Finite Group Databasebeta

← #6541469

Subgroups — #6541469

Order 512.

1699 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37686C211yesmaximal, characteristic, complemented
2#34460C211yesmaximal, characteristic
3#29990C211yesmaximal, characteristic, complemented
4#29975C211yesmaximal, characteristic, complemented
5#29972C211yesmaximal, characteristic, complemented
6#29281C211yesmaximal, characteristic, complemented
7#29217C211yesmaximal, characteristic, complemented
8#29174C211yesmaximal, characteristic, complemented
9#29161C211yesmaximal, characteristic, complemented
10#26454C211yesmaximal, characteristic, complemented
11#26442C211yesmaximal, characteristic, complemented
12#26357C211yesmaximal, characteristic, complemented
13#26348C211yesmaximal, characteristic, complemented
14#26341C211yesmaximal, characteristic, complemented
15#26338C211yesmaximal, characteristic, complemented
16#26058C211yesmaximal, characteristic, complemented
17#26049C211yesmaximal, characteristic, complemented
18#26008C211yesmaximal, characteristic, complemented
19#25998C211yesmaximal, characteristic, complemented
20#25992C211yesmaximal, characteristic, complemented
21#25988C211yesmaximal, characteristic, complemented
22#24309C211yesmaximal, characteristic, complemented
23#24298C211yesmaximal, characteristic, complemented
24#23786C211yesmaximal, characteristic, complemented
25#23557C211yesmaximal, characteristic, complemented
26C2×#2058C211yesmaximal, characteristic, complemented
27#22697C211yesmaximal, characteristic, complemented
28#22659C211yesmaximal, characteristic, complemented
29#22654C211yesmaximal, characteristic, complemented
30#22495C211yesmaximal, characteristic
31#22485C211yesmaximal, characteristic
32C2×#547C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#476C2211yescharacteristic
37C2×#474C2211yescharacteristic
38C2×#474C2211yescharacteristic
39C2×#435C2211yescharacteristic
40C2×C8×D4C2211yescharacteristic
41C2×#428C2211yescharacteristic
42C2×#427C2211yescharacteristic
43C22×#106C2211yescharacteristic
44C22×#106C2211yescharacteristic
45#2851C2211yescharacteristic
46#2734—21no—
47#2729—21no—
48#2713—21no—
49#2677—21no—
50#2660C2211yescharacteristic
51#2628C2211yescharacteristic
52#2551C2211yescharacteristic
53#2550C2211yescharacteristic
54#2473—21no—
55#2449—21no—
56#2442C2211yescharacteristic
57#2440C2211yescharacteristic
58#2440C2211yescharacteristic
59#2439C2211yescharacteristic
60#2434—21no—
61#2409—21no—
62#2378—21no—
63#2376—21no—
64#2369C2211yescharacteristic
65#2363C2211yescharacteristic
66#2361C2211yescharacteristic
67#2359—21no—
68#2352C2211yescharacteristic
69#2352C2211yescharacteristic
70#2349C2211yescharacteristic
71D4×C4⋊C4C2211yescharacteristic
72#2345C2211yescharacteristic
73#2344C2211yescharacteristic
74#2339—21no—
75#2335—21no—
76#2331C2211yescharacteristic
77#2331C2211yescharacteristic
78#2329—21no—
79#2324C2211yescharacteristic
80#2322—21no—
81#2319C2211yescharacteristic
82#2316C2211yescharacteristic
83#2311—21no—
84C4×#121C2211yescharacteristic
85C2×#389C2211yescharacteristic
86#2290C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2101C2211yescharacteristic
91#2099C2211yescharacteristic
92#2094C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2088C2211yescharacteristic
100#2087C2211yescharacteristic
101#2087C2211yescharacteristic
102#2087C2211yescharacteristic
103#2086C2211yescharacteristic
104#2086C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2058C2211yescharacteristic
113#2058C2211yescharacteristic
114#2058C2211yescharacteristic
115#2058C2211yescharacteristic
116#2058C2211yescharacteristic
117#2058C2211yescharacteristic
118#2058C2211yescharacteristic
119#2058C2211yescharacteristic
120#2058C2211yescharacteristic
121#2057C2211yescharacteristic
122#2057C2211yescharacteristic
123#2057C2211yescharacteristic
124#2025C2211yescharacteristic
125#2023C2211yescharacteristic
126#2023C2211yescharacteristic
127#1993C2211yescharacteristic
128#1990C2211yescharacteristic
129#1989C2211yescharacteristic
130#1988C2211yescharacteristic
131#1988C2211yescharacteristic
132#1988C2211yescharacteristic
133#1988C2211yescharacteristic
134#1987C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1948C2211yescharacteristic
141#1948C2211yescharacteristic
142#1947C2211yescharacteristic
143#1940C2211yescharacteristic
144#1939C2211yescharacteristic
145#1921C2211yescharacteristic
146#1921C2211yescharacteristic
147#1920C2211yescharacteristic
148#1919C2211yescharacteristic
149#1919C2211yescharacteristic
150#1919C2211yescharacteristic
151#1918C2211yescharacteristic
152#1918C2211yescharacteristic
153#1895C2211yescharacteristic
154#1893C2211yescharacteristic
155#1893C2211yescharacteristic
156#1893C2211yescharacteristic
157#1875C2211yescharacteristic
158#1874C2211yescharacteristic
159#1874C2211yescharacteristic
160#1874C2211yescharacteristic
161#1864C2211yescharacteristic
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1862C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1854C2211yescharacteristic
168#1853C2211yescharacteristic
169#1853C2211yescharacteristic
170#1852C2211yescharacteristic
171#1852C2211yescharacteristic
172#1852C2211yescharacteristic
173#1851C2211yescharacteristic
174#1850C2211yescharacteristic
175#1850C2211yescharacteristic
176#1850C2211yescharacteristic
177#1847C2211yescharacteristic
178#1846C2211yescharacteristic
179#1832C2211yescharacteristic
180#1824C2211yescharacteristic
181#1823C2211yescharacteristic
182#1823C2211yescharacteristic
183#1823C2211yescharacteristic
184#1809C2211yescharacteristic
185#1808C2211yescharacteristic
186#1807C2211yescharacteristic
187#1807C2211yescharacteristic
188#1804C2211yescharacteristic
189#1802C2211yescharacteristic
190#1798C2211yescharacteristic
191#1797C2211yescharacteristic
192#1776C2211yescharacteristic
193C4×#106C2211yescharacteristic
194#1768C2211yescharacteristic
195#1762C2211yescharacteristic
196C4×#102C2211yescharacteristic
197#1736C2211yescharacteristic
198C2×#340C2211yescharacteristic
199C2×#340C2211yescharacteristic
200C2×#340C2211yescharacteristic
201#1729C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×#41—21no—
204C23×Q8—21no—
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#547—24no—
210#547Q818yescomplemented
211#544—42no—
212#544—42no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8—42no—
218C2×C4⋊Q8—42no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×#125—21no—
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117—21no—
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4—21no—
249C22×C4⋊C4—21no—
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C42C2311yescharacteristic
257#478—42no—
258#476—42no—
259#474—42no—
260#474—42no—
261#435—24no—
262C8×D4—24no—
263#428—42no—
264#427—42no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#106—42no—
274C2×#106—42no—
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309#400—21no—
310#400—21no—
311#399—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#396—21no—
319#395—21no—
320#395—21no—
321#395—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#393—21no—
328#393—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#390—21no—
338#390—21no—
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
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#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388D411yescharacteristic
372#388D411yescharacteristic
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#387D411yescharacteristic
387#387D411yescharacteristic
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386D411yescharacteristic
395#386D411yescharacteristic
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385D411yescharacteristic
408#385D411yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#381—21no—
416#381—21no—
417#380—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429C4×C4⋊C4—21no—
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×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445#376C2311yescharacteristic
446C2×#95—21no—
447C2×#95—21no—
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#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C2×#41—28no—
495C2×#41—82no—
496C2×#41—82no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8—44no—
504C22×Q8—82no—
505C22×Q8—82no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4C2×D411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C2×D411yescharacteristic
520C23×C4C2×D411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C22×C8—22no—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—22no—
530C22×C8—22no—
531C22×C8—22no—
532C22×C8—41no—
533C22×C8—41no—
534C22×C8—41no—
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C4⋊Q8—22no—
544C4⋊Q8—22no—
545C4⋊Q8—22no—
546C4⋊Q8—22no—
547C4⋊Q8—22no—
548C4⋊Q8—22no—
549C4⋊Q8—41no—
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554C4⋊Q8—44no—
555C4⋊Q8—44no—
556C4⋊Q8—44no—
557C4⋊Q8—82no—
558C4⋊Q8C2×Q814yescomplemented
559#125—22no—
560#125—41no—
561#125—41no—
562#125—41no—
563#125—44no—
564#123—28no—
565#123—28no—
566C22⋊Q8—28no—
567C22⋊Q8—44no—
568C22⋊Q8—44no—
569C22⋊Q8—82no—
570C22⋊Q8—82no—
571#121—22no—
572#121—22no—
573#121C2×Q814yes—
574#121C2×Q814yescomplemented
575C4×D4—22no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—82no—
581C4×D4—82no—
582C4×D4—82no—
583C4×D4C2×Q814yes—
584C4×D4C2×Q814yescomplemented
585C4×D4#4114yes—
586#117—22no—
587#117—41no—
588#117—41no—
589#117—41no—
590#117—41no—
591#117—41no—
592#117—82no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—44no—
638C2×C4⋊C4—82no—
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×Q814yes—
645C2×C4⋊C4C2×Q814yescomplemented
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—41no—
696C2×C42—41no—
697C2×C42C2×D411yescharacteristic
698C2×C42C2×D411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704#107—22no—
705#107—22no—
706#107—22no—
707#107—41no—
708#107—41no—
709#107—41no—
710#107—41no—
711#107—41no—
712#106—22no—
713#106—22no—
714#106—22no—
715#106—22no—
716#106—22no—
717#106—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722#106—41no—
723#106—41no—
724C4⋊C8—22no—
725C4⋊C8—22no—
726C4⋊C8—22no—
727C4⋊C8—22no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740C22⋊C8—22no—
741C22⋊C8—22no—
742C22⋊C8—22no—
743C22⋊C8—22no—
744#97—22no—
745C4×C8—22no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791C24—21no—
792C24C22×D411yescharacteristic
793C24C22×D411yescharacteristic
794#41—816no—
795C2×Q8—24no—
796C2×Q8—24no—
797C2×Q8—42no—
798C2×Q8—42no—
799C2×Q8—42no—
800C2×Q8—42no—
801C2×Q8—42no—
802C2×Q8—42no—
803C2×Q8—81no—
804C2×Q8—81no—
805C2×Q8—81no—
806C2×Q8—81no—
807C2×Q8—81no—
808C2×Q8—81no—
809C2×Q8—81no—
810C2×Q8—81no—
811C2×Q8—81no—
812C2×Q8—81no—
813C2×Q8—816no—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4C22⋊Q814yes—
828C2×D4C22×Q812yes—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—24no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—24no—
846C22×C4—22no—
847C22×C4—24no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—41no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×Q812yes—
898C22×C4C22×Q812yes—
899C22×C4C2×#4112yes—
900C22×C4C2×#4112yes—
901C22×C4C2511yescharacteristic
902M16—44no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—44no—
926C2×C8—44no—
927C2×C8—44no—
928C2×C82−1+412yes—
929C2×C82−1+412yes—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—22no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4C22⋊Q814yes—
994C4⋊C4C22×Q812yes—
995C4⋊C4C22×Q812yes—
996C4⋊C4C22×Q812yes—
997C4⋊C4H(5,𝔽2)12yes—
998C4⋊C4H(5,𝔽2)12yes—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—24no—
1002C22⋊C4—24no—
1003C22⋊C4—24no—
1004C22⋊C4—22no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4C22⋊Q814yes—
1023C22⋊C4C22⋊Q814yes—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—41no—
1033C42—41no—
1034C42—42no—
1035C42—81no—
1036C42—81no—
1037C42—81no—
1038C42—81no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C42C22×Q812yes—
1044C42C2×#4112yes—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—22no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23C2×C22⋊Q812yes—
1063C23C2×C22⋊Q812yes—
1064C23#57612yes—
1065C23#57712yes—
1066C23C23×D411yescharacteristic
1067Q8—84no—
1068Q8—84no—
1069Q8—84no—
1070Q8—84no—
1071Q8—84no—
1072Q8—162no—
1073D4—28no—
1074D4—22no—
1075D4—22no—
1076D4—48no—
1077D4—41no—
1078D4—41no—
1079D4—84no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—44no—
1125C2×C4—44no—
1126C2×C4—48no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—84no—
1168C2×C4—84no—
1169C2×C4—84no—
1170C2×C4—84no—
1171C2×C4—162no—
1172C2×C4—162no—
1173C2×C4—162no—
1174C2×C4—162no—
1175C2×C4C2×C22⋊Q812yes—
1176C2×C4C2×C22⋊Q812yes—
1177C2×C4C2×C22⋊Q812yes—
1178C2×C4C2×C22⋊Q812yes—
1179C2×C4#57712yes—
1180C2×C4C23×Q811yescharacteristic
1181C2×C4C22×#4111yescharacteristic
1182C2×C4C2×H(5,𝔽2)11yescharacteristic
1183C2×C4C2×H(5,𝔽2)11yescharacteristic
1184C2×C4C2×2−1+411yescharacteristic
1185C2×C4C2×2−1+411yescharacteristic
1186C8—22no—
1187C8—22no—
1188C8—41no—
1189C8—41no—
1190C8—41no—
1191C8—41no—
1192C8—41no—
1193C8—41no—
1194C22—22no—
1195C22—22no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—22no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22#308114yes—
1215C22C22×C22⋊Q811yescharacteristic
1216C22#348411yescharacteristic
1217C22#349911yescharacteristic
1218C22C2×#57611yescharacteristic
1219C22C2×#57711yescharacteristic
1220C22C2×#57711yescharacteristic
1221C22#358611yescharacteristic
1222C4—22no—
1223C4—22no—
1224C4—22no—
1225C4—22no—
1226C4—22no—
1227C4—41no—
1228C4—41no—
1229C4—42no—
1230C4—42no—
1231C4—42no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—42no—
1238C4—42no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4#350311yescharacteristic
1250C4#350311yescharacteristic
1251C4#352011yescharacteristic
1252C4#352011yescharacteristic
1253C2—24no—
1254C2—42no—
1255C2—82no—
1256C2#3573911yescharacteristic
1257C2C2×#308111yescharacteristic
1258C2#6049711yescharacteristic
1259C2#6161111yescharacteristic
1260C2#6162911yescharacteristic
1261C2#6248611yescharacteristic
1262C2#6251511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#547C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37686C2semidirect
3. #29990C2semidirect
4. #29975C2semidirect
5. #29972C2semidirect
6. #29281C2semidirect
7. #29217C2semidirect
8. #29174C2semidirect
9. #29161C2semidirect
10. #26454C2semidirect
11. #26442C2semidirect
12. #26357C2semidirect
13. #26348C2semidirect
14. #26341C2semidirect
15. #26338C2semidirect
16. #26058C2semidirect
17. #26049C2semidirect
18. #26008C2semidirect
19. #25998C2semidirect
20. #25992C2semidirect
21. #25988C2semidirect
22. #24309C2semidirect
23. #24298C2semidirect
24. #23786C2semidirect
25. #23557C2semidirect
26. C2×#2058C2semidirect
27. #22697C2semidirect
28. #22659C2semidirect
29. #22654C2semidirect
210. #547Q8semidirect
558. C4⋊Q8C2×Q8semidirect
574. #121C2×Q8semidirect
584. C4×D4C2×Q8semidirect
645. C2×C4⋊C4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#376862
#344602
#299902
#299752
#299722
#292812
#292172
#291742
#291612
#264542
#264422
#263572
#263482
#263412
#263382
#260582
#260492
#260082
#259982
#259922
#259882
#243092
#242982
#237862
#235572
C2×#20582
#226972
#226592
#226542
#224952
#224852