Finite Group Databasebeta

← #7629673

Subgroups — #7629673

Order 512.

8033 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3483C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#36066C211yesmaximal, characteristic, complemented
4#36062C213yesmaximal, complemented
5#36051C213yesmaximal, complemented
6#36049C211yesmaximal, characteristic, complemented
7#36029C212yesmaximal, complemented
8#36028C216yesmaximal, complemented
9#35948C211yesmaximal, characteristic, complemented
10#35941C213yesmaximal, complemented
11#35937C211yesmaximal, characteristic, complemented
12#35930C213yesmaximal, complemented
13#35831C212yesmaximal, complemented
14#35830C216yesmaximal, complemented
15#34964C213yesmaximal, complemented
16#34937C213yesmaximal, complemented
17#34925C216yesmaximal, complemented
18#34889C216yesmaximal, complemented
19#34624C213yesmaximal, complemented
20#34547C213yesmaximal, complemented
21C4×#550C212yesmaximal, complemented
22C4×#548C212yesmaximal, complemented
23C4×#520C211yesmaximal, characteristic, complemented
24#3483—216no—
25#3480—216no—
26C2×#559C2213yes—
27C2×Q82C2211yescharacteristic
28C2×#557C2211yescharacteristic
29C2×#556C2213yes—
30C2×#555C2216yes—
31C2×#555C2213yes—
32C2×#553C2213yes—
33C2×#553C2213yes—
34C2×#550C2213yes—
35C2×#550C2212yes—
36C2×#550C2211yescharacteristic
37C2×#550C2212yes—
38C2×#550C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2212yes—
41C2×#548C2211yescharacteristic
42C2×#532C2213yes—
43C2×#532C2216yes—
44C2×#532C2213yes—
45C2×#532C2216yes—
46C2×#529C2213yes—
47C2×#529C2213yes—
48C2×#520C2212yes—
49C2×C4×#41C2212yes—
50C2×C4×#41C2211yescharacteristic
51C2×C4×#41C2213yes—
52C2×C4×#41C2213yes—
53C2×C4×#41C2211yescharacteristic
54C22×C4×Q8C2211yescharacteristic
55#2662C22112yes—
56#2661C2216yes—
57#2661C2216yes—
58#2660C2213yes—
59#2657C2213yes—
60#2641C2213yes—
61#2640C2213yes—
62#2620C2216yes—
63#2619C2216yes—
64#2601C22112yes—
65#2592C2213yes—
66#2584C2213yes—
67#2562C2213yes—
68#2559C22112yes—
69#2557C22112yes—
70#2555C22112yes—
71#2555C22112yes—
72#2551C2216yes—
73#2550C2216yes—
74#2548C2213yes—
75#2547C2213yes—
76#2546C2213yes—
77#2545C2216yes—
78#2544C2216yes—
79#2544C2216yes—
80#2543C2216yes—
81#2543C2216yes—
82#2541C2216yes—
83#2541C2213yes—
84#2541C2216yes—
85#2540C2216yes—
86#2540C2213yes—
87#2537C2216yes—
88#2535C2216yes—
89#2521C22112yes—
90#2498C2216yes—
91#2492C2216yes—
92#2491C2216yes—
93#2491C2216yes—
94#2491C22112yes—
95#2490C2216yes—
96#2464C22112yes—
97#2430C2216yes—
98#2428C2216yes—
99#2428C22112yes—
100#2428C2216yes—
101#2428C2216yes—
102#2427C2216yes—
103#2417C2216yes—
104#2416C2216yes—
105#2416C2216yes—
106#2416C2216yes—
107#2399C2213yes—
108#2398C2213yes—
109#2398C2213yes—
110#2397C2213yes—
111#2396C2213yes—
112#2396C2216yes—
113#2396C2211yescharacteristic
114#2395C2216yes—
115#2395C2213yes—
116#2395C2213yes—
117#2392C2213yes—
118#2392C2216yes—
119#2392C2213yes—
120#2392C2216yes—
121#2392C2216yes—
122#2392C2216yes—
123#2388C22112yes—
124#2388C2213yes—
125#2388C2213yes—
126#2388C2216yes—
127#2367C2216yes—
128#2366C2216yes—
129#2363C2216yes—
130#2363C2216yes—
131#2362C2216yes—
132#2361C2216yes—
133#2354C2216yes—
134#2352C2216yes—
135#2351C2212yes—
136Q8×C4⋊C4C2212yes—
137#2341C2212yes—
138#2341C2212yes—
139#2341C2212yes—
140Q8×C22⋊C4C2212yes—
141C4×#127C2216yes—
142C4×#124C2216yes—
143C4×C22⋊Q8C2216yes—
144C4×#121C22112yes—
145C4×#121C2216yes—
146C4×#121C2216yes—
147C4×#121C2216yes—
148#2297C2216yes—
149#2276C2211yescharacteristic
150#2276C2211yescharacteristic
151#2275C2213yes—
152#2275C2213yes—
153#2274C2216yes—
154C42×Q8C2212yes—
155C42×D4C2216yes—
156C42×D4C2216yes—
157C42×D4C2216yes—
158C4×#117C2213yes—
159C2×C4×C4⋊C4C2213yes—
160C22×#41C2311yescharacteristic
161C22×#41C2312yes—
162C22×#41C2313yes—
163C22×#41C2311yescharacteristic
164C22×#41C2313yes—
165C22×#41C2316yes—
166C23×Q8C2311yescharacteristic
167#559—224no—
168Q82—28no—
169#557—28no—
170#556—224no—
171#555—224no—
172#555—248no—
173#553—224no—
174#553—224no—
175#550—28no—
176#550—216no—
177#550—28no—
178#550—216no—
179#550—224no—
180#548—28no—
181#548—28no—
182#548—216no—
183#532—224no—
184#532—248no—
185#532—224no—
186#532—424no—
187C2×C4⋊Q8C2313yes—
188C2×C4⋊Q8C2316yes—
189C2×C4⋊Q8C2313yes—
190C2×C4⋊Q8C2316yes—
191C2×#127C2316yes—
192C2×#127C2313yes—
193C2×#127C2316yes—
194C2×#127C2313yes—
195C2×#127C2316yes—
196#529—224no—
197#529—224no—
198C2×#126C2316yes—
199C2×#126C2316yes—
200C2×#125C2313yes—
201C2×#125C2313yes—
202C2×#124C2313yes—
203C2×#124C2316yes—
204C2×#124C2316yes—
205C2×#124C2313yes—
206C2×#124C23112yes—
207C2×#124C2316yes—
208C2×#124C2316yes—
209C2×#124C2316yes—
210C2×#123C2316yes—
211C2×#123C2316yes—
212C2×C22⋊Q8C2316yes—
213C2×C22⋊Q8C2313yes—
214C2×C22⋊Q8C2313yes—
215C2×#121C2316yes—
216C2×#121C2316yes—
217C2×#121C2316yes—
218C2×#121C2313yes—
219C2×#121C2316yes—
220C2×#121C2316yes—
221C2×#121C2313yes—
222C2×#121C2316yes—
223C2×#121C2313yes—
224C2×#121C2316yes—
225C2×#121C23112yes—
226C2×#121C2313yes—
227C2×#121C2316yes—
228C2×#121C23112yes—
229C2×#121C23112yes—
230C2×#121C23112yes—
231#520—216no—
232C4×#41—28no—
233C4×#41—216no—
234C4×#41—224no—
235C4×#41—224no—
236C4×#41D4116yescomplemented
237C2×C4×Q8—28no—
238C2×C4×Q8C2313yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2313yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2313yes—
246C2×C4×Q8C2313yes—
247C2×C4×Q8C2313yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2312yes—
251C2×C4×D4C2313yes—
252C2×C4×D4C2316yes—
253C2×C4×D4C2313yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2316yes—
256C2×C4×D4C2316yes—
257C2×C4×D4C2313yes—
258C2×C4×D4C2316yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2316yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2313yes—
263C2×C4×D4C2313yes—
264C2×C4×D4C2313yes—
265C2×C4×D4C2313yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2313yes—
268C2×C4×D4C2313yes—
269C2×C4×D4C2316yes—
270C2×C4×D4C2316yes—
271C2×C4×D4C2316yes—
272C2×C4×D4C23112yes—
273C2×C4×D4C2316yes—
274C2×C4×D4C2316yes—
275C2×C4×D4C2313yes—
276C2×C4×D4C2313yes—
277C2×#117C2316yes—
278C2×#117C2316yes—
279C2×#117C2313yes—
280C2×#117C2316yes—
281C2×#117C2311yescharacteristic
282C2×#117C2313yes—
283C2×#117C2313yes—
284C2×#117C2313yes—
285C2×#117C2313yes—
286C22×C4⋊C4C2313yes—
287C22×C4⋊C4C2316yes—
288C22×C42C2313yes—
289C22×C42C2313yes—
290C22×C42C2316yes—
291C22×C42C2316yes—
292C22×C42C2313yes—
293#400C2313yes—
294#400C2311yescharacteristic
295#400C2316yes—
296#399C2311yescharacteristic
297#399C2313yes—
298#399C2316yes—
299#398C2316yes—
300#398C2316yes—
301#398C2312yes—
302#398C2313yes—
303#398C2316yes—
304#398C2313yes—
305#397C2316yes—
306#397C2313yes—
307#397C2316yes—
308#397C2316yes—
309#397C2316yes—
310#397C2313yes—
311#396C2316yes—
312#396C23112yes—
313#396C2316yes—
314#396C2312yes—
315#396C2316yes—
316#395C2313yes—
317#395C2311yescharacteristic
318#395C2316yes—
319#395C23112yes—
320#394C2316yes—
321#394C23112yes—
322#394C2316yes—
323#394C23112yes—
324#394C23112yes—
325#394C2313yes—
326#394C23112yes—
327#394C2316yes—
328#394C2316yes—
329#394C2316yes—
330#394C2316yes—
331#394C2316yes—
332#394C2313yes—
333#394C2316yes—
334#393C2313yes—
335#393C23112yes—
336#393C2311yescharacteristic
337#393C2316yes—
338#392C23112yes—
339#392C23112yes—
340#392C2316yes—
341#392C2316yes—
342#392C2313yes—
343#392C2313yes—
344#392C2316yes—
345#392C23112yes—
346#392C2316yes—
347#391C2316yes—
348#391C2316yes—
349#391C2316yes—
350#391C2316yes—
351#390C2316yes—
352#390C2316yes—
353#390C23112yes—
354#390C23112yes—
355#390C2316yes—
356#390C2316yes—
357#390C2316yes—
358#390C2316yes—
359#390C23112yes—
360#390C2316yes—
361#390C2316yes—
362#389C23112yes—
363#389C2316yes—
364#389C2316yes—
365#389C2316yes—
366#389C2316yes—
367#388C23112yes—
368#388C23112yes—
369#388C23112yes—
370#388C23112yes—
371#388C23112yes—
372#388C23112yes—
373#388C23112yes—
374#387C23112yes—
375#386C23112yes—
376#386C23112yes—
377#386C23112yes—
378#386C23112yes—
379#386C23112yes—
380#386C23112yes—
381#386C23112yes—
382#385C23112yes—
383#384C2316yes—
384#382C2316yes—
385#380C2316yes—
386#380C2316yes—
387#380C2316yes—
388#380C2316yes—
389#380C23112yes—
390C4×C4⋊C4C2313yes—
391C4×C4⋊C4C2313yes—
392C4×C4⋊C4C2316yes—
393C4×C4⋊C4C2316yes—
394C4×C4⋊C4C2316yes—
395C4×C4⋊C4C2316yes—
396C4×C4⋊C4C2316yes—
397C4×C4⋊C4C2316yes—
398C4×C4⋊C4C2316yes—
399C4×C4⋊C4C2313yes—
400C4×C4⋊C4C2311yescharacteristic
401C4×C4⋊C4C2316yes—
402C4×C4⋊C4C2312yes—
403C4×C4⋊C4C2316yes—
404C4×C4⋊C4C2316yes—
405C4×C4⋊C4C2316yes—
406C4×C4⋊C4C2316yes—
407C4×C22⋊C4C2316yes—
408C4×C22⋊C4C2316yes—
409C4×C22⋊C4C2316yes—
410C4×C22⋊C4C2316yes—
411C4×C22⋊C4C2316yes—
412C4×C22⋊C4C2316yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2312yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C23112yes—
419C4×C22⋊C4C2313yes—
420C4×C22⋊C4C2313yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C23112yes—
424C4×C22⋊C4C23112yes—
425#376C2313yes—
426#376C2313yes—
427C2×#95C2316yes—
428C43C2316yes—
429C2×#41—24no—
430C2×#41—28no—
431C2×#41—28no—
432C2×#41—28no—
433C2×#41—28no—
434C2×#41—28no—
435C2×#41—212no—
436C2×#41—212no—
437C2×#41—224no—
438C2×#41—212no—
439C2×#41—46no—
440C2×#41—412no—
441C2×#41—412no—
442C2×#41—412no—
443C2×#41C2×D418yes—
444C22×Q8—24no—
445C22×Q8—28no—
446C22×Q8C2411yescharacteristic
447C22×Q8C2413yes—
448C22×Q8C2413yes—
449C22×Q8C2416yes—
450C22×Q8C2411yescharacteristic
451C22×D4C2413yes—
452C22×D4C2416yes—
453C22×D4C2416yes—
454C22×D4C2413yes—
455C22×D4C2413yes—
456C22×D4C2413yes—
457C22×D4C2416yes—
458C22×D4C2413yes—
459C22×D4C2416yes—
460C22×D4C2413yes—
461C22×D4C2416yes—
462C22×D4C24112yes—
463C22×D4C24112yes—
464C22×D4C2416yes—
465C23×C4C2413yes—
466C23×C4C2416yes—
467C23×C4C2413yes—
468C23×C4C2413yes—
469C23×C4C2416yes—
470C23×C4C2416yes—
471C23×C4C2413yes—
472C23×C4C2413yes—
473C23×C4C2411yescharacteristic
474C23×C4C2413yes—
475C23×C4C24112yes—
476C23×C4C2413yes—
477C23×C4C2413yes—
478C4⋊Q8—224no—
479C4⋊Q8—212no—
480C4⋊Q8—212no—
481C4⋊Q8—412no—
482#127—224no—
483#127—212no—
484#127—212no—
485#127—224no—
486#127—412no—
487#126—224no—
488#126—224no—
489#125—212no—
490#125—212no—
491#124—212no—
492#124—248no—
493#124—224no—
494#124—212no—
495#124—224no—
496#124—224no—
497#124—412no—
498#124—412no—
499#123—224no—
500#123—224no—
501C22⋊Q8—212no—
502C22⋊Q8—212no—
503C22⋊Q8—224no—
504#121—212no—
505#121—212no—
506#121—224no—
507#121—212no—
508#121—224no—
509#121—224no—
510#121—212no—
511#121—224no—
512#121—224no—
513#121—224no—
514#121—224no—
515#121—248no—
516#121—224no—
517#121—424no—
518#121—424no—
519#121—424no—
520C4×Q8—24no—
521C4×Q8—24no—
522C4×Q8—28no—
523C4×Q8—28no—
524C4×Q8—212no—
525C4×Q8—212no—
526C4×Q8—24no—
527C4×Q8—212no—
528C4×Q8—212no—
529C4×Q8—212no—
530C4×Q8C2×D418yes—
531C4×Q8C2×D418yes—
532C4×Q8#41116yescomplemented
533C4×D4—224no—
534C4×D4—212no—
535C4×D4—224no—
536C4×D4—212no—
537C4×D4—212no—
538C4×D4—212no—
539C4×D4—224no—
540C4×D4—224no—
541C4×D4—224no—
542C4×D4—212no—
543C4×D4—224no—
544C4×D4—212no—
545C4×D4—224no—
546C4×D4—212no—
547C4×D4—212no—
548C4×D4—212no—
549C4×D4—212no—
550C4×D4—224no—
551C4×D4—224no—
552C4×D4—224no—
553C4×D4—412no—
554C4×D4—424no—
555C4×D4—412no—
556C4×D4—412no—
557C4×D4C2×D4124yes—
558C4×D4C2×D4124yes—
559#117—212no—
560#117—212no—
561#117—212no—
562#117—224no—
563#117—24no—
564#117—212no—
565#117—224no—
566#117—224no—
567#117C2×D4124yes—
568C2×C4⋊C4—212no—
569C2×C4⋊C4—224no—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2413yes—
582C2×C4⋊C4C2413yes—
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C2413yes—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2413yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C2416yes—
593C2×C4⋊C4C24112yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C2413yes—
596C2×C4⋊C4C2413yes—
597C2×C4⋊C4C2416yes—
598C2×C22⋊C4C2411yescharacteristic
599C2×C22⋊C4C2411yescharacteristic
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C24112yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C2413yes—
605C2×C22⋊C4C2413yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2413yes—
608C2×C22⋊C4C2413yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2412yes—
612C2×C22⋊C4C2412yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C24112yes—
622C2×C22⋊C4C24112yes—
623C2×C22⋊C4C24112yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C24112yes—
629C2×C22⋊C4C2416yes—
630C2×C42—212no—
631C2×C42—212no—
632C2×C42—224no—
633C2×C42—412no—
634C2×C42C2×D4124yes—
635C2×C42C2416yes—
636C2×C42C2413yes—
637C2×C42C2416yes—
638C2×C42C2413yes—
639C2×C42C2416yes—
640C2×C42C2413yes—
641C2×C42C2413yes—
642C2×C42C2411yescharacteristic
643C2×C42C2413yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2416yes—
647C2×C42C2416yes—
648C2×C42C2416yes—
649C2×C42C2416yes—
650C2×C42C2416yes—
651C2×C42C2413yes—
652C2×C42C2413yes—
653C2×C42C2411yescharacteristic
654C2×C42C2413yes—
655C2×C42C2416yes—
656#95C2413yes—
657#95C2413yes—
658#95C24112yes—
659#95C2411yescharacteristic
660#95C2411yescharacteristic
661#95C2416yes—
662#95C2416yes—
663#95C2412yes—
664#95C2412yes—
665#95C2412yes—
666#95C2412yes—
667#95C2416yes—
668#95C2416yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C2416yes—
673#95C2416yes—
674#95C2416yes—
675#95C24112yes—
676#95C24112yes—
677C24C2513yes—
678C24C2516yes—
679C24C2513yes—
680C24C2511yescharacteristic
681#41—232no—
682#41—448no—
683#41—448no—
684#41—416no—
685#41—432no—
686#41—848no—
687C2×Q8—22no—
688C2×Q8—26no—
689C2×Q8—26no—
690C2×Q8—212no—
691C2×Q8—212no—
692C2×Q8—26no—
693C2×Q8—24no—
694C2×Q8—43no—
695C2×Q8—46no—
696C2×Q8—46no—
697C2×Q8—416no—
698C2×Q8C22×D414yes—
699C2×Q8C2×#4118yes—
700C2×D4—26no—
701C2×D4—212no—
702C2×D4—26no—
703C2×D4—212no—
704C2×D4—26no—
705C2×D4—26no—
706C2×D4—212no—
707C2×D4—224no—
708C2×D4—26no—
709C2×D4—26no—
710C2×D4—26no—
711C2×D4—212no—
712C2×D4—212no—
713C2×D4—212no—
714C2×D4—212no—
715C2×D4—212no—
716C2×D4—212no—
717C2×D4—212no—
718C2×D4—212no—
719C2×D4—224no—
720C2×D4—26no—
721C2×D4—212no—
722C2×D4—46no—
723C2×D4—46no—
724C2×D4—46no—
725C2×D4—43no—
726C2×D4—43no—
727C2×D4—46no—
728C2×D4—46no—
729C2×D4—43no—
730C2×D4—412no—
731C2×D4—412no—
732C2×D4—412no—
733C2×D4—412no—
734C2×D4—46no—
735C2×D4—46no—
736C2×D4—412no—
737C2×D4C22×D4112yes—
738C22×C4—22no—
739C22×C4—212no—
740C22×C4—26no—
741C22×C4—26no—
742C22×C4—22no—
743C22×C4—26no—
744C22×C4—26no—
745C22×C4—212no—
746C22×C4—212no—
747C22×C4—26no—
748C22×C4—212no—
749C22×C4—212no—
750C22×C4—212no—
751C22×C4—212no—
752C22×C4—212no—
753C22×C4—212no—
754C22×C4—26no—
755C22×C4—212no—
756C22×C4—26no—
757C22×C4—212no—
758C22×C4—26no—
759C22×C4—26no—
760C22×C4—224no—
761C22×C4—46no—
762C22×C4—46no—
763C22×C4—412no—
764C22×C4—46no—
765C22×C4—46no—
766C22×C4—412no—
767C22×C4C22×D4112yes—
768C22×C4C22×D4112yes—
769C22×C4C22×D4112yes—
770C22×C4H(5,𝔽2)14yes—
771C22×C4C2512yes—
772C22×C4C2516yes—
773C22×C4C2512yes—
774C22×C4C2511yescharacteristic
775C22×C4C2511yescharacteristic
776C22×C4C2513yes—
777C22×C4C2513yes—
778C22×C4C2516yes—
779C22×C4C2513yes—
780C22×C4C2511yescharacteristic
781C22×C4C2513yes—
782C22×C4C2513yes—
783C22×C4C2511yescharacteristic
784C22×C4C2512yes—
785C22×C4C2516yes—
786C22×C4C2511yescharacteristic
787C22×C4C2512yes—
788C22×C4C2513yes—
789C22×C4C2511yescharacteristic
790C4⋊C4—26no—
791C4⋊C4—212no—
792C4⋊C4—24no—
793C4⋊C4—22no—
794C4⋊C4—22no—
795C4⋊C4—22no—
796C4⋊C4—212no—
797C4⋊C4—26no—
798C4⋊C4—212no—
799C4⋊C4—26no—
800C4⋊C4—26no—
801C4⋊C4—26no—
802C4⋊C4—26no—
803C4⋊C4—26no—
804C4⋊C4—212no—
805C4⋊C4—212no—
806C4⋊C4—212no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—212no—
810C4⋊C4—212no—
811C4⋊C4—24no—
812C4⋊C4—212no—
813C4⋊C4—46no—
814C4⋊C4—412no—
815C4⋊C4C22×D4112yes—
816C4⋊C4C22×D4112yes—
817C4⋊C4C2×#41124yes—
818C22⋊C4—212no—
819C22⋊C4—26no—
820C22⋊C4—26no—
821C22⋊C4—212no—
822C22⋊C4—212no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—212no—
826C22⋊C4—224no—
827C22⋊C4—212no—
828C22⋊C4—26no—
829C22⋊C4—212no—
830C22⋊C4—26no—
831C22⋊C4—212no—
832C22⋊C4—212no—
833C22⋊C4—212no—
834C22⋊C4—24no—
835C22⋊C4—212no—
836C22⋊C4—212no—
837C22⋊C4—212no—
838C22⋊C4—224no—
839C22⋊C4—212no—
840C22⋊C4—24no—
841C22⋊C4—212no—
842C22⋊C4—46no—
843C22⋊C4—46no—
844C22⋊C4—46no—
845C22⋊C4—46no—
846C22⋊C4—412no—
847C22⋊C4—412no—
848C22⋊C4—412no—
849C22⋊C4C22×D4124yes—
850C42—22no—
851C42—24no—
852C42—212no—
853C42—26no—
854C42—26no—
855C42—26no—
856C42—212no—
857C42—26no—
858C42—26no—
859C42—212no—
860C42—212no—
861C42—24no—
862C42—46no—
863C42—46no—
864C42—46no—
865C42—46no—
866C42C22×D4112yes—
867C42C22×D414yes—
868C42C22×D4112yes—
869C42C22×D4112yes—
870C42C2×#41124yes—
871C23—21no—
872C23—26no—
873C23—22no—
874C23—23no—
875C23—22no—
876C23—21no—
877C23—23no—
878C23—26no—
879C23—23no—
880C23—26no—
881C23—26no—
882C23—26no—
883C23—26no—
884C23—26no—
885C23—23no—
886C23—26no—
887C23—23no—
888C23—26no—
889C23—26no—
890C23—26no—
891C23C23×D416yes—
892C23C2×H(5,𝔽2)12yes—
893C23C2611yescharacteristic
894Q8—28no—
895Q8—412no—
896Q8—412no—
897Q8—812no—
898Q8#532116yescomplemented
899D4—224no—
900D4—424no—
901D4—412no—
902D4—412no—
903D4—424no—
904D4—424no—
905D4—412no—
906D4—412no—
907D4—412no—
908D4—424no—
909D4—824no—
910D4—812no—
911D4—812no—
912D4—824no—
913C2×C4—21no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—26no—
917C2×C4—23no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—26no—
921C2×C4—26no—
922C2×C4—23no—
923C2×C4—21no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—224no—
927C2×C4—224no—
928C2×C4—28no—
929C2×C4—22no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—23no—
933C2×C4—23no—
934C2×C4—26no—
935C2×C4—23no—
936C2×C4—22no—
937C2×C4—26no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—26no—
941C2×C4—22no—
942C2×C4—26no—
943C2×C4—26no—
944C2×C4—23no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—26no—
948C2×C4—22no—
949C2×C4—26no—
950C2×C4—23no—
951C2×C4—26no—
952C2×C4—412no—
953C2×C4—424no—
954C2×C4—412no—
955C2×C4—424no—
956C2×C4—412no—
957C2×C4—412no—
958C2×C4—424no—
959C2×C4—824no—
960C2×C4—86no—
961C2×C4—86no—
962C2×C4C23×D416yes—
963C2×C4C23×D412yes—
964C2×C4C23×D412yes—
965C2×C4C23×D416yes—
966C2×C4C23×D416yes—
967C2×C4C23×D412yes—
968C2×C4C22×#4114yes—
969C2×C4C22×#41112yes—
970C2×C4C22×#41112yes—
971C2×C4C2×H(5,𝔽2)12yes—
972C2×C4C2×H(5,𝔽2)12yes—
973C2×C4#58514yes—
974C2×C4#58512yes—
975C22—22no—
976C22—26no—
977C22—24no—
978C22—26no—
979C22—26no—
980C22—46no—
981C22—42no—
982C22—46no—
983C22—41no—
984C22—41no—
985C22—46no—
986C22—46no—
987C22—46no—
988C22—43no—
989C22—46no—
990C22—46no—
991C22—46no—
992C22—46no—
993C22—46no—
994C22—43no—
995C22—43no—
996C22—46no—
997C22C24×D411yescharacteristic
998C22C23×#4112yes—
999C22C22×H(5,𝔽2)11yescharacteristic
1000C22C2×#58511yescharacteristic
1001C22C2×#58512yes—
1002C4—24no—
1003C4—26no—
1004C4—22no—
1005C4—212no—
1006C4—26no—
1007C4—22no—
1008C4—24no—
1009C4—22no—
1010C4—42no—
1011C4—43no—
1012C4—46no—
1013C4—46no—
1014C4—41no—
1015C4—43no—
1016C4—42no—
1017C4—41no—
1018C4—43no—
1019C4C2×#532112yes—
1020C4#348814yes—
1021C2—42no—
1022C2—46no—
1023C2—83no—
1024C2—86no—
1025C2C22×#53211yescharacteristic
1026C2#6279312yes—
1027C2C2×#348811yescharacteristic
1028C2#6280012yes—
1029C2#6281111yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3483C2semidirect
2. C2×#3480C2semidirect
3. #36066C2semidirect
4. #36062C2semidirect
5. #36051C2semidirect
6. #36049C2semidirect
7. #36029C2semidirect
8. #36028C2semidirect
9. #35948C2semidirect
10. #35941C2semidirect
11. #35937C2semidirect
12. #35930C2semidirect
13. #35831C2semidirect
14. #35830C2semidirect
15. #34964C2semidirect
16. #34937C2semidirect
17. #34925C2semidirect
18. #34889C2semidirect
19. #34624C2semidirect
20. #34547C2semidirect
21. C4×#550C2semidirect
22. C4×#548C2semidirect
23. C4×#520C2semidirect
236. C4×#41D4semidirect
532. C4×Q8#41semidirect
898. Q8#532semidirect

Maximal subgroups

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

subgroupindex
C2×#34832
C2×#34802
#360662
#360622
#360512
#360492
#360292
#360282
#359482
#359412
#359372
#359302
#358312
#358302
#349642
#349372
#349252
#348892
#346242
#345472
C4×#5502
C4×#5482
C4×#5202