Group #18075883 — subgroups

Subgroups — #18075883

Order 4864.

486 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14563703	C₂	1	2	yes	maximal
2	#14561478	C₂	1	4	yes	maximal
3	C₂×C₁₉×#383	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
5	#11926299	—	2	4	no	—
6	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#383	—	2	4	no	—
8	C₂×C₁₉×#95	C₄	1	2	yes	—
9	C₂×C₁₉×#95	C₄	1	2	yes	—
10	C₂×C₁₉×#95	C₂²	1	2	yes	—
11	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
13	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₁₉	—	2	4	no	—
16	C₂×C₄²×C₁₉	D₄	1	4	yes	—
17	C₂²×C₁₉⋊C₈	—	2	4	no	—
18	C₁₉×#95	—	2	4	no	—
19	C₁₉×#95	—	2	4	no	—
20	C₁₉×#95	—	2	4	no	—
21	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
22	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	—	2	2	no	—
24	C₂²×C₄×C₁₉	—	2	2	no	—
25	C₂²×C₄×C₁₉	—	2	4	no	—
26	C₂²×C₄×C₁₉	—	2	4	no	—
27	C₂²×C₄×C₁₉	—	2	8	no	—
28	C₂²×C₄×C₁₉	—	4	2	no	—
29	C₂²×C₄×C₁₉	—	4	2	no	—
30	C₂²×C₄×C₁₉	—	4	4	no	—
31	C₂²×C₄×C₁₉	—	4	4	no	—
32	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
33	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
34	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
35	C₂²×C₄×C₁₉	#41	1	4	yes	—
36	C₄²×C₁₉	—	2	8	no	—
37	C₂×C₁₉⋊C₈	—	4	8	no	—
38	C₂×C₁₉⋊C₈	—	4	4	no	—
39	#8705	—	19	1	no	maximal, Sylow
40	C₂³×C₁₉	—	2	2	no	—
41	C₂³×C₁₉	—	2	2	no	—
42	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
43	C₂³×C₁₉	#117	1	2	yes	—
44	C₂³×C₁₉	#131	1	4	yes	—
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	—	2	4	no	—
49	C₂×C₄×C₁₉	—	2	4	no	—
50	C₂×C₄×C₁₉	—	4	4	no	—
51	C₂×C₄×C₁₉	—	4	4	no	—
52	C₂×C₄×C₁₉	—	4	4	no	—
53	C₂×C₄×C₁₉	—	4	4	no	—
54	C₂×C₄×C₁₉	—	4	4	no	—
55	C₂×C₄×C₁₉	—	4	4	no	—
56	C₂×C₄×C₁₉	—	8	8	no	—
57	C₂×C₄×C₁₉	#123	1	4	yes	—
58	C₁₉⋊C₈	—	8	4	no	—
59	C₂×#383	D₁₉	1	1	yes	characteristic
60	#1817	—	19	2	no	—
61	#1280	—	19	4	no	—
62	C₂²×C₁₉	—	2	2	no	—
63	C₂²×C₁₉	—	2	2	no	—
64	C₂²×C₁₉	—	2	8	no	—
65	C₂²×C₁₉	#381	1	1	yes	characteristic
66	C₂²×C₁₉	#408	1	2	yes	—
67	C₂²×C₁₉	#410	1	2	yes	—
68	C₂²×C₁₉	#413	1	2	yes	—
69	C₂²×C₁₉	#433	1	4	yes	—
70	C₄×C₁₉	—	2	4	no	—
71	C₄×C₁₉	—	4	2	no	—
72	C₄×C₁₉	—	4	2	no	—
73	C₄×C₁₉	—	8	4	no	—
74	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
75	C₂×C₂²⋊C₈	—	19	4	no	—
76	#383	—	2	4	no	—
77	C₂×#95	Dic₁₉	1	2	yes	—
78	C₂×#95	Dic₁₉	1	2	yes	—
79	C₂×#95	C₂×D₁₉	1	2	yes	—
80	#336	—	38	4	no	—
81	C₂×C₁₉	—	2	4	no	—
82	C₂×C₁₉	#1473	1	4	yes	—
83	C₂×C₁₉	#1818	1	1	yes	characteristic
84	C₂×C₁₉	#1820	1	1	yes	characteristic
85	C₂×C₁₉	#1822	1	1	yes	characteristic
86	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
87	C₂³×C₄	C₂×Dic₁₉	1	4	yes	—
88	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
89	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
90	C₂²×C₈	—	38	4	no	—
91	C₂×C₄²	—	2	4	no	—
92	C₂×C₄²	C₂²⋊D₁₉	1	4	yes	—
93	C₂²⋊C₈	—	38	8	no	—
94	#95	—	2	4	no	—
95	#95	—	2	4	no	—
96	#95	—	2	4	no	—
97	C₁₉	#8705	1	1	yes	characteristic, complemented, Sylow
98	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
99	C₂²×C₄	—	2	4	no	—
100	C₂²×C₄	—	2	2	no	—
101	C₂²×C₄	—	2	2	no	—
102	C₂²×C₄	—	2	4	no	—
103	C₂²×C₄	—	2	8	no	—
104	C₂²×C₄	—	4	2	no	—
105	C₂²×C₄	—	4	2	no	—
106	C₂²×C₄	—	4	4	no	—
107	C₂²×C₄	—	4	4	no	—
108	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
109	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
110	C₂²×C₄	#64541	1	4	yes	—
111	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
112	C₂×C₈	—	76	8	no	—
113	C₂×C₈	—	76	4	no	—
114	C₄²	—	2	8	no	—
115	C₂³	—	2	2	no	—
116	C₂³	—	2	2	no	—
117	C₂³	#10597372	1	2	yes	—
118	C₂³	#10597394	1	4	yes	—
119	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
120	C₂×C₄	—	2	4	no	—
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	4	4	no	—
126	C₂×C₄	—	4	4	no	—
127	C₂×C₄	—	4	4	no	—
128	C₂×C₄	—	4	4	no	—
129	C₂×C₄	—	4	4	no	—
130	C₂×C₄	—	4	4	no	—
131	C₂×C₄	—	8	8	no	—
132	C₂×C₄	#10597375	1	4	yes	—
133	C₈	—	152	4	no	—
134	C₂²	—	2	2	no	—
135	C₂²	—	2	2	no	—
136	C₂²	—	2	8	no	—
137	C₂²	#11926407	1	1	yes	characteristic
138	C₂²	#11926511	1	2	yes	—
139	C₂²	#11926518	1	2	yes	—
140	C₂²	#11926528	1	2	yes	—
141	C₂²	#11926605	1	4	yes	—
142	C₄	—	2	4	no	—
143	C₄	—	4	2	no	—
144	C₄	—	4	2	no	—
145	C₄	—	8	4	no	—
146	C₂	—	2	4	no	—
147	C₂	#14562004	1	4	yes	—
148	C₂	#14563706	1	1	yes	characteristic
149	C₂	#14563712	1	1	yes	characteristic
150	C₂	#14563718	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563703

C₂

yes

maximal

#14561478

C₂

yes

maximal

C₂×C₁₉×#383

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926299

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#383

—

C₂×C₁₉×#95

C₄

yes

—

C₂×C₁₉×#95

C₄

yes

—

C₂×C₁₉×#95

C₂²

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×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

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8705

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

#117

yes

—

C₂³×C₁₉

#131

yes

—

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#123

yes

—

C₁₉⋊C₈

—

C₂×#383

D₁₉

yes

characteristic

#1817

—

#1280

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#381

yes

characteristic

C₂²×C₁₉

#408

yes

—

C₂²×C₁₉

#410

yes

—

C₂²×C₁₉

#413

yes

—

C₂²×C₁₉

#433

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂²×C₄²

C₂×D₁₉

yes

characteristic

C₂×C₂²⋊C₈

—

#383

—

C₂×#95

Dic₁₉

yes

—

C₂×#95

Dic₁₉

yes

—

C₂×#95

C₂×D₁₉

yes

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

#1473

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

C₂³×C₄

C₂×Dic₁₉

yes

—

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

C₂³×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

C₂²⋊D₁₉

yes

—

C₂²⋊C₈

—

#95

—

#95

—

#95

—

C₁₉

#8705

yes

characteristic, complemented, Sylow

C₂⁴

C₂²×Dic₁₉

yes

characteristic

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

109

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

110

C₂²×C₄

#64541

yes

—

111

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₄²

—

115

C₂³

—

116

C₂³

—

117

C₂³

#10597372

yes

—

118

C₂³

#10597394

yes

—

119

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

#10597375

yes

—

133

C₈

—

152

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

#11926407

yes

characteristic

138

C₂²

#11926511

yes

—

139

C₂²

#11926518

yes

—

140

C₂²

#11926528

yes

—

141

C₂²

#11926605

yes

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₂

—

147

C₂

#14562004

yes

—

148

C₂

#14563706

yes

characteristic

149

C₂

#14563712

yes

characteristic

150

C₂

#14563718

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator, prime radical	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#383	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#383	D₁₉
hypocenter	C₁₉	#8705
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#383

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator, prime radical

C₂⁴×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#383

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂³×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#383

N	H ≅ G/N	type
97. C₁₉	#8705	semidirect

H ≅ G/N

type

97. C₁₉

#8705

semidirect

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

subgroup	index
#14563703	2
#14561478	2
C₂×C₁₉×#383	2
#8705	19

subgroup

index

#14563703

#14561478

C₂×C₁₉×#383

#8705

Subgroups — #18075883

Conjugacy classes of subgroups

Complements

Maximal subgroups