Subgroups — #17996872

Order 4736.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557935	C₂	1	1	yes	maximal, characteristic
2	#14557360	C₂	1	2	yes	maximal
3	#14557358	C₂	1	2	yes	maximal
4	C₄×#10596925	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#499	C₂	1	1	yes	maximal, characteristic
6	#11924528	—	2	1	no	—
7	C₂×#10596925	C₂²	1	1	yes	characteristic
8	C₂×#10596925	C₂²	1	1	yes	characteristic
9	#11924470	C₂²	1	2	yes	—
10	#11924468	—	2	1	no	—
11	#125×C₃₇	—	2	1	no	—
12	#107×C₃₇	C₂²	1	2	yes	—
13	#106×C₃₇	—	2	1	no	—
14	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
16	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₃₇	—	2	2	no	—
18	C₄⋊C₄×C₃₇	—	4	2	no	—
19	C₄²×C₃₇	D₄	1	1	yes	characteristic
20	C₄⋊Dic₃₇	—	2	2	no	—
21	#10596936	—	4	2	no	—
22	#10596925	Q₈	1	2	yes	—
23	#10596925	Q₈	1	2	yes	—
24	C₂×C₄×C₃₇	—	4	2	no	—
25	C₂×C₄×C₃₇	D₈	1	2	yes	—
26	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₃₇	—	4	2	no	—
28	C₈×C₃₇	Q₁₆	1	2	yes	—
29	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
30	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
31	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
32	C₄×C₃₇	—	2	2	no	—
33	C₄×C₃₇	—	8	2	no	—
34	C₄×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
35	C₄×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
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	2	yes	—
40	#499	—	37	1	no	—
41	#499	D₃₇	1	1	yes	characteristic
42	#367	—	37	2	no	—
43	#366	—	37	2	no	—
44	C₄×C₁₆	—	37	1	no	—
45	C₃₇	#2253	1	1	yes	characteristic, complemented, Sylow
46	#125	—	2	1	no	—
47	#125	—	74	1	no	—
48	C₂×C₁₆	—	37	1	no	—
49	C₂×C₁₆	—	37	1	no	—
50	#107	—	37	2	no	—
51	#107	C₂×D₃₇	1	2	yes	—
52	#106	—	2	1	no	—
53	#106	—	74	1	no	—
54	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
55	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
56	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
57	C₄⋊C₄	—	2	2	no	—
58	C₄⋊C₄	—	4	2	no	—
59	C₄⋊C₄	—	74	2	no	—
60	C₄⋊C₄	—	148	2	no	—
61	C₄²	C₂²⋊D₃₇	1	1	yes	characteristic
62	C₁₆	—	37	2	no	—
63	C₁₆	—	37	2	no	—
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	148	2	no	—
66	C₂×C₄	#10596939	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
68	C₈	#10596942	1	2	yes	—
69	C₈	Q₈×D₃₇	1	1	yes	characteristic
70	C₈	Q₈×D₃₇	1	1	yes	characteristic
71	C₂²	C₂×#10596939	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	296	2	no	—
75	C₄	#11924534	1	1	yes	characteristic
76	C₄	C₂×#10596942	1	1	yes	characteristic
77	C₂	#14557936	1	1	yes	characteristic
78	C₂	#14557963	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#10596939
commutator, cosocle	C₂×C₈×C₃₇	C₂³
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₃₇×#499	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₈
hypercenter	#499	D₃₇
hypocenter	C₃₇	#2253
LCS	G ▷ C₂×C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

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

Maximal subgroups

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

subgroup	index
#14557935	2
#14557360	2
#14557358	2
C₄×#10596925	2
C₃₇×#499	2
#2253	37