Finite Group Databasebeta

← #7041192

Subgroups — #7041192

Order 512.

1676 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59198C211yesmaximal, characteristic, complemented
2#59022C211yesmaximal, characteristic
3#32016C211yesmaximal, characteristic, complemented
4#31781C211yesmaximal, characteristic, complemented
5#31756C211yesmaximal, characteristic, complemented
6#31693C211yesmaximal, characteristic, complemented
7#31674C211yesmaximal, characteristic, complemented
8#31445C211yesmaximal, characteristic, complemented
9#31356C211yesmaximal, characteristic, complemented
10#31278C211yesmaximal, characteristic, complemented
11#27695C211yesmaximal, characteristic, complemented
12#27601C211yesmaximal, characteristic, complemented
13#27546C211yesmaximal, characteristic, complemented
14#27527C211yesmaximal, characteristic, complemented
15#27333C211yesmaximal, characteristic, complemented
16#27181C211yesmaximal, characteristic, complemented
17#26412C211yesmaximal, characteristic, complemented
18#26301C211yesmaximal, characteristic, complemented
19#26218C211yesmaximal, characteristic, complemented
20#26202C211yesmaximal, characteristic, complemented
21#25250C211yesmaximal, characteristic, complemented
22#24971C211yesmaximal, characteristic, complemented
23#24962C211yesmaximal, characteristic, complemented
24#24576C211yesmaximal, characteristic, complemented
25#24094C211yesmaximal, characteristic, complemented
26#24004C211yesmaximal, characteristic, complemented
27C2×#2076C211yesmaximal, characteristic, complemented
28#22920C211yesmaximal, characteristic, complemented
29#22491C211yesmaximal, characteristic, complemented
30#22032C211yesmaximal, characteristic, complemented
31#21763C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#551—21no—
34C2×#525C2211yescharacteristic
35C2×#483C2211yescharacteristic
36C2×#480C2211yescharacteristic
37C2×#435C2211yescharacteristic
38C22×#107C2211yescharacteristic
39C22×C22⋊C8C2211yescharacteristic
40#2722—21no—
41#2717—21no—
42#2705—21no—
43#2694—21no—
44#2547C2211yescharacteristic
45#2539—21no—
46#2538C2211yescharacteristic
47#2501C2211yescharacteristic
48#2496C2211yescharacteristic
49#2496C2211yescharacteristic
50#2490C2211yescharacteristic
51#2486C2211yescharacteristic
52#2486C2211yescharacteristic
53#2486C2211yescharacteristic
54#2483—21no—
55#2467—21no—
56#2454—21no—
57#2441C2211yescharacteristic
58#2440C2211yescharacteristic
59#2440C2211yescharacteristic
60#2438—21no—
61#2438—21no—
62#2425—21no—
63#2423C2211yescharacteristic
64#2419—21no—
65#2419—21no—
66#2416C2211yescharacteristic
67#2414C2211yescharacteristic
68#2411—21no—
69#2407C2211yescharacteristic
70#2360C2211yescharacteristic
71#2359—21no—
72#2354C2211yescharacteristic
73D4×C4⋊C4C2211yescharacteristic
74D4×C4⋊C4C2211yescharacteristic
75#2344C2211yescharacteristic
76#2344C2211yescharacteristic
77#2341C2211yescharacteristic
78C4×#120C2211yescharacteristic
79C2×#380C2211yescharacteristic
80C2×#380C2211yescharacteristic
81C2×#380C2211yescharacteristic
82#2100C2211yescharacteristic, complemented
83#2099C2211yescharacteristic, complemented
84#2099C2211yescharacteristic, complemented
85#2099C2211yescharacteristic, complemented
86#2088C2211yescharacteristic, complemented
87#2087C2211yescharacteristic, complemented
88#2083C2211yescharacteristic, complemented
89#2083C2211yescharacteristic, complemented
90#2077C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic, complemented
95#2076C2211yescharacteristic
96#2076C2211yescharacteristic
97#2076C2211yescharacteristic
98#2076C2211yescharacteristic
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic
101#2076C2211yescharacteristic
102#2076C2211yescharacteristic
103#2076C2211yescharacteristic, complemented
104#2071C2211yescharacteristic, complemented
105#2071C2211yescharacteristic, complemented
106#2067C2211yescharacteristic, complemented
107#2067C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic, complemented
110#2059C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic, complemented
115#2036C2211yescharacteristic, complemented
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic, complemented
119#2034C2211yescharacteristic, complemented
120#2024C2211yescharacteristic, complemented
121#2023C2211yescharacteristic, complemented
122#1992C2211yescharacteristic, complemented
123#1990C2211yescharacteristic, complemented
124#1989C2211yescharacteristic, complemented
125#1988C2211yescharacteristic, complemented
126#1954C2211yescharacteristic
127#1954C2211yescharacteristic
128#1947C2211yescharacteristic, complemented
129#1947C2211yescharacteristic, complemented
130#1944C2211yescharacteristic, complemented
131#1941C2211yescharacteristic, complemented
132#1936C2211yescharacteristic, complemented
133#1934C2211yescharacteristic, complemented
134#1934C2211yescharacteristic, complemented
135#1933C2211yescharacteristic, complemented
136#1927C2211yescharacteristic, complemented
137#1926C2211yescharacteristic, complemented
138#1925C2211yescharacteristic, complemented
139#1925C2211yescharacteristic, complemented
140#1924C2211yescharacteristic
141#1924C2211yescharacteristic
142#1923C2211yescharacteristic
143#1923C2211yescharacteristic
144#1920C2211yescharacteristic, complemented
145#1919C2211yescharacteristic, complemented
146#1919C2211yescharacteristic, complemented
147#1919C2211yescharacteristic, complemented
148#1895C2211yescharacteristic, complemented
149#1894C2211yescharacteristic, complemented
150#1893C2211yescharacteristic
151#1893C2211yescharacteristic
152#1892C2211yescharacteristic
153#1892C2211yescharacteristic
154#1874C2211yescharacteristic
155#1874C2211yescharacteristic
156#1874C2211yescharacteristic
157#1874C2211yescharacteristic, complemented
158#1872C2211yescharacteristic
159#1872C2211yescharacteristic
160#1872C2211yescharacteristic
161#1872C2211yescharacteristic, complemented
162#1870C2211yescharacteristic
163#1870C2211yescharacteristic
164#1869C2211yescharacteristic
165#1865C2211yescharacteristic, complemented
166#1865C2211yescharacteristic, complemented
167#1863C2211yescharacteristic, complemented
168#1863C2211yescharacteristic, complemented
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic, complemented
172#1854C2211yescharacteristic, complemented
173#1853C2211yescharacteristic
174#1853C2211yescharacteristic
175#1853C2211yescharacteristic
176#1853C2211yescharacteristic
177#1850C2211yescharacteristic
178#1834C2211yescharacteristic, complemented
179#1825C2211yescharacteristic
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic, complemented
182#1824C2211yescharacteristic
183#1824C2211yescharacteristic
184#1824C2211yescharacteristic, complemented
185#1823C2211yescharacteristic
186#1823C2211yescharacteristic
187#1809C2211yescharacteristic, complemented
188#1803C2211yescharacteristic, complemented
189#1803C2211yescharacteristic, complemented
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1779C2211yescharacteristic
195C4×#106C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C8×C22⋊C4C2211yescharacteristic
199#1736C2211yescharacteristic, complemented
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#552—24no—
209#552—42no—
210#551—48no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#126—21no—
215C2×#125—21no—
216C2×#125C2311yescharacteristic
217C2×#124—21no—
218#525—24no—
219#525—42no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120D411yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
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×#117—21no—
248C2×#117—21no—
249C2×#117—21no—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C22⋊C4—21no—
260C22×C22⋊C4—21no—
261C22×C22⋊C4—21no—
262#483—24no—
263#480—42no—
264#435—42no—
265C2×#107—42no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×C22⋊C8—42no—
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#400—21no—
315#400—21no—
316#399—21no—
317#399—21no—
318#399—21no—
319#399—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#395—21no—
339#395—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#392—21no—
345#392—21no—
346#391—21no—
347#391C2311yescharacteristic
348#390—21no—
349#390—21no—
350#390—21no—
351#390—21no—
352#390—21no—
353#390—21no—
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—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#386—21no—
385#386—21no—
386#386D411yescharacteristic
387#386D411yescharacteristic
388#386D411yescharacteristic
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385D411yescharacteristic
398#385D411yescharacteristic
399#385D411yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#381—21no—
405#381—21no—
406#381—21no—
407#381—21no—
408#381—21no—
409#380—21no—
410#380—21no—
411#380—21no—
412#380—21no—
413#380—21no—
414#380—21no—
415#380—21no—
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#379D411yescharacteristic
433C4×C4⋊C4—21no—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443C2×#95—21no—
444C2×#95—21no—
445C2×#95—21no—
446#340C2311yescharacteristic
447#340C2311yescharacteristic
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#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C25C2×D411yescharacteristic
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C22×Q8—21no—
496C22×Q8C2411yescharacteristic
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4C2×D411yescharacteristic
502C22×D4C2×D411yescharacteristic
503C22×D4C2×D411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—22no—
506C23×C4—22no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—41no—
516C23×C4—41no—
517C23×C4—41no—
518C23×C4—41no—
519C23×C4C2×D411yescharacteristic
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C2×M16—41no—
527C2×M16—41no—
528C2×M16—41no—
529C22×C8—22no—
530C22×C8—22no—
531C22×C8—41no—
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—41no—
544C4⋊Q8—41no—
545#126—44no—
546#126—44no—
547#126—44no—
548#125—22no—
549#125—41no—
550#125—44no—
551#124—44no—
552#123—44no—
553#123—44no—
554#123—44no—
555#123—44no—
556#123—44no—
557#123—44no—
558#123—82no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—44no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—44no—
566C22⋊Q8#4114yes—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—41no—
571#121—41no—
572#121—41no—
573#121—82no—
574#120—24no—
575#120—44no—
576C4×Q8—22no—
577C4×Q8—41no—
578C4×Q8—41no—
579C4×Q8—41no—
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—22no—
591#117—22no—
592#117—44no—
593#117—44no—
594#117—41no—
595#117—41no—
596#117—44no—
597C2×C4⋊C4—21no—
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—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
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×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⋊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⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—44no—
690C2×C22⋊C4—44no—
691C2×C22⋊C4—82no—
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715#107—41no—
716#107—41no—
717#107—41no—
718#107—41no—
719#107—41no—
720#107—41no—
721#106—22no—
722#106—22no—
723#106—41no—
724#106—41no—
725#106—41no—
726#106—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730#103—22no—
731#103—22no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746C22⋊C8—22no—
747C22⋊C8—22no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755C22⋊C8—41no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758C22⋊C8—41no—
759#97—41no—
760C4×C8—41no—
761C4×C8—41no—
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#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798C24—22no—
799C24—22no—
800C24—22no—
801C24—22no—
802C24—21no—
803C24—41no—
804C24—41no—
805C24—41no—
806C24C22×D411yescharacteristic
807C24C22×D411yescharacteristic
808C24C22×D411yescharacteristic
809C24C22×D411yescharacteristic
810#41—82no—
811#41—82no—
812#41—82no—
813#41—82no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—42no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×Q8C2×#4112yes—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—41no—
836C2×D4—41no—
837C2×D4—41no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—22no—
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—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—22no—
876C22×C4—22no—
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—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—82no—
912C22×C4—82no—
913C22×C4—82no—
914C22×C4—82no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C2×#4112yes—
935C22×C4H(5,𝔽2)12yes—
936C22×C4C2511yescharacteristic
937M16—82no—
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—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—44no—
963C2×C8—82no—
964C4⋊C4—24no—
965C4⋊C4—22no—
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—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4C2×#4112yes—
1026C22⋊C4—24no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4AGL(1,ℤ/8)14yes—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42—42no—
1078C42—42no—
1079C42—42no—
1080C42—81no—
1081C42—81no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—44no—
1107C23—44no—
1108C23—44no—
1109C23—44no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—82no—
1118C23—82no—
1119C23—82no—
1120C23#54612yes—
1121C23C2×AGL(1,ℤ/8)12yes—
1122C23#57712yes—
1123C23#57812yes—
1124C23C23×D411yescharacteristic
1125Q8—22no—
1126Q8—22no—
1127Q8—41no—
1128Q8—41no—
1129Q8—162no—
1130D4—44no—
1131D4—44no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—82no—
1137D4—84no—
1138D4—84no—
1139D4—84no—
1140D4—162no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
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—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—82no—
1230C2×C4—82no—
1231C2×C4—82no—
1232C2×C4—84no—
1233C2×C4—84no—
1234C2×C4—84no—
1235C2×C4—84no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4#54612yes—
1241C2×C4C2×AGL(1,ℤ/8)12yes—
1242C2×C4C2×AGL(1,ℤ/8)12yes—
1243C2×C4C22×#4111yescharacteristic
1244C2×C4C2×H(5,𝔽2)11yescharacteristic
1245C2×C4#58511yescharacteristic
1246C2×C4#58511yescharacteristic
1247C2×C4#58511yescharacteristic
1248C2×C4#58511yescharacteristic
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—88no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22#333214yes—
1293C22C2×#54611yescharacteristic
1294C22#348511yescharacteristic
1295C22#348511yescharacteristic
1296C22C22×AGL(1,ℤ/8)11yescharacteristic
1297C22C2×#57711yescharacteristic
1298C22C2×#57811yescharacteristic
1299C22#358411yescharacteristic
1300C4—22no—
1301C4—22no—
1302C4—22no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—42no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—42no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4#352111yescharacteristic
1326C4#352111yescharacteristic
1327C4#353311yescharacteristic
1328C4#354511yescharacteristic
1329C2—24no—
1330C2—42no—
1331C2—81no—
1332C2—81no—
1333C2—161no—
1334C2#4352511yescharacteristic
1335C2C2×#333211yescharacteristic
1336C2#6117311yescharacteristic
1337C2#6173311yescharacteristic
1338C2#6173711yescharacteristic
1339C2#6176711yescharacteristic
1340C2#6177011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59022C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59198C2semidirect
3. #32016C2semidirect
4. #31781C2semidirect
5. #31756C2semidirect
6. #31693C2semidirect
7. #31674C2semidirect
8. #31445C2semidirect
9. #31356C2semidirect
10. #31278C2semidirect
11. #27695C2semidirect
12. #27601C2semidirect
13. #27546C2semidirect
14. #27527C2semidirect
15. #27333C2semidirect
16. #27181C2semidirect
17. #26412C2semidirect
18. #26301C2semidirect
19. #26218C2semidirect
20. #26202C2semidirect
21. #25250C2semidirect
22. #24971C2semidirect
23. #24962C2semidirect
24. #24576C2semidirect
25. #24094C2semidirect
26. #24004C2semidirect
27. C2×#2076C2semidirect
28. #22920C2semidirect
29. #22491C2semidirect
30. #22032C2semidirect
31. #21763C2semidirect
82. #2100C22semidirect
83. #2099C22semidirect
84. #2099C22semidirect
85. #2099C22semidirect
86. #2088C22semidirect
87. #2087C22semidirect
88. #2083C22semidirect
89. #2083C22semidirect
94. #2077C22semidirect
103. #2076C22semidirect
104. #2071C22semidirect
105. #2071C22semidirect
106. #2067C22semidirect
107. #2067C22semidirect
108. #2066C22semidirect
109. #2065C22semidirect
110. #2059C22semidirect
111. #2059C22semidirect
114. #2036C22semidirect
115. #2036C22semidirect
118. #2034C22semidirect
119. #2034C22semidirect
120. #2024C22semidirect
121. #2023C22semidirect
122. #1992C22semidirect
123. #1990C22semidirect
124. #1989C22semidirect
125. #1988C22semidirect
128. #1947C22semidirect
129. #1947C22semidirect
130. #1944C22semidirect
131. #1941C22semidirect
132. #1936C22semidirect
133. #1934C22semidirect
134. #1934C22semidirect
135. #1933C22semidirect
136. #1927C22semidirect
137. #1926C22semidirect
138. #1925C22semidirect
139. #1925C22semidirect
144. #1920C22semidirect
145. #1919C22semidirect
146. #1919C22semidirect
147. #1919C22semidirect
148. #1895C22semidirect
149. #1894C22semidirect
157. #1874C22semidirect
161. #1872C22semidirect
165. #1865C22semidirect
166. #1865C22semidirect
167. #1863C22semidirect
168. #1863C22semidirect
171. #1854C22semidirect
172. #1854C22semidirect
178. #1834C22semidirect
181. #1825C22semidirect
184. #1824C22semidirect
187. #1809C22semidirect
188. #1803C22semidirect
189. #1803C22semidirect
195. C4×#106C22semidirect
196. #1763C22semidirect
197. C4×#103C22semidirect
199. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#591982
#590222
#320162
#317812
#317562
#316932
#316742
#314452
#313562
#312782
#276952
#276012
#275462
#275272
#273332
#271812
#264122
#263012
#262182
#262022
#252502
#249712
#249622
#245762
#240942
#240042
C2×#20762
#229202
#224912
#220322
#217632