Subgroups — #14558613

Order 2368.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924624	C₂	1	8	yes	maximal, complemented
2	D₃₇⋊M₁₆	C₂	1	6	yes	maximal, complemented
3	C₂×#10596966	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₃₇	C₄	1	1	yes	characteristic
5	#10596966	C₄	1	4	yes	—
6	#10596966	C₂²	1	4	yes	—
7	C₂×D₁₄₈	C₄	1	3	yes	—
8	C₂×C₄×D₃₇	C₂²	1	3	yes	—
9	#10596957	C₂²	1	4	yes	—
10	#10596953	C₂²	1	12	yes	complemented
11	D₃₇⋊C₈	C₂²	1	12	yes	complemented
12	C₂²×D₃₇	C₂×C₄	1	3	yes	—
13	Q₈×C₃₇	C₂×C₄	1	4	yes	—
14	C₂×C₄×C₃₇	C₂×C₄	1	3	yes	—
15	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
16	D₁₄₈	C₂×C₄	1	12	yes	—
17	C₄×D₃₇	C₂×C₄	1	6	yes	—
18	C₄×D₃₇	C₂³	1	6	yes	—
19	#64438	C₂³	1	8	yes	—
20	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
21	C₂×D₃₇	—	4	3	no	—
22	C₂×D₃₇	C₂²×C₄	1	6	yes	—
23	C₄×C₃₇	C₂²×C₄	1	6	yes	—
24	Dic₃₇	C₂²×C₄	1	1	yes	characteristic
25	Dic₃₇	C₂⁴	1	1	yes	characteristic
26	C₂×C₃₇	—	2	1	no	—
27	C₂×C₃₇	C₂³×C₄	1	1	yes	characteristic
28	D₃₇	—	2	6	no	—
29	#568	—	37	1	no	maximal, Sylow
30	C₃₇	#568	1	1	yes	characteristic, complemented, Sylow
31	C₂×#41	—	37	1	no	—
32	#131	—	37	8	no	—
33	C₂×M₁₆	—	37	6	no	—
34	#41	—	37	4	no	—
35	#41	—	37	4	no	—
36	C₂×Q₈	#3866	1	1	yes	characteristic
37	C₂×D₄	—	37	3	no	—
38	C₂²×C₄	—	37	3	no	—
39	M₁₆	—	37	12	no	—
40	M₁₆	—	37	4	no	—
41	C₂×C₈	—	37	12	no	—
42	C₂³	—	37	3	no	—
43	Q₈	C₂×#3866	1	4	yes	—
44	D₄	—	37	12	no	—
45	C₂×C₄	—	37	1	no	—
46	C₂×C₄	—	37	6	no	—
47	C₂×C₄	—	37	6	no	—
48	C₂×C₄	C₂×#3866	1	3	yes	—
49	C₈	—	37	8	no	—
50	C₂²	—	37	6	no	—
51	C₂²	—	148	3	no	—
52	C₂²	C₂²×#3866	1	1	yes	characteristic
53	C₄	—	37	1	no	—
54	C₄	—	37	1	no	—
55	C₄	C₂²×#3866	1	6	yes	—
56	C₂	—	2	1	no	—
57	C₂	—	74	6	no	—
58	C₂	C₂³×#3866	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×#3866
commutator, socle	C₂×C₃₇	C₂³×C₄
Fitting	C₂×Q₈×C₃₇	C₄
prime radical	C₂×#10596966	C₂
cosocle	Dic₃₇	C₂⁴
hypercenter	C₂×Q₈	#3866
hypocenter	C₃₇	#568
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. #11924624	C₂	semidirect
2. D₃₇⋊M₁₆	C₂	semidirect
10. #10596953	C₂²	semidirect
11. D₃₇⋊C₈	C₂²	semidirect
30. C₃₇	#568	semidirect

Maximal subgroups

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

subgroup	index
#11924624	2
D₃₇⋊M₁₆	2
C₂×#10596966	2
#568	37