Group #18010938 — subgroups

Subgroups — #18010938

Order 4736.

152 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 72 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	D₃₇⋊M₃₂	C₂	1	2	yes	maximal
2	#14558456	C₂	1	2	yes	maximal, complemented
3	#14558455	C₂	1	2	yes	maximal, complemented
4	#14557490	C₂	1	1	yes	maximal, characteristic
5	#11924611	—	2	2	no	—
6	#11924610	C₂²	1	4	yes	—
7	D₃₇⋊C₁₆	—	2	2	no	—
8	C₂×#10596929	C₄	1	1	yes	characteristic
9	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
10	#11924493	C₄	1	1	yes	characteristic
11	#11924446	C₄	1	1	yes	characteristic
12	C₄×#64436	C₂²	1	1	yes	characteristic
13	C₈×Dic₃₇	C₂²	1	1	yes	characteristic
14	#97×C₃₇	C₄	1	1	yes	characteristic
15	C₂×C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
19	#10596938	—	2	1	no	—
20	#10596936	—	2	1	no	—
21	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
22	C₂×#64436	C₂×C₄	1	1	yes	characteristic
23	C₂×#64436	C₂³	1	1	yes	characteristic
24	#10596929	C₈	1	4	yes	—
25	C₈×D₃₇	D₄	1	2	yes	—
26	C₈×D₃₇	Q₈	1	2	yes	—
27	#10596927	—	2	4	no	—
28	C₂²×D₃₇	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₃₇	—	2	1	no	—
30	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₃₇	—	2	1	no	—
32	C₂×Dic₃₇	M₁₆	1	1	yes	characteristic
33	C₄×D₃₇	C₄⋊C₄	1	2	yes	—
34	C₄×D₃₇	C₂×C₈	1	2	yes	—
35	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
36	C₈×C₃₇	C₂×C₈	1	2	yes	—
37	#64436	C₂×C₈	1	2	yes	—
38	#64436	C₂×D₄	1	1	yes	characteristic
39	#64436	C₂×Q₈	1	1	yes	characteristic
40	C₂²×C₃₇	C₂×M₁₆	1	1	yes	characteristic
41	C₂×D₃₇	—	4	1	no	—
42	C₂×D₃₇	C₄⋊C₈	1	2	yes	—
43	C₄×C₃₇	—	4	1	no	—
44	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₄×C₃₇	C₂²×C₈	1	1	yes	characteristic
46	Dic₃₇	—	4	1	no	—
47	Dic₃₇	C₄⋊C₈	1	2	yes	—
48	#2153	—	37	1	no	maximal, Sylow
49	C₂×C₃₇	—	2	1	no	—
50	C₂×C₃₇	C₂×C₄⋊C₈	1	1	yes	characteristic
51	D₃₇	—	2	2	no	—
52	C₂×M₃₂	—	37	2	no	—
53	#405	—	37	1	no	—
54	#364	—	37	2	no	—
55	#364	—	37	2	no	—
56	C₃₇	#2153	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	—	37	1	no	—
58	C₂²×C₈	—	37	1	no	—
59	#117	—	37	1	no	—
60	M₃₂	—	37	4	no	—
61	M₃₂	—	74	2	no	—
62	C₂×C₁₆	—	74	2	no	—
63	#97	—	37	1	no	—
64	#97	#3866	1	1	yes	characteristic
65	C₄×C₈	—	37	1	no	—
66	C₄×C₈	—	37	1	no	—
67	C₂²×C₄	—	37	1	no	—
68	M₁₆	—	37	4	no	—
69	C₂×C₈	—	37	1	no	—
70	C₂×C₈	—	37	1	no	—
71	C₂×C₈	—	37	2	no	—
72	C₂×C₈	—	37	2	no	—
73	C₂×C₈	C₂×#3866	1	1	yes	characteristic
74	C₂×C₈	C₂×#3866	1	1	yes	characteristic
75	C₄⋊C₄	—	74	1	no	—
76	C₂²⋊C₄	—	74	1	no	—
77	C₄²	—	37	1	no	—
78	C₄²	C₂×#3866	1	1	yes	characteristic
79	C₁₆	—	74	4	no	—
80	C₂³	—	37	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	37	1	no	—
83	C₂×C₄	—	37	2	no	—
84	C₂×C₄	—	37	2	no	—
85	C₂×C₄	—	74	1	no	—
86	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
87	C₈	—	37	1	no	—
88	C₈	—	37	1	no	—
89	C₈	—	37	2	no	—
90	C₈	D₃₇⋊C₈	1	2	yes	—
91	C₈	C₄⋊#3866	1	2	yes	—
92	C₂²	—	37	2	no	—
93	C₂²	—	148	1	no	—
94	C₂²	D₃₇⋊M₁₆	1	1	yes	characteristic
95	C₄	—	4	1	no	—
96	C₄	—	37	2	no	—
97	C₄	—	148	1	no	—
98	C₄	C₂×C₄⋊#3866	1	1	yes	characteristic
99	C₄	C₂×D₃₇⋊C₈	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	74	2	no	—
102	C₂	D₃₇⋊(C₄⋊C₈)	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₃₇⋊M₃₂

C₂

yes

maximal

#14558456

C₂

yes

maximal, complemented

#14558455

C₂

yes

maximal, complemented

#14557490

C₂

yes

maximal, characteristic

#11924611

—

#11924610

C₂²

yes

—

D₃₇⋊C₁₆

—

C₂×#10596929

C₄

yes

characteristic

C₂×C₈×D₃₇

C₂²

yes

characteristic

#11924493

C₄

yes

characteristic

#11924446

C₄

yes

characteristic

C₄×#64436

C₂²

yes

characteristic

C₈×Dic₃₇

C₂²

yes

characteristic

#97×C₃₇

C₄

yes

characteristic

C₂×C₄×D₃₇

C₂×C₄

yes

characteristic

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₄²×C₃₇

C₂×C₄

yes

characteristic

#10596938

—

#10596936

—

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₂×#64436

C₂×C₄

yes

characteristic

C₂×#64436

C₂³

yes

characteristic

#10596929

C₈

yes

—

C₈×D₃₇

D₄

yes

—

C₈×D₃₇

Q₈

yes

—

#10596927

—

C₂²×D₃₇

M₁₆

yes

characteristic

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

—

C₂×Dic₃₇

M₁₆

yes

characteristic

C₄×D₃₇

C₄⋊C₄

yes

—

C₄×D₃₇

C₂×C₈

yes

—

C₈×C₃₇

C₄⋊C₄

yes

—

C₈×C₃₇

C₂×C₈

yes

—

#64436

C₂×C₈

yes

—

#64436

C₂×D₄

yes

characteristic

#64436

C₂×Q₈

yes

characteristic

C₂²×C₃₇

C₂×M₁₆

yes

characteristic

C₂×D₃₇

—

C₂×D₃₇

C₄⋊C₈

yes

—

C₄×C₃₇

—

C₄×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₃₇

C₂²×C₈

yes

characteristic

Dic₃₇

—

Dic₃₇

C₄⋊C₈

yes

—

#2153

—

maximal, Sylow

C₂×C₃₇

—

C₂×C₃₇

C₂×C₄⋊C₈

yes

characteristic

D₃₇

—

C₂×M₃₂

—

#405

—

#364

—

#364

—

C₃₇

#2153

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×#3866

yes

characteristic

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×#3866

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

D₃₇⋊C₈

yes

—

C₈

C₄⋊#3866

yes

—

C₂²

—

C₂²

—

148

—

C₂²

D₃₇⋊M₁₆

yes

characteristic

C₄

—

C₄

—

C₄

—

148

—

C₄

C₂×C₄⋊#3866

yes

characteristic

C₄

C₂×D₃₇⋊C₈

yes

characteristic

100

C₂

—

101

C₂

—

102

C₂

D₃₇⋊(C₄⋊C₈)

yes

characteristic

	subgroup	G/H
center	C₄	C₂×C₄⋊#3866
commutator	C₄×C₃₇	C₂²×C₈
Frattini	C₂×C₄	C₂²×#3866
Fitting	#97×C₃₇	C₄
socle	C₂×C₃₇	C₂×C₄⋊C₈
prime radical	C₂²×D₃₇	M₁₆
cosocle	C₂×#64436	C₂³
hypercenter	#97	#3866
hypocenter	C₃₇	#2153
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

subgroup

G/H

center

C₄

C₂×C₄⋊#3866

commutator

C₄×C₃₇

C₂²×C₈

Frattini

C₂×C₄

C₂²×#3866

Fitting

#97×C₃₇

C₄

socle

C₂×C₃₇

C₂×C₄⋊C₈

prime radical

C₂²×D₃₇

M₁₆

C₂³

C₃₇

G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

N	H ≅ G/N	type
2. #14558456	C₂	semidirect
3. #14558455	C₂	semidirect
56. C₃₇	#2153	semidirect

H ≅ G/N

type

2. #14558456

C₂

semidirect

3. #14558455

C₂

semidirect

56. C₃₇

#2153

semidirect

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

subgroup	index
D₃₇⋊M₃₂	2
#14558456	2
#14558455	2
#14557490	2
#2153	37

subgroup

index

D₃₇⋊M₃₂

Subgroups — #18010938

Conjugacy classes of subgroups

Complements

Maximal subgroups