Group #18076061 — subgroups

Subgroups — #18076061

Order 4864.

566 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14563559	C₂	1	2	yes	maximal
2	#14561543	C₂	1	4	yes	maximal
3	C₁₉×#2310	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597293	—	2	4	no	—
5	#11926508	C₂²	1	4	yes	—
6	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×#117	C₄	1	2	yes	—
8	C₁₉×#391	—	2	4	no	—
9	C₁₉×#381	C₄	1	2	yes	—
10	C₁₉×#381	C₂²	1	2	yes	—
11	C₂²×Q₈×C₁₉	—	2	4	no	—
12	C₂²×Q₈×C₁₉	—	4	4	no	—
13	C₂²×Q₈×C₁₉	D₄	1	4	yes	—
14	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₁₉×#117	—	4	4	no	—
18	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
20	C₂×C₄²×C₁₉	—	2	2	no	—
21	C₂×#64520	—	2	4	no	—
22	C₁₉×#95	—	2	4	no	—
23	C₁₉×#95	—	2	4	no	—
24	#10597293	—	4	8	no	—
25	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
26	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×Q₈×C₁₉	—	2	8	no	—
28	C₂×Q₈×C₁₉	—	2	8	no	—
29	C₂×Q₈×C₁₉	—	4	4	no	—
30	C₂×Q₈×C₁₉	—	4	16	no	—
31	C₂²×C₄×C₁₉	—	2	2	no	—
32	C₂²×C₄×C₁₉	—	2	4	no	—
33	C₂²×C₄×C₁₉	—	2	2	no	—
34	C₂²×C₄×C₁₉	—	2	4	no	—
35	C₂²×C₄×C₁₉	—	4	2	no	—
36	C₂²×C₄×C₁₉	—	4	2	no	—
37	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
40	C₂²×C₄×C₁₉	#41	1	4	yes	—
41	C₄⋊C₄×C₁₉	—	4	4	no	—
42	C₂²⋊C₄×C₁₉	—	4	4	no	—
43	C₄²×C₁₉	—	4	4	no	—
44	#64520	—	4	8	no	—
45	C₂×C₁₉⋊C₈	—	4	4	no	—
46	#8753	—	19	1	no	maximal, Sylow
47	C₂³×C₁₉	—	2	2	no	—
48	C₂³×C₁₉	—	4	2	no	—
49	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
50	C₂³×C₁₉	#117	1	2	yes	—
51	Q₈×C₁₉	—	4	16	no	—
52	C₂×C₄×C₁₉	—	2	8	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	4	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	4	no	—
58	C₂×C₄×C₁₉	—	4	4	no	—
59	C₂×C₄×C₁₉	—	4	4	no	—
60	C₂×C₄×C₁₉	—	4	8	no	—
61	C₂×C₄×C₁₉	—	4	4	no	—
62	C₂×C₄×C₁₉	#99	1	4	yes	—
63	C₂×C₄×C₁₉	#123	1	4	yes	—
64	C₁₉⋊C₈	—	8	4	no	—
65	#2310	D₁₉	1	1	yes	characteristic
66	#1784	—	19	2	no	—
67	#1306	—	19	4	no	—
68	C₂²×C₁₉	—	2	2	no	—
69	C₂²×C₁₉	—	2	2	no	—
70	C₂²×C₁₉	—	2	4	no	—
71	C₂²×C₁₉	—	4	4	no	—
72	C₂²×C₁₉	#381	1	1	yes	characteristic
73	C₂²×C₁₉	C₂×#99	1	2	yes	—
74	C₄×C₁₉	—	2	4	no	—
75	C₄×C₁₉	—	2	4	no	—
76	C₄×C₁₉	—	4	2	no	—
77	C₄×C₁₉	—	8	4	no	—
78	C₂³×Q₈	C₂×D₁₉	1	1	yes	characteristic
79	C₂×#117	Dic₁₉	1	2	yes	—
80	C₂×#101	—	38	4	no	—
81	#407	—	19	4	no	—
82	#391	—	2	4	no	—
83	#381	Dic₁₉	1	2	yes	—
84	#381	C₂×D₁₉	1	2	yes	—
85	C₂×C₁₉	—	2	2	no	—
86	C₂×C₁₉	—	4	2	no	—
87	C₂×C₁₉	#1819	1	1	yes	characteristic
88	C₂×C₁₉	#1830	1	2	yes	—
89	C₂²×Q₈	—	2	4	no	—
90	C₂²×Q₈	—	4	4	no	—
91	C₂²×Q₈	C₂²⋊D₁₉	1	4	yes	—
92	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
93	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
94	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
95	C₂×M₁₆	—	38	4	no	—
96	#117	—	4	4	no	—
97	C₂×C₄⋊C₄	—	2	2	no	—
98	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	4	yes	—
99	C₂×C₄²	—	2	2	no	—
100	#101	—	76	8	no	—
101	C₂²⋊C₈	—	38	8	no	—
102	#95	—	2	4	no	—
103	#95	—	2	4	no	—
104	C₁₉	#8753	1	1	yes	characteristic, complemented, Sylow
105	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
106	C₂×Q₈	—	2	8	no	—
107	C₂×Q₈	—	2	8	no	—
108	C₂×Q₈	—	4	4	no	—
109	C₂×Q₈	—	4	16	no	—
110	C₂²×C₄	—	2	2	no	—
111	C₂²×C₄	—	2	4	no	—
112	C₂²×C₄	—	2	2	no	—
113	C₂²×C₄	—	2	4	no	—
114	C₂²×C₄	—	4	2	no	—
115	C₂²×C₄	—	4	2	no	—
116	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
117	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
118	C₂²×C₄	#64541	1	4	yes	—
119	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
120	M₁₆	—	76	8	no	—
121	C₂×C₈	—	76	4	no	—
122	C₄⋊C₄	—	4	4	no	—
123	C₂²⋊C₄	—	4	4	no	—
124	C₄²	—	4	4	no	—
125	C₂³	—	2	2	no	—
126	C₂³	—	4	2	no	—
127	C₂³	#10597372	1	2	yes	—
128	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
129	Q₈	—	4	16	no	—
130	C₂×C₄	—	2	8	no	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	4	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	2	4	no	—
136	C₂×C₄	—	4	4	no	—
137	C₂×C₄	—	4	4	no	—
138	C₂×C₄	—	4	8	no	—
139	C₂×C₄	—	4	4	no	—
140	C₂×C₄	#10597291	1	4	yes	—
141	C₂×C₄	#10597375	1	4	yes	—
142	C₈	—	152	4	no	—
143	C₂²	—	2	2	no	—
144	C₂²	—	2	2	no	—
145	C₂²	—	2	4	no	—
146	C₂²	—	4	4	no	—
147	C₂²	#11926407	1	1	yes	characteristic
148	C₂²	C₂×#10597291	1	2	yes	—
149	C₄	—	2	4	no	—
150	C₄	—	2	4	no	—
151	C₄	—	4	2	no	—
152	C₄	—	8	4	no	—
153	C₂	—	2	2	no	—
154	C₂	—	4	2	no	—
155	C₂	#14563709	1	1	yes	characteristic
156	C₂	#14563749	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563559

C₂

yes

maximal

#14561543

C₂

yes

maximal

C₁₉×#2310

C₂

yes

maximal, characteristic

C₂×#10597293

—

#11926508

C₂²

yes

—

C₂³×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#117

C₄

yes

—

C₁₉×#391

—

C₁₉×#381

C₄

yes

—

C₁₉×#381

C₂²

yes

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×#64520

—

C₁₉×#95

—

C₁₉×#95

—

#10597293

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

#41

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

#8753

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

#117

yes

—

Q₈×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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₁₉⋊C₈

—

#2310

D₁₉

yes

characteristic

#1784

—

#1306

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#381

yes

characteristic

C₂²×C₁₉

C₂×#99

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂³×Q₈

C₂×D₁₉

yes

characteristic

C₂×#117

Dic₁₉

yes

—

—

—

—

Dic₁₉

yes

—

#381

C₂×D₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1819

yes

characteristic

C₂×C₁₉

#1830

yes

—

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

C₂²⋊D₁₉

yes

—

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

C₂³×C₄

C₂²×D₁₉

yes

characteristic

C₂×M₁₆

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

C₂×Dic₁₉

yes

—

C₂×C₄²

—

100

#101

—

101

C₂²⋊C₈

—

102

#95

—

103

#95

—

104

C₁₉

#8753

yes

characteristic, complemented, Sylow

105

C₂⁴

C₂²×Dic₁₉

yes

characteristic

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

117

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

118

C₂²×C₄

#64541

yes

—

119

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

120

M₁₆

—

121

C₂×C₈

—

122

C₄⋊C₄

—

123

C₂²⋊C₄

—

124

C₄²

—

125

C₂³

—

126

C₂³

—

127

C₂³

#10597372

yes

—

128

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

129

Q₈

—

130

C₂×C₄

—

131

C₂×C₄

—

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

#10597291

yes

—

141

C₂×C₄

#10597375

yes

—

142

C₈

—

152

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

#11926407

yes

characteristic

148

C₂²

C₂×#10597291

yes

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₂

—

154

C₂

—

155

C₂

#14563709

yes

characteristic

156

C₂

#14563749

yes

—

	subgroup	G/H
center	C₂²	#11926407
commutator, prime radical	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#2310	C₂
socle	C₂²×C₁₉	#381
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2310	D₁₉
hypocenter	C₁₉	#8753
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2310

subgroup

G/H

center

C₂²

#11926407

commutator, prime radical

C₂⁴×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₁₉×#2310

C₂

socle

C₂²×C₁₉

#381

cosocle

C₂³×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2310

N	H ≅ G/N	type
104. C₁₉	#8753	semidirect

H ≅ G/N

type

104. C₁₉

#8753

semidirect

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

subgroup	index
#14563559	2
#14561543	2
C₁₉×#2310	2
#8753	19

subgroup

index

#14563559

#14561543

C₁₉×#2310

#8753

Subgroups — #18076061

Conjugacy classes of subgroups

Complements

Maximal subgroups