Subgroups — #14558513

Order 2368.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924615	C₂	1	2	yes	maximal, complemented
2	#11924594	C₂	1	4	yes	maximal, complemented
3	C₂×#10596964	C₂	1	1	yes	maximal, characteristic
4	C₂×D₄×C₃₇	C₄	1	1	yes	characteristic, complemented
5	C₂×C₂²⋊D₃₇	C₂²	1	2	yes	—
6	C₂²×Dic₃₇	C₄	1	2	yes	complemented
7	#10596964	—	2	2	no	—
8	#10596964	—	2	2	no	—
9	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
10	C₂×Dic₇₄	C₄	1	1	yes	characteristic, complemented
11	C₂²⋊#3866	C₂²	1	4	yes	—
12	C₄⋊#3866	—	2	2	no	—
13	C₄×#3866	—	2	2	no	—
14	C₂³×C₃₇	C₂×C₄	1	2	yes	—
15	C₂²×D₃₇	C₂³	1	1	yes	characteristic
16	C₂×#3866	—	2	4	no	—
17	D₄×C₃₇	—	2	2	no	—
18	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
19	C₂²⋊D₃₇	—	2	4	no	—
20	C₂×Dic₃₇	—	2	2	no	—
21	C₂×Dic₃₇	—	2	2	no	—
22	C₂×Dic₃₇	C₂×C₄	1	2	yes	—
23	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
24	C₄×D₃₇	D₄	1	2	yes	—
25	C₄×D₃₇	D₄	1	2	yes	—
26	Dic₇₄	—	2	2	no	—
27	C₂²×C₃₇	—	2	2	no	—
28	C₂²×C₃₇	—	4	2	no	—
29	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
30	C₂×D₃₇	—	4	1	no	—
31	C₂×D₃₇	C₂×D₄	1	2	yes	—
32	#3866	—	4	4	no	—
33	C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
34	Dic₃₇	—	2	2	no	—
35	Dic₃₇	C₂²⋊C₄	1	1	yes	characteristic
36	Dic₃₇	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₃₇	—	2	1	no	—
38	C₂×C₃₇	—	4	2	no	—
39	C₂×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	D₃₇	—	2	2	no	—
41	#410	—	37	1	no	maximal, Sylow
42	C₃₇	#410	1	1	yes	characteristic, complemented, Sylow
43	C₂×#41	—	37	1	no	—
44	#117	—	37	2	no	—
45	#99	—	37	4	no	—
46	#41	—	74	2	no	—
47	#41	—	74	2	no	—
48	C₂×Q₈	—	37	1	no	—
49	C₂×D₄	—	37	2	no	—
50	C₂×D₄	#3866	1	1	yes	characteristic, complemented
51	C₂²×C₄	—	37	1	no	—
52	C₂²×C₄	—	37	2	no	—
53	C₄⋊C₄	—	74	2	no	—
54	C₂²⋊C₄	—	37	4	no	—
55	C₄²	—	74	2	no	—
56	C₂³	—	37	1	no	—
57	C₂³	C₂×#3866	1	2	yes	—
58	Q₈	—	74	2	no	—
59	D₄	—	2	2	no	—
60	D₄	—	74	4	no	—
61	C₂×C₄	—	37	1	no	—
62	C₂×C₄	—	37	2	no	—
63	C₂×C₄	—	37	2	no	—
64	C₂×C₄	—	37	2	no	—
65	C₂×C₄	—	74	2	no	—
66	C₂×C₄	—	74	2	no	—
67	C₂×C₄	—	74	4	no	—
68	C₂×C₄	C₂×#3866	1	1	yes	characteristic
69	C₂²	—	2	2	no	—
70	C₂²	—	4	2	no	—
71	C₂²	—	37	2	no	—
72	C₂²	—	148	1	no	—
73	C₂²	C₂²×#3866	1	1	yes	characteristic
74	C₄	—	37	1	no	—
75	C₄	—	37	1	no	—
76	C₄	—	74	2	no	—
77	C₄	—	148	4	no	—
78	C₄	C₂²⋊#3866	1	2	yes	—
79	C₂	—	2	1	no	—
80	C₂	—	4	2	no	—
81	C₂	—	74	2	no	—
82	C₂	C₂×C₂²⋊#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊#3866
commutator	C₂²×C₃₇	C₂²×C₄
Frattini	C₂²	C₂²×#3866
Fitting	C₂×D₄×C₃₇	C₄
socle	C₂×C₃₇	C₂×C₂²⋊C₄
prime radical	C₂×#10596964	C₂
cosocle	C₂²×D₃₇	C₂³
hypercenter	C₂×D₄	#3866
hypocenter	C₃₇	#410
LCS	G ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. #11924615	C₂	semidirect
2. #11924594	C₂	semidirect
4. C₂×D₄×C₃₇	C₄	semidirect
6. C₂²×Dic₃₇	C₄	semidirect
10. C₂×Dic₇₄	C₄	semidirect
42. C₃₇	#410	semidirect
50. C₂×D₄	#3866	semidirect

Maximal subgroups

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

subgroup	index
#11924615	2
#11924594	2
C₂×#10596964	2
#410	37