Finite Group Databasebeta

← #6993670

Subgroups — #6993670

Order 512.

1290 conjugacy classes of subgroups.

The subgroup lattice has 1151 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38279C211yesmaximal, characteristic
2#37392C211yesmaximal, characteristic
3#32832C211yesmaximal, characteristic, complemented
4#32824C211yesmaximal, characteristic, complemented
5#32297C211yesmaximal, characteristic
6#32291C211yesmaximal, characteristic
7#32290C211yesmaximal, characteristic
8#32284C211yesmaximal, characteristic
9#31956C211yesmaximal, characteristic
10#31940C211yesmaximal, characteristic
11#31940C211yesmaximal, characteristic
12#31939C211yesmaximal, characteristic
13#30313C211yesmaximal, characteristic, complemented
14#30308C211yesmaximal, characteristic, complemented
15#29993C211yesmaximal, characteristic, complemented
16#29988C211yesmaximal, characteristic, complemented
17#29701C211yesmaximal, characteristic
18#29565C211yesmaximal, characteristic, complemented
19#29553C211yesmaximal, characteristic, complemented
20#28546C211yesmaximal, characteristic, complemented
21#28535C211yesmaximal, characteristic, complemented
22#27745C211yesmaximal, characteristic, complemented
23#27730C211yesmaximal, characteristic, complemented
24#25822C211yesmaximal, characteristic
25#25467C211yesmaximal, characteristic, complemented
26#25459C211yesmaximal, characteristic, complemented
27#24826C211yesmaximal, characteristic, complemented
28#24817C211yesmaximal, characteristic, complemented
29#24311C211yesmaximal, characteristic
30#23586C211yesmaximal, characteristic
31#22637C211yesmaximal, characteristic
32C2×#544C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#499C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#479C2211yescharacteristic
38C2×#479C2211yescharacteristic
39C2×#477C2211yescharacteristic
40C2×#441C2211yescharacteristic
41C2×C4×Q16C2211yescharacteristic
42#2864C2211yescharacteristic
43#2862C2211yescharacteristic
44#2859C2211yescharacteristic
45#2794—21no—
46#2793—21no—
47#2772—21no—
48#2766—21no—
49#2719—21no—
50#2719—21no—
51#2713—21no—
52#2713—21no—
53#2698—21no—
54#2698—21no—
55#2689—21no—
56#2689—21no—
57#2660C2211yescharacteristic
58#2647C2211yescharacteristic
59#2642C2211yescharacteristic
60#2629C2211yescharacteristic
61#2590—21no—
62#2571C2211yescharacteristic
63#2568C2211yescharacteristic
64#2567C2211yescharacteristic
65#2565C2211yescharacteristic
66#2565C2211yescharacteristic
67#2565C2211yescharacteristic
68#2529—21no—
69#2528—21no—
70#2525—21no—
71#2503C2211yescharacteristic
72#2502C2211yescharacteristic
73#2499C2211yescharacteristic
74#2499C2211yescharacteristic
75#2497C2211yescharacteristic
76#2494C2211yescharacteristic
77#2421C2211yescharacteristic
78#2421C2211yescharacteristic
79#2370C2211yescharacteristic
80Q8×C4⋊C4C2211yescharacteristic
81#2323C2211yescharacteristic
82#2320C2211yescharacteristic
83#2298C2211yescharacteristic
84#2295C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2100C2211yescharacteristic
89#2097C2211yescharacteristic
90#2097C2211yescharacteristic
91#2097C2211yescharacteristic
92#2097C2211yescharacteristic
93#2097C2211yescharacteristic
94#2096C2211yescharacteristic
95#2096C2211yescharacteristic
96#2095C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2084C2211yescharacteristic
100#2084C2211yescharacteristic
101#2083C2211yescharacteristic
102#2083C2211yescharacteristic
103#2083C2211yescharacteristic
104#2083C2211yescharacteristic
105#2074C2211yescharacteristic
106#2074C2211yescharacteristic
107#2074C2211yescharacteristic
108#2074C2211yescharacteristic
109#2068C2211yescharacteristic
110#2068C2211yescharacteristic
111#2068C2211yescharacteristic
112#2068C2211yescharacteristic
113#2066C2211yescharacteristic
114#2066C2211yescharacteristic
115#2066C2211yescharacteristic
116#2066C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2059C2211yescharacteristic
120#2059C2211yescharacteristic
121#2059C2211yescharacteristic
122#2059C2211yescharacteristic
123#2058C2211yescharacteristic
124#2057C2211yescharacteristic
125#2057C2211yescharacteristic
126#2043C2211yescharacteristic
127#2043C2211yescharacteristic
128#2043C2211yescharacteristic
129#2036C2211yescharacteristic
130#2036C2211yescharacteristic
131#2036C2211yescharacteristic
132#2035C2211yescharacteristic
133#2035C2211yescharacteristic
134#2035C2211yescharacteristic
135#2026C2211yescharacteristic
136#2026C2211yescharacteristic
137#2024C2211yescharacteristic
138#2016C2211yescharacteristic
139#2001C2211yescharacteristic
140#2001C2211yescharacteristic
141#1992C2211yescharacteristic
142#1990C2211yescharacteristic
143#1989C2211yescharacteristic
144#1988C2211yescharacteristic
145#1971C2211yescharacteristic
146#1969C2211yescharacteristic
147#1969C2211yescharacteristic
148#1969C2211yescharacteristic
149#1949C2211yescharacteristic
150#1948C2211yescharacteristic
151#1948C2211yescharacteristic
152#1947C2211yescharacteristic
153#1940C2211yescharacteristic
154#1939C2211yescharacteristic
155#1935C2211yescharacteristic
156#1933C2211yescharacteristic
157#1933C2211yescharacteristic
158#1933C2211yescharacteristic
159#1928C2211yescharacteristic
160#1928C2211yescharacteristic
161#1928C2211yescharacteristic
162#1927C2211yescharacteristic
163#1924C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1923C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1878C2211yescharacteristic
170#1878C2211yescharacteristic
171#1873C2211yescharacteristic
172#1872C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1853C2211yescharacteristic
177#1852C2211yescharacteristic
178#1852C2211yescharacteristic
179#1847C2211yescharacteristic
180#1846C2211yescharacteristic
181#1846C2211yescharacteristic
182#1845C2211yescharacteristic
183#1836C2211yescharacteristic
184#1835C2211yescharacteristic
185#1835C2211yescharacteristic
186#1835C2211yescharacteristic
187#1832C2211yescharacteristic
188#1831C2211yescharacteristic
189#1805C2211yescharacteristic
190#1803C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1803C2211yescharacteristic
194#1803C2211yescharacteristic
195#1798C2211yescharacteristic
196#1771C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198#1763C2211yescharacteristic
199C4×#103C2211yescharacteristic
200#1750C2211yescharacteristic
201#1746C2211yescharacteristic
202#1744C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205#544—42no—
206#544—42no—
207#541—42no—
208#541—42no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#125—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235#501—42no—
236#499—42no—
237#479—42no—
238#479—42no—
239#479—42no—
240#477—42no—
241#441—42no—
242C4×Q16—42no—
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297#401—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388D411yescharacteristic
383#388D411yescharacteristic
384#388D411yescharacteristic
385#388D411yescharacteristic
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387D411yescharacteristic
412#387D411yescharacteristic
413#387D411yescharacteristic
414#387D411yescharacteristic
415#385—21no—
416#385—21no—
417#384—21no—
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#383—21no—
425#382—21no—
426#382—21no—
427#382—21no—
428#382—21no—
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#381—21no—
437#381—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451#376—21no—
452#376C2311yescharacteristic
453C43C2311yescharacteristic
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#340C2311yescharacteristic
477#340C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8C2411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C23×C4—21no—
496C23×C4C2411yescharacteristic
497C2×Q16—22no—
498C2×Q16—22no—
499C2×Q16—22no—
500C2×Q16—22no—
501C2×Q16—41no—
502C2×Q16—41no—
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513C4⋊Q8—41no—
514C4⋊Q8—41no—
515C4⋊Q8—41no—
516C4⋊Q8—41no—
517C4⋊Q8—44no—
518#126—44no—
519#126—44no—
520#125—22no—
521#125—22no—
522#125—22no—
523#125—22no—
524#125—41no—
525#125—41no—
526#125—41no—
527#125—41no—
528#125—44no—
529#125—44no—
530#125—44no—
531C22⋊Q8—22no—
532C22⋊Q8—44no—
533C22⋊Q8—44no—
534C22⋊Q8—41no—
535C22⋊Q8—41no—
536C22⋊Q8—41no—
537C22⋊Q8—41no—
538C22⋊Q8—41no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—41no—
548C4×Q8—41no—
549#117—22no—
550#117—22no—
551#117—41no—
552#117—41no—
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⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42C2×D411yescharacteristic
639C2×C42C2×D411yescharacteristic
640C2×C42C2×D411yescharacteristic
641C2×C42C2×D411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648#107—41no—
649#107—41no—
650#107—41no—
651#107—41no—
652#107—41no—
653#107—41no—
654#107—41no—
655#107—41no—
656#107—41no—
657#107—41no—
658#106—41no—
659#106—41no—
660#106—41no—
661#106—41no—
662#106—41no—
663#106—41no—
664#106—41no—
665#106—41no—
666C4⋊C8—22no—
667C4⋊C8—22no—
668C4⋊C8—41no—
669C4⋊C8—41no—
670C4⋊C8—41no—
671C4⋊C8—41no—
672#103—22no—
673#103—22no—
674#103—41no—
675#103—41no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692C22⋊C8—22no—
693C22⋊C8—22no—
694C22⋊C8—41no—
695C22⋊C8—41no—
696#97—22no—
697#97—22no—
698C4×C8—22no—
699C4×C8—22no—
700C4×C8—22no—
701C4×C8—22no—
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#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765C24C22×D411yescharacteristic
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—42no—
784C2×Q8—42no—
785C2×Q8—81no—
786C2×Q8—81no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q82−1+412yes—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—42no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C2511yescharacteristic
829Q16—44no—
830Q16—44no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C82−1+412yes—
854C2×C82−1+412yes—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—41no—
885C4⋊C4—41no—
886C4⋊C4—41no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C22⋊C4—22no—
930C22⋊C4—22no—
931C22⋊C4—22no—
932C22⋊C4—41no—
933C22⋊C4—41no—
934C22⋊C4—41no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C42—22no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—41no—
954C42—41no—
955C42—41no—
956C42—42no—
957C42—42no—
958C42—42no—
959C42—42no—
960C42—42no—
961C42—42no—
962C42—81no—
963C42—81no—
964C42—81no—
965C42H(5,𝔽2)12yes—
966C42H(5,𝔽2)12yes—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23C23×D411yescharacteristic
975Q8—22no—
976Q8—22no—
977Q8—41no—
978Q8—41no—
979Q8—41no—
980Q8—41no—
981Q8—41no—
982Q8—41no—
983Q8—41no—
984Q8—41no—
985Q8—41no—
986Q8—41no—
987Q8—162no—
988Q8—162no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—162no—
1078C2×C4#53512yes—
1079C2×C4#53512yes—
1080C2×C4#57812yes—
1081C2×C4C2×H(5,𝔽2)11yescharacteristic
1082C2×C4C2×H(5,𝔽2)11yescharacteristic
1083C2×C4C2×2−1+411yescharacteristic
1084C2×C4C2×2−1+411yescharacteristic
1085C2×C4C2×2−1+411yescharacteristic
1086C2×C4#58511yescharacteristic
1087C8—22no—
1088C8—22no—
1089C8—41no—
1090C8—41no—
1091C8—41no—
1092C8—41no—
1093C8—41no—
1094C8—41no—
1095C22—41no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—41no—
1102C22C2×#53511yescharacteristic
1103C22#348911yescharacteristic
1104C22#349911yescharacteristic
1105C22C2×#57811yescharacteristic
1106C22#358411yescharacteristic
1107C22#358411yescharacteristic
1108C22#358611yescharacteristic
1109C4—22no—
1110C4—22no—
1111C4—22no—
1112C4—41no—
1113C4—41no—
1114C4—41no—
1115C4—41no—
1116C4—41no—
1117C4—41no—
1118C4—41no—
1119C4—41no—
1120C4—42no—
1121C4—41no—
1122C4—41no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4—81no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4#353811yescharacteristic
1139C4#353811yescharacteristic
1140C4#354711yescharacteristic
1141C4#354711yescharacteristic
1142C2—81no—
1143C2#4299411yescharacteristic
1144C2#6082311yescharacteristic
1145C2#6083711yescharacteristic
1146C2#6219811yescharacteristic
1147C2#6221411yescharacteristic
1148C2#6249611yescharacteristic
1149C2#6251711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32832C2semidirect
4. #32824C2semidirect
13. #30313C2semidirect
14. #30308C2semidirect
15. #29993C2semidirect
16. #29988C2semidirect
18. #29565C2semidirect
19. #29553C2semidirect
20. #28546C2semidirect
21. #28535C2semidirect
22. #27745C2semidirect
23. #27730C2semidirect
25. #25467C2semidirect
26. #25459C2semidirect
27. #24826C2semidirect
28. #24817C2semidirect

Maximal subgroups

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

subgroupindex
#382792
#373922
#328322
#328242
#322972
#322912
#322902
#322842
#319562
#319402
#319392
#303132
#303082
#299932
#299882
#297012
#295652
#295532
#285462
#285352
#277452
#277302
#258222
#254672
#254592
#248262
#248172
#243112
#235862
#226372