Subgroups — #14557323

Order 2368.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924453	C₂	1	1	yes	maximal, characteristic
2	#11924451	C₂	1	1	yes	maximal, characteristic
3	#123×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×D₄×C₃₇	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₃₇	C₄	1	1	yes	characteristic, complemented
6	C₄⋊C₄×C₃₇	—	2	1	no	—
7	C₂²⋊C₄×C₃₇	—	2	1	no	—
8	C₂²⋊C₄×C₃₇	C₄	1	1	yes	characteristic, complemented
9	C₂²⋊Dic₃₇	—	2	1	no	—
10	#10596934	—	2	1	no	—
11	C₂³×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂³×C₃₇	D₄	1	1	yes	characteristic
13	D₄×C₃₇	—	4	1	no	—
14	C₂×C₄×C₃₇	—	2	1	no	—
15	C₂×C₄×C₃₇	—	2	1	no	—
16	C₂×C₄×C₃₇	—	4	1	no	—
17	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
18	C₂×Dic₃₇	—	4	1	no	—
19	#64436	—	4	1	no	—
20	C₂²×C₃₇	—	2	1	no	—
21	C₂²×C₃₇	—	2	1	no	—
22	C₂²×C₃₇	—	4	1	no	—
23	C₂²×C₃₇	—	4	1	no	—
24	C₂²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₄×C₃₇	—	2	1	no	—
26	C₄×C₃₇	—	4	1	no	—
27	C₄×C₃₇	—	4	1	no	—
28	Dic₃₇	—	8	1	no	—
29	C₂×C₃₇	—	2	1	no	—
30	C₂×C₃₇	—	4	1	no	—
31	C₂×C₃₇	—	4	1	no	—
32	C₂×C₃₇	#99	1	1	yes	characteristic
33	#352	—	37	1	no	maximal, Sylow
34	C₃₇	#352	1	1	yes	characteristic, complemented, Sylow
35	#123	D₃₇	1	1	yes	characteristic
36	#100	—	37	1	no	—
37	#99	—	37	1	no	—
38	C₂×D₄	C₂×D₃₇	1	1	yes	characteristic
39	C₂²×C₄	Dic₃₇	1	1	yes	characteristic, complemented
40	M₁₆	—	74	1	no	—
41	C₄⋊C₄	—	2	1	no	—
42	C₂²⋊C₄	—	2	1	no	—
43	C₂²⋊C₄	—	74	1	no	—
44	C₂²⋊C₄	Dic₃₇	1	1	yes	characteristic, complemented
45	C₂³	C₂×Dic₃₇	1	1	yes	characteristic
46	C₂³	C₂²⋊D₃₇	1	1	yes	characteristic
47	D₄	—	4	1	no	—
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	4	1	no	—
51	C₂×C₄	—	148	1	no	—
52	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
53	C₈	—	148	1	no	—
54	C₂²	—	2	1	no	—
55	C₂²	—	2	1	no	—
56	C₂²	—	4	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	C₂²⋊Dic₃₇	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	—	4	1	no	—
61	C₄	—	4	1	no	—
62	C₄	—	296	1	no	—
63	C₂	—	2	1	no	—
64	C₂	—	4	1	no	—
65	C₂	—	4	1	no	—
66	C₂	#11924451	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11924451
commutator	C₂³×C₃₇	C₂×C₄
Frattini	C₂×D₄	C₂×D₃₇
Fitting	#123×C₃₇	C₂
socle	C₂×C₃₇	#99
prime radical, cosocle	C₂×D₄×C₃₇	C₂²
hypercenter	#123	D₃₇
hypocenter	C₃₇	#352
LCS	G ▷ C₂³×C₃₇ ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×D₄ ◁ #123

Complements

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

N	H ≅ G/N	type
5. C₂²×C₄×C₃₇	C₄	semidirect
8. C₂²⋊C₄×C₃₇	C₄	semidirect
34. C₃₇	#352	semidirect
39. C₂²×C₄	Dic₃₇	semidirect
44. C₂²⋊C₄	Dic₃₇	semidirect

Maximal subgroups

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

subgroup	index
#11924453	2
#11924451	2
#123×C₃₇	2
#352	37