Group #18069928 — subgroups

Subgroups — #18069928

Order 4864.

222 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 43 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	#14561586	C₂	1	2	yes	maximal, complemented
2	C₁₉×#1962	C₂	1	1	yes	maximal, characteristic
3	#11926326	—	2	2	no	—
4	C₁₉×#532	C₄	1	1	yes	characteristic
5	C₁₉×#423	C₂²	1	1	yes	characteristic
6	C₂×C₁₉×#104	—	2	2	no	—
7	C₄³×C₁₉	C₄	1	1	yes	characteristic
8	C₂×#41×C₁₉	—	2	1	no	—
9	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
10	C₁₉×C₄⋊Q₈	C₈	1	1	yes	characteristic
11	C₁₉×#127	C₈	1	1	yes	characteristic
12	C₁₉×#124	—	2	1	no	—
13	C₁₉×#121	—	4	1	no	—
14	C₄×D₄×C₁₉	—	4	1	no	—
15	C₂×C₄²×C₁₉	—	2	1	no	—
16	C₂×C₄²×C₁₉	—	4	1	no	—
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₁₉×C₄⋊C₈	—	4	1	no	—
19	C₁₉×#104	—	4	4	no	—
20	#10597269	—	4	2	no	—
21	#41×C₁₉	—	4	2	no	—
22	#41×C₁₉	—	4	2	no	—
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	—	4	1	no	—
26	C₂×D₄×C₁₉	—	4	1	no	—
27	C₂²×C₄×C₁₉	—	2	1	no	—
28	C₂²×C₄×C₁₉	—	4	1	no	—
29	C₂²×C₄×C₁₉	—	4	1	no	—
30	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	M₁₆×C₁₉	—	4	2	no	—
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₄⋊C₄×C₁₉	—	4	1	no	—
34	C₂²⋊C₄×C₁₉	—	4	2	no	—
35	C₄²×C₁₉	—	2	1	no	—
36	C₄²×C₁₉	—	2	2	no	—
37	C₄²×C₁₉	—	4	1	no	—
38	C₄²×C₁₉	—	4	4	no	—
39	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
40	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
41	C₁₉⋊C₁₆	—	8	2	no	—
42	#7357	—	19	1	no	maximal, Sylow
43	C₂³×C₁₉	—	4	1	no	—
44	C₂³×C₁₉	#100	1	1	yes	characteristic
45	Q₈×C₁₉	—	4	2	no	—
46	D₄×C₁₉	—	4	2	no	—
47	D₄×C₁₉	—	8	2	no	—
48	D₄×C₁₉	—	8	2	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	—	4	4	no	—
56	C₂×C₄×C₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	—	8	1	no	—
58	C₂×C₄×C₁₉	—	8	1	no	—
59	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
61	C₈×C₁₉	—	4	2	no	—
62	#1962	D₁₉	1	1	yes	characteristic
63	#1327	—	19	2	no	—
64	C₂²×C₁₉	—	2	1	no	—
65	C₂²×C₁₉	—	4	1	no	—
66	C₂²×C₁₉	—	8	2	no	—
67	C₂²×C₁₉	—	8	1	no	—
68	C₂²×C₁₉	#323	1	1	yes	characteristic
69	C₄×C₁₉	—	2	2	no	—
70	C₄×C₁₉	—	2	1	no	—
71	C₄×C₁₉	—	4	1	no	—
72	C₄×C₁₉	—	4	4	no	—
73	C₄×C₁₉	—	8	1	no	—
74	C₄×C₁₉	#353	1	1	yes	characteristic
75	C₄×C₁₉	#355	1	1	yes	characteristic
76	#532	Dic₁₉	1	1	yes	characteristic
77	#423	C₂×D₁₉	1	1	yes	characteristic
78	C₂×#104	—	2	2	no	—
79	C₄³	Dic₁₉	1	1	yes	characteristic
80	#349	—	38	2	no	—
81	C₂×C₁₉	—	2	1	no	—
82	C₂×C₁₉	—	4	1	no	—
83	C₂×C₁₉	—	16	1	no	—
84	C₂×C₁₉	#1318	1	1	yes	characteristic
85	C₂×#41	—	2	1	no	—
86	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
87	C₄⋊Q₈	C₁₉⋊C₈	1	1	yes	characteristic
88	#127	C₁₉⋊C₈	1	1	yes	characteristic
89	#124	—	2	1	no	—
90	#121	—	4	1	no	—
91	C₄×D₄	—	4	1	no	—
92	C₂×C₄²	—	2	1	no	—
93	C₂×C₄²	—	4	1	no	—
94	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
95	M₃₂	—	76	2	no	—
96	C₄⋊C₈	—	4	1	no	—
97	#104	—	4	4	no	—
98	C₁₉	#7357	1	1	yes	characteristic, complemented, Sylow
99	#41	—	4	2	no	—
100	#41	—	4	2	no	—
101	C₂×Q₈	—	2	1	no	—
102	C₂×D₄	—	2	1	no	—
103	C₂×D₄	—	4	1	no	—
104	C₂×D₄	—	4	1	no	—
105	C₂²×C₄	—	2	1	no	—
106	C₂²×C₄	—	4	1	no	—
107	C₂²×C₄	—	4	1	no	—
108	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
109	M₁₆	—	4	2	no	—
110	C₂×C₈	—	2	2	no	—
111	C₄⋊C₄	—	4	1	no	—
112	C₂²⋊C₄	—	4	2	no	—
113	C₄²	—	2	1	no	—
114	C₄²	—	2	2	no	—
115	C₄²	—	4	1	no	—
116	C₄²	—	4	4	no	—
117	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
118	C₄²	#64520	1	1	yes	characteristic
119	C₁₆	—	152	2	no	—
120	C₂³	—	4	1	no	—
121	C₂³	#10597290	1	1	yes	characteristic
122	Q₈	—	4	2	no	—
123	D₄	—	4	2	no	—
124	D₄	—	8	2	no	—
125	D₄	—	8	2	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	—	4	4	no	—
133	C₂×C₄	—	4	1	no	—
134	C₂×C₄	—	8	1	no	—
135	C₂×C₄	—	8	1	no	—
136	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
137	C₂×C₄	#10597291	1	1	yes	characteristic
138	C₈	—	4	2	no	—
139	C₂²	—	2	1	no	—
140	C₂²	—	4	1	no	—
141	C₂²	—	8	2	no	—
142	C₂²	—	8	1	no	—
143	C₂²	#11926268	1	1	yes	characteristic
144	C₄	—	2	2	no	—
145	C₄	—	2	1	no	—
146	C₄	—	4	1	no	—
147	C₄	—	4	4	no	—
148	C₄	—	8	1	no	—
149	C₄	#11926337	1	1	yes	characteristic
150	C₄	#11926341	1	1	yes	characteristic
151	C₂	—	2	1	no	—
152	C₂	—	4	1	no	—
153	C₂	—	16	1	no	—
154	C₂	#14561567	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561586

C₂

yes

maximal, complemented

C₁₉×#1962

C₂

yes

maximal, characteristic

#11926326

—

C₁₉×#532

C₄

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×#104

—

C₄³×C₁₉

C₄

yes

characteristic

C₂×#41×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

C₈

yes

characteristic

C₁₉×#127

C₈

yes

characteristic

C₁₉×#124

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×#104

—

#10597269

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

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

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₁₉⋊C₁₆

—

#7357

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#100

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

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

#99

yes

characteristic

C₈×C₁₉

—

#1962

D₁₉

yes

characteristic

#1327

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#323

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

yes

characteristic

#423

C₂×D₁₉

yes

characteristic

C₂×#104

—

C₄³

Dic₁₉

yes

characteristic

#349

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1318

yes

characteristic

C₂×#41

—

C₂×M₁₆

C₂²⋊D₁₉

yes

—

C₄⋊Q₈

C₁₉⋊C₈

yes

characteristic

#127

C₁₉⋊C₈

yes

characteristic

#124

—

#121

—

C₄×D₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

M₃₂

—

C₄⋊C₈

—

#104

—

C₁₉

#7357

yes

characteristic, complemented, Sylow

#41

—

100

#41

—

101

C₂×Q₈

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

109

M₁₆

—

110

C₂×C₈

—

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

113

C₄²

—

114

C₄²

—

115

C₄²

—

116

C₄²

—

117

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

118

C₄²

#64520

yes

characteristic

119

C₁₆

—

152

—

120

C₂³

—

121

C₂³

#10597290

yes

characteristic

122

Q₈

—

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

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

137

C₂×C₄

#10597291

yes

characteristic

138

C₈

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

#11926268

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

#11926337

yes

characteristic

150

C₄

#11926341

yes

characteristic

151

C₂

—

152

C₂

—

153

C₂

—

154

C₂

#14561567

yes

characteristic

	subgroup	G/H
center	C₄	#11926337
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#423	C₂×D₁₉
Fitting	C₁₉×#1962	C₂
socle	C₂×C₁₉	#1318
prime radical	C₁₉×#532	C₄
cosocle	C₁₉×#423	C₂²
hypercenter	#1962	D₁₉
hypocenter	C₁₉	#7357
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1962

subgroup

G/H

center

C₄

#11926337

commutator

C₄²×C₁₉

C₂×C₈

Frattini

#423

C₂×D₁₉

Fitting

C₁₉×#1962

C₂

socle

C₂×C₁₉

#1318

prime radical

C₁₉×#532

C₄

cosocle

C₁₉×#423

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1962

N	H ≅ G/N	type
1. #14561586	C₂	semidirect
98. C₁₉	#7357	semidirect

H ≅ G/N

type

1. #14561586

C₂

semidirect

98. C₁₉

#7357

semidirect

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

subgroup	index
#14561586	2
C₁₉×#1962	2
#7357	19

subgroup

index

#14561586

C₁₉×#1962

#7357

Subgroups — #18069928

Conjugacy classes of subgroups

Complements

Maximal subgroups