Subgroups — #436×C₃₆₇ #37553754

Order 23488.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₃₆₇	C₂	1	2	yes	maximal, complemented
2	C₄×D₄×C₃₆₇	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×C₃₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊C₈×C₃₆₇	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₃₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₃₆₇	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₃₆₇	C₂²	1	2	yes	—
8	M₁₆×C₃₆₇	—	2	4	no	—
9	C₂×C₈×C₃₆₇	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₃₆₇	C₂²	1	2	yes	—
11	C₂×C₈×C₃₆₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₃₆₇	C₄	1	1	yes	characteristic
13	C₂²⋊C₄×C₃₆₇	C₄	1	2	yes	—
14	C₄²×C₃₆₇	C₂²	1	1	yes	characteristic
15	C₂³×C₃₆₇	C₂×C₄	1	2	yes	—
16	D₄×C₃₆₇	—	2	2	no	—
17	C₂×C₄×C₃₆₇	—	2	2	no	—
18	C₂×C₄×C₃₆₇	—	2	2	no	—
19	C₂×C₄×C₃₆₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₃₆₇	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₃₆₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₃₆₇	C₂³	1	1	yes	characteristic
23	C₈×C₃₆₇	—	2	2	no	—
24	C₈×C₃₆₇	—	2	1	no	—
25	C₈×C₃₆₇	D₄	1	2	yes	complemented
26	C₂²×C₃₆₇	—	2	2	no	—
27	C₂²×C₃₆₇	—	2	2	no	—
28	C₂²×C₃₆₇	—	2	2	no	—
29	C₂²×C₃₆₇	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₃₆₇	—	2	2	no	—
31	C₄×C₃₆₇	—	2	1	no	—
32	C₄×C₃₆₇	M₁₆	1	2	yes	complemented
33	C₄×C₃₆₇	C₂×D₄	1	1	yes	characteristic
34	C₄×C₃₆₇	#41	1	1	yes	characteristic
35	C₂×C₃₆₇	—	4	2	no	—
36	C₂×C₃₆₇	C₄×D₄	1	1	yes	characteristic
37	C₂×C₃₆₇	C₂×M₁₆	1	1	yes	characteristic
38	C₂×C₃₆₇	#131	1	1	yes	characteristic
39	C₃₆₇	#436	1	1	yes	characteristic, direct product factor, Sylow
40	#436	C₃₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂×M₁₆	C₂×C₃₆₇	1	2	yes	complemented
42	C₄×D₄	C₂×C₃₆₇	1	1	yes	characteristic
43	C₄⋊C₈	C₂×C₃₆₇	1	1	yes	characteristic, complemented
44	C₂²⋊C₈	C₂×C₃₆₇	1	2	yes	complemented
45	C₄×C₈	C₂×C₃₆₇	1	1	yes	characteristic, complemented
46	C₂×D₄	C₄×C₃₆₇	1	1	yes	characteristic
47	C₂²×C₄	C₂²×C₃₆₇	1	2	yes	—
48	M₁₆	—	2	4	no	—
49	C₂×C₈	C₂²×C₃₆₇	1	1	yes	characteristic
50	C₂×C₈	C₂²×C₃₆₇	1	2	yes	—
51	C₂×C₈	C₂²×C₃₆₇	1	1	yes	characteristic
52	C₄⋊C₄	C₄×C₃₆₇	1	1	yes	characteristic
53	C₂²⋊C₄	C₄×C₃₆₇	1	2	yes	—
54	C₄²	C₂²×C₃₆₇	1	1	yes	characteristic
55	C₂³	C₂×C₄×C₃₆₇	1	2	yes	—
56	D₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	C₂×C₄×C₃₆₇	1	1	yes	characteristic
60	C₂×C₄	C₂×C₄×C₃₆₇	1	2	yes	—
61	C₂×C₄	C₂×C₄×C₃₆₇	1	1	yes	characteristic
62	C₂×C₄	C₂³×C₃₆₇	1	1	yes	characteristic
63	C₈	—	2	2	no	—
64	C₈	—	2	1	no	—
65	C₈	D₄×C₃₆₇	1	2	yes	complemented
66	C₂²	—	2	2	no	—
67	C₂²	—	2	2	no	—
68	C₂²	—	2	2	no	—
69	C₂²	C₂²×C₄×C₃₆₇	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	2	1	no	—
72	C₄	M₁₆×C₃₆₇	1	2	yes	complemented
73	C₄	C₂×D₄×C₃₆₇	1	1	yes	characteristic
74	C₄	#41×C₃₆₇	1	1	yes	characteristic
75	C₂	—	4	2	no	—
76	C₂	C₄×D₄×C₃₆₇	1	1	yes	characteristic
77	C₂	C₂×M₁₆×C₃₆₇	1	1	yes	characteristic
78	C₂	#131×C₃₆₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×M₁₆×C₃₆₇	C₂	semidirect
3. C₄⋊C₈×C₃₆₇	C₂	semidirect
4. C₂²⋊C₈×C₃₆₇	C₂	semidirect
5. C₄×C₈×C₃₆₇	C₂	semidirect
25. C₈×C₃₆₇	D₄	semidirect
32. C₄×C₃₆₇	M₁₆	semidirect
39. C₃₆₇	#436	direct (N × H)
40. #436	C₃₆₇	direct (N × H)
41. C₂×M₁₆	C₂×C₃₆₇	semidirect
43. C₄⋊C₈	C₂×C₃₆₇	semidirect
44. C₂²⋊C₈	C₂×C₃₆₇	semidirect
45. C₄×C₈	C₂×C₃₆₇	semidirect
65. C₈	D₄×C₃₆₇	semidirect
72. C₄	M₁₆×C₃₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₃₆₇	2
C₄×D₄×C₃₆₇	2
C₄⋊C₈×C₃₆₇	2
C₂²⋊C₈×C₃₆₇	2
C₄×C₈×C₃₆₇	2
#436	367

Subgroups — #436×C367 #37553754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #436×C₃₆₇ #37553754