619C2214yescomplemented
116#2619C2212yescomplemented
117#2617C2218yescomplemented
118#2615C2214yescomplemented
119#2615C2214yescomplemented
120#2614C2214yescomplemented
121#2613C2214yes—
122#2610C2214yes—
123#2610C2214yescomplemented
124#2604C2214yescomplemented
125#2603C2214yescomplemented
126#2601C2218yescomplemented
127#2599C2214yescomplemented
128#2598C2214yescomplemented
129#2580C2212yescomplemented
130#2580C2212yescomplemented
131#2563C2212yescomplemented
132#2563C2212yescomplemented
133#2561C2214yescomplemented
134#2557C2218yescomplemented
135#2555C2218yescomplemented
136#2550C2214yescomplemented
137#2544C2218yescomplemented
138#2541C2212yes—
139#2541C2214yes—
140#2541C2212yescomplemented
141#2539C2214yescomplemented
142#2537C2214yescomplemented
143#2535C2212yes—
144#2535C2212yescomplemented
145#2534C2218yescomplemented
146#2491C2214yescomplemented
147#2490C2214yes—
148#2481C2218yescomplemented
149#2467C2218yescomplemented
150#2464C2218yescomplemented
151#2464C2218yescomplemented
152#2457C2218yescomplemented
153#2456C2218yescomplemented
154#2448C2214yescomplemented
155#2445C2214yes—
156#2443C2218yescomplemented
157#2436C2214yescomplemented
158#2433C2214yes—
159#2433C2214yes—
160#2431C2214yescomplemented
161#2430C2214yescomplemented
162#2430C2214yescomplemented
163#2428C2218yescomplemented
164#2424C2218yescomplemented
165#2421C2214yescomplemented
166#2420C2214yes—
167#2418C2218yescomplemented
168#2416C2214yescomplemented
169#2416C2214yescomplemented
170#2408C2214yes—
171#2407C2214yescomplemented
172#2404C2214yescomplemented
173#2404C2214yescomplemented
174#2398C2214yescomplemented
175#2397C2214yescomplemented
176#2396C2212yescomplemented
177#2396C2212yescomplemented
178#2392C2212yes—
179#2392C2218yescomplemented
180#2392C2212yescomplemented
181#2392C2214yescomplemented
182#2388C2214yescomplemented
183#2388C2214yescomplemented
184#2366C2214yescomplemented
185#2363C2214yescomplemented
186#2361C2214yescomplemented
187#2357C2212yes—
188#2357C2212yes—
189#2356C2212yescomplemented
190#2356C2212yescomplemented
191#2353C2214yescomplemented
192#2353C2214yescomplemented
193#2352C2214yescomplemented
194#2314C2214yescomplemented
195#2311C2212yes—
196#2285C2211yescharacteristic, complemented
197#2283C2212yescomplemented
198#2283C2212yescomplemented
199C2×#382C2211yescharacteristic, complemented
200#2274C2212yescomplemented
201C22×#41C2312yes—
202C22×#41C2312yes—
203C22×#41C2312yes—
204C22×#41C2312yes—
205C22×#41C2312yes—
206C22×#41C2311yescharacteristic
207C23×Q8C2312yes—
208C23×D4C2312yes—
209C23×D4C2312yes—
210#559—28no—
211#557—28no—
212#556—28no—
213#555—216no—
214#553—232no—
215#553—216no—
216#551—232no—
217#550—216no—
218#550—28no—
219#550—28no—
220#550—216no—
221D4×Q8—28no—
222#548—216no—
223#547—28no—
224#547—216no—
225#546—216no—
226#546—216no—
227D42—28no—
228#542—216no—
229#540—216no—
230#540—232no—
231#538—232no—
232#532—28no—
233#532—216no—
234#532—28no—
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×#127C2312yes—
240C2×#127C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#127C2314yes—
243C2×#127C2312yes—
244C2×#127C2314yes—
245C2×#127C2318yes—
246#529—216no—
247#529—28no—
248#529—216no—
249#529—28no—
250C2×#126C2314yes—
251C2×#126C2312yes—
252C2×#126C2312yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#125C2311yescharacteristic
256C2×#125C2311yescharacteristic
257C2×#125C2312yes—
258C2×#125C2314yes—
259C2×#124—216no—
260C2×#124C2311yescharacteristic
261C2×#124C2311yescharacteristic
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2314yes—
267C2×#124C2314yes—
268C2×#124C2314yes—
269C2×#124C2312yes—
270C2×#124C2318yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2312yes—
274C2×#123C2312yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2318yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2311yescharacteristic
284C2×C22⋊Q8C2311yescharacteristic
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×#121C2314yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2314yes—
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2311yescharacteristic
296C2×#121C2311yescharacteristic
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2314yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×#121C2314yes—
309C2×#121C2314yes—
310C2×#121C2318yes—
311C2×#121C2318yes—
312C2×#121C2318yes—
313C2×#121C2318yes—
314C2×#120C2314yes—
315C2×#120C2314yes—
316C2×#120C2318yes—
317C2×#120C2318yes—
318C2×#120C2318yes—
319#520—216no—
320#518—216no—
321C4×#41D4116yescomplemented
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2311yescharacteristic
344C2×C4×D4C2314yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2314yes—
349C2×C4×D4C2318yes—
350C2×C4×D4C2318yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2311yescharacteristic
354C2×C4×D4C2311yescharacteristic
355C2×#117C2314yes—
356C2×#117C2314yes—
357C2×#117C2312yes—
358C2×#117C2312yes—
359C2×#117C2312yes—
360C2×#117C2312yes—
361C2×#117C2312yes—
362C2×#117C2311yescharacteristic
363C22×C4⋊C4C2312yes—
364C22×C4⋊C4C2314yes—
365C22×C4⋊C4C2312yes—
366C22×C22⋊C4C2314yes—
367C22×C22⋊C4C2314yes—
368C22×C22⋊C4C2314yes—
369C22×C42C2312yes—
370C22×C42C2311yescharacteristic
371#400C2318yes—
372#400C2312yes—
373#400C2312yes—
374#400C2314yes—
375#400C2314yes—
376#399C2312yes—
377#399C2314yes—
378#399C2312yes—
379#399C2314yes—
380#399C2318yes—
381#399C2314yes—
382#399C2314yes—
383#398C2318yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#397C2312yes—
390#397C2314yes—
391#397C2314yes—
392#397C2312yes—
393#397C2318yes—
394#397C2318yes—
395#397C2318yes—
396#397C2318yes—
397#397C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2318yes—
401#396C2318yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#395C2312yes—
407#395C2312yes—
408#395C2314yes—
409#395C2314yes—
410#395C2318yes—
411#394C2318yes—
412#394C2318yes—
413#394C2318yes—
414#394C2312yes—
415#394C2314yes—
416#394C2318yes—
417#394C2314yes—
418#394C2318yes—
419#394C2318yes—
420#394C2318yes—
421#394C2318yes—
422#394C2312yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2318yes—
427#394C2314yes—
428#394C2314yes—
429#394C2318yes—
430#394C2318yes—
431#394C2314yes—
432#394C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2312yes—
441#393C2312yes—
442#393C2314yes—
443#393C2318yes—
444#392C2314yes—
445#392C2314yes—
446#392C2318yes—
447#392C2318yes—
448#392C2314yes—
449#392C2314yes—
450#392C2312yes—
451#392C2312yes—
452#392C2314yes—
453#392C2314yes—
454#392C2314yes—
455#392C2314yes—
456#392C2318yes—
457#392C2318yes—
458#392C2318yes—
459#392C2318yes—
460#392C2318yes—
461#392C2314yes—
462#392C2314yes—
463#392C2318yes—
464#392C2318yes—
465#392C2318yes—
466#392C2314yes—
467#391C2314yes—
468#391C2318yes—
469#390C2314yes—
470#390C2314yes—
471#390C2314yes—
472#390C2314yes—
473#390C2314yes—
474#390C2318yes—
475#390C2318yes—
476#390C2318yes—
477#390C2318yes—
478#389C2314yes—
479#389C2314yes—
480#389C2318yes—
481#388C2318yes—
482#388C2318yes—
483#388C2318yes—
484#388C2318yes—
485#388C2318yes—
486#388C2318yes—
487#388C2318yes—
488#388C2318yes—
489#388C2318yes—
490#388C2318yes—
491#387C2318yes—
492#387C2318yes—
493#387C2318yes—
494#387C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2318yes—
499#386C2318yes—
500#386C2318yes—
501#386C2318yes—
502#386C2318yes—
503#386C2318yes—
504#386C2318yes—
505#386C2318yes—
506#386C2318yes—
507#386C2318yes—
508#386C2318yes—
509#386C2318yes—
510#385C2318yes—
511#385C2318yes—
512#385C2318yes—
513#385C2318yes—
514#384C2312yes—
515#383C2314yes—
516#383C2314yes—
517#382C2314yes—
518#382C2311yescharacteristic
519#382C2312yes—
520#382C2311yescharacteristic
521#382C2312yes—
522#382C2312yes—
523#382C2312yes—
524#381C2314yes—
525#381C2318yes—
526#381C2314yes—
527#380C2318yes—
528#380C2318yes—
529#380C2314yes—
530#380C2314yes—
531#380C2314yes—
532#380C2314yes—
533#380C2312yes—
534#380C2312yes—
535#379C2318yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C22⋊C4C2314yes—
544C4×C22⋊C4C2318yes—
545C4×C22⋊C4C2318yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550#376C2314yes—
551#376C2314yes—
552C2×#95C2312yes—
553C2×#95C2312yes—
554C25C2414yes—
555C2×#41—28no—
556C2×#41—28no—
557C2×#41—28no—
558C2×#41—28no—
559C2×#41—28no—
560C2×#41—42no—
561C2×#41—42no—
562C2×#41—44no—
563C2×#41—44no—
564C2×#41—84no—
565C2×#41—84no—
566C2×#41—84no—
567C2×#41—84no—
568C2×#41C2×D418yes—
569C22×Q8—28no—
570C22×Q8—84no—
571C22×Q8C2411yescharacteristic
572C22×Q8C2411yescharacteristic
573C22×Q8C2412yes—
574C22×Q8C2411yescharacteristic
575C22×Q8C2412yes—
576C22×Q8C2414yes—
577C22×D4—28no—
578C22×D4—28no—
579C22×D4—44no—
580C22×D4—44no—
581C22×D4—84no—
582C22×D4C2412yes—
583C22×D4C2412yes—
584C22×D4C2411yescharacteristic
585C22×D4C2414yes—
586C22×D4C2414yes—
587C22×D4C2412yes—
588C22×D4C2412yes—
589C22×D4C2414yes—
590C22×D4C2412yes—
591C22×D4C2412yes—
592C22×D4C2414yes—
593C22×D4C2411yescharacteristic
594C22×D4C2412yes—
595C22×D4C2412yes—
596C22×D4C2411yescharacteristic
597C22×D4C2414yes—
598C22×D4C2414yes—
599C22×D4C2414yes—
600C22×D4C2414yes—
601C22×D4C2414yes—
602C22×D4C2414yes—
603C22×D4C2418yes—
604C22×D4C2418yes—
605C22×D4C2418yes—
606C22×D4C2418yes—
607C22×D4C2412yes—
608C23×C4C2412yes—
609C23×C4C2412yes—
610C23×C4C2411yescharacteristic
611C23×C4C2414yes—
612C23×C4C2414yes—
613C23×C4C2414yes—
614C23×C4C2414yes—
615C23×C4C2414yes—
616C23×C4C2414yes—
617C23×C4C2414yes—
618C23×C4C2414yes—
619C23×C4C2412yes—
620C23×C4C2412yes—
621C23×C4C2412yes—
622C23×C4C2411yescharacteristic
623C23×C4C2411yescharacteristic
624C4⋊Q8—28no—
625C4⋊Q8—24no—
626C4⋊Q8—28no—
627C4⋊Q8—24no—
628#127—28no—
629#127—216no—
630#127—24no—
631#127—24no—
632#127—28no—
633#127—48no—
634#127—88no—
635#126—216no—
636#126—216no—
637#126—28no—
638#126—216no—
639#126—28no—
640#125—28no—
641#125—216no—
642#125—24no—
643#125—24no—
644#124—28no—
645#124—216no—
646#124—24no—
647#124—28no—
648#124—216no—
649#124—28no—
650#124—28no—
651#124—216no—
652#124—24no—
653#124—28no—
654#124—88no—
655#123—28no—
656#123—216no—
657#123—28no—
658#123—216no—
659#123—216no—
660#123—216no—
661#123—216no—
662#123—216no—
663#123—216no—
664#123—88no—
665C22⋊Q8—28no—
666C22⋊Q8—28no—
667C22⋊Q8—28no—
668C22⋊Q8—24no—
669C22⋊Q8—24no—
670C22⋊Q8—216no—
671C22⋊Q8—216no—
672#121—216no—
673#121—28no—
674#121—216no—
675#121—28no—
676#121—24no—
677#121—28no—
678#121—24no—
679#121—28no—
680#121—216no—
681#121—28no—
682#121—28no—
683#121—28no—
684#121—216no—
685#121—28no—
686#121—216no—
687#121—28no—
688#121—216no—
689#121—216no—
690#121—216no—
691#121—216no—
692#121—48no—
693#121—48no—
694#121—88no—
695#121—88no—
696#121—88no—
697#121—88no—
698#120—216no—
699#120—216no—
700#120—88no—
701#120—88no—
702#120—88no—
703C4×Q8—28no—
704C4×Q8—28no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—28no—
708C4×Q8C2×D418yes—
709C4×Q8C2×D418yes—
710C4×D4—28no—
711C4×D4—216no—
712C4×D4—28no—
713C4×D4—28no—
714C4×D4—216no—
715C4×D4—28no—
716C4×D4—28no—
717C4×D4—216no—
718C4×D4—216no—
719C4×D4—28no—
720C4×D4—216no—
721C4×D4—28no—
722C4×D4—24no—
723C4×D4—28no—
724C4×D4—24no—
725C4×D4—28no—
726C4×D4—28no—
727C4×D4—216no—
728C4×D4—28no—
729C4×D4—48no—
730C4×D4—88no—
731C4×D4—88no—
732C4×D4C2×D418yes—
733C4×D4C2×D4116yes—
734C4×D4C2×D418yes—
735C4×D4C2×D4116yes—
736#117—28no—
737#117—28no—
738#117—216no—
739#117—28no—
740#117—216no—
741#117—44no—
742#117C2×D4116yes—
743#117C2×D418yes—
744C2×C4⋊C4—28no—
745C2×C4⋊C4—216no—
746C2×C4⋊C4—44no—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2418yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2418yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2412yes—
784C2×C22⋊C4—216no—
785C2×C22⋊C4—216no—
786C2×C22⋊C4—216no—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2418yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2418yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2418yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2418yes—
822C2×C22⋊C4C2418yes—
823C2×C22⋊C4C2418yes—
824C2×C22⋊C4C2418yes—
825C2×C22⋊C4C2418yes—
826C2×C22⋊C4C2418yes—
827C2×C22⋊C4C2418yes—
828C2×C22⋊C4C2418yes—
829C2×C22⋊C4C2418yes—
830C2×C22⋊C4C2418yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C42C2×D4116yes—
836C2×C42C2×D418yes—
837C2×C42C2414yes—
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2414yes—
841C2×C42C2414yes—
842C2×C42C2418yes—
843C2×C42C2418yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2411yescharacteristic
847C2×C42C2411yescharacteristic
848C2×C42C2411yescharacteristic
849C2×C42C2412yes—
850C2×C42C2411yescharacteristic
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2412yes—
856#95C2412yes—
857#95C2418yes—
858#95C2418yes—
859#95C2414yes—
860#95C2412yes—
861#95C2412yes—
862#95C2418yes—
863#95C2418yes—
864#95C2418yes—
865#95C2418yes—
866#95C2414yes—
867#95C2414yes—
868#95C2418yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2418yes—
873#95C2418yes—
874#95C2418yes—
875C24—28no—
876C24—44no—
877C24—44no—
878C24—48no—
879C24—48no—
880C24C2512yes—
881C24C2514yes—
882C24C2512yes—
883C24C2514yes—
884C24C2512yes—
885C24C2511yescharacteristic
886#41—416no—
887#41—432no—
888#41—816no—
889#41—816no—
890#41—816no—
891#41—816no—
892C2×Q8—22no—
893C2×Q8—24no—
894C2×Q8—22no—
895C2×Q8—24no—
896C2×Q8—28no—
897C2×Q8—22no—
898C2×Q8—22no—
899C2×Q8—42no—
900C2×Q8—44no—
901C2×Q8—42no—
902C2×Q8—44no—
903C2×Q8—48no—
904C2×Q8—816no—
905C2×Q8C22×D414yes—
906C2×D4—28no—
907C2×D4—24no—
908C2×D4—28no—
909C2×D4—24no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—24no—
915C2×D4—28no—
916C2×D4—24no—
917C2×D4—22no—
918C2×D4—24no—
919C2×D4—22no—
920C2×D4—24no—
921C2×D4—24no—
922C2×D4—24no—
923C2×D4—28no—
924C2×D4—28no—
925C2×D4—22no—
926C2×D4—22no—
927C2×D4—24no—
928C2×D4—24no—
929C2×D4—24no—
930C2×D4—24no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—42no—
934C2×D4—44no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—44no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—42no—
941C2×D4—44no—
942C2×D4—48no—
943C2×D4—48no—
944C2×D4—44no—
945C2×D4—48no—
946C2×D4—48no—
947C2×D4—48no—
948C2×D4—48no—
949C2×D4—48no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—48no—
955C2×D4—48no—
956C2×D4—48no—
957C2×D4—48no—
958C2×D4—48no—
959C2×D4—44no—
960C2×D4—48no—
961C2×D4—48no—
962C2×D4—48no—
963C2×D4—48no—
964C2×D4—48no—
965C2×D4—48no—
966C2×D4—48no—
967C2×D4—432no—
968C2×D4—816no—
969C2×D4C22×D414yes—
970C2×D4C22×D418yes—
971C22×C4—22no—
972C22×C4—22no—
973C22×C4—28no—
974C22×C4—28no—
975C22×C4—24no—
976C22×C4—24no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—28no—
982C22×C4—28no—
983C22×C4—28no—
984C22×C4—28no—
985C22×C4—28no—
986C22×C4—44no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—48no—
995C22×C4—48no—
996C22×C4—48no—
997C22×C4—48no—
998C22×C4—48no—
999C22×C4—48no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4C22×D414yes—
1004C22×C4C22×D418yes—
1005C22×C4C22×D418yes—
1006C22×C4C22×D418yes—
1007C22×C4C22×D414yes—
1008C22×C4C22×D414yes—
1009C22×C4C2514yes—
1010C22×C4C2518yes—
1011C22×C4C2514yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2514yes—
1015C22×C4C2512yes—
1016C22×C4C2514yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2512yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2511yescharacteristic
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027C22×C4C2511yescharacteristic
1028C22×C4C2511yescharacteristic
1029C4⋊C4—28no—
1030C4⋊C4—24no—
1031C4⋊C4—28no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—28no—
1039C4⋊C4—22no—
1040C4⋊C4—24no—
1041C4⋊C4—22no—
1042C4⋊C4—22no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—28no—
1046C4⋊C4—22no—
1047C4⋊C4—24no—
1048C4⋊C4—28no—
1049C4⋊C4—28no—
1050C4⋊C4—24no—
1051C4⋊C4—28no—
1052C4⋊C4—44no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—48no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—48no—
1061C4⋊C4—44no—
1062C4⋊C4C22×D414yes—
1063C4⋊C4C22×D418yes—
1064C4⋊C4C22×D414yes—
1065C4⋊C4C22×D418yes—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—24no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—28no—
1072C22⋊C4—24no—
1073C22⋊C4—24no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—24no—
1081C22⋊C4—28no—
1082C22⋊C4—24no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—24no—
1086C22⋊C4—24no—
1087C22⋊C4—28no—
1088C22⋊C4—24no—
1089C22⋊C4—28no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—48no—
1095C22⋊C4—48no—
1096C22⋊C4—48no—
1097C22⋊C4—48no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—48no—
1101C22⋊C4—48no—
1102C22⋊C4—48no—
1103C22⋊C4—48no—
1104C22⋊C4—48no—
1105C22⋊C4—48no—
1106C22⋊C4—48no—
1107C22⋊C4—48no—
1108C22⋊C4—48no—
1109C22⋊C4—48no—
1110C22⋊C4—44no—
1111C22⋊C4C22×D418yes—
1112C22⋊C4C22×D418yes—
1113C22⋊C4C22×D418yes—
1114C42—28no—
1115C42—24no—
1116C42—28no—
1117C42—24no—
1118C42—28no—
1119C42—48no—
1120C42—48no—
1121C42C22×D414yes—
1122C42C22×D418yes—
1123C42C22×D418yes—
1124C42C22×D414yes—
1125C42C22×D414yes—
1126C42C22×D414yes—
1127C42C22×D418yes—
1128C23—21no—
1129C23—21no—
1130C23—22no—
1131C23—22no—
1132C23—24no—
1133C23—24no—
1134C23—22no—
1135C23—22no—
1136C23—22no—
1137C23—24no—
1138C23—24no—
1139C23—22no—
1140C23—22no—
1141C23—22no—
1142C23—24no—
1143C23—24no—
1144C23—22no—
1145C23—22no—
1146C23—24no—
1147C23—24no—
1148C23—28no—
1149C23—28no—
1150C23—24no—
1151C23—24no—
1152C23—28no—
1153C23—24no—
1154C23—28no—
1155C23—24no—
1156C23—416no—
1157C23—88no—
1158C23—88no—
1159C23—168no—
1160C23—168no—
1161C23C23×D414yes—
1162C23C23×D412yes—
1163C23C2611yescharacteristic
1164Q8—28no—
1165Q8—44no—
1166Q8—48no—
1167Q8—44no—
1168Q8—48no—
1169Q8—88no—
1170D4—28no—
1171D4—48no—
1172D4—44no—
1173D4—48no—
1174D4—416no—
1175D4—48no—
1176D4—44no—
1177D4—416no—
1178D4—48no—
1179D4—48no—
1180D4—84no—
1181D4—84no—
1182D4—88no—
1183D4—88no—
1184D4—84no—
1185D4—88no—
1186D4—84no—
1187D4—88no—
1188D4—88no—
1189D4—88no—
1190D4—88no—
1191D4—816no—
1192D4—88no—
1193D4—816no—
1194D4—168no—
1195D4—168no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—28no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—28no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—28no—
1225C2×C4—28no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—28no—
1232C2×C4—28no—
1233C2×C4—24no—
1234C2×C4—48no—
1235C2×C4—48no—
1236C2×C4—48no—
1237C2×C4—44no—
1238C2×C4—44no—
1239C2×C4—416no—
1240C2×C4—48no—
1241C2×C4—48no—
1242C2×C4—88no—
1243C2×C4—88no—
1244C2×C4—88no—
1245C2×C4—88no—
1246C2×C4—88no—
1247C2×C4—88no—
1248C2×C4—164no—
1249C2×C4C23×D414yes—
1250C2×C4C23×D414yes—
1251C2×C4C23×D412yes—
1252C2×C4C23×D412yes—
1253C2×C4C23×D412yes—
1254C2×C4C23×D412yes—
1255C2×C4C23×D412yes—
1256C2×C4C23×D414yes—
1257C2×C4C23×D412yes—
1258C2×C4#58512yes—
1259C2×C4#58512yes—
1260C22—24no—
1261C22—22no—
1262C22—22no—
1263C22—24no—
1264C22—22no—
1265C22—24no—
1266C22—42no—
1267C22—44no—
1268C22—42no—
1269C22—44no—
1270C22—48no—
1271C22—48no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—48no—
1276C22—44no—
1277C22—48no—
1278C22—44no—
1279C22—42no—
1280C22—44no—
1281C22—44no—
1282C22—42no—
1283C22—44no—
1284C22—42no—
1285C22—42no—
1286C22—44no—
1287C22—42no—
1288C22—42no—
1289C22—44no—
1290C22—1616no—
1291C22C24×D411yescharacteristic
1292C22C2×#58511yescharacteristic
1293C22C2×#58511yescharacteristic
1294C22H(7,𝔽2)12yes—
1295C22H(7,𝔽2)12yes—
1296C4—22no—
1297C4—22no—
1298C4—24no—
1299C4—22no—
1300C4—22no—
1301C4—24no—
1302C4—22no—
1303C4—24no—
1304C4—44no—
1305C4—44no—
1306C4—48no—
1307C4—42no—
1308C4—42no—
1309C4—44no—
1310C4—44no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4#344914yes—
1316C2—42no—
1317C2—44no—
1318C2—84no—
1319C2—82no—
1320C2—84no—
1321C2—82no—
1322C2C2×#344911yescharacteristic
1323C2#6285211yescharacteristic
1324C2#6285211yescharacteristic
1325C2#6305112yes—
1326C2#6306012yes—
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×#3517C2semidirect
2. C2×#3514C2semidirect
3. #42951C2semidirect
4. #42876C2semidirect
5. #42875C2semidirect
6. #42431C2semidirect
7. #42430C2semidirect
8. #42152C2semidirect
9. #41995C2semidirect
10. #41955C2semidirect
11. #40501C2semidirect
12. #40500C2semidirect
13. #37639C2semidirect
14. #37606C2semidirect
15. #37554C2semidirect
16. #37554C2semidirect
17. #37541C2semidirect
18. #37536C2semidirect
19. #36687C2semidirect
20. #36684C2semidirect
21. #36019C2semidirect
22. #35844C2semidirect
23. #35830C2semidirect
24. #35741C2semidirect
25. #35730C2semidirect
26. #34189C2semidirect
30. C2×#557C22semidirect
33. C2×#553C22semidirect
34. C2×#553C22semidirect
38. C2×#550C22semidirect
39. C2×#550C22semidirect
43. C2×#547C22semidirect
49. C2×#540C22semidirect
52. C2×#532C22semidirect
53. C2×#532C22semidirect
56. C2×#529C22semidirect
57. C2×#529C22semidirect
59. C2×#520C22semidirect
62. #2823C22semidirect
63. #2822C22semidirect
64. #2821C22semidirect
66. #2820C22semidirect
67. #2820C22semidirect
68. #2820C22semidirect
71. #2819C22semidirect
72. #2819C22semidirect
73. #2819C22semidirect
74. #2818C22semidirect
75. #2816C22semidirect
77. #2814C22semidirect
78. #2814C22semidirect
80. #2813C22semidirect
81. #2813C22semidirect
82. #2694C22semidirect
83. #2690C22semidirect
84. #2688C22semidirect
85. #2687C22semidirect
87. #2676C22semidirect
88. #2673C22semidirect
89. #2673C22semidirect
90. #2672C22semidirect
92. #2669C22semidirect
93. #2668C22semidirect
94. #2663C22semidirect
95. #2662C22semidirect
97. #2657C22semidirect
99. #2656C22semidirect
100. #2640C22semidirect
101. #2639C22semidirect
102. #2639C22semidirect
103. #2638C22semidirect
104. #2636C22semidirect
105. #2636C22semidirect
106. #2635C22semidirect
107. #2632C22semidirect
109. #2631C22semidirect
110. #2631C22semidirect
111. #2630C22semidirect
112. #2628C22semidirect
113. #2628C22semidirect
115. #2619C22semidirect
116. #2619C22semidirect
117. #2617C22semidirect
118. #2615C22semidirect
119. #2615C22semidirect
120. #2614C22semidirect
123. #2610C22semidirect
124. #2604C22semidirect
125. #2603C22semidirect
126. #2601C22semidirect
127. #2599C22semidirect
128. #2598C22semidirect
129. #2580C22semidirect
130. #2580C22semidirect
131. #2563C22semidirect
132. #2563C22semidirect
133. #2561C22semidirect
134. #2557C22semidirect
135. #2555C22semidirect
136. #2550C22semidirect
137. #2544C22semidirect
140. #2541C22semidirect
141. #2539C22semidirect
142. #2537C22semidirect
144. #2535C22semidirect
145. #2534C22semidirect
146. #2491C22semidirect
148. #2481C22semidirect
149. #2467C22semidirect
150. #2464C22semidirect
151. #2464C22semidirect
152. #2457C22semidirect
153. #2456C22semidirect
154. #2448C22semidirect
156. #2443C22semidirect
157. #2436C22semidirect
160. #2431C22semidirect
161. #2430C22semidirect
162. #2430C22semidirect
163. #2428C22semidirect
164. #2424C22semidirect
165. #2421C22semidirect
167. #2418C22semidirect
168. #2416C22semidirect
169. #2416C22semidirect
171. #2407C22semidirect
172. #2404C22semidirect
173. #2404C22semidirect
174. #2398C22semidirect
175. #2397C22semidirect
176. #2396C22semidirect
177. #2396C22semidirect
179. #2392C22semidirect
180. #2392C22semidirect
181. #2392C22semidirect
182. #2388C22semidirect
183. #2388C22semidirect
184. #2366C22semidirect
185. #2363C22semidirect
186. #2361C22semidirect
189. #2356C22semidirect
190. #2356C22semidirect
191. #2353C22semidirect
192. #2353C22semidirect
193. #2352C22semidirect
194. #2314C22semidirect
196. #2285C22semidirect
197. #2283C22semidirect
198. #2283C22semidirect
199. C2×#382C22semidirect
200. #2274C22semidirect
321. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35172
C2×#35142
#429512
#428762
#428752
#424312
#424302
#421522
#419952
#419552
#405012
#405002
#376392
#376062
#375542
#375412
#375362
#366872
#366842
#360192
#358442
#358302
#357412
#357302
#341892