Group #18069514 — subgroups

Subgroups — #18069514

Order 4864.

222 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14565434	C₂	1	2	yes	maximal
2	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₉⋊C₁₆)	—	2	2	no	—
4	C₂²⋊(C₁₉⋊C₁₆)	C₄	1	4	yes	—
5	C₄×C₁₉⋊C₁₆	—	2	2	no	—
6	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#322	—	2	2	no	—
10	C₂²×C₈×C₁₉	C₈	1	2	yes	—
11	C₂²×C₈×C₁₉	C₈	1	2	yes	—
12	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
13	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₄×C₈×C₁₉	—	2	1	no	—
15	C₄×C₈×C₁₉	—	2	1	no	—
16	C₄×C₈×C₁₉	—	2	1	no	—
17	C₄×C₈×C₁₉	—	2	1	no	—
18	C₄×C₈×C₁₉	D₄	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	C₄²	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
25	C₂×C₈×C₁₉	—	2	2	no	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₂×C₈×C₁₉	—	2	2	no	—
28	C₂×C₈×C₁₉	—	4	2	no	—
29	C₂×C₈×C₁₉	—	4	2	no	—
30	C₂×C₈×C₁₉	C₁₆	1	4	yes	complemented
31	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
32	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
33	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
35	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
36	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
37	C₁₉⋊C₁₆	—	4	4	no	—
38	#7195	—	19	1	no	maximal, Sylow
39	C₂³×C₁₉	C₄×C₈	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×C₁₆	1	2	yes	—
49	C₂×C₄×C₁₉	M₃₂	1	2	yes	—
50	C₈×C₁₉	—	2	2	no	—
51	C₈×C₁₉	—	2	2	no	—
52	C₈×C₁₉	—	2	4	no	—
53	C₈×C₁₉	—	4	2	no	—
54	#2162	—	19	2	no	—
55	C₂×#322	D₁₉	1	1	yes	characteristic
56	C₂²×C₁₉	—	2	1	no	—
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	#336	1	1	yes	characteristic
59	C₂²×C₁₉	C₄×C₁₆	1	1	yes	characteristic
60	C₂²×C₁₉	#346	1	1	yes	characteristic
61	C₄×C₁₉	—	2	1	no	—
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	#344	1	2	yes	—
64	C₄×C₁₉	C₂²⋊C₁₆	1	2	yes	—
65	C₄×C₁₉	#349	1	2	yes	—
66	C₄×C₁₉	C₄⋊C₁₆	1	2	yes	—
67	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
68	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
69	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
70	C₄⋊C₁₆	—	38	2	no	—
71	C₂²⋊C₁₆	—	19	4	no	—
72	C₄×C₁₆	—	38	2	no	—
73	#322	—	2	2	no	—
74	C₂×C₁₉	—	2	1	no	—
75	C₂×C₁₉	—	2	1	no	—
76	C₂×C₁₉	#1281	1	1	yes	characteristic
77	C₂×C₁₉	#1374	1	1	yes	characteristic
78	C₂×C₁₉	#1377	1	1	yes	characteristic
79	C₂²×C₈	C₁₉⋊C₈	1	2	yes	—
80	C₂²×C₈	C₁₉⋊C₈	1	2	yes	—
81	C₂²×C₈	C₄×D₁₉	1	2	yes	—
82	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
83	C₂×C₁₆	—	38	4	no	—
84	C₄×C₈	—	2	1	no	—
85	C₄×C₈	—	2	1	no	—
86	C₄×C₈	—	2	1	no	—
87	C₄×C₈	—	2	1	no	—
88	C₄×C₈	Dic₃₈	1	1	yes	characteristic
89	C₄×C₈	D₇₆	1	1	yes	characteristic
90	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
91	C₁₉	#7195	1	1	yes	characteristic, complemented, Sylow
92	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
93	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
94	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	4	2	no	—
99	C₂×C₈	—	4	2	no	—
100	C₂×C₈	C₁₉⋊C₁₆	1	4	yes	complemented
101	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
102	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
103	C₄²	#64520	1	1	yes	characteristic
104	C₄²	#64520	1	1	yes	characteristic
105	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
106	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
107	C₁₆	—	76	4	no	—
108	C₂³	C₄×C₁₉⋊C₈	1	1	yes	characteristic
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	#10597260	1	1	yes	characteristic
112	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
113	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
114	C₂×C₄	C₂×C₁₉⋊C₁₆	1	2	yes	—
115	C₂×C₄	#10597269	1	2	yes	—
116	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
117	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
118	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
119	C₈	—	2	2	no	—
120	C₈	—	2	2	no	—
121	C₈	—	2	4	no	—
122	C₈	—	4	2	no	—
123	C₂²	—	2	1	no	—
124	C₂²	—	2	1	no	—
125	C₂²	#11926299	1	1	yes	characteristic
126	C₂²	C₄×C₁₉⋊C₁₆	1	1	yes	characteristic
127	C₂²	#11926320	1	1	yes	characteristic
128	C₄	—	2	1	no	—
129	C₄	—	2	1	no	—
130	C₄	#11926315	1	2	yes	—
131	C₄	C₂²⋊(C₁₉⋊C₁₆)	1	2	yes	—
132	C₄	#11926326	1	2	yes	—
133	C₄	C₄⋊(C₁₉⋊C₁₆)	1	2	yes	—
134	C₂	—	2	1	no	—
135	C₂	—	2	1	no	—
136	C₂	#14561480	1	1	yes	characteristic
137	C₂	#14561713	1	1	yes	characteristic
138	C₂	#14561719	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565434

C₂

yes

maximal

C₂×C₁₉×#322

C₂

yes

maximal, characteristic

C₄⋊(C₁₉⋊C₁₆)

—

C₂²⋊(C₁₉⋊C₁₆)

C₄

yes

—

C₄×C₁₉⋊C₁₆

—

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₂²×C₈×C₁₉

C₈

yes

—

C₂²×C₈×C₁₉

C₈

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₁₆

yes

complemented

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₁₉⋊C₁₆

—

#7195

—

maximal, Sylow

C₂³×C₁₉

C₄×C₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₁₆

yes

—

C₂×C₄×C₁₉

M₃₂

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#2162

—

C₂×#322

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#336

yes

characteristic

C₂²×C₁₉

C₄×C₁₆

yes

characteristic

C₂²×C₁₉

#346

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#344

yes

—

C₄×C₁₉

C₂²⋊C₁₆

yes

—

C₄×C₁₉

#349

yes

—

C₄×C₁₉

C₄⋊C₁₆

yes

—

C₂×C₄×C₈

Dic₁₉

yes

characteristic

C₂×C₄×C₈

Dic₁₉

yes

characteristic

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

#322

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

C₁₉⋊C₈

yes

—

C₂²×C₈

C₁₉⋊C₈

yes

—

C₂²×C₈

C₄×D₁₉

yes

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₃₈

yes

characteristic

C₄×C₈

D₇₆

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

—

C₁₉

#7195

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

C₁₉⋊C₁₆

yes

complemented

101

C₂×C₈

Dic₁₉⋊C₄

yes

—

102

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

103

C₄²

#64520

yes

characteristic

104

C₄²

#64520

yes

characteristic

105

C₄²

C₄⋊Dic₁₉

yes

characteristic

106

C₄²

C₂²⋊Dic₁₉

yes

characteristic

107

C₁₆

—

108

C₂³

C₄×C₁₉⋊C₈

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

#10597260

yes

characteristic

112

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

characteristic

113

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

characteristic

114

C₂×C₄

C₂×C₁₉⋊C₁₆

yes

—

115

C₂×C₄

#10597269

yes

—

116

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

117

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

118

C₂×C₄

C₁₉⋊#95

yes

characteristic

119

C₈

—

120

C₈

—

121

C₈

—

122

C₈

—

123

C₂²

—

124

C₂²

—

125

C₂²

#11926299

yes

characteristic

126

C₂²

C₄×C₁₉⋊C₁₆

yes

characteristic

127

C₂²

#11926320

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

#11926315

yes

—

131

C₄

C₂²⋊(C₁₉⋊C₁₆)

yes

—

132

C₄

#11926326

yes

—

133

C₄

C₄⋊(C₁₉⋊C₁₆)

yes

—

134

C₂

—

135

C₂

—

136

C₂

#14561480

yes

characteristic

137

C₂

#14561713

yes

characteristic

138

C₂

#14561719

yes

characteristic

	subgroup	G/H
center	C₄²	C₂²⋊Dic₁₉
commutator	C₂²×C₁₉	C₄×C₁₆
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle	C₂²×C₁₉	#336
prime radical	C₂³×C₁₉	C₄×C₈
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#7195
LCS	G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ C₂×#322

subgroup

G/H

center

C₄²

C₂²⋊Dic₁₉

commutator

C₂²×C₁₉

C₄×C₁₆

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₂×C₁₉×#322

C₂

socle

C₂²×C₁₉

#336

prime radical

C₂³×C₁₉

C₄×C₈

cosocle

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ C₂×#322

N	H ≅ G/N	type
30. C₂×C₈×C₁₉	C₁₆	semidirect
91. C₁₉	#7195	semidirect
100. C₂×C₈	C₁₉⋊C₁₆	semidirect

H ≅ G/N

type

30. C₂×C₈×C₁₉

C₁₆

semidirect

91. C₁₉

#7195

semidirect

100. C₂×C₈

C₁₉⋊C₁₆

semidirect

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

subgroup	index
#14565434	2
C₂×C₁₉×#322	2
#7195	19

subgroup

index

#14565434

C₂×C₁₉×#322

#7195

Subgroups — #18069514

Conjugacy classes of subgroups

Complements

Maximal subgroups