Subgroups — #14558391

Order 2368.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924603	C₂	1	2	yes	maximal, complemented
2	#11924532	C₂	1	1	yes	maximal, characteristic
3	C₂×D₄×C₃₇	C₄	1	1	yes	characteristic
4	C₂×C₂²⋊D₃₇	—	2	2	no	—
5	C₂×D₁₄₈	C₄	1	1	yes	characteristic
6	C₂×#64438	—	2	2	no	—
7	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
8	C₂³×C₃₇	—	2	1	no	—
9	C₂²×D₃₇	—	2	1	no	—
10	D₄×C₃₇	—	4	1	no	—
11	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂²⋊D₃₇	—	4	2	no	—
13	C₂²⋊D₃₇	—	4	2	no	—
14	C₂×Dic₃₇	D₄	1	2	yes	—
15	D₁₄₈	—	4	1	no	—
16	#64438	—	4	2	no	—
17	C₂²×C₃₇	—	4	1	no	—
18	C₂²×C₃₇	—	4	2	no	—
19	C₂²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×D₃₇	—	4	1	no	—
21	C₂×D₃₇	—	4	2	no	—
22	C₄×C₃₇	—	2	1	no	—
23	Dic₃₇	D₈	1	2	yes	—
24	Dic₃₇	SD₁₆	1	2	yes	—
25	C₂×C₃₇	—	8	1	no	—
26	C₂×C₃₇	#100	1	1	yes	characteristic
27	C₂×C₃₇	#102	1	2	yes	—
28	D₃₇	—	8	1	no	—
29	#331	—	37	1	no	maximal, Sylow
30	C₃₇	#331	1	1	yes	characteristic, complemented, Sylow
31	#127	—	37	1	no	—
32	C₄⋊C₈	—	37	2	no	—
33	C₂×D₄	—	37	1	no	—
34	C₂×D₄	—	74	2	no	—
35	C₂×D₄	#3866	1	1	yes	characteristic
36	C₂×C₈	—	74	2	no	—
37	C₄²	—	37	1	no	—
38	C₂³	—	2	1	no	—
39	C₂³	—	74	1	no	—
40	D₄	—	4	1	no	—
41	D₄	—	148	1	no	—
42	D₄	—	148	2	no	—
43	D₄	—	148	2	no	—
44	C₂×C₄	—	37	2	no	—
45	C₂×C₄	C₂×#3866	1	1	yes	characteristic
46	C₈	—	148	2	no	—
47	C₂²	—	4	1	no	—
48	C₂²	—	4	2	no	—
49	C₂²	—	148	1	no	—
50	C₂²	—	148	2	no	—
51	C₂²	C₂²⋊#3866	1	1	yes	characteristic
52	C₄	—	2	1	no	—
53	C₄	—	37	2	no	—
54	C₄	—	37	2	no	—
55	C₂	—	8	1	no	—
56	C₂	—	296	1	no	—
57	C₂	#11924596	1	1	yes	characteristic
58	C₂	#11924598	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²⋊#3866
commutator	C₂×C₄×C₃₇	C₂×C₄
Frattini	C₂×C₄	C₂×#3866
Fitting	C₂×D₄×C₃₇	C₄
socle	C₂²×C₃₇	C₂²⋊C₄
prime radical	#11924532	C₂
cosocle	C₄×Dic₃₇	C₂²
hypercenter	C₂×D₄	#3866
hypocenter	C₃₇	#331
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. #11924603	C₂	semidirect
30. C₃₇	#331	semidirect

Maximal subgroups

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

subgroup	index
#11924603	2
#11924532	2
#331	37