Group #18003533 — subgroups

Subgroups — #18003533

Order 4736.

348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 181 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	#14558090	C₂	1	1	yes	maximal, characteristic
2	#14557662	C₂	1	8	yes	maximal, complemented
3	#14557561	C₂	1	2	yes	maximal
4	#14557491	C₂	1	2	yes	maximal
5	C₂×#11924447	C₂	1	1	yes	maximal, characteristic
6	C₃₇×#423	C₂	1	1	yes	maximal, characteristic
7	C₂²×#64436	C₂²	1	1	yes	characteristic
8	C₂²×#64436	C₂²	1	1	yes	characteristic
9	#11924536	C₄	1	2	yes	—
10	#11924528	C₄	1	2	yes	—
11	#11924515	C₄	1	4	yes	—
12	C₄×Dic₇₄	C₂²	1	4	yes	—
13	#11924495	C₂²	1	2	yes	—
14	#11924465	C₂²	1	8	yes	—
15	#11924447	C₂²	1	4	yes	—
16	#11924446	C₂²	1	4	yes	—
17	C₈×Dic₃₇	C₂²	1	4	yes	—
18	C₂×M₁₆×C₃₇	C₂²	1	2	yes	—
19	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
20	C₄⋊C₈×C₃₇	C₂²	1	4	yes	—
21	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
23	C₂×Dic₇₄	C₂×C₄	1	4	yes	—
24	M₁₆×C₃₇	—	2	4	no	—
25	C₂×C₈×C₃₇	C₂³	1	4	yes	—
26	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
27	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
28	C₄²×C₃₇	C₂³	1	2	yes	—
29	C₂²⋊Dic₃₇	C₂×C₄	1	4	yes	—
30	C₄⋊Dic₃₇	C₂×C₄	1	4	yes	—
31	C₄⋊Dic₃₇	C₂×C₄	1	4	yes	—
32	#10596936	C₂×C₄	1	8	yes	—
33	C₄×Dic₃₇	C₂³	1	4	yes	—
34	C₂×#64436	—	2	2	no	—
35	C₂×#64436	Q₈	1	4	yes	complemented
36	C₂×#64436	C₂³	1	2	yes	—
37	C₂×#64436	C₂³	1	2	yes	—
38	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₃₇	—	4	2	no	—
40	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
41	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
42	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₄×C₃₇	C₂×Q₈	1	2	yes	—
44	C₂×C₄×C₃₇	#41	1	2	yes	—
45	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
46	C₂×Dic₃₇	C₂²×C₄	1	8	yes	—
47	Dic₇₄	—	4	4	no	—
48	C₈×C₃₇	—	2	4	no	—
49	#64436	—	2	2	no	—
50	#64436	C₂×Q₈	1	4	yes	—
51	C₂²×C₃₇	—	2	2	no	—
52	C₂²×C₃₇	C₄×Q₈	1	2	yes	—
53	C₂²×C₃₇	C₂³×C₄	1	1	yes	characteristic
54	C₄×C₃₇	—	2	2	no	—
55	C₄×C₃₇	—	2	2	no	—
56	C₄×C₃₇	C₄×Q₈	1	2	yes	—
57	C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
58	C₄×C₃₇	C₂×#41	1	1	yes	characteristic
59	Dic₃₇	—	2	8	no	—
60	#2961	—	37	1	no	maximal, Sylow
61	C₂×C₃₇	—	2	2	no	—
62	C₂×C₃₇	C₂×C₄×Q₈	1	1	yes	characteristic
63	C₂×C₃₇	#568	1	2	yes	—
64	#533	—	37	1	no	—
65	#446	—	37	8	no	—
66	#424	—	37	2	no	—
67	#423	D₃₇	1	1	yes	characteristic
68	#405	—	37	2	no	—
69	C₂×#97	—	37	1	no	—
70	C₃₇	#2961	1	1	yes	characteristic, complemented, Sylow
71	C₂×M₁₆	C₂×D₃₇	1	2	yes	—
72	C₂²×C₈	—	37	1	no	—
73	C₂²×C₈	—	37	1	no	—
74	C₄⋊Q₈	—	37	2	no	—
75	#125	—	37	2	no	—
76	C₂²⋊Q₈	—	37	4	no	—
77	C₄×Q₈	—	37	4	no	—
78	#117	—	37	2	no	—
79	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
80	C₄⋊C₈	—	37	8	no	—
81	C₄⋊C₈	C₂×D₃₇	1	4	yes	—
82	#97	—	37	4	no	—
83	#97	—	37	4	no	—
84	C₄×C₈	—	37	4	no	—
85	C₂×Q₈	—	37	4	no	—
86	C₂²×C₄	C₄×D₃₇	1	2	yes	—
87	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
88	M₁₆	—	2	4	no	—
89	C₂×C₈	—	37	4	no	—
90	C₂×C₈	—	37	2	no	—
91	C₂×C₈	—	37	2	no	—
92	C₂×C₈	—	74	2	no	—
93	C₂×C₈	C₂²×D₃₇	1	4	yes	—
94	C₄⋊C₄	—	37	8	no	—
95	C₄⋊C₄	—	37	4	no	—
96	C₄⋊C₄	—	37	4	no	—
97	C₂²⋊C₄	—	37	4	no	—
98	C₄²	—	37	4	no	—
99	C₄²	C₄×D₃₇	1	1	yes	characteristic
100	C₄²	C₄×D₃₇	1	1	yes	characteristic
101	C₄²	C₂²×D₃₇	1	2	yes	—
102	C₂³	C₂×C₄×D₃₇	1	1	yes	characteristic
103	Q₈	—	148	4	no	—
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	—	37	8	no	—
106	C₂×C₄	C₂×C₄×D₃₇	1	2	yes	—
107	C₂×C₄	C₂×C₄×D₃₇	1	2	yes	—
108	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
109	C₂×C₄	#10596964	1	2	yes	—
110	C₂×C₄	Q₈×D₃₇	1	2	yes	—
111	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
112	C₈	—	2	4	no	—
113	C₈	—	37	4	no	—
114	C₈	—	74	2	no	—
115	C₂²	—	2	2	no	—
116	C₂²	#11924501	1	2	yes	—
117	C₂²	C₂²×C₄×D₃₇	1	1	yes	characteristic
118	C₄	—	2	2	no	—
119	C₄	—	2	2	no	—
120	C₄	—	74	8	no	—
121	C₄	#11924501	1	2	yes	—
122	C₄	C₂×Q₈×D₃₇	1	1	yes	characteristic
123	C₄	C₂×#10596964	1	1	yes	characteristic
124	C₂	—	2	2	no	—
125	C₂	C₂×#11924501	1	1	yes	characteristic
126	C₂	#14558299	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14558090

C₂

yes

maximal, characteristic

#14557662

C₂

yes

maximal, complemented

#14557561

C₂

yes

maximal

#14557491

C₂

yes

maximal

C₂×#11924447

C₂

yes

maximal, characteristic

C₃₇×#423

C₂

yes

maximal, characteristic

C₂²×#64436

C₂²

yes

characteristic

C₂²×#64436

C₂²

yes

characteristic

#11924536

C₄

yes

—

#11924528

C₄

yes

—

#11924515

C₄

yes

—

C₄×Dic₇₄

C₂²

yes

—

#11924495

C₂²

yes

—

#11924465

C₂²

yes

—

#11924447

C₂²

yes

—

#11924446

C₂²

yes

—

C₈×Dic₃₇

C₂²

yes

—

C₂×M₁₆×C₃₇

C₂²

yes

—

C₂×C₄²×C₃₇

C₂²

yes

characteristic

C₄⋊C₈×C₃₇

C₂²

yes

—

C₂²×C₄×C₃₇

C₂×C₄

yes

—

C₂²×C₄×C₃₇

C₂³

yes

characteristic

C₂×Dic₇₄

C₂×C₄

yes

—

M₁₆×C₃₇

—

C₂×C₈×C₃₇

C₂³

yes

—

C₄²×C₃₇

C₂×C₄

yes

characteristic

C₄²×C₃₇

C₂×C₄

yes

characteristic

C₄²×C₃₇

C₂³

yes

—

C₂²⋊Dic₃₇

C₂×C₄

yes

—

C₄⋊Dic₃₇

C₂×C₄

yes

—

C₄⋊Dic₃₇

C₂×C₄

yes

—

#10596936

C₂×C₄

yes

—

C₄×Dic₃₇

C₂³

yes

—

C₂×#64436

—

C₂×#64436

Q₈

yes

complemented

C₂×#64436

C₂³

yes

—

C₂×#64436

C₂³

yes

—

C₂³×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₂²×C₄

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

C₂×Q₈

yes

—

C₂×C₄×C₃₇

#41

yes

—

C₂×C₄×C₃₇

C₂⁴

yes

characteristic

C₂×Dic₃₇

C₂²×C₄

yes

—

Dic₇₄

—

C₈×C₃₇

—

#64436

—

#64436

C₂×Q₈

yes

—

C₂²×C₃₇

—

C₂²×C₃₇

C₄×Q₈

yes

—

C₂²×C₃₇

C₂³×C₄

yes

characteristic

C₄×C₃₇

—

C₄×C₃₇

—

C₄×C₃₇

C₄×Q₈

yes

—

C₄×C₃₇

C₂²×Q₈

yes

characteristic

C₄×C₃₇

C₂×#41

yes

characteristic

Dic₃₇

—

#2961

—

maximal, Sylow

C₂×C₃₇

—

C₂×C₃₇

C₂×C₄×Q₈

yes

characteristic

C₂×C₃₇

#568

yes

—

—

—

—

D₃₇

yes

characteristic

#405

—

C₂×#97

—

C₃₇

#2961

yes

characteristic, complemented, Sylow

C₂×M₁₆

C₂×D₃₇

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂×D₃₇

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

C₂×D₃₇

yes

—

#97

—

#97

—

C₄×C₈

—

C₂×Q₈

—

C₂²×C₄

C₄×D₃₇

yes

—

C₂²×C₄

C₂²×D₃₇

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₃₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₃₇

yes

characteristic

100

C₄²

C₄×D₃₇

yes

characteristic

101

C₄²

C₂²×D₃₇

yes

—

102

C₂³

C₂×C₄×D₃₇

yes

characteristic

103

Q₈

—

148

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₂×C₄×D₃₇

yes

—

107

C₂×C₄

C₂×C₄×D₃₇

yes

—

108

C₂×C₄

C₂×C₄×D₃₇

yes

characteristic

109

C₂×C₄

#10596964

yes

—

110

C₂×C₄

Q₈×D₃₇

yes

—

111

C₂×C₄

C₂³×D₃₇

yes

characteristic

112

C₈

—

113

C₈

—

114

C₈

—

115

C₂²

—

116

C₂²

#11924501

yes

—

117

C₂²

C₂²×C₄×D₃₇

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

#11924501

yes

—

122

C₄

C₂×Q₈×D₃₇

yes

characteristic

123

C₄

C₂×#10596964

yes

characteristic

124

C₂

—

125

C₂

C₂×#11924501

yes

characteristic

126

C₂

#14558299

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₃₇
commutator, socle	C₂²×C₃₇	C₂³×C₄
Fitting	C₃₇×#423	C₂
prime radical	C₂³×C₃₇	C₂²×C₄
cosocle	C₂×C₄×C₃₇	C₂⁴
hypercenter	#423	D₃₇
hypocenter	C₃₇	#2961
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ #423

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₃₇

commutator, socle

C₂²×C₃₇

C₂³×C₄

Fitting

C₃₇×#423

C₂

prime radical

C₂³×C₃₇

C₂²×C₄

cosocle

C₂×C₄×C₃₇

C₂⁴

D₃₇

C₃₇

G ▷ C₂²×C₃₇ ▷ C₃₇

C₁ ◁ C₂×C₄ ◁ #423

N	H ≅ G/N	type
2. #14557662	C₂	semidirect
35. C₂×#64436	Q₈	semidirect
70. C₃₇	#2961	semidirect

H ≅ G/N

type

2. #14557662

C₂

semidirect

35. C₂×#64436

Q₈

semidirect

70. C₃₇

#2961

semidirect

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

subgroup	index
#14558090	2
#14557662	2
#14557561	2
#14557491	2
C₂×#11924447	2
C₃₇×#423	2
#2961	37

subgroup

index

C₃₇×#423

Subgroups — #18003533

Conjugacy classes of subgroups

Complements

Maximal subgroups