Finite Group Databasebeta

← #7654268

Subgroups — #7654268

Order 512.

7221 conjugacy classes of subgroups.

The subgroup lattice has 1055 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3482C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#42674C216yesmaximal, complemented
4#42476C216yesmaximal, complemented
5#39883C216yesmaximal, complemented
6#39882C216yesmaximal, complemented
7#39727C213yesmaximal, complemented
8#39726C213yesmaximal, complemented
9#39137C213yesmaximal, complemented
10#39136C213yesmaximal, complemented
11#37616C213yesmaximal, complemented
12#36577C211yesmaximal, characteristic, complemented
13#36576C211yesmaximal, characteristic, complemented
14#36455C211yesmaximal, characteristic, complemented
15#36445C211yesmaximal, characteristic, complemented
16#36431C212yesmaximal, complemented
17#36430C212yesmaximal, complemented
18#36018C212yesmaximal, complemented
19#35771C212yesmaximal, complemented
20#35292C213yesmaximal, complemented
21#35189C213yesmaximal, complemented
22#34976C213yesmaximal, complemented
23#34182C211yesmaximal, characteristic, complemented
24#3482—216no—
25#3480—216no—
26C2×#559C2213yes—
27C2×#557C2211yescharacteristic
28C2×#557C2211yescharacteristic
29C2×#556C2213yes—
30C2×#556C2213yes—
31C2×#553C2216yes—
32C2×#552C2213yes—
33C2×#552C2213yes—
34C2×#550C2211yescharacteristic
35C2×#550C2212yes—
36C2×D4×Q8C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2212yes—
40C2×#548C2212yes—
41C2×#547C2213yes—
42C2×#533C2213yes—
43C2×#532C2213yes—
44C2×#529C2213yes—
45C2×#529C2216yes—
46C2×#529C2213yes—
47C2×#519C2212yes—
48C2×C4×#41C2212yes—
49C2×C4×#41C2211yescharacteristic
50C2×C4×#41C2213yes—
51C2×C4×#41C2213yes—
52C22×C4×Q8C2211yescharacteristic
53C22×C4×Q8C2211yescharacteristic
54#2857C2213yes—
55#2857C2213yes—
56#2856C2213yes—
57#2856C2213yes—
58#2851C2216yes—
59#2850C2216yes—
60#2813C22112yes—
61#2727C22112yes—
62#2725C22112yes—
63#2707C22112yes—
64#2705C22112yes—
65#2705C22112yes—
66#2702C22112yes—
67#2682C22112yes—
68#2681C22112yes—
69#2636C22112yes—
70#2630C22112yes—
71#2624C2216yes—
72#2620C2216yes—
73#2620C2216yes—
74#2620C2216yes—
75#2619C2216yes—
76#2615C2216yes—
77#2609C2216yes—
78#2609C2216yes—
79#2601C22112yes—
80#2592C2216yes—
81#2582C2213yes—
82#2582C2213yes—
83#2580C2216yes—
84#2568C2213yes—
85#2566C2216yes—
86#2548C2213yes—
87#2548C2216yes—
88#2545C2216yes—
89#2544C2216yes—
90#2542C2213yes—
91#2541C2213yes—
92#2540C2216yes—
93#2538C2213yes—
94#2538C2213yes—
95#2538C2213yes—
96#2538C2213yes—
97#2538C2216yes—
98#2537C2213yes—
99#2537C2213yes—
100#2536C2216yes—
101#2535C2216yes—
102#2485C2213yes—
103#2485C2211yescharacteristic
104#2485C2216yes—
105#2454C2216yes—
106#2454C2216yes—
107#2453C2216yes—
108#2452C2216yes—
109#2442C2216yes—
110#2441C2216yes—
111#2441C2216yes—
112#2439C2216yes—
113#2429C2216yes—
114#2428C2216yes—
115#2428C2216yes—
116#2427C2216yes—
117#2426C2216yes—
118#2426C2216yes—
119#2426C2216yes—
120#2426C2216yes—
121#2416C2216yes—
122#2415C2216yes—
123#2415C2216yes—
124#2414C2216yes—
125#2414C2216yes—
126#2414C2216yes—
127#2414C2216yes—
128#2414C2216yes—
129#2407C2216yes—
130#2407C2213yes—
131#2407C2216yes—
132#2407C2213yes—
133#2392C2216yes—
134#2392C2216yes—
135#2351C2212yes—
136#2351C2212yes—
137#2351C2216yes—
138Q8×C4⋊C4C2213yes—
139Q8×C4⋊C4C2213yes—
140Q8×C4⋊C4C2212yes—
141Q8×C4⋊C4C2211yescharacteristic
142Q8×C4⋊C4C2211yescharacteristic
143#2341C2212yes—
144#2341C2212yes—
145#2341C2212yes—
146Q8×C22⋊C4C2212yes—
147#2324C2216yes—
148#2324C2216yes—
149#2324C2216yes—
150#2323C2216yes—
151#2316C2216yes—
152C4×C22⋊Q8C2213yes—
153C4×C22⋊Q8C2216yes—
154C4×C22⋊Q8C2213yes—
155C4×#121C2213yes—
156C4×#121C2216yes—
157C4×#121C2213yes—
158#2285C2213yes—
159#2285C2213yes—
160C22×#41C2311yescharacteristic
161C22×#41C2312yes—
162C22×#41C2313yes—
163C22×#41C2313yes—
164C23×Q8C2311yescharacteristic
165C23×Q8C2311yescharacteristic
166#559—224no—
167#557—28no—
168#557—28no—
169#556—224no—
170#556—224no—
171#553—248no—
172#552—224no—
173#552—224no—
174#550—28no—
175#550—48no—
176D4×Q8—28no—
177#548—216no—
178#548—28no—
179#548—28no—
180#548—48no—
181#547—224no—
182#533—224no—
183#532—224no—
184C2×C4⋊Q8C2313yes—
185C2×C4⋊Q8C2313yes—
186C2×C4⋊Q8C2313yes—
187C2×#127C2313yes—
188C2×#127C2316yes—
189#529—248no—
190#529—224no—
191#529—224no—
192C2×#126C2316yes—
193C2×#126C23112yes—
194C2×#126C2316yes—
195C2×#125C2313yes—
196C2×#125C2313yes—
197C2×#125C2316yes—
198C2×#125C2316yes—
199C2×#124C2316yes—
200C2×#124C2313yes—
201C2×#124C2313yes—
202C2×#124C2316yes—
203C2×#124C2316yes—
204C2×#123C2316yes—
205C2×#123C23112yes—
206C2×#123C2316yes—
207C2×C22⋊Q8C2313yes—
208C2×C22⋊Q8C2313yes—
209C2×C22⋊Q8C2313yes—
210C2×C22⋊Q8C2316yes—
211C2×C22⋊Q8C2316yes—
212C2×C22⋊Q8C2313yes—
213C2×C22⋊Q8C2316yes—
214C2×C22⋊Q8C2316yes—
215C2×C22⋊Q8C2313yes—
216C2×C22⋊Q8C2313yes—
217C2×C22⋊Q8C2316yes—
218C2×#121C2316yes—
219C2×#121C2313yes—
220C2×#121C2316yes—
221C2×#121C2313yes—
222C2×#121C2316yes—
223C2×#121C2316yes—
224C2×#121C2316yes—
225C2×#121C2316yes—
226C2×#121C2316yes—
227C2×#121C2313yes—
228C2×#121C2316yes—
229C2×#121C2316yes—
230C2×#121C2313yes—
231C2×#121C2316yes—
232#519—48no—
233C4×#41—216no—
234C4×#41—28no—
235C4×#41—224no—
236C4×#41—224no—
237C2×C4×Q8—28no—
238C2×C4×Q8D4116yescomplemented
239C2×C4×Q8C2313yes—
240C2×C4×Q8C2313yes—
241C2×C4×Q8C2313yes—
242C2×C4×Q8C2313yes—
243C2×C4×Q8C2313yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2313yes—
250C2×C4×Q8C2316yes—
251C2×C4×Q8C2316yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2313yes—
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2313yes—
256C2×C4×D4C2316yes—
257C2×C4×D4C2316yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2313yes—
265C2×C4×D4C2313yes—
266C2×C4×D4C2313yes—
267C2×C4×D4C2316yes—
268C2×C4×D4C2313yes—
269C2×C4×D4C2313yes—
270C2×C4×D4C2313yes—
271C2×C4×D4C2316yes—
272C2×C4×D4C2316yes—
273C2×#117C2316yes—
274C2×#117C2313yes—
275C2×#117C2313yes—
276C2×#117C2316yes—
277C2×#117C2313yes—
278C2×#117C2311yescharacteristic
279C2×#117C2313yes—
280C2×#117C2316yes—
281C2×#117C2316yes—
282C2×#117C2316yes—
283C22×C4⋊C4C2313yes—
284C22×C4⋊C4C2313yes—
285C22×C42C2316yes—
286C22×C42C2313yes—
287C22×C42C2313yes—
288C22×C42C2313yes—
289#400C23112yes—
290#399C23112yes—
291#399C23112yes—
292#398C23112yes—
293#398C2316yes—
294#398C2316yes—
295#397C23112yes—
296#397C2316yes—
297#397C2312yes—
298#396C23112yes—
299#396C23112yes—
300#396C23112yes—
301#396C23112yes—
302#396C2316yes—
303#396C2316yes—
304#396C2316yes—
305#396C2316yes—
306#396C23112yes—
307#396C23112yes—
308#394C23112yes—
309#394C2316yes—
310#394C2316yes—
311#394C23112yes—
312#394C23112yes—
313#394C2316yes—
314#394C23112yes—
315#394C23112yes—
316#394C23112yes—
317#394C2316yes—
318#394C2316yes—
319#394C23112yes—
320#394C2312yes—
321#393C23112yes—
322#392C2316yes—
323#392C23112yes—
324#392C23112yes—
325#392C2316yes—
326#392C23112yes—
327#391C2313yes—
328#391C2316yes—
329#391C2316yes—
330#391C2313yes—
331#391C2316yes—
332#391C2316yes—
333#390C2316yes—
334#390C2316yes—
335#390C2316yes—
336#390C2316yes—
337#390C2316yes—
338#390C23112yes—
339#390C23112yes—
340#390C23112yes—
341#390C2316yes—
342#390C2316yes—
343#390C2313yes—
344#390C2316yes—
345#390C2316yes—
346#390C2313yes—
347#390C2316yes—
348#389C2316yes—
349#389C2316yes—
350#389C2316yes—
351#389C2316yes—
352#389C23112yes—
353#389C23112yes—
354#389C2313yes—
355#389C23112yes—
356#389C2313yes—
357#389C2316yes—
358#389C2316yes—
359#389C2316yes—
360#389C2316yes—
361#389C2311yescharacteristic
362#389C2316yes—
363#389C2316yes—
364#389C2316yes—
365#389C2316yes—
366#389C2311yescharacteristic
367#388C23112yes—
368#388C23112yes—
369#388C23112yes—
370#388C23112yes—
371#388C23112yes—
372#388C2316yes—
373#388C2312yes—
374#388C2316yes—
375#388C2316yes—
376#387C23112yes—
377#387C2316yes—
378#387C2312yes—
379#387C2316yes—
380#387C2316yes—
381#386C2316yes—
382#386C23112yes—
383#386C23112yes—
384#386C2316yes—
385#386C2316yes—
386#386C2316yes—
387#385C2316yes—
388#385C23112yes—
389#385C2316yes—
390#385C23112yes—
391#385C2316yes—
392#385C2316yes—
393#384C2316yes—
394#384C2313yes—
395#384C2313yes—
396#384C2313yes—
397#384C2313yes—
398#382C2316yes—
399#382C2316yes—
400#382C2316yes—
401#380C2316yes—
402#380C2316yes—
403#380C2313yes—
404#380C2313yes—
405#380C2316yes—
406#380C2316yes—
407#380C2316yes—
408#380C2316yes—
409#380C2316yes—
410#380C2316yes—
411#380C2311yescharacteristic
412#380C2313yes—
413#380C2316yes—
414#380C2316yes—
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417C4×C4⋊C4C2316yes—
418C4×C4⋊C4C2313yes—
419C4×C4⋊C4C2316yes—
420C4×C4⋊C4C2316yes—
421C4×C4⋊C4C2313yes—
422C4×C4⋊C4C2316yes—
423C4×C4⋊C4C2316yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C2316yes—
426C4×C22⋊C4C2316yes—
427C4×C22⋊C4C2316yes—
428C2×#41—24no—
429C2×#41—28no—
430C2×#41—28no—
431C2×#41—24no—
432C2×#41—24no—
433C2×#41—28no—
434C2×#41—212no—
435C2×#41—212no—
436C2×#41—46no—
437C2×#41—46no—
438C2×#41—46no—
439C2×#41—46no—
440C22×Q8—24no—
441C22×Q8—24no—
442C22×Q8—24no—
443C22×Q8—24no—
444C22×Q8—24no—
445C22×Q8C2×D418yes—
446C22×Q8C2413yes—
447C22×Q8C2413yes—
448C22×Q8C2413yes—
449C22×Q8C2413yes—
450C22×Q8C2411yescharacteristic
451C22×D4C2411yescharacteristic
452C22×D4C2413yes—
453C22×D4C2416yes—
454C22×D4C2413yes—
455C22×D4C2413yes—
456C22×D4C2416yes—
457C22×D4C2413yes—
458C22×D4C2416yes—
459C22×D4C2416yes—
460C22×D4C2416yes—
461C22×D4C24112yes—
462C23×C4C2413yes—
463C23×C4C2413yes—
464C23×C4C2416yes—
465C23×C4C2413yes—
466C23×C4C2411yescharacteristic
467C23×C4C2413yes—
468C23×C4C2413yes—
469C23×C4C2413yes—
470C23×C4C2411yescharacteristic
471C23×C4C2416yes—
472C23×C4C2416yes—
473C23×C4C2413yes—
474C4⋊Q8—212no—
475C4⋊Q8—212no—
476C4⋊Q8—212no—
477#127—212no—
478#127—412no—
479#126—224no—
480#126—248no—
481#126—224no—
482#125—212no—
483#125—224no—
484#125—224no—
485#125—212no—
486#124—212no—
487#124—224no—
488#124—212no—
489#124—224no—
490#124—412no—
491#123—224no—
492#123—224no—
493#123—248no—
494C22⋊Q8—224no—
495C22⋊Q8—212no—
496C22⋊Q8—212no—
497C22⋊Q8—212no—
498C22⋊Q8—224no—
499C22⋊Q8—212no—
500C22⋊Q8—412no—
501C22⋊Q8—46no—
502C22⋊Q8—412no—
503C22⋊Q8—46no—
504C22⋊Q8—412no—
505#121—212no—
506#121—224no—
507#121—224no—
508#121—212no—
509#121—224no—
510#121—412no—
511#121—412no—
512#121—46no—
513#121—412no—
514#121—46no—
515#121—412no—
516#121—412no—
517#121—412no—
518#121—412no—
519C4×Q8—24no—
520C4×Q8—28no—
521C4×Q8—24no—
522C4×Q8—28no—
523C4×Q8—28no—
524C4×Q8—212no—
525C4×Q8—212no—
526C4×Q8—212no—
527C4×Q8—212no—
528C4×Q8—212no—
529C4×Q8—212no—
530C4×Q8—412no—
531C4×Q8—412no—
532C4×Q8C2×D418yes—
533C4×Q8C2×D418yes—
534C4×Q8C2×D4124yes—
535C4×Q8C2×D4124yes—
536C4×D4—24no—
537C4×D4—212no—
538C4×D4—212no—
539C4×D4—212no—
540C4×D4—224no—
541C4×D4—224no—
542C4×D4—212no—
543C4×D4—224no—
544C4×D4—212no—
545C4×D4—212no—
546C4×D4—224no—
547C4×D4—212no—
548C4×D4—212no—
549C4×D4—212no—
550C4×D4—224no—
551C4×D4—412no—
552C4×D4—412no—
553#117—24no—
554#117—212no—
555#117—212no—
556#117—224no—
557#117—224no—
558#117—212no—
559#117—212no—
560#117—224no—
561#117—412no—
562#117—412no—
563C2×C4⋊C4—212no—
564C2×C4⋊C4C2×D4124yes—
565C2×C4⋊C4C2413yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2413yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2413yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2413yes—
578C2×C4⋊C4C2413yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2413yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2416yes—
593C2×C4⋊C4C2416yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C2416yes—
596C2×C4⋊C4C2416yes—
597C2×C4⋊C4C2416yes—
598C2×C4⋊C4C2416yes—
599C2×C4⋊C4C2416yes—
600C2×C4⋊C4C24112yes—
601C2×C4⋊C4C2413yes—
602C2×C4⋊C4C2413yes—
603C2×C4⋊C4C2416yes—
604C2×C22⋊C4C2411yescharacteristic
605C2×C22⋊C4C2411yescharacteristic
606C2×C22⋊C4C2412yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C24112yes—
609C2×C22⋊C4C2413yes—
610C2×C22⋊C4C2413yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2413yes—
614C2×C22⋊C4C2413yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C24112yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C24112yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C24112yes—
631C2×C22⋊C4C24112yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C2416yes—
635C2×C22⋊C4C24112yes—
636C2×C42—212no—
637C2×C42—224no—
638C2×C42—212no—
639C2×C42C2×D4124yes—
640C2×C42C2413yes—
641C2×C42C2412yes—
642C2×C42C2413yes—
643C2×C42C2416yes—
644C2×C42C2413yes—
645C2×C42C2416yes—
646C2×C42C2416yes—
647C2×C42C2416yes—
648C2×C42C2413yes—
649C2×C42C2413yes—
650C2×C42C2411yescharacteristic
651C2×C42C24112yes—
652C2×C42C2413yes—
653C2×C42C2413yes—
654C2×C42C2413yes—
655C2×C42C2413yes—
656#95C2412yes—
657#95C2412yes—
658#95C2412yes—
659#95C2416yes—
660#95C2416yes—
661#95C2416yes—
662#95C2416yes—
663#95C2416yes—
664#95C2412yes—
665#95C2412yes—
666#95C2416yes—
667#95C2416yes—
668#95C2416yes—
669#95C2416yes—
670#95C24112yes—
671#95C2416yes—
672#95C2416yes—
673#95C24112yes—
674#95C24112yes—
675C24C2513yes—
676C24C2516yes—
677C24C2511yescharacteristic
678C24C2511yescharacteristic
679#41—448no—
680#41—448no—
681#41—416no—
682#41—432no—
683C2×Q8—232no—
684C2×Q8—26no—
685C2×Q8—26no—
686C2×Q8—26no—
687C2×Q8—26no—
688C2×Q8—26no—
689C2×Q8—26no—
690C2×Q8—26no—
691C2×Q8—26no—
692C2×Q8—26no—
693C2×Q8—26no—
694C2×Q8—43no—
695C2×Q8—416no—
696C2×Q8C22×D4112yes—
697C2×Q8C22×D414yes—
698C2×Q8H(5,𝔽2)14yes—
699C2×Q82−1+414yes—
700C2×D4—22no—
701C2×D4—22no—
702C2×D4—212no—
703C2×D4—26no—
704C2×D4—26no—
705C2×D4—212no—
706C2×D4—26no—
707C2×D4—26no—
708C2×D4—212no—
709C2×D4—26no—
710C2×D4—212no—
711C2×D4—212no—
712C2×D4—26no—
713C2×D4—26no—
714C2×D4—212no—
715C2×D4—22no—
716C2×D4—26no—
717C2×D4—26no—
718C2×D4—43no—
719C2×D4—43no—
720C2×D4—46no—
721C2×D4—46no—
722C2×D4—43no—
723C2×D4—46no—
724C2×D4—46no—
725C2×D4—46no—
726C2×D4—46no—
727C2×D4—46no—
728C2×D4—46no—
729C2×D4—46no—
730C2×D4—412no—
731C2×D4—412no—
732C2×D4—412no—
733C22×C4—26no—
734C22×C4—26no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—26no—
738C22×C4—22no—
739C22×C4—26no—
740C22×C4—26no—
741C22×C4—26no—
742C22×C4—212no—
743C22×C4—212no—
744C22×C4—26no—
745C22×C4—26no—
746C22×C4—26no—
747C22×C4—26no—
748C22×C4—212no—
749C22×C4—26no—
750C22×C4—212no—
751C22×C4—26no—
752C22×C4—22no—
753C22×C4—26no—
754C22×C4—26no—
755C22×C4—26no—
756C22×C4—22no—
757C22×C4—212no—
758C22×C4—43no—
759C22×C4—43no—
760C22×C4—43no—
761C22×C4—43no—
762C22×C4—46no—
763C22×C4—46no—
764C22×C4—46no—
765C22×C4—46no—
766C22×C4C22×D414yes—
767C22×C4C22×D4112yes—
768C22×C4C22×D4112yes—
769C22×C4C2512yes—
770C22×C4C2516yes—
771C22×C4C2512yes—
772C22×C4C2512yes—
773C22×C4C2511yescharacteristic
774C22×C4C2516yes—
775C22×C4C2513yes—
776C22×C4C2516yes—
777C22×C4C2513yes—
778C22×C4C2512yes—
779C22×C4C2511yescharacteristic
780C22×C4C2513yes—
781C22×C4C2511yescharacteristic
782C22×C4C2513yes—
783C22×C4C2513yes—
784C22×C4C2513yes—
785C22×C4C2511yescharacteristic
786C22×C4C2513yes—
787C22×C4C2511yescharacteristic
788C4⋊C4—26no—
789C4⋊C4—212no—
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—22no—
793C4⋊C4—212no—
794C4⋊C4—26no—
795C4⋊C4—26no—
796C4⋊C4—26no—
797C4⋊C4—212no—
798C4⋊C4—26no—
799C4⋊C4—212no—
800C4⋊C4—26no—
801C4⋊C4—26no—
802C4⋊C4—212no—
803C4⋊C4—212no—
804C4⋊C4—212no—
805C4⋊C4—212no—
806C4⋊C4—212no—
807C4⋊C4—22no—
808C4⋊C4—26no—
809C4⋊C4—26no—
810C4⋊C4—22no—
811C4⋊C4—24no—
812C4⋊C4—46no—
813C4⋊C4—46no—
814C4⋊C4—42no—
815C4⋊C4—46no—
816C4⋊C4—46no—
817C4⋊C4—46no—
818C4⋊C4—46no—
819C4⋊C4—46no—
820C4⋊C4—46no—
821C4⋊C4—46no—
822C4⋊C4—412no—
823C4⋊C4—46no—
824C4⋊C4C22×D4112yes—
825C4⋊C4C22×D4112yes—
826C4⋊C4C22×D4124yes—
827C22⋊C4—22no—
828C22⋊C4—24no—
829C22⋊C4—26no—
830C22⋊C4—24no—
831C22⋊C4—22no—
832C22⋊C4—212no—
833C22⋊C4—224no—
834C22⋊C4—26no—
835C22⋊C4—212no—
836C22⋊C4—212no—
837C22⋊C4—26no—
838C22⋊C4—26no—
839C22⋊C4—212no—
840C22⋊C4—212no—
841C22⋊C4—224no—
842C22⋊C4—212no—
843C22⋊C4—42no—
844C22⋊C4—46no—
845C22⋊C4—42no—
846C22⋊C4—46no—
847C22⋊C4—46no—
848C22⋊C4—46no—
849C22⋊C4—46no—
850C22⋊C4—46no—
851C22⋊C4—412no—
852C22⋊C4—412no—
853C22⋊C4—46no—
854C22⋊C4—412no—
855C22⋊C4—46no—
856C22⋊C4—46no—
857C22⋊C4—412no—
858C22⋊C4—46no—
859C42—24no—
860C42—22no—
861C42—26no—
862C42—26no—
863C42—212no—
864C42—26no—
865C42—212no—
866C42—26no—
867C42—26no—
868C42—212no—
869C42—212no—
870C42—412no—
871C42C22×D4112yes—
872C42C22×D4112yes—
873C42C22×D4112yes—
874C42C22×D4112yes—
875C23—21no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—21no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—23no—
888C23—26no—
889C23—26no—
890C23—23no—
891C23—23no—
892C23—26no—
893C23—26no—
894C23—23no—
895C23—23no—
896C23—23no—
897C23—26no—
898C23—26no—
899C23—26no—
900C23—23no—
901C23C23×D412yes—
902C23#58512yes—
903C23C2611yescharacteristic
904Q8—224no—
905Q8—412no—
906Q8—412no—
907Q8—412no—
908Q8#537116yes—
909D4—28no—
910D4—412no—
911D4—424no—
912D4—412no—
913D4—412no—
914D4—424no—
915D4—412no—
916D4—812no—
917D4—812no—
918D4—812no—
919D4—1612no—
920C2×C4—21no—
921C2×C4—23no—
922C2×C4—23no—
923C2×C4—23no—
924C2×C4—23no—
925C2×C4—23no—
926C2×C4—23no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—224no—
931C2×C4—28no—
932C2×C4—21no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—23no—
937C2×C4—26no—
938C2×C4—23no—
939C2×C4—23no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—26no—
943C2×C4—26no—
944C2×C4—21no—
945C2×C4—23no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—21no—
949C2×C4—23no—
950C2×C4—22no—
951C2×C4—26no—
952C2×C4—22no—
953C2×C4—21no—
954C2×C4—23no—
955C2×C4—23no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—22no—
961C2×C4—26no—
962C2×C4—23no—
963C2×C4—26no—
964C2×C4—26no—
965C2×C4—23no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—412no—
969C2×C4—412no—
970C2×C4—412no—
971C2×C4—424no—
972C2×C4—412no—
973C2×C4—424no—
974C2×C4—412no—
975C2×C4—44no—
976C2×C4—412no—
977C2×C4—812no—
978C2×C4C23×D412yes—
979C2×C4C23×D416yes—
980C2×C4C23×D416yes—
981C2×C4C23×D416yes—
982C2×C4C23×D416yes—
983C2×C4C23×D412yes—
984C2×C4C2×H(5,𝔽2)16yes—
985C2×C4C2×2−1+416yes—
986C2×C4#58512yes—
987C2×C4#58512yes—
988C2×C4#58512yes—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—46no—
1004C22—43no—
1005C22—43no—
1006C22—46no—
1007C22—46no—
1008C22—43no—
1009C22—43no—
1010C22—46no—
1011C22—46no—
1012C22—43no—
1013C22—43no—
1014C22—46no—
1015C22—43no—
1016C22—46no—
1017C22C24×D411yescharacteristic
1018C22C22×H(5,𝔽2)11yescharacteristic
1019C22C22×2−1+411yescharacteristic
1020C22C2×#58511yescharacteristic
1021C22C2×#58511yescharacteristic
1022C22C2×#58511yescharacteristic
1023C22C2×#58511yescharacteristic
1024C4—22no—
1025C4—26no—
1026C4—22no—
1027C4—26no—
1028C4—26no—
1029C4—46no—
1030C4—42no—
1031C4—42no—
1032C4—46no—
1033C4—41no—
1034C4—43no—
1035C4—46no—
1036C4—43no—
1037C4—42no—
1038C4—42no—
1039C4—41no—
1040C4—43no—
1041C4C2×#537112yes—
1042C4#348714yes—
1043C2—42no—
1044C2—42no—
1045C2—83no—
1046C2—86no—
1047C2C22×#53711yescharacteristic
1048C2C2×#348711yescharacteristic
1049C2#6281111yescharacteristic
1050C2#6301911yescharacteristic
1051C2#6303311yescharacteristic
1052C2#6303411yescharacteristic
1053C2#6303511yescharacteristic
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×#3482C2semidirect
2. C2×#3480C2semidirect
3. #42674C2semidirect
4. #42476C2semidirect
5. #39883C2semidirect
6. #39882C2semidirect
7. #39727C2semidirect
8. #39726C2semidirect
9. #39137C2semidirect
10. #39136C2semidirect
11. #37616C2semidirect
12. #36577C2semidirect
13. #36576C2semidirect
14. #36455C2semidirect
15. #36445C2semidirect
16. #36431C2semidirect
17. #36430C2semidirect
18. #36018C2semidirect
19. #35771C2semidirect
20. #35292C2semidirect
21. #35189C2semidirect
22. #34976C2semidirect
23. #34182C2semidirect
238. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34822
C2×#34802
#426742
#424762
#398832
#398822
#397272
#397262
#391372
#391362
#376162
#365772
#365762
#364552
#364452
#364312
#364302
#360182
#357712
#352922
#351892
#349762
#341822