Group #18069383 — subgroups

Subgroups — #18069383

Order 4864.

234 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 95 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	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₉⋊C₁₆)	—	2	2	no	—
4	C₂²⋊(C₁₉⋊C₁₆)	—	2	2	no	—
5	#11926320	C₄	1	4	yes	complemented
6	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₄³×C₁₉	C₄	1	1	yes	characteristic
9	C₁₉×#336	—	2	2	no	—
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	C₄×C₈×C₁₉	—	2	1	no	—
17	C₄×C₈×C₁₉	C₈	1	2	yes	—
18	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
21	C₂×C₁₉⋊C₁₆	—	2	4	no	—
22	C₂²×C₄×C₁₉	—	2	2	no	—
23	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₂×C₈×C₁₉	—	4	2	no	—
28	C₂×C₈×C₁₉	—	4	2	no	—
29	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
30	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
31	C₄²×C₁₉	—	2	4	no	—
32	C₄²×C₁₉	—	4	2	no	—
33	C₄²×C₁₉	—	4	2	no	—
34	C₄²×C₁₉	C₄²	1	1	yes	characteristic
35	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
36	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
37	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
38	C₁₉⋊C₁₆	—	4	4	no	—
39	#7143	—	19	1	no	maximal, Sylow
40	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	4	no	—
45	C₂×C₄×C₁₉	—	4	2	no	—
46	C₂×C₄×C₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
53	C₈×C₁₉	—	2	2	no	—
54	C₈×C₁₉	—	2	2	no	—
55	C₈×C₁₉	—	4	2	no	—
56	#2163	—	19	2	no	—
57	#1744	D₁₉	1	1	yes	characteristic
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	—	2	1	no	—
60	C₂²×C₁₉	#336	1	1	yes	characteristic
61	C₂²×C₁₉	#349	1	2	yes	—
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	—	2	1	no	—
66	C₄×C₁₉	—	4	4	no	—
67	C₄×C₁₉	H(3,ℤ/4)	1	2	yes	—
68	C₄×C₁₉	#364	1	2	yes	—
69	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
70	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
71	C₄³	Dic₁₉	1	1	yes	characteristic
72	C₄⋊C₁₆	—	38	2	no	—
73	C₂²⋊C₁₆	—	38	2	no	—
74	#346	—	19	4	no	—
75	#336	—	2	2	no	—
76	C₂×C₁₉	—	2	2	no	—
77	C₂×C₁₉	#1274	1	1	yes	characteristic
78	C₂×C₁₉	#1376	1	1	yes	characteristic
79	C₂×C₁₉	#1377	1	1	yes	characteristic
80	C₂²×C₈	—	2	1	no	—
81	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
82	C₂×C₄²	—	2	1	no	—
83	C₂×C₄²	—	2	1	no	—
84	C₂×C₄²	C₁₉⋊C₈	1	2	yes	—
85	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
86	C₂×C₁₆	—	38	4	no	—
87	C₄×C₈	—	2	1	no	—
88	C₄×C₈	C₁₉⋊C₈	1	2	yes	—
89	C₄×C₈	Dic₃₈	1	1	yes	characteristic
90	C₄×C₈	C₄×D₁₉	1	2	yes	—
91	C₄×C₈	D₇₆	1	1	yes	characteristic
92	C₁₉	#7143	1	1	yes	characteristic, complemented, Sylow
93	C₂²×C₄	—	2	2	no	—
94	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
95	C₂²×C₄	#64520	1	1	yes	characteristic
96	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	4	2	no	—
99	C₂×C₈	—	4	2	no	—
100	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
101	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
102	C₄²	—	2	4	no	—
103	C₄²	—	4	2	no	—
104	C₄²	—	4	2	no	—
105	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
106	C₄²	#64520	1	1	yes	characteristic
107	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
108	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
109	C₁₆	—	76	4	no	—
110	C₂³	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	4	no	—
115	C₂×C₄	—	4	2	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	C₄×C₁₉⋊C₈	1	1	yes	characteristic
118	C₂×C₄	#10597260	1	1	yes	characteristic
119	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
120	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
121	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
122	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	—	2	2	no	—
125	C₈	—	4	2	no	—
126	C₂²	—	2	1	no	—
127	C₂²	—	2	1	no	—
128	C₂²	#11926299	1	1	yes	characteristic
129	C₂²	#11926326	1	2	yes	—
130	C₄	—	2	1	no	—
131	C₄	—	2	1	no	—
132	C₄	—	2	1	no	—
133	C₄	—	2	1	no	—
134	C₄	—	4	4	no	—
135	C₄	#11926300	1	2	yes	—
136	C₄	#11926365	1	2	yes	—
137	C₂	—	2	2	no	—
138	C₂	#14561464	1	1	yes	characteristic
139	C₂	#14561717	1	1	yes	characteristic
140	C₂	#14561719	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565438

C₂

yes

maximal

C₁₉×#1744

C₂

yes

maximal, characteristic

C₄⋊(C₁₉⋊C₁₆)

—

C₂²⋊(C₁₉⋊C₁₆)

—

#11926320

C₄

yes

complemented

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄³×C₁₉

C₄

yes

characteristic

C₁₉×#336

—

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

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

—

#7143

—

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

—

#2163

—

#1744

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

H(3,ℤ/4)

yes

—

C₄×C₁₉

#364

yes

—

C₂×C₄×C₈

Dic₁₉

yes

characteristic

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄³

Dic₁₉

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

#336

—

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

—

C₄×C₈

—

C₄×C₈

C₁₉⋊C₈

yes

—

C₄×C₈

Dic₃₈

yes

characteristic

C₄×C₈

C₄×D₁₉

yes

—

C₄×C₈

D₇₆

yes

characteristic

C₁₉

#7143

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

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

Dic₁₉⋊C₄

yes

—

101

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

102

C₄²

—

103

C₄²

—

104

C₄²

—

105

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

106

C₄²

#64520

yes

characteristic

107

C₄²

C₄×Dic₁₉

yes

characteristic

108

C₄²

C₄⋊Dic₁₉

yes

characteristic

109

C₁₆

—

110

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

C₄×C₁₉⋊C₈

yes

characteristic

118

C₂×C₄

#10597260

yes

characteristic

119

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

characteristic

120

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

characteristic

121

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

122

C₂×C₄

C₁₉⋊#95

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

126

C₂²

—

127

C₂²

—

128

C₂²

#11926299

yes

characteristic

129

C₂²

#11926326

yes

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

#11926300

yes

—

136

C₄

#11926365

yes

—

137

C₂

—

138

C₂

#14561464

yes

characteristic

139

C₂

#14561717

yes

characteristic

140

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	C₁₉×#1744	C₂
socle	C₂²×C₁₉	#336
prime radical	C₂³×C₁₉	C₂²⋊C₈
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	#1744	D₁₉
hypocenter	C₁₉	#7143
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1744

subgroup

G/H

center

C₂×C₄

C₁₉⋊#95

commutator

C₂×C₄×C₁₉

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₁₉×#1744

C₂

socle

C₂²×C₁₉

#336

prime radical

C₂³×C₁₉

C₂²⋊C₈

cosocle

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1744

N	H ≅ G/N	type
5. #11926320	C₄	semidirect
92. C₁₉	#7143	semidirect

H ≅ G/N

type

5. #11926320

C₄

semidirect

92. C₁₉

#7143

semidirect

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

subgroup	index
#14565438	2
C₁₉×#1744	2
#7143	19

subgroup

index

#14565438

C₁₉×#1744

#7143

Subgroups — #18069383

Conjugacy classes of subgroups

Complements

Maximal subgroups