Finite Group Databasebeta

← #6537435

Subgroups — #6537435

Order 512.

1665 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37686C211yesmaximal, characteristic, complemented
2#34473C211yesmaximal, characteristic
3#29991C211yesmaximal, characteristic, complemented
4#29961C211yesmaximal, characteristic, complemented
5#29958C211yesmaximal, characteristic, complemented
6#29264C211yesmaximal, characteristic, complemented
7#29171C211yesmaximal, characteristic, complemented
8#29164C211yesmaximal, characteristic, complemented
9#29153C211yesmaximal, characteristic, complemented
10#26474C211yesmaximal, characteristic, complemented
11#26466C211yesmaximal, characteristic, complemented
12#26435C211yesmaximal, characteristic, complemented
13#26430C211yesmaximal, characteristic, complemented
14#26429C211yesmaximal, characteristic, complemented
15#26414C211yesmaximal, characteristic, complemented
16#26036C211yesmaximal, characteristic, complemented
17#26030C211yesmaximal, characteristic, complemented
18#25975C211yesmaximal, characteristic, complemented
19#25975C211yesmaximal, characteristic, complemented
20#25969C211yesmaximal, characteristic, complemented
21#25959C211yesmaximal, characteristic, complemented
22#24311C211yesmaximal, characteristic, complemented
23#24302C211yesmaximal, characteristic, complemented
24#23787C211yesmaximal, characteristic, complemented
25#23458C211yesmaximal, characteristic, complemented
26#23452C211yesmaximal, characteristic, complemented
27#22716C211yesmaximal, characteristic, complemented
28#22709C211yesmaximal, characteristic, complemented
29#22699C211yesmaximal, characteristic, complemented
30#22431C211yesmaximal, characteristic
31#22420C211yesmaximal, characteristic
32C2×#547C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#477C2211yescharacteristic
38C2×#477C2211yescharacteristic
39C2×#436C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#417C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#416C2211yescharacteristic
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#2377—21no—
63#2376—21no—
64#2374—21no—
65#2365C2211yescharacteristic
66#2362C2211yescharacteristic
67#2360C2211yescharacteristic
68#2357C2211yescharacteristic
69#2352C2211yescharacteristic
70#2352C2211yescharacteristic
71D4×C4⋊C4C2211yescharacteristic
72#2345—21no—
73#2341C2211yescharacteristic
74#2341C2211yescharacteristic
75#2335—21no—
76#2335—21no—
77#2333—21no—
78#2331C2211yescharacteristic
79#2327C2211yescharacteristic
80#2323C2211yescharacteristic
81#2319C2211yescharacteristic
82#2313—21no—
83#2311C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85#2297C2211yescharacteristic
86#2290C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2100C2211yescharacteristic
90#2097C2211yescharacteristic
91#2097C2211yescharacteristic
92#2093C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2088C2211yescharacteristic
96#2087C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2066C2211yescharacteristic
104#2066C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic
108#2057C2211yescharacteristic
109#2057C2211yescharacteristic
110#2026C2211yescharacteristic
111#2026C2211yescharacteristic
112#2026C2211yescharacteristic
113#2025C2211yescharacteristic
114#2025C2211yescharacteristic
115#2024C2211yescharacteristic
116#2024C2211yescharacteristic
117#2024C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#2024C2211yescharacteristic
121#2024C2211yescharacteristic
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic
124#2023C2211yescharacteristic
125#2023C2211yescharacteristic
126#2023C2211yescharacteristic
127#1989C2211yescharacteristic
128#1988C2211yescharacteristic
129#1987C2211yescharacteristic
130#1987C2211yescharacteristic
131#1981C2211yescharacteristic
132#1981C2211yescharacteristic
133#1960C2211yescharacteristic
134#1956C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1947C2211yescharacteristic
139#1940C2211yescharacteristic
140#1939C2211yescharacteristic
141#1921C2211yescharacteristic
142#1919C2211yescharacteristic
143#1919C2211yescharacteristic
144#1918C2211yescharacteristic
145#1894C2211yescharacteristic
146#1894C2211yescharacteristic
147#1894C2211yescharacteristic
148#1892C2211yescharacteristic
149#1873C2211yescharacteristic
150#1872C2211yescharacteristic
151#1872C2211yescharacteristic
152#1872C2211yescharacteristic
153#1865C2211yescharacteristic
154#1865C2211yescharacteristic
155#1865C2211yescharacteristic
156#1863C2211yescharacteristic
157#1863C2211yescharacteristic
158#1863C2211yescharacteristic
159#1863C2211yescharacteristic
160#1863C2211yescharacteristic
161#1854C2211yescharacteristic
162#1854C2211yescharacteristic
163#1854C2211yescharacteristic
164#1853C2211yescharacteristic
165#1852C2211yescharacteristic
166#1852C2211yescharacteristic
167#1852C2211yescharacteristic
168#1852C2211yescharacteristic
169#1851C2211yescharacteristic
170#1851C2211yescharacteristic
171#1851C2211yescharacteristic
172#1850C2211yescharacteristic
173#1836C2211yescharacteristic
174#1835C2211yescharacteristic
175#1832C2211yescharacteristic
176#1809C2211yescharacteristic
177#1809C2211yescharacteristic
178#1809C2211yescharacteristic
179#1808C2211yescharacteristic
180#1805C2211yescharacteristic
181#1805C2211yescharacteristic
182#1804C2211yescharacteristic
183#1803C2211yescharacteristic
184#1803C2211yescharacteristic
185#1802C2211yescharacteristic
186#1798C2211yescharacteristic
187#1797C2211yescharacteristic
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1776C2211yescharacteristic
193C4×#107C2211yescharacteristic
194#1768C2211yescharacteristic
195#1762C2211yescharacteristic
196C4×#102C2211yescharacteristic
197#1736C2211yescharacteristic
198#1736C2211yescharacteristic
199#1736C2211yescharacteristic
200C2×#340C2211yescharacteristic
201#1729C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×Q8—21no—
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#547—24no—
211#547Q818yescomplemented
212#544—42no—
213#544—42no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—42no—
219C2×C4⋊Q8—42no—
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×#125—21no—
227C2×#125C2311yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121—21no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
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×C42C2311yescharacteristic
255#479—42no—
256#477—42no—
257#477—42no—
258#477—42no—
259#436—24no—
260#435—24no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281#417—42no—
282#417—42no—
283#417—42no—
284#416—42no—
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#400—21no—
316#400—21no—
317#399—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#396—21no—
325#395—21no—
326#395—21no—
327#395—21no—
328#395—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#393—21no—
334#393—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#390—21no—
344#390—21no—
345#390—21no—
346#390—21no—
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388D411yescharacteristic
376#388D411yescharacteristic
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#387D411yescharacteristic
395#387D411yescharacteristic
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386D411yescharacteristic
403#386D411yescharacteristic
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#385D411yescharacteristic
414#385D411yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#381—21no—
422#381—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455#376C2311yescharacteristic
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—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41C2×Q814yes—
505C2×#41C2×Q814yescomplemented
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8—21no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8—44no—
512C22×Q8—82no—
513C22×Q8—82no—
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×D4—21no—
517C22×D4—21no—
518C22×D4C2×D411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×M16—22no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C2×M16—41no—
536C2×M16—41no—
537C2×M16—41no—
538C2×M16—41no—
539C2×M16—41no—
540C22×C8—22no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C4⋊Q8—22no—
552C4⋊Q8—22no—
553C4⋊Q8—22no—
554C4⋊Q8—22no—
555C4⋊Q8—22no—
556C4⋊Q8—22no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—44no—
563C4⋊Q8—44no—
564C4⋊Q8—44no—
565C4⋊Q8—82no—
566C4⋊Q8C2×Q814yescomplemented
567#125—22no—
568#125—41no—
569#125—41no—
570#125—41no—
571#125—44no—
572#123—28no—
573#123—28no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—44no—
577C22⋊Q8—44no—
578C22⋊Q8—82no—
579C22⋊Q8—82no—
580C22⋊Q8C2×Q814yes—
581C22⋊Q8C2×Q814yescomplemented
582#121—28no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×D4—22no—
592C4×D4—82no—
593C4×D4C2×Q814yes—
594C4×D4C2×Q814yescomplemented
595C4×D4#4114yes—
596#117—22no—
597#117—41no—
598#117—41no—
599#117—41no—
600#117—41no—
601#117—41no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—28no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
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—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—44no—
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—41no—
702C2×C42—41no—
703C2×C42C2×D411yescharacteristic
704C2×C42C2×D411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710#107—22no—
711#107—22no—
712#107—41no—
713#107—41no—
714#107—41no—
715#107—41no—
716#107—41no—
717#107—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722C4⋊C8—22no—
723C4⋊C8—22no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
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—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#102—22no—
747#102—22no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754C22⋊C8—22no—
755C22⋊C8—22no—
756C22⋊C8—22no—
757C22⋊C8—22no—
758#97—22no—
759C4×C8—22no—
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#95—21no—
794#95—21no—
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805C24—21no—
806C24C22×D411yescharacteristic
807C24C22×D411yescharacteristic
808#41—44no—
809#41—44no—
810#41—44no—
811#41—44no—
812#41—82no—
813#41—82no—
814#41—82no—
815#41—82no—
816C2×Q8—24no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—42no—
828C2×Q8—42no—
829C2×Q8—42no—
830C2×Q8—42no—
831C2×Q8—42no—
832C2×Q8—42no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×Q8—81no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—816no—
842C2×Q8C22×Q812yes—
843C2×Q8C22×Q812yes—
844C2×D4—24no—
845C2×D4—24no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4C22⋊Q814yes—
858C2×D4C22×Q812yes—
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—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—22no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×Q812yes—
922C22×C4C22×Q812yes—
923C22×C4C2×#4112yes—
924C22×C4C2×#4112yes—
925C22×C4C2511yescharacteristic
926M16—82no—
927M16—82no—
928M16—82no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—82no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—24no—
959C4⋊C4—22no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4C22⋊Q814yes—
1015C4⋊C4C22×Q812yes—
1016C4⋊C4H(5,𝔽2)12yes—
1017C4⋊C4H(5,𝔽2)12yes—
1018C22⋊C4—24no—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—22no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4C22⋊Q814yes—
1044C22⋊C4C22⋊Q814yes—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—41no—
1054C42—41no—
1055C42—42no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C42—81no—
1061C42—81no—
1062C42—81no—
1063C42—81no—
1064C42—81no—
1065C42—81no—
1066C42C22×Q812yes—
1067C42C2×#4112yes—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—22no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23C2×C22⋊Q812yes—
1088C23C2×C22⋊Q812yes—
1089C23C23×D411yescharacteristic
1090Q8—22no—
1091Q8—22no—
1092Q8—22no—
1093Q8—22no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—41no—
1098Q8—84no—
1099Q8—84no—
1100Q8—84no—
1101Q8—84no—
1102Q8—162no—
1103D4—22no—
1104D4—22no—
1105D4—44no—
1106D4—41no—
1107D4—41no—
1108D4—84no—
1109D4—84no—
1110C2×C4—21no—
1111C2×C4—21no—
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—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—44no—
1155C2×C4—44no—
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—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—84no—
1197C2×C4—84no—
1198C2×C4—84no—
1199C2×C4—84no—
1200C2×C4—84no—
1201C2×C4—162no—
1202C2×C4—162no—
1203C2×C4C2×C22⋊Q812yes—
1204C2×C4C2×C22⋊Q812yes—
1205C2×C4C2×C22⋊Q812yes—
1206C2×C4C2×C22⋊Q812yes—
1207C2×C4#57812yes—
1208C2×C4C23×Q811yescharacteristic
1209C2×C4C22×#4111yescharacteristic
1210C2×C4C2×H(5,𝔽2)11yescharacteristic
1211C2×C4C2×H(5,𝔽2)11yescharacteristic
1212C2×C4#58511yescharacteristic
1213C2×C4#58511yescharacteristic
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—22no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22C22×C22⋊Q811yescharacteristic
1244C22#348411yescharacteristic
1245C22#350011yescharacteristic
1246C22C2×#57811yescharacteristic
1247C22#358511yescharacteristic
1248C22#358511yescharacteristic
1249C22#358611yescharacteristic
1250C4—22no—
1251C4—22no—
1252C4—22no—
1253C4—22no—
1254C4—22no—
1255C4—42no—
1256C4—41no—
1257C4—42no—
1258C4—42no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—42no—
1266C4—42no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4#350111yescharacteristic
1278C4#350111yescharacteristic
1279C4#351411yescharacteristic
1280C4#351411yescharacteristic
1281C2—42no—
1282C2—42no—
1283C2—82no—
1284C2#3570211yescharacteristic
1285C2#6049311yescharacteristic
1286C2#6049811yescharacteristic
1287C2#6161211yescharacteristic
1288C2#6164311yescharacteristic
1289C2#6256611yescharacteristic
1290C2#6261911yescharacteristic
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. #29991C2semidirect
4. #29961C2semidirect
5. #29958C2semidirect
6. #29264C2semidirect
7. #29171C2semidirect
8. #29164C2semidirect
9. #29153C2semidirect
10. #26474C2semidirect
11. #26466C2semidirect
12. #26435C2semidirect
13. #26430C2semidirect
14. #26429C2semidirect
15. #26414C2semidirect
16. #26036C2semidirect
17. #26030C2semidirect
18. #25975C2semidirect
19. #25975C2semidirect
20. #25969C2semidirect
21. #25959C2semidirect
22. #24311C2semidirect
23. #24302C2semidirect
24. #23787C2semidirect
25. #23458C2semidirect
26. #23452C2semidirect
27. #22716C2semidirect
28. #22709C2semidirect
29. #22699C2semidirect
211. #547Q8semidirect
505. C2×#41C2×Q8semidirect
566. C4⋊Q8C2×Q8semidirect
581. C22⋊Q8C2×Q8semidirect
594. C4×D4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#376862
#344732
#299912
#299612
#299582
#292642
#291712
#291642
#291532
#264742
#264662
#264352
#264302
#264292
#264142
#260362
#260302
#259752
#259692
#259592
#243112
#243022
#237872
#234582
#234522
#227162
#227092
#226992
#224312
#224202