Group #18085308 — subgroups

Subgroups — #18085308

Order 4864.

934 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 934 conjugacy classes of subgroups — too many to draw. Only its 169 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×#11926921	C₂	1	3	yes	maximal, complemented
2	#14564441	C₂	1	3	yes	maximal, complemented
3	C₁₉×#1273	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₁₅₂	—	2	6	no	—
5	C₂×#10597320	C₂²	1	3	yes	—
6	#11926921	—	2	12	no	—
7	C₂×#10597278	—	2	6	no	—
8	#11926414	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
10	C₂²×D₇₆	—	2	3	no	—
11	C₂²×D₇₆	—	2	6	no	—
12	C₂²×C₈×C₁₉	D₄	1	6	yes	—
13	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
14	C₂×C₄⋊Dic₁₉	—	2	3	no	—
15	C₂×D₁₅₂	—	2	24	no	—
16	C₂×D₁₅₂	—	4	12	no	—
17	C₂×D₁₅₂	—	4	12	no	—
18	#10597320	—	2	6	no	—
19	#10597320	—	2	3	no	—
20	#10597320	D₄	1	6	yes	—
21	C₄×C₈×C₁₉	—	2	6	no	—
22	#10597278	—	4	12	no	—
23	C₂³×D₁₉	—	4	3	no	—
24	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
25	C₂²×Dic₁₉	—	4	1	no	—
26	C₂×D₇₆	—	2	12	no	—
27	C₂×D₇₆	—	2	6	no	—
28	C₂×D₇₆	—	4	6	no	—
29	C₂×D₇₆	—	4	12	no	—
30	C₂×D₇₆	—	4	6	no	—
31	C₂×D₇₆	—	4	12	no	—
32	C₂×D₇₆	—	4	3	no	—
33	C₂×D₇₆	—	4	6	no	—
34	C₂×C₈×C₁₉	—	2	6	no	—
35	C₂×C₈×C₁₉	—	2	6	no	—
36	C₂×C₈×C₁₉	D₈	1	12	yes	complemented
37	C₄²×C₁₉	C₂×D₄	1	3	yes	—
38	C₄²×C₁₉	#41	1	1	yes	characteristic
39	C₄⋊Dic₁₉	—	4	6	no	—
40	D₁₅₂	—	4	48	no	—
41	#10304	—	19	1	no	maximal, Sylow
42	C₂³×C₁₉	#127	1	1	yes	characteristic
43	C₂²×D₁₉	—	4	6	no	—
44	C₂²×D₁₉	—	8	3	no	—
45	C₂²×D₁₉	—	8	6	no	—
46	C₂²×D₁₉	—	8	3	no	—
47	C₂²×D₁₉	—	8	6	no	—
48	C₂×C₄×C₁₉	#120	1	3	yes	—
49	C₂×C₄×C₁₉	#121	1	3	yes	—
50	C₂×C₄×C₁₉	C₂×D₈	1	6	yes	—
51	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	6	yes	—
52	C₂×Dic₁₉	—	8	3	no	—
53	D₇₆	—	4	24	no	—
54	D₇₆	—	4	12	no	—
55	D₇₆	—	8	6	no	—
56	D₇₆	—	8	12	no	—
57	C₈×C₁₉	—	2	12	no	—
58	C₂×#493	—	19	3	no	—
59	#1957	—	19	3	no	—
60	#1273	D₁₉	1	1	yes	characteristic, complemented
61	C₂²×C₁₉	#392	1	1	yes	characteristic
62	C₂²×C₁₉	#493	1	3	yes	—
63	C₂²×C₁₉	#496	1	3	yes	—
64	C₂×D₁₉	—	8	12	no	—
65	C₂×D₁₉	—	8	6	no	—
66	C₂×D₁₉	—	16	3	no	—
67	C₂×D₁₉	—	16	3	no	—
68	C₂×D₁₉	—	16	6	no	—
69	C₄×C₁₉	#447	1	6	yes	—
70	C₄×C₁₉	#459	1	6	yes	—
71	Dic₁₉	—	16	1	no	—
72	C₂²×D₈	—	38	6	no	—
73	C₂×#127	—	19	3	no	—
74	#493	—	38	12	no	—
75	C₂×#102	—	38	6	no	—
76	C₂×C₄×C₈	C₂×D₁₉	1	3	yes	—
77	#384	—	19	1	no	—
78	C₂×C₁₉	#1712	1	1	yes	characteristic
79	C₂×C₁₉	#1721	1	3	yes	—
80	C₂×C₁₉	#2011	1	3	yes	—
81	D₁₉	—	16	6	no	—
82	C₂²×D₄	—	38	6	no	—
83	C₂²×D₄	—	38	3	no	—
84	C₂×D₈	—	38	24	no	—
85	C₂×D₈	—	76	12	no	—
86	C₂×D₈	—	76	12	no	—
87	C₂²×C₈	D₇₆	1	6	yes	—
88	#127	—	19	6	no	—
89	#127	—	38	6	no	—
90	#127	—	38	3	no	—
91	C₂×C₄⋊C₄	—	38	3	no	—
92	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
93	#102	—	76	12	no	—
94	C₄×C₈	—	2	6	no	—
95	C₁₉	#10304	1	1	yes	characteristic, complemented, Sylow
96	C₂⁴	—	76	3	no	—
97	C₂×D₄	—	38	12	no	—
98	C₂×D₄	—	38	6	no	—
99	C₂×D₄	—	76	3	no	—
100	C₂×D₄	—	76	6	no	—
101	C₂×D₄	—	76	6	no	—
102	C₂×D₄	—	76	12	no	—
103	C₂×D₄	—	76	12	no	—
104	C₂×D₄	—	76	6	no	—
105	C₂²×C₄	—	76	1	no	—
106	C₂²×C₄	C₂×D₇₆	1	3	yes	—
107	D₈	—	76	48	no	—
108	C₂×C₈	—	2	6	no	—
109	C₂×C₈	—	2	6	no	—
110	C₂×C₈	D₁₅₂	1	12	yes	complemented
111	C₄⋊C₄	—	76	6	no	—
112	C₄²	D₄×D₁₉	1	3	yes	—
113	C₄²	#64545	1	1	yes	characteristic
114	C₂³	—	76	6	no	—
115	C₂³	—	152	3	no	—
116	C₂³	—	152	6	no	—
117	C₂³	—	152	6	no	—
118	C₂³	—	152	3	no	—
119	C₂³	#10597320	1	1	yes	characteristic
120	D₄	—	76	24	no	—
121	D₄	—	76	12	no	—
122	D₄	—	152	6	no	—
123	D₄	—	152	12	no	—
124	C₂×C₄	—	152	3	no	—
125	C₂×C₄	#10597328	1	3	yes	—
126	C₂×C₄	#10597341	1	3	yes	—
127	C₂×C₄	C₂×D₁₅₂	1	6	yes	—
128	C₂×C₄	#10597354	1	6	yes	—
129	C₈	—	2	12	no	—
130	C₂²	—	304	3	no	—
131	C₂²	—	304	3	no	—
132	C₂²	—	304	6	no	—
133	C₂²	—	152	12	no	—
134	C₂²	—	152	6	no	—
135	C₂²	#11926454	1	1	yes	characteristic
136	C₂²	#11926921	1	3	yes	—
137	C₂²	#11926933	1	3	yes	—
138	C₄	—	304	1	no	—
139	C₄	#11926680	1	6	yes	—
140	C₄	#11926740	1	6	yes	—
141	C₂	—	304	6	no	—
142	C₂	#14563250	1	1	yes	characteristic
143	C₂	#14563301	1	3	yes	—
144	C₂	#14564708	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926921

C₂

yes

maximal, complemented

#14564441

C₂

yes

maximal, complemented

C₁₉×#1273

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₅₂

—

C₂×#10597320

C₂²

yes

—

#11926921

—

C₂×#10597278

—

#11926414

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

#10597320

—

#10597320

—

#10597320

D₄

yes

—

C₄×C₈×C₁₉

—

#10597278

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

complemented

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

D₁₅₂

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₂×#493

—

#1957

—

#1273

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

#392

yes

characteristic

C₂²×C₁₉

#493

yes

—

C₂²×C₁₉

#496

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

#447

yes

—

C₄×C₁₉

#459

yes

—

Dic₁₉

—

C₂²×D₈

—

C₂×#127

—

#493

—

C₂×#102

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

#384

—

C₂×C₁₉

#1712

yes

characteristic

C₂×C₁₉

#1721

yes

—

C₂×C₁₉

#2011

yes

—

D₁₉

—

C₂²×D₄

—

C₂²×D₄

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂²×C₈

D₇₆

yes

—

#127

—

#127

—

#127

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#102

—

C₄×C₈

—

C₁₉

#10304

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂²×C₄

—

106

C₂²×C₄

C₂×D₇₆

yes

—

107

D₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

D₁₅₂

yes

complemented

111

C₄⋊C₄

—

112

C₄²

D₄×D₁₉

yes

—

113

C₄²

#64545

yes

characteristic

114

C₂³

—

115

C₂³

—

152

—

116

C₂³

—

152

—

117

C₂³

—

152

—

118

C₂³

—

152

—

119

C₂³

#10597320

yes

characteristic

120

D₄

—

121

D₄

—

122

D₄

—

152

—

123

D₄

—

152

—

124

C₂×C₄

—

152

—

125

C₂×C₄

#10597328

yes

—

126

C₂×C₄

#10597341

yes

—

127

C₂×C₄

C₂×D₁₅₂

yes

—

128

C₂×C₄

#10597354

yes

—

129

C₈

—

130

C₂²

—

304

—

131

C₂²

—

304

—

132

C₂²

—

304

—

133

C₂²

—

152

—

134

C₂²

—

152

—

135

C₂²

#11926454

yes

characteristic

136

C₂²

#11926921

yes

—

137

C₂²

#11926933

yes

—

138

C₄

—

304

—

139

C₄

#11926680

yes

—

140

C₄

#11926740

yes

—

141

C₂

—

304

—

142

C₂

#14563250

yes

characteristic

143

C₂

#14563301

yes

—

144

C₂

#14564708

yes

—

	subgroup	G/H
center	C₂³	#10597320
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1273	C₂
socle	C₂³×C₁₉	#127
hypercenter	#1273	D₁₉
hypocenter	C₁₉	#10304
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center

C₂³

#10597320

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1273

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
1. C₂×#11926921	C₂	semidirect
2. #14564441	C₂	semidirect
3. C₁₉×#1273	C₂	semidirect
36. C₂×C₈×C₁₉	D₈	semidirect
60. #1273	D₁₉	semidirect
95. C₁₉	#10304	semidirect
110. C₂×C₈	D₁₅₂	semidirect

H ≅ G/N

type

1. C₂×#11926921

C₂

semidirect

2. #14564441

C₂

semidirect

3. C₁₉×#1273

C₂

semidirect

36. C₂×C₈×C₁₉

D₈

semidirect

60. #1273

D₁₉

semidirect

95. C₁₉

#10304

semidirect

110. C₂×C₈

D₁₅₂

semidirect

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

subgroup	index
C₂×#11926921	2
#14564441	2
C₁₉×#1273	2
#10304	19

subgroup

index

C₂×#11926921

#14564441

C₁₉×#1273

#10304

Subgroups — #18085308

Conjugacy classes of subgroups

Complements

Maximal subgroups