Group #14572066 — subgroups

Subgroups — C₂²×(C₂×D₁₉)⋊C₈ #14572066

Order 2432.

1072 conjugacy classes of subgroups; only the 389 normal subgroups are shown.

normal subgroups only

This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 389 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	C₂³×C₄×D₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×(C₂×D₁₉)⋊C₈	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×D₁₉	C₄	1	1	yes	characteristic
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂³×Dic₁₉	C₄	1	1	yes	characteristic
8	C₂²×C₄×D₁₉	—	2	4	no	—
9	C₂²×C₄×D₁₉	—	2	4	no	—
10	C₂²×C₄×D₁₉	C₄	1	6	yes	—
11	C₂²×C₄×D₁₉	C₂²	1	6	yes	—
12	C₂²×C₈×C₁₉	—	2	4	no	—
13	C₂²×C₈×C₁₉	C₂²	1	6	yes	complemented
14	C₂²×C₁₉⋊C₈	—	2	4	no	—
15	C₂²×C₁₉⋊C₈	C₂²	1	6	yes	complemented
16	(C₂×D₁₉)⋊C₈	C₂²	1	16	yes	direct product factor
17	C₂⁴×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂³×D₁₉	—	2	4	no	—
19	C₂³×D₁₉	—	2	4	no	—
20	C₂³×D₁₉	C₈	1	8	yes	complemented
21	C₂³×D₁₉	C₂×C₄	1	6	yes	—
22	C₂²×C₄×C₁₉	C₂×C₄	1	3	yes	—
23	C₂²×C₄×C₁₉	D₄	1	4	yes	—
24	C₂²×C₄×C₁₉	D₄	1	4	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
26	C₂²×Dic₁₉	—	2	4	no	—
27	C₂²×Dic₁₉	C₂×C₄	1	6	yes	—
28	C₂×C₄×D₁₉	—	2	24	no	—
29	C₂×C₄×D₁₉	—	2	12	no	—
30	C₂×C₄×D₁₉	—	2	12	no	—
31	C₂×C₄×D₁₉	C₂×C₄	1	12	yes	—
32	C₂×C₄×D₁₉	C₂³	1	4	yes	—
33	C₂×C₈×C₁₉	—	2	12	no	—
34	C₂×C₈×C₁₉	C₂³	1	4	yes	complemented
35	C₂×C₁₉⋊C₈	—	2	12	no	—
36	C₂×C₁₉⋊C₈	C₂³	1	4	yes	complemented
37	C₂³×C₁₉	C₂²⋊C₄	1	4	yes	—
38	C₂³×C₁₉	C₂×C₈	1	4	yes	—
39	C₂³×C₁₉	M₁₆	1	4	yes	—
40	C₂³×C₁₉	C₂²×C₄	1	3	yes	—
41	C₂²×D₁₉	—	2	32	no	—
42	C₂²×D₁₉	—	2	12	no	—
43	C₂²×D₁₉	—	2	12	no	—
44	C₂²×D₁₉	C₂×C₈	1	24	yes	complemented
45	C₂²×D₁₉	C₂²×C₄	1	4	yes	—
46	C₂×C₄×C₁₉	C₂²⋊C₄	1	12	yes	—
47	C₂×C₄×C₁₉	C₂²×C₄	1	3	yes	—
48	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
49	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
50	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
51	C₂×Dic₁₉	—	2	12	no	—
52	C₂×Dic₁₉	C₂²×C₄	1	4	yes	—
53	C₄×D₁₉	—	2	24	no	—
54	C₄×D₁₉	—	2	4	no	—
55	C₄×D₁₉	—	2	4	no	—
56	C₈×C₁₉	—	2	4	no	—
57	C₁₉⋊C₈	—	2	4	no	—
58	C₂²×C₂²⋊C₈	—	19	1	no	maximal, Sylow
59	C₂²×C₁₉	C₂²⋊C₈	1	16	yes	complemented
60	C₂²×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
61	C₂²×C₁₉	C₂²×C₈	1	6	yes	—
62	C₂²×C₁₉	C₂×M₁₆	1	6	yes	—
63	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
64	C₂×D₁₉	—	2	4	no	—
65	C₂×D₁₉	—	2	4	no	—
66	C₂×D₁₉	—	2	48	no	—
67	C₂×D₁₉	C₂²×C₈	1	8	yes	complemented
68	C₄×C₁₉	C₂×C₂²⋊C₄	1	6	yes	—
69	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
70	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
71	Dic₁₉	—	2	4	no	—
72	C₂⁴×C₄	—	19	1	no	—
73	C₂³×C₈	—	19	1	no	—
74	C₂³×C₈	D₁₉	1	1	yes	characteristic, complemented
75	C₂×C₂²⋊C₈	—	19	12	no	—
76	C₂×C₁₉	C₂×C₂²⋊C₈	1	12	yes	complemented
77	C₂×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₁₉	C₂³×C₈	1	1	yes	characteristic
79	C₂×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
80	D₁₉	—	2	8	no	—
81	C₂⁵	—	19	1	no	—
82	C₂³×C₄	—	19	1	no	—
83	C₂³×C₄	—	19	6	no	—
84	C₂³×C₄	—	19	6	no	—
85	C₂³×C₄	—	38	4	no	—
86	C₂³×C₄	—	38	4	no	—
87	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
88	C₂²×C₈	—	2	4	no	—
89	C₂²×C₈	—	19	6	no	—
90	C₂²×C₈	—	38	4	no	—
91	C₂²×C₈	C₂×D₁₉	1	6	yes	complemented
92	C₂²⋊C₈	—	19	16	no	—
93	C₁₉	C₂²×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
94	C₂⁴	—	19	8	no	—
95	C₂⁴	—	19	6	no	—
96	C₂⁴	—	38	4	no	—
97	C₂⁴	—	38	4	no	—
98	C₂⁴	C₄×D₁₉	1	1	yes	characteristic
99	C₂²×C₄	—	19	6	no	—
100	C₂²×C₄	—	19	12	no	—
101	C₂²×C₄	—	19	4	no	—
102	C₂²×C₄	—	38	4	no	—
103	C₂²×C₄	—	38	24	no	—
104	C₂²×C₄	—	38	12	no	—
105	C₂²×C₄	—	38	12	no	—
106	C₂²×C₄	C₄×D₁₉	1	3	yes	—
107	C₂²×C₄	D₇₆	1	4	yes	—
108	C₂²×C₄	C₂²⋊D₁₉	1	4	yes	—
109	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
110	C₂×C₈	—	2	12	no	—
111	C₂×C₈	—	19	4	no	—
112	C₂×C₈	—	38	12	no	—
113	C₂×C₈	C₂²×D₁₉	1	4	yes	complemented
114	C₂³	—	19	4	no	—
115	C₂³	—	19	24	no	—
116	C₂³	—	38	32	no	—
117	C₂³	—	38	12	no	—
118	C₂³	—	38	12	no	—
119	C₂³	C₈×D₁₉	1	4	yes	—
120	C₂³	#64515	1	4	yes	—
121	C₂³	(C₂×D₁₉)⋊C₄	1	4	yes	—
122	C₂³	C₂×C₄×D₁₉	1	3	yes	—
123	C₂×C₄	—	19	4	no	—
124	C₂×C₄	—	38	12	no	—
125	C₂×C₄	—	38	4	no	—
126	C₂×C₄	—	38	4	no	—
127	C₂×C₄	—	38	24	no	—
128	C₂×C₄	(C₂×D₁₉)⋊C₄	1	12	yes	—
129	C₂×C₄	C₂×C₄×D₁₉	1	3	yes	—
130	C₂×C₄	C₂×D₇₆	1	6	yes	—
131	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
132	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
133	C₈	—	2	4	no	—
134	C₈	—	38	4	no	—
135	C₂²	—	19	8	no	—
136	C₂²	—	38	4	no	—
137	C₂²	—	38	4	no	—
138	C₂²	—	38	48	no	—
139	C₂²	(C₂×D₁₉)⋊C₈	1	16	yes	direct product factor
140	C₂²	C₂×C₈×D₁₉	1	6	yes	—
141	C₂²	C₂×#64515	1	6	yes	—
142	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	6	yes	—
143	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
144	C₄	—	38	4	no	—
145	C₄	C₂×(C₂×D₁₉)⋊C₄	1	6	yes	—
146	C₄	C₂²×D₇₆	1	1	yes	characteristic
147	C₄	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
148	C₂	—	38	8	no	—
149	C₂	C₂×(C₂×D₁₉)⋊C₈	1	12	yes	direct product factor
150	C₂	C₂²×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
151	C₂	C₂²×C₈×D₁₉	1	1	yes	characteristic
152	C₂	C₂²×#64515	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₄×D₁₉

C₂

yes

maximal, characteristic

C₂³×C₁₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₂×(C₂×D₁₉)⋊C₈

C₂

yes

maximal, direct product factor

C₂³×C₈×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂⁴×D₁₉

C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂³×Dic₁₉

C₄

yes

characteristic

C₂²×C₄×D₁₉

—

C₂²×C₄×D₁₉

—

C₂²×C₄×D₁₉

C₄

yes

—

C₂²×C₄×D₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂²

yes

complemented

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₂²

yes

complemented

(C₂×D₁₉)⋊C₈

C₂²

yes

direct product factor

C₂⁴×C₁₉

C₂×C₄

yes

characteristic

C₂³×D₁₉

—

C₂³×D₁₉

—

C₂³×D₁₉

C₈

yes

complemented

C₂³×D₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

C₂×C₄

yes

—

C₂×C₄×D₁₉

C₂³

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

complemented

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂³

yes

complemented

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂×C₈

yes

—

C₂³×C₁₉

M₁₆

yes

—

C₂³×C₁₉

C₂²×C₄

yes

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₂×C₈

yes

complemented

C₂²×D₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂²×C₄

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₂²×C₂²⋊C₈

—

maximal, Sylow

C₂²×C₁₉

C₂²⋊C₈

yes

complemented

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂²×C₁₉

C₂²×C₈

yes

—

C₂²×C₁₉

C₂×M₁₆

yes

—

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

C₂²×C₈

yes

complemented

C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

C₄×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

C₂²×D₄

yes

characteristic

Dic₁₉

—

C₂⁴×C₄

—

C₂³×C₈

—

C₂³×C₈

D₁₉

yes

characteristic, complemented

C₂×C₂²⋊C₈

—

C₂×C₁₉

C₂×C₂²⋊C₈

yes

complemented

C₂×C₁₉

C₂²×C₂²⋊C₄

yes

characteristic

C₂×C₁₉

C₂³×C₈

yes

characteristic

C₂×C₁₉

C₂²×M₁₆

yes

characteristic

D₁₉

—

C₂⁵

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

complemented

C₂²⋊C₈

—

C₁₉

C₂²×C₂²⋊C₈

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

C₄×D₁₉

yes

characteristic

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

C₄×D₁₉

yes

—

107

C₂²×C₄

D₇₆

yes

—

108

C₂²×C₄

C₂²⋊D₁₉

yes

—

109

C₂²×C₄

C₂²×D₁₉

yes

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

C₂²×D₁₉

yes

complemented

114

C₂³

—

115

C₂³

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

C₈×D₁₉

yes

—

120

C₂³

#64515

yes

—

121

C₂³

(C₂×D₁₉)⋊C₄

yes

—

122

C₂³

C₂×C₄×D₁₉

yes

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

129

C₂×C₄

C₂×C₄×D₁₉

yes

—

130

C₂×C₄

C₂×D₇₆

yes

—

131

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

132

C₂×C₄

C₂³×D₁₉

yes

characteristic

133

C₈

—

134

C₈

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

(C₂×D₁₉)⋊C₈

yes

direct product factor

140

C₂²

C₂×C₈×D₁₉

yes

—

141

C₂²

C₂×#64515

yes

—

142

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

—

143

C₂²

C₂²×C₄×D₁₉

yes

characteristic

144

C₄

—

145

C₄

C₂×(C₂×D₁₉)⋊C₄

yes

—

146

C₄

C₂²×D₇₆

yes

characteristic

147

C₄

C₂²×C₂²⋊D₁₉

yes

characteristic

148

C₂

—

149

C₂

C₂×(C₂×D₁₉)⋊C₈

yes

direct product factor

150

C₂

C₂²×(C₂×D₁₉)⋊C₄

yes

characteristic

151

C₂

C₂²×C₈×D₁₉

yes

characteristic

152

C₂

C₂²×#64515

yes

characteristic

	subgroup	G/H
center	C₂³×C₄	C₂×D₁₉
commutator	C₂×C₁₉	C₂³×C₈
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂³×C₈×C₁₉	C₂
socle	C₂⁴×C₁₉	C₂×C₄
prime radical	C₂⁴×D₁₉	C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	C₂³×C₈	D₁₉
hypocenter	C₁₉	C₂²×C₂²⋊C₈
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂³×C₈

subgroup

G/H

center

C₂³×C₄

C₂×D₁₉

commutator

C₂×C₁₉

C₂³×C₈

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂³×C₈×C₁₉

C₂

socle

C₂⁴×C₁₉

C₂×C₄

prime radical

C₂⁴×D₁₉

C₄

cosocle

C₂×C₄×C₁₉

C₂⁴

hypercenter

C₂³×C₈

D₁₉

hypocenter

C₁₉

C₂²×C₂²⋊C₈

LCS

G ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³×C₄ ◁ C₂³×C₈

N	H ≅ G/N	type
2. C₂³×C₁₉⋊C₈	C₂	semidirect
3. C₂×(C₂×D₁₉)⋊C₈	C₂	direct (N × H)
4. C₂³×C₈×C₁₉	C₂	semidirect
13. C₂²×C₈×C₁₉	C₂²	semidirect
15. C₂²×C₁₉⋊C₈	C₂²	semidirect
16. (C₂×D₁₉)⋊C₈	C₂²	direct (N × H)
20. C₂³×D₁₉	C₈	semidirect
34. C₂×C₈×C₁₉	C₂³	semidirect
36. C₂×C₁₉⋊C₈	C₂³	semidirect
44. C₂²×D₁₉	C₂×C₈	semidirect
59. C₂²×C₁₉	C₂²⋊C₈	semidirect
67. C₂×D₁₉	C₂²×C₈	semidirect
74. C₂³×C₈	D₁₉	semidirect
76. C₂×C₁₉	C₂×C₂²⋊C₈	semidirect
91. C₂²×C₈	C₂×D₁₉	semidirect
93. C₁₉	C₂²×C₂²⋊C₈	semidirect
113. C₂×C₈	C₂²×D₁₉	semidirect
139. C₂²	(C₂×D₁₉)⋊C₈	direct (N × H)
149. C₂	C₂×(C₂×D₁₉)⋊C₈	direct (N × H)

H ≅ G/N

type

2. C₂³×C₁₉⋊C₈

C₂

semidirect

3. C₂×(C₂×D₁₉)⋊C₈

C₂

direct (N × H)

4. C₂³×C₈×C₁₉

C₂

semidirect

13. C₂²×C₈×C₁₉

C₂²

semidirect

15. C₂²×C₁₉⋊C₈

C₂²

semidirect

16. (C₂×D₁₉)⋊C₈

C₂²

direct (N × H)

20. C₂³×D₁₉

C₈

semidirect

34. C₂×C₈×C₁₉

C₂³

semidirect

36. C₂×C₁₉⋊C₈

C₂³

semidirect

44. C₂²×D₁₉

C₂×C₈

semidirect

59. C₂²×C₁₉

C₂²⋊C₈

semidirect

67. C₂×D₁₉

C₂²×C₈

semidirect

74. C₂³×C₈

D₁₉

semidirect

76. C₂×C₁₉

C₂×C₂²⋊C₈

semidirect

91. C₂²×C₈

C₂×D₁₉

semidirect

93. C₁₉

C₂²×C₂²⋊C₈

semidirect

113. C₂×C₈

C₂²×D₁₉

semidirect

139. C₂²

(C₂×D₁₉)⋊C₈

direct (N × H)

149. C₂

C₂×(C₂×D₁₉)⋊C₈

direct (N × H)

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

subgroup	index
C₂³×C₄×D₁₉	2
C₂³×C₁₉⋊C₈	2
C₂×(C₂×D₁₉)⋊C₈	2
C₂³×C₈×C₁₉	2
C₂²×C₂²⋊C₈	19

subgroup

index

C₂³×C₄×D₁₉

C₂³×C₁₉⋊C₈

C₂×(C₂×D₁₉)⋊C₈

C₂³×C₈×C₁₉

C₂²×C₂²⋊C₈

Subgroups — C₂²×(C₂×D₁₉)⋊C₈ #14572066

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C22×(C2×D19)⋊C8 #14572066

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×(C₂×D₁₉)⋊C₈ #14572066