Subgroups — #14557888

Order 2368.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924528	C₂	1	1	yes	maximal, characteristic, complemented
2	#11924524	C₂	1	1	yes	maximal, characteristic
3	#11924461	C₂	1	2	yes	maximal, complemented
4	#11924458	C₂	1	2	yes	maximal
5	C₄×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₄₈	C₂²	1	1	yes	characteristic
7	C₂×Dic₇₄	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₃₇	C₂²	1	2	yes	—
9	C₄²×C₃₇	C₂²	1	1	yes	characteristic
10	#10596938	—	2	2	no	—
11	C₄⋊Dic₃₇	C₂²	1	2	yes	—
12	#10596936	—	2	2	no	—
13	C₂²×D₃₇	—	2	1	no	—
14	C₂×C₄×C₃₇	D₄	1	2	yes	—
15	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
16	C₂×Dic₃₇	—	2	2	no	—
17	C₂×Dic₃₇	—	2	1	no	—
18	D₁₄₈	—	2	2	no	—
19	Dic₇₄	—	2	2	no	—
20	C₈×C₃₇	—	2	2	no	—
21	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
22	C₂×D₃₇	—	4	1	no	—
23	C₂×D₃₇	—	4	2	no	—
24	C₄×C₃₇	—	2	2	no	—
25	C₄×C₃₇	#41	1	2	yes	—
26	Dic₃₇	—	4	1	no	—
27	Dic₃₇	—	4	2	no	—
28	C₂×C₃₇	#124	1	1	yes	characteristic
29	C₂×C₃₇	#135	1	2	yes	—
30	D₃₇	—	8	1	no	—
31	#488	—	37	1	no	maximal, Sylow
32	C₃₇	#488	1	1	yes	characteristic, complemented, Sylow
33	#125	—	37	1	no	—
34	#124	—	37	1	no	—
35	#103	—	37	2	no	—
36	#102	—	37	2	no	—
37	C₄×C₈	D₃₇	1	1	yes	characteristic, complemented
38	C₂×Q₈	—	37	1	no	—
39	C₂×D₄	—	37	1	no	—
40	C₂×C₈	C₂×D₃₇	1	2	yes	—
41	C₄⋊C₄	—	37	2	no	—
42	C₄⋊C₄	—	74	2	no	—
43	C₂²⋊C₄	—	74	2	no	—
44	C₄²	C₂×D₃₇	1	1	yes	characteristic
45	C₂³	—	74	1	no	—
46	Q₈	—	74	2	no	—
47	D₄	—	74	2	no	—
48	C₂×C₄	—	74	1	no	—
49	C₂×C₄	—	74	2	no	—
50	C₂×C₄	D₁₄₈	1	2	yes	—
51	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
52	C₈	—	2	2	no	—
53	C₂²	—	148	1	no	—
54	C₂²	—	148	2	no	—
55	C₂²	C₂×D₁₄₈	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	148	1	no	—
58	C₄	—	148	2	no	—
59	C₄	#10596962	1	2	yes	—
60	C₂	—	296	1	no	—
61	C₂	#11924524	1	1	yes	characteristic
62	C₂	#11924558	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₄₈
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	C₄×C₈×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
prime radical	C₂×D₁₄₈	C₂²
hypercenter	C₄×C₈	D₃₇
hypocenter	C₃₇	#488
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #11924528	C₂	semidirect
3. #11924461	C₂	semidirect
5. C₄×C₈×C₃₇	C₂	semidirect
32. C₃₇	#488	semidirect
37. C₄×C₈	D₃₇	semidirect

Maximal subgroups

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

subgroup	index
#11924528	2
#11924524	2
#11924461	2
#11924458	2
C₄×C₈×C₃₇	2
#488	37