Group #18010797 — subgroups

Subgroups — #18010797

Order 4736.

200 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 110 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	C₂×D₃₇⋊C₁₆	C₂	1	2	yes	maximal
2	#14558422	C₂	1	2	yes	maximal, complemented
3	#14558421	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₃₇	C₂	1	1	yes	maximal, characteristic
5	D₃₇⋊C₁₆	C₄	1	8	yes	complemented
6	C₂×#10596927	C₂²	1	4	yes	—
7	C₂×C₈×D₃₇	C₄	1	1	yes	characteristic
8	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
9	C₄²×D₃₇	C₄	1	1	yes	characteristic
10	C₄×#64436	C₂²	1	1	yes	characteristic
11	C₈×Dic₃₇	C₄	1	1	yes	characteristic
12	C₈×Dic₃₇	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₃₇	C₄	1	1	yes	characteristic
14	C₂×C₄×D₃₇	C₈	1	2	yes	—
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	C₄×Dic₃₇	C₈	1	2	yes	—
20	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
21	C₂×#64436	C₂×C₄	1	1	yes	characteristic
22	C₂×#64436	C₂³	1	1	yes	characteristic
23	C₈×D₃₇	C₈	1	4	yes	—
24	C₈×D₃₇	C₂×C₄	1	4	yes	—
25	#10596927	C₂×C₄	1	8	yes	complemented
26	C₂²×D₃₇	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₃₇	C₂×C₈	1	2	yes	—
28	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×Dic₃₇	C₂×C₈	1	2	yes	—
30	C₂×Dic₃₇	C₂×C₈	1	1	yes	characteristic
31	C₄×D₃₇	—	2	4	no	—
32	C₄×D₃₇	C₄²	1	2	yes	—
33	C₄×D₃₇	C₂×C₈	1	2	yes	—
34	C₈×C₃₇	C₄²	1	2	yes	—
35	C₈×C₃₇	C₂×C₈	1	2	yes	—
36	#64436	C₂×C₈	1	2	yes	—
37	#64436	C₂²×C₄	1	2	yes	—
38	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
39	C₂×D₃₇	C₄×C₈	1	2	yes	—
40	C₂×D₃₇	M₃₂	1	4	yes	—
41	C₄×C₃₇	—	2	2	no	—
42	C₄×C₃₇	C₂×C₄²	1	1	yes	characteristic
43	C₄×C₃₇	C₂²×C₈	1	1	yes	characteristic
44	Dic₃₇	—	2	2	no	—
45	Dic₃₇	C₄×C₈	1	2	yes	—
46	C₂×#346	—	37	1	no	maximal, Sylow
47	C₂×C₃₇	C₂×C₄×C₈	1	1	yes	characteristic
48	C₂×C₃₇	C₂×M₃₂	1	2	yes	—
49	D₃₇	#346	1	4	yes	complemented
50	C₂²×C₁₆	—	37	2	no	—
51	C₂×C₄×C₈	—	37	1	no	—
52	#346	—	37	2	no	—
53	#346	—	37	2	no	—
54	C₃₇	C₂×#346	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₈	—	37	1	no	—
56	C₂²×C₈	—	37	1	no	—
57	C₂×C₄²	—	37	1	no	—
58	C₂×C₁₆	—	37	4	no	—
59	C₂×C₁₆	—	37	8	no	—
60	C₄×C₈	—	37	1	no	—
61	C₄×C₈	—	37	1	no	—
62	C₄×C₈	—	37	1	no	—
63	C₄×C₈	#3866	1	1	yes	characteristic
64	C₂²×C₄	—	37	1	no	—
65	C₂²×C₄	—	37	2	no	—
66	C₂×C₈	—	37	1	no	—
67	C₂×C₈	—	37	1	no	—
68	C₂×C₈	—	37	4	no	—
69	C₂×C₈	—	37	4	no	—
70	C₂×C₈	C₂×#3866	1	1	yes	characteristic
71	C₂×C₈	C₂×#3866	1	1	yes	characteristic
72	C₄²	—	37	2	no	—
73	C₄²	—	37	1	no	—
74	C₄²	C₂×#3866	1	1	yes	characteristic
75	C₁₆	—	37	8	no	—
76	C₂³	—	37	1	no	—
77	C₂×C₄	—	37	1	no	—
78	C₂×C₄	—	37	2	no	—
79	C₂×C₄	—	37	2	no	—
80	C₂×C₄	—	37	2	no	—
81	C₂×C₄	—	74	4	no	—
82	C₂×C₄	D₃₇⋊C₈	1	2	yes	—
83	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
84	C₈	—	37	2	no	—
85	C₈	—	37	2	no	—
86	C₈	D₃₇⋊C₈	1	2	yes	—
87	C₈	C₄×#3866	1	2	yes	—
88	C₂²	—	37	2	no	—
89	C₂²	—	37	4	no	—
90	C₂²	C₂×D₃₇⋊C₈	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	37	2	no	—
93	C₄	—	74	2	no	—
94	C₄	C₂×C₄×#3866	1	1	yes	characteristic
95	C₄	C₂×D₃₇⋊C₈	1	1	yes	characteristic
96	C₂	—	37	4	no	—
97	C₂	C₄×D₃₇⋊C₈	1	1	yes	characteristic
98	C₂	D₃₇⋊M₃₂	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₃₇⋊C₁₆

C₂

yes

maximal

#14558422

C₂

yes

maximal, complemented

#14558421

C₂

yes

maximal, complemented

C₄×C₈×D₃₇

C₂

yes

maximal, characteristic

D₃₇⋊C₁₆

C₄

yes

complemented

C₂×#10596927

C₂²

yes

—

C₂×C₈×D₃₇

C₄

yes

characteristic

C₂×C₈×D₃₇

C₂²

yes

characteristic

C₄²×D₃₇

C₄

yes

characteristic

C₄×#64436

C₂²

yes

characteristic

C₈×Dic₃₇

C₄

yes

characteristic

C₈×Dic₃₇

C₂²

yes

characteristic

C₄×C₈×C₃₇

C₄

yes

characteristic

C₂×C₄×D₃₇

C₈

yes

—

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

C₄×Dic₃₇

C₈

yes

—

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₂×#64436

C₂×C₄

yes

characteristic

C₂×#64436

C₂³

yes

characteristic

C₈×D₃₇

C₈

yes

—

C₈×D₃₇

C₂×C₄

yes

—

#10596927

C₂×C₄

yes

complemented

C₂²×D₃₇

C₂×C₈

yes

characteristic

C₂×C₄×C₃₇

C₂×C₈

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

C₂×C₈

yes

—

C₂×Dic₃₇

C₂×C₈

yes

characteristic

C₄×D₃₇

—

C₄×D₃₇

C₄²

yes

—

C₄×D₃₇

C₂×C₈

yes

—

C₈×C₃₇

C₄²

yes

—

C₈×C₃₇

C₂×C₈

yes

—

#64436

C₂×C₈

yes

—

#64436

C₂²×C₄

yes

—

C₂²×C₃₇

C₂²×C₈

yes

characteristic

C₂×D₃₇

C₄×C₈

yes

—

C₂×D₃₇

M₃₂

yes

—

C₄×C₃₇

—

C₄×C₃₇

C₂×C₄²

yes

characteristic

C₄×C₃₇

C₂²×C₈

yes

characteristic

Dic₃₇

—

Dic₃₇

C₄×C₈

yes

—

C₂×#346

—

maximal, Sylow

C₂×C₃₇

C₂×C₄×C₈

yes

characteristic

C₂×C₃₇

C₂×M₃₂

yes

—

D₃₇

#346

yes

complemented

C₂²×C₁₆

—

C₂×C₄×C₈

—

#346

—

#346

—

C₃₇

C₂×#346

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#3866

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

C₂×#3866

yes

characteristic

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₃₇⋊C₈

yes

—

C₂×C₄

C₂²×#3866

yes

characteristic

C₈

—

C₈

—

C₈

D₃₇⋊C₈

yes

—

C₈

C₄×#3866

yes

—

C₂²

—

C₂²

—

C₂²

C₂×D₃₇⋊C₈

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

C₂×C₄×#3866

yes

characteristic

C₄

C₂×D₃₇⋊C₈

yes

characteristic

C₂

—

C₂

C₄×D₃₇⋊C₈

yes

characteristic

C₂

D₃₇⋊M₃₂

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×#3866
commutator	C₂×C₃₇	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#3866
Fitting	C₄×C₈×C₃₇	C₄
socle	C₂²×C₃₇	C₂²×C₈
prime radical	C₂²×D₃₇	C₂×C₈
cosocle	C₂×#64436	C₂³
hypercenter	C₄×C₈	#3866
hypocenter	C₃₇	C₂×#346
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

subgroup

G/H

center

C₂×C₈

C₂×#3866

commutator

C₂×C₃₇

C₂×C₄×C₈

Frattini

C₂×C₄

C₂²×#3866

Fitting

C₄×C₈×C₃₇

C₄

socle

C₂²×C₃₇

C₂²×C₈

prime radical

C₂²×D₃₇

C₂×C₈

C₂³

C₄×C₈

C₃₇

G ▷ C₂×C₃₇ ▷ C₃₇

C₁ ◁ C₂×C₈ ◁ C₄×C₈

N	H ≅ G/N	type
2. #14558422	C₂	semidirect
3. #14558421	C₂	semidirect
5. D₃₇⋊C₁₆	C₄	semidirect
25. #10596927	C₂×C₄	semidirect
49. D₃₇	#346	semidirect
54. C₃₇	C₂×#346	semidirect

H ≅ G/N

type

2. #14558422

C₂

semidirect

3. #14558421

C₂

semidirect

5. D₃₇⋊C₁₆

C₄

semidirect

25. #10596927

C₂×C₄

semidirect

49. D₃₇

#346

semidirect

54. C₃₇

C₂×#346

semidirect

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

subgroup	index
C₂×D₃₇⋊C₁₆	2
#14558422	2
#14558421	2
C₄×C₈×D₃₇	2
C₂×#346	37

subgroup

index

C₂×D₃₇⋊C₁₆

#14558422

#14558421

C₄×C₈×D₃₇

C₂×#346

Subgroups — #18010797

Conjugacy classes of subgroups

Complements

Maximal subgroups