Group #18069073 — subgroups

Subgroups — #18069073

Order 4864.

294 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 135 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	#14563752	C₂	1	2	yes	maximal
2	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
4	#11926299	—	2	2	no	—
5	#11926299	C₄	1	4	yes	—
6	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
7	C₄³×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#336	—	2	2	no	—
9	C₂²×C₈×C₁₉	—	2	2	no	—
10	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
11	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	D₄	1	2	yes	—
13	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	—	2	4	no	—
16	C₄×C₈×C₁₉	—	2	2	no	—
17	C₄×C₈×C₁₉	C₈	1	4	yes	complemented
18	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
19	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
20	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
24	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₈×C₁₉	—	2	4	no	—
26	C₂×C₈×C₁₉	—	4	4	no	—
27	C₄²×C₁₉	—	2	2	no	—
28	C₄²×C₁₉	—	4	2	no	—
29	C₄²×C₁₉	—	4	2	no	—
30	C₄²×C₁₉	C₂×C₈	1	2	yes	—
31	C₄²×C₁₉	M₁₆	1	2	yes	—
32	C₄²×C₁₉	D₈	1	1	yes	characteristic
33	C₄²×C₁₉	SD₁₆	1	2	yes	—
34	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
35	C₂×C₁₉⋊C₈	—	4	4	no	—
36	C₂×C₁₉⋊C₈	—	4	4	no	—
37	C₂×C₁₉⋊C₈	—	4	4	no	—
38	#7018	—	19	1	no	maximal, Sylow
39	C₂³×C₁₉	#95	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	2	no	—
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	2	no	—
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
48	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
50	C₂×C₄×C₁₉	#102	1	2	yes	—
51	C₂×C₄×C₁₉	#103	1	2	yes	—
52	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
53	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#108	1	2	yes	—
56	C₈×C₁₉	—	4	4	no	—
57	C₁₉⋊C₈	—	8	4	no	—
58	#1831	—	19	2	no	—
59	#1744	D₁₉	1	1	yes	characteristic
60	C₂²×C₁₉	#336	1	1	yes	characteristic
61	C₂²×C₁₉	H(3,ℤ/4)	1	2	yes	—
62	C₂²×C₁₉	#340	1	1	yes	characteristic
63	C₂²×C₁₉	#341	1	1	yes	characteristic
64	C₂²×C₁₉	#344	1	2	yes	—
65	C₄×C₁₉	—	2	1	no	—
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	2	2	no	—
68	C₄×C₁₉	—	2	2	no	—
69	C₄×C₁₉	—	2	2	no	—
70	C₄×C₁₉	—	4	2	no	—
71	C₄×C₁₉	#334	1	2	yes	—
72	C₄×C₁₉	#335	1	2	yes	—
73	C₂×C₄⋊C₈	—	38	2	no	—
74	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
75	C₄³	C₂×D₁₉	1	1	yes	characteristic
76	#336	—	2	2	no	—
77	#336	—	19	4	no	—
78	#336	—	38	2	no	—
79	C₂×C₁₉	#1274	1	1	yes	characteristic
80	C₂×C₁₉	#1277	1	1	yes	characteristic
81	C₂×C₁₉	#1281	1	1	yes	characteristic
82	C₂×C₁₉	#1286	1	2	yes	—
83	C₂×C₁₉	#1287	1	2	yes	—
84	C₂²×C₈	—	2	2	no	—
85	C₂²×C₈	—	38	4	no	—
86	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
87	C₂×C₄²	C₄×D₁₉	1	2	yes	—
88	C₂×C₄²	D₇₆	1	1	yes	characteristic
89	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
90	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
91	C₄⋊C₈	—	76	2	no	—
92	C₄⋊C₈	—	76	2	no	—
93	C₄×C₈	—	2	2	no	—
94	C₄×C₈	C₁₉⋊C₈	1	4	yes	complemented
95	C₁₉	#7018	1	1	yes	characteristic, complemented, Sylow
96	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
97	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
98	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
99	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
100	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
101	C₂×C₈	—	2	4	no	—
102	C₂×C₈	—	4	4	no	—
103	C₂×C₈	—	76	4	no	—
104	C₂×C₈	—	76	4	no	—
105	C₂×C₈	—	76	4	no	—
106	C₄²	—	2	2	no	—
107	C₄²	—	4	2	no	—
108	C₄²	—	4	2	no	—
109	C₄²	#64516	1	2	yes	—
110	C₄²	D₁₅₂	1	1	yes	characteristic
111	C₄²	Dic₇₆	1	1	yes	characteristic
112	C₄²	C₂×C₁₉⋊C₈	1	2	yes	—
113	C₄²	#64520	1	2	yes	—
114	C₂³	C₁₉⋊#95	1	1	yes	characteristic
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	C₄×C₁₉⋊C₈	1	1	yes	characteristic
123	C₂×C₄	#10597260	1	1	yes	characteristic
124	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
125	C₂×C₄	#10597273	1	2	yes	—
126	C₂×C₄	#10597274	1	1	yes	characteristic
127	C₂×C₄	#10597275	1	1	yes	characteristic
128	C₂×C₄	#10597276	1	2	yes	—
129	C₂×C₄	#10597278	1	2	yes	—
130	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
131	C₈	—	4	4	no	—
132	C₈	—	152	4	no	—
133	C₂²	#11926299	1	1	yes	characteristic
134	C₂²	#11926300	1	2	yes	—
135	C₂²	#11926307	1	1	yes	characteristic
136	C₂²	#11926309	1	1	yes	characteristic
137	C₂²	#11926315	1	2	yes	—
138	C₄	—	2	2	no	—
139	C₄	—	2	1	no	—
140	C₄	—	2	1	no	—
141	C₄	—	2	2	no	—
142	C₄	—	2	2	no	—
143	C₄	—	4	2	no	—
144	C₄	#11926295	1	2	yes	—
145	C₄	#11926297	1	2	yes	—
146	C₂	#14561464	1	1	yes	characteristic
147	C₂	#14561470	1	1	yes	characteristic
148	C₂	#14561480	1	1	yes	characteristic
149	C₂	#14561494	1	2	yes	—
150	C₂	#14561497	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563752

C₂

yes

maximal

C₁₉×#1744

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

#11926299

—

#11926299

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₄

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

Q₈

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₈

yes

complemented

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

—

C₄²×C₁₉

M₁₆

yes

—

C₄²×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

Q₁₆

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄×C₈

yes

characteristic

C₂×C₄×C₁₉

#97

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

#102

yes

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

C₄⋊C₈

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1831

—

#1744

D₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#334

yes

—

C₄×C₁₉

#335

yes

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

Dic₁₉

yes

—

C₄³

C₂×D₁₉

yes

—

—

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#1287

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

Dic₃₈

yes

characteristic

C₂×C₄²

C₄×D₁₉

yes

—

C₂×C₄²

D₇₆

yes

characteristic

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

C₂×C₄²

C₂²⋊D₁₉

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

C₁₉⋊C₈

yes

complemented

C₁₉

#7018

yes

characteristic, complemented, Sylow

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

C₂²×C₄

Dic₁₉⋊C₄

yes

—

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

100

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₄²

—

107

C₄²

—

108

C₄²

—

109

C₄²

#64516

yes

—

110

C₄²

D₁₅₂

yes

characteristic

111

C₄²

Dic₇₆

yes

characteristic

112

C₄²

C₂×C₁₉⋊C₈

yes

—

113

C₄²

#64520

yes

—

114

C₂³

C₁₉⋊#95

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

C₄×C₁₉⋊C₈

yes

characteristic

123

C₂×C₄

#10597260

yes

characteristic

124

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

—

125

C₂×C₄

#10597273

yes

—

126

C₂×C₄

#10597274

yes

characteristic

127

C₂×C₄

#10597275

yes

characteristic

128

C₂×C₄

#10597276

yes

—

129

C₂×C₄

#10597278

yes

—

130

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

—

131

C₈

—

132

C₈

—

152

—

133

C₂²

#11926299

yes

characteristic

134

C₂²

#11926300

yes

—

135

C₂²

#11926307

yes

characteristic

136

C₂²

#11926309

yes

characteristic

137

C₂²

#11926315

yes

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

#11926295

yes

—

145

C₄

#11926297

yes

—

146

C₂

#14561464

yes

characteristic

147

C₂

#14561470

yes

characteristic

148

C₂

#14561480

yes

characteristic

149

C₂

#14561494

yes

—

150

C₂

#14561497

yes

—

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂×C₄×C₁₉	C₄×C₈
Frattini	C₄³	C₂×D₁₉
Fitting	C₁₉×#1744	C₂
socle, prime radical	C₂³×C₁₉	#95
cosocle	C₄³×C₁₉	C₂²
hypercenter	#1744	D₁₉
hypocenter	C₁₉	#7018
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1744

subgroup

G/H

center

C₂³

C₁₉⋊#95

commutator

C₂×C₄×C₁₉

C₄×C₈

Frattini

C₄³

C₂×D₁₉

Fitting

C₁₉×#1744

C₂

socle, prime radical

C₂³×C₁₉

#95

cosocle

C₄³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1744

N	H ≅ G/N	type
17. C₄×C₈×C₁₉	C₈	semidirect
94. C₄×C₈	C₁₉⋊C₈	semidirect
95. C₁₉	#7018	semidirect

H ≅ G/N

type

17. C₄×C₈×C₁₉

C₈

semidirect

94. C₄×C₈

C₁₉⋊C₈

semidirect

95. C₁₉

#7018

semidirect

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

subgroup	index
#14563752	2
C₁₉×#1744	2
#7018	19

subgroup

index

#14563752

C₁₉×#1744

#7018

Subgroups — #18069073

Conjugacy classes of subgroups

Complements

Maximal subgroups