Finite Group Databasebeta

← #6997439

Subgroups — #6997439

Order 512.

1699 conjugacy classes of subgroups.

The subgroup lattice has 1291 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59125C211yesmaximal, characteristic
2#38973C211yesmaximal, characteristic, complemented
3#32364C211yesmaximal, characteristic, complemented
4#32342C211yesmaximal, characteristic, complemented
5#32271C211yesmaximal, characteristic, complemented
6#32267C211yesmaximal, characteristic, complemented
7#31452C211yesmaximal, characteristic, complemented
8#31446C211yesmaximal, characteristic, complemented
9#30796C211yesmaximal, characteristic, complemented
10#30789C211yesmaximal, characteristic, complemented
11#29161C211yesmaximal, characteristic, complemented
12#28079C211yesmaximal, characteristic, complemented
13#28077C211yesmaximal, characteristic, complemented
14#26873C211yesmaximal, characteristic, complemented
15#26857C211yesmaximal, characteristic, complemented
16#26140C211yesmaximal, characteristic, complemented
17#26126C211yesmaximal, characteristic, complemented
18#26077C211yesmaximal, characteristic, complemented
19#26071C211yesmaximal, characteristic, complemented
20#25816C211yesmaximal, characteristic, complemented
21#25252C211yesmaximal, characteristic, complemented
22#25238C211yesmaximal, characteristic, complemented
23#24939C211yesmaximal, characteristic, complemented
24#24935C211yesmaximal, characteristic, complemented
25#24100C211yesmaximal, characteristic, complemented
26#24088C211yesmaximal, characteristic, complemented
27C2×#2057C211yesmaximal, characteristic, complemented
28#23117C211yesmaximal, characteristic, complemented
29#22661C211yesmaximal, characteristic, complemented
30D4×#107C211yesmaximal, characteristic, complemented
31#22082C211yesmaximal, characteristic, complemented
32C2×#548—21no—
33C2×#547C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C2×#501C2211yescharacteristic
36C2×#501C2211yescharacteristic
37C2×#481C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#480C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×C8×D4C2211yescharacteristic
42C2×#428C2211yescharacteristic
43C22×#107C2211yescharacteristic
44C22×#107C2211yescharacteristic
45C22×#107C2211yescharacteristic
46#2851C2211yescharacteristic
47#2776—21no—
48#2773—21no—
49#2771—21no—
50#2694—21no—
51#2674—21no—
52#2674—21no—
53#2643—21no—
54#2547C2211yescharacteristic
55#2542C2211yescharacteristic
56#2508C2211yescharacteristic
57#2506C2211yescharacteristic
58#2495C2211yescharacteristic
59#2494C2211yescharacteristic
60#2491C2211yescharacteristic
61#2491C2211yescharacteristic
62#2487C2211yescharacteristic
63#2487C2211yescharacteristic
64#2486C2211yescharacteristic
65#2485C2211yescharacteristic
66#2473—21no—
67#2443—21no—
68#2443—21no—
69#2443—21no—
70#2442C2211yescharacteristic
71#2441C2211yescharacteristic
72#2440C2211yescharacteristic
73#2440C2211yescharacteristic
74#2432—21no—
75#2429—21no—
76#2416C2211yescharacteristic
77#2416C2211yescharacteristic
78#2409—21no—
79#2365C2211yescharacteristic
80#2352C2211yescharacteristic
81D4×C4⋊C4C2211yescharacteristic
82D4×C4⋊C4C2211yescharacteristic
83D4×C4⋊C4C2211yescharacteristic
84#2318—21no—
85C4×#121C2211yescharacteristic
86C4×#121C2211yescharacteristic
87C2×#389C2211yescharacteristic
88#2101C2211yescharacteristic
89#2100C2211yescharacteristic
90#2099C2211yescharacteristic
91#2093C2211yescharacteristic
92#2092C2211yescharacteristic
93#2092C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2085C2211yescharacteristic
97#2084C2211yescharacteristic
98#2083C2211yescharacteristic
99#2083C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2076C2211yescharacteristic
105#2076C2211yescharacteristic
106#2076C2211yescharacteristic
107#2075C2211yescharacteristic
108#2067C2211yescharacteristic
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic
111#2058C2211yescharacteristic
112#2058C2211yescharacteristic
113#2057C2211yescharacteristic
114#2057C2211yescharacteristic
115#2057C2211yescharacteristic
116#2057C2211yescharacteristic
117#2057C2211yescharacteristic
118#2057C2211yescharacteristic
119#2057C2211yescharacteristic
120#2057C2211yescharacteristic
121#2057C2211yescharacteristic
122#2057C2211yescharacteristic
123#2034C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2025C2211yescharacteristic
128#1993C2211yescharacteristic
129#1993C2211yescharacteristic
130#1949C2211yescharacteristic
131#1947C2211yescharacteristic
132#1947C2211yescharacteristic
133#1947C2211yescharacteristic
134#1944C2211yescharacteristic
135#1944C2211yescharacteristic
136#1943C2211yescharacteristic
137#1941C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1934C2211yescharacteristic
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic
144#1924C2211yescharacteristic
145#1924C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1920C2211yescharacteristic
151#1920C2211yescharacteristic
152#1919C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1918C2211yescharacteristic
156#1917C2211yescharacteristic
157#1916C2211yescharacteristic
158#1895C2211yescharacteristic
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic
161#1893C2211yescharacteristic
162#1874C2211yescharacteristic
163#1870C2211yescharacteristic
164#1869C2211yescharacteristic
165#1869C2211yescharacteristic
166#1869C2211yescharacteristic
167#1864C2211yescharacteristic
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1853C2211yescharacteristic
174#1853C2211yescharacteristic
175#1853C2211yescharacteristic
176#1852C2211yescharacteristic
177#1852C2211yescharacteristic
178#1852C2211yescharacteristic
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1847C2211yescharacteristic
185#1845C2211yescharacteristic
186#1824C2211yescharacteristic
187#1824C2211yescharacteristic
188#1823C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1808C2211yescharacteristic
192#1808C2211yescharacteristic
193#1807C2211yescharacteristic
194#1807C2211yescharacteristic
195#1776C2211yescharacteristic
196C4×#107C2211yescharacteristic
197#1753C2211yescharacteristic
198#1752C2211yescharacteristic
199#1749C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×#41—21no—
204C23×Q8—21no—
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#548—48no—
210#547—42no—
211#547—42no—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8—42no—
215C2×C4⋊Q8—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#125—21no—
221C2×#125C2311yescharacteristic
222C2×#124—21no—
223C2×#124—21no—
224C2×#124—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121D411yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×C4×Q8—21no—
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4—21no—
250C22×C4⋊C4—21no—
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C42C2311yescharacteristic
259#501—42no—
260#501—42no—
261#482—42no—
262#481—24no—
263#480—42no—
264#435—24no—
265C8×D4—24no—
266#428—42no—
267C2×#107—42no—
268C2×#107—42no—
269C2×#107—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
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×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#401—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#399—21no—
324#399—21no—
325#399—21no—
326#399—21no—
327#399—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#395—21no—
344#395—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#393—21no—
351#393—21no—
352#391—21no—
353#391—21no—
354#390D411yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389D411yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388D411yescharacteristic
386#388D411yescharacteristic
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#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386D411yescharacteristic
404#386D411yescharacteristic
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#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#383—21no—
422#382—21no—
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#381—21no—
426#380—21no—
427#380D411yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451C2×#95—21no—
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—44no—
495C2×#41—44no—
496C2×#41—82no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8—44no—
502C22×Q8—44no—
503C22×Q8—82no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4C2×D411yescharacteristic
508C22×D4C2×D411yescharacteristic
509C22×D4C2×D411yescharacteristic
510C22×D4C2411yescharacteristic
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
523C23×C4C2411yescharacteristic
524C2×M16—22no—
525C2×M16—22no—
526C2×M16—41no—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—22no—
530C22×C8—22no—
531C22×C8—22no—
532C22×C8—22no—
533C22×C8—41no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—22no—
545C4⋊Q8—22no—
546C4⋊Q8—22no—
547C4⋊Q8—22no—
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552C4⋊Q8—44no—
553C4⋊Q8—44no—
554#125—41no—
555#125—41no—
556#125—82no—
557#124—44no—
558#124—44no—
559#124—44no—
560#123—44no—
561#123—44no—
562#123—82no—
563C22⋊Q8—44no—
564C22⋊Q8—44no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567C22⋊Q8—82no—
568#121—24no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—41no—
574#121—41no—
575#121—44no—
576#121—44no—
577C4×Q8—44no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—44no—
587C4×D4—44no—
588C4×D4—44no—
589C4×D4—44no—
590#117—41no—
591#117—41no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
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—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—44no—
639C2×C4⋊C4—82no—
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
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⋊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⋊C4—21no—
683C2×C22⋊C4—21no—
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×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—41no—
701C2×C42—41no—
702C2×C42C2×D411yescharacteristic
703C2×C42C2×D411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708#107—22no—
709#107—22no—
710#107—22no—
711#107—22no—
712#107—22no—
713#107—22no—
714#107—22no—
715#107—41no—
716#107—41no—
717#107—41no—
718#107—41no—
719#107—41no—
720#107—41no—
721#107—41no—
722#107—41no—
723#107—41no—
724#106—22no—
725#106—22no—
726#106—22no—
727#106—22no—
728#106—22no—
729#106—41no—
730#106—41no—
731#106—41no—
732C4⋊C8—22no—
733C4⋊C8—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742C22⋊C8—22no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—22no—
746C22⋊C8—22no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8#4114yescomplemented
750#97—22no—
751#97—41no—
752#97—41no—
753C4×C8—22no—
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#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795C24—21no—
796C24C22×D411yescharacteristic
797C24C22×D411yescharacteristic
798C24C22×D411yescharacteristic
799#41—816no—
800C2×Q8—24no—
801C2×Q8—42no—
802C2×Q8—42no—
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—42no—
806C2×Q8—42no—
807C2×Q8—42no—
808C2×Q8—42no—
809C2×Q8—42no—
810C2×Q8—81no—
811C2×Q8—81no—
812C2×Q8—816no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—41no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4AGL(1,ℤ/8)14yes—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—22no—
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—21no—
870C22×C4—21no—
871C22×C4—41no—
872C22×C4—41no—
873C22×C4—41no—
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—42no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C2×#4112yes—
910C22×C42−1+412yes—
911C22×C4C2511yescharacteristic
912M16—44no—
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—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—44no—
934C2×C8—44no—
935C2×C8—44no—
936C2×C8C2×#4112yes—
937C2×C8C2×#4112yes—
938C2×C82−1+412yes—
939C2×C82−1+412yes—
940C4⋊C4—24no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—22no—
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—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—41no—
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—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4H(5,𝔽2)12yes—
1006C4⋊C4H(5,𝔽2)12yes—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
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—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—41no—
1050C42—41no—
1051C42—42no—
1052C42—42no—
1053C42—42no—
1054C42—42no—
1055C42—81no—
1056C42—81no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23#54712yes—
1082C23C2×AGL(1,ℤ/8)12yes—
1083C23C2×AGL(1,ℤ/8)12yes—
1084C23#57812yes—
1085C23C23×D411yescharacteristic
1086Q8—48no—
1087Q8—84no—
1088Q8—84no—
1089Q8—84no—
1090D4—28no—
1091D4—44no—
1092D4—44no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—84no—
1098D4—84no—
1099D4—84no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
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—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—21no—
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—44no—
1137C2×C4—44no—
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—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—84no—
1190C2×C4—84no—
1191C2×C4—84no—
1192C2×C4—84no—
1193C2×C4—84no—
1194C2×C4—84no—
1195C2×C4—162no—
1196C2×C4—162no—
1197C2×C4#54712yes—
1198C2×C4C2×AGL(1,ℤ/8)12yes—
1199C2×C4#57612yes—
1200C2×C4C22×#4111yescharacteristic
1201C2×C4C2×H(5,𝔽2)11yescharacteristic
1202C2×C4C2×H(5,𝔽2)11yescharacteristic
1203C2×C4C2×2−1+411yescharacteristic
1204C2×C4C2×2−1+411yescharacteristic
1205C2×C4C2×2−1+411yescharacteristic
1206C8—22no—
1207C8—22no—
1208C8—22no—
1209C8—22no—
1210C8—41no—
1211C8—41no—
1212C8—41no—
1213C8—41no—
1214C22—22no—
1215C22—22no—
1216C22—22no—
1217C22—22no—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22#334314yes—
1242C22C2×#54711yescharacteristic
1243C22#348411yescharacteristic
1244C22#349911yescharacteristic
1245C22C22×AGL(1,ℤ/8)11yescharacteristic
1246C22C2×#57611yescharacteristic
1247C22C2×#57811yescharacteristic
1248C22#358611yescharacteristic
1249C4—22no—
1250C4—22no—
1251C4—22no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—42no—
1257C4—42no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4#352011yescharacteristic
1276C4#352011yescharacteristic
1277C4#355211yescharacteristic
1278C4#355211yescharacteristic
1279C2—24no—
1280C2—42no—
1281C2—81no—
1282C2—161no—
1283C2#4300411yescharacteristic
1284C2C2×#334311yescharacteristic
1285C2#6127811yescharacteristic
1286C2#6159111yescharacteristic
1287C2#6161211yescharacteristic
1288C2#6248811yescharacteristic
1289C2#6250311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59125C2
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
2. #38973C2semidirect
3. #32364C2semidirect
4. #32342C2semidirect
5. #32271C2semidirect
6. #32267C2semidirect
7. #31452C2semidirect
8. #31446C2semidirect
9. #30796C2semidirect
10. #30789C2semidirect
11. #29161C2semidirect
12. #28079C2semidirect
13. #28077C2semidirect
14. #26873C2semidirect
15. #26857C2semidirect
16. #26140C2semidirect
17. #26126C2semidirect
18. #26077C2semidirect
19. #26071C2semidirect
20. #25816C2semidirect
21. #25252C2semidirect
22. #25238C2semidirect
23. #24939C2semidirect
24. #24935C2semidirect
25. #24100C2semidirect
26. #24088C2semidirect
27. C2×#2057C2semidirect
28. #23117C2semidirect
29. #22661C2semidirect
30. D4×#107C2semidirect
31. #22082C2semidirect
749. C22⋊C8#41semidirect

Maximal subgroups

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

subgroupindex
#591252
#389732
#323642
#323422
#322712
#322672
#314522
#314462
#307962
#307892
#291612
#280792
#280772
#268732
#268572
#261402
#261262
#260772
#260712
#258162
#252522
#252382
#249392
#249352
#241002
#240882
C2×#20572
#231172
#226612
D4×#1072
#220822