Group #18069929 — subgroups

Subgroups — #18069929

Order 4864.

180 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 43 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	#14564603	C₂	1	1	yes	maximal, characteristic
2	#14561581	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1325	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597316	C₄	1	1	yes	characteristic
5	C₂×#10597260	C₄	1	1	yes	characteristic
6	#11926306	—	2	1	no	—
7	#11926306	—	2	1	no	—
8	#11926270	—	2	1	no	—
9	C₁₉×#384	C₂²	1	1	yes	characteristic
10	C₁₉×#324	—	2	1	no	—
11	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
12	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄⋊Dic₁₉	—	2	1	no	—
16	C₂×Dic₁₉⋊C₄	—	4	1	no	—
17	C₂²×C₁₉⋊C₈	—	2	1	no	—
18	#10597316	—	2	1	no	—
19	#10597316	—	4	1	no	—
20	#10597316	C₈	1	2	yes	complemented
21	C₁₉×C₂²⋊C₈	—	4	1	no	—
22	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
23	#10597260	—	4	1	no	—
24	C₂²×C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄×C₁₉	—	2	1	no	—
26	C₂²×C₄×C₁₉	—	2	1	no	—
27	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂²×Dic₁₉	—	4	1	no	—
29	C₂×C₈×C₁₉	—	8	1	no	—
30	C₄⋊C₄×C₁₉	—	4	1	no	—
31	C₄⋊C₄×C₁₉	—	4	1	no	—
32	C₄⋊C₄×C₁₉	—	8	2	no	—
33	C₄²×C₁₉	—	2	1	no	—
34	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
35	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
36	C₄⋊Dic₁₉	—	2	2	no	—
37	C₄⋊Dic₁₉	—	4	1	no	—
38	Dic₁₉⋊C₄	—	4	2	no	—
39	Dic₁₉⋊C₄	—	4	2	no	—
40	C₂×C₁₉⋊C₈	—	2	2	no	—
41	C₂×C₁₉⋊C₈	—	4	1	no	—
42	C₂×C₁₉⋊C₈	—	4	1	no	—
43	C₂×C₁₉⋊C₈	—	8	1	no	—
44	#7358	—	19	1	no	maximal, Sylow
45	C₂³×C₁₉	#99	1	1	yes	characteristic
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	4	1	no	—
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	—	8	1	no	—
55	C₂×C₄×C₁₉	—	8	1	no	—
56	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
58	C₂×Dic₁₉	—	4	2	no	—
59	C₂×Dic₁₉	—	8	1	no	—
60	C₂×Dic₁₉	—	8	1	no	—
61	C₈×C₁₉	—	16	1	no	—
62	C₁₉⋊C₈	—	4	2	no	—
63	C₁₉⋊C₈	—	16	1	no	—
64	#1992	—	19	1	no	—
65	#1325	—	19	1	no	—
66	#1325	D₁₉	1	1	yes	characteristic
67	C₂²×C₁₉	—	2	1	no	—
68	C₂²×C₁₉	—	2	1	no	—
69	C₂²×C₁₉	#323	1	1	yes	characteristic
70	C₂²×C₁₉	#354	1	1	yes	characteristic
71	C₂²×C₁₉	#356	1	1	yes	characteristic
72	C₄×C₁₉	—	2	1	no	—
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	—	4	1	no	—
75	C₄×C₁₉	—	4	1	no	—
76	C₄×C₁₉	—	8	1	no	—
77	C₄×C₁₉	—	8	1	no	—
78	Dic₁₉	—	8	2	no	—
79	C₂×#125	—	19	1	no	—
80	C₂×#97	—	19	1	no	—
81	#384	C₂×D₁₉	1	1	yes	characteristic
82	#340	—	38	1	no	—
83	#340	—	38	1	no	—
84	#324	—	2	1	no	—
85	#324	—	38	1	no	—
86	C₂×C₁₉	—	2	1	no	—
87	C₂×C₁₉	—	2	1	no	—
88	C₂×C₁₉	#1319	1	1	yes	characteristic
89	C₂×C₁₉	#1412	1	1	yes	characteristic
90	C₂×C₁₉	#1413	1	1	yes	characteristic
91	C₂²×C₈	—	38	1	no	—
92	#125	—	19	2	no	—
93	#125	—	38	1	no	—
94	#125	—	76	1	no	—
95	C₂×C₄⋊C₄	—	4	1	no	—
96	C₂×C₄⋊C₄	—	38	1	no	—
97	C₂×C₄⋊C₄	—	76	1	no	—
98	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
99	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
100	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
101	C₂²⋊C₈	—	4	1	no	—
102	C₂²⋊C₈	—	76	1	no	—
103	#97	—	76	1	no	—
104	C₁₉	#7358	1	1	yes	characteristic, complemented, Sylow
105	C₂²×C₄	—	2	1	no	—
106	C₂²×C₄	—	2	1	no	—
107	C₂²×C₄	—	2	1	no	—
108	C₂²×C₄	—	76	1	no	—
109	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
110	C₂×C₈	—	8	1	no	—
111	C₂×C₈	—	38	2	no	—
112	C₂×C₈	—	76	1	no	—
113	C₂×C₈	—	76	1	no	—
114	C₂×C₈	—	152	1	no	—
115	C₄⋊C₄	—	4	1	no	—
116	C₄⋊C₄	—	4	1	no	—
117	C₄⋊C₄	—	8	2	no	—
118	C₄⋊C₄	—	38	2	no	—
119	C₄⋊C₄	—	76	2	no	—
120	C₄⋊C₄	—	76	2	no	—
121	C₄⋊C₄	—	76	1	no	—
122	C₄²	—	2	1	no	—
123	C₄²	C₈×D₁₉	1	1	yes	characteristic
124	C₄²	#64515	1	1	yes	characteristic
125	C₂³	#10597263	1	1	yes	characteristic
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	4	1	no	—
131	C₂×C₄	—	4	1	no	—
132	C₂×C₄	—	4	1	no	—
133	C₂×C₄	—	4	1	no	—
134	C₂×C₄	—	8	1	no	—
135	C₂×C₄	—	8	1	no	—
136	C₂×C₄	—	76	2	no	—
137	C₂×C₄	—	152	1	no	—
138	C₂×C₄	—	152	1	no	—
139	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
140	C₂×C₄	#10597280	1	1	yes	characteristic
141	C₈	—	16	1	no	—
142	C₈	—	304	1	no	—
143	C₈	—	76	2	no	—
144	C₂²	—	2	1	no	—
145	C₂²	—	2	1	no	—
146	C₂²	#11926267	1	1	yes	characteristic
147	C₂²	#11926338	1	1	yes	characteristic
148	C₂²	#11926342	1	1	yes	characteristic
149	C₄	—	2	1	no	—
150	C₄	—	2	1	no	—
151	C₄	—	4	1	no	—
152	C₄	—	4	1	no	—
153	C₄	—	8	1	no	—
154	C₄	—	8	1	no	—
155	C₄	—	152	2	no	—
156	C₂	—	2	1	no	—
157	C₂	—	2	1	no	—
158	C₂	#14561568	1	1	yes	characteristic
159	C₂	#14561805	1	1	yes	characteristic
160	C₂	#14561807	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564603

C₂

yes

maximal, characteristic

#14561581

C₂

yes

maximal, characteristic

C₁₉×#1325

C₂

yes

maximal, characteristic

C₂×#10597316

C₄

yes

characteristic

C₂×#10597260

C₄

yes

—

—

—

C₁₉×#384

C₂²

yes

characteristic

C₁₉×#324

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×Dic₁₉⋊C₄

—

C₂²×C₁₉⋊C₈

—

#10597316

—

#10597316

—

#10597316

C₈

yes

complemented

C₁₉×C₂²⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

#10597260

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

#100

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1992

—

#1325

—

#1325

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

C₂×#125

—

C₂×#97

—

#384

C₂×D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

#125

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₇₆

yes

characteristic

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

100

C₂×C₄²

C₄×D₁₉

yes

characteristic

101

C₂²⋊C₈

—

102

C₂²⋊C₈

—

103

#97

—

104

C₁₉

#7358

yes

characteristic, complemented, Sylow

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

152

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄²

—

123

C₄²

C₈×D₁₉

yes

characteristic

124

C₄²

#64515

yes

characteristic

125

C₂³

#10597263

yes

characteristic

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

152

—

138

C₂×C₄

—

152

—

139

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

140

C₂×C₄

#10597280

yes

characteristic

141

C₈

—

142

C₈

—

304

—

143

C₈

—

144

C₂²

—

145

C₂²

—

146

C₂²

#11926267

yes

characteristic

147

C₂²

#11926338

yes

characteristic

148

C₂²

#11926342

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

152

—

156

C₂

—

157

C₂

—

158

C₂

#14561568

yes

characteristic

159

C₂

#14561805

yes

characteristic

160

C₂

#14561807

yes

characteristic

	subgroup	G/H
center	C₂²	#11926338
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#384	C₂×D₁₉
Fitting	C₁₉×#1325	C₂
socle	C₂²×C₁₉	#354
prime radical	C₂³×C₁₉	#99
cosocle	C₁₉×#384	C₂²
hypercenter	#1325	D₁₉
hypocenter	C₁₉	#7358
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #384 ◁ #1325

subgroup

G/H

center

C₂²

#11926338

commutator

C₄²×C₁₉

C₂×C₈

Frattini

#384

C₂×D₁₉

Fitting

C₁₉×#1325

C₂

C₂²×C₁₉

C₂³×C₁₉

C₁₉×#384

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #384 ◁ #1325

N	H ≅ G/N	type
20. #10597316	C₈	semidirect
104. C₁₉	#7358	semidirect

H ≅ G/N

type

20. #10597316

C₈

semidirect

104. C₁₉

#7358

semidirect

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

subgroup	index
#14564603	2
#14561581	2
C₁₉×#1325	2
#7358	19

subgroup

index

#14564603

#14561581

C₁₉×#1325

#7358

Subgroups — #18069929

Conjugacy classes of subgroups

Complements

Maximal subgroups