Subgroups — #460×C₃₆₇ #37553778

Order 23488.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×C₃₆₇	C₂	1	2	yes	maximal, complemented
2	#127×C₃₆₇	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₈×C₃₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊C₈×C₃₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#102×C₃₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×Q₈×C₃₆₇	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₃₆₇	—	2	1	no	—
8	C₂×D₄×C₃₆₇	—	2	1	no	—
9	C₂×D₄×C₃₆₇	C₂²	1	2	yes	—
10	SD₁₆×C₃₆₇	—	2	4	no	—
11	C₂×C₈×C₃₆₇	C₂²	1	2	yes	—
12	C₄⋊C₄×C₃₆₇	—	2	1	no	—
13	C₄⋊C₄×C₃₆₇	C₂²	1	1	yes	characteristic
14	C₄²×C₃₆₇	—	2	1	no	—
15	C₄²×C₃₆₇	C₂²	1	1	yes	characteristic
16	C₂³×C₃₆₇	—	2	2	no	—
17	Q₈×C₃₆₇	—	2	1	no	—
18	Q₈×C₃₆₇	D₄	1	2	yes	complemented
19	D₄×C₃₆₇	—	2	2	no	—
20	D₄×C₃₆₇	—	2	2	no	—
21	D₄×C₃₆₇	—	4	2	no	—
22	D₄×C₃₆₇	—	4	2	no	—
23	C₂×C₄×C₃₆₇	—	2	1	no	—
24	C₂×C₄×C₃₆₇	—	2	1	no	—
25	C₂×C₄×C₃₆₇	D₄	1	1	yes	characteristic
26	C₂×C₄×C₃₆₇	D₄	1	1	yes	characteristic
27	C₂×C₄×C₃₆₇	C₂³	1	1	yes	characteristic
28	C₈×C₃₆₇	—	2	2	no	—
29	C₂²×C₃₆₇	—	4	2	no	—
30	C₂²×C₃₆₇	—	4	2	no	—
31	C₂²×C₃₆₇	—	4	2	no	—
32	C₂²×C₃₆₇	C₂×D₄	1	1	yes	characteristic
33	C₄×C₃₆₇	—	2	2	no	—
34	C₄×C₃₆₇	—	2	1	no	—
35	C₄×C₃₆₇	—	4	1	no	—
36	C₄×C₃₆₇	SD₁₆	1	2	yes	complemented
37	C₄×C₃₆₇	C₂×D₄	1	1	yes	characteristic
38	C₄×C₃₆₇	#41	1	1	yes	characteristic
39	C₂×C₃₆₇	—	8	2	no	—
40	C₂×C₃₆₇	#121	1	1	yes	characteristic
41	C₂×C₃₆₇	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×C₃₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
43	C₃₆₇	#460	1	1	yes	characteristic, direct product factor, Sylow
44	#460	C₃₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×SD₁₆	C₂×C₃₆₇	1	2	yes	complemented
46	#127	C₂×C₃₆₇	1	1	yes	characteristic
47	C₄×Q₈	C₂×C₃₆₇	1	1	yes	characteristic, complemented
48	C₄⋊C₈	C₂×C₃₆₇	1	1	yes	characteristic, complemented
49	#102	C₂×C₃₆₇	1	2	yes	complemented
50	C₂×Q₈	C₂²×C₃₆₇	1	1	yes	characteristic
51	C₂×D₄	—	2	1	no	—
52	C₂×D₄	—	2	1	no	—
53	C₂×D₄	C₂²×C₃₆₇	1	2	yes	—
54	SD₁₆	—	2	4	no	—
55	C₂×C₈	C₂²×C₃₆₇	1	2	yes	—
56	C₄⋊C₄	—	2	1	no	—
57	C₄⋊C₄	C₂²×C₃₆₇	1	1	yes	characteristic
58	C₄²	—	2	1	no	—
59	C₄²	C₂²×C₃₆₇	1	1	yes	characteristic
60	C₂³	—	2	2	no	—
61	Q₈	—	2	1	no	—
62	Q₈	D₄×C₃₆₇	1	2	yes	complemented
63	D₄	—	2	2	no	—
64	D₄	—	2	2	no	—
65	D₄	—	4	2	no	—
66	D₄	—	4	2	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	D₄×C₃₆₇	1	1	yes	characteristic
70	C₂×C₄	D₄×C₃₆₇	1	1	yes	characteristic
71	C₂×C₄	C₂³×C₃₆₇	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₂²	—	4	2	no	—
74	C₂²	—	4	2	no	—
75	C₂²	—	4	2	no	—
76	C₂²	C₂×D₄×C₃₆₇	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	2	1	no	—
79	C₄	—	4	1	no	—
80	C₄	SD₁₆×C₃₆₇	1	2	yes	complemented
81	C₄	C₂×D₄×C₃₆₇	1	1	yes	characteristic
82	C₄	#41×C₃₆₇	1	1	yes	characteristic
83	C₂	—	8	2	no	—
84	C₂	#121×C₃₆₇	1	1	yes	characteristic
85	C₂	C₂×SD₁₆×C₃₆₇	1	1	yes	characteristic
86	C₂	AGL(1,ℤ/8)×C₃₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₆₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃₆₇
prime radical	#127×C₃₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₆₇ ◁ C₄²×C₃₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×C₃₆₇	C₂	semidirect
3. C₄×Q₈×C₃₆₇	C₂	semidirect
4. C₄⋊C₈×C₃₆₇	C₂	semidirect
5. #102×C₃₆₇	C₂	semidirect
18. Q₈×C₃₆₇	D₄	semidirect
36. C₄×C₃₆₇	SD₁₆	semidirect
43. C₃₆₇	#460	direct (N × H)
44. #460	C₃₆₇	direct (N × H)
45. C₂×SD₁₆	C₂×C₃₆₇	semidirect
47. C₄×Q₈	C₂×C₃₆₇	semidirect
48. C₄⋊C₈	C₂×C₃₆₇	semidirect
49. #102	C₂×C₃₆₇	semidirect
62. Q₈	D₄×C₃₆₇	semidirect
80. C₄	SD₁₆×C₃₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×C₃₆₇	2
#127×C₃₆₇	2
C₄×Q₈×C₃₆₇	2
C₄⋊C₈×C₃₆₇	2
#102×C₃₆₇	2
#460	367

Subgroups — #460×C367 #37553778

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #460×C₃₆₇ #37553778