Finite Group Databasebeta

← #7646528

Subgroups — #7646528

Order 512.

6800 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3518C211yesmaximal, characteristic, complemented
2C2×#3460C211yesmaximal, characteristic, complemented
3#42987C212yesmaximal, complemented
4#42979C212yesmaximal, complemented
5#42915C212yesmaximal, complemented
6#42908C212yesmaximal, complemented
7#42158C214yesmaximal, complemented
8#42156C214yesmaximal, complemented
9#39469C212yesmaximal, complemented
10#39468C212yesmaximal, complemented
11#39125C212yesmaximal, complemented
12#39124C212yesmaximal, complemented
13#37845C214yesmaximal, complemented
14#37844C214yesmaximal, complemented
15#37560C212yesmaximal, complemented
16#37550C212yesmaximal, complemented
17#36745C218yesmaximal, complemented
18#35675C214yesmaximal, complemented
19#35297C211yesmaximal, characteristic, complemented
20#35236C211yesmaximal, characteristic, complemented
21#35234C212yesmaximal, complemented
22#35180C212yesmaximal, complemented
23#35169C214yesmaximal, complemented
24#34946C211yesmaximal, characteristic, complemented
25#34911C211yesmaximal, characteristic, complemented
26#34127C211yesmaximal, characteristic, complemented
27#3518—216no—
28C2×Q82C2211yescharacteristic, complemented
29C2×#556C2212yes—
30C2×#556C2212yes—
31C2×#556C2211yescharacteristic, complemented
32C2×#556C2214yescomplemented
33C2×#555C2212yes—
34C2×#555C2211yescharacteristic, complemented
35C2×D4×Q8C2211yescharacteristic, complemented
36C2×#548C2212yes—
37#3460—216no—
38C2×#544C2211yescharacteristic
39C2×#542C2214yes—
40C2×#542C2212yes—
41C2×#542C2212yes—
42C2×#542C2212yescomplemented
43C2×#540C2212yes—
44C2×#540C2212yes—
45C2×#538C2214yes—
46C2×#537C2211yescharacteristic
47C2×#535C2211yescharacteristic
48C2×#535C2211yescharacteristic
49C2×#533C2211yescharacteristic
50C2×#533C2212yescomplemented
51C2×#532C2212yes—
52C2×#532C2212yes—
53C2×#529C2211yescharacteristic
54C2×#529C2212yes—
55C2×#529C2212yes—
56C2×#529C2212yescomplemented
57C2×#525C2214yes—
58C2×#519C2212yescomplemented
59C2×C4×#41C2211yescharacteristic
60C2×C4×#41C2211yescharacteristic
61C22×C4×D4C2211yescharacteristic
62#2857C2212yescomplemented
63#2857C2212yescomplemented
64#2854C2218yescomplemented
65#2850C2218yescomplemented
66#2848C2212yes—
67#2847C2212yes—
68#2821C2214yescomplemented
69#2818C2214yes—
70#2817C2214yescomplemented
71#2816C2214yes—
72#2723C2218yescomplemented
73#2716C2218yescomplemented
74#2715C2218yescomplemented
75#2712C2218yescomplemented
76#2700C2218yes—
77#2698C2218yes—
78#2696C2218yescomplemented
79#2691C2218yescomplemented
80#2688C2218yes—
81#2686C2218yes—
82#2685C2218yes—
83#2684C2218yes—
84#2676C2218yescomplemented
85#2674C2218yescomplemented
86#2670C2218yes—
87#2668C2218yes—
88#2664C2214yescomplemented
89#2663C2218yescomplemented
90#2662C2214yes—
91#2661C2218yescomplemented
92#2639C2214yes—
93#2639C2214yescomplemented
94#2636C2214yes—
95#2635C2214yes—
96#2635C2214yescomplemented
97#2634C2214yescomplemented
98#2632C2214yes—
99#2628C2214yescomplemented
100#2628C2214yescomplemented
101#2625C2212yes—
102#2616C2212yes—
103#2616C2214yescomplemented
104#2615C2214yescomplemented
105#2610C2218yescomplemented
106#2604C2218yescomplemented
107#2604C2212yescomplemented
108#2603C2212yescomplemented
109#2602C2214yes—
110#2601C2218yescomplemented
111#2592C2218yescomplemented
112#2592C2211yescharacteristic, complemented
113#2584C2211yescharacteristic, complemented
114#2584C2212yescomplemented
115#2581C2212yescomplemented
116#2568C2214yescomplemented
117#2564C2214yescomplemented
118#2563C2212yes—
119#2563C2214yescomplemented
120#2562C2212yes—
121#2562C2212yes—
122#2562C2212yes—
123#2562C2211yescharacteristic, complemented
124#2562C2212yescomplemented
125#2561C2214yes—
126#2559C2218yescomplemented
127#2557C2218yescomplemented
128#2555C2218yescomplemented
129#2553C2218yescomplemented
130#2550C2214yescomplemented
131#2548C2214yes—
132#2547C2212yes—
133#2547C2214yescomplemented
134#2544C2214yes—
135#2543C2214yes—
136#2540C2214yes—
137#2540C2212yes—
138#2540C2211yescharacteristic, complemented
139#2538C2212yes—
140#2537C2212yes—
141#2536C2214yescomplemented
142#2536C2212yescomplemented
143#2535C2214yescomplemented
144#2535C2214yescomplemented
145#2503C2212yes—
146#2491C2214yes—
147#2489C2214yescomplemented
148#2487C2212yes—
149#2485C2214yes—
150#2485C2214yescomplemented
151#2485C2214yescomplemented
152#2477C2218yescomplemented
153#2471C2218yescomplemented
154#2465C2218yescomplemented
155#2458C2218yescomplemented
156#2451C2214yescomplemented
157#2448C2214yes—
158#2439C2214yescomplemented
159#2436C2214yes—
160#2435C2212yes—
161#2428C2214yes—
162#2427C2214yescomplemented
163#2426C2214yes—
164#2421C2214yescomplemented
165#2417C2214yescomplemented
166#2416C2214yescomplemented
167#2415C2212yes—
168#2415C2214yes—
169#2414C2214yes—
170#2414C2212yes—
171#2411C2214yes—
172#2409C2214yescomplemented
173#2408C2212yes—
174#2398C2214yes—
175#2395C2212yes—
176#2388C2212yes—
177#2355C2212yescomplemented
178#2352C2214yes—
179D4×C4⋊C4C2212yescomplemented
180#2347C2212yes—
181#2343C2214yescomplemented
182#2339C2212yes—
183#2324C2214yes—
184#2324C2214yescomplemented
185#2323C2214yescomplemented
186#2323C2214yescomplemented
187#2311C2214yescomplemented
188#2311C2214yescomplemented
189C4×#124C2214yes—
190C4×C22⋊Q8C2212yescomplemented
191C4×#121C2212yescomplemented
192#2295C2212yescomplemented
193#2293C2214yescomplemented
194#2290C2214yes—
195#2285C2211yescharacteristic
196#2283C2212yescomplemented
197#2280C2214yes—
198C42×D4C2212yescomplemented
199C4×#117C2211yescharacteristic
200C2×C4×C4⋊C4C2212yescomplemented
201C22×#41C2314yes—
202C22×#41C2311yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2312yes—
205C23×D4C2311yescharacteristic
206C24×C4C2312yes—
207Q82—28no—
208#556—216no—
209#556—28no—
210#556—216no—
211#556—232no—
212#555—216no—
213#555—28no—
214D4×Q8—28no—
215#548—216no—
216#544—28no—
217#542—216no—
218#542—232no—
219#542—216no—
220#542—216no—
221#540—216no—
222#540—216no—
223#538—232no—
224#537—28no—
225#535—28no—
226#535—28no—
227#533—28no—
228#533—216no—
229#532—216no—
230#532—216no—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×#127C2312yes—
240C2×#127C2312yes—
241#529—216no—
242#529—216no—
243#529—28no—
244#529—216no—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2312yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#125C2311yescharacteristic
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#124C2314yes—
257C2×#124C2311yescharacteristic
258C2×#124C2312yes—
259C2×#124C2314yes—
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#124C2314yes—
263C2×#124C2312yes—
264C2×#124C2314yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#124C2318yes—
268#525—232no—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2312yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2311yescharacteristic
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×#121C2312yes—
292C2×#121C2311yescharacteristic
293C2×#121C2314yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×#121C2312yes—
308C2×#121C2318yes—
309C2×#120C2314yes—
310C2×#120C2314yes—
311C2×#120C2314yes—
312#519—216no—
313C4×#41—28no—
314C4×#41D4116yescomplemented
315C2×C4×Q8C2314yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2314yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2314yes—
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×D4—28no—
329C2×C4×D4C2312yes—
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2314yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2311yescharacteristic
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2311yescharacteristic
349C2×#117C2312yes—
350C2×#117C2312yes—
351C2×#117C2312yes—
352C2×#117C2314yes—
353C2×#117C2312yes—
354C2×#117C2314yes—
355C2×#117C2311yescharacteristic
356C2×#117C2312yes—
357C2×#117C2314yes—
358C2×#117C2312yes—
359C2×#117C2312yes—
360C2×#117C2312yes—
361C2×#117C2312yes—
362C2×#117C2311yescharacteristic
363C22×C4⋊C4C2311yescharacteristic
364C22×C4⋊C4C2314yes—
365C22×C22⋊C4C2312yes—
366C22×C42C2312yes—
367C22×C42C2314yes—
368C22×C42C2311yescharacteristic
369C22×C42C2312yes—
370#400C2314yes—
371#400C2314yes—
372#400C2318yes—
373#400C2314yes—
374#400C2314yes—
375#400C2312yes—
376#400C2318yes—
377#399C2318yes—
378#399C2314yes—
379#399C2312yes—
380#399C2318yes—
381#398C2312yes—
382#398C2314yes—
383#398C2318yes—
384#398C2318yes—
385#397C2318yes—
386#397C2318yes—
387#397C2318yes—
388#397C2318yes—
389#397C2312yes—
390#397C2318yes—
391#397C2318yes—
392#397C2314yes—
393#397C2318yes—
394#396C2318yes—
395#396C2318yes—
396#396C2318yes—
397#395C2312yes—
398#395C2314yes—
399#395C2318yes—
400#395C2318yes—
401#395C2318yes—
402#394C2314yes—
403#394C2314yes—
404#394C2318yes—
405#394C2318yes—
406#394C2314yes—
407#394C2314yes—
408#394C2312yes—
409#394C2318yes—
410#394C2318yes—
411#394C2318yes—
412#394C2314yes—
413#394C2314yes—
414#394C2318yes—
415#394C2318yes—
416#394C2318yes—
417#394C2318yes—
418#393C2318yes—
419#393C2318yes—
420#393C2318yes—
421#393C2318yes—
422#393C2312yes—
423#393C2318yes—
424#393C2318yes—
425#392C2312yes—
426#392C2318yes—
427#392C2314yes—
428#392C2318yes—
429#392C2314yes—
430#392C2318yes—
431#392C2318yes—
432#391C2318yes—
433#391C2318yes—
434#391C2318yes—
435#391C2312yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#390C2314yes—
441#390C2318yes—
442#390C2318yes—
443#390C2318yes—
444#390C2318yes—
445#390C2314yes—
446#390C2312yes—
447#390C2318yes—
448#390C2314yes—
449#390C2314yes—
450#389C2318yes—
451#389C2314yes—
452#389C2318yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2312yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#388C2318yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#388C2314yes—
467#388C2318yes—
468#388C2318yes—
469#388C2318yes—
470#388C2318yes—
471#388C2314yes—
472#388C2314yes—
473#388C2318yes—
474#388C2314yes—
475#388C2318yes—
476#388C2318yes—
477#388C2314yes—
478#388C2318yes—
479#388C2318yes—
480#387C2318yes—
481#387C2318yes—
482#387C2318yes—
483#387C2318yes—
484#387C2314yes—
485#387C2318yes—
486#387C2318yes—
487#386C2318yes—
488#386C2318yes—
489#386C2318yes—
490#386C2318yes—
491#386C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2314yes—
495#386C2318yes—
496#386C2318yes—
497#386C2314yes—
498#386C2318yes—
499#386C2318yes—
500#385C2318yes—
501#385C2318yes—
502#385C2314yes—
503#385C2318yes—
504#385C2314yes—
505#384C2312yes—
506#383C2314yes—
507#382C2314yes—
508#382C2318yes—
509#382C2312yes—
510#382C2314yes—
511#381C2314yes—
512#381C2318yes—
513#380C2314yes—
514#380C2314yes—
515#380C2314yes—
516#380C2314yes—
517#380C2314yes—
518#380C2314yes—
519#380C2312yes—
520#380C2314yes—
521#380C2312yes—
522#380C2314yes—
523#380C2318yes—
524#380C2314yes—
525#380C2314yes—
526#380C2312yes—
527#380C2312yes—
528#380C2314yes—
529#380C2314yes—
530#379C2318yes—
531#379C2314yes—
532C4×C4⋊C4C2311yescharacteristic
533C4×C4⋊C4C2311yescharacteristic
534C4×C4⋊C4C2312yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C22⋊C4C2312yes—
543C4×C22⋊C4C2312yes—
544C4×C22⋊C4C2318yes—
545C4×C22⋊C4C2314yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2318yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550#376C2312yes—
551#376C2314yes—
552C2×#95C2314yes—
553C43C2312yes—
554C25C2412yes—
555C2×#41—24no—
556C2×#41—216no—
557C2×#41—44no—
558C2×#41—48no—
559C2×#41—48no—
560C2×#41—44no—
561C2×#41C2×D418yes—
562C22×Q8—28no—
563C22×Q8—48no—
564C22×Q8C2411yescharacteristic
565C22×Q8C2412yes—
566C22×Q8C2411yescharacteristic
567C22×Q8C2411yescharacteristic
568C22×Q8C2414yes—
569C22×Q8C2412yes—
570C22×Q8C2414yes—
571C22×Q8C2414yes—
572C22×D4—24no—
573C22×D4—44no—
574C22×D4C2411yescharacteristic
575C22×D4C2412yes—
576C22×D4C2411yescharacteristic
577C22×D4C2412yes—
578C22×D4C2412yes—
579C22×D4C2411yescharacteristic
580C22×D4C2412yes—
581C22×D4C2414yes—
582C22×D4C2414yes—
583C22×D4C2414yes—
584C22×D4C2414yes—
585C22×D4C2414yes—
586C22×D4C2414yes—
587C22×D4C2414yes—
588C22×D4C2418yes—
589C22×D4C2412yes—
590C23×C4—28no—
591C23×C4—48no—
592C23×C4C2412yes—
593C23×C4C2414yes—
594C23×C4C2412yes—
595C23×C4C2412yes—
596C23×C4C2412yes—
597C23×C4C2411yescharacteristic
598C23×C4C2411yescharacteristic
599C23×C4C2412yes—
600C23×C4C2414yes—
601C23×C4C2412yes—
602C23×C4C2414yes—
603C23×C4C2418yes—
604C23×C4C2411yescharacteristic
605C23×C4C2412yes—
606C23×C4C2412yes—
607C4⋊Q8—28no—
608C4⋊Q8—28no—
609C4⋊Q8—216no—
610C4⋊Q8—28no—
611C4⋊Q8—24no—
612C4⋊Q8—28no—
613C4⋊Q8—24no—
614C4⋊Q8—28no—
615#127—28no—
616#127—28no—
617#126—216no—
618#126—216no—
619#126—216no—
620#126—216no—
621#126—216no—
622#126—28no—
623#126—216no—
624#125—28no—
625#125—24no—
626#125—28no—
627#125—28no—
628#124—28no—
629#124—28no—
630#124—216no—
631#124—216no—
632#124—216no—
633#124—216no—
634#124—216no—
635#124—24no—
636#124—28no—
637#124—216no—
638#124—48no—
639#124—88no—
640#123—216no—
641#123—28no—
642#123—216no—
643#123—216no—
644#123—216no—
645#123—216no—
646C22⋊Q8—28no—
647C22⋊Q8—28no—
648C22⋊Q8—24no—
649C22⋊Q8—28no—
650C22⋊Q8—28no—
651C22⋊Q8—216no—
652C22⋊Q8—28no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—28no—
656C22⋊Q8—216no—
657C22⋊Q8—216no—
658C22⋊Q8—48no—
659C22⋊Q8—44no—
660C22⋊Q8—48no—
661C22⋊Q8—84no—
662#121—216no—
663#121—28no—
664#121—28no—
665#121—216no—
666#121—28no—
667#121—24no—
668#121—28no—
669#121—28no—
670#121—28no—
671#121—216no—
672#121—28no—
673#121—28no—
674#121—216no—
675#121—216no—
676#121—48no—
677#121—44no—
678#121—48no—
679#121—88no—
680#120—216no—
681#120—216no—
682#120—84no—
683C4×Q8—28no—
684C4×Q8—28no—
685C4×Q8—216no—
686C4×Q8—24no—
687C4×Q8—24no—
688C4×Q8—28no—
689C4×Q8—216no—
690C4×Q8—24no—
691C4×Q8—28no—
692C4×Q8—28no—
693C4×Q8—216no—
694C4×Q8C2×D418yes—
695C4×Q8C2×D418yes—
696C4×D4—28no—
697C4×D4—28no—
698C4×D4—216no—
699C4×D4—28no—
700C4×D4—216no—
701C4×D4—28no—
702C4×D4—28no—
703C4×D4—28no—
704C4×D4—28no—
705C4×D4—24no—
706C4×D4—24no—
707C4×D4—216no—
708C4×D4—24no—
709C4×D4—28no—
710C4×D4—48no—
711C4×D4—48no—
712C4×D4C2×D4116yes—
713C4×D4C2×D418yes—
714C4×D4C2×D4116yes—
715C4×D4C2×D418yes—
716#117—24no—
717#117—28no—
718#117—28no—
719#117—28no—
720#117—28no—
721#117—216no—
722#117—28no—
723#117—28no—
724#117—216no—
725#117—216no—
726#117—44no—
727#117—82no—
728#117C2×D418yes—
729#117C2×D4116yes—
730C2×C4⋊C4—24no—
731C2×C4⋊C4—48no—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2418yes—
768C2×C4⋊C4C2418yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2412yes—
774C2×C22⋊C4—28no—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2418yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2418yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2418yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C42—28no—
820C2×C42—84no—
821C2×C42C2×D418yes—
822C2×C42C2×D4116yes—
823C2×C42C2412yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2414yes—
830C2×C42C2414yes—
831C2×C42C2412yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2418yes—
835C2×C42C2412yes—
836C2×C42C2412yes—
837C2×C42C2411yescharacteristic
838C2×C42C2412yes—
839C2×C42C2411yescharacteristic
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2411yescharacteristic
843C2×C42C2411yescharacteristic
844#95C2412yes—
845#95C2414yes—
846#95C2418yes—
847#95C2412yes—
848#95C2414yes—
849#95C2418yes—
850#95C2418yes—
851#95C2414yes—
852#95C2418yes—
853#95C2418yes—
854#95C2414yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2418yes—
864#95C2418yes—
865#95C2418yes—
866#95C2418yes—
867#95C2418yes—
868#95C2418yes—
869C24—24no—
870C24—44no—
871C24—42no—
872C24—44no—
873C24—42no—
874C24C2514yes—
875C24C2512yes—
876C24C2512yes—
877C24C2511yescharacteristic
878C24C2512yes—
879#41—416no—
880#41—416no—
881#41—832no—
882C2×Q8—22no—
883C2×Q8—22no—
884C2×Q8—28no—
885C2×Q8—24no—
886C2×Q8—24no—
887C2×Q8—28no—
888C2×Q8—28no—
889C2×Q8—24no—
890C2×Q8—24no—
891C2×Q8—28no—
892C2×Q8—48no—
893C2×Q8—42no—
894C2×Q8—42no—
895C2×Q8—44no—
896C2×Q8—42no—
897C2×Q8—44no—
898C2×Q8—44no—
899C2×Q8—44no—
900C2×Q8—432no—
901C2×Q8C22×D414yes—
902C2×D4—24no—
903C2×D4—28no—
904C2×D4—24no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—22no—
909C2×D4—24no—
910C2×D4—24no—
911C2×D4—22no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—24no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—24no—
918C2×D4—44no—
919C2×D4—42no—
920C2×D4—44no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—416no—
924C2×D4—44no—
925C2×D4—42no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—42no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—44no—
941C2×D4—48no—
942C2×D4—48no—
943C2×D4—48no—
944C2×D4C22×D414yes—
945C2×D4C22×D418yes—
946C22×C4—28no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—28no—
953C22×C4—24no—
954C22×C4—28no—
955C22×C4—24no—
956C22×C4—28no—
957C22×C4—28no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—28no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—28no—
964C22×C4—42no—
965C22×C4—41no—
966C22×C4—41no—
967C22×C4—42no—
968C22×C4—48no—
969C22×C4—44no—
970C22×C4—48no—
971C22×C4—48no—
972C22×C4—48no—
973C22×C4—42no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—42no—
978C22×C4—816no—
979C22×C4C22×D414yes—
980C22×C4C22×D414yes—
981C22×C4C22×D418yes—
982C22×C4C22×D414yes—
983C22×C4C22×D418yes—
984C22×C4C22×D418yes—
985C22×C4C2514yes—
986C22×C4C2514yes—
987C22×C4C2518yes—
988C22×C4C2512yes—
989C22×C4C2514yes—
990C22×C4C2512yes—
991C22×C4C2514yes—
992C22×C4C2512yes—
993C22×C4C2514yes—
994C22×C4C2512yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2511yescharacteristic
999C22×C4C2511yescharacteristic
1000C22×C4C2512yes—
1001C22×C4C2512yes—
1002C22×C4C2511yescharacteristic
1003C22×C4C2511yescharacteristic
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—24no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—28no—
1017C4⋊C4—24no—
1018C4⋊C4—24no—
1019C4⋊C4—28no—
1020C4⋊C4—24no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—24no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—24no—
1029C4⋊C4—28no—
1030C4⋊C4—24no—
1031C4⋊C4—28no—
1032C4⋊C4—24no—
1033C4⋊C4—28no—
1034C4⋊C4—24no—
1035C4⋊C4—28no—
1036C4⋊C4—48no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—48no—
1041C4⋊C4—44no—
1042C4⋊C4—48no—
1043C4⋊C4—48no—
1044C4⋊C4C22×D414yes—
1045C4⋊C4C22×D418yes—
1046C4⋊C4C22×D414yes—
1047C4⋊C4C22×D418yes—
1048C22⋊C4—24no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—24no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—24no—
1058C22⋊C4—28no—
1059C22⋊C4—24no—
1060C22⋊C4—24no—
1061C22⋊C4—24no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—24no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—24no—
1069C22⋊C4—28no—
1070C22⋊C4—48no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—48no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—48no—
1077C22⋊C4—44no—
1078C22⋊C4—48no—
1079C22⋊C4—48no—
1080C22⋊C4—44no—
1081C22⋊C4—48no—
1082C22⋊C4—44no—
1083C22⋊C4—48no—
1084C22⋊C4—48no—
1085C22⋊C4—48no—
1086C22⋊C4—48no—
1087C22⋊C4—48no—
1088C22⋊C4—44no—
1089C22⋊C4C22×D418yes—
1090C22⋊C4C22×D418yes—
1091C22⋊C4C22×D418yes—
1092C42—24no—
1093C42—24no—
1094C42—24no—
1095C42—28no—
1096C42—28no—
1097C42—28no—
1098C42—28no—
1099C42—24no—
1100C42—28no—
1101C42—42no—
1102C42—44no—
1103C42—48no—
1104C42—42no—
1105C42—44no—
1106C42C22×D414yes—
1107C42C22×D414yes—
1108C42C22×D414yes—
1109C42C22×D418yes—
1110C42C22×D418yes—
1111C42C22×D414yes—
1112C42C22×D418yes—
1113C23—22no—
1114C23—24no—
1115C23—24no—
1116C23—22no—
1117C23—21no—
1118C23—22no—
1119C23—22no—
1120C23—21no—
1121C23—22no—
1122C23—24no—
1123C23—22no—
1124C23—22no—
1125C23—24no—
1126C23—24no—
1127C23—24no—
1128C23—22no—
1129C23—22no—
1130C23—24no—
1131C23—24no—
1132C23—24no—
1133C23—22no—
1134C23—22no—
1135C23—24no—
1136C23—22no—
1137C23—24no—
1138C23—22no—
1139C23—22no—
1140C23—48no—
1141C23—84no—
1142C23—84no—
1143C23—88no—
1144C23—88no—
1145C23C23×D412yes—
1146C23C23×D414yes—
1147C23C2611yescharacteristic
1148Q8—28no—
1149Q8—416no—
1150Q8—44no—
1151Q8—48no—
1152Q8—44no—
1153Q8—84no—
1154Q8—88no—
1155Q8—88no—
1156D4—28no—
1157D4—48no—
1158D4—48no—
1159D4—44no—
1160D4—48no—
1161D4—48no—
1162D4—44no—
1163D4—88no—
1164D4—88no—
1165D4—88no—
1166D4—88no—
1167D4—84no—
1168D4—88no—
1169D4—88no—
1170D4—88no—
1171D4—168no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—28no—
1183C2×C4—28no—
1184C2×C4—216no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—28no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—28no—
1202C2×C4—28no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—28no—
1211C2×C4—22no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—44no—
1219C2×C4—48no—
1220C2×C4—48no—
1221C2×C4—416no—
1222C2×C4—48no—
1223C2×C4—48no—
1224C2×C4—416no—
1225C2×C4—48no—
1226C2×C4—84no—
1227C2×C4—88no—
1228C2×C4—84no—
1229C2×C4—816no—
1230C2×C4C23×D412yes—
1231C2×C4C23×D414yes—
1232C2×C4C23×D412yes—
1233C2×C4C23×D414yes—
1234C2×C4C23×D412yes—
1235C2×C4C23×D412yes—
1236C2×C4C23×D414yes—
1237C2×C4C23×D412yes—
1238C2×C4C23×D412yes—
1239C2×C4#58514yes—
1240C2×C4#58514yes—
1241C22—22no—
1242C22—24no—
1243C22—24no—
1244C22—22no—
1245C22—22no—
1246C22—24no—
1247C22—44no—
1248C22—42no—
1249C22—44no—
1250C22—42no—
1251C22—44no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—44no—
1257C22—42no—
1258C22—44no—
1259C22—42no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—42no—
1265C22—42no—
1266C22—44no—
1267C22—42no—
1268C22—42no—
1269C22—44no—
1270C22—816no—
1271C22C24×D411yescharacteristic
1272C22C2×#58512yes—
1273C22C2×#58512yes—
1274C22H(7,𝔽2)11yescharacteristic
1275C222−1+611yescharacteristic
1276C4—22no—
1277C4—24no—
1278C4—22no—
1279C4—22no—
1280C4—24no—
1281C4—22no—
1282C4—24no—
1283C4—44no—
1284C4—42no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—44no—
1289C4—44no—
1290C4—44no—
1291C4—48no—
1292C4—42no—
1293C4—42no—
1294C4—44no—
1295C4#344914yes—
1296C4#350014yes—
1297C2—44no—
1298C2—42no—
1299C2—82no—
1300C2—82no—
1301C2—84no—
1302C2C2×#344911yescharacteristic
1303C2C2×#350011yescharacteristic
1304C2#6285311yescharacteristic
1305C2#6293612yes—
1306C2#6293812yes—
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×#3518C2semidirect
2. C2×#3460C2semidirect
3. #42987C2semidirect
4. #42979C2semidirect
5. #42915C2semidirect
6. #42908C2semidirect
7. #42158C2semidirect
8. #42156C2semidirect
9. #39469C2semidirect
10. #39468C2semidirect
11. #39125C2semidirect
12. #39124C2semidirect
13. #37845C2semidirect
14. #37844C2semidirect
15. #37560C2semidirect
16. #37550C2semidirect
17. #36745C2semidirect
18. #35675C2semidirect
19. #35297C2semidirect
20. #35236C2semidirect
21. #35234C2semidirect
22. #35180C2semidirect
23. #35169C2semidirect
24. #34946C2semidirect
25. #34911C2semidirect
26. #34127C2semidirect
28. C2×Q82C22semidirect
31. C2×#556C22semidirect
32. C2×#556C22semidirect
34. C2×#555C22semidirect
35. C2×D4×Q8C22semidirect
42. C2×#542C22semidirect
50. C2×#533C22semidirect
56. C2×#529C22semidirect
58. C2×#519C22semidirect
62. #2857C22semidirect
63. #2857C22semidirect
64. #2854C22semidirect
65. #2850C22semidirect
68. #2821C22semidirect
70. #2817C22semidirect
72. #2723C22semidirect
73. #2716C22semidirect
74. #2715C22semidirect
75. #2712C22semidirect
78. #2696C22semidirect
79. #2691C22semidirect
84. #2676C22semidirect
85. #2674C22semidirect
88. #2664C22semidirect
89. #2663C22semidirect
91. #2661C22semidirect
93. #2639C22semidirect
96. #2635C22semidirect
97. #2634C22semidirect
99. #2628C22semidirect
100. #2628C22semidirect
103. #2616C22semidirect
104. #2615C22semidirect
105. #2610C22semidirect
106. #2604C22semidirect
107. #2604C22semidirect
108. #2603C22semidirect
110. #2601C22semidirect
111. #2592C22semidirect
112. #2592C22semidirect
113. #2584C22semidirect
114. #2584C22semidirect
115. #2581C22semidirect
116. #2568C22semidirect
117. #2564C22semidirect
119. #2563C22semidirect
123. #2562C22semidirect
124. #2562C22semidirect
126. #2559C22semidirect
127. #2557C22semidirect
128. #2555C22semidirect
129. #2553C22semidirect
130. #2550C22semidirect
133. #2547C22semidirect
138. #2540C22semidirect
141. #2536C22semidirect
142. #2536C22semidirect
143. #2535C22semidirect
144. #2535C22semidirect
147. #2489C22semidirect
150. #2485C22semidirect
151. #2485C22semidirect
152. #2477C22semidirect
153. #2471C22semidirect
154. #2465C22semidirect
155. #2458C22semidirect
156. #2451C22semidirect
158. #2439C22semidirect
162. #2427C22semidirect
164. #2421C22semidirect
165. #2417C22semidirect
166. #2416C22semidirect
172. #2409C22semidirect
177. #2355C22semidirect
179. D4×C4⋊C4C22semidirect
181. #2343C22semidirect
184. #2324C22semidirect
185. #2323C22semidirect
186. #2323C22semidirect
187. #2311C22semidirect
188. #2311C22semidirect
190. C4×C22⋊Q8C22semidirect
191. C4×#121C22semidirect
192. #2295C22semidirect
193. #2293C22semidirect
196. #2283C22semidirect
198. C42×D4C22semidirect
200. C2×C4×C4⋊C4C22semidirect
314. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35182
C2×#34602
#429872
#429792
#429152
#429082
#421582
#421562
#394692
#394682
#391252
#391242
#378452
#378442
#375602
#375502
#367452
#356752
#352972
#352362
#352342
#351802
#351692
#349462
#349112
#341272