Group #18072989 — subgroups

Subgroups — #18072989

Order 4864.

330 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14563322	C₂	1	1	yes	maximal, characteristic
2	#14561928	C₂	1	2	yes	maximal
3	#14561465	C₂	1	2	yes	maximal
4	#14561464	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1274	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×#10597260	C₄	1	2	yes	—
8	C₂×#10597260	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₉⋊C₈	C₄	1	2	yes	—
10	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	#11926266	C₄	1	4	yes	complemented
12	#11926265	C₄	1	4	yes	complemented
13	C₁₉×#431	C₂²	1	2	yes	—
14	C₁₉×#376	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
17	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
20	C₁₉×C₄⋊C₈	—	2	2	no	—
21	C₁₉×C₂²⋊C₈	—	2	2	no	—
22	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
23	C₁₉×#95	—	2	2	no	—
24	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
25	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
26	#10597260	—	2	4	no	—
27	#10597260	—	2	1	no	—
28	#10597260	—	2	1	no	—
29	C₄×C₁₉⋊C₈	—	2	4	no	—
30	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
31	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
32	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
33	C₂²×C₄×C₁₉	—	2	2	no	—
34	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	#41	1	2	yes	—
36	C₂×C₈×C₁₉	—	2	4	no	—
37	C₄²×C₁₉	—	2	2	no	—
38	C₄²×C₁₉	M₁₆	1	4	yes	—
39	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
40	C₄²×C₁₉	#41	1	1	yes	characteristic
41	C₄²×C₁₉	#41	1	1	yes	characteristic
42	C₂×C₁₉⋊C₈	—	2	2	no	—
43	C₂×C₁₉⋊C₈	—	2	2	no	—
44	C₂×C₁₉⋊C₈	—	2	2	no	—
45	C₂×C₁₉⋊C₈	—	2	2	no	—
46	C₂×C₁₉⋊C₈	—	2	4	no	—
47	C₂×C₁₉⋊C₈	C₄²	1	1	yes	characteristic
48	C₂×C₁₉⋊C₈	C₄²	1	2	yes	—
49	C₂×C₁₉⋊C₈	C₄²	1	1	yes	characteristic
50	C₂×C₁₉⋊C₈	M₁₆	1	4	yes	—
51	#8140	—	19	1	no	maximal, Sylow
52	C₂³×C₁₉	#117	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	C₂×C₄²	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#117	1	2	yes	—
58	C₂×C₄×C₁₉	#117	1	2	yes	—
59	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
61	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
62	C₈×C₁₉	—	4	4	no	—
63	C₁₉⋊C₈	—	2	1	no	—
64	C₁₉⋊C₈	—	2	1	no	—
65	C₁₉⋊C₈	—	2	2	no	—
66	C₁₉⋊C₈	—	2	4	no	—
67	C₁₉⋊C₈	—	4	4	no	—
68	#1726	—	19	1	no	—
69	#1452	—	19	2	no	—
70	#1275	—	19	2	no	—
71	#1274	—	19	1	no	—
72	#1274	D₁₉	1	1	yes	characteristic
73	C₂²×C₁₉	—	2	2	no	—
74	C₂²×C₁₉	#376	1	1	yes	characteristic
75	C₂²×C₁₉	#432	1	2	yes	—
76	C₄×C₁₉	—	2	2	no	—
77	C₄×C₁₉	—	2	2	no	—
78	C₄×C₁₉	—	4	4	no	—
79	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
80	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
81	C₄×C₁₉	#432	1	2	yes	—
82	#431	—	19	2	no	—
83	#431	C₂×D₁₉	1	2	yes	—
84	C₂×#97	—	19	2	no	—
85	C₂×#97	—	19	1	no	—
86	C₂×C₄×C₈	—	19	1	no	—
87	C₂×C₄×C₈	—	19	2	no	—
88	#376	C₂×D₁₉	1	1	yes	characteristic
89	#322	—	19	4	no	—
90	#322	—	19	4	no	—
91	C₂×C₁₉	—	2	2	no	—
92	C₂×C₁₉	#1745	1	1	yes	characteristic
93	C₂×C₁₉	#1747	1	2	yes	—
94	C₂²×C₈	—	19	1	no	—
95	C₂²×C₈	—	19	1	no	—
96	C₂²×C₈	—	19	2	no	—
97	C₂×C₄²	C₄×D₁₉	1	2	yes	—
98	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
99	C₄⋊C₈	—	2	2	no	—
100	C₄⋊C₈	—	38	2	no	—
101	C₂²⋊C₈	—	2	2	no	—
102	C₂²⋊C₈	—	38	2	no	—
103	#97	—	38	4	no	—
104	#97	—	38	1	no	—
105	#97	—	38	1	no	—
106	C₄×C₈	—	19	2	no	—
107	C₄×C₈	—	19	2	no	—
108	C₄×C₈	—	19	4	no	—
109	C₄×C₈	—	38	4	no	—
110	C₄×C₈	C₄×D₁₉	1	4	yes	—
111	#95	—	2	2	no	—
112	C₁₉	#8140	1	1	yes	characteristic, complemented, Sylow
113	C₂²×C₄	—	2	2	no	—
114	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
115	C₂²×C₄	#64543	1	2	yes	—
116	C₂×C₈	—	2	4	no	—
117	C₂×C₈	—	19	1	no	—
118	C₂×C₈	—	19	1	no	—
119	C₂×C₈	—	19	2	no	—
120	C₂×C₈	—	19	4	no	—
121	C₂×C₈	—	38	2	no	—
122	C₂×C₈	—	38	2	no	—
123	C₂×C₈	—	38	2	no	—
124	C₂×C₈	—	38	2	no	—
125	C₂×C₈	—	38	4	no	—
126	C₄²	—	2	2	no	—
127	C₄²	#64515	1	4	yes	—
128	C₄²	C₂×C₄×D₁₉	1	2	yes	—
129	C₄²	#64543	1	1	yes	characteristic
130	C₄²	#64545	1	1	yes	characteristic
131	C₂³	#10597323	1	1	yes	characteristic
132	C₂×C₄	—	2	4	no	—
133	C₂×C₄	—	4	2	no	—
134	C₂×C₄	—	4	4	no	—
135	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
136	C₂×C₄	#10597323	1	2	yes	—
137	C₂×C₄	#10597338	1	2	yes	—
138	C₂×C₄	#10597338	1	1	yes	characteristic
139	C₂×C₄	C₂×#64515	1	2	yes	—
140	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
141	C₈	—	4	4	no	—
142	C₈	—	38	4	no	—
143	C₈	—	38	1	no	—
144	C₈	—	38	1	no	—
145	C₈	—	38	2	no	—
146	C₈	—	76	4	no	—
147	C₂²	—	2	2	no	—
148	C₂²	#11926389	1	1	yes	characteristic
149	C₂²	#11926598	1	2	yes	—
150	C₄	—	2	2	no	—
151	C₄	—	2	2	no	—
152	C₄	—	4	4	no	—
153	C₄	C₄×#64515	1	1	yes	characteristic
154	C₄	#11926496	1	1	yes	characteristic
155	C₄	#11926600	1	2	yes	—
156	C₂	—	2	2	no	—
157	C₂	#14563382	1	1	yes	characteristic
158	C₂	#14563389	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563322

C₂

yes

maximal, characteristic

#14561928

C₂

yes

maximal

#14561465

C₂

yes

maximal

#14561464

C₂

yes

maximal, characteristic

C₁₉×#1274

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₂×#10597260

C₄

yes

—

C₂×#10597260

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926266

C₄

yes

complemented

#11926265

C₄

yes

complemented

C₁₉×#431

C₂²

yes

—

C₁₉×#376

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

—

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄²

yes

characteristic

C₂×C₁₉⋊C₈

C₄²

yes

—

C₂×C₁₉⋊C₈

C₄²

yes

characteristic

C₂×C₁₉⋊C₈

M₁₆

yes

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#117

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

—

—

—

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

#376

yes

characteristic

C₂²×C₁₉

#432

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×M₁₆

yes

characteristic

C₄×C₁₉

C₄×M₁₆

yes

characteristic

C₄×C₁₉

#432

yes

—

#431

—

#431

C₂×D₁₉

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

C₂×D₁₉

yes

characteristic

#322

—

#322

—

C₂×C₁₉

—

C₂×C₁₉

#1745

yes

characteristic

C₂×C₁₉

#1747

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

C₄×D₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

100

C₄⋊C₈

—

101

C₂²⋊C₈

—

102

C₂²⋊C₈

—

103

#97

—

104

#97

—

105

#97

—

106

C₄×C₈

—

107

C₄×C₈

—

108

C₄×C₈

—

109

C₄×C₈

—

110

C₄×C₈

C₄×D₁₉

yes

—

111

#95

—

112

C₁₉

#8140

yes

characteristic, complemented, Sylow

113

C₂²×C₄

—

114

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

115

C₂²×C₄

#64543

yes

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₄²

—

127

C₄²

#64515

yes

—

128

C₄²

C₂×C₄×D₁₉

yes

—

129

C₄²

#64543

yes

characteristic

130

C₄²

#64545

yes

characteristic

131

C₂³

#10597323

yes

characteristic

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

C₄²×D₁₉

yes

characteristic

136

C₂×C₄

#10597323

yes

—

137

C₂×C₄

#10597338

yes

—

138

C₂×C₄

#10597338

yes

characteristic

139

C₂×C₄

C₂×#64515

yes

—

140

C₂×C₄

M₁₆×D₁₉

yes

—

141

C₈

—

142

C₈

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

147

C₂²

—

148

C₂²

#11926389

yes

characteristic

149

C₂²

#11926598

yes

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

C₄×#64515

yes

characteristic

154

C₄

#11926496

yes

characteristic

155

C₄

#11926600

yes

—

156

C₂

—

157

C₂

#14563382

yes

characteristic

158

C₂

#14563389

yes

—

	subgroup	G/H
center	C₂×C₄	C₄²×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1274	C₂
socle	C₂²×C₁₉	#376
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1274	D₁₉
hypocenter	C₁₉	#8140
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #1274

subgroup

G/H

center

C₂×C₄

C₄²×D₁₉

commutator

C₂×C₄×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1274

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄ ◁ #1274

N	H ≅ G/N	type
11. #11926266	C₄	semidirect
12. #11926265	C₄	semidirect
112. C₁₉	#8140	semidirect

H ≅ G/N

type

11. #11926266

C₄

semidirect

12. #11926265

C₄

semidirect

112. C₁₉

#8140

semidirect

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

subgroup	index
#14563322	2
#14561928	2
#14561465	2
#14561464	2
C₁₉×#1274	2
#8140	19

subgroup

index

C₁₉×#1274

Subgroups — #18072989

Conjugacy classes of subgroups

Complements

Maximal subgroups