Group #14557447 — subgroups

Subgroups — #14557447

Order 2368.

238 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 65 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×#10596936	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊Dic₃₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊Dic₃₇	C₂	1	2	yes	maximal, complemented
4	#11924443	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₄×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂⁴×C₃₇	C₂²	1	2	yes	—
7	C₂×D₄×C₃₇	—	2	4	no	—
8	C₂×D₄×C₃₇	—	2	2	no	—
9	C₂²×C₄×C₃₇	C₂²	1	1	yes	characteristic
10	C₂²×Dic₃₇	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃₇	C₂²	1	2	yes	—
12	C₂²×Dic₃₇	C₂²	1	1	yes	characteristic
13	C₂²⋊Dic₃₇	—	2	4	no	—
14	C₂²⋊Dic₃₇	—	2	4	no	—
15	#10596936	—	2	2	no	—
16	C₂³×C₃₇	—	2	2	no	—
17	C₂³×C₃₇	—	2	2	no	—
18	C₂³×C₃₇	—	2	2	no	—
19	C₂³×C₃₇	—	2	2	no	—
20	C₂³×C₃₇	—	2	2	no	—
21	C₂³×C₃₇	—	2	2	no	—
22	C₂³×C₃₇	D₄	1	4	yes	—
23	C₂³×C₃₇	C₂³	1	1	yes	characteristic
24	D₄×C₃₇	—	2	8	no	—
25	C₂×C₄×C₃₇	—	2	2	no	—
26	C₂×C₄×C₃₇	D₄	1	2	yes	—
27	C₂×Dic₃₇	—	2	1	no	—
28	C₂×Dic₃₇	—	2	1	no	—
29	C₂×Dic₃₇	—	2	1	no	—
30	C₂×Dic₃₇	—	2	2	no	—
31	C₂×Dic₃₇	—	2	2	no	—
32	C₂×Dic₃₇	—	2	2	no	—
33	C₂×Dic₃₇	—	2	2	no	—
34	C₂×Dic₃₇	D₄	1	2	yes	complemented
35	C₂²×C₃₇	—	2	4	no	—
36	C₂²×C₃₇	—	2	4	no	—
37	C₂²×C₃₇	—	2	4	no	—
38	C₂²×C₃₇	—	4	2	no	—
39	C₂²×C₃₇	—	4	2	no	—
40	C₂²×C₃₇	—	4	2	no	—
41	C₂²×C₃₇	—	4	2	no	—
42	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₃₇	C₂×D₄	1	2	yes	—
44	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₃₇	#41	1	1	yes	characteristic
46	C₂²×C₃₇	#41	1	2	yes	—
47	C₄×C₃₇	—	2	2	no	—
48	Dic₃₇	—	2	2	no	—
49	Dic₃₇	—	4	1	no	—
50	Dic₃₇	—	4	2	no	—
51	C₂×C₃₇	—	4	4	no	—
52	C₂×C₃₇	#120	1	1	yes	characteristic
53	C₂×C₃₇	#121	1	1	yes	characteristic
54	C₂×C₃₇	#121	1	2	yes	—
55	C₂×C₃₇	#123	1	2	yes	—
56	C₂×C₃₇	#124	1	1	yes	characteristic
57	#394	—	37	1	no	maximal, Sylow
58	C₃₇	#394	1	1	yes	characteristic, complemented, Sylow
59	C₂²×D₄	D₃₇	1	1	yes	characteristic
60	C₂×C₄⋊C₄	—	37	1	no	—
61	C₂×C₂²⋊C₄	—	37	2	no	—
62	C₂×C₂²⋊C₄	—	37	2	no	—
63	#95	—	37	1	no	—
64	C₂⁴	C₂×D₃₇	1	2	yes	—
65	C₂×D₄	—	2	4	no	—
66	C₂×D₄	—	2	2	no	—
67	C₂²×C₄	—	37	1	no	—
68	C₂²×C₄	—	37	2	no	—
69	C₂²×C₄	—	37	1	no	—
70	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
71	C₄⋊C₄	—	74	2	no	—
72	C₂²⋊C₄	—	74	4	no	—
73	C₂²⋊C₄	—	74	4	no	—
74	C₂³	—	2	2	no	—
75	C₂³	—	2	2	no	—
76	C₂³	—	2	2	no	—
77	C₂³	—	2	2	no	—
78	C₂³	—	2	2	no	—
79	C₂³	—	2	2	no	—
80	C₂³	C₂²⋊D₃₇	1	4	yes	—
81	C₂³	C₂²×D₃₇	1	1	yes	characteristic
82	D₄	—	2	8	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	37	2	no	—
85	C₂×C₄	—	74	1	no	—
86	C₂×C₄	—	74	1	no	—
87	C₂×C₄	—	74	2	no	—
88	C₂×C₄	—	74	2	no	—
89	C₂×C₄	—	74	2	no	—
90	C₂×C₄	—	74	2	no	—
91	C₂×C₄	—	74	1	no	—
92	C₂×C₄	C₂²⋊D₃₇	1	2	yes	—
93	C₂²	—	2	4	no	—
94	C₂²	—	2	4	no	—
95	C₂²	—	2	4	no	—
96	C₂²	—	4	2	no	—
97	C₂²	—	4	2	no	—
98	C₂²	—	4	2	no	—
99	C₂²	—	4	2	no	—
100	C₂²	D₄×D₃₇	1	1	yes	characteristic
101	C₂²	#10596964	1	1	yes	characteristic
102	C₂²	#10596964	1	2	yes	—
103	C₂²	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
104	C₂²	C₂×C₂²⋊D₃₇	1	2	yes	—
105	C₄	—	2	2	no	—
106	C₄	—	74	2	no	—
107	C₄	—	148	1	no	—
108	C₄	—	148	2	no	—
109	C₂	—	4	4	no	—
110	C₂	#11924505	1	1	yes	characteristic
111	C₂	#11924507	1	1	yes	characteristic
112	C₂	#11924508	1	2	yes	—
113	C₂	#11924517	1	2	yes	—
114	C₂	#11924523	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10596936

C₂

yes

maximal, characteristic, complemented

C₂×C₂²⋊Dic₃₇

C₂

yes

maximal, complemented

C₂×C₂²⋊Dic₃₇

C₂

yes

maximal, complemented

#11924443

C₂

yes

maximal, characteristic, complemented

C₂²×D₄×C₃₇

C₂

yes

maximal, characteristic

C₂⁴×C₃₇

C₂²

yes

—

C₂×D₄×C₃₇

—

C₂×D₄×C₃₇

—

C₂²×C₄×C₃₇

C₂²

yes

characteristic

C₂²×Dic₃₇

C₂²

yes

characteristic

C₂²×Dic₃₇

C₂²

yes

—

C₂²×Dic₃₇

C₂²

yes

characteristic

C₂²⋊Dic₃₇

—

C₂²⋊Dic₃₇

—

#10596936

—

C₂³×C₃₇

—

C₂³×C₃₇

—

C₂³×C₃₇

—

C₂³×C₃₇

—

C₂³×C₃₇

—

C₂³×C₃₇

—

C₂³×C₃₇

D₄

yes

—

C₂³×C₃₇

C₂³

yes

characteristic

D₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

D₄

yes

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

D₄

yes

complemented

C₂²×C₃₇

—

C₂²×C₃₇

—

C₂²×C₃₇

—

C₂²×C₃₇

—

C₂²×C₃₇

—

C₂²×C₃₇

—

C₂²×C₃₇

—

C₂²×C₃₇

C₂×D₄

yes

characteristic

C₂²×C₃₇

C₂×D₄

yes

—

C₂²×C₃₇

C₂×D₄

yes

C₂²×C₃₇

yes

C₂²×C₃₇

yes

—

C₄×C₃₇

—

Dic₃₇

—

Dic₃₇

—

Dic₃₇

—

C₂×C₃₇

—

C₂×C₃₇

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

—

C₂×C₃₇

#123

yes

—

C₂×C₃₇

yes

—

C₃₇

yes

characteristic, complemented, Sylow

C₂²×D₄

D₃₇

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

C₂⁴

C₂×D₃₇

yes

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₃₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²⋊D₃₇

yes

—

C₂³

C₂²×D₃₇

yes

characteristic

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊D₃₇

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

D₄×D₃₇

yes

characteristic

101

C₂²

#10596964

yes

characteristic

102

C₂²

#10596964

yes

—

103

C₂²

C₂×C₂²⋊D₃₇

yes

characteristic

104

C₂²

C₂×C₂²⋊D₃₇

yes

—

105

C₄

—

106

C₄

—

107

C₄

—

148

—

108

C₄

—

148

—

109

C₂

—

110

C₂

#11924505

yes

characteristic

111

C₂

#11924507

yes

characteristic

112

C₂

#11924508

yes

—

113

C₂

#11924517

yes

—

114

C₂

#11924523

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃₇
commutator, socle, cosocle	C₂³×C₃₇	C₂³
Fitting, prime radical	C₂²×D₄×C₃₇	C₂
hypercenter	C₂²×D₄	D₃₇
hypocenter	C₃₇	#394
LCS	G ▷ C₂³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂²×D₄

subgroup

G/H

center, Frattini

C₂³

C₂²×D₃₇

commutator, socle, cosocle

C₂³×C₃₇

C₂³

Fitting, prime radical

C₂²×D₄×C₃₇

C₂

hypercenter

C₂²×D₄

D₃₇

C₃₇

G ▷ C₂³×C₃₇ ▷ C₃₇

C₁ ◁ C₂³ ◁ C₂²×D₄

N	H ≅ G/N	type
1. C₂×#10596936	C₂	semidirect
2. C₂×C₂²⋊Dic₃₇	C₂	semidirect
3. C₂×C₂²⋊Dic₃₇	C₂	semidirect
4. #11924443	C₂	semidirect
34. C₂×Dic₃₇	D₄	semidirect
58. C₃₇	#394	semidirect

H ≅ G/N

type

1. C₂×#10596936

C₂

semidirect

2. C₂×C₂²⋊Dic₃₇

C₂

semidirect

3. C₂×C₂²⋊Dic₃₇

C₂

semidirect

4. #11924443

C₂

semidirect

34. C₂×Dic₃₇

D₄

semidirect

58. C₃₇

#394

semidirect

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

subgroup	index
C₂×#10596936	2
C₂×C₂²⋊Dic₃₇	2
#11924443	2
C₂²×D₄×C₃₇	2
#394	37

subgroup

index

C₂×#10596936

C₂×C₂²⋊Dic₃₇

#11924443

C₂²×D₄×C₃₇

#394

Subgroups — #14557447

Conjugacy classes of subgroups

Complements

Maximal subgroups