Subgroups — C₃₆₇⋊#401 #37554129

Order 23488.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₆₇⋊#95	C₂	1	3	yes	maximal
2	C₃₆₇⋊#95	C₂	1	3	yes	maximal
3	#95×C₃₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₃₆₇	C₂²	1	3	yes	—
5	C₂²×Dic₃₆₇	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₃₆₇	C₂²	1	3	yes	—
7	C₂×Dic₃₆₇	—	2	3	no	—
8	C₂×Dic₃₆₇	—	2	3	no	—
9	C₂×Dic₃₆₇	—	2	3	no	—
10	C₂×Dic₃₆₇	—	2	3	no	—
11	C₂³×C₃₆₇	C₂³	1	1	yes	characteristic
12	C₂×C₄×C₃₆₇	—	2	6	no	—
13	C₂×C₄×C₃₆₇	—	2	3	no	—
14	C₂²×C₃₆₇	#41	1	3	yes	—
15	C₂²×C₃₆₇	#41	1	3	yes	—
16	C₂²×C₃₆₇	#41	1	1	yes	characteristic
17	C₄×C₃₆₇	—	4	3	no	—
18	Dic₃₆₇	—	4	1	no	—
19	Dic₃₆₇	—	4	3	no	—
20	C₂×C₃₆₇	#126	1	3	yes	—
21	C₂×C₃₆₇	#126	1	1	yes	characteristic
22	C₂×C₃₆₇	#126	1	3	yes	—
23	C₃₆₇	#401	1	1	yes	characteristic, complemented, Sylow
24	#401	—	367	1	no	maximal, Sylow
25	#95	—	367	3	no	—
26	#95	—	367	3	no	—
27	#95	D₃₆₇	1	1	yes	characteristic
28	C₂²×C₄	—	367	3	no	—
29	C₂²×C₄	—	367	1	no	—
30	C₂²×C₄	C₂×D₃₆₇	1	3	yes	—
31	C₂³	C₂²×D₃₆₇	1	1	yes	characteristic
32	C₂×C₄	—	2	6	no	—
33	C₂×C₄	—	2	3	no	—
34	C₂×C₄	—	734	3	no	—
35	C₂×C₄	—	734	3	no	—
36	C₂×C₄	—	734	3	no	—
37	C₂×C₄	—	734	3	no	—
38	C₂²	#19154576	1	3	yes	—
39	C₂²	#19154577	1	3	yes	—
40	C₂²	#19154578	1	1	yes	characteristic
41	C₄	—	4	3	no	—
42	C₄	—	1468	1	no	—
43	C₄	—	1468	3	no	—
44	C₂	#26044254	1	3	yes	—
45	C₂	#26044255	1	1	yes	characteristic
46	C₂	#26044256	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃₆₇
commutator, socle, prime radical, cosocle	C₂³×C₃₆₇	C₂³
Fitting	#95×C₃₆₇	C₂
hypercenter	#95	D₃₆₇
hypocenter	C₃₆₇	#401
LCS	G ▷ C₂³×C₃₆₇ ▷ C₃₆₇
UCS	C₁ ◁ C₂³ ◁ #95

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

N	H ≅ G/N	type
23. C₃₆₇	#401	semidirect

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