Finite Group Databasebeta

← #6589488

Subgroups — #6589488

Order 512.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1271 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36232C211yesmaximal, characteristic
2#36116C211yesmaximal, characteristic
3#33217C211yesmaximal, characteristic, complemented
4#33151C211yesmaximal, characteristic, complemented
5#32957C211yesmaximal, characteristic, complemented
6#28867C211yesmaximal, characteristic, complemented
7#28856C211yesmaximal, characteristic, complemented
8#28105C211yesmaximal, characteristic, complemented
9#28098C211yesmaximal, characteristic, complemented
10#27741C211yesmaximal, characteristic, complemented
11#27181C211yesmaximal, characteristic, complemented
12#27176C211yesmaximal, characteristic, complemented
13#27058C211yesmaximal, characteristic, complemented
14#27051C211yesmaximal, characteristic, complemented
15#26104C211yesmaximal, characteristic, complemented
16#25716C211yesmaximal, characteristic, complemented
17#25463C211yesmaximal, characteristic, complemented
18#25352C211yesmaximal, characteristic, complemented
19#25024C211yesmaximal, characteristic, complemented
20#24945C211yesmaximal, characteristic, complemented
21#24933C211yesmaximal, characteristic, complemented
22#24867C211yesmaximal, characteristic, complemented
23#24863C211yesmaximal, characteristic, complemented
24#23073C211yesmaximal, characteristic, complemented
25#22947C211yesmaximal, characteristic, complemented
26#22934C211yesmaximal, characteristic, complemented
27#22711C211yesmaximal, characteristic, complemented
28#22705C211yesmaximal, characteristic, complemented
29#22491C211yesmaximal, characteristic, complemented
30#21489C211yesmaximal, characteristic
31C2×#1763C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#529—21no—
34C22×C4×Q8C2211yescharacteristic
35C2×#501C2211yescharacteristic
36C2×#484C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#477C2211yescharacteristic
39C2×#477C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C2×C8×D4C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#97C2211yescharacteristic
46#2857C2211yescharacteristic
47#2855—21no—
48#2852—21no—
49#2851C2211yescharacteristic
50#2604—21no—
51#2599—21no—
52#2565C2211yescharacteristic
53#2552C2211yescharacteristic
54#2547C2211yescharacteristic
55#2536C2211yescharacteristic
56#2496C2211yescharacteristic
57#2496C2211yescharacteristic
58#2486C2211yescharacteristic
59#2486C2211yescharacteristic
60#2478—21no—
61#2478—21no—
62#2473—21no—
63#2462—21no—
64#2458—21no—
65#2453—21no—
66#2447—21no—
67#2443—21no—
68#2423C2211yescharacteristic
69#2421C2211yescharacteristic
70#2419—21no—
71#2419—21no—
72#2409C2211yescharacteristic
73#2409C2211yescharacteristic
74#2365C2211yescharacteristic
75#2362C2211yescharacteristic
76#2360C2211yescharacteristic
77#2356C2211yescharacteristic
78#2352C2211yescharacteristic
79D4×C4⋊C4C2211yescharacteristic
80D4×C4⋊C4C2211yescharacteristic
81D4×C4⋊C4C2211yescharacteristic
82D4×C4⋊C4C2211yescharacteristic
83#2344C2211yescharacteristic
84#2344C2211yescharacteristic
85C4×#121C2211yescharacteristic
86#2290—21no—
87C2×C4×C4⋊C4C2211yescharacteristic
88#2101C2211yescharacteristic
89#2099C2211yescharacteristic
90#2096C2211yescharacteristic
91#2095C2211yescharacteristic
92#2085C2211yescharacteristic
93#2083C2211yescharacteristic
94#2077C2211yescharacteristic
95#2076C2211yescharacteristic
96#2075C2211yescharacteristic
97#2075C2211yescharacteristic
98#2072C2211yescharacteristic
99#2072C2211yescharacteristic
100#2068C2211yescharacteristic
101#2068C2211yescharacteristic
102#2066C2211yescharacteristic
103#2066C2211yescharacteristic
104#2036C2211yescharacteristic
105#2036C2211yescharacteristic
106#2036C2211yescharacteristic
107#2036C2211yescharacteristic
108#2035C2211yescharacteristic
109#2035C2211yescharacteristic
110#2035C2211yescharacteristic
111#2035C2211yescharacteristic
112#1993C2211yescharacteristic
113#1992C2211yescharacteristic
114#1989C2211yescharacteristic
115#1989C2211yescharacteristic
116#1955C2211yescharacteristic
117#1949C2211yescharacteristic
118#1949C2211yescharacteristic
119#1949C2211yescharacteristic
120#1948C2211yescharacteristic
121#1947C2211yescharacteristic
122#1947C2211yescharacteristic
123#1944C2211yescharacteristic
124#1944C2211yescharacteristic
125#1943C2211yescharacteristic
126#1943C2211yescharacteristic
127#1940C2211yescharacteristic
128#1935C2211yescharacteristic
129#1935C2211yescharacteristic
130#1933C2211yescharacteristic
131#1933C2211yescharacteristic
132#1928C2211yescharacteristic
133#1928C2211yescharacteristic
134#1927C2211yescharacteristic
135#1927C2211yescharacteristic
136#1924C2211yescharacteristic
137#1924C2211yescharacteristic
138#1921C2211yescharacteristic
139#1921C2211yescharacteristic
140#1921C2211yescharacteristic
141#1920C2211yescharacteristic
142#1919C2211yescharacteristic
143#1919C2211yescharacteristic
144#1918C2211yescharacteristic
145#1918C2211yescharacteristic
146#1894C2211yescharacteristic
147#1894C2211yescharacteristic
148#1892C2211yescharacteristic
149#1892C2211yescharacteristic
150#1872C2211yescharacteristic
151#1872C2211yescharacteristic
152#1869C2211yescharacteristic
153#1869C2211yescharacteristic
154#1863C2211yescharacteristic
155#1863C2211yescharacteristic
156#1863C2211yescharacteristic
157#1863C2211yescharacteristic
158#1854C2211yescharacteristic
159#1854C2211yescharacteristic
160#1853C2211yescharacteristic
161#1853C2211yescharacteristic
162#1852C2211yescharacteristic
163#1852C2211yescharacteristic
164#1852C2211yescharacteristic
165#1852C2211yescharacteristic
166#1852C2211yescharacteristic
167#1852C2211yescharacteristic
168#1847C2211yescharacteristic
169#1836C2211yescharacteristic
170#1834C2211yescharacteristic
171#1825C2211yescharacteristic
172#1823C2211yescharacteristic
173#1823C2211yescharacteristic
174#1823C2211yescharacteristic
175#1809C2211yescharacteristic
176#1808C2211yescharacteristic
177#1808C2211yescharacteristic
178#1808C2211yescharacteristic
179#1807C2211yescharacteristic
180#1807C2211yescharacteristic
181#1803C2211yescharacteristic
182#1803C2211yescharacteristic
183#1797C2211yescharacteristic
184#1787C2211yescharacteristic
185#1787C2211yescharacteristic
186#1776C2211yescharacteristic
187C4×#107C2211yescharacteristic
188#1771C2211yescharacteristic
189#1763C2211yescharacteristic
190#1763C2211yescharacteristic
191#1763C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197#1753C2211yescharacteristic
198#1752C2211yescharacteristic
199#1736C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#552—24no—
209#552—42no—
210C2×C4⋊Q8C2311yescharacteristic
211#529—48no—
212C2×#126—21no—
213C2×#126—21no—
214C2×#126—21no—
215C2×#125—21no—
216C2×#125—21no—
217C2×#125C2311yescharacteristic
218C2×#124—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121D411yescharacteristic
228C2×C4×Q8—21no—
229C2×C4×Q8—21no—
230C2×C4×Q8—21no—
231C2×C4×Q8—24no—
232C2×C4×Q8—42no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117—21no—
245C2×#117—21no—
246C2×#117—21no—
247C2×#117C2311yescharacteristic
248C22×C4⋊C4—21no—
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C42—21no—
256C22×C42—21no—
257C22×C42C2311yescharacteristic
258#501—42no—
259#484—24no—
260#483—24no—
261#477—24no—
262#477—42no—
263#435—24no—
264#435—42no—
265C8×D4—24no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×#103—24no—
287C2×#103—24no—
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×#97—42no—
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319#400—21no—
320#400—21no—
321#400—21no—
322#399—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#395—21no—
339#395—21no—
340#394—21no—
341#393—21no—
342#393—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#390D411yescharacteristic
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389D411yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388D411yescharacteristic
375#388D411yescharacteristic
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#387—21no—
393#387—21no—
394#387—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386D411yescharacteristic
399#386D411yescharacteristic
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#383—21no—
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#381—21no—
421#381—21no—
422#381—21no—
423#381—21no—
424#380—21no—
425#380D411yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454#376—21no—
455C2×#95—21no—
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#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—22no—
497C22×Q8—22no—
498C22×Q8—22no—
499C22×Q8—22no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×D4C2×D411yescharacteristic
505C22×D4C2×D411yescharacteristic
506C22×D4C2×D411yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4C2×D411yescharacteristic
515C23×C4C2×D411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C2×M16—22no—
520C2×M16—41no—
521C2×M16—41no—
522C22×C8—22no—
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—41no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8#4114yes—
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C4⋊Q8—22no—
540C4⋊Q8—22no—
541#126—44no—
542#126—44no—
543#126—44no—
544#125—22no—
545#125—22no—
546#125—44no—
547#125—44no—
548#124—44no—
549#123—44no—
550#123—44no—
551#123—44no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—22no—
555C22⋊Q8—22no—
556C22⋊Q8—41no—
557C22⋊Q8—41no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560C22⋊Q8—44no—
561#121—24no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—22no—
565C4×Q8—22no—
566C4×Q8—22no—
567C4×Q8—44no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—44no—
571C4×Q8—44no—
572C4×Q8#4114yes—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—44no—
580C4×D4—44no—
581C4×D4—44no—
582C4×D4—44no—
583#117—22no—
584#117—44no—
585#117—44no—
586#117—44no—
587#117—41no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
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—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—44no—
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C42—21no—
681C2×C42—22no—
682C2×C42—22no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
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—44no—
696C2×C42—44no—
697C2×C42C2×D411yescharacteristic
698C2×C42C2×D411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703#107—22no—
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#107—41no—
713#106—22no—
714#106—22no—
715#106—41no—
716#106—41no—
717#106—41no—
718#106—41no—
719C4⋊C8—22no—
720C4⋊C8—22no—
721C4⋊C8—22no—
722C4⋊C8—22no—
723#103—22no—
724#103—22no—
725#103—22no—
726#103—22no—
727#103—22no—
728#103—22no—
729#103—22no—
730#103—22no—
731#103—22no—
732#103—22no—
733#103—22no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103#4114yes—
739C22⋊C8—22no—
740C22⋊C8—22no—
741C22⋊C8—22no—
742C22⋊C8—22no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747#97—22no—
748#97—22no—
749#97—22no—
750#97—41no—
751#97—41no—
752C4×C8—22no—
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#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799C24C22×D411yescharacteristic
800C24C22×D411yescharacteristic
801C24C22×D411yescharacteristic
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—28no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—42no—
814C2×Q8—42no—
815C2×Q8—44no—
816C2×Q8—44no—
817C2×Q8—44no—
818C2×Q8—42no—
819C2×Q8—42no—
820C2×Q8—42no—
821C2×Q8—42no—
822C2×Q8C2×#4112yes—
823C2×Q8C2×#4112yes—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—22no—
831C2×D4—41no—
832C2×D4AGL(1,ℤ/8)14yes—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
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—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—41no—
870C22×C4—41no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C2×#4112yes—
904C22×C42−1+412yes—
905C22×C4C2511yescharacteristic
906M16—82no—
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—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—44no—
929C2×C8—44no—
930C2×C8—82no—
931C2×C8C2×#4112yes—
932C2×C8C2×#4112yes—
933C2×C8C2×#4112yes—
934C4⋊C4—24no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—22no—
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—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—41no—
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—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4C2×#4112yes—
999C4⋊C4C2×#4112yes—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—81no—
1027C42—22no—
1028C42—22no—
1029C42—24no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—42no—
1037C42—42no—
1038C42—42no—
1039C42—42no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C42—42no—
1045C42—42no—
1046C42—42no—
1047C42—81no—
1048C42C2×#4112yes—
1049C42H(5,𝔽2)12yes—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23#54712yes—
1068C23C2×AGL(1,ℤ/8)12yes—
1069C23C2×AGL(1,ℤ/8)12yes—
1070C23#57812yes—
1071C23C23×D411yescharacteristic
1072Q8—22no—
1073Q8—22no—
1074Q8—22no—
1075Q8—22no—
1076Q8—48no—
1077Q8—41no—
1078Q8—41no—
1079Q8—41no—
1080Q8—41no—
1081Q8—84no—
1082D4—28no—
1083D4—44no—
1084D4—44no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—44no—
1123C2×C4—44no—
1124C2×C4—48no—
1125C2×C4—41no—
1126C2×C4—41no—
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—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—84no—
1178C2×C4—84no—
1179C2×C4—84no—
1180C2×C4—84no—
1181C2×C4—84no—
1182C2×C4—84no—
1183C2×C4#54612yes—
1184C2×C4#54612yes—
1185C2×C4#54712yes—
1186C2×C4C2×AGL(1,ℤ/8)12yes—
1187C2×C4C22×#4111yescharacteristic
1188C2×C4C22×#4111yescharacteristic
1189C2×C4C22×#4111yescharacteristic
1190C2×C4C2×H(5,𝔽2)11yescharacteristic
1191C2×C4C2×2−1+411yescharacteristic
1192C2×C4#58511yescharacteristic
1193C8—22no—
1194C8—22no—
1195C8—22no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C8—41no—
1200C8—41no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—22no—
1205C22—22no—
1206C22—22no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22#334314yes—
1222C22C2×#54611yescharacteristic
1223C22C2×#54711yescharacteristic
1224C22D4×#4111yescharacteristic
1225C22C22×AGL(1,ℤ/8)11yescharacteristic
1226C22C2×#57811yescharacteristic
1227C22#358611yescharacteristic
1228C22#358611yescharacteristic
1229C4—22no—
1230C4—22no—
1231C4—22no—
1232C4—22no—
1233C4—41no—
1234C4—42no—
1235C4—41no—
1236C4—41no—
1237C4—42no—
1238C4—42no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—42no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4#344411yescharacteristic
1257C4#349511yescharacteristic
1258C4#350511yescharacteristic
1259C4#352011yescharacteristic
1260C2—24no—
1261C2—42no—
1262C2—81no—
1263C2#3614311yescharacteristic
1264C2#6116111yescharacteristic
1265C2#6118611yescharacteristic
1266C2C2×#334311yescharacteristic
1267C2#6129211yescharacteristic
1268C2#6145211yescharacteristic
1269C2#6152511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33217C2semidirect
4. #33151C2semidirect
5. #32957C2semidirect
6. #28867C2semidirect
7. #28856C2semidirect
8. #28105C2semidirect
9. #28098C2semidirect
10. #27741C2semidirect
11. #27181C2semidirect
12. #27176C2semidirect
13. #27058C2semidirect
14. #27051C2semidirect
15. #26104C2semidirect
16. #25716C2semidirect
17. #25463C2semidirect
18. #25352C2semidirect
19. #25024C2semidirect
20. #24945C2semidirect
21. #24933C2semidirect
22. #24867C2semidirect
23. #24863C2semidirect
24. #23073C2semidirect
25. #22947C2semidirect
26. #22934C2semidirect
27. #22711C2semidirect
28. #22705C2semidirect
29. #22491C2semidirect
31. C2×#1763C2semidirect

Maximal subgroups

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

subgroupindex
#362322
#361162
#332172
#331512
#329572
#288672
#288562
#281052
#280982
#277412
#271812
#271762
#270582
#270512
#261042
#257162
#254632
#253522
#250242
#249452
#249332
#248672
#248632
#230732
#229472
#229342
#227112
#227052
#224912
#214892
C2×#17632