Subgroups — #14558436

Order 2368.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924596	C₂	1	1	yes	maximal, characteristic
2	#11924594	C₂	1	1	yes	maximal, characteristic
3	#11924520	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊D₃₇	C₂²	1	1	yes	characteristic
5	C₂²×Dic₃₇	C₄	1	1	yes	characteristic, complemented
6	C₂²⋊#3866	—	2	1	no	—
7	#10596957	—	2	1	no	—
8	C₂²⋊C₄×C₃₇	C₄	1	1	yes	characteristic, complemented
9	#10596938	—	2	1	no	—
10	C₄⋊Dic₃₇	—	2	1	no	—
11	C₂³×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×D₃₇	D₄	1	1	yes	characteristic
13	C₂×#3866	—	4	1	no	—
14	C₂×C₄×C₃₇	—	2	1	no	—
15	C₂²⋊D₃₇	—	4	1	no	—
16	C₂×Dic₃₇	—	2	1	no	—
17	C₂×Dic₃₇	—	4	1	no	—
18	C₂×Dic₃₇	D₄	1	1	yes	characteristic
19	#64438	—	4	1	no	—
20	C₂²×C₃₇	—	2	1	no	—
21	C₂²×C₃₇	—	4	1	no	—
22	C₂²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₃₇	—	2	1	no	—
24	C₂×D₃₇	—	4	1	no	—
25	#3866	—	8	1	no	—
26	C₄×C₃₇	—	4	1	no	—
27	Dic₃₇	—	2	1	no	—
28	Dic₃₇	—	4	1	no	—
29	C₂×C₃₇	—	2	1	no	—
30	C₂×C₃₇	—	4	1	no	—
31	C₂×C₃₇	#99	1	1	yes	characteristic
32	D₃₇	—	4	1	no	—
33	#352	—	37	1	no	maximal, Sylow
34	C₃₇	#352	1	1	yes	characteristic, complemented, Sylow
35	#123	—	37	1	no	—
36	#100	—	37	1	no	—
37	#99	—	37	1	no	—
38	C₂×D₄	—	37	1	no	—
39	C₂²×C₄	—	37	1	no	—
40	M₁₆	—	74	1	no	—
41	C₄⋊C₄	—	74	1	no	—
42	C₂²⋊C₄	—	74	1	no	—
43	C₂²⋊C₄	—	74	1	no	—
44	C₂²⋊C₄	#3866	1	1	yes	characteristic, complemented
45	C₂³	—	37	1	no	—
46	C₂³	C₂×#3866	1	1	yes	characteristic
47	D₄	—	148	1	no	—
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	—	37	1	no	—
50	C₂×C₄	—	74	1	no	—
51	C₂×C₄	—	148	1	no	—
52	C₂×C₄	—	148	1	no	—
53	C₈	—	148	1	no	—
54	C₂²	—	2	1	no	—
55	C₂²	—	4	1	no	—
56	C₂²	—	74	1	no	—
57	C₂²	—	148	1	no	—
58	C₂²	C₂²⋊#3866	1	1	yes	characteristic
59	C₄	—	4	1	no	—
60	C₄	—	296	1	no	—
61	C₄	—	74	1	no	—
62	C₄	—	148	1	no	—
63	C₂	—	2	1	no	—
64	C₂	—	4	1	no	—
65	C₂	—	148	1	no	—
66	C₂	#11924595	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11924595
commutator	C₂³×C₃₇	C₂×C₄
Frattini	C₂³	C₂×#3866
Fitting	C₂²⋊C₄×C₃₇	C₄
socle	C₂×C₃₇	#99
prime radical, cosocle	C₂×C₂²⋊D₃₇	C₂²
hypercenter	C₂²⋊C₄	#3866
hypocenter	C₃₇	#352
LCS	G ▷ C₂³×C₃₇ ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂³ ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
5. C₂²×Dic₃₇	C₄	semidirect
8. C₂²⋊C₄×C₃₇	C₄	semidirect
34. C₃₇	#352	semidirect
44. C₂²⋊C₄	#3866	semidirect

Maximal subgroups

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

subgroup	index
#11924596	2
#11924594	2
#11924520	2
#352	37