Group #18069918 — subgroups

Subgroups — #18069918

Order 4864.

256 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14561579	C₂	1	2	yes	maximal, complemented
2	C₁₉×#1961	C₂	1	1	yes	maximal, characteristic
3	#11926270	—	2	2	no	—
4	C₂×C₁₉×#127	C₄	1	1	yes	characteristic
5	C₂×C₁₉×#102	—	2	2	no	—
6	C₂×C₁₉×#97	C₄	1	1	yes	characteristic
7	C₁₉×#382	C₂²	1	1	yes	characteristic
8	C₂²×D₄×C₁₉	—	2	1	no	—
9	C₂²×D₄×C₁₉	—	4	1	no	—
10	C₂²×C₈×C₁₉	—	2	1	no	—
11	C₁₉×#127	—	2	1	no	—
12	C₁₉×#127	—	4	1	no	—
13	C₁₉×#127	C₈	1	2	yes	complemented
14	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₁₉×#102	—	4	4	no	—
17	C₁₉×#97	—	4	1	no	—
18	C₁₉×#95	—	4	1	no	—
19	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
20	C₂⁴×C₁₉	—	4	1	no	—
21	C₂×D₄×C₁₉	—	2	2	no	—
22	C₂×D₄×C₁₉	—	4	2	no	—
23	C₂×D₄×C₁₉	—	4	2	no	—
24	C₂×D₄×C₁₉	—	4	2	no	—
25	C₂×D₄×C₁₉	—	4	2	no	—
26	C₂×D₄×C₁₉	—	4	1	no	—
27	C₂×D₄×C₁₉	—	8	4	no	—
28	C₂²×C₄×C₁₉	—	2	1	no	—
29	C₂²×C₄×C₁₉	—	2	2	no	—
30	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₉	—	2	2	no	—
32	C₂×C₈×C₁₉	—	4	1	no	—
33	C₂×C₈×C₁₉	—	4	1	no	—
34	C₄⋊C₄×C₁₉	—	4	2	no	—
35	C₄²×C₁₉	—	2	1	no	—
36	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
37	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
38	C₂×C₁₉⋊C₈	—	8	2	no	—
39	#7352	—	19	1	no	maximal, Sylow
40	C₂³×C₁₉	—	4	2	no	—
41	C₂³×C₁₉	—	8	4	no	—
42	C₂³×C₁₉	—	8	1	no	—
43	C₂³×C₁₉	—	8	1	no	—
44	C₂³×C₁₉	#99	1	1	yes	characteristic
45	D₄×C₁₉	—	4	4	no	—
46	D₄×C₁₉	—	8	2	no	—
47	D₄×C₁₉	—	8	4	no	—
48	D₄×C₁₉	—	8	4	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	4	2	no	—
54	C₂×C₄×C₁₉	—	4	2	no	—
55	C₂×C₄×C₁₉	—	8	2	no	—
56	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
58	C₈×C₁₉	—	4	2	no	—
59	C₁₉⋊C₈	—	16	2	no	—
60	#1961	D₁₉	1	1	yes	characteristic
61	#1324	—	19	2	no	—
62	C₂²×C₁₉	—	2	2	no	—
63	C₂²×C₁₉	—	8	4	no	—
64	C₂²×C₁₉	—	8	2	no	—
65	C₂²×C₁₉	—	16	2	no	—
66	C₂²×C₁₉	—	16	2	no	—
67	C₂²×C₁₉	#323	1	1	yes	characteristic
68	C₂²×C₁₉	#353	1	1	yes	characteristic
69	C₂²×C₁₉	#355	1	1	yes	characteristic
70	C₄×C₁₉	—	2	1	no	—
71	C₄×C₁₉	—	2	1	no	—
72	C₄×C₁₉	—	4	1	no	—
73	C₄×C₁₉	—	4	1	no	—
74	C₄×C₁₉	—	8	2	no	—
75	C₂×#127	Dic₁₉	1	1	yes	characteristic
76	C₂×#102	—	2	2	no	—
77	C₂×#97	Dic₁₉	1	1	yes	characteristic
78	#382	C₂×D₁₉	1	1	yes	characteristic
79	#324	—	38	2	no	—
80	C₂×C₁₉	—	2	1	no	—
81	C₂×C₁₉	—	2	1	no	—
82	C₂×C₁₉	—	16	2	no	—
83	C₂×C₁₉	#1318	1	1	yes	characteristic
84	C₂×C₁₉	#1406	1	2	yes	—
85	C₂²×D₄	—	2	1	no	—
86	C₂²×D₄	—	4	1	no	—
87	C₂²×C₈	—	2	1	no	—
88	#127	—	2	1	no	—
89	#127	—	4	1	no	—
90	#127	C₁₉⋊C₈	1	2	yes	complemented
91	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
92	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
93	#102	—	4	4	no	—
94	C₂²⋊C₈	—	76	2	no	—
95	#97	—	4	1	no	—
96	#95	—	4	1	no	—
97	C₁₉	#7352	1	1	yes	characteristic, complemented, Sylow
98	C₂⁴	—	4	1	no	—
99	C₂×D₄	—	2	2	no	—
100	C₂×D₄	—	4	2	no	—
101	C₂×D₄	—	4	2	no	—
102	C₂×D₄	—	4	2	no	—
103	C₂×D₄	—	4	2	no	—
104	C₂×D₄	—	4	1	no	—
105	C₂×D₄	—	8	4	no	—
106	C₂²×C₄	—	2	1	no	—
107	C₂²×C₄	—	2	2	no	—
108	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
109	C₂×C₈	—	2	2	no	—
110	C₂×C₈	—	4	1	no	—
111	C₂×C₈	—	4	1	no	—
112	C₂×C₈	—	152	2	no	—
113	C₄⋊C₄	—	4	2	no	—
114	C₄²	—	2	1	no	—
115	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
116	C₄²	#64520	1	1	yes	characteristic
117	C₂³	—	4	2	no	—
118	C₂³	—	8	4	no	—
119	C₂³	—	8	1	no	—
120	C₂³	—	8	1	no	—
121	C₂³	#10597291	1	1	yes	characteristic
122	D₄	—	4	4	no	—
123	D₄	—	8	2	no	—
124	D₄	—	8	4	no	—
125	D₄	—	8	4	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	4	2	no	—
131	C₂×C₄	—	4	2	no	—
132	C₂×C₄	—	8	2	no	—
133	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
134	C₂×C₄	#10597290	1	1	yes	characteristic
135	C₈	—	4	2	no	—
136	C₈	—	304	2	no	—
137	C₂²	—	2	2	no	—
138	C₂²	—	8	4	no	—
139	C₂²	—	8	2	no	—
140	C₂²	—	16	2	no	—
141	C₂²	—	16	2	no	—
142	C₂²	#11926268	1	1	yes	characteristic
143	C₂²	#11926337	1	1	yes	characteristic
144	C₂²	#11926341	1	1	yes	characteristic
145	C₄	—	2	1	no	—
146	C₄	—	2	1	no	—
147	C₄	—	4	1	no	—
148	C₄	—	4	1	no	—
149	C₄	—	8	2	no	—
150	C₂	—	2	1	no	—
151	C₂	—	2	1	no	—
152	C₂	—	16	2	no	—
153	C₂	#14561567	1	1	yes	characteristic
154	C₂	#14561792	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14561579

C₂

yes

maximal, complemented

C₁₉×#1961

C₂

yes

maximal, characteristic

#11926270

—

C₂×C₁₉×#127

C₄

yes

characteristic

C₂×C₁₉×#102

—

C₂×C₁₉×#97

C₄

yes

characteristic

C₁₉×#382

C₂²

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

C₈

yes

complemented

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#102

—

C₁₉×#97

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₂×C₁₉⋊C₈

—

#7352

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#99

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

#100

yes

characteristic

C₈×C₁₉

—

C₁₉⋊C₈

—

#1961

D₁₉

yes

characteristic

#1324

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×#127

Dic₁₉

yes

characteristic

C₂×#102

—

C₂×#97

Dic₁₉

yes

characteristic

#382

C₂×D₁₉

yes

characteristic

#324

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1318

yes

characteristic

C₂×C₁₉

#1406

yes

—

C₂²×D₄

—

C₂²×D₄

—

C₂²×C₈

—

#127

—

#127

—

#127

C₁₉⋊C₈

yes

complemented

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

#102

—

C₂²⋊C₈

—

#97

—

#95

—

C₁₉

#7352

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

152

—

113

C₄⋊C₄

—

114

C₄²

—

115

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

116

C₄²

#64520

yes

characteristic

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

—

121

C₂³

#10597291

yes

characteristic

122

D₄

—

123

D₄

—

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

134

C₂×C₄

#10597290

yes

characteristic

135

C₈

—

136

C₈

—

304

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

#11926268

yes

characteristic

143

C₂²

#11926337

yes

characteristic

144

C₂²

#11926341

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₂

—

151

C₂

—

152

C₂

—

153

C₂

#14561567

yes

characteristic

154

C₂

#14561792

yes

—

	subgroup	G/H
center	C₂²	#11926337
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#382	C₂×D₁₉
Fitting	C₁₉×#1961	C₂
socle	C₂²×C₁₉	#353
prime radical	C₂×C₁₉×#127	C₄
cosocle	C₁₉×#382	C₂²
hypercenter	#1961	D₁₉
hypocenter	C₁₉	#7352
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #382 ◁ #1961

subgroup

G/H

center

C₂²

#11926337

commutator

C₄²×C₁₉

C₂×C₈

Frattini

#382

C₂×D₁₉

Fitting

C₁₉×#1961

C₂

socle

C₂²×C₁₉

#353

prime radical

C₂×C₁₉×#127

C₄

cosocle

C₁₉×#382

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #382 ◁ #1961

N	H ≅ G/N	type
1. #14561579	C₂	semidirect
13. C₁₉×#127	C₈	semidirect
90. #127	C₁₉⋊C₈	semidirect
97. C₁₉	#7352	semidirect

H ≅ G/N

type

1. #14561579

C₂

semidirect

13. C₁₉×#127

C₈

semidirect

90. #127

C₁₉⋊C₈

semidirect

97. C₁₉

#7352

semidirect

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

subgroup	index
#14561579	2
C₁₉×#1961	2
#7352	19

subgroup

index

#14561579

C₁₉×#1961

#7352

Subgroups — #18069918

Conjugacy classes of subgroups

Complements

Maximal subgroups