Group #17990481 — subgroups

Subgroups — C₃₇×#1663 #17990481

Order 4736.

172 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#564	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#501	C₂	1	2	yes	maximal
3	C₃₇×#491	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#330	C₂	1	2	yes	maximal
5	C₃₇×#330	C₂	1	1	yes	maximal, characteristic
6	C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
7	#125×C₃₇	—	2	2	no	—
8	#125×C₃₇	—	2	2	no	—
9	#125×C₃₇	—	2	2	no	—
10	#125×C₃₇	C₂²	1	1	yes	characteristic
11	#125×C₃₇	C₂²	1	2	yes	—
12	#107×C₃₇	—	2	2	no	—
13	#106×C₃₇	—	2	2	no	—
14	#103×C₃₇	—	2	2	no	—
15	#97×C₃₇	C₂²	1	1	yes	characteristic
16	#97×C₃₇	C₂²	1	2	yes	—
17	C₂×Q₈×C₃₇	—	2	1	no	—
18	C₂×C₈×C₃₇	—	2	2	no	—
19	C₂×C₈×C₃₇	—	2	1	no	—
20	C₄⋊C₄×C₃₇	—	2	2	no	—
21	C₄⋊C₄×C₃₇	—	2	2	no	—
22	C₄⋊C₄×C₃₇	—	2	2	no	—
23	C₄⋊C₄×C₃₇	—	2	2	no	—
24	C₄⋊C₄×C₃₇	—	2	2	no	—
25	C₄⋊C₄×C₃₇	—	2	2	no	—
26	C₄⋊C₄×C₃₇	—	2	2	no	—
27	C₄⋊C₄×C₃₇	D₄	1	2	yes	—
28	C₄⋊C₄×C₃₇	D₄	1	2	yes	—
29	C₄⋊C₄×C₃₇	D₄	1	2	yes	—
30	C₄²×C₃₇	—	2	2	no	—
31	C₄²×C₃₇	C₂³	1	1	yes	characteristic
32	Q₈×C₃₇	—	4	2	no	—
33	C₂×C₄×C₃₇	—	2	2	no	—
34	C₂×C₄×C₃₇	—	2	2	no	—
35	C₂×C₄×C₃₇	—	2	2	no	—
36	C₂×C₄×C₃₇	—	4	1	no	—
37	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
38	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
39	C₈×C₃₇	—	2	4	no	—
40	C₈×C₃₇	—	4	1	no	—
41	C₂²×C₃₇	#120	1	1	yes	characteristic
42	C₄×C₃₇	—	2	1	no	—
43	C₄×C₃₇	—	2	2	no	—
44	C₄×C₃₇	—	4	2	no	—
45	C₄×C₃₇	—	4	2	no	—
46	C₄×C₃₇	—	4	2	no	—
47	C₄×C₃₇	—	8	1	no	—
48	#1663	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂×C₃₇	#454	1	1	yes	characteristic
50	C₂×C₃₇	#456	1	2	yes	—
51	#564	C₂×C₃₇	1	1	yes	characteristic
52	#501	C₂×C₃₇	1	2	yes	—
53	#491	C₂×C₃₇	1	1	yes	characteristic
54	#330	C₂×C₃₇	1	2	yes	—
55	#330	C₂×C₃₇	1	1	yes	characteristic
56	C₃₇	#1663	1	1	yes	characteristic, direct product factor, Sylow
57	C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
58	#125	—	2	2	no	—
59	#125	—	2	2	no	—
60	#125	—	2	2	no	—
61	#125	C₂²×C₃₇	1	1	yes	characteristic
62	#125	C₂²×C₃₇	1	2	yes	—
63	#107	—	2	2	no	—
64	#106	—	2	2	no	—
65	#103	—	2	2	no	—
66	#97	C₂²×C₃₇	1	1	yes	characteristic
67	#97	C₂²×C₃₇	1	2	yes	—
68	C₂×Q₈	—	2	1	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	2	1	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	2	2	no	—
74	C₄⋊C₄	—	2	2	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	2	2	no	—
77	C₄⋊C₄	—	2	2	no	—
78	C₄⋊C₄	D₄×C₃₇	1	2	yes	—
79	C₄⋊C₄	D₄×C₃₇	1	2	yes	—
80	C₄⋊C₄	D₄×C₃₇	1	2	yes	—
81	C₄²	—	2	2	no	—
82	C₄²	C₂³×C₃₇	1	1	yes	characteristic
83	Q₈	—	4	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	—	4	1	no	—
88	C₂×C₄	C₂×D₄×C₃₇	1	2	yes	—
89	C₂×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
90	C₈	—	2	4	no	—
91	C₈	—	4	1	no	—
92	C₂²	#120×C₃₇	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	4	2	no	—
96	C₄	—	4	2	no	—
97	C₄	—	4	2	no	—
98	C₄	—	8	1	no	—
99	C₂	C₃₇×#454	1	1	yes	characteristic
100	C₂	C₃₇×#456	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃₇×#564

C₂

yes

maximal, characteristic

C₃₇×#501

C₂

yes

maximal

C₃₇×#491

C₂

yes

maximal, characteristic

C₃₇×#330

C₂

yes

maximal

C₃₇×#330

C₂

yes

maximal, characteristic

C₄⋊Q₈×C₃₇

C₂²

yes

characteristic

#125×C₃₇

—

#125×C₃₇

—

#125×C₃₇

—

#125×C₃₇

C₂²

yes

characteristic

#125×C₃₇

C₂²

yes

—

#107×C₃₇

—

#106×C₃₇

—

#103×C₃₇

—

#97×C₃₇

C₂²

yes

characteristic

#97×C₃₇

C₂²

yes

—

C₂×Q₈×C₃₇

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

—

C₄⋊C₄×C₃₇

—

C₄⋊C₄×C₃₇

—

C₄⋊C₄×C₃₇

—

C₄⋊C₄×C₃₇

—

C₄⋊C₄×C₃₇

—

C₄⋊C₄×C₃₇

—

C₄⋊C₄×C₃₇

—

C₄⋊C₄×C₃₇

D₄

yes

—

C₄⋊C₄×C₃₇

D₄

yes

—

C₄⋊C₄×C₃₇

D₄

yes

—

C₄²×C₃₇

—

C₄²×C₃₇

C₂³

yes

characteristic

Q₈×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₂×D₄

yes

—

C₂×C₄×C₃₇

C₂×D₄

yes

characteristic

C₈×C₃₇

—

C₈×C₃₇

—

C₂²×C₃₇

#120

yes

characteristic

C₄×C₃₇

—

C₄×C₃₇

—

C₄×C₃₇

—

C₄×C₃₇

—

C₄×C₃₇

—

C₄×C₃₇

—

#1663

C₃₇

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₃₇

#454

yes

characteristic

C₂×C₃₇

#456

yes

—

#564

C₂×C₃₇

yes

characteristic

#501

C₂×C₃₇

yes

—

#491

C₂×C₃₇

yes

characteristic

#330

C₂×C₃₇

yes

—

#330

C₂×C₃₇

yes

characteristic

C₃₇

#1663

yes

characteristic, direct product factor, Sylow

C₄⋊Q₈

C₂²×C₃₇

yes

—

—

—

C₂²×C₃₇

yes

characteristic

#125

C₂²×C₃₇

yes

—

—

—

—

C₂²×C₃₇

yes

characteristic

#97

C₂²×C₃₇

yes

—

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₄×C₃₇

yes

—

C₄⋊C₄

D₄×C₃₇

yes

—

C₄⋊C₄

D₄×C₃₇

yes

—

C₄²

—

C₄²

C₂³×C₃₇

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄×C₃₇

yes

—

C₂×C₄

C₂×D₄×C₃₇

yes

characteristic

C₈

—

C₈

—

C₂²

#120×C₃₇

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₂

C₃₇×#454

yes

characteristic

100

C₂

C₃₇×#456

yes

—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₇	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₃₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄²×C₃₇ ◁ G

subgroup

G/H

center, socle, prime radical

C₂²×C₃₇

#120

commutator, Frattini, cosocle

C₄²

C₂³×C₃₇

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₃₇ ◁ C₄²×C₃₇ ◁ G

N	H ≅ G/N	type
48. #1663	C₃₇	direct (N × H)
56. C₃₇	#1663	direct (N × H)

H ≅ G/N

type

48. #1663

C₃₇

direct (N × H)

56. C₃₇

#1663

direct (N × H)

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

subgroup	index
C₃₇×#564	2
C₃₇×#501	2
C₃₇×#491	2
C₃₇×#330	2
#1663	37

subgroup

index

C₃₇×#564

C₃₇×#501

C₃₇×#491

C₃₇×#330

#1663

Subgroups — C₃₇×#1663 #17990481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C37×#1663 #17990481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#1663 #17990481