Group #18070323 — subgroups

Subgroups — #18070323

Order 4864.

286 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 59 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	#14565320	C₂	1	2	yes	maximal
2	C₁₉×#1962	C₂	1	1	yes	maximal, characteristic
3	#11926528	—	2	2	no	—
4	#11926343	—	2	2	no	—
5	#11926341	C₄	1	4	yes	complemented
6	C₁₉×#532	C₂²	1	1	yes	characteristic
7	C₁₉×#423	C₄	1	1	yes	characteristic
8	C₂×C₁₉×#104	—	2	2	no	—
9	C₄³×C₁₉	C₄	1	1	yes	characteristic
10	C₂×#41×C₁₉	D₄	1	2	yes	—
11	C₂×M₁₆×C₁₉	—	2	1	no	—
12	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
13	C₁₉×#127	Q₈	1	1	yes	characteristic
14	C₁₉×#124	C₂×C₄	1	2	yes	—
15	C₁₉×#121	—	4	1	no	—
16	C₄×D₄×C₁₉	—	4	1	no	—
17	C₂×C₄²×C₁₉	—	2	1	no	—
18	C₂×C₄²×C₁₉	—	4	1	no	—
19	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×#64520	—	4	2	no	—
21	C₁₉×C₄⋊C₈	—	4	1	no	—
22	C₁₉×#104	—	4	4	no	—
23	#10597293	—	2	4	no	—
24	#10597290	—	4	2	no	—
25	#41×C₁₉	—	4	2	no	—
26	#41×C₁₉	—	4	2	no	—
27	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
28	C₂×D₄×C₁₉	—	2	2	no	—
29	C₂×D₄×C₁₉	—	4	1	no	—
30	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
31	C₂²×C₄×C₁₉	—	2	1	no	—
32	C₂²×C₄×C₁₉	—	2	2	no	—
33	C₂²×C₄×C₁₉	—	4	1	no	—
34	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	M₁₆×C₁₉	—	4	2	no	—
36	C₂×C₈×C₁₉	—	4	1	no	—
37	C₄⋊C₄×C₁₉	—	4	1	no	—
38	C₂²⋊C₄×C₁₉	—	4	2	no	—
39	C₄²×C₁₉	—	2	1	no	—
40	C₄²×C₁₉	—	2	2	no	—
41	C₄²×C₁₉	—	4	1	no	—
42	C₄²×C₁₉	—	4	4	no	—
43	C₄²×C₁₉	C₄²	1	1	yes	characteristic
44	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
45	#64520	—	4	4	no	—
46	#64520	—	8	2	no	—
47	C₂×C₁₉⋊C₈	—	8	2	no	—
48	#7501	—	19	1	no	maximal, Sylow
49	C₂³×C₁₉	—	2	2	no	—
50	C₂³×C₁₉	#99	1	1	yes	characteristic
51	Q₈×C₁₉	—	4	2	no	—
52	D₄×C₁₉	—	4	2	no	—
53	D₄×C₁₉	—	8	2	no	—
54	D₄×C₁₉	—	8	2	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	4	2	no	—
61	C₂×C₄×C₁₉	—	4	2	no	—
62	C₂×C₄×C₁₉	—	4	4	no	—
63	C₂×C₄×C₁₉	—	4	2	no	—
64	C₂×C₄×C₁₉	—	4	2	no	—
65	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
67	C₈×C₁₉	—	8	1	no	—
68	C₁₉⋊C₈	—	8	4	no	—
69	#2132	—	19	2	no	—
70	#1962	D₁₉	1	1	yes	characteristic
71	C₂²×C₁₉	—	2	1	no	—
72	C₂²×C₁₉	—	4	1	no	—
73	C₂²×C₁₉	—	4	2	no	—
74	C₂²×C₁₉	—	8	2	no	—
75	C₂²×C₁₉	#342	1	1	yes	characteristic
76	C₄×C₁₉	—	2	2	no	—
77	C₄×C₁₉	—	2	1	no	—
78	C₄×C₁₉	—	4	1	no	—
79	C₄×C₁₉	—	4	4	no	—
80	C₄×C₁₉	—	4	2	no	—
81	C₄×C₁₉	#353	1	1	yes	characteristic
82	C₄×C₁₉	#354	1	1	yes	characteristic
83	#532	C₂×D₁₉	1	1	yes	characteristic
84	#423	Dic₁₉	1	1	yes	characteristic
85	C₂×#104	—	2	2	no	—
86	#413	—	38	2	no	—
87	C₄³	Dic₁₉	1	1	yes	characteristic
88	#356	—	38	2	no	—
89	#355	—	19	4	no	—
90	C₂×C₁₉	—	2	1	no	—
91	C₂×C₁₉	—	4	1	no	—
92	C₂×C₁₉	—	8	2	no	—
93	C₂×C₁₉	#1393	1	1	yes	characteristic
94	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
95	C₂×M₁₆	—	2	1	no	—
96	C₂×M₁₆	—	76	2	no	—
97	C₄⋊Q₈	D₇₆	1	1	yes	characteristic
98	#127	Dic₃₈	1	1	yes	characteristic
99	#124	C₄×D₁₉	1	2	yes	—
100	#121	—	4	1	no	—
101	C₄×D₄	—	4	1	no	—
102	C₂×C₄²	—	2	1	no	—
103	C₂×C₄²	—	4	1	no	—
104	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
105	C₄⋊C₈	—	4	1	no	—
106	#104	—	4	4	no	—
107	#101	—	38	4	no	—
108	#100	—	76	2	no	—
109	C₁₉	#7501	1	1	yes	characteristic, complemented, Sylow
110	#41	—	4	2	no	—
111	#41	—	4	2	no	—
112	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
113	C₂×D₄	—	2	2	no	—
114	C₂×D₄	—	4	1	no	—
115	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
116	C₂²×C₄	—	2	1	no	—
117	C₂²×C₄	—	2	2	no	—
118	C₂²×C₄	—	4	1	no	—
119	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
120	M₁₆	—	4	2	no	—
121	M₁₆	—	76	4	no	—
122	M₁₆	—	152	2	no	—
123	C₂×C₈	—	4	1	no	—
124	C₂×C₈	—	152	2	no	—
125	C₄⋊C₄	—	4	1	no	—
126	C₂²⋊C₄	—	4	2	no	—
127	C₄²	—	2	1	no	—
128	C₄²	—	2	2	no	—
129	C₄²	—	4	1	no	—
130	C₄²	—	4	4	no	—
131	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
132	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
133	C₂³	—	2	2	no	—
134	C₂³	#10597291	1	1	yes	characteristic
135	Q₈	—	4	2	no	—
136	D₄	—	4	2	no	—
137	D₄	—	8	2	no	—
138	D₄	—	8	2	no	—
139	C₂×C₄	—	2	1	no	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	2	1	no	—
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	4	2	no	—
145	C₂×C₄	—	4	2	no	—
146	C₂×C₄	—	4	4	no	—
147	C₂×C₄	—	4	2	no	—
148	C₂×C₄	—	4	2	no	—
149	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
150	C₂×C₄	#10597291	1	1	yes	characteristic
151	C₈	—	8	1	no	—
152	C₈	—	152	4	no	—
153	C₂²	—	2	1	no	—
154	C₂²	—	4	1	no	—
155	C₂²	—	4	2	no	—
156	C₂²	—	8	2	no	—
157	C₂²	#11926311	1	1	yes	characteristic
158	C₄	—	2	2	no	—
159	C₄	—	2	1	no	—
160	C₄	—	4	1	no	—
161	C₄	—	4	4	no	—
162	C₄	—	4	2	no	—
163	C₄	#11926337	1	1	yes	characteristic
164	C₄	#11926339	1	1	yes	characteristic
165	C₂	—	2	1	no	—
166	C₂	—	4	1	no	—
167	C₂	—	8	2	no	—
168	C₂	#14561760	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565320

C₂

yes

maximal

C₁₉×#1962

C₂

yes

maximal, characteristic

#11926528

—

#11926343

—

#11926341

C₄

yes

complemented

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#423

C₄

yes

characteristic

C₂×C₁₉×#104

—

C₄³×C₁₉

C₄

yes

characteristic

C₂×#41×C₁₉

D₄

yes

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×#127

Q₈

yes

characteristic

C₁₉×#124

C₂×C₄

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×#104

—

#10597293

—

#10597290

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₄²

yes

characteristic

C₄²×C₁₉

C₄⋊C₄

yes

characteristic

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

#7501

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#99

yes

characteristic

Q₈×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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₁₉⋊C₈

—

#2132

—

#1962

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#342

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×D₁₉

yes

characteristic

#423

Dic₁₉

yes

characteristic

C₂×#104

—

#413

—

C₄³

Dic₁₉

yes

characteristic

#356

—

#355

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1393

yes

characteristic

C₂×#41

C₂²⋊D₁₉

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₄⋊Q₈

D₇₆

yes

characteristic

#127

Dic₃₈

yes

characteristic

#124

C₄×D₁₉

yes

—

100

#121

—

101

C₄×D₄

—

102

C₂×C₄²

—

103

C₂×C₄²

—

104

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

105

C₄⋊C₈

—

106

#104

—

107

#101

—

108

#100

—

109

C₁₉

#7501

yes

characteristic, complemented, Sylow

110

#41

—

111

#41

—

112

C₂×Q₈

(C₂×D₁₉)⋊C₄

yes

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

Dic₁₉⋊C₄

yes

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

120

M₁₆

—

121

M₁₆

—

122

M₁₆

—

152

—

123

C₂×C₈

—

124

C₂×C₈

—

152

—

125

C₄⋊C₄

—

126

C₂²⋊C₄

—

127

C₄²

—

128

C₄²

—

129

C₄²

—

130

C₄²

—

131

C₄²

C₄×Dic₁₉

yes

characteristic

132

C₄²

C₄⋊Dic₁₉

yes

characteristic

133

C₂³

—

134

C₂³

#10597291

yes

characteristic

135

Q₈

—

136

D₄

—

137

D₄

—

138

D₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

C₁₉⋊#95

yes

characteristic

150

C₂×C₄

#10597291

yes

characteristic

151

C₈

—

152

C₈

—

152

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

#11926311

yes

characteristic

158

C₄

—

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

#11926337

yes

characteristic

164

C₄

#11926339

yes

characteristic

165

C₂

—

166

C₂

—

167

C₂

—

168

C₂

#14561760

yes

characteristic

	subgroup	G/H
center	C₄	#11926339
commutator	C₄²×C₁₉	C₄²
Frattini	#532	C₂×D₁₉
Fitting	C₁₉×#1962	C₂
socle	C₂×C₁₉	#1393
prime radical, cosocle	C₁₉×#532	C₂²
hypercenter	#1962	D₁₉
hypocenter	C₁₉	#7501
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #532 ◁ #1962

subgroup

G/H

center

C₄

#11926339

commutator

C₄²×C₁₉

C₄²

Frattini

#532

C₂×D₁₉

Fitting

C₁₉×#1962

C₂

socle

C₂×C₁₉

#1393

prime radical, cosocle

C₁₉×#532

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #532 ◁ #1962

N	H ≅ G/N	type
5. #11926341	C₄	semidirect
109. C₁₉	#7501	semidirect

H ≅ G/N

type

5. #11926341

C₄

semidirect

109. C₁₉

#7501

semidirect

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

subgroup	index
#14565320	2
C₁₉×#1962	2
#7501	19

subgroup

index

#14565320

C₁₉×#1962

#7501

Subgroups — #18070323

Conjugacy classes of subgroups

Complements

Maximal subgroups