Subgroups — #14558469

Order 2368.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#3866	C₂	1	2	yes	maximal
2	(C₂×#3866)⋊C₄	C₂	1	4	yes	maximal
3	C₄²×D₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#3866	C₂²	1	4	yes	—
5	C₂×C₄×D₃₇	C₂²	1	2	yes	—
6	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
7	C₄×#3866	C₄	1	8	yes	complemented
8	C₄²×C₃₇	C₄	1	1	yes	characteristic, complemented
9	C₄×Dic₃₇	C₄	1	2	yes	complemented
10	C₄×Dic₃₇	C₄	1	1	yes	characteristic, complemented
11	C₂²×D₃₇	C₂³	1	1	yes	characteristic
12	C₂×#3866	—	2	8	no	—
13	C₂×#3866	C₂×C₄	1	8	yes	—
14	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₃₇	C₂×C₄	1	2	yes	—
17	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
18	C₄×D₃₇	—	2	4	no	—
19	C₄×D₃₇	C₂×C₄	1	4	yes	—
20	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
21	C₂×D₃₇	C₂²×C₄	1	2	yes	—
22	C₂×D₃₇	#41	1	4	yes	—
23	#3866	—	2	8	no	—
24	C₄×C₃₇	—	2	2	no	—
25	C₄×C₃₇	C₄²	1	2	yes	—
26	Dic₃₇	—	2	2	no	—
27	Dic₃₇	C₄²	1	2	yes	—
28	C₂×C₃₇	C₂×C₄²	1	1	yes	characteristic
29	C₂×C₃₇	#117	1	2	yes	—
30	D₃₇	#117	1	4	yes	—
31	#376	—	37	1	no	maximal, Sylow
32	C₃₇	#376	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₄²	—	37	2	no	—
34	C₂×C₄²	—	37	1	no	—
35	#95	—	37	4	no	—
36	C₂²×C₄	—	37	1	no	—
37	C₂²×C₄	—	37	4	no	—
38	C₂²×C₄	—	37	2	no	—
39	C₄²	—	37	8	no	—
40	C₄²	—	37	2	no	—
41	C₄²	—	37	1	no	—
42	C₄²	#3866	1	1	yes	characteristic, complemented
43	C₂³	—	37	1	no	—
44	C₂×C₄	—	37	1	no	—
45	C₂×C₄	—	37	4	no	—
46	C₂×C₄	—	37	8	no	—
47	C₂×C₄	—	37	2	no	—
48	C₂×C₄	—	74	4	no	—
49	C₂×C₄	—	74	8	no	—
50	C₂×C₄	C₂×#3866	1	2	yes	—
51	C₂×C₄	C₂×#3866	1	1	yes	characteristic
52	C₂²	—	37	2	no	—
53	C₂²	—	37	4	no	—
54	C₂²	C₂²×#3866	1	1	yes	characteristic
55	C₄	—	2	2	no	—
56	C₄	—	37	2	no	—
57	C₄	—	74	8	no	—
58	C₄	—	74	2	no	—
59	C₄	C₄×#3866	1	2	yes	—
60	C₂	—	37	4	no	—
61	C₂	C₂×C₄×#3866	1	1	yes	characteristic
62	C₂	#11924615	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#3866
commutator	C₂×C₃₇	C₂×C₄²
Frattini	C₂²	C₂²×#3866
Fitting	C₄²×C₃₇	C₄
socle	C₂²×C₃₇	C₂²×C₄
prime radical, cosocle	C₂²×D₃₇	C₂³
hypercenter	C₄²	#3866
hypocenter	C₃₇	#376
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
7. C₄×#3866	C₄	semidirect
8. C₄²×C₃₇	C₄	semidirect
9. C₄×Dic₃₇	C₄	semidirect
10. C₄×Dic₃₇	C₄	semidirect
32. C₃₇	#376	semidirect
42. C₄²	#3866	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#3866	2
(C₂×#3866)⋊C₄	2
C₄²×D₃₇	2
#376	37