Subgroups — #14557786

Order 2368.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₉₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#11924510	C₂	1	2	yes	maximal, complemented
3	#11924468	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924458	C₂	1	2	yes	maximal, complemented
5	C₂×M₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×C₃₇	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊D₃₇	—	2	2	no	—
8	C₂×D₁₄₈	C₂²	1	2	yes	—
9	M₁₆×C₃₇	—	2	2	no	—
10	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
12	#10596938	—	2	2	no	—
13	C₄⋊Dic₃₇	C₂²	1	2	yes	—
14	D₂₉₆	—	2	2	no	—
15	C₂³×C₃₇	D₄	1	1	yes	characteristic
16	C₂²×D₃₇	—	2	2	no	—
17	C₂×C₄×C₃₇	—	2	1	no	—
18	C₂×C₄×C₃₇	—	2	1	no	—
19	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
20	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
21	C₂²⋊D₃₇	—	4	4	no	—
22	C₂×Dic₃₇	—	2	2	no	—
23	D₁₄₈	—	2	2	no	—
24	D₁₄₈	—	2	2	no	—
25	C₈×C₃₇	—	2	1	no	—
26	C₈×C₃₇	D₄	1	2	yes	complemented
27	C₂²×C₃₇	—	2	1	no	—
28	C₂²×C₃₇	—	2	2	no	—
29	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
30	C₂×D₃₇	—	4	2	no	—
31	C₂×D₃₇	—	4	2	no	—
32	C₂×D₃₇	—	4	2	no	—
33	C₄×C₃₇	—	2	1	no	—
34	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
35	C₄×C₃₇	#41	1	1	yes	characteristic
36	Dic₃₇	—	4	2	no	—
37	C₂×C₃₇	—	4	1	no	—
38	C₂×C₃₇	#121	1	1	yes	characteristic
39	C₂×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
40	D₃₇	—	8	2	no	—
41	#469	—	37	1	no	maximal, Sylow
42	C₃₇	#469	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₈	—	37	1	no	—
44	C₂×M₁₆	D₃₇	1	1	yes	characteristic, complemented
45	#121	—	37	2	no	—
46	#106	—	37	1	no	—
47	#102	—	37	2	no	—
48	C₂×D₄	—	37	2	no	—
49	C₂×D₄	—	74	2	no	—
50	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
51	D₈	—	74	2	no	—
52	M₁₆	—	2	2	no	—
53	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
54	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
55	C₄⋊C₄	—	37	2	no	—
56	C₂²⋊C₄	—	74	2	no	—
57	C₂³	—	74	2	no	—
58	C₂³	D₁₄₈	1	1	yes	characteristic
59	D₄	—	74	2	no	—
60	D₄	—	74	2	no	—
61	D₄	—	148	4	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	74	2	no	—
65	C₂×C₄	D₁₄₈	1	1	yes	characteristic
66	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
67	C₈	—	2	1	no	—
68	C₈	C₂²⋊D₃₇	1	2	yes	complemented
69	C₂²	—	2	1	no	—
70	C₂²	—	2	2	no	—
71	C₂²	—	148	2	no	—
72	C₂²	—	148	2	no	—
73	C₂²	—	148	2	no	—
74	C₂²	C₂×D₁₄₈	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	148	2	no	—
77	C₄	#10596962	1	1	yes	characteristic
78	C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
79	C₂	—	4	1	no	—
80	C₂	—	296	2	no	—
81	C₂	#11924510	1	1	yes	characteristic
82	C₂	#11924564	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₄₈
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	C₂×M₁₆×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
hypercenter	C₂×M₁₆	D₃₇
hypocenter	C₃₇	#469
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₉₆	C₂	semidirect
2. #11924510	C₂	semidirect
3. #11924468	C₂	semidirect
4. #11924458	C₂	semidirect
5. C₂×M₁₆×C₃₇	C₂	semidirect
26. C₈×C₃₇	D₄	semidirect
42. C₃₇	#469	semidirect
44. C₂×M₁₆	D₃₇	semidirect
68. C₈	C₂²⋊D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₉₆	2
#11924510	2
#11924468	2
#11924458	2
C₂×M₁₆×C₃₇	2
#469	37