Group #18069601 — subgroups

Subgroups — #18069601

Order 4864.

192 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 59 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	#14563784	C₂	1	1	yes	maximal, characteristic
2	#14561938	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2165	C₂	1	1	yes	maximal, characteristic
4	C₄×#64520	—	2	1	no	—
5	#11926315	—	2	1	no	—
6	#11926304	—	2	1	no	—
7	C₁₉⋊#338	C₄	1	1	yes	characteristic
8	#11926301	C₄	1	1	yes	characteristic
9	#11926266	—	2	1	no	—
10	#11926265	C₄	1	1	yes	characteristic, complemented
11	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic, complemented
12	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#364	—	2	1	no	—
14	C₁₉×#349	—	2	1	no	—
15	C₁₉×#347	C₄	1	2	yes	complemented
16	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
19	#10597372	—	2	1	no	—
20	C₂×#64520	—	2	2	no	—
21	C₂×#64520	—	2	1	no	—
22	C₁₉×M₃₂	—	2	2	no	—
23	C₁₉×#97	C₂×C₄	1	1	yes	characteristic
24	C₁₉×#97	Q₈	1	1	yes	characteristic
25	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
27	#10597260	—	2	2	no	—
28	C₄×C₁₉⋊C₈	—	2	1	no	—
29	C₄×C₁₉⋊C₈	—	2	1	no	—
30	C₂²×C₄×C₁₉	—	2	1	no	—
31	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
32	M₁₆×C₁₉	—	4	1	no	—
33	M₁₆×C₁₉	—	4	1	no	—
34	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
35	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
38	C₄²×C₁₉	—	2	1	no	—
39	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
41	C₂²⋊Dic₁₉	—	4	1	no	—
42	C₄⋊Dic₁₉	—	4	1	no	—
43	C₄×Dic₁₉	—	4	1	no	—
44	#64520	—	4	4	no	—
45	#64520	—	4	1	no	—
46	#64520	—	4	1	no	—
47	C₂×C₁₉⋊C₈	—	2	2	no	—
48	C₂×C₁₉⋊C₈	—	2	2	no	—
49	C₂×C₁₉⋊C₈	—	4	1	no	—
50	C₁₆×C₁₉	—	4	2	no	—
51	#7225	—	19	1	no	maximal, Sylow
52	C₂³×C₁₉	#104	1	1	yes	characteristic
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	2	1	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	4	2	no	—
58	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
60	C₂×Dic₁₉	—	8	1	no	—
61	C₈×C₁₉	—	2	1	no	—
62	C₈×C₁₉	—	2	1	no	—
63	C₈×C₁₉	—	2	1	no	—
64	C₈×C₁₉	—	2	1	no	—
65	C₁₉⋊C₈	—	2	4	no	—
66	C₁₉⋊C₈	—	4	2	no	—
67	C₁₉⋊C₈	—	8	1	no	—
68	#2165	D₁₉	1	1	yes	characteristic
69	#1841	—	19	1	no	—
70	#1455	—	19	1	no	—
71	C₂²×C₁₉	—	2	1	no	—
72	C₂²×C₁₉	—	4	1	no	—
73	C₂²×C₁₉	#339	1	1	yes	characteristic
74	C₄×C₁₉	—	2	2	no	—
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	4	1	no	—
77	C₄×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
78	C₄×C₁₉	#344	1	1	yes	characteristic
79	Dic₁₉	—	16	1	no	—
80	C₄×M₁₆	—	38	1	no	—
81	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
82	#364	—	2	1	no	—
83	#349	—	2	1	no	—
84	#347	Dic₁₉	1	2	yes	complemented
85	#344	—	38	1	no	—
86	#339	—	38	1	no	—
87	#338	—	19	1	no	—
88	H(3,ℤ/4)	—	19	1	no	—
89	#322	—	19	1	no	—
90	#322	—	38	1	no	—
91	C₈²	—	19	1	no	—
92	C₂×C₁₉	—	2	1	no	—
93	C₂×C₁₉	—	4	1	no	—
94	C₂×C₁₉	#1288	1	1	yes	characteristic
95	C₂×M₁₆	—	38	2	no	—
96	C₂×M₁₆	—	38	1	no	—
97	C₂×M₁₆	C₄×D₁₉	1	1	yes	characteristic
98	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
99	#117	—	38	1	no	—
100	C₂×C₄²	D₇₆	1	1	yes	characteristic
101	M₃₂	—	2	2	no	—
102	#97	—	38	2	no	—
103	#97	Dic₃₈	1	1	yes	characteristic
104	#97	C₂×Dic₁₉	1	1	yes	characteristic
105	C₄×C₈	—	38	1	no	—
106	C₄×C₈	—	38	1	no	—
107	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
108	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
109	C₁₉	#7225	1	1	yes	characteristic, complemented, Sylow
110	C₂²×C₄	—	2	1	no	—
111	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
112	M₁₆	—	4	1	no	—
113	M₁₆	—	4	1	no	—
114	M₁₆	—	76	4	no	—
115	M₁₆	—	76	1	no	—
116	M₁₆	—	76	1	no	—
117	C₂×C₈	—	38	2	no	—
118	C₂×C₈	—	38	2	no	—
119	C₂×C₈	—	76	1	no	—
120	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
121	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
122	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
123	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
124	C₄⋊C₄	—	76	1	no	—
125	C₂²⋊C₄	—	76	1	no	—
126	C₄²	—	2	1	no	—
127	C₄²	—	76	1	no	—
128	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
129	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
130	C₁₆	—	4	2	no	—
131	C₂³	#10597282	1	1	yes	characteristic
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	2	1	no	—
135	C₂×C₄	—	2	1	no	—
136	C₂×C₄	—	4	2	no	—
137	C₂×C₄	—	152	1	no	—
138	C₂×C₄	#10597282	1	1	yes	characteristic
139	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
140	C₈	—	2	1	no	—
141	C₈	—	2	1	no	—
142	C₈	—	2	1	no	—
143	C₈	—	2	1	no	—
144	C₈	—	38	4	no	—
145	C₈	—	76	2	no	—
146	C₈	—	152	1	no	—
147	C₂²	—	2	1	no	—
148	C₂²	—	4	1	no	—
149	C₂²	#11926305	1	1	yes	characteristic
150	C₄	—	2	2	no	—
151	C₄	—	2	1	no	—
152	C₄	—	4	1	no	—
153	C₄	—	304	1	no	—
154	C₄	#11926300	1	1	yes	characteristic
155	C₄	#11926316	1	1	yes	characteristic
156	C₂	—	2	1	no	—
157	C₂	—	4	1	no	—
158	C₂	#14561501	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563784

C₂

yes

maximal, characteristic

#14561938

C₂

yes

maximal, characteristic

C₁₉×#2165

C₂

yes

maximal, characteristic

C₄×#64520

—

#11926315

—

#11926304

—

C₁₉⋊#338

C₄

yes

characteristic

#11926301

C₄

yes

characteristic

#11926266

—

#11926265

C₄

yes

characteristic, complemented

C₈×C₁₉⋊C₈

C₄

yes

characteristic, complemented

C₄×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#364

—

C₁₉×#349

—

C₁₉×#347

C₄

yes

complemented

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

—

—

C₁₉×M₃₂

—

C₁₉×#97

C₂×C₄

yes

characteristic

C₁₉×#97

Q₈

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₄⋊C₄

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2165

D₁₉

yes

characteristic

#1841

—

#1455

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#339

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₄×M₁₆

—

C₄×M₁₆

C₂×D₁₉

yes

—

—

Dic₁₉

yes

—

—

—

—

—

—

C₈²

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1288

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₄×D₁₉

yes

characteristic

C₂×M₁₆

C₂²⋊D₁₉

yes

characteristic

#117

—

100

C₂×C₄²

D₇₆

yes

characteristic

101

M₃₂

—

102

#97

—

103

#97

Dic₃₈

yes

characteristic

104

#97

C₂×Dic₁₉

yes

characteristic

105

C₄×C₈

—

106

C₄×C₈

—

107

C₄×C₈

C₄×D₁₉

yes

characteristic

108

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

109

C₁₉

#7225

yes

characteristic, complemented, Sylow

110

C₂²×C₄

—

111

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

M₁₆

—

116

M₁₆

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

C₄×Dic₁₉

yes

characteristic

121

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

122

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

123

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

124

C₄⋊C₄

—

125

C₂²⋊C₄

—

126

C₄²

—

127

C₄²

—

128

C₄²

C₄⋊Dic₁₉

yes

characteristic

129

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

130

C₁₆

—

131

C₂³

#10597282

yes

characteristic

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

152

—

138

C₂×C₄

#10597282

yes

characteristic

139

C₂×C₄

C₁₉⋊#95

yes

characteristic

140

C₈

—

141

C₈

—

142

C₈

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

152

—

147

C₂²

—

148

C₂²

—

149

C₂²

#11926305

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

304

—

154

C₄

#11926300

yes

characteristic

155

C₄

#11926316

yes

characteristic

156

C₂

—

157

C₂

—

158

C₂

#14561501

yes

characteristic

	subgroup	G/H
center	C₄	#11926300
commutator	C₂×C₈×C₁₉	C₄²
Frattini	C₄×M₁₆	C₂×D₁₉
Fitting	C₁₉×#2165	C₂
socle	C₂×C₁₉	#1288
prime radical	C₂³×C₁₉	#104
cosocle	C₄×M₁₆×C₁₉	C₂²
hypercenter	#2165	D₁₉
hypocenter	C₁₉	#7225
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #2165

subgroup

G/H

center

C₄

#11926300

commutator

C₂×C₈×C₁₉

C₄²

Frattini

C₄×M₁₆

C₂×D₁₉

Fitting

C₁₉×#2165

C₂

C₂×C₁₉

C₂³×C₁₉

C₄×M₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ #2165

N	H ≅ G/N	type
10. #11926265	C₄	semidirect
11. C₈×C₁₉⋊C₈	C₄	semidirect
15. C₁₉×#347	C₄	semidirect
84. #347	Dic₁₉	semidirect
109. C₁₉	#7225	semidirect

H ≅ G/N

type

10. #11926265

C₄

semidirect

11. C₈×C₁₉⋊C₈

C₄

semidirect

15. C₁₉×#347

C₄

semidirect

84. #347

Dic₁₉

semidirect

109. C₁₉

#7225

semidirect

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

subgroup	index
#14563784	2
#14561938	2
C₁₉×#2165	2
#7225	19

subgroup

index

#14563784

#14561938

C₁₉×#2165

#7225

Subgroups — #18069601

Conjugacy classes of subgroups

Complements

Maximal subgroups