Group #17995383 — subgroups

Subgroups — #17995383

Order 4736.

184 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 79 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	#14557581	C₂	1	1	yes	maximal, characteristic
2	C₂×#11924471	C₂	1	1	yes	maximal, characteristic
3	C₂×#11924471	C₂	1	1	yes	maximal, characteristic
4	#14557491	C₂	1	1	yes	maximal, characteristic
5	#14557305	C₂	1	1	yes	maximal, characteristic
6	#14557304	C₂	1	1	yes	maximal, characteristic
7	C₃₇×#430	C₂	1	1	yes	maximal, characteristic
8	C₂×#10596934	C₂²	1	1	yes	characteristic
9	C₂×#10596934	C₂²	1	1	yes	characteristic
10	C₂²×#64436	C₂²	1	1	yes	characteristic
11	#11924495	C₂²	1	1	yes	characteristic
12	#11924471	—	2	2	no	—
13	#11924471	—	2	1	no	—
14	#11924471	—	2	1	no	—
15	#11924471	C₄	1	4	yes	complemented
16	#11924446	—	2	1	no	—
17	C₈×Dic₃₇	—	2	1	no	—
18	C₂×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
20	C₂×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
21	#108×C₃₇	—	2	2	no	—
22	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
23	M₁₆×C₃₇	—	2	1	no	—
24	M₁₆×C₃₇	—	2	1	no	—
25	M₁₆×C₃₇	—	2	1	no	—
26	M₁₆×C₃₇	—	2	1	no	—
27	M₁₆×C₃₇	C₂×C₄	1	2	yes	—
28	M₁₆×C₃₇	D₄	1	2	yes	—
29	C₂×C₈×C₃₇	—	2	1	no	—
30	C₂×C₈×C₃₇	—	2	1	no	—
31	C₂×C₈×C₃₇	—	2	1	no	—
32	C₂²⋊Dic₃₇	Q₈	1	2	yes	—
33	C₄⋊Dic₃₇	—	2	1	no	—
34	C₄×Dic₃₇	—	2	1	no	—
35	#10596934	—	2	1	no	—
36	#10596934	—	2	1	no	—
37	#10596934	—	2	1	no	—
38	#10596934	C₂×C₄	1	2	yes	—
39	C₂×#64436	—	2	1	no	—
40	C₂×#64436	—	2	1	no	—
41	C₂×#64436	C₂×C₄	1	2	yes	—
42	C₂×#64436	D₄	1	1	yes	characteristic
43	C₂×#64436	D₄	1	1	yes	characteristic
44	C₂×#64436	Q₈	1	2	yes	—
45	C₂³×C₃₇	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₄×C₃₇	#41	1	1	yes	characteristic
51	C₂×C₄×C₃₇	#41	1	1	yes	characteristic
52	C₂×Dic₃₇	—	2	2	no	—
53	C₈×C₃₇	—	2	2	no	—
54	C₈×C₃₇	—	2	2	no	—
55	C₈×C₃₇	—	4	1	no	—
56	#64436	—	2	2	no	—
57	#64436	—	4	1	no	—
58	#64436	C₄⋊C₄	1	2	yes	—
59	#64436	C₄⋊C₄	1	2	yes	—
60	C₂²×C₃₇	—	4	1	no	—
61	C₂²×C₃₇	C₄×Q₈	1	1	yes	characteristic
62	C₂²×C₃₇	C₂²⋊Q₈	1	1	yes	characteristic
63	C₂²×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
64	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
66	C₄×C₃₇	#121	1	1	yes	characteristic
67	C₄×C₃₇	#125	1	1	yes	characteristic
68	Dic₃₇	—	4	2	no	—
69	#1953	—	37	1	no	maximal, Sylow
70	C₂×C₃₇	—	2	1	no	—
71	C₂×C₃₇	—	2	1	no	—
72	C₂×C₃₇	—	2	1	no	—
73	C₂×C₃₇	#389	1	1	yes	characteristic
74	#430	—	37	1	no	—
75	#430	D₃₇	1	1	yes	characteristic
76	C₂×#108	—	37	1	no	—
77	C₂×#108	—	37	1	no	—
78	#405	—	37	1	no	—
79	#344	—	37	1	no	—
80	#344	—	37	1	no	—
81	C₃₇	#1953	1	1	yes	characteristic, complemented, Sylow
82	C₂×M₁₆	—	37	1	no	—
83	C₂×M₁₆	—	37	1	no	—
84	C₂×M₁₆	C₂×D₃₇	1	1	yes	characteristic
85	C₂×M₁₆	C₂×D₃₇	1	1	yes	characteristic
86	C₂×M₁₆	C₂×D₃₇	1	1	yes	characteristic
87	C₂²×C₈	—	37	1	no	—
88	#117	—	37	1	no	—
89	#108	—	2	2	no	—
90	#108	—	37	4	no	—
91	#108	—	74	1	no	—
92	#108	—	74	1	no	—
93	#108	—	74	2	no	—
94	#97	—	74	1	no	—
95	C₄×C₈	—	74	1	no	—
96	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
97	M₁₆	—	2	1	no	—
98	M₁₆	—	2	1	no	—
99	M₁₆	—	2	1	no	—
100	M₁₆	—	2	1	no	—
101	M₁₆	—	37	2	no	—
102	M₁₆	—	74	1	no	—
103	M₁₆	—	74	1	no	—
104	M₁₆	—	74	1	no	—
105	M₁₆	C₄×D₃₇	1	2	yes	—
106	M₁₆	C₂²⋊D₃₇	1	2	yes	—
107	C₂×C₈	—	2	1	no	—
108	C₂×C₈	—	2	1	no	—
109	C₂×C₈	—	2	1	no	—
110	C₂×C₈	—	37	2	no	—
111	C₂×C₈	—	37	1	no	—
112	C₂×C₈	—	37	1	no	—
113	C₂×C₈	—	37	2	no	—
114	C₂×C₈	—	74	1	no	—
115	C₂×C₈	—	74	1	no	—
116	C₄⋊C₄	—	74	1	no	—
117	C₂²⋊C₄	—	37	2	no	—
118	C₄²	—	74	1	no	—
119	C₂³	Q₈×D₃₇	1	1	yes	characteristic
120	C₂×C₄	—	74	2	no	—
121	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
122	C₂×C₄	#10596962	1	1	yes	characteristic
123	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
124	C₂×C₄	#10596964	1	1	yes	characteristic
125	C₂×C₄	Q₈×D₃₇	1	1	yes	characteristic
126	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
127	C₈	—	2	2	no	—
128	C₈	—	2	2	no	—
129	C₈	—	4	1	no	—
130	C₈	—	37	2	no	—
131	C₈	—	37	2	no	—
132	C₈	—	74	2	no	—
133	C₈	—	148	1	no	—
134	C₂²	—	4	1	no	—
135	C₂²	#11924501	1	1	yes	characteristic
136	C₂²	#11924514	1	1	yes	characteristic
137	C₂²	#11924534	1	1	yes	characteristic
138	C₄	—	148	2	no	—
139	C₄	C₄⋊C₄×D₃₇	1	1	yes	characteristic
140	C₄	C₄×C₂²⋊D₃₇	1	1	yes	characteristic
141	C₄	#11924508	1	1	yes	characteristic
142	C₄	#11924526	1	1	yes	characteristic
143	C₂	—	2	1	no	—
144	C₂	—	2	1	no	—
145	C₂	—	2	1	no	—
146	C₂	#14557428	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14557581

C₂

yes

maximal, characteristic

C₂×#11924471

C₂

yes

maximal, characteristic

C₂×#11924471

C₂

yes

maximal, characteristic

#14557491

C₂

yes

maximal, characteristic

#14557305

C₂

yes

maximal, characteristic

#14557304

C₂

yes

maximal, characteristic

C₃₇×#430

C₂

yes

maximal, characteristic

C₂×#10596934

C₂²

yes

characteristic

C₂×#10596934

C₂²

yes

characteristic

C₂²×#64436

C₂²

yes

characteristic

#11924495

C₂²

yes

—

—

—

C₄

yes

complemented

#11924446

—

C₈×Dic₃₇

—

C₂×M₁₆×C₃₇

C₂²

yes

characteristic

C₂×M₁₆×C₃₇

C₂²

yes

characteristic

C₂×M₁₆×C₃₇

C₂²

yes

characteristic

#108×C₃₇

—

C₂²×C₄×C₃₇

C₂³

yes

characteristic

M₁₆×C₃₇

—

M₁₆×C₃₇

—

M₁₆×C₃₇

—

M₁₆×C₃₇

—

M₁₆×C₃₇

C₂×C₄

yes

—

M₁₆×C₃₇

D₄

yes

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

—

C₂²⋊Dic₃₇

Q₈

yes

—

C₄⋊Dic₃₇

—

C₄×Dic₃₇

—

—

—

—

C₂×C₄

yes

—

C₂×#64436

—

C₂×#64436

—

C₂×#64436

C₂×C₄

yes

—

C₂×#64436

D₄

yes

characteristic

C₂×#64436

D₄

yes

characteristic

C₂×#64436

Q₈

yes

—

C₂³×C₃₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

C₂×D₄

yes

characteristic

C₂×C₄×C₃₇

C₂×D₄

yes

characteristic

C₂×C₄×C₃₇

C₂×Q₈

yes

C₂×C₄×C₃₇

yes

C₂×C₄×C₃₇

yes

C₂×Dic₃₇

—

C₈×C₃₇

—

C₈×C₃₇

—

C₈×C₃₇

—

#64436

—

#64436

—

#64436

C₄⋊C₄

yes

—

#64436

C₄⋊C₄

yes

—

C₂²×C₃₇

—

C₂²×C₃₇

C₄×Q₈

yes

characteristic

C₂²×C₃₇

C₂²⋊Q₈

yes

characteristic

C₂²×C₃₇

C₄⋊Q₈

yes

characteristic

C₄×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₃₇

C₄×D₄

yes

C₄×C₃₇

yes

C₄×C₃₇

yes

Dic₃₇

—

#1953

—

maximal, Sylow

C₂×C₃₇

—

C₂×C₃₇

—

C₂×C₃₇

—

C₂×C₃₇

yes

—

D₃₇

yes

—

—

—

—

—

C₃₇

#1953

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₃₇

yes

characteristic

C₂×M₁₆

C₂×D₃₇

yes

characteristic

C₂×M₁₆

C₂×D₃₇

yes

characteristic

C₂²×C₈

—

—

—

—

—

—

—

—

C₄×C₈

—

C₂²×C₄

C₂²×D₃₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

100

M₁₆

—

101

M₁₆

—

102

M₁₆

—

103

M₁₆

—

104

M₁₆

—

105

M₁₆

C₄×D₃₇

yes

—

106

M₁₆

C₂²⋊D₃₇

yes

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₄⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

—

119

C₂³

Q₈×D₃₇

yes

characteristic

120

C₂×C₄

—

121

C₂×C₄

C₂×C₄×D₃₇

yes

characteristic

122

C₂×C₄

#10596962

yes

characteristic

123

C₂×C₄

D₄×D₃₇

yes

characteristic

124

C₂×C₄

#10596964

yes

characteristic

125

C₂×C₄

Q₈×D₃₇

yes

characteristic

126

C₂×C₄

C₂×C₂²⋊D₃₇

yes

characteristic

127

C₈

—

128

C₈

—

129

C₈

—

130

C₈

—

131

C₈

—

132

C₈

—

133

C₈

—

148

—

134

C₂²

—

135

C₂²

#11924501

yes

characteristic

136

C₂²

#11924514

yes

characteristic

137

C₂²

#11924534

yes

characteristic

138

C₄

—

148

—

139

C₄

C₄⋊C₄×D₃₇

yes

characteristic

140

C₄

C₄×C₂²⋊D₃₇

yes

characteristic

141

C₄

#11924508

yes

characteristic

142

C₄

#11924526

yes

characteristic

143

C₂

—

144

C₂

—

145

C₂

—

146

C₂

#14557428

yes

characteristic

	subgroup	G/H
center	C₄	#11924508
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₃₇×#430	C₂
socle	C₂×C₃₇	#389
prime radical	C₂³×C₃₇	C₂×Q₈
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	#430	D₃₇
hypocenter	C₃₇	#1953
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

subgroup

G/H

center

C₄

#11924508

commutator

C₂×C₄×C₃₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₃₇

Fitting

C₃₇×#430

C₂

socle

C₂×C₃₇

#389

prime radical

C₂³×C₃₇

C₂×Q₈

cosocle

C₂²×C₄×C₃₇

C₂³

D₃₇

C₃₇

G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

N	H ≅ G/N	type
15. #11924471	C₄	semidirect
81. C₃₇	#1953	semidirect

H ≅ G/N

type

15. #11924471

C₄

semidirect

81. C₃₇

#1953

semidirect

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

subgroup	index
#14557581	2
C₂×#11924471	2
#14557491	2
#14557305	2
#14557304	2
C₃₇×#430	2
#1953	37

subgroup

index

C₃₇×#430

Subgroups — #17995383

Conjugacy classes of subgroups

Complements

Maximal subgroups