Subgroups — #17996873

Order 4736.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557934	C₂	1	2	yes	maximal
2	#14557360	C₂	1	2	yes	maximal
3	#14557359	C₂	1	1	yes	maximal, characteristic
4	C₁₆×Dic₃₇	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#366	C₂	1	1	yes	maximal, characteristic
6	#11924527	—	2	2	no	—
7	C₂×#10596925	C₂²	1	1	yes	characteristic
8	#11924470	C₂²	1	2	yes	—
9	#11924467	—	2	2	no	—
10	C₈×Dic₃₇	C₂²	1	1	yes	characteristic
11	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
12	#107×C₃₇	C₂²	1	2	yes	—
13	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
14	C₄⋊C₄×C₃₇	—	2	2	no	—
15	C₄⋊Dic₃₇	—	2	2	no	—
16	C₄⋊Dic₃₇	—	4	2	no	—
17	#10596936	—	4	2	no	—
18	C₄×Dic₃₇	D₄	1	1	yes	characteristic
19	C₂×#64436	D₄	1	1	yes	characteristic
20	C₁₆×C₃₇	Q₈	1	2	yes	—
21	#10596925	Q₈	1	2	yes	—
22	C₂×C₄×C₃₇	—	4	2	no	—
23	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
24	C₂×Dic₃₇	—	4	2	no	—
25	C₂×Dic₃₇	D₈	1	1	yes	characteristic
26	C₂×Dic₃₇	D₈	1	1	yes	characteristic
27	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
28	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
29	#64436	Q₁₆	1	2	yes	—
30	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
31	C₄×C₃₇	—	8	2	no	—
32	C₄×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
33	C₄×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
34	Dic₃₇	—	2	1	no	—
35	Dic₃₇	—	2	1	no	—
36	Dic₃₇	—	8	2	no	—
37	#2253	—	37	1	no	maximal, Sylow
38	C₂×C₃₇	#500	1	1	yes	characteristic
39	C₂×C₃₇	#508	1	1	yes	characteristic
40	C₂×C₃₇	#508	1	1	yes	characteristic
41	#499	—	37	2	no	—
42	#367	—	37	2	no	—
43	#366	—	37	1	no	—
44	#366	D₃₇	1	1	yes	characteristic
45	C₄×C₁₆	—	37	1	no	—
46	C₃₇	#2253	1	1	yes	characteristic, complemented, Sylow
47	#125	—	74	2	no	—
48	C₂×C₁₆	—	37	1	no	—
49	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
50	#107	—	37	2	no	—
51	#107	C₂×D₃₇	1	2	yes	—
52	#106	—	74	2	no	—
53	C₄×C₈	—	37	1	no	—
54	C₂×C₈	—	37	1	no	—
55	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
56	C₄⋊C₄	—	2	2	no	—
57	C₄⋊C₄	—	74	2	no	—
58	C₄⋊C₄	—	148	2	no	—
59	C₄⋊C₄	—	148	2	no	—
60	C₄²	—	37	1	no	—
61	C₁₆	—	37	2	no	—
62	C₁₆	Dic₇₄	1	2	yes	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	—	37	1	no	—
65	C₂×C₄	—	37	1	no	—
66	C₂×C₄	—	148	2	no	—
67	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
68	C₈	—	37	2	no	—
69	C₈	C₂×Dic₇₄	1	1	yes	characteristic
70	C₈	Q₈×D₃₇	1	1	yes	characteristic
71	C₂²	D₈×D₃₇	1	1	yes	characteristic
72	C₄	—	8	2	no	—
73	C₄	—	296	2	no	—
74	C₄	—	74	1	no	—
75	C₄	—	74	1	no	—
76	C₄	#11924535	1	1	yes	characteristic
77	C₄	Q₁₆×D₃₇	1	1	yes	characteristic
78	C₂	#14557937	1	1	yes	characteristic
79	C₂	#14557962	1	1	yes	characteristic
80	C₂	#14557966	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₃₇
commutator, cosocle	C₂×C₈×C₃₇	C₂³
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₃₇×#366	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₈
hypercenter	#366	D₃₇
hypocenter	C₃₇	#2253
LCS	G ▷ C₂×C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

Complements

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

N	H ≅ G/N	type
46. C₃₇	#2253	semidirect

Maximal subgroups

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

subgroup	index
#14557934	2
#14557360	2
#14557359	2
C₁₆×Dic₃₇	2
C₃₇×#366	2
#2253	37