Finite Group Databasebeta

← #7658945

Subgroups — #7658945

Order 512.

6476 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3512C211yesmaximal, characteristic, complemented
2C2×#3518C211yesmaximal, characteristic, complemented
3#42984C212yesmaximal, complemented
4#42908C212yesmaximal, complemented
5#42813C212yesmaximal, complemented
6#42808C212yesmaximal, complemented
7#42440C214yesmaximal, complemented
8#42315C214yesmaximal, complemented
9#42299C218yesmaximal, complemented
10#42158C214yesmaximal, complemented
11#41422C214yesmaximal, complemented
12#41419C214yesmaximal, complemented
13#37640C211yesmaximal, characteristic, complemented
14#37608C212yesmaximal, complemented
15#37555C212yesmaximal, complemented
16#37549C211yesmaximal, characteristic, complemented
17#37541C212yesmaximal, complemented
18#37540C211yesmaximal, characteristic, complemented
19#36699C212yesmaximal, complemented
20#36687C211yesmaximal, characteristic, complemented
21#36089C212yesmaximal, complemented
22#36062C212yesmaximal, complemented
23#35856C212yesmaximal, complemented
24#35832C214yesmaximal, complemented
25#35759C212yesmaximal, complemented
26#34191C211yesmaximal, characteristic, complemented
27#3518—216no—
28#3512—216no—
29C2×Q82C2211yescharacteristic
30C2×#556C2211yescharacteristic
31C2×#556C2214yes—
32C2×#556C2212yes—
33C2×#556C2212yes—
34C2×#555C2212yes—
35C2×#555C2211yescharacteristic
36C2×#553C2212yes—
37C2×#553C2214yes—
38C2×#553C2212yes—
39C2×#553C2214yes—
40C2×#552C2212yes—
41C2×#552C2212yes—
42C2×D4×Q8C2211yescharacteristic
43C2×#548C2212yes—
44C2×#542C2214yes—
45C2×#542C2212yes—
46C2×#541C2212yes—
47C2×#540C2212yes—
48C2×#537C2211yescharacteristic
49C2×#537C2211yescharacteristic
50C2×#533C2211yescharacteristic
51C2×#533C2212yes—
52C2×#532C2211yescharacteristic
53C2×#529C2211yescharacteristic
54C2×#529C2212yes—
55C2×#529C2212yes—
56C2×#529C2212yes—
57C22×#125C2211yescharacteristic
58C2×#520C2211yescharacteristic
59C2×#520C2211yescharacteristic
60C2×#519C2212yes—
61C2×C4×#41C2211yescharacteristic
62#2822C2212yes—
63#2822C2212yes—
64#2822C2212yes—
65#2821C2214yes—
66#2821C2214yes—
67#2821C2212yes—
68#2820C2212yes—
69#2820C2212yes—
70#2820C2211yescharacteristic
71#2820C2211yescharacteristic
72#2820C2212yes—
73#2819C2211yescharacteristic
74#2819C2211yescharacteristic
75#2818C2212yes—
76#2817C2214yes—
77#2816C2212yes—
78#2816C2214yes—
79#2815C2212yes—
80#2814C2218yes—
81#2813C2214yes—
82#2722C2218yes—
83#2720C2218yes—
84#2715C2218yes—
85#2713C2218yes—
86#2696C2218yes—
87#2691C2218yes—
88#2688C2218yes—
89#2686C2218yes—
90#2686C2218yes—
91#2676C2218yes—
92#2674C2218yes—
93#2671C2218yes—
94#2664C2214yes—
95#2663C2214yes—
96#2661C2214yes—
97#2660C2212yes—
98#2659C2214yes—
99#2642C2212yes—
100#2639C2214yes—
101#2638C2214yes—
102#2637C2218yes—
103#2637C2214yes—
104#2637C2214yes—
105#2636C2214yes—
106#2636C2214yes—
107#2635C2214yes—
108#2634C2214yes—
109#2630C2218yes—
110#2629C2214yes—
111#2628C2214yes—
112#2627C2214yes—
113#2627C2212yes—
114#2624C2214yes—
115#2621C2214yes—
116#2620C2214yes—
117#2618C2218yes—
118#2618C2212yes—
119#2616C2212yes—
120#2616C2212yes—
121#2609C2218yes—
122#2604C2214yes—
123#2603C2214yes—
124#2601C2218yes—
125#2599C2214yes—
126#2598C2214yes—
127#2584C2212yes—
128#2581C2214yes—
129#2567C2212yes—
130#2565C2214yes—
131#2564C2214yes—
132#2564C2214yes—
133#2562C2212yes—
134#2559C2218yes—
135#2555C2218yes—
136#2548C2212yes—
137#2547C2212yes—
138#2543C2214yes—
139#2543C2214yes—
140#2542C2212yes—
141#2538C2214yes—
142#2537C2214yes—
143#2536C2214yes—
144#2535C2214yes—
145#2521C2218yes—
146#2503C2212yes—
147#2502C2212yes—
148#2498C2214yes—
149#2498C2214yes—
150#2496C2218yes—
151#2487C2212yes—
152#2486C2212yes—
153#2484C2214yes—
154#2475C2218yes—
155#2471C2218yes—
156#2468C2218yes—
157#2466C2218yes—
158#2462C2218yes—
159#2461C2218yes—
160#2459C2218yes—
161#2458C2218yes—
162#2440C2214yes—
163#2439C2214yes—
164#2427C2214yes—
165#2427C2214yes—
166#2423C2214yes—
167#2421C2214yes—
168#2417C2214yes—
169#2417C2218yes—
170#2415C2214yes—
171#2413C2214yes—
172#2409C2214yes—
173#2409C2214yes—
174#2399C2214yes—
175#2398C2212yes—
176#2398C2214yes—
177#2397C2212yes—
178#2396C2218yes—
179#2395C2214yes—
180#2395C2214yes—
181#2392C2214yes—
182#2388C2212yes—
183#2388C2212yes—
184#2362C2214yes—
185#2360C2214yes—
186#2355C2212yes—
187#2354C2214yes—
188#2352C2214yes—
189#2352C2214yes—
190D4×C4⋊C4C2212yes—
191#2346C2212yes—
192#2343C2214yes—
193#2339C2212yes—
194#2320C2212yes—
195#2318C2214yes—
196#2285C2211yescharacteristic
197#2283C2211yescharacteristic
198#2283C2212yes—
199C2×#382C2212yes—
200#2275C2212yes—
201C22×#41C2311yescharacteristic
202C22×#41C2311yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2312yes—
205Q82—28no—
206#556—28no—
207#556—216no—
208#556—216no—
209#556—232no—
210#555—216no—
211#555—28no—
212#553—232no—
213#553—232no—
214#553—216no—
215#553—216no—
216#552—216no—
217#552—216no—
218D4×Q8—28no—
219#548—216no—
220#542—232no—
221#542—216no—
222#541—216no—
223#540—216no—
224#537—28no—
225#537—28no—
226#533—28no—
227#533—216no—
228#532—28no—
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2312yes—
236C2×#127C2311yescharacteristic
237#529—216no—
238#529—216no—
239#529—28no—
240#529—216no—
241C2×#126C2312yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#125—28no—
251C2×#125C2312yes—
252C2×#125C2312yes—
253C2×#125C2311yescharacteristic
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#124C2311yescharacteristic
260C2×#124C2311yescharacteristic
261C2×#124C2311yescharacteristic
262C2×#124C2314yes—
263C2×#124C2312yes—
264C2×#124C2314yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#124C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2312yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×C22⋊Q8C2311yescharacteristic
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2318yes—
290C2×#121C2312yes—
291C2×#121C2312yes—
292C2×#121C2311yescharacteristic
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2312yes—
304C2×#121C2318yes—
305#520—28no—
306#520—28no—
307#519—216no—
308C4×#41D4116yescomplemented
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2314yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2314yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2314yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×#117C2314yes—
342C2×#117C2314yes—
343C2×#117C2312yes—
344C2×#117C2314yes—
345C2×#117C2312yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2314yes—
351C2×#117C2312yes—
352C2×#117C2312yes—
353C2×#117C2312yes—
354C2×#117C2311yescharacteristic
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2312yes—
358C22×C4⋊C4C2311yescharacteristic
359C22×C4⋊C4C2311yescharacteristic
360C22×C4⋊C4C2312yes—
361C22×C4⋊C4C2314yes—
362C22×C42C2311yescharacteristic
363C22×C42C2312yes—
364#400C2318yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2318yes—
373#399C2312yes—
374#399C2312yes—
375#399C2318yes—
376#399C2314yes—
377#399C2314yes—
378#399C2314yes—
379#399C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2318yes—
384#398C2318yes—
385#398C2314yes—
386#398C2314yes—
387#398C2318yes—
388#398C2314yes—
389#398C2318yes—
390#398C2314yes—
391#398C2318yes—
392#398C2318yes—
393#398C2318yes—
394#397C2318yes—
395#397C2318yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2312yes—
401#397C2314yes—
402#397C2318yes—
403#397C2318yes—
404#397C2318yes—
405#396C2318yes—
406#396C2318yes—
407#396C2318yes—
408#396C2314yes—
409#396C2314yes—
410#396C2318yes—
411#396C2318yes—
412#396C2318yes—
413#395C2312yes—
414#395C2314yes—
415#395C2318yes—
416#395C2314yes—
417#395C2312yes—
418#395C2314yes—
419#395C2318yes—
420#395C2318yes—
421#395C2318yes—
422#394C2312yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2318yes—
428#394C2318yes—
429#394C2314yes—
430#394C2312yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2318yes—
436#394C2318yes—
437#394C2318yes—
438#394C2318yes—
439#394C2318yes—
440#393C2312yes—
441#393C2312yes—
442#393C2318yes—
443#393C2312yes—
444#393C2312yes—
445#393C2318yes—
446#393C2318yes—
447#392C2312yes—
448#392C2312yes—
449#392C2314yes—
450#392C2314yes—
451#392C2312yes—
452#392C2312yes—
453#392C2318yes—
454#392C2314yes—
455#392C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2318yes—
461#390C2318yes—
462#390C2314yes—
463#390C2318yes—
464#389C2318yes—
465#389C2314yes—
466#389C2318yes—
467#389C2314yes—
468#389C2314yes—
469#389C2318yes—
470#389C2318yes—
471#388C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#387C2318yes—
482#387C2318yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#386C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2314yes—
499#386C2318yes—
500#386C2318yes—
501#385C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2318yes—
506#385C2314yes—
507#385C2318yes—
508#384C2314yes—
509#384C2314yes—
510#384C2312yes—
511#383C2312yes—
512#383C2314yes—
513#382C2311yescharacteristic
514#382C2311yescharacteristic
515#382C2312yes—
516#382C2314yes—
517#382C2314yes—
518#382C2314yes—
519#382C2314yes—
520#381C2314yes—
521#381C2312yes—
522#381C2314yes—
523#381C2318yes—
524#380C2314yes—
525#380C2314yes—
526#380C2318yes—
527#380C2312yes—
528#380C2312yes—
529#380C2314yes—
530#380C2312yes—
531#380C2314yes—
532#380C2314yes—
533#380C2318yes—
534#380C2318yes—
535#380C2318yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2318yes—
542C4×C4⋊C4C2318yes—
543C4×C22⋊C4C2314yes—
544C4×C22⋊C4C2312yes—
545C4×C22⋊C4C2318yes—
546C4×C22⋊C4C2318yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550#376C2312yes—
551#376C2314yes—
552C2×#95C2314yes—
553C2×#95C2314yes—
554C2×#41—24no—
555C2×#41—24no—
556C2×#41—44no—
557C2×#41—44no—
558C2×#41—44no—
559C2×#41C2×D418yes—
560C22×Q8—28no—
561C22×Q8—48no—
562C22×Q8C2412yes—
563C22×Q8C2411yescharacteristic
564C22×Q8C2411yescharacteristic
565C22×Q8C2414yes—
566C22×Q8C2411yescharacteristic
567C22×Q8C2411yescharacteristic
568C22×Q8C2414yes—
569C22×Q8C2412yes—
570C22×D4C2411yescharacteristic
571C22×D4C2411yescharacteristic
572C22×D4C2412yes—
573C22×D4C2412yes—
574C22×D4C2411yescharacteristic
575C22×D4C2411yescharacteristic
576C22×D4C2414yes—
577C22×D4C2414yes—
578C22×D4C2414yes—
579C22×D4C2412yes—
580C22×D4C2412yes—
581C22×D4C2412yes—
582C22×D4C2414yes—
583C22×D4C2414yes—
584C22×D4C2412yes—
585C23×C4C2412yes—
586C23×C4C2412yes—
587C23×C4C2412yes—
588C23×C4C2411yescharacteristic
589C23×C4C2412yes—
590C23×C4C2412yes—
591C23×C4C2414yes—
592C23×C4C2414yes—
593C23×C4C2414yes—
594C23×C4C2418yes—
595C23×C4C2411yescharacteristic
596C23×C4C2411yescharacteristic
597C23×C4C2412yes—
598C23×C4C2412yes—
599C23×C4C2412yes—
600C4⋊Q8—28no—
601C4⋊Q8—216no—
602C4⋊Q8—24no—
603C4⋊Q8—28no—
604C4⋊Q8—24no—
605C4⋊Q8—28no—
606C4⋊Q8—24no—
607#127—24no—
608#126—216no—
609#126—216no—
610#126—216no—
611#126—216no—
612#126—216no—
613#126—216no—
614#126—216no—
615#126—216no—
616#126—28no—
617#125—216no—
618#125—216no—
619#125—28no—
620#125—28no—
621#125—28no—
622#125—28no—
623#125—28no—
624#125—24no—
625#124—28no—
626#124—216no—
627#124—216no—
628#124—216no—
629#124—216no—
630#124—24no—
631#124—24no—
632#124—24no—
633#124—84no—
634#123—28no—
635#123—216no—
636#123—216no—
637#123—216no—
638#123—216no—
639#123—216no—
640#123—84no—
641C22⋊Q8—28no—
642C22⋊Q8—28no—
643C22⋊Q8—28no—
644C22⋊Q8—28no—
645C22⋊Q8—24no—
646C22⋊Q8—28no—
647C22⋊Q8—28no—
648C22⋊Q8—216no—
649C22⋊Q8—28no—
650C22⋊Q8—216no—
651C22⋊Q8—28no—
652C22⋊Q8—216no—
653C22⋊Q8—48no—
654C22⋊Q8—48no—
655C22⋊Q8—88no—
656#121—28no—
657#121—28no—
658#121—216no—
659#121—216no—
660#121—28no—
661#121—216no—
662#121—28no—
663#121—28no—
664#121—24no—
665#121—28no—
666#121—28no—
667#121—28no—
668#121—216no—
669#121—216no—
670#121—88no—
671C4×Q8—28no—
672C4×Q8—28no—
673C4×Q8—216no—
674C4×Q8—216no—
675C4×Q8—28no—
676C4×Q8—28no—
677C4×Q8—28no—
678C4×Q8—28no—
679C4×Q8—24no—
680C4×Q8—216no—
681C4×Q8—28no—
682C4×Q8C2×D418yes—
683C4×Q8C2×D418yes—
684C4×D4—28no—
685C4×D4—216no—
686C4×D4—216no—
687C4×D4—216no—
688C4×D4—216no—
689C4×D4—216no—
690C4×D4—28no—
691C4×D4—28no—
692C4×D4—28no—
693C4×D4—24no—
694C4×D4—28no—
695C4×D4—28no—
696C4×D4—48no—
697C4×D4—48no—
698C4×D4—48no—
699C4×D4C2×D4116yes—
700C4×D4C2×D418yes—
701C4×D4C2×D4116yes—
702C4×D4C2×D418yes—
703#117—28no—
704#117—28no—
705#117—28no—
706#117—28no—
707#117—216no—
708#117—28no—
709#117—28no—
710#117—216no—
711#117—28no—
712#117—216no—
713#117—216no—
714#117—82no—
715#117C2×D418yes—
716#117C2×D4116yes—
717C2×C4⋊C4—24no—
718C2×C4⋊C4—24no—
719C2×C4⋊C4—28no—
720C2×C4⋊C4—28no—
721C2×C4⋊C4—28no—
722C2×C4⋊C4—28no—
723C2×C4⋊C4—84no—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2418yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2418yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2418yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C42C2×D418yes—
814C2×C42C2×D4116yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2412yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2418yes—
825C2×C42C2412yes—
826C2×C42C2411yescharacteristic
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2411yescharacteristic
830C2×C42C2411yescharacteristic
831C2×C42C2411yescharacteristic
832#95C2412yes—
833#95C2412yes—
834#95C2414yes—
835#95C2414yes—
836#95C2418yes—
837#95C2418yes—
838#95C2412yes—
839#95C2414yes—
840#95C2412yes—
841#95C2418yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2418yes—
846#95C2418yes—
847#95C2418yes—
848#95C2418yes—
849#95C2414yes—
850#95C2418yes—
851#95C2418yes—
852#95C2414yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860C24C2512yes—
861C24C2512yes—
862C24C2512yes—
863C24C2512yes—
864C24C2511yescharacteristic
865#41—416no—
866#41—416no—
867#41—416no—
868C2×Q8—22no—
869C2×Q8—28no—
870C2×Q8—24no—
871C2×Q8—22no—
872C2×Q8—22no—
873C2×Q8—28no—
874C2×Q8—24no—
875C2×Q8—24no—
876C2×Q8—28no—
877C2×Q8—48no—
878C2×Q8—42no—
879C2×Q8—42no—
880C2×Q8—42no—
881C2×Q8—44no—
882C2×Q8—42no—
883C2×Q8—44no—
884C2×Q8—42no—
885C2×Q8—432no—
886C2×Q8C22×D414yes—
887C2×D4—24no—
888C2×D4—24no—
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—24no—
893C2×D4—22no—
894C2×D4—22no—
895C2×D4—22no—
896C2×D4—24no—
897C2×D4—24no—
898C2×D4—24no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—44no—
913C2×D4—42no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—42no—
917C2×D4—44no—
918C2×D4—48no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4C22×D414yes—
922C2×D4C22×D418yes—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—28no—
929C22×C4—24no—
930C22×C4—28no—
931C22×C4—28no—
932C22×C4—28no—
933C22×C4—28no—
934C22×C4—28no—
935C22×C4—42no—
936C22×C4—41no—
937C22×C4—44no—
938C22×C4—42no—
939C22×C4—41no—
940C22×C4—42no—
941C22×C4—48no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—42no—
945C22×C4—48no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—42no—
949C22×C4—48no—
950C22×C4—48no—
951C22×C4—48no—
952C22×C4C22×D414yes—
953C22×C4C22×D414yes—
954C22×C4C22×D414yes—
955C22×C4C22×D418yes—
956C22×C4C22×D418yes—
957C22×C4C22×D418yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2518yes—
961C22×C4C2514yes—
962C22×C4C2512yes—
963C22×C4C2514yes—
964C22×C4C2512yes—
965C22×C4C2512yes—
966C22×C4C2514yes—
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2514yes—
970C22×C4C2511yescharacteristic
971C22×C4C2512yes—
972C22×C4C2511yescharacteristic
973C22×C4C2512yes—
974C22×C4C2511yescharacteristic
975C22×C4C2511yescharacteristic
976C22×C4C2512yes—
977C22×C4C2511yescharacteristic
978C22×C4C2511yescharacteristic
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—28no—
986C4⋊C4—28no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—22no—
991C4⋊C4—24no—
992C4⋊C4—22no—
993C4⋊C4—28no—
994C4⋊C4—24no—
995C4⋊C4—28no—
996C4⋊C4—24no—
997C4⋊C4—28no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—24no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—28no—
1006C4⋊C4—24no—
1007C4⋊C4—28no—
1008C4⋊C4—24no—
1009C4⋊C4—28no—
1010C4⋊C4—42no—
1011C4⋊C4—44no—
1012C4⋊C4—48no—
1013C4⋊C4—42no—
1014C4⋊C4—44no—
1015C4⋊C4—48no—
1016C4⋊C4—48no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—48no—
1020C4⋊C4—48no—
1021C4⋊C4—48no—
1022C4⋊C4—48no—
1023C4⋊C4C22×D414yes—
1024C4⋊C4C22×D414yes—
1025C4⋊C4C22×D418yes—
1026C4⋊C4C22×D418yes—
1027C22⋊C4—28no—
1028C22⋊C4—28no—
1029C22⋊C4—28no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—24no—
1034C22⋊C4—28no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—24no—
1038C22⋊C4—24no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—24no—
1044C22⋊C4—24no—
1045C22⋊C4—24no—
1046C22⋊C4—28no—
1047C22⋊C4—24no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—48no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—48no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—48no—
1060C22⋊C4—48no—
1061C22⋊C4—48no—
1062C22⋊C4—48no—
1063C22⋊C4—44no—
1064C22⋊C4—48no—
1065C22⋊C4C22×D418yes—
1066C22⋊C4C22×D418yes—
1067C22⋊C4C22×D418yes—
1068C42—28no—
1069C42—28no—
1070C42—28no—
1071C42—28no—
1072C42—28no—
1073C42—28no—
1074C42—24no—
1075C42—28no—
1076C42—48no—
1077C42—44no—
1078C42C22×D414yes—
1079C42C22×D418yes—
1080C42C22×D414yes—
1081C42C22×D418yes—
1082C42C22×D418yes—
1083C42C22×D414yes—
1084C42C22×D414yes—
1085C23—24no—
1086C23—22no—
1087C23—21no—
1088C23—22no—
1089C23—22no—
1090C23—21no—
1091C23—24no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—24no—
1097C23—24no—
1098C23—24no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—24no—
1103C23—22no—
1104C23—24no—
1105C23—24no—
1106C23—22no—
1107C23—22no—
1108C23C23×D414yes—
1109C23C23×D412yes—
1110C23C2611yescharacteristic
1111Q8—28no—
1112Q8—44no—
1113Q8—416no—
1114Q8—44no—
1115Q8—44no—
1116Q8—48no—
1117Q8—88no—
1118Q8—84no—
1119D4—28no—
1120D4—48no—
1121D4—44no—
1122D4—44no—
1123D4—44no—
1124D4—48no—
1125D4—48no—
1126D4—84no—
1127D4—84no—
1128D4—88no—
1129D4—84no—
1130D4—88no—
1131D4—88no—
1132D4—88no—
1133D4—88no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—28no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—28no—
1158C2×C4—24no—
1159C2×C4—28no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—28no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—28no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—28no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—48no—
1177C2×C4—44no—
1178C2×C4—48no—
1179C2×C4—44no—
1180C2×C4—48no—
1181C2×C4—416no—
1182C2×C4—48no—
1183C2×C4—48no—
1184C2×C4—48no—
1185C2×C4—88no—
1186C2×C4—88no—
1187C2×C4—84no—
1188C2×C4—84no—
1189C2×C4—168no—
1190C2×C4C23×D414yes—
1191C2×C4C23×D412yes—
1192C2×C4C23×D414yes—
1193C2×C4C23×D414yes—
1194C2×C4C23×D412yes—
1195C2×C4C23×D412yes—
1196C2×C4C23×D412yes—
1197C2×C4C23×D412yes—
1198C2×C4C23×D412yes—
1199C2×C4#58514yes—
1200C22—22no—
1201C22—24no—
1202C22—22no—
1203C22—24no—
1204C22—22no—
1205C22—24no—
1206C22—44no—
1207C22—42no—
1208C22—44no—
1209C22—42no—
1210C22—44no—
1211C22—44no—
1212C22—44no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22C24×D411yescharacteristic
1226C22C2×#58512yes—
1227C22H(7,𝔽2)11yescharacteristic
1228C222−1+611yescharacteristic
1229C222−1+612yes—
1230C4—22no—
1231C4—24no—
1232C4—22no—
1233C4—22no—
1234C4—24no—
1235C4—22no—
1236C4—22no—
1237C4—24no—
1238C4—44no—
1239C4—48no—
1240C4—44no—
1241C4—44no—
1242C4—44no—
1243C4—42no—
1244C4—44no—
1245C4—42no—
1246C4—42no—
1247C4—42no—
1248C4—42no—
1249C4—44no—
1250C4#344914yes—
1251C2—42no—
1252C2—44no—
1253C2—82no—
1254C2—82no—
1255C2—82no—
1256C2C2×#344911yescharacteristic
1257C2#6285311yescharacteristic
1258C2#6285911yescharacteristic
1259C2#6305312yes—
1260C2#6306512yes—
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×#3512C2semidirect
2. C2×#3518C2semidirect
3. #42984C2semidirect
4. #42908C2semidirect
5. #42813C2semidirect
6. #42808C2semidirect
7. #42440C2semidirect
8. #42315C2semidirect
9. #42299C2semidirect
10. #42158C2semidirect
11. #41422C2semidirect
12. #41419C2semidirect
13. #37640C2semidirect
14. #37608C2semidirect
15. #37555C2semidirect
16. #37549C2semidirect
17. #37541C2semidirect
18. #37540C2semidirect
19. #36699C2semidirect
20. #36687C2semidirect
21. #36089C2semidirect
22. #36062C2semidirect
23. #35856C2semidirect
24. #35832C2semidirect
25. #35759C2semidirect
26. #34191C2semidirect
308. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35122
C2×#35182
#429842
#429082
#428132
#428082
#424402
#423152
#422992
#421582
#414222
#414192
#376402
#376082
#375552
#375492
#375412
#375402
#366992
#366872
#360892
#360622
#358562
#358322
#357592
#341912