Subgroups — #481×C₃₆₇ #37553799

Order 23488.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#121×C₃₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×C₃₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#106×C₃₆₇	C₂	1	2	yes	maximal, complemented
4	#102×C₃₆₇	C₂	1	2	yes	maximal, complemented
5	C₂²⋊C₈×C₃₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₃₆₇	—	2	1	no	—
7	C₂×D₄×C₃₆₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₃₆₇	—	2	1	no	—
9	C₂²×C₄×C₃₆₇	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₃₆₇	C₂²	1	2	yes	—
11	C₄⋊C₄×C₃₆₇	—	2	1	no	—
12	C₄⋊C₄×C₃₆₇	C₂²	1	2	yes	—
13	C₄⋊C₄×C₃₆₇	C₂²	1	1	yes	characteristic
14	C₂²⋊C₄×C₃₆₇	—	2	1	no	—
15	C₂³×C₃₆₇	—	2	1	no	—
16	C₂³×C₃₆₇	D₄	1	1	yes	characteristic
17	D₄×C₃₆₇	—	2	2	no	—
18	D₄×C₃₆₇	—	4	2	no	—
19	C₂×C₄×C₃₆₇	—	2	2	no	—
20	C₂×C₄×C₃₆₇	—	2	1	no	—
21	C₂×C₄×C₃₆₇	—	2	2	no	—
22	C₂×C₄×C₃₆₇	—	4	2	no	—
23	C₂×C₄×C₃₆₇	D₄	1	1	yes	characteristic
24	C₂×C₄×C₃₆₇	C₂³	1	1	yes	characteristic
25	C₈×C₃₆₇	—	2	2	no	—
26	C₂²×C₃₆₇	—	2	1	no	—
27	C₂²×C₃₆₇	—	2	1	no	—
28	C₂²×C₃₆₇	—	4	1	no	—
29	C₂²×C₃₆₇	—	4	1	no	—
30	C₂²×C₃₆₇	—	4	1	no	—
31	C₂²×C₃₆₇	SD₁₆	1	2	yes	—
32	C₂²×C₃₆₇	C₂×D₄	1	1	yes	characteristic
33	C₄×C₃₆₇	—	2	1	no	—
34	C₄×C₃₆₇	—	4	1	no	—
35	C₄×C₃₆₇	—	4	2	no	—
36	C₄×C₃₆₇	#41	1	2	yes	—
37	C₂×C₃₆₇	—	2	2	no	—
38	C₂×C₃₆₇	—	8	1	no	—
39	C₂×C₃₆₇	#123	1	1	yes	characteristic
40	C₂×C₃₆₇	C₂×SD₁₆	1	1	yes	characteristic
41	C₂×C₃₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
42	C₃₆₇	#481	1	1	yes	characteristic, direct product factor, Sylow
43	#481	C₃₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	#121	C₂×C₃₆₇	1	1	yes	characteristic
45	C₂×C₄⋊C₄	C₂×C₃₆₇	1	1	yes	characteristic, complemented
46	#106	C₂×C₃₆₇	1	2	yes	complemented
47	#102	C₂×C₃₆₇	1	2	yes	complemented
48	C₂²⋊C₈	C₂×C₃₆₇	1	1	yes	characteristic, complemented
49	C₂×D₄	—	2	1	no	—
50	C₂×D₄	C₂²×C₃₆₇	1	1	yes	characteristic
51	C₂²×C₄	—	2	1	no	—
52	C₂²×C₄	C₂²×C₃₆₇	1	1	yes	characteristic
53	C₂×C₈	C₂²×C₃₆₇	1	2	yes	—
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	C₂²×C₃₆₇	1	2	yes	—
56	C₄⋊C₄	C₂²×C₃₆₇	1	1	yes	characteristic
57	C₂²⋊C₄	—	2	1	no	—
58	C₂³	—	2	1	no	—
59	C₂³	D₄×C₃₆₇	1	1	yes	characteristic
60	D₄	—	2	2	no	—
61	D₄	—	4	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	D₄×C₃₆₇	1	1	yes	characteristic
67	C₂×C₄	C₂³×C₃₆₇	1	1	yes	characteristic
68	C₈	—	2	2	no	—
69	C₂²	—	2	1	no	—
70	C₂²	—	2	1	no	—
71	C₂²	—	4	1	no	—
72	C₂²	—	4	1	no	—
73	C₂²	—	4	1	no	—
74	C₂²	SD₁₆×C₃₆₇	1	2	yes	—
75	C₂²	C₂×D₄×C₃₆₇	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	4	2	no	—
79	C₄	#41×C₃₆₇	1	2	yes	—
80	C₂	—	2	2	no	—
81	C₂	—	8	1	no	—
82	C₂	#123×C₃₆₇	1	1	yes	characteristic
83	C₂	C₂×SD₁₆×C₃₆₇	1	1	yes	characteristic
84	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	#121×C₃₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₆₇ ◁ C₂²×C₄×C₃₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄⋊C₄×C₃₆₇	C₂	semidirect
3. #106×C₃₆₇	C₂	semidirect
4. #102×C₃₆₇	C₂	semidirect
5. C₂²⋊C₈×C₃₆₇	C₂	semidirect
42. C₃₆₇	#481	direct (N × H)
43. #481	C₃₆₇	direct (N × H)
45. C₂×C₄⋊C₄	C₂×C₃₆₇	semidirect
46. #106	C₂×C₃₆₇	semidirect
47. #102	C₂×C₃₆₇	semidirect
48. C₂²⋊C₈	C₂×C₃₆₇	semidirect

Maximal subgroups

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

subgroup	index
#121×C₃₆₇	2
C₂×C₄⋊C₄×C₃₆₇	2
#106×C₃₆₇	2
#102×C₃₆₇	2
C₂²⋊C₈×C₃₆₇	2
#481	367

Subgroups — #481×C367 #37553799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #481×C₃₆₇ #37553799