Finite Group Databasebeta

← #7689672

Subgroups — #7689672

Order 512.

8086 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3522C211yesmaximal, characteristic, complemented
2C2×#3483C211yesmaximal, characteristic, complemented
3#59652C213yesmaximal, complemented
4#59057C213yesmaximal, complemented
5#59056C213yesmaximal, complemented
6#59051C216yesmaximal, complemented
7#44933C216yesmaximal, complemented
8#44897C216yesmaximal, complemented
9#39745C213yesmaximal, complemented
10#39138C213yesmaximal, complemented
11#37772C216yesmaximal, complemented
12#36592C211yesmaximal, characteristic, complemented
13#36576C211yesmaximal, characteristic, complemented
14#36493C213yesmaximal, complemented
15#36455C211yesmaximal, characteristic, complemented
16#36430C212yesmaximal, complemented
17#36128C213yesmaximal, complemented
18#36066C212yesmaximal, complemented
19#36029C212yesmaximal, complemented
20#34727C213yesmaximal, complemented
21#34335C211yesmaximal, characteristic, complemented
22#34295C212yesmaximal, complemented
23C4×#548C211yesmaximal, characteristic, complemented
24#3522—216no—
25#3483—216no—
26C2×#559C2213yes—
27C2×Q82C2211yescharacteristic
28C2×#555C2213yes—
29C2×#555C2216yes—
30C2×#554C2213yes—
31C2×#550C2213yes—
32C2×#550C2211yescharacteristic
33C2×#550C2212yes—
34C2×#550C2211yescharacteristic
35C2×#550C2212yes—
36C2×#550C2216yes—
37C2×#550C2212yes—
38C2×#550C2212yes—
39C2×#548C2212yes—
40C2×#548C2211yescharacteristic
41C2×#548C2212yes—
42C2×#547C2216yes—
43C2×#542C2216yes—
44C2×#532C2213yes—
45C2×#532C2213yes—
46C2×#532C2216yes—
47C2×#529C2213yes—
48C2×#520C2212yes—
49C2×C4×#41C2212yes—
50C2×C4×#41C2211yescharacteristic
51C2×C4×#41C2213yes—
52C22×C4×Q8C2211yescharacteristic
53#2867C2213yes—
54#2856C2213yes—
55#2856C2213yes—
56#2850C2216yes—
57#2733C22112yes—
58#2730C22112yes—
59#2730C22112yes—
60#2714C22112yes—
61#2673C22112yes—
62#2673C22112yes—
63#2673C22112yes—
64#2657C2216yes—
65#2619C2216yes—
66#2548C2216yes—
67#2548C2213yes—
68#2544C2216yes—
69#2541C2216yes—
70#2541C2216yes—
71#2541C2213yes—
72#2541C2216yes—
73#2541C2216yes—
74#2541C2216yes—
75#2541C2213yes—
76#2541C2216yes—
77#2541C2216yes—
78#2541C2213yes—
79#2540C2216yes—
80#2540C2216yes—
81#2540C2216yes—
82#2538C2213yes—
83#2537C2213yes—
84#2535C2216yes—
85#2535C2216yes—
86#2490C2216yes—
87#2479C2216yes—
88#2471C22112yes—
89#2471C2216yes—
90#2467C2216yes—
91#2456C22112yes—
92#2456C2216yes—
93#2454C2213yes—
94#2448C2213yes—
95#2441C2213yes—
96#2431C2216yes—
97#2431C2216yes—
98#2431C2213yes—
99#2431C2216yes—
100#2431C22112yes—
101#2428C2216yes—
102#2428C2213yes—
103#2428C2216yes—
104#2428C2216yes—
105#2428C2216yes—
106#2428C2216yes—
107#2428C2216yes—
108#2427C2216yes—
109#2426C22112yes—
110#2426C2216yes—
111#2423C2211yescharacteristic
112#2416C2216yes—
113#2416C2216yes—
114#2416C2216yes—
115#2415C2216yes—
116#2414C2216yes—
117#2414C2216yes—
118#2414C2213yes—
119#2407C22112yes—
120#2407C2213yes—
121#2397C2216yes—
122#2392C2216yes—
123#2369C2213yes—
124#2367C2213yes—
125#2366C2216yes—
126#2366C2216yes—
127#2365C2216yes—
128#2363C2216yes—
129#2363C2216yes—
130#2362C2213yes—
131#2361C2213yes—
132#2361C2216yes—
133#2355C2213yes—
134#2352C2216yes—
135#2352C2213yes—
136#2351C2212yes—
137#2351C2211yescharacteristic
138Q8×C4⋊C4C2211yescharacteristic
139#2341C2212yes—
140#2341C2211yescharacteristic
141#2341C2212yes—
142Q8×C22⋊C4C2211yescharacteristic
143#2331C2216yes—
144#2328C2216yes—
145#2324C2216yes—
146C4×C4⋊Q8C2213yes—
147C4×#127C2213yes—
148C4×#124C2213yes—
149C4×C22⋊Q8C2213yes—
150C4×#121C2216yes—
151C4×#121C2213yes—
152C4×#121C2213yes—
153C4×#121C2216yes—
154C4×#121C2213yes—
155#2295C2213yes—
156#2290C2216yes—
157#2276C2212yes—
158C42×Q8C2211yescharacteristic
159C42×D4C2213yes—
160C22×#41C2311yescharacteristic
161C22×#41C2312yes—
162C22×#41C2312yes—
163C22×#41C2313yes—
164C22×#41C2316yes—
165C22×#41C2316yes—
166C23×Q8C2311yescharacteristic
167#559—224no—
168Q82D4116yescomplemented
169#555—224no—
170#555—248no—
171#554—224no—
172#550—28no—
173#550—216no—
174#550—224no—
175#550—28no—
176#550—216no—
177#550—424no—
178#550—48no—
179#550—48no—
180#548—216no—
181#548—28no—
182#548—48no—
183#547—248no—
184#542—248no—
185#532—224no—
186#532—248no—
187#532—224no—
188C2×C4⋊Q8C2313yes—
189C2×C4⋊Q8C2316yes—
190C2×#127C2316yes—
191C2×#127C2313yes—
192C2×#127C2313yes—
193C2×#127C2316yes—
194C2×#127C2313yes—
195C2×#127C2316yes—
196C2×#127C2316yes—
197C2×#127C2316yes—
198C2×#127C2316yes—
199C2×#127C23112yes—
200C2×#127C2316yes—
201#529—224no—
202C2×#126C2316yes—
203C2×#125C2313yes—
204C2×#124C2316yes—
205C2×#124C2313yes—
206C2×#124C2313yes—
207C2×#124C23112yes—
208C2×#124C2316yes—
209C2×#124C2316yes—
210C2×#124C2316yes—
211C2×#123C2316yes—
212C2×#123C23112yes—
213C2×C22⋊Q8C2313yes—
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C23112yes—
216C2×C22⋊Q8C2316yes—
217C2×C22⋊Q8C2316yes—
218C2×#121C2316yes—
219C2×#121C2313yes—
220C2×#121C2316yes—
221C2×#121C2313yes—
222C2×#121C2316yes—
223C2×#121C2316yes—
224C2×#121C2316yes—
225C2×#121C2316yes—
226C2×#121C2316yes—
227C2×#121C23112yes—
228C2×#121C2316yes—
229C2×#121C2316yes—
230C2×#121C2316yes—
231C2×#121C2313yes—
232C2×#121C2316yes—
233C2×#121C2316yes—
234C2×#121C2316yes—
235C2×#121C2316yes—
236C2×#121C2316yes—
237C2×#121C2316yes—
238C2×#121C2316yes—
239C2×#121C2313yes—
240C2×#121C23112yes—
241C2×#121C23112yes—
242#520—216no—
243C4×#41—28no—
244C4×#41—216no—
245C4×#41—224no—
246C2×C4×Q8—28no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2313yes—
252C2×C4×Q8C2313yes—
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2316yes—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2313yes—
258C2×C4×Q8C2311yescharacteristic
259C2×C4×D4C2316yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2316yes—
264C2×C4×D4C2313yes—
265C2×C4×D4C2313yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2313yes—
268C2×C4×D4C2316yes—
269C2×C4×D4C2316yes—
270C2×C4×D4C2313yes—
271C2×C4×D4C2316yes—
272C2×C4×D4C2316yes—
273C2×C4×D4C2316yes—
274C2×C4×D4C2313yes—
275C2×C4×D4C2316yes—
276C2×C4×D4C23112yes—
277C2×C4×D4C2316yes—
278C2×C4×D4C2316yes—
279C2×C4×D4C2313yes—
280C2×#117C2316yes—
281C2×#117C2313yes—
282C2×#117C2316yes—
283C2×#117C2313yes—
284C2×#117C2316yes—
285C22×C4⋊C4C2313yes—
286C22×C4⋊C4C2316yes—
287C22×C42C2316yes—
288C22×C42C2313yes—
289C22×C42C2313yes—
290#399C2312yes—
291#399C2316yes—
292#399C2316yes—
293#399C2316yes—
294#398C2312yes—
295#397C2316yes—
296#397C23112yes—
297#396C2316yes—
298#396C2316yes—
299#396C23112yes—
300#394C2316yes—
301#394C23112yes—
302#394C2316yes—
303#394C2316yes—
304#394C23112yes—
305#394C23112yes—
306#394C23112yes—
307#394C23112yes—
308#392C23112yes—
309#392C23112yes—
310#392C2316yes—
311#392C2316yes—
312#392C2316yes—
313#392C2316yes—
314#392C2316yes—
315#392C23112yes—
316#392C23112yes—
317#392C23112yes—
318#392C23112yes—
319#392C23112yes—
320#392C23112yes—
321#392C23112yes—
322#391C2316yes—
323#391C23112yes—
324#391C2313yes—
325#391C2313yes—
326#391C2313yes—
327#391C2311yescharacteristic
328#390C2313yes—
329#390C2313yes—
330#390C2316yes—
331#390C2316yes—
332#390C2316yes—
333#390C23112yes—
334#390C2316yes—
335#390C2316yes—
336#390C2316yes—
337#390C2313yes—
338#390C2313yes—
339#390C2313yes—
340#390C2316yes—
341#390C2316yes—
342#390C2316yes—
343#390C23112yes—
344#390C23112yes—
345#390C23112yes—
346#390C2316yes—
347#390C2313yes—
348#389C2313yes—
349#389C2316yes—
350#389C2313yes—
351#389C2316yes—
352#389C2316yes—
353#389C2313yes—
354#389C2313yes—
355#389C2313yes—
356#389C2316yes—
357#389C2311yescharacteristic
358#388C23112yes—
359#388C2316yes—
360#388C23112yes—
361#388C2316yes—
362#388C2316yes—
363#388C2316yes—
364#388C2316yes—
365#388C2316yes—
366#388C2312yes—
367#388C2316yes—
368#388C2316yes—
369#387C2316yes—
370#387C23112yes—
371#387C2316yes—
372#387C2316yes—
373#387C2316yes—
374#387C2312yes—
375#386C23112yes—
376#386C2316yes—
377#386C23112yes—
378#386C23112yes—
379#386C23112yes—
380#386C23112yes—
381#386C2316yes—
382#386C23112yes—
383#386C2316yes—
384#386C23112yes—
385#386C2316yes—
386#386C2316yes—
387#386C2316yes—
388#386C2316yes—
389#385C2316yes—
390#385C2316yes—
391#385C2316yes—
392#384C2311yescharacteristic
393#384C2313yes—
394#382C2313yes—
395#382C2316yes—
396#380C2316yes—
397#380C2313yes—
398#380C2313yes—
399#380C2316yes—
400#380C2316yes—
401#380C2313yes—
402#380C2311yescharacteristic
403C4×C4⋊C4C2316yes—
404C4×C4⋊C4C2316yes—
405C4×C4⋊C4C2316yes—
406C4×C4⋊C4C2313yes—
407C4×C4⋊C4C2313yes—
408C4×C4⋊C4C2316yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2313yes—
411C4×C4⋊C4C2313yes—
412C4×C4⋊C4C2316yes—
413C4×C4⋊C4C2313yes—
414C4×C4⋊C4C2313yes—
415C4×C22⋊C4C2313yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2313yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2313yes—
420C4×C22⋊C4C23112yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2313yes—
423C4×C22⋊C4C2311yescharacteristic
424C4×C22⋊C4C2313yes—
425#376C2316yes—
426C43C2313yes—
427C2×#41—212no—
428C2×#41—24no—
429C2×#41—28no—
430C2×#41—28no—
431C2×#41—224no—
432C2×#41—224no—
433C2×#41—24no—
434C2×#41—28no—
435C2×#41—28no—
436C2×#41—28no—
437C2×#41—24no—
438C2×#41—28no—
439C2×#41—412no—
440C2×#41—412no—
441C2×#41—46no—
442C2×#41—46no—
443C2×#41—86no—
444C2×#41—86no—
445C22×Q8—24no—
446C22×Q8—24no—
447C22×Q8—24no—
448C22×Q8C2413yes—
449C22×Q8C2411yescharacteristic
450C22×Q8C2416yes—
451C22×Q8C2411yescharacteristic
452C22×D4C2413yes—
453C22×D4C2416yes—
454C22×D4C2413yes—
455C22×D4C2416yes—
456C22×D4C2413yes—
457C22×D4C2413yes—
458C22×D4C2416yes—
459C22×D4C2416yes—
460C22×D4C2416yes—
461C22×D4C2416yes—
462C22×D4C24112yes—
463C22×D4C2416yes—
464C22×D4C24112yes—
465C22×D4C2416yes—
466C22×D4C2416yes—
467C22×D4C2416yes—
468C22×D4C24112yes—
469C22×D4C24112yes—
470C23×C4C2416yes—
471C23×C4C2413yes—
472C23×C4C2416yes—
473C23×C4C2413yes—
474C23×C4C2413yes—
475C23×C4C2411yescharacteristic
476C23×C4C2413yes—
477C23×C4C2416yes—
478C23×C4C2413yes—
479C23×C4C24112yes—
480C23×C4C2416yes—
481C4⋊Q8C2×D4124yes—
482C4⋊Q8C2×D4148yes—
483#127—212no—
484#127—224no—
485#127—212no—
486#127—224no—
487#127—412no—
488#127—46no—
489#127—412no—
490#127—412no—
491#127—412no—
492#127—424no—
493#127—86no—
494#126—224no—
495#125—212no—
496#124—212no—
497#124—224no—
498#124—248no—
499#124—224no—
500#124—224no—
501#124—212no—
502#124—412no—
503#123—224no—
504#123—248no—
505C22⋊Q8—24no—
506C22⋊Q8—248no—
507C22⋊Q8—224no—
508C22⋊Q8—212no—
509C22⋊Q8—412no—
510#121—212no—
511#121—224no—
512#121—224no—
513#121—224no—
514#121—224no—
515#121—224no—
516#121—248no—
517#121—224no—
518#121—212no—
519#121—224no—
520#121—224no—
521#121—224no—
522#121—412no—
523#121—424no—
524#121—46no—
525#121—46no—
526#121—412no—
527#121—412no—
528#121—412no—
529#121—412no—
530#121—412no—
531#121—412no—
532#121—412no—
533#121—812no—
534C4×Q8—24no—
535C4×Q8—24no—
536C4×Q8—24no—
537C4×Q8—28no—
538C4×Q8—24no—
539C4×Q8—212no—
540C4×Q8—212no—
541C4×Q8—412no—
542C4×Q8C2×D418yes—
543C4×Q8C2×D4116yes—
544C4×Q8C2×D4124yes—
545C4×Q8#4118yescomplemented
546C4×D4—224no—
547C4×D4—212no—
548C4×D4—212no—
549C4×D4—224no—
550C4×D4—224no—
551C4×D4—224no—
552C4×D4—212no—
553C4×D4—212no—
554C4×D4—212no—
555C4×D4—224no—
556C4×D4—224no—
557C4×D4—224no—
558C4×D4—224no—
559C4×D4—212no—
560C4×D4—212no—
561C4×D4—224no—
562C4×D4—46no—
563C4×D4—412no—
564C4×D4—412no—
565C4×D4—412no—
566C4×D4—424no—
567#117—224no—
568#117—212no—
569#117—212no—
570#117—224no—
571#117—224no—
572C2×C4⋊C4—212no—
573C2×C4⋊C4—224no—
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2413yes—
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2413yes—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2416yes—
587C2×C4⋊C4C2413yes—
588C2×C4⋊C4C2416yes—
589C2×C4⋊C4C2413yes—
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2416yes—
594C2×C4⋊C4C2413yes—
595C2×C4⋊C4C2416yes—
596C2×C4⋊C4C2416yes—
597C2×C4⋊C4C2416yes—
598C2×C4⋊C4C2413yes—
599C2×C4⋊C4C2413yes—
600C2×C4⋊C4C2416yes—
601C2×C4⋊C4C2413yes—
602C2×C22⋊C4C24112yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C2416yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2412yes—
610C2×C22⋊C4C2411yescharacteristic
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2413yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C24112yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2413yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C24112yes—
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2413yes—
628C2×C22⋊C4C2413yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C24112yes—
632C2×C22⋊C4C24112yes—
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C2416yes—
635C2×C22⋊C4C2411yescharacteristic
636C2×C42—212no—
637C2×C42—212no—
638C2×C42—224no—
639C2×C42C2416yes—
640C2×C42C2413yes—
641C2×C42C2413yes—
642C2×C42C2413yes—
643C2×C42C2411yescharacteristic
644C2×C42C2412yes—
645C2×C42C2413yes—
646C2×C42C2416yes—
647C2×C42C2413yes—
648C2×C42C2413yes—
649C2×C42C2413yes—
650C2×C42C2413yes—
651C2×C42C2411yescharacteristic
652C2×C42C24112yes—
653C2×C42C2413yes—
654C2×C42C2416yes—
655C2×C42C2413yes—
656C2×C42C2413yes—
657#95C2412yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C2411yescharacteristic
662#95C2411yescharacteristic
663#95C2412yes—
664#95C2416yes—
665#95C2412yes—
666#95C2416yes—
667#95C2413yes—
668#95C2413yes—
669#95C2413yes—
670#95C2413yes—
671#95C2416yes—
672#95C2416yes—
673#95C2416yes—
674#95C2412yes—
675#95C2416yes—
676#95C24112yes—
677#95C2416yes—
678C24C2516yes—
679C24C2513yes—
680C24C2516yes—
681C24C2511yescharacteristic
682#41—448no—
683#41—416no—
684#41—432no—
685#41—432no—
686#41—848no—
687#41—848no—
688C2×Q8—26no—
689C2×Q8—26no—
690C2×Q8—26no—
691C2×Q8—22no—
692C2×Q8—22no—
693C2×Q8—46no—
694C2×Q8—46no—
695C2×Q8—416no—
696C2×Q8C22×D414yes—
697C2×Q8C22×D4124yes—
698C2×Q8C22×D414yes—
699C2×Q8C2×#4114yes—
700C2×Q8H(5,𝔽2)14yes—
701C2×D4—26no—
702C2×D4—212no—
703C2×D4—212no—
704C2×D4—26no—
705C2×D4—212no—
706C2×D4—212no—
707C2×D4—26no—
708C2×D4—212no—
709C2×D4—26no—
710C2×D4—212no—
711C2×D4—212no—
712C2×D4—224no—
713C2×D4—212no—
714C2×D4—26no—
715C2×D4—26no—
716C2×D4—212no—
717C2×D4—212no—
718C2×D4—212no—
719C2×D4—224no—
720C2×D4—212no—
721C2×D4—212no—
722C2×D4—26no—
723C2×D4—212no—
724C2×D4—26no—
725C2×D4—26no—
726C2×D4—26no—
727C2×D4—26no—
728C2×D4—43no—
729C2×D4—46no—
730C2×D4—46no—
731C2×D4—46no—
732C2×D4—46no—
733C2×D4—46no—
734C2×D4—412no—
735C2×D4—46no—
736C2×D4—46no—
737C2×D4—46no—
738C2×D4—412no—
739C2×D4—46no—
740C2×D4—46no—
741C2×D4—46no—
742C2×D4—412no—
743C2×D4—412no—
744C2×D4—46no—
745C2×D4—46no—
746C2×D4—46no—
747C2×D4—46no—
748C2×D4—46no—
749C2×D4—412no—
750C2×D4—412no—
751C2×D4—412no—
752C2×D4—412no—
753C2×D4—412no—
754C2×D4—412no—
755C22×C4—26no—
756C22×C4—22no—
757C22×C4—26no—
758C22×C4—26no—
759C22×C4—212no—
760C22×C4—212no—
761C22×C4—26no—
762C22×C4—26no—
763C22×C4—26no—
764C22×C4—212no—
765C22×C4—212no—
766C22×C4—26no—
767C22×C4—212no—
768C22×C4—212no—
769C22×C4—26no—
770C22×C4—26no—
771C22×C4—212no—
772C22×C4—26no—
773C22×C4—212no—
774C22×C4—26no—
775C22×C4—212no—
776C22×C4—22no—
777C22×C4—26no—
778C22×C4—22no—
779C22×C4—26no—
780C22×C4—224no—
781C22×C4—46no—
782C22×C4—46no—
783C22×C4—43no—
784C22×C4—43no—
785C22×C4—46no—
786C22×C4—412no—
787C22×C4—412no—
788C22×C4C2513yes—
789C22×C4C2512yes—
790C22×C4C2513yes—
791C22×C4C2516yes—
792C22×C4C2513yes—
793C22×C4C2511yescharacteristic
794C22×C4C2512yes—
795C22×C4C2511yescharacteristic
796C22×C4C2513yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2513yes—
800C22×C4C2516yes—
801C22×C4C2511yescharacteristic
802C22×C4C2513yes—
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C22×C4C2513yes—
806C22×C4C2511yescharacteristic
807C4⋊C4—26no—
808C4⋊C4—212no—
809C4⋊C4—212no—
810C4⋊C4—24no—
811C4⋊C4—26no—
812C4⋊C4—22no—
813C4⋊C4—24no—
814C4⋊C4—22no—
815C4⋊C4—212no—
816C4⋊C4—24no—
817C4⋊C4—26no—
818C4⋊C4—26no—
819C4⋊C4—26no—
820C4⋊C4—212no—
821C4⋊C4—212no—
822C4⋊C4—22no—
823C4⋊C4—26no—
824C4⋊C4—43no—
825C4⋊C4—42no—
826C4⋊C4—42no—
827C4⋊C4—46no—
828C4⋊C4—46no—
829C4⋊C4—46no—
830C4⋊C4C22×D4124yes—
831C4⋊C4C22×D4112yes—
832C4⋊C4C22×D4112yes—
833C4⋊C4C22×D4124yes—
834C4⋊C4C2×#41112yes—
835C22⋊C4—212no—
836C22⋊C4—212no—
837C22⋊C4—224no—
838C22⋊C4—212no—
839C22⋊C4—212no—
840C22⋊C4—212no—
841C22⋊C4—212no—
842C22⋊C4—24no—
843C22⋊C4—212no—
844C22⋊C4—224no—
845C22⋊C4—212no—
846C22⋊C4—22no—
847C22⋊C4—212no—
848C22⋊C4—212no—
849C22⋊C4—26no—
850C22⋊C4—212no—
851C22⋊C4—26no—
852C22⋊C4—212no—
853C22⋊C4—43no—
854C22⋊C4—43no—
855C22⋊C4—42no—
856C22⋊C4—46no—
857C22⋊C4—46no—
858C22⋊C4—46no—
859C22⋊C4—46no—
860C22⋊C4—412no—
861C22⋊C4—46no—
862C22⋊C4—46no—
863C22⋊C4—412no—
864C22⋊C4—46no—
865C22⋊C4—412no—
866C22⋊C4—46no—
867C22⋊C4—46no—
868C22⋊C4H(5,𝔽2)14yes—
869C42—24no—
870C42—26no—
871C42—22no—
872C42—26no—
873C42—212no—
874C42—26no—
875C42—26no—
876C42—26no—
877C42—26no—
878C42—212no—
879C42—26no—
880C42—26no—
881C42—22no—
882C42—412no—
883C42—43no—
884C42C22×D4112yes—
885C42C22×D4124yes—
886C42C2×#41112yes—
887C23—21no—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—26no—
894C23—23no—
895C23—26no—
896C23—23no—
897C23—26no—
898C23—26no—
899C23—23no—
900C23—26no—
901C23—26no—
902C23—26no—
903C23—26no—
904C23—23no—
905C23—26no—
906C23—23no—
907C23—26no—
908C23—26no—
909C23—23no—
910C23—26no—
911C23—23no—
912C23—26no—
913C23—26no—
914C23C2×H(5,𝔽2)12yes—
915C23C2611yescharacteristic
916Q8—28no—
917Q8—424no—
918Q8—412no—
919Q8#550116yescomplemented
920D4—412no—
921D4—424no—
922D4—424no—
923D4—424no—
924D4—412no—
925D4—424no—
926D4—412no—
927D4—412no—
928D4—812no—
929D4—812no—
930D4—824no—
931D4—812no—
932D4—812no—
933D4—824no—
934D4—812no—
935D4—812no—
936D4—1612no—
937D4—1612no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—23no—
941C2×C4—23no—
942C2×C4—26no—
943C2×C4—23no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—21no—
949C2×C4—23no—
950C2×C4—26no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—23no—
954C2×C4—22no—
955C2×C4—21no—
956C2×C4—23no—
957C2×C4—23no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—23no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—26no—
965C2×C4—23no—
966C2×C4—26no—
967C2×C4—23no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—23no—
971C2×C4—22no—
972C2×C4—23no—
973C2×C4—21no—
974C2×C4—23no—
975C2×C4—26no—
976C2×C4—22no—
977C2×C4—21no—
978C2×C4—23no—
979C2×C4—23no—
980C2×C4—23no—
981C2×C4—22no—
982C2×C4—412no—
983C2×C4—424no—
984C2×C4—412no—
985C2×C4—424no—
986C2×C4—412no—
987C2×C4—424no—
988C2×C4—412no—
989C2×C4—424no—
990C2×C4—44no—
991C2×C4—412no—
992C2×C4—824no—
993C2×C4C23×D416yes—
994C2×C4C23×D414yes—
995C2×C4C23×D4112yes—
996C2×C4C23×D416yes—
997C2×C4C23×D412yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4116yes—
1000C2×C4C22×#4116yes—
1001C2×C4C2×H(5,𝔽2)12yes—
1002C2×C4C2×H(5,𝔽2)12yes—
1003C2×C4C2×H(5,𝔽2)16yes—
1004C2×C4#58512yes—
1005C2×C4#58512yes—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—43no—
1014C22—46no—
1015C22—46no—
1016C22—46no—
1017C22—46no—
1018C22—43no—
1019C22—46no—
1020C22—46no—
1021C22—43no—
1022C22—46no—
1023C22—43no—
1024C22—46no—
1025C22—43no—
1026C22—46no—
1027C22—46no—
1028C22—43no—
1029C22—46no—
1030C22—46no—
1031C22—46no—
1032C22—43no—
1033C22—46no—
1034C22C24×D411yescharacteristic
1035C22C23×#4111yescharacteristic
1036C22C22×H(5,𝔽2)11yescharacteristic
1037C22C22×H(5,𝔽2)11yescharacteristic
1038C22C2×#58511yescharacteristic
1039C22C2×#58511yescharacteristic
1040C22H(7,𝔽2)11yescharacteristic
1041C4—22no—
1042C4—26no—
1043C4—212no—
1044C4—22no—
1045C4—22no—
1046C4—24no—
1047C4—26no—
1048C4—43no—
1049C4—46no—
1050C4—41no—
1051C4—43no—
1052C4—42no—
1053C4—43no—
1054C4—42no—
1055C4—41no—
1056C4—42no—
1057C4—43no—
1058C4C2×#550112yes—
1059C4#348714yes—
1060C2—42no—
1061C2—86no—
1062C2—83no—
1063C2—86no—
1064C2C22×#55011yescharacteristic
1065C2C2×#348711yescharacteristic
1066C2#6280011yescharacteristic
1067C2#6292311yescharacteristic
1068C2D4×H(5,𝔽2)11yescharacteristic
1069C2#6300611yescharacteristic
1070C2#6301411yescharacteristic
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×#3522C2semidirect
2. C2×#3483C2semidirect
3. #59652C2semidirect
4. #59057C2semidirect
5. #59056C2semidirect
6. #59051C2semidirect
7. #44933C2semidirect
8. #44897C2semidirect
9. #39745C2semidirect
10. #39138C2semidirect
11. #37772C2semidirect
12. #36592C2semidirect
13. #36576C2semidirect
14. #36493C2semidirect
15. #36455C2semidirect
16. #36430C2semidirect
17. #36128C2semidirect
18. #36066C2semidirect
19. #36029C2semidirect
20. #34727C2semidirect
21. #34335C2semidirect
22. #34295C2semidirect
23. C4×#548C2semidirect
168. Q82D4semidirect
545. C4×Q8#41semidirect
919. Q8#550semidirect

Maximal subgroups

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

subgroupindex
C2×#35222
C2×#34832
#596522
#590572
#590562
#590512
#449332
#448972
#397452
#391382
#377722
#365922
#365762
#364932
#364552
#364302
#361282
#360662
#360292
#347272
#343352
#342952
C4×#5482