Group #18069397 — subgroups

Subgroups — #18069397

Order 4864.

266 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 103 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	#14565438	C₂	1	2	yes	maximal
2	C₄×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₉⋊C₁₆)	C₄	1	4	yes	complemented
4	C₂²⋊(C₁₉⋊C₁₆)	—	2	2	no	—
5	#11926320	—	2	2	no	—
6	C₂×C₁₉×#97	—	2	2	no	—
7	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₄³×C₁₉	C₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	—	2	1	no	—
11	C₂²×C₈×C₁₉	D₄	1	2	yes	—
12	C₂×C₄²×C₁₉	—	2	1	no	—
13	C₂×C₄²×C₁₉	—	2	1	no	—
14	C₂×C₄²×C₁₉	C₈	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₁₉×#97	—	2	8	no	—
17	C₄×C₈×C₁₉	—	2	1	no	—
18	C₄×C₈×C₁₉	C₈	1	2	yes	—
19	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
22	C₂×C₁₉⋊C₁₆	—	2	4	no	—
23	C₂²×C₄×C₁₉	—	2	2	no	—
24	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
27	C₂×C₈×C₁₉	—	2	4	no	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₂×C₈×C₁₉	—	2	4	no	—
30	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
31	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
32	C₄²×C₁₉	—	2	4	no	—
33	C₄²×C₁₉	—	4	2	no	—
34	C₄²×C₁₉	—	4	2	no	—
35	C₄²×C₁₉	C₄²	1	1	yes	characteristic
36	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
37	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
38	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
39	C₁₉⋊C₁₆	—	4	4	no	—
40	#7149	—	19	1	no	maximal, Sylow
41	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
50	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
54	C₈×C₁₉	—	2	4	no	—
55	C₈×C₁₉	—	2	2	no	—
56	C₈×C₁₉	#104	1	4	yes	—
57	#2163	—	19	2	no	—
58	C₄×#97	D₁₉	1	1	yes	characteristic
59	C₂²×C₁₉	—	2	1	no	—
60	C₂²×C₁₉	—	2	1	no	—
61	C₂²×C₁₉	#336	1	1	yes	characteristic
62	C₂²×C₁₉	#349	1	2	yes	—
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	—	2	1	no	—
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	4	4	no	—
68	C₄×C₁₉	#339	1	2	yes	—
69	C₄×C₁₉	#347	1	2	yes	—
70	C₂×#97	—	2	2	no	—
71	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
72	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
73	C₄³	Dic₁₉	1	1	yes	characteristic
74	C₄⋊C₁₆	—	19	4	no	—
75	C₂²⋊C₁₆	—	38	2	no	—
76	#346	—	38	2	no	—
77	C₂×C₁₉	—	2	2	no	—
78	C₂×C₁₉	#1276	1	1	yes	characteristic
79	C₂×C₁₉	#1375	1	1	yes	characteristic
80	C₂×C₁₉	#1377	1	1	yes	characteristic
81	C₂²×C₈	—	2	1	no	—
82	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
83	C₂×C₄²	—	2	1	no	—
84	C₂×C₄²	—	2	1	no	—
85	C₂×C₄²	C₁₉⋊C₈	1	2	yes	—
86	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
87	C₂×C₁₆	—	38	4	no	—
88	#97	—	2	8	no	—
89	C₄×C₈	—	2	1	no	—
90	C₄×C₈	C₁₉⋊C₈	1	2	yes	—
91	C₄×C₈	Dic₃₈	1	1	yes	characteristic
92	C₄×C₈	C₄×D₁₉	1	2	yes	—
93	C₄×C₈	D₇₆	1	1	yes	characteristic
94	C₁₉	#7149	1	1	yes	characteristic, complemented, Sylow
95	C₂²×C₄	—	2	2	no	—
96	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
97	C₂²×C₄	#64520	1	1	yes	characteristic
98	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
99	C₂×C₈	—	2	4	no	—
100	C₂×C₈	—	2	2	no	—
101	C₂×C₈	—	2	4	no	—
102	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
103	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
104	C₄²	—	2	4	no	—
105	C₄²	—	4	2	no	—
106	C₄²	—	4	2	no	—
107	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
108	C₄²	#64520	1	1	yes	characteristic
109	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
110	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
111	C₁₆	—	76	4	no	—
112	C₂³	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	C₄×C₁₉⋊C₈	1	1	yes	characteristic
120	C₂×C₄	#10597260	1	1	yes	characteristic
121	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
122	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
123	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
124	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
125	C₈	—	2	4	no	—
126	C₈	—	2	2	no	—
127	C₈	#10597262	1	4	yes	—
128	C₂²	—	2	1	no	—
129	C₂²	—	2	1	no	—
130	C₂²	#11926299	1	1	yes	characteristic
131	C₂²	#11926326	1	2	yes	—
132	C₄	—	2	1	no	—
133	C₄	—	2	1	no	—
134	C₄	—	2	1	no	—
135	C₄	—	2	1	no	—
136	C₄	—	4	4	no	—
137	C₄	#11926304	1	2	yes	—
138	C₄	#11926322	1	2	yes	—
139	C₂	—	2	2	no	—
140	C₂	#14561468	1	1	yes	characteristic
141	C₂	#14561715	1	1	yes	characteristic
142	C₂	#14561719	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565438

C₂

yes

maximal

C₄×C₁₉×#97

C₂

yes

maximal, characteristic

C₄⋊(C₁₉⋊C₁₆)

C₄

yes

complemented

C₂²⋊(C₁₉⋊C₁₆)

—

#11926320

—

C₂×C₁₉×#97

—

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄³×C₁₉

C₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₈

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₈

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₄²

yes

characteristic

C₄²×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₁₉⋊C₁₆

—

#7149

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

C₄×C₈

yes

characteristic

C₂×C₄×C₁₉

#97

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#104

yes

—

#2163

—

C₄×#97

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#336

yes

characteristic

C₂²×C₁₉

#349

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#339

yes

—

C₄×C₁₉

#347

yes

—

C₂×#97

—

C₂×C₄×C₈

Dic₁₉

yes

characteristic

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄³

Dic₁₉

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₁₉⋊C₈

yes

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

C₂×C₁₆

—

#97

—

C₄×C₈

—

C₄×C₈

C₁₉⋊C₈

yes

—

C₄×C₈

Dic₃₈

yes

characteristic

C₄×C₈

C₄×D₁₉

yes

—

C₄×C₈

D₇₆

yes

characteristic

C₁₉

#7149

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

C₂²×C₄

#64520

yes

characteristic

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

Dic₁₉⋊C₄

yes

—

103

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

104

C₄²

—

105

C₄²

—

106

C₄²

—

107

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

108

C₄²

#64520

yes

characteristic

109

C₄²

C₄×Dic₁₉

yes

characteristic

110

C₄²

C₄⋊Dic₁₉

yes

characteristic

111

C₁₆

—

112

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

C₄×C₁₉⋊C₈

yes

characteristic

120

C₂×C₄

#10597260

yes

characteristic

121

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

characteristic

122

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

characteristic

123

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

124

C₂×C₄

C₁₉⋊#95

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

#10597262

yes

—

128

C₂²

—

129

C₂²

—

130

C₂²

#11926299

yes

characteristic

131

C₂²

#11926326

yes

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

#11926304

yes

—

138

C₄

#11926322

yes

—

139

C₂

—

140

C₂

#14561468

yes

characteristic

141

C₂

#14561715

yes

characteristic

142

C₂

#14561719

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₁₉⋊#95
commutator	C₂×C₄×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₄×C₁₉×#97	C₂
socle	C₂²×C₁₉	#336
prime radical	C₂³×C₁₉	C₂²⋊C₈
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₄×#97	D₁₉
hypocenter	C₁₉	#7149
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₄×#97

subgroup

G/H

center

C₂×C₄

C₁₉⋊#95

commutator

C₂×C₄×C₁₉

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₄×C₁₉×#97

C₂

socle

C₂²×C₁₉

#336

prime radical

C₂³×C₁₉

C₂²⋊C₈

cosocle

C₂×C₄×C₈×C₁₉

C₂²

hypercenter

C₄×#97

D₁₉

hypocenter

C₁₉

#7149

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₄×#97

N	H ≅ G/N	type
3. C₄⋊(C₁₉⋊C₁₆)	C₄	semidirect
94. C₁₉	#7149	semidirect

H ≅ G/N

type

3. C₄⋊(C₁₉⋊C₁₆)

C₄

semidirect

94. C₁₉

#7149

semidirect

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

subgroup	index
#14565438	2
C₄×C₁₉×#97	2
#7149	19

subgroup

index

#14565438

C₄×C₁₉×#97

#7149

Subgroups — #18069397

Conjugacy classes of subgroups

Complements

Maximal subgroups