Group #18071293 — subgroups

Subgroups — #18071293

Order 4864.

448 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 83 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	#14564869	C₂	1	3	yes	maximal
2	#14561458	C₂	1	3	yes	maximal, complemented
3	C₁₉×#2810	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10597320	C₂²	1	1	yes	characteristic
5	C₂×#10597266	—	2	3	no	—
6	C₂×#10597266	—	2	3	no	—
7	#11926299	C₂²	1	3	yes	—
8	C₁₉×#400	—	2	3	no	—
9	C₁₉×#389	C₂²	1	3	yes	—
10	C₁₉×#387	—	2	3	no	—
11	C₂²×D₇₆	—	2	3	no	—
12	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
13	C₂×C₄⋊C₄×C₁₉	D₄	1	3	yes	—
14	C₂×C₄⋊C₄×C₁₉	D₄	1	3	yes	—
15	C₂×C₄²×C₁₉	—	2	1	no	—
16	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
17	C₂²×C₁₉⋊C₈	—	2	3	no	—
18	#10597320	—	4	2	no	—
19	C₁₉×#95	—	2	3	no	—
20	C₁₉×#95	—	2	3	no	—
21	C₁₉×#95	—	2	1	no	—
22	C₁₉×#95	—	2	3	no	—
23	#10597266	—	4	6	no	—
24	#10597266	—	4	6	no	—
25	C₂³×D₁₉	—	4	1	no	—
26	C₂²×C₄×C₁₉	—	2	3	no	—
27	C₂²×C₄×C₁₉	—	2	3	no	—
28	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
29	C₂×D₇₆	—	2	6	no	—
30	C₂×D₇₆	—	4	3	no	—
31	C₂×D₇₆	—	4	3	no	—
32	C₂×D₇₆	—	4	3	no	—
33	C₂×D₇₆	—	4	3	no	—
34	C₂×D₇₆	—	4	3	no	—
35	C₄⋊C₄×C₁₉	—	2	3	no	—
36	C₄⋊C₄×C₁₉	—	2	3	no	—
37	C₄⋊C₄×C₁₉	—	4	3	no	—
38	C₄⋊C₄×C₁₉	—	4	3	no	—
39	C₄⋊C₄×C₁₉	—	4	3	no	—
40	C₄²×C₁₉	—	4	1	no	—
41	C₄²×C₁₉	—	8	1	no	—
42	C₂×C₁₉⋊C₈	—	4	3	no	—
43	C₂×C₁₉⋊C₈	—	4	3	no	—
44	C₂×C₁₉⋊C₈	—	4	3	no	—
45	#7744	—	19	1	no	maximal, Sylow
46	C₂³×C₁₉	#120	1	1	yes	characteristic
47	C₂²×D₁₉	—	4	2	no	—
48	C₂²×D₁₉	—	8	3	no	—
49	C₂²×D₁₉	—	8	3	no	—
50	C₂×C₄×C₁₉	—	2	3	no	—
51	C₂×C₄×C₁₉	—	2	3	no	—
52	C₂×C₄×C₁₉	—	4	3	no	—
53	C₂×C₄×C₁₉	—	4	3	no	—
54	C₂×C₄×C₁₉	—	4	3	no	—
55	C₂×C₄×C₁₉	—	4	3	no	—
56	C₂×C₄×C₁₉	—	4	3	no	—
57	C₂×C₄×C₁₉	—	4	3	no	—
58	C₂×C₄×C₁₉	#135	1	3	yes	—
59	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	3	yes	—
60	D₇₆	—	4	6	no	—
61	D₇₆	—	4	6	no	—
62	D₇₆	—	8	3	no	—
63	D₇₆	—	8	3	no	—
64	C₁₉⋊C₈	—	8	3	no	—
65	#2810	D₁₉	1	1	yes	characteristic, complemented
66	#2041	—	19	3	no	—
67	#1271	—	19	3	no	—
68	C₂²×C₁₉	#449	1	3	yes	—
69	C₂²×C₁₉	#454	1	3	yes	—
70	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
71	C₂×D₁₉	—	8	6	no	—
72	C₂×D₁₉	—	16	3	no	—
73	C₂×D₁₉	—	16	1	no	—
74	C₄×C₁₉	—	2	3	no	—
75	C₄×C₁₉	—	2	3	no	—
76	C₄×C₁₉	—	8	3	no	—
77	C₄×C₁₉	—	8	3	no	—
78	C₂×#127	—	19	1	no	—
79	C₂×#102	—	38	3	no	—
80	C₂×#102	—	38	3	no	—
81	#400	—	2	3	no	—
82	#389	C₂×D₁₉	1	3	yes	—
83	#387	—	2	3	no	—
84	#336	—	19	3	no	—
85	C₂×C₁₉	#1597	1	3	yes	—
86	C₂×C₁₉	#1628	1	3	yes	—
87	C₂×C₁₉	#1658	1	1	yes	characteristic
88	D₁₉	—	16	2	no	—
89	C₂²×D₄	—	38	3	no	—
90	C₂²×C₈	—	38	3	no	—
91	#127	—	76	2	no	—
92	C₂×C₄⋊C₄	—	2	3	no	—
93	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	3	yes	—
94	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	3	yes	—
95	C₂×C₄²	—	2	1	no	—
96	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
97	#102	—	76	6	no	—
98	#102	—	76	6	no	—
99	#95	—	2	3	no	—
100	#95	—	2	3	no	—
101	#95	—	2	1	no	—
102	#95	—	2	3	no	—
103	C₁₉	#7744	1	1	yes	characteristic, complemented, Sylow
104	C₂⁴	—	76	1	no	—
105	C₂×D₄	—	38	6	no	—
106	C₂×D₄	—	76	3	no	—
107	C₂×D₄	—	76	3	no	—
108	C₂×D₄	—	76	3	no	—
109	C₂×D₄	—	76	3	no	—
110	C₂×D₄	—	76	3	no	—
111	C₂²×C₄	—	2	3	no	—
112	C₂²×C₄	—	2	3	no	—
113	C₂²×C₄	C₂×C₂²⋊D₁₉	1	3	yes	—
114	C₂×C₈	—	76	3	no	—
115	C₂×C₈	—	76	3	no	—
116	C₂×C₈	—	76	3	no	—
117	C₄⋊C₄	—	2	3	no	—
118	C₄⋊C₄	—	2	3	no	—
119	C₄⋊C₄	—	4	3	no	—
120	C₄⋊C₄	—	4	3	no	—
121	C₄⋊C₄	—	4	3	no	—
122	C₄²	—	4	1	no	—
123	C₄²	—	8	1	no	—
124	C₂³	—	76	2	no	—
125	C₂³	—	152	3	no	—
126	C₂³	—	152	3	no	—
127	C₂³	#10597399	1	1	yes	characteristic
128	D₄	—	76	6	no	—
129	D₄	—	76	6	no	—
130	D₄	—	152	3	no	—
131	D₄	—	152	3	no	—
132	C₂×C₄	—	2	3	no	—
133	C₂×C₄	—	2	3	no	—
134	C₂×C₄	—	4	3	no	—
135	C₂×C₄	—	4	3	no	—
136	C₂×C₄	—	4	3	no	—
137	C₂×C₄	—	4	3	no	—
138	C₂×C₄	—	4	3	no	—
139	C₂×C₄	—	4	3	no	—
140	C₂×C₄	#10597395	1	3	yes	—
141	C₂×C₄	#10597396	1	3	yes	—
142	C₈	—	152	3	no	—
143	C₂²	—	304	1	no	—
144	C₂²	—	304	3	no	—
145	C₂²	—	152	6	no	—
146	C₂²	#11926689	1	3	yes	—
147	C₂²	#11926717	1	3	yes	—
148	C₂²	#11926731	1	1	yes	characteristic
149	C₄	—	2	3	no	—
150	C₄	—	2	3	no	—
151	C₄	—	8	3	no	—
152	C₄	—	8	3	no	—
153	C₂	—	304	2	no	—
154	C₂	#14562564	1	3	yes	—
155	C₂	#14562745	1	3	yes	—
156	C₂	#14562937	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564869

C₂

yes

maximal

#14561458

C₂

yes

maximal, complemented

C₁₉×#2810

C₂

yes

maximal, characteristic, complemented

C₂×#10597320

C₂²

yes

—

—

C₂²

yes

—

C₁₉×#400

—

C₁₉×#389

C₂²

yes

—

C₁₉×#387

—

C₂²×D₇₆

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

#10597320

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

#10597266

—

#10597266

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₁₉⋊C₈

—

#2810

D₁₉

yes

characteristic, complemented

#2041

—

#1271

—

C₂²×C₁₉

#449

yes

—

C₂²×C₁₉

#454

yes

—

C₂²×C₁₉

B(4,𝔽₂)

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

—

—

—

—

C₂×D₁₉

yes

—

#387

—

#336

—

C₂×C₁₉

#1597

yes

—

C₂×C₁₉

#1628

yes

—

C₂×C₁₉

#1658

yes

characteristic

D₁₉

—

C₂²×D₄

—

C₂²×C₈

—

#127

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₉

yes

—

—

—

100

#95

—

101

#95

—

102

#95

—

103

C₁₉

#7744

yes

characteristic, complemented, Sylow

104

C₂⁴

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄²

—

123

C₄²

—

124

C₂³

—

125

C₂³

—

152

—

126

C₂³

—

152

—

127

C₂³

#10597399

yes

characteristic

128

D₄

—

129

D₄

—

130

D₄

—

152

—

131

D₄

—

152

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

#10597395

yes

—

141

C₂×C₄

#10597396

yes

—

142

C₈

—

152

—

143

C₂²

—

304

—

144

C₂²

—

304

—

145

C₂²

—

152

—

146

C₂²

#11926689

yes

—

147

C₂²

#11926717

yes

—

148

C₂²

#11926731

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₂

—

304

—

154

C₂

#14562564

yes

—

155

C₂

#14562745

yes

—

156

C₂

#14562937

yes

characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2810	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#10597320	C₂²
hypercenter	#2810	D₁₉
hypocenter	C₁₉	#7744
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2810

subgroup

G/H

center

C₂³

#10597399

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2810

C₂

C₂³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂³×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2810

N	H ≅ G/N	type
2. #14561458	C₂	semidirect
3. C₁₉×#2810	C₂	semidirect
65. #2810	D₁₉	semidirect
103. C₁₉	#7744	semidirect

H ≅ G/N

type

2. #14561458

C₂

semidirect

3. C₁₉×#2810

C₂

semidirect

65. #2810

D₁₉

semidirect

103. C₁₉

#7744

semidirect

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

subgroup	index
#14564869	2
#14561458	2
C₁₉×#2810	2
#7744	19

subgroup

index

#14564869

#14561458

C₁₉×#2810

#7744

Subgroups — #18071293

Conjugacy classes of subgroups

Complements

Maximal subgroups