Group #17994444 — subgroups

Subgroups — #17994444

Order 4736.

316 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 161 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×#11924465	C₂	1	2	yes	maximal
2	C₂×C₈×Dic₃₇	C₂	1	2	yes	maximal
3	C₄²×Dic₃₇	C₂	1	1	yes	maximal, characteristic
4	#14557288	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64436	C₂²	1	2	yes	—
7	C₂×C₄×Dic₃₇	C₄	1	2	yes	—
8	C₂×C₄×Dic₃₇	C₄	1	2	yes	—
9	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
11	#11924465	C₄	1	8	yes	complemented
12	C₈×Dic₃₇	—	2	4	no	—
13	C₂²×C₈×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
17	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₃₇	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₃₇	—	2	2	no	—
21	C₂×C₈×C₃₇	—	2	2	no	—
22	C₂×C₈×C₃₇	C₂×C₄	1	4	yes	—
23	C₄²×C₃₇	—	2	2	no	—
24	C₄×Dic₃₇	—	2	4	no	—
25	C₄×Dic₃₇	C₈	1	8	yes	complemented
26	C₄×Dic₃₇	C₂×C₄	1	4	yes	—
27	C₄×Dic₃₇	D₄	1	2	yes	—
28	C₄×Dic₃₇	Q₈	1	2	yes	—
29	C₂×#64436	—	2	2	no	—
30	C₂×#64436	—	2	2	no	—
31	C₂×#64436	C₂×C₄	1	4	yes	—
32	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₃₇	—	2	2	no	—
34	C₂×C₄×C₃₇	—	2	2	no	—
35	C₂×C₄×C₃₇	C₂×C₈	1	4	yes	—
36	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
37	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₃₇	#41	1	2	yes	—
40	C₂×Dic₃₇	—	2	2	no	—
41	C₂×Dic₃₇	C₄²	1	2	yes	—
42	C₂×Dic₃₇	C₄²	1	2	yes	—
43	C₂×Dic₃₇	C₄⋊C₄	1	4	yes	—
44	C₂×Dic₃₇	C₂×C₈	1	4	yes	—
45	C₂×Dic₃₇	C₂×C₈	1	4	yes	—
46	C₂×Dic₃₇	M₁₆	1	4	yes	—
47	C₈×C₃₇	—	2	4	no	—
48	#64436	—	2	4	no	—
49	C₂²×C₃₇	C₂×C₄²	1	1	yes	characteristic
50	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₃₇	#117	1	1	yes	characteristic
52	C₂²×C₃₇	C₂²×C₈	1	2	yes	—
53	C₂²×C₃₇	C₂×M₁₆	1	2	yes	—
54	C₄×C₃₇	—	2	4	no	—
55	C₄×C₃₇	C₄×D₄	1	2	yes	—
56	C₄×C₃₇	C₄×Q₈	1	2	yes	—
57	Dic₃₇	—	2	2	no	—
58	Dic₃₇	C₄×C₈	1	4	yes	complemented
59	Dic₃₇	C₄⋊C₈	1	8	yes	complemented
60	C₄×C₄⋊C₈	—	37	1	no	maximal, Sylow
61	C₂×C₃₇	C₄×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₃₇	C₂×C₄×C₈	1	1	yes	characteristic
63	C₂×C₃₇	C₄×M₁₆	1	1	yes	characteristic
64	C₂×C₃₇	C₂×C₄⋊C₈	1	2	yes	—
65	C₂×C₃₇	#431	1	2	yes	—
66	C₂×C₄⋊C₈	—	37	2	no	—
67	C₂×C₄×C₈	—	37	2	no	—
68	C₄³	—	37	1	no	—
69	#336	—	37	1	no	—
70	#336	D₃₇	1	1	yes	characteristic
71	C₃₇	C₄×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₈	—	37	2	no	—
73	C₂²×C₈	C₂×D₃₇	1	2	yes	—
74	C₂×C₄²	—	37	2	no	—
75	C₂×C₄²	—	37	1	no	—
76	C₂×C₄²	—	37	1	no	—
77	C₂×C₄²	—	37	2	no	—
78	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
79	C₄⋊C₈	—	37	8	no	—
80	C₄×C₈	—	74	4	no	—
81	C₂²×C₄	—	37	1	no	—
82	C₂²×C₄	—	37	2	no	—
83	C₂²×C₄	—	37	1	no	—
84	C₂²×C₄	C₄×D₃₇	1	2	yes	—
85	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	37	4	no	—
89	C₂×C₈	—	74	2	no	—
90	C₂×C₈	—	74	2	no	—
91	C₂×C₈	C₄×D₃₇	1	4	yes	—
92	C₄²	—	2	2	no	—
93	C₄²	—	37	8	no	—
94	C₄²	—	37	4	no	—
95	C₄²	—	37	2	no	—
96	C₄²	—	37	2	no	—
97	C₄²	—	74	4	no	—
98	C₂³	C₂×C₄×D₃₇	1	1	yes	characteristic
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	37	2	no	—
102	C₂×C₄	—	37	4	no	—
103	C₂×C₄	—	37	4	no	—
104	C₂×C₄	—	37	4	no	—
105	C₂×C₄	—	37	4	no	—
106	C₂×C₄	—	37	2	no	—
107	C₂×C₄	—	74	2	no	—
108	C₂×C₄	C₈×D₃₇	1	4	yes	—
109	C₂×C₄	C₂×C₄×D₃₇	1	2	yes	—
110	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
111	C₂×C₄	#10596964	1	2	yes	—
112	C₂×C₄	Q₈×D₃₇	1	1	yes	characteristic
113	C₈	—	2	4	no	—
114	C₈	—	74	4	no	—
115	C₂²	C₄²×D₃₇	1	1	yes	characteristic
116	C₂²	C₄⋊C₄×D₃₇	1	1	yes	characteristic
117	C₂²	#11924492	1	1	yes	characteristic
118	C₂²	C₂×C₈×D₃₇	1	2	yes	—
119	C₂²	M₁₆×D₃₇	1	2	yes	—
120	C₄	—	2	4	no	—
121	C₄	—	37	4	no	—
122	C₄	—	37	8	no	—
123	C₄	—	74	2	no	—
124	C₄	#11924496	1	2	yes	—
125	C₄	#11924501	1	2	yes	—
126	C₂	#14557384	1	1	yes	characteristic
127	C₂	C₄×C₈×D₃₇	1	1	yes	characteristic
128	C₂	#14557485	1	1	yes	characteristic
129	C₂	C₄⋊C₈×D₃₇	1	2	yes	—
130	C₂	#14557583	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11924465

C₂

yes

maximal

C₂×C₈×Dic₃₇

C₂

yes

maximal

C₄²×Dic₃₇

C₂

yes

maximal, characteristic

#14557288

C₂

yes

maximal, characteristic

C₃₇×#336

C₂

yes

maximal, characteristic

C₂²×#64436

C₂²

yes

—

C₂×C₄×Dic₃₇

C₄

yes

—

C₂×C₄×Dic₃₇

C₄

yes

—

C₂×C₄×Dic₃₇

C₂²

yes

characteristic

C₂×C₄×Dic₃₇

C₂²

yes

characteristic

#11924465

C₄

yes

complemented

C₈×Dic₃₇

—

C₂²×C₈×C₃₇

C₂²

yes

—

C₂×C₄²×C₃₇

C₂²

yes

characteristic

C₂²×C₄×C₃₇

C₂×C₄

yes

—

C₂²×C₄×C₃₇

C₂³

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

C₂×C₄

yes

—

C₄²×C₃₇

—

C₄×Dic₃₇

—

C₄×Dic₃₇

C₈

yes

complemented

C₄×Dic₃₇

C₂×C₄

yes

—

C₄×Dic₃₇

D₄

yes

—

C₄×Dic₃₇

Q₈

yes

—

C₂×#64436

—

C₂×#64436

—

C₂×#64436

C₂×C₄

yes

—

C₂³×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₂×C₈

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

—

C₂×C₄×C₃₇

C₂×D₄

yes

characteristic

C₂×C₄×C₃₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₃₇

#41

yes

—

C₂×Dic₃₇

—

C₂×Dic₃₇

C₄²

yes

—

C₂×Dic₃₇

C₄²

yes

—

C₂×Dic₃₇

C₄⋊C₄

yes

—

C₂×Dic₃₇

C₂×C₈

yes

—

C₂×Dic₃₇

C₂×C₈

yes

—

C₂×Dic₃₇

M₁₆

yes

—

C₈×C₃₇

—

#64436

—

C₂²×C₃₇

C₂×C₄²

yes

characteristic

C₂²×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₃₇

#117

yes

characteristic

C₂²×C₃₇

C₂²×C₈

yes

—

C₂²×C₃₇

C₂×M₁₆

yes

—

C₄×C₃₇

—

C₄×C₃₇

C₄×D₄

yes

—

C₄×C₃₇

C₄×Q₈

yes

—

Dic₃₇

—

Dic₃₇

C₄×C₈

yes

complemented

Dic₃₇

C₄⋊C₈

yes

complemented

C₄×C₄⋊C₈

—

maximal, Sylow

C₂×C₃₇

C₄×C₄⋊C₄

yes

characteristic

C₂×C₃₇

C₂×C₄×C₈

yes

characteristic

C₂×C₃₇

C₄×M₁₆

yes

characteristic

C₂×C₃₇

C₂×C₄⋊C₈

yes

—

C₂×C₃₇

#431

yes

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

C₄³

—

#336

—

#336

D₃₇

yes

characteristic

C₃₇

C₄×C₄⋊C₈

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₃₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₃₇

yes

characteristic

C₄⋊C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₃₇

yes

—

C₂²×C₄

C₂²×D₃₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₃₇

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂×C₄×D₃₇

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

C₈×D₃₇

yes

—

109

C₂×C₄

C₂×C₄×D₃₇

yes

—

110

C₂×C₄

D₄×D₃₇

yes

characteristic

111

C₂×C₄

#10596964

yes

—

112

C₂×C₄

Q₈×D₃₇

yes

characteristic

113

C₈

—

114

C₈

—

115

C₂²

C₄²×D₃₇

yes

characteristic

116

C₂²

C₄⋊C₄×D₃₇

yes

characteristic

117

C₂²

#11924492

yes

characteristic

118

C₂²

C₂×C₈×D₃₇

yes

—

119

C₂²

M₁₆×D₃₇

yes

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

#11924496

yes

—

125

C₄

#11924501

yes

—

126

C₂

#14557384

yes

characteristic

127

C₂

C₄×C₈×D₃₇

yes

characteristic

128

C₂

#14557485

yes

characteristic

129

C₂

C₄⋊C₈×D₃₇

yes

—

130

C₂

#14557583

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₃₇
commutator	C₂×C₃₇	C₂×C₄×C₈
Fitting	C₃₇×#336	C₂
socle, prime radical	C₂³×C₃₇	C₂²×C₄
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	#336	D₃₇
hypocenter	C₃₇	C₄×C₄⋊C₈
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₃₇

commutator

C₂×C₃₇

C₂×C₄×C₈

Fitting

C₃₇×#336

C₂

socle, prime radical

C₂³×C₃₇

C₂²×C₄

cosocle

C₂²×C₄×C₃₇

C₂³

hypercenter

#336

D₃₇

hypocenter

C₃₇

C₄×C₄⋊C₈

LCS

G ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
11. #11924465	C₄	semidirect
25. C₄×Dic₃₇	C₈	semidirect
58. Dic₃₇	C₄×C₈	semidirect
59. Dic₃₇	C₄⋊C₈	semidirect
71. C₃₇	C₄×C₄⋊C₈	semidirect

H ≅ G/N

type

11. #11924465

C₄

semidirect

25. C₄×Dic₃₇

C₈

semidirect

58. Dic₃₇

C₄×C₈

semidirect

59. Dic₃₇

C₄⋊C₈

semidirect

71. C₃₇

C₄×C₄⋊C₈

semidirect

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

subgroup	index
C₂×#11924465	2
C₂×C₈×Dic₃₇	2
C₄²×Dic₃₇	2
#14557288	2
C₃₇×#336	2
C₄×C₄⋊C₈	37

subgroup

index

C₂×#11924465

C₂×C₈×Dic₃₇

C₄²×Dic₃₇

#14557288

C₃₇×#336

C₄×C₄⋊C₈

Subgroups — #17994444

Conjugacy classes of subgroups

Complements

Maximal subgroups