Finite Group Databasebeta

← #7656168

Subgroups — #7656168

Order 512.

7954 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3516C211yesmaximal, characteristic, complemented
2C2×#3497C211yesmaximal, characteristic, complemented
3#42880C213yesmaximal, complemented
4#42876C213yesmaximal, complemented
5#42792C213yesmaximal, complemented
6#42788C213yesmaximal, complemented
7#42434C216yesmaximal, complemented
8#42433C216yesmaximal, complemented
9#39954C216yesmaximal, complemented
10#39950C216yesmaximal, complemented
11#37559C213yesmaximal, complemented
12#37550C213yesmaximal, complemented
13#36467C212yesmaximal, complemented
14#36465C212yesmaximal, complemented
15#36029C211yesmaximal, characteristic, complemented
16#36018C211yesmaximal, characteristic, complemented
17#35757C212yesmaximal, complemented
18#35737C211yesmaximal, characteristic, complemented
19#35700C211yesmaximal, characteristic, complemented
20#35687C212yesmaximal, complemented
21#35191C213yesmaximal, complemented
22#34624C213yesmaximal, complemented
23#34128C211yesmaximal, characteristic, complemented
24C22×2−1+4C2212yes—
25#3516—216no—
26#3497—216no—
27C2×#557C2211yescharacteristic
28C2×#556C2213yes—
29C2×#554C2213yes—
30C2×#553C2213yes—
31C2×#552C2213yes—
32C2×#550C2213yes—
33C2×#550C2211yescharacteristic
34C2×#550C2212yes—
35C2×D4×Q8C2213yes—
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×D4×Q8C2212yes—
39C2×#548C2216yes—
40C2×#548C2212yes—
41C2×#548C2211yescharacteristic
42C2×#548C2211yescharacteristic
43C2×#548C2212yes—
44C2×#548C2212yes—
45C2×#542C2213yes—
46C2×#541C2213yes—
47C2×#537C2216yes—
48C2×#532C2213yes—
49C2×#532C2213yes—
50C2×#529C2213yes—
51C2×#529C2213yes—
52C2×#520C2211yescharacteristic
53C2×#519C2211yescharacteristic
54C22×C4×Q8C2211yescharacteristic
55#2861C2216yes—
56#2858C2216yes—
57#2821C2216yes—
58#2818C2216yes—
59#2816C2216yes—
60#2815C2216yes—
61#2723C22112yes—
62#2720C22112yes—
63#2714C22112yes—
64#2711C22112yes—
65#2696C22112yes—
66#2692C22112yes—
67#2676C22112yes—
68#2673C22112yes—
69#2662C2216yes—
70#2662C2216yes—
71#2661C2211yescharacteristic
72#2661C2213yes—
73#2661C2213yes—
74#2661C2213yes—
75#2661C2216yes—
76#2660C2213yes—
77#2657C2213yes—
78#2641C2213yes—
79#2640C2213yes—
80#2635C22112yes—
81#2633C2216yes—
82#2631C2216yes—
83#2621C2213yes—
84#2621C2213yes—
85#2620C2216yes—
86#2619C2216yes—
87#2619C2213yes—
88#2619C2213yes—
89#2616C2216yes—
90#2615C2216yes—
91#2610C22112yes—
92#2603C2216yes—
93#2603C2216yes—
94#2603C2216yes—
95#2603C2216yes—
96#2592C2216yes—
97#2562C2216yes—
98#2548C2213yes—
99#2547C2213yes—
100#2546C2213yes—
101#2542C2216yes—
102#2541C2216yes—
103#2541C2213yes—
104#2540C2216yes—
105#2540C2216yes—
106#2540C2216yes—
107#2540C2216yes—
108#2536C2213yes—
109#2536C2213yes—
110#2535C2213yes—
111#2535C2213yes—
112#2492C2216yes—
113#2491C2216yes—
114#2490C2216yes—
115#2489C2216yes—
116#2436C2216yes—
117#2434C2216yes—
118#2432C2216yes—
119#2432C2216yes—
120#2431C2216yes—
121#2431C2216yes—
122#2429C2216yes—
123#2428C2216yes—
124#2427C2216yes—
125#2426C2216yes—
126#2417C2216yes—
127#2416C2216yes—
128#2415C2216yes—
129#2414C2216yes—
130#2414C22112yes—
131#2409C2216yes—
132#2409C2216yes—
133#2407C2216yes—
134#2407C2216yes—
135#2407C2216yes—
136#2407C2216yes—
137#2392C2213yes—
138#2392C2213yes—
139#2392C2213yes—
140#2392C2213yes—
141#2388C2216yes—
142#2388C2216yes—
143#2356C2213yes—
144#2356C2213yes—
145#2351C2211yescharacteristic
146#2351C2211yescharacteristic
147#2344C2216yes—
148#2341C2212yes—
149#2341C2212yes—
150Q8×C22⋊C4C2212yes—
151Q8×C22⋊C4C2212yes—
152Q8×C22⋊C4C2212yes—
153#2324C22112yes—
154C4×#127C2216yes—
155C4×#124C2216yes—
156#2295C2216yes—
157#2283C2213yes—
158C42×Q8C2212yes—
159C4×#117C2213yes—
160C2×2−1+4—216no—
161C2×2−1+4—48no—
162C2×2−1+4—48no—
163C22×#41C2312yes—
164C22×#41C2311yescharacteristic
165C22×#41C2316yes—
166C22×#41C2316yes—
167C22×#41C2316yes—
168C23×Q8C2312yes—
169C23×Q8C2311yescharacteristic
170C23×Q8C2311yescharacteristic
171C23×Q8C2316yes—
172#557—28no—
173#556—224no—
174#554—224no—
175#553—224no—
176#552—224no—
177#550—28no—
178#550—224no—
179#550—48no—
180D4×Q8—28no—
181D4×Q8—28no—
182D4×Q8—224no—
183D4×Q8—48no—
184#548—28no—
185#548—216no—
186#548—248no—
187#548—28no—
188#548—48no—
189#548—48no—
190#542—224no—
191#541—224no—
192#537—248no—
193#532—224no—
194#532—224no—
195C2×C4⋊Q8C2313yes—
196C2×C4⋊Q8C2313yes—
197C2×C4⋊Q8C2313yes—
198C2×C4⋊Q8C2313yes—
199C2×C4⋊Q8C2316yes—
200C2×#127C2313yes—
201C2×#127C2313yes—
202C2×#127C2316yes—
203C2×#127C2316yes—
204#529—224no—
205#529—224no—
206C2×#126C2316yes—
207C2×#126C2313yes—
208C2×#126C2313yes—
209C2×#126C2316yes—
210C2×#125C2313yes—
211C2×#125C2313yes—
212C2×#125C2316yes—
213C2×#125C2313yes—
214C2×#124C2316yes—
215C2×#124C2313yes—
216C2×#124C2316yes—
217C2×#124C2313yes—
218C2×#124C2313yes—
219C2×#124C2316yes—
220C2×#124C2316yes—
221C2×#124C2316yes—
222C2×#123C2311yescharacteristic
223C2×#123C2313yes—
224C2×#123C2316yes—
225C2×C22⋊Q8C2313yes—
226C2×C22⋊Q8C2313yes—
227C2×C22⋊Q8C2313yes—
228C2×C22⋊Q8C2313yes—
229C2×C22⋊Q8C2316yes—
230C2×C22⋊Q8C2316yes—
231C2×C22⋊Q8C23112yes—
232C2×C22⋊Q8C2316yes—
233C2×C22⋊Q8C2313yes—
234C2×C22⋊Q8C2316yes—
235C2×C22⋊Q8C2316yes—
236C2×C22⋊Q8C2316yes—
237C2×C22⋊Q8C2316yes—
238C2×#121C2316yes—
239C2×#121C2313yes—
240C2×#121C2313yes—
241C2×#121C2316yes—
242C2×#121C2311yescharacteristic
243C2×#121C2313yes—
244C2×#121C2316yes—
245C2×#121C23112yes—
246C2×#121C2316yes—
247C2×#121C2313yes—
248C2×#121C23112yes—
249C2×#121C2316yes—
250C2×#121C2316yes—
251C2×#121C2316yes—
252C2×#121C2316yes—
253#520—28no—
254#519—28no—
255C2×C4×Q8D4116yescomplemented
256C2×C4×Q8C2313yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2313yes—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2313yes—
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2313yes—
267C2×C4×D4C2313yes—
268C2×C4×D4C2316yes—
269C2×C4×D4C2316yes—
270C2×C4×D4C2316yes—
271C2×C4×D4C2316yes—
272C2×C4×D4C2313yes—
273C2×C4×D4C2313yes—
274C2×C4×D4C2313yes—
275C2×C4×D4C2313yes—
276C2×C4×D4C2313yes—
277C2×C4×D4C2313yes—
278C2×C4×D4C2316yes—
279C2×C4×D4C2316yes—
280C2×C4×D4C2316yes—
281C2×C4×D4C2316yes—
282C2×#117C2316yes—
283C2×#117C2313yes—
284C2×#117C2313yes—
285C2×#117C2313yes—
286C2×#117C2316yes—
287C22×C4⋊C4C2313yes—
288C22×C4⋊C4C2313yes—
289C22×C42C2313yes—
290#400C23112yes—
291#399C23112yes—
292#399C23112yes—
293#398C2316yes—
294#398C2316yes—
295#398C2313yes—
296#398C2316yes—
297#398C2313yes—
298#398C2313yes—
299#398C2311yescharacteristic
300#397C2313yes—
301#397C2316yes—
302#397C23112yes—
303#397C2313yes—
304#397C2316yes—
305#397C2316yes—
306#397C2313yes—
307#397C2311yescharacteristic
308#396C2316yes—
309#396C2316yes—
310#396C2316yes—
311#396C2316yes—
312#395C23112yes—
313#395C2316yes—
314#395C2316yes—
315#394C2316yes—
316#394C2316yes—
317#394C2316yes—
318#394C23112yes—
319#394C23112yes—
320#394C2313yes—
321#394C2316yes—
322#394C23112yes—
323#394C2313yes—
324#394C2316yes—
325#394C2313yes—
326#394C2316yes—
327#394C2316yes—
328#394C2316yes—
329#394C2316yes—
330#394C2312yes—
331#394C2316yes—
332#394C2311yescharacteristic
333#394C2316yes—
334#394C2316yes—
335#393C23112yes—
336#393C23112yes—
337#393C2316yes—
338#393C2316yes—
339#392C2313yes—
340#392C2316yes—
341#392C23112yes—
342#392C23112yes—
343#392C2313yes—
344#392C2316yes—
345#392C2316yes—
346#392C2316yes—
347#392C23112yes—
348#392C2312yes—
349#392C2313yes—
350#392C2316yes—
351#392C2316yes—
352#392C23112yes—
353#392C2316yes—
354#392C2316yes—
355#392C2311yescharacteristic
356#391C2316yes—
357#391C2316yes—
358#391C2316yes—
359#391C2316yes—
360#391C2316yes—
361#391C2316yes—
362#391C2316yes—
363#390C2312yes—
364#390C2316yes—
365#390C2316yes—
366#390C2316yes—
367#390C2316yes—
368#390C2316yes—
369#390C23112yes—
370#390C23112yes—
371#390C2316yes—
372#390C2316yes—
373#390C2316yes—
374#390C2316yes—
375#390C23112yes—
376#390C23112yes—
377#390C2316yes—
378#389C23112yes—
379#389C2316yes—
380#389C2316yes—
381#388C2316yes—
382#388C23112yes—
383#388C2316yes—
384#388C2316yes—
385#388C23112yes—
386#388C23112yes—
387#388C23112yes—
388#388C23112yes—
389#388C2312yes—
390#387C23112yes—
391#387C23112yes—
392#386C23112yes—
393#386C23112yes—
394#386C23112yes—
395#386C23112yes—
396#386C23112yes—
397#386C23112yes—
398#385C23112yes—
399#385C23112yes—
400#385C23112yes—
401#385C23112yes—
402#384C2316yes—
403#383C2316yes—
404#382C2313yes—
405#382C2313yes—
406#382C2316yes—
407#381C2316yes—
408#380C2316yes—
409#380C2316yes—
410#380C2316yes—
411#380C2316yes—
412#380C23112yes—
413#380C2316yes—
414C4×C4⋊C4C2316yes—
415C4×C4⋊C4C2316yes—
416C4×C4⋊C4C2316yes—
417C4×C4⋊C4C2316yes—
418C4×C4⋊C4C2313yes—
419C4×C4⋊C4C2313yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C2311yescharacteristic
426C4×C22⋊C4C2313yes—
427#376C2316yes—
428#376C2313yes—
429#376C2313yes—
430C43C2316yes—
4312−1+4—4128no—
432C2×#41—24no—
433C2×#41—224no—
434C2×#41—28no—
435C2×#41—24no—
436C2×#41—28no—
437C2×#41—24no—
438C2×#41—28no—
439C2×#41—224no—
440C2×#41—224no—
441C2×#41—412no—
442C2×#41—412no—
443C2×#41—412no—
444C2×#41—412no—
445C2×#41—412no—
446C2×#41—412no—
447C22×Q8—24no—
448C22×Q8—24no—
449C22×Q8—24no—
450C22×Q8—224no—
451C22×Q8—28no—
452C22×Q8—24no—
453C22×Q8—28no—
454C22×Q8—24no—
455C22×Q8—28no—
456C22×Q8—412no—
457C22×Q8—412no—
458C22×Q8C2×D418yes—
459C22×Q8C2413yes—
460C22×Q8C2416yes—
461C22×Q8C2413yes—
462C22×Q8C2413yes—
463C22×Q8C2416yes—
464C22×Q8C2411yescharacteristic
465C22×D4C2413yes—
466C22×D4C2416yes—
467C22×D4C2413yes—
468C22×D4C2411yescharacteristic
469C22×D4C2413yes—
470C22×D4C2411yescharacteristic
471C22×D4C2412yes—
472C22×D4C2416yes—
473C22×D4C2416yes—
474C22×D4C2413yes—
475C22×D4C2416yes—
476C22×D4C2416yes—
477C22×D4C2412yes—
478C22×D4C2416yes—
479C22×D4C2416yes—
480C22×D4C2416yes—
481C22×D4C24112yes—
482C23×C4C2413yes—
483C23×C4C2413yes—
484C23×C4C2416yes—
485C23×C4C2416yes—
486C23×C4C2413yes—
487C23×C4C2416yes—
488C23×C4C24112yes—
489C23×C4C2413yes—
490C23×C4C2411yescharacteristic
491C4⋊Q8—212no—
492C4⋊Q8—212no—
493C4⋊Q8—212no—
494C4⋊Q8—212no—
495C4⋊Q8—412no—
496#127—212no—
497#127—212no—
498#127—412no—
499#127—412no—
500#126—224no—
501#126—224no—
502#126—212no—
503#126—212no—
504#125—224no—
505#125—212no—
506#125—212no—
507#125—212no—
508#124—212no—
509#124—212no—
510#124—212no—
511#124—224no—
512#124—224no—
513#124—412no—
514#124—412no—
515#124—412no—
516#123—24no—
517#123—212no—
518#123—224no—
519C22⋊Q8—212no—
520C22⋊Q8—212no—
521C22⋊Q8—212no—
522C22⋊Q8—212no—
523C22⋊Q8—224no—
524C22⋊Q8—224no—
525C22⋊Q8—248no—
526C22⋊Q8—212no—
527C22⋊Q8—224no—
528C22⋊Q8—412no—
529C22⋊Q8—412no—
530C22⋊Q8—412no—
531C22⋊Q8—412no—
532#121—212no—
533#121—212no—
534#121—24no—
535#121—212no—
536#121—224no—
537#121—224no—
538#121—224no—
539#121—224no—
540#121—248no—
541#121—212no—
542#121—424no—
543#121—412no—
544#121—412no—
545#121—412no—
546#121—412no—
547C4×Q8—24no—
548C4×Q8—24no—
549C4×Q8—28no—
550C4×Q8—28no—
551C4×Q8—212no—
552C4×Q8—212no—
553C4×Q8—212no—
554C4×Q8C2×D418yes—
555C4×Q8C2×D4124yes—
556C4×Q8C2×D418yes—
557C4×Q8C2×D4124yes—
558C4×D4—212no—
559C4×D4—212no—
560C4×D4—224no—
561C4×D4—212no—
562C4×D4—212no—
563C4×D4—212no—
564C4×D4—224no—
565C4×D4—224no—
566C4×D4—212no—
567C4×D4—212no—
568C4×D4—224no—
569C4×D4—412no—
570C4×D4—412no—
571C4×D4—412no—
572C4×D4—412no—
573#117—212no—
574#117—212no—
575#117—212no—
576#117—224no—
577#117—412no—
578C2×C4⋊C4—212no—
579C2×C4⋊C4C2×D4124yes—
580C2×C4⋊C4C2413yes—
581C2×C4⋊C4C2413yes—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C2413yes—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2413yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C2416yes—
589C2×C4⋊C4C2413yes—
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C2416yes—
593C2×C4⋊C4C2413yes—
594C2×C4⋊C4C2413yes—
595C2×C4⋊C4C2416yes—
596C2×C4⋊C4C2413yes—
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2416yes—
599C2×C4⋊C4C2416yes—
600C2×C4⋊C4C2413yes—
601C2×C4⋊C4C2416yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2416yes—
604C2×C4⋊C4C2416yes—
605C2×C4⋊C4C2416yes—
606C2×C4⋊C4C24112yes—
607C2×C4⋊C4C2413yes—
608C2×C4⋊C4C2413yes—
609C2×C4⋊C4C2416yes—
610C2×C22⋊C4C2413yes—
611C2×C22⋊C4C2411yescharacteristic
612C2×C22⋊C4C2412yes—
613C2×C22⋊C4C2413yes—
614C2×C22⋊C4C2413yes—
615C2×C22⋊C4C2413yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2411yescharacteristic
620C2×C22⋊C4C2413yes—
621C2×C22⋊C4C2411yescharacteristic
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C24112yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2413yes—
627C2×C22⋊C4C2413yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C2416yes—
635C2×C22⋊C4C2416yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C2416yes—
638C2×C22⋊C4C2416yes—
639C2×C22⋊C4C24112yes—
640C2×C22⋊C4C24112yes—
641C2×C22⋊C4C24112yes—
642C2×C22⋊C4C2416yes—
643C2×C22⋊C4C2416yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2416yes—
646C2×C22⋊C4C2416yes—
647C2×C22⋊C4C2416yes—
648C2×C22⋊C4C24112yes—
649C2×C42C2×D4124yes—
650C2×C42C2416yes—
651C2×C42C2413yes—
652C2×C42C2413yes—
653C2×C42C2416yes—
654C2×C42C2416yes—
655C2×C42C2416yes—
656C2×C42C2416yes—
657C2×C42C2412yes—
658C2×C42C2416yes—
659C2×C42C2413yes—
660C2×C42C2413yes—
661C2×C42C2413yes—
662C2×C42C2413yes—
663#95C2411yescharacteristic
664#95C2411yescharacteristic
665#95C2413yes—
666#95C2413yes—
667#95C2416yes—
668#95C2416yes—
669#95C24112yes—
670#95C2416yes—
671#95C2416yes—
672#95C2412yes—
673#95C2412yes—
674#95C2416yes—
675#95C2416yes—
676#95C2416yes—
677#95C2416yes—
678#95C2416yes—
679#95C2416yes—
680#95C24112yes—
681#95C24112yes—
682#95C24112yes—
683C24C2511yescharacteristic
684C24C2513yes—
685C24C2512yes—
686C24C2516yes—
687C24C2511yescharacteristic
688#41—496no—
689#41—496no—
690#41—496no—
691#41—416no—
692#41—432no—
693C2×Q8—232no—
694C2×Q8—26no—
695C2×Q8—212no—
696C2×Q8—212no—
697C2×Q8—26no—
698C2×Q8—26no—
699C2×Q8—26no—
700C2×Q8—26no—
701C2×Q8—26no—
702C2×Q8—212no—
703C2×Q8—212no—
704C2×Q8—46no—
705C2×Q8—46no—
706C2×Q8—46no—
707C2×Q8—496no—
708C2×Q8—416no—
709C2×Q8—432no—
710C2×Q8C22×D4112yes—
711C2×Q8C22×D414yes—
712C2×Q8H(5,𝔽2)14yes—
713C2×Q8H(5,𝔽2)14yes—
714C2×D4—26no—
715C2×D4—22no—
716C2×D4—212no—
717C2×D4—24no—
718C2×D4—22no—
719C2×D4—26no—
720C2×D4—26no—
721C2×D4—212no—
722C2×D4—212no—
723C2×D4—212no—
724C2×D4—212no—
725C2×D4—26no—
726C2×D4—26no—
727C2×D4—26no—
728C2×D4—212no—
729C2×D4—212no—
730C2×D4—24no—
731C2×D4—212no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—46no—
736C2×D4—42no—
737C2×D4—46no—
738C2×D4—46no—
739C2×D4—46no—
740C2×D4—42no—
741C2×D4—46no—
742C2×D4—42no—
743C2×D4—46no—
744C2×D4—46no—
745C2×D4—46no—
746C2×D4—46no—
747C2×D4—412no—
748C2×D4—46no—
749C2×D4—46no—
750C2×D4—46no—
751C2×D4—46no—
752C2×D4—46no—
753C2×D4—46no—
754C2×D4—46no—
755C2×D4—46no—
756C2×D4—412no—
757C2×D4—412no—
758C2×D4—412no—
759C22×C4—26no—
760C22×C4—26no—
761C22×C4—26no—
762C22×C4—26no—
763C22×C4—224no—
764C22×C4—212no—
765C22×C4—212no—
766C22×C4—26no—
767C22×C4—26no—
768C22×C4—26no—
769C22×C4—26no—
770C22×C4—212no—
771C22×C4—212no—
772C22×C4—212no—
773C22×C4—212no—
774C22×C4—212no—
775C22×C4—46no—
776C22×C4—42no—
777C22×C4—412no—
778C22×C4—412no—
779C22×C4—412no—
780C22×C4C22×D4112yes—
781C22×C4C22×D414yes—
782C22×C4C22×D4112yes—
783C22×C4C2516yes—
784C22×C4C2516yes—
785C22×C4C2512yes—
786C22×C4C2511yescharacteristic
787C22×C4C2511yescharacteristic
788C22×C4C2513yes—
789C22×C4C2513yes—
790C22×C4C2512yes—
791C22×C4C2516yes—
792C22×C4C2513yes—
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C22×C4C2513yes—
796C22×C4C2513yes—
797C22×C4C2513yes—
798C22×C4C2511yescharacteristic
799C22×C4C2512yes—
800C22×C4C2513yes—
801C4⋊C4—26no—
802C4⋊C4—26no—
803C4⋊C4—22no—
804C4⋊C4—26no—
805C4⋊C4—26no—
806C4⋊C4—26no—
807C4⋊C4—26no—
808C4⋊C4—212no—
809C4⋊C4—26no—
810C4⋊C4—22no—
811C4⋊C4—212no—
812C4⋊C4—212no—
813C4⋊C4—26no—
814C4⋊C4—26no—
815C4⋊C4—212no—
816C4⋊C4—26no—
817C4⋊C4—22no—
818C4⋊C4—26no—
819C4⋊C4—212no—
820C4⋊C4—212no—
821C4⋊C4—212no—
822C4⋊C4—46no—
823C4⋊C4—42no—
824C4⋊C4—46no—
825C4⋊C4—46no—
826C4⋊C4—46no—
827C4⋊C4—412no—
828C4⋊C4C22×D4112yes—
829C4⋊C4C22×D4112yes—
830C4⋊C4C22×D4124yes—
831C22⋊C4—22no—
832C22⋊C4—26no—
833C22⋊C4—26no—
834C22⋊C4—22no—
835C22⋊C4—26no—
836C22⋊C4—26no—
837C22⋊C4—26no—
838C22⋊C4—212no—
839C22⋊C4—24no—
840C22⋊C4—212no—
841C22⋊C4—22no—
842C22⋊C4—212no—
843C22⋊C4—212no—
844C22⋊C4—224no—
845C22⋊C4—212no—
846C22⋊C4—26no—
847C22⋊C4—26no—
848C22⋊C4—24no—
849C22⋊C4—212no—
850C22⋊C4—24no—
851C22⋊C4—42no—
852C22⋊C4—46no—
853C22⋊C4—46no—
854C22⋊C4—46no—
855C22⋊C4—412no—
856C22⋊C4—46no—
857C22⋊C4—42no—
858C22⋊C4—42no—
859C22⋊C4—46no—
860C22⋊C4—46no—
861C22⋊C4—46no—
862C22⋊C4—46no—
863C22⋊C4—46no—
864C22⋊C4—46no—
865C22⋊C4—412no—
866C22⋊C4—412no—
867C22⋊C4—412no—
868C22⋊C4—46no—
869C22⋊C4—46no—
870C42—212no—
871C42—26no—
872C42—26no—
873C42—212no—
874C42—212no—
875C42—212no—
876C42—42no—
877C42—46no—
878C42—46no—
879C42C22×D4112yes—
880C42C22×D4112yes—
881C42C22×D4112yes—
882C42C22×D4112yes—
883C23—21no—
884C23—21no—
885C23—22no—
886C23—22no—
887C23—23no—
888C23—21no—
889C23—22no—
890C23—26no—
891C23—21no—
892C23—23no—
893C23—22no—
894C23—26no—
895C23—21no—
896C23—23no—
897C23—22no—
898C23—26no—
899C23—22no—
900C23—26no—
901C23—26no—
902C23—26no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—26no—
907C23—26no—
908C23—22no—
909C23—22no—
910C23—26no—
911C23C23×D412yes—
912C23C2611yescharacteristic
913Q8—224no—
914Q8—424no—
915Q8—412no—
916Q8—424no—
917Q8—86no—
918Q8#535116yes—
919D4—44no—
920D4—412no—
921D4—48no—
922D4—424no—
923D4—412no—
924D4—44no—
925D4—48no—
926D4—424no—
927D4—412no—
928D4—424no—
929D4—812no—
930D4—86no—
931D4—812no—
932D4—812no—
933D4—812no—
934D4—812no—
935D4—1612no—
936C2×C4—22no—
937C2×C4—23no—
938C2×C4—23no—
939C2×C4—26no—
940C2×C4—26no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—224no—
945C2×C4—21no—
946C2×C4—23no—
947C2×C4—21no—
948C2×C4—23no—
949C2×C4—23no—
950C2×C4—22no—
951C2×C4—26no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—26no—
955C2×C4—26no—
956C2×C4—21no—
957C2×C4—23no—
958C2×C4—22no—
959C2×C4—26no—
960C2×C4—21no—
961C2×C4—23no—
962C2×C4—22no—
963C2×C4—26no—
964C2×C4—26no—
965C2×C4—22no—
966C2×C4—26no—
967C2×C4—26no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—26no—
971C2×C4—26no—
972C2×C4—22no—
973C2×C4—26no—
974C2×C4—412no—
975C2×C4—44no—
976C2×C4—448no—
977C2×C4—412no—
978C2×C4—424no—
979C2×C4—424no—
980C2×C4—412no—
981C2×C4—812no—
982C2×C4C23×D416yes—
983C2×C4C23×D412yes—
984C2×C4C23×D412yes—
985C2×C4C23×D416yes—
986C2×C4C23×D416yes—
987C2×C4C23×D416yes—
988C2×C4C2×H(5,𝔽2)16yes—
989C2×C4C2×H(5,𝔽2)16yes—
990C2×C4#58514yes—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—42no—
995C22—42no—
996C22—43no—
997C22—41no—
998C22—42no—
999C22—46no—
1000C22—42no—
1001C22—46no—
1002C22—43no—
1003C22—41no—
1004C22—42no—
1005C22—42no—
1006C22—46no—
1007C22—46no—
1008C22—46no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—46no—
1013C22—46no—
1014C22—46no—
1015C22—42no—
1016C22—46no—
1017C22—42no—
1018C22—41no—
1019C22—43no—
1020C22C24×D411yescharacteristic
1021C22C22×H(5,𝔽2)11yescharacteristic
1022C22C22×H(5,𝔽2)11yescharacteristic
1023C22C2×#58512yes—
1024C222−1+612yes—
1025C4—26no—
1026C4—26no—
1027C4—22no—
1028C4—22no—
1029C4—24no—
1030C4—26no—
1031C4—43no—
1032C4—41no—
1033C4—43no—
1034C4—41no—
1035C4—46no—
1036C4—42no—
1037C4—46no—
1038C4—41no—
1039C4—42no—
1040C4—46no—
1041C4—43no—
1042C4C2×#535112yes—
1043C2—42no—
1044C2—83no—
1045C2—81no—
1046C2—82no—
1047C2—86no—
1048C2C22×#53511yescharacteristic
1049C2#6281211yescharacteristic
1050C2#6284811yescharacteristic
1051C2#6291912yes—
1052C2#6292212yes—
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×#3516C2semidirect
2. C2×#3497C2semidirect
3. #42880C2semidirect
4. #42876C2semidirect
5. #42792C2semidirect
6. #42788C2semidirect
7. #42434C2semidirect
8. #42433C2semidirect
9. #39954C2semidirect
10. #39950C2semidirect
11. #37559C2semidirect
12. #37550C2semidirect
13. #36467C2semidirect
14. #36465C2semidirect
15. #36029C2semidirect
16. #36018C2semidirect
17. #35757C2semidirect
18. #35737C2semidirect
19. #35700C2semidirect
20. #35687C2semidirect
21. #35191C2semidirect
22. #34624C2semidirect
23. #34128C2semidirect
255. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35162
C2×#34972
#428802
#428762
#427922
#427882
#424342
#424332
#399542
#399502
#375592
#375502
#364672
#364652
#360292
#360182
#357572
#357372
#357002
#356872
#351912
#346242
#341282