Group #18087572 — subgroups

Subgroups — #18087572

Order 4864.

316 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 101 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	#14564616	C₂	1	1	yes	maximal, characteristic
2	#14563789	C₂	1	1	yes	maximal, characteristic
3	#14562406	C₂	1	2	yes	maximal
4	#14562039	C₂	1	2	yes	maximal
5	C₁₉×#1274	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	1	yes	characteristic
7	#11926568	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
10	#11926304	—	2	2	no	—
11	#11926295	—	2	4	no	—
12	#11926276	—	2	4	no	—
13	C₁₉×#431	C₂²	1	2	yes	—
14	C₁₉×#376	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₁₉	D₄	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
17	#10597372	—	2	1	no	—
18	#10597370	—	2	2	no	—
19	C₂×#64520	—	2	1	no	—
20	C₂²×C₁₉⋊C₈	—	2	2	no	—
21	#10597316	—	2	1	no	—
22	#10597315	Q₈	1	2	yes	—
23	C₄×Dic₃₈	—	2	2	no	—
24	C₁₉×C₄⋊C₈	—	2	2	no	—
25	C₁₉×C₂²⋊C₈	—	2	2	no	—
26	C₄×C₈×C₁₉	D₄	1	4	yes	—
27	C₁₉×#95	—	2	2	no	—
28	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
29	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
30	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
31	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
32	C₂²×C₄×C₁₉	—	2	2	no	—
33	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	#41	1	2	yes	—
35	C₂×Dic₃₈	—	2	2	no	—
36	C₂×C₈×C₁₉	—	2	4	no	—
37	C₄²×C₁₉	—	2	2	no	—
38	C₄²×C₁₉	SD₁₆	1	4	yes	—
39	C₄²×C₁₉	C₂×D₄	1	2	yes	—
40	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	C₄²×C₁₉	#41	1	1	yes	characteristic
42	C₂²⋊Dic₁₉	—	4	1	no	—
43	C₄⋊Dic₁₉	—	2	2	no	—
44	C₄⋊Dic₁₉	—	2	2	no	—
45	Dic₁₉⋊C₄	—	4	2	no	—
46	C₄×Dic₁₉	—	4	1	no	—
47	#64520	—	4	2	no	—
48	C₂×C₁₉⋊C₈	—	4	2	no	—
49	C₂×C₁₉⋊C₈	—	4	1	no	—
50	C₂×C₁₉⋊C₈	—	4	4	no	—
51	#10670	—	19	1	no	maximal, Sylow
52	C₂³×C₁₉	#123	1	1	yes	characteristic
53	C₂×C₄×C₁₉	—	2	4	no	—
54	C₂×C₄×C₁₉	—	4	2	no	—
55	C₂×C₄×C₁₉	—	4	4	no	—
56	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
57	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#123	1	2	yes	—
59	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
61	C₂×C₄×C₁₉	#137	1	2	yes	—
62	C₂×Dic₁₉	—	4	2	no	—
63	Dic₃₈	—	4	4	no	—
64	C₈×C₁₉	—	4	4	no	—
65	C₁₉⋊C₈	—	8	2	no	—
66	C₁₉⋊C₈	—	8	1	no	—
67	#1995	—	19	1	no	—
68	#1843	—	19	1	no	—
69	#1570	—	19	2	no	—
70	#1481	—	19	2	no	—
71	#1274	D₁₉	1	1	yes	characteristic
72	C₂²×C₁₉	—	2	2	no	—
73	C₂²×C₁₉	#399	1	1	yes	characteristic
74	C₂²×C₁₉	#483	1	2	yes	—
75	C₄×C₁₉	—	2	2	no	—
76	C₄×C₁₉	—	2	2	no	—
77	C₄×C₁₉	—	4	4	no	—
78	C₄×C₁₉	#475	1	2	yes	—
79	C₄×C₁₉	#492	1	1	yes	characteristic
80	C₄×C₁₉	#497	1	1	yes	characteristic
81	Dic₁₉	—	8	2	no	—
82	#533	—	19	1	no	—
83	#431	C₂×D₁₉	1	2	yes	—
84	#423	—	19	1	no	—
85	C₂×C₄⋊C₈	—	19	2	no	—
86	C₂×C₄⋊C₈	—	38	2	no	—
87	#376	C₂×D₁₉	1	1	yes	characteristic
88	#339	—	38	2	no	—
89	#334	—	38	4	no	—
90	Q₈⋊C₈	—	38	4	no	—
91	C₂×C₁₉	—	2	2	no	—
92	C₂×C₁₉	#2096	1	1	yes	characteristic
93	C₂×C₁₉	#2098	1	2	yes	—
94	C₂×M₁₆	—	38	1	no	—
95	C₂²×C₈	—	38	2	no	—
96	C₄⋊Q₈	—	19	2	no	—
97	#125	—	38	1	no	—
98	C₂²⋊Q₈	—	38	2	no	—
99	C₄×Q₈	—	38	2	no	—
100	#117	—	38	1	no	—
101	C₂×C₄²	D₇₆	1	2	yes	—
102	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
103	C₄⋊C₈	—	2	2	no	—
104	C₄⋊C₈	—	38	2	no	—
105	C₄⋊C₈	—	38	2	no	—
106	C₄⋊C₈	—	38	2	no	—
107	C₄⋊C₈	—	76	4	no	—
108	C₂²⋊C₈	—	2	2	no	—
109	C₄×C₈	D₇₆	1	4	yes	—
110	#95	—	2	2	no	—
111	C₁₉	#10670	1	1	yes	characteristic, complemented, Sylow
112	C₂×Q₈	—	38	2	no	—
113	C₂²×C₄	—	2	2	no	—
114	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
115	C₂²×C₄	#64543	1	2	yes	—
116	M₁₆	—	76	2	no	—
117	C₂×C₈	—	2	4	no	—
118	C₂×C₈	—	76	2	no	—
119	C₂×C₈	—	76	1	no	—
120	C₂×C₈	—	76	4	no	—
121	C₄⋊C₄	—	38	2	no	—
122	C₄⋊C₄	—	38	2	no	—
123	C₄⋊C₄	—	76	2	no	—
124	C₂²⋊C₄	—	76	1	no	—
125	C₄²	—	2	2	no	—
126	C₄²	—	76	1	no	—
127	C₄²	#64516	1	4	yes	—
128	C₄²	C₂×D₇₆	1	2	yes	—
129	C₄²	#64543	1	1	yes	characteristic
130	C₄²	Q₈×D₁₉	1	1	yes	characteristic
131	C₂³	#10597332	1	1	yes	characteristic
132	Q₈	—	76	4	no	—
133	C₂×C₄	—	2	4	no	—
134	C₂×C₄	—	4	2	no	—
135	C₂×C₄	—	4	4	no	—
136	C₂×C₄	—	76	2	no	—
137	C₂×C₄	#10597320	1	1	yes	characteristic
138	C₂×C₄	#10597332	1	2	yes	—
139	C₂×C₄	#10597343	1	2	yes	—
140	C₂×C₄	#10597343	1	1	yes	characteristic
141	C₂×C₄	C₂×#64516	1	2	yes	—
142	C₂×C₄	#10597355	1	2	yes	—
143	C₈	—	4	4	no	—
144	C₈	—	152	2	no	—
145	C₈	—	152	1	no	—
146	C₂²	—	2	2	no	—
147	C₂²	#11926481	1	1	yes	characteristic
148	C₂²	#11926875	1	2	yes	—
149	C₄	—	2	2	no	—
150	C₄	—	2	2	no	—
151	C₄	—	4	4	no	—
152	C₄	—	152	2	no	—
153	C₄	#11926830	1	2	yes	—
154	C₄	#11926917	1	1	yes	characteristic
155	C₄	#11926938	1	1	yes	characteristic
156	C₂	—	2	2	no	—
157	C₂	#14565177	1	1	yes	characteristic
158	C₂	#14565189	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564616

C₂

yes

maximal, characteristic

#14563789

C₂

yes

maximal, characteristic

#14562406

C₂

yes

maximal

#14562039

C₂

yes

maximal

C₁₉×#1274

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

#11926568

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926304

—

#11926295

—

#11926276

—

C₁₉×#431

C₂²

yes

—

C₁₉×#376

C₂²

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂²×C₁₉⋊C₈

—

#10597316

—

#10597315

Q₈

yes

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

C₁₉×#95

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

—

—

—

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

#399

yes

characteristic

C₂²×C₁₉

#483

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#475

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#533

—

#431

C₂×D₁₉

yes

—

#423

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

#376

C₂×D₁₉

yes

characteristic

#339

—

#334

—

Q₈⋊C₈

—

C₂×C₁₉

—

C₂×C₁₉

#2096

yes

characteristic

C₂×C₁₉

#2098

yes

—

C₂×M₁₆

—

C₂²×C₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

100

#117

—

101

C₂×C₄²

D₇₆

yes

—

102

C₂×C₄²

C₂²×D₁₉

yes

characteristic

103

C₄⋊C₈

—

104

C₄⋊C₈

—

105

C₄⋊C₈

—

106

C₄⋊C₈

—

107

C₄⋊C₈

—

108

C₂²⋊C₈

—

109

C₄×C₈

D₇₆

yes

—

110

#95

—

111

C₁₉

#10670

yes

characteristic, complemented, Sylow

112

C₂×Q₈

—

113

C₂²×C₄

—

114

C₂²×C₄

C₂×D₇₆

yes

characteristic

115

C₂²×C₄

#64543

yes

—

116

M₁₆

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₂²⋊C₄

—

125

C₄²

—

126

C₄²

—

127

C₄²

#64516

yes

—

128

C₄²

C₂×D₇₆

yes

—

129

C₄²

#64543

yes

characteristic

130

C₄²

Q₈×D₁₉

yes

characteristic

131

C₂³

#10597332

yes

characteristic

132

Q₈

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

#10597320

yes

characteristic

138

C₂×C₄

#10597332

yes

—

139

C₂×C₄

#10597343

yes

—

140

C₂×C₄

#10597343

yes

characteristic

141

C₂×C₄

C₂×#64516

yes

—

142

C₂×C₄

#10597355

yes

—

143

C₈

—

144

C₈

—

152

—

145

C₈

—

152

—

146

C₂²

—

147

C₂²

#11926481

yes

characteristic

148

C₂²

#11926875

yes

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

152

—

153

C₄

#11926830

yes

—

154

C₄

#11926917

yes

characteristic

155

C₄

#11926938

yes

characteristic

156

C₂

—

157

C₂

#14565177

yes

characteristic

158

C₂

#14565189

yes

—

	subgroup	G/H
center	C₂×C₄	#10597320
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1274	C₂
socle	C₂²×C₁₉	#399
prime radical	C₂³×C₁₉	#123
hypercenter	#1274	D₁₉
hypocenter	C₁₉	#10670
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1274

subgroup

G/H

center

C₂×C₄

#10597320

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1274

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1274

N	H ≅ G/N	type
111. C₁₉	#10670	semidirect

H ≅ G/N

type

111. C₁₉

#10670

semidirect

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

subgroup	index
#14564616	2
#14563789	2
#14562406	2
#14562039	2
C₁₉×#1274	2
#10670	19

subgroup

index

C₁₉×#1274

Subgroups — #18087572

Conjugacy classes of subgroups

Complements

Maximal subgroups