Finite Group Databasebeta

← #7657949

Subgroups — #7657949

Order 512.

6624 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3515C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#42877C212yesmaximal, complemented
4#42791C212yesmaximal, complemented
5#42683C212yesmaximal, complemented
6#42678C212yesmaximal, complemented
7#42168C214yesmaximal, complemented
8#41990C214yesmaximal, complemented
9#41382C214yesmaximal, complemented
10#40503C214yesmaximal, complemented
11#39889C214yesmaximal, complemented
12#38383C218yesmaximal, complemented
13#37619C211yesmaximal, characteristic, complemented
14#37607C212yesmaximal, complemented
15#37559C211yesmaximal, characteristic, complemented
16#37543C212yesmaximal, complemented
17#36230C214yesmaximal, complemented
18#35938C212yesmaximal, complemented
19#35909C212yesmaximal, complemented
20#35846C212yesmaximal, complemented
21#35704C212yesmaximal, complemented
22#35248C211yesmaximal, characteristic, complemented
23#35138C212yesmaximal, complemented
24#34636C212yesmaximal, complemented
25#34602C211yesmaximal, characteristic, complemented
26#34197C211yesmaximal, characteristic, complemented
27#3515—216no—
28#3480—216no—
29C2×#559C2211yescharacteristic
30C2×#559C2212yes—
31C2×#557C2211yescharacteristic
32C2×#557C2211yescharacteristic
33C2×#556C2211yescharacteristic
34C2×#556C2212yes—
35C2×#554C2211yescharacteristic
36C2×#554C2211yescharacteristic
37C2×#553C2212yes—
38C2×#553C2214yes—
39C2×#553C2212yes—
40C2×#552C2212yes—
41C2×#552C2212yes—
42C2×#552C2214yes—
43C2×#550C2211yescharacteristic
44C2×#548C2212yes—
45C2×#547C2211yescharacteristic
46C2×#547C2212yes—
47C2×#541C2212yes—
48C2×#539C2214yes—
49C2×#533C2211yescharacteristic
50C2×#532C2211yescharacteristic
51C2×#532C2212yes—
52C2×#529C2211yescharacteristic
53C2×#529C2212yes—
54C2×#529C2212yes—
55C2×#529C2214yes—
56C22×#125C2212yes—
57C2×#520C2212yes—
58C2×C4×#41C2212yes—
59C2×C4×#41C2212yes—
60C2×C4×#41C2211yescharacteristic
61C22×C4×Q8C2211yescharacteristic
62#2855C2214yes—
63#2851C2218yes—
64#2822C2214yes—
65#2820C2214yes—
66#2816C2214yes—
67#2816C2212yes—
68#2815C2212yes—
69#2814C2214yes—
70#2813C2214yes—
71#2726C2218yes—
72#2725C2218yes—
73#2710C2218yes—
74#2707C2218yes—
75#2706C2218yes—
76#2705C2218yes—
77#2701C2218yes—
78#2701C2218yes—
79#2699C2218yes—
80#2687C2218yes—
81#2682C2218yes—
82#2674C2218yes—
83#2664C2214yes—
84#2664C2214yes—
85#2664C2214yes—
86#2662C2214yes—
87#2661C2214yes—
88#2658C2212yes—
89#2640C2212yes—
90#2638C2214yes—
91#2638C2214yes—
92#2637C2214yes—
93#2637C2214yes—
94#2636C2214yes—
95#2635C2214yes—
96#2635C2214yes—
97#2634C2211yescharacteristic
98#2634C2211yescharacteristic
99#2634C2212yes—
100#2634C2212yes—
101#2633C2212yes—
102#2633C2212yes—
103#2633C2212yes—
104#2632C2211yescharacteristic
105#2632C2211yescharacteristic
106#2631C2212yes—
107#2630C2218yes—
108#2627C2212yes—
109#2624C2214yes—
110#2623C2214yes—
111#2623C2212yes—
112#2623C2214yes—
113#2621C2212yes—
114#2619C2212yes—
115#2618C2212yes—
116#2614C2212yes—
117#2611C2214yes—
118#2611C2214yes—
119#2611C2218yes—
120#2609C2218yes—
121#2604C2214yes—
122#2603C2214yes—
123#2603C2214yes—
124#2602C2218yes—
125#2592C2212yes—
126#2591C2214yes—
127#2584C2214yes—
128#2583C2214yes—
129#2581C2212yes—
130#2581C2212yes—
131#2580C2214yes—
132#2579C2218yes—
133#2568C2212yes—
134#2562C2214yes—
135#2560C2218yes—
136#2556C2218yes—
137#2548C2212yes—
138#2546C2212yes—
139#2546C2214yes—
140#2546C2212yes—
141#2545C2214yes—
142#2540C2212yes—
143#2519C2218yes—
144#2503C2212yes—
145#2487C2214yes—
146#2486C2214yes—
147#2484C2214yes—
148#2484C2214yes—
149#2478C2218yes—
150#2476C2218yes—
151#2468C2218yes—
152#2466C2218yes—
153#2466C2218yes—
154#2457C2218yes—
155#2456C2218yes—
156#2455C2218yes—
157#2454C2214yes—
158#2453C2214yes—
159#2452C2218yes—
160#2447C2214yes—
161#2445C2214yes—
162#2434C2212yes—
163#2432C2214yes—
164#2432C2214yes—
165#2431C2214yes—
166#2429C2214yes—
167#2429C2214yes—
168#2427C2214yes—
169#2426C2214yes—
170#2407C2214yes—
171#2406C2214yes—
172#2399C2212yes—
173#2398C2212yes—
174#2396C2212yes—
175#2396C2212yes—
176#2396C2214yes—
177#2395C2214yes—
178#2392C2214yes—
179#2388C2214yes—
180#2367C2214yes—
181#2365C2214yes—
182#2361C2214yes—
183#2360C2214yes—
184#2357C2212yes—
185#2357C2214yes—
186#2351C2212yes—
187#2346C2212yes—
188#2346C2214yes—
189#2341C2212yes—
190#2327C2214yes—
191#2322C2218yes—
192#2319C2214yes—
193#2319C2212yes—
194C4×#123C2214yes—
195#2290C2218yes—
196#2283C2211yescharacteristic
197#2283C2212yes—
198#2283C2212yes—
199#2283C2211yescharacteristic
200#2276C2212yes—
201C22×#41C2312yes—
202C22×#41C2312yes—
203C22×#41C2312yes—
204C22×#41C2311yescharacteristic
205C23×Q8C2311yescharacteristic
206#559—28no—
207#559—216no—
208#557—28no—
209#557—28no—
210#556—216no—
211#556—28no—
212#554—28no—
213#554—28no—
214#553—216no—
215#553—232no—
216#553—216no—
217#552—216no—
218#552—232no—
219#552—216no—
220#550—28no—
221#548—216no—
222#547—216no—
223#547—28no—
224#541—216no—
225#539—232no—
226#533—28no—
227#532—216no—
228#532—28no—
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2314yes—
236C2×#127C2311yescharacteristic
237C2×#127C2312yes—
238#529—232no—
239#529—216no—
240#529—28no—
241#529—216no—
242C2×#126C2314yes—
243C2×#126C2312yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#125—216no—
250C2×#125C2314yes—
251C2×#125C2312yes—
252C2×#125C2314yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2311yescharacteristic
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2312yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2311yescharacteristic
264C2×#124C2314yes—
265C2×#124C2312yes—
266C2×#124C2312yes—
267C2×#124C2314yes—
268C2×#123C2314yes—
269C2×#123C2312yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2318yes—
277C2×#123C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2311yescharacteristic
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2312yes—
292C2×#121C2311yescharacteristic
293C2×#121C2312yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299#520—216no—
300C4×#41—216no—
301C4×#41—216no—
302C4×#41D4116yescomplemented
303C2×C4×Q8—28no—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2314yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2318yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2312yes—
342C2×#117C2314yes—
343C2×#117C2314yes—
344C2×#117C2314yes—
345C2×#117C2312yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2314yes—
349C2×#117C2311yescharacteristic
350C2×#117C2312yes—
351C22×C4⋊C4C2314yes—
352C22×C4⋊C4C2314yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2311yescharacteristic
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2312yes—
358C22×C42C2314yes—
359C22×C42C2312yes—
360C22×C42C2311yescharacteristic
361C22×C42C2312yes—
362#400C2312yes—
363#400C2314yes—
364#400C2312yes—
365#400C2314yes—
366#400C2318yes—
367#400C2314yes—
368#400C2314yes—
369#400C2312yes—
370#400C2312yes—
371#399C2318yes—
372#399C2314yes—
373#399C2318yes—
374#399C2314yes—
375#399C2314yes—
376#399C2312yes—
377#399C2312yes—
378#398C2318yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2318yes—
383#398C2314yes—
384#398C2318yes—
385#398C2314yes—
386#398C2318yes—
387#398C2312yes—
388#398C2314yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2318yes—
394#397C2314yes—
395#397C2318yes—
396#397C2314yes—
397#397C2318yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2318yes—
403#396C2318yes—
404#396C2318yes—
405#396C2318yes—
406#396C2318yes—
407#396C2314yes—
408#396C2314yes—
409#396C2318yes—
410#396C2318yes—
411#395C2312yes—
412#395C2314yes—
413#395C2314yes—
414#395C2312yes—
415#395C2312yes—
416#395C2314yes—
417#395C2312yes—
418#394C2318yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2318yes—
423#394C2318yes—
424#394C2318yes—
425#394C2314yes—
426#394C2318yes—
427#394C2318yes—
428#394C2312yes—
429#394C2318yes—
430#394C2312yes—
431#394C2318yes—
432#394C2318yes—
433#393C2318yes—
434#393C2314yes—
435#393C2312yes—
436#393C2312yes—
437#393C2314yes—
438#392C2318yes—
439#392C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2318yes—
443#392C2318yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#390C2318yes—
451#390C2318yes—
452#390C2314yes—
453#390C2318yes—
454#390C2314yes—
455#390C2318yes—
456#390C2314yes—
457#389C2314yes—
458#389C2318yes—
459#389C2318yes—
460#389C2318yes—
461#389C2318yes—
462#389C2314yes—
463#389C2314yes—
464#389C2318yes—
465#389C2318yes—
466#389C2318yes—
467#389C2318yes—
468#389C2318yes—
469#388C2318yes—
470#388C2318yes—
471#388C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2314yes—
479#388C2318yes—
480#388C2318yes—
481#388C2314yes—
482#388C2318yes—
483#387C2318yes—
484#387C2314yes—
485#387C2318yes—
486#387C2314yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#387C2318yes—
492#387C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2314yes—
499#386C2318yes—
500#385C2318yes—
501#385C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2318yes—
506#385C2318yes—
507#385C2318yes—
508#385C2318yes—
509#385C2318yes—
510#385C2314yes—
511#385C2318yes—
512#383C2312yes—
513#383C2311yescharacteristic
514#383C2311yescharacteristic
515#382C2314yes—
516#382C2314yes—
517#382C2312yes—
518#382C2312yes—
519#382C2314yes—
520#381C2312yes—
521#381C2312yes—
522#381C2314yes—
523#381C2318yes—
524#381C2318yes—
525#381C2314yes—
526#381C2314yes—
527#380C2318yes—
528#380C2318yes—
529#380C2312yes—
530#380C2314yes—
531#380C2314yes—
532#380C2312yes—
533C4×C4⋊C4C2318yes—
534C4×C4⋊C4C2314yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2318yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C22⋊C4C2318yes—
543C4×C22⋊C4C2314yes—
544C4×C22⋊C4C2314yes—
545C4×C22⋊C4C2312yes—
546C4×C22⋊C4C2312yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2314yes—
549C4×C22⋊C4C2318yes—
550#376C2314yes—
551#376C2312yes—
552#376C2312yes—
553#376C2314yes—
554C2×#41—28no—
555C2×#41—28no—
556C2×#41—28no—
557C2×#41—44no—
558C2×#41—48no—
559C2×#41—48no—
560C2×#41—44no—
561C2×#41—44no—
562C2×#41C2×D418yes—
563C22×Q8—24no—
564C22×Q8—44no—
565C22×Q8C2411yescharacteristic
566C22×Q8C2412yes—
567C22×Q8C2412yes—
568C22×Q8C2412yes—
569C22×Q8C2411yescharacteristic
570C22×Q8C2411yescharacteristic
571C22×Q8C2411yescharacteristic
572C22×Q8C2412yes—
573C22×D4C2412yes—
574C22×D4C2414yes—
575C22×D4C2411yescharacteristic
576C22×D4C2411yescharacteristic
577C22×D4C2414yes—
578C22×D4C2414yes—
579C22×D4C2412yes—
580C22×D4C2412yes—
581C22×D4C2414yes—
582C22×D4C2412yes—
583C22×D4C2418yes—
584C22×D4C2412yes—
585C23×C4C2412yes—
586C23×C4C2412yes—
587C23×C4C2414yes—
588C23×C4C2411yescharacteristic
589C23×C4C2414yes—
590C23×C4C2414yes—
591C23×C4C2412yes—
592C23×C4C2414yes—
593C23×C4C2414yes—
594C23×C4C2414yes—
595C23×C4C2411yescharacteristic
596C23×C4C2412yes—
597C23×C4C2412yes—
598C23×C4C2412yes—
599C23×C4C2411yescharacteristic
600C4⋊Q8—28no—
601C4⋊Q8—28no—
602C4⋊Q8—24no—
603C4⋊Q8—24no—
604C4⋊Q8—24no—
605C4⋊Q8—48no—
606C4⋊Q8—48no—
607#127—28no—
608#127—24no—
609#126—216no—
610#126—216no—
611#126—216no—
612#126—216no—
613#126—216no—
614#126—28no—
615#126—216no—
616#125—216no—
617#125—216no—
618#125—216no—
619#125—28no—
620#125—24no—
621#125—28no—
622#125—216no—
623#125—216no—
624#125—28no—
625#125—28no—
626#125—28no—
627#124—28no—
628#124—28no—
629#124—216no—
630#124—24no—
631#124—28no—
632#124—28no—
633#124—48no—
634#123—216no—
635#123—28no—
636#123—216no—
637#123—216no—
638#123—216no—
639#123—216no—
640#123—216no—
641#123—216no—
642#123—48no—
643#123—416no—
644C22⋊Q8—28no—
645C22⋊Q8—28no—
646C22⋊Q8—24no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—28no—
650C22⋊Q8—216no—
651C22⋊Q8—216no—
652C22⋊Q8—28no—
653C22⋊Q8—216no—
654C22⋊Q8—48no—
655#121—216no—
656#121—216no—
657#121—216no—
658#121—28no—
659#121—28no—
660#121—24no—
661#121—28no—
662#121—28no—
663#121—216no—
664#121—48no—
665C4×Q8—28no—
666C4×Q8—28no—
667C4×Q8—28no—
668C4×Q8—24no—
669C4×Q8—28no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—28no—
674C4×Q8—28no—
675C4×Q8—28no—
676C4×Q8—28no—
677C4×Q8—24no—
678C4×Q8—28no—
679C4×Q8—48no—
680C4×Q8C2×D418yes—
681C4×Q8C2×D418yes—
682C4×D4—28no—
683C4×D4—216no—
684C4×D4—216no—
685C4×D4—216no—
686C4×D4—216no—
687C4×D4—28no—
688C4×D4—28no—
689C4×D4—28no—
690C4×D4—216no—
691C4×D4—216no—
692C4×D4—216no—
693C4×D4—28no—
694C4×D4—28no—
695C4×D4—28no—
696C4×D4—24no—
697C4×D4—28no—
698C4×D4—416no—
699C4×D4C2×D418yes—
700C4×D4C2×D4116yes—
701C4×D4C2×D418yes—
702C4×D4C2×D4116yes—
703#117—28no—
704#117—28no—
705#117—216no—
706#117—216no—
707#117—216no—
708#117—28no—
709#117—216no—
710#117C2×D418yes—
711#117C2×D4116yes—
712C2×C4⋊C4—28no—
713C2×C4⋊C4—24no—
714C2×C4⋊C4—216no—
715C2×C4⋊C4—28no—
716C2×C4⋊C4—216no—
717C2×C4⋊C4—28no—
718C2×C4⋊C4—28no—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2418yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2418yes—
756C2×C4⋊C4C2418yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2418yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2418yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2418yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C42—28no—
806C2×C42—216no—
807C2×C42C2×D418yes—
808C2×C42C2×D4116yes—
809C2×C42C2412yes—
810C2×C42C2414yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2412yes—
814C2×C42C2414yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2414yes—
819C2×C42C2418yes—
820C2×C42C2418yes—
821C2×C42C2414yes—
822C2×C42C2412yes—
823C2×C42C2411yescharacteristic
824C2×C42C2412yes—
825C2×C42C2411yescharacteristic
826C2×C42C2411yescharacteristic
827C2×C42C2412yes—
828C2×C42C2411yescharacteristic
829#95C2412yes—
830#95C2412yes—
831#95C2414yes—
832#95C2414yes—
833#95C2412yes—
834#95C2418yes—
835#95C2414yes—
836#95C2418yes—
837#95C2414yes—
838#95C2412yes—
839#95C2414yes—
840#95C2412yes—
841#95C2414yes—
842#95C2414yes—
843#95C2418yes—
844#95C2414yes—
845#95C2414yes—
846#95C2418yes—
847#95C2418yes—
848#95C2414yes—
849#95C2412yes—
850#95C2414yes—
851#95C2418yes—
852#95C2414yes—
853#95C2414yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860C24C2512yes—
861C24C2514yes—
862C24C2511yescharacteristic
863C24C2512yes—
864#41—416no—
865#41—432no—
866#41—432no—
867#41—432no—
868C2×Q8—22no—
869C2×Q8—22no—
870C2×Q8—24no—
871C2×Q8—22no—
872C2×Q8—24no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—24no—
876C2×Q8—24no—
877C2×Q8—28no—
878C2×Q8—24no—
879C2×Q8—24no—
880C2×Q8—24no—
881C2×Q8—42no—
882C2×Q8—42no—
883C2×Q8—42no—
884C2×Q8—44no—
885C2×Q8—416no—
886C2×Q8C22×D414yes—
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—28no—
890C2×D4—24no—
891C2×D4—28no—
892C2×D4—22no—
893C2×D4—24no—
894C2×D4—24no—
895C2×D4—24no—
896C2×D4—24no—
897C2×D4—28no—
898C2×D4—28no—
899C2×D4—42no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—48no—
905C2×D4—44no—
906C2×D4—48no—
907C2×D4—48no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—48no—
911C2×D4—48no—
912C2×D4C22×D414yes—
913C2×D4C22×D418yes—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—28no—
917C22×C4—24no—
918C22×C4—28no—
919C22×C4—28no—
920C22×C4—28no—
921C22×C4—24no—
922C22×C4—28no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—28no—
927C22×C4—28no—
928C22×C4—44no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—48no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—48no—
939C22×C4—48no—
940C22×C4—48no—
941C22×C4—44no—
942C22×C4C22×D414yes—
943C22×C4C22×D414yes—
944C22×C4C22×D418yes—
945C22×C4C22×D418yes—
946C22×C4C22×D418yes—
947C22×C4C22×D414yes—
948C22×C4C2518yes—
949C22×C4C2512yes—
950C22×C4C2514yes—
951C22×C4C2514yes—
952C22×C4C2512yes—
953C22×C4C2512yes—
954C22×C4C2512yes—
955C22×C4C2514yes—
956C22×C4C2514yes—
957C22×C4C2514yes—
958C22×C4C2512yes—
959C22×C4C2512yes—
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2512yes—
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C22×C4C2512yes—
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2511yescharacteristic
970C4⋊C4—28no—
971C4⋊C4—24no—
972C4⋊C4—22no—
973C4⋊C4—24no—
974C4⋊C4—22no—
975C4⋊C4—24no—
976C4⋊C4—22no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—28no—
980C4⋊C4—24no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—24no—
984C4⋊C4—22no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—24no—
993C4⋊C4—28no—
994C4⋊C4—24no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—24no—
1001C4⋊C4—24no—
1002C4⋊C4—28no—
1003C4⋊C4—216no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—48no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—48no—
1011C4⋊C4—48no—
1012C4⋊C4—44no—
1013C4⋊C4—48no—
1014C4⋊C4—48no—
1015C4⋊C4—48no—
1016C4⋊C4C22×D414yes—
1017C4⋊C4C22×D414yes—
1018C4⋊C4C22×D418yes—
1019C4⋊C4C22×D418yes—
1020C22⋊C4—28no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—28no—
1024C22⋊C4—24no—
1025C22⋊C4—24no—
1026C22⋊C4—28no—
1027C22⋊C4—28no—
1028C22⋊C4—28no—
1029C22⋊C4—24no—
1030C22⋊C4—28no—
1031C22⋊C4—24no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—28no—
1036C22⋊C4—24no—
1037C22⋊C4—28no—
1038C22⋊C4—48no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—48no—
1042C22⋊C4—44no—
1043C22⋊C4—48no—
1044C22⋊C4—48no—
1045C22⋊C4—48no—
1046C22⋊C4—44no—
1047C22⋊C4—48no—
1048C22⋊C4—48no—
1049C22⋊C4—48no—
1050C22⋊C4—44no—
1051C22⋊C4—48no—
1052C22⋊C4—48no—
1053C22⋊C4C22×D418yes—
1054C22⋊C4C22×D418yes—
1055C22⋊C4C22×D418yes—
1056C42—24no—
1057C42—24no—
1058C42—28no—
1059C42—28no—
1060C42—24no—
1061C42—24no—
1062C42—28no—
1063C42—28no—
1064C42—24no—
1065C42—28no—
1066C42—48no—
1067C42—48no—
1068C42—44no—
1069C42C22×D418yes—
1070C42C22×D414yes—
1071C42C22×D418yes—
1072C42C22×D414yes—
1073C42C22×D414yes—
1074C42C22×D414yes—
1075C42C22×D418yes—
1076C23—22no—
1077C23—24no—
1078C23—22no—
1079C23—24no—
1080C23—22no—
1081C23—24no—
1082C23—22no—
1083C23—24no—
1084C23—24no—
1085C23—22no—
1086C23—24no—
1087C23—28no—
1088C23—24no—
1089C23—22no—
1090C23—24no—
1091C23—28no—
1092C23C23×D412yes—
1093C23C23×D414yes—
1094C23C2611yescharacteristic
1095Q8—28no—
1096Q8—28no—
1097Q8—48no—
1098Q8—44no—
1099Q8—44no—
1100Q8—48no—
1101Q8—48no—
1102Q8—84no—
1103D4—28no—
1104D4—48no—
1105D4—416no—
1106D4—44no—
1107D4—48no—
1108D4—416no—
1109D4—416no—
1110D4—48no—
1111D4—84no—
1112D4—84no—
1113D4—88no—
1114D4—816no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—28no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—28no—
1139C2×C4—28no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—28no—
1145C2×C4—22no—
1146C2×C4—28no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—28no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—48no—
1157C2×C4—44no—
1158C2×C4—44no—
1159C2×C4—48no—
1160C2×C4—48no—
1161C2×C4—416no—
1162C2×C4—48no—
1163C2×C4—416no—
1164C2×C4—416no—
1165C2×C4—48no—
1166C2×C4—88no—
1167C2×C4—88no—
1168C2×C4—88no—
1169C2×C4—84no—
1170C2×C4C23×D412yes—
1171C2×C4C23×D412yes—
1172C2×C4C23×D414yes—
1173C2×C4C23×D414yes—
1174C2×C4C23×D412yes—
1175C2×C4C23×D412yes—
1176C2×C4C23×D412yes—
1177C2×C4C23×D414yes—
1178C2×C4C23×D412yes—
1179C2×C4#58514yes—
1180C2×C4#58514yes—
1181C22—22no—
1182C22—24no—
1183C22—22no—
1184C22—24no—
1185C22—22no—
1186C22—24no—
1187C22—44no—
1188C22—48no—
1189C22—44no—
1190C22—42no—
1191C22—44no—
1192C22—42no—
1193C22—44no—
1194C22—42no—
1195C22—44no—
1196C22—48no—
1197C22—44no—
1198C22—48no—
1199C22C24×D411yescharacteristic
1200C22C2×#58512yes—
1201C22C2×#58512yes—
1202C222−1+612yes—
1203C4—24no—
1204C4—22no—
1205C4—24no—
1206C4—22no—
1207C4—22no—
1208C4—24no—
1209C4—22no—
1210C4—22no—
1211C4—24no—
1212C4—42no—
1213C4—42no—
1214C4—44no—
1215C4—42no—
1216C4—42no—
1217C4—42no—
1218C4—42no—
1219C4—44no—
1220C4—44no—
1221C4—44no—
1222C4—44no—
1223C4—48no—
1224C4#344914yes—
1225C2—42no—
1226C2—44no—
1227C2—84no—
1228C2—82no—
1229C2C2×#344911yescharacteristic
1230C2#6281111yescharacteristic
1231C2#6285911yescharacteristic
1232C2#6296714yes—
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×#3515C2semidirect
2. C2×#3480C2semidirect
3. #42877C2semidirect
4. #42791C2semidirect
5. #42683C2semidirect
6. #42678C2semidirect
7. #42168C2semidirect
8. #41990C2semidirect
9. #41382C2semidirect
10. #40503C2semidirect
11. #39889C2semidirect
12. #38383C2semidirect
13. #37619C2semidirect
14. #37607C2semidirect
15. #37559C2semidirect
16. #37543C2semidirect
17. #36230C2semidirect
18. #35938C2semidirect
19. #35909C2semidirect
20. #35846C2semidirect
21. #35704C2semidirect
22. #35248C2semidirect
23. #35138C2semidirect
24. #34636C2semidirect
25. #34602C2semidirect
26. #34197C2semidirect
302. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35152
C2×#34802
#428772
#427912
#426832
#426782
#421682
#419902
#413822
#405032
#398892
#383832
#376192
#376072
#375592
#375432
#362302
#359382
#359092
#358462
#357042
#352482
#351382
#346362
#346022
#341972