Finite Group Databasebeta

← #6559797

Subgroups — #6559797

Order 512.

1226 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
1#39622C211yesmaximal, characteristic
2#39177C211yesmaximal, characteristic
3#30315C211yesmaximal, characteristic
4#30314C211yesmaximal, characteristic
5#30308C211yesmaximal, characteristic
6#29326C211yesmaximal, characteristic
7#29324C211yesmaximal, characteristic
8#29316C211yesmaximal, characteristic
9#28822C211yesmaximal, characteristic
10#28820C211yesmaximal, characteristic
11#28815C211yesmaximal, characteristic
12#28812C211yesmaximal, characteristic
13#28812C211yesmaximal, characteristic
14#28811C211yesmaximal, characteristic
15#28808C211yesmaximal, characteristic
16#28807C211yesmaximal, characteristic
17#28796C211yesmaximal, characteristic
18#28794C211yesmaximal, characteristic
19#28793C211yesmaximal, characteristic
20#28792C211yesmaximal, characteristic
21#28698C211yesmaximal, characteristic
22#28697C211yesmaximal, characteristic
23#28690C211yesmaximal, characteristic
24#23845C211yesmaximal, characteristic
25#23843C211yesmaximal, characteristic
26#23836C211yesmaximal, characteristic
27#22744C211yesmaximal, characteristic
28#22741C211yesmaximal, characteristic
29#22731C211yesmaximal, characteristic
30#22725C211yesmaximal, characteristic
31#20571C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#501C2211yescharacteristic
34C2×#500C2211yescharacteristic
35C2×#499C2211yescharacteristic
36C2×#499C2211yescharacteristic
37C2×#499C2211yescharacteristic
38C2×#446C2211yescharacteristic
39C2×C8×Q8C2211yescharacteristic
40#2864C2211yescharacteristic
41#2859C2211yescharacteristic
42#2809—21no—
43#2806—21no—
44#2806—21no—
45#2799—21no—
46#2792—21no—
47#2792—21no—
48#2791—21no—
49#2774—21no—
50#2660C2211yescharacteristic
51#2660C2211yescharacteristic
52#2647C2211yescharacteristic
53#2647C2211yescharacteristic
54#2590—21no—
55#2586—21no—
56#2586—21no—
57#2585—21no—
58#2571C2211yescharacteristic
59#2570C2211yescharacteristic
60#2570C2211yescharacteristic
61#2552C2211yescharacteristic
62#2552C2211yescharacteristic
63#2552C2211yescharacteristic
64#2550C2211yescharacteristic
65#2550C2211yescharacteristic
66#2550C2211yescharacteristic
67#2550C2211yescharacteristic
68#2550C2211yescharacteristic
69#2550C2211yescharacteristic
70#2520—21no—
71#2511—21no—
72#2507—21no—
73#2507—21no—
74#2355C2211yescharacteristic
75#2355C2211yescharacteristic
76#2355C2211yescharacteristic
77#2355C2211yescharacteristic
78#2331C2211yescharacteristic
79#2330C2211yescharacteristic
80#2330C2211yescharacteristic
81#2330C2211yescharacteristic
82C4×#125C2211yescharacteristic
83C4×#125C2211yescharacteristic
84#2295C2211yescharacteristic
85#2085C2211yescharacteristic
86#2085C2211yescharacteristic
87#2085C2211yescharacteristic
88#2085C2211yescharacteristic
89#2085C2211yescharacteristic
90#2085C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2084C2211yescharacteristic
94#2084C2211yescharacteristic
95#2084C2211yescharacteristic
96#2084C2211yescharacteristic
97#2084C2211yescharacteristic
98#2083C2211yescharacteristic
99#2083C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2083C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2058C2211yescharacteristic
120#2058C2211yescharacteristic
121#2058C2211yescharacteristic
122#2058C2211yescharacteristic
123#2058C2211yescharacteristic
124#2057C2211yescharacteristic
125#1993C2211yescharacteristic
126#1992C2211yescharacteristic
127#1991C2211yescharacteristic
128#1991C2211yescharacteristic
129#1991C2211yescharacteristic
130#1990C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1949C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1949C2211yescharacteristic
144#1949C2211yescharacteristic
145#1949C2211yescharacteristic
146#1949C2211yescharacteristic
147#1948C2211yescharacteristic
148#1948C2211yescharacteristic
149#1947C2211yescharacteristic
150#1947C2211yescharacteristic
151#1947C2211yescharacteristic
152#1947C2211yescharacteristic
153#1947C2211yescharacteristic
154#1947C2211yescharacteristic
155#1944C2211yescharacteristic
156#1944C2211yescharacteristic
157#1944C2211yescharacteristic
158#1943C2211yescharacteristic
159#1942C2211yescharacteristic
160#1942C2211yescharacteristic
161#1942C2211yescharacteristic
162#1942C2211yescharacteristic
163#1942C2211yescharacteristic
164#1941C2211yescharacteristic
165#1941C2211yescharacteristic
166#1941C2211yescharacteristic
167#1847C2211yescharacteristic
168#1847C2211yescharacteristic
169#1846C2211yescharacteristic
170#1846C2211yescharacteristic
171#1846C2211yescharacteristic
172#1844C2211yescharacteristic
173#1836C2211yescharacteristic
174#1836C2211yescharacteristic
175#1835C2211yescharacteristic
176#1835C2211yescharacteristic
177#1835C2211yescharacteristic
178#1834C2211yescharacteristic
179#1776C2211yescharacteristic
180#1776C2211yescharacteristic
181#1776C2211yescharacteristic
182#1776C2211yescharacteristic
183C4×#107C2211yescharacteristic
184C4×#107C2211yescharacteristic
185C4×#107C2211yescharacteristic
186C4×#106C2211yescharacteristic
187C4×#106C2211yescharacteristic
188C4×#106C2211yescharacteristic
189C4×#106C2211yescharacteristic
190C4×#106C2211yescharacteristic
191#1771C2211yescharacteristic
192#1771C2211yescharacteristic
193#1770C2211yescharacteristic
194C8×C4⋊C4C2211yescharacteristic
195C8×C4⋊C4C2211yescharacteristic
196C8×C4⋊C4C2211yescharacteristic
197#1768C2211yescharacteristic
198#1768C2211yescharacteristic
199C4×C4⋊C8C2211yescharacteristic
200#1746C2211yescharacteristic
201#1746C2211yescharacteristic
202#1744C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×#125C2311yescharacteristic
207C2×#125C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214#501—42no—
215#501—42no—
216#500—42no—
217#499—42no—
218#499—42no—
219#499—42no—
220#446Q818yescomplemented
221C8×Q8Q818yescomplemented
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×#97C2311yescharacteristic
261C2×#97C2311yescharacteristic
262C2×#97C2311yescharacteristic
263C2×#97C2311yescharacteristic
264C2×C4×C8C2311yescharacteristic
265C2×C4×C8C2311yescharacteristic
266C2×C4×C8C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#395—21no—
303#395—21no—
304#395—21no—
305#395—21no—
306#395—21no—
307#395—21no—
308#395—21no—
309#395—21no—
310#395—21no—
311#395—21no—
312#391—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391D411yescharacteristic
325#391D411yescharacteristic
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389D411yescharacteristic
347#389D411yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387D411yescharacteristic
393#387D411yescharacteristic
394#387D411yescharacteristic
395#387D411yescharacteristic
396#384—21no—
397#384—21no—
398#384—21no—
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#382—21no—
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441#376C2311yescharacteristic
442#376C2311yescharacteristic
443C43C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8C2×D411yescharacteristic
490C22×C8C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C4⋊Q8—22no—
499C4⋊Q8—41no—
500C4⋊Q8—41no—
501C4⋊Q8—41no—
502C4⋊Q8—41no—
503C4⋊Q8—41no—
504#125—22no—
505#125—22no—
506#125—22no—
507#125—22no—
508#125—41no—
509#125—41no—
510#125—41no—
511#125—41no—
512#125—41no—
513#125—41no—
514#125—41no—
515#125—41no—
516#125—41no—
517#125—41no—
518C4×Q8C2×Q814yes—
519C4×Q8C2×Q814yes—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C42—21no—
593C2×C42—21no—
594C2×C42—21no—
595C2×C42—21no—
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—21no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42C2×D411yescharacteristic
605C2×C42C2×D411yescharacteristic
606C2×C42C2×D411yescharacteristic
607C2×C42C2×D411yescharacteristic
608C2×C42C2411yescharacteristic
609C2×C42C2411yescharacteristic
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615#107—22no—
616#107—22no—
617#107—22no—
618#107—22no—
619#107—22no—
620#107—22no—
621#107—22no—
622#107—41no—
623#107—41no—
624#107—41no—
625#107—41no—
626#107—41no—
627#107—41no—
628#107—41no—
629#107—41no—
630#107—41no—
631#106—22no—
632#106—22no—
633#106—22no—
634#106—22no—
635#106—22no—
636#106—22no—
637#106—22no—
638#106—41no—
639#106—41no—
640#106—41no—
641#106—41no—
642#106—41no—
643#106—41no—
644#106—41no—
645#106—41no—
646#106—41no—
647C4⋊C8C2×Q814yes—
648C4⋊C8C2×Q814yes—
649C4⋊C8C2×Q814yes—
650C4⋊C8C2×Q814yes—
651C4⋊C8C2×Q814yes—
652C4⋊C8C2×Q814yes—
653#97—41no—
654#97—41no—
655#97C2×Q814yes—
656#97C2×Q814yes—
657C4×C8—41no—
658C4×C8—41no—
659C4×C8—41no—
660C4×C8—41no—
661C4×C8C2×Q814yes—
662C4×C8C2×Q814yes—
663C4×C8C2×Q814yes—
664C4×C8C2×Q814yes—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729C2×Q8—41no—
730C2×Q8—41no—
731C2×Q8—42no—
732C2×Q8—81no—
733C2×Q8—81no—
734C2×Q8—81no—
735C2×Q8—81no—
736C2×Q8—81no—
737C2×Q8—81no—
738C2×Q8—81no—
739C2×Q8—81no—
740C2×Q8C4⋊Q814yes—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4C22×D411yescharacteristic
758C22×C4C22×D411yescharacteristic
759C22×C4C22×D411yescharacteristic
760C22×C4C22×D411yescharacteristic
761C22×C4C22×D411yescharacteristic
762C22×C4C22×D411yescharacteristic
763C22×C4C22×D411yescharacteristic
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D411yescharacteristic
770C22×C4C22×D411yescharacteristic
771C22×C4C2511yescharacteristic
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8C22×Q812yes—
789C2×C8C22×Q812yes—
790C2×C8C22×Q812yes—
791C2×C8C22×Q812yes—
792C2×C8C22×Q812yes—
793C2×C8C22×Q812yes—
794C2×C8C22×Q812yes—
795C2×C8C22×Q812yes—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—41no—
828C4⋊C4—41no—
829C4⋊C4—41no—
830C4⋊C4—41no—
831C4⋊C4—41no—
832C4⋊C4—41no—
833C4⋊C4—42no—
834C4⋊C4—42no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—81no—
839C4⋊C4—81no—
840C4⋊C4—81no—
841C4⋊C4—81no—
842C4⋊C4—81no—
843C4⋊C4—81no—
844C4⋊C4—81no—
845C4⋊C4—81no—
846C4⋊C4—81no—
847C4⋊C4—81no—
848C4⋊C4—81no—
849C4⋊C4—81no—
850C4⋊C4—81no—
851C4⋊C4—81no—
852C4⋊C4—81no—
853C4⋊C4—81no—
854C4⋊C4—81no—
855C4⋊C4—81no—
856C4⋊C4—81no—
857C4⋊C4—81no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4C4⋊Q814yes—
879C4⋊C4C4⋊Q814yes—
880C4⋊C4C4⋊Q814yes—
881C4⋊C4H(5,𝔽2)12yes—
882C4⋊C42−1+412yes—
883C4⋊C42−1+412yes—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42—21no—
889C42—21no—
890C42—21no—
891C42—21no—
892C42—41no—
893C42—41no—
894C42—41no—
895C42—41no—
896C42—81no—
897C42—81no—
898C42—81no—
899C42—81no—
900C42—81no—
901C42—81no—
902C42—81no—
903C42—81no—
904C42—81no—
905C42—81no—
906C42—81no—
907C42—81no—
908C42C22×Q812yes—
909C42C22×Q812yes—
910C42C22×Q812yes—
911C42C22×Q812yes—
912C42C22×Q812yes—
913C42C22×Q812yes—
914C23C23×D411yescharacteristic
915Q8—44no—
916Q8—162no—
917Q8—162no—
918Q8—162no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4C2×C4⋊Q812yes—
1004C2×C4C2×C4⋊Q812yes—
1005C2×C4C2×C4⋊Q812yes—
1006C2×C4C2×C4⋊Q812yes—
1007C2×C4C2×C4⋊Q812yes—
1008C2×C4C2×C4⋊Q812yes—
1009C2×C4C23×Q811yescharacteristic
1010C2×C4C23×Q811yescharacteristic
1011C2×C4C2×H(5,𝔽2)11yescharacteristic
1012C2×C4C2×2−1+411yescharacteristic
1013C2×C4C2×2−1+411yescharacteristic
1014C2×C4#58511yescharacteristic
1015C8—22no—
1016C8—22no—
1017C8—22no—
1018C8—22no—
1019C8—22no—
1020C8—22no—
1021C8—22no—
1022C8—22no—
1023C22C22×C4⋊Q811yescharacteristic
1024C22#348611yescharacteristic
1025C22#348811yescharacteristic
1026C22#358411yescharacteristic
1027C22#358411yescharacteristic
1028C22#358411yescharacteristic
1029C22#358411yescharacteristic
1030C4—22no—
1031C4—22no—
1032C4—22no—
1033C4—22no—
1034C4—22no—
1035C4—22no—
1036C4—41no—
1037C4—41no—
1038C4—41no—
1039C4—42no—
1040C4—41no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—42no—
1046C4—42no—
1047C4—81no—
1048C4—81no—
1049C4—81no—
1050C4—81no—
1051C4—81no—
1052C4—81no—
1053C4—81no—
1054C4—81no—
1055C4—81no—
1056C4—81no—
1057C4—81no—
1058C4—81no—
1059C4—81no—
1060C4#350211yescharacteristic
1061C4#350211yescharacteristic
1062C4#350311yescharacteristic
1063C4#350311yescharacteristic
1064C2#3593711yescharacteristic
1065C2#6066011yescharacteristic
1066C2#6066611yescharacteristic
1067C2#6186711yescharacteristic
1068C2#6186711yescharacteristic
1069C2#6206011yescharacteristic
1070C2#6206111yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
220. #446Q8semidirect
221. C8×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#396222
#391772
#303152
#303142
#303082
#293262
#293242
#293162
#288222
#288202
#288152
#288122
#288112
#288082
#288072
#287962
#287942
#287932
#287922
#286982
#286972
#286902
#238452
#238432
#238362
#227442
#227412
#227312
#227252
#205712