Group #14571917 — subgroups

Subgroups — #14571917

Order 2432.

1224 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 237 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	C₂×#10597376	C₂	1	3	yes	maximal, complemented
2	C₂×#10597399	C₂	1	2	yes	maximal, complemented
3	#11926423	C₂	1	6	yes	maximal, complemented
4	#11926404	C₂	1	3	yes	maximal, complemented
5	C₂⁴×C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂⁵×C₁₉	C₂²	1	1	yes	characteristic
7	C₂³×C₄×C₁₉	—	2	12	no	—
8	C₂³×C₄×C₁₉	C₂²	1	3	yes	—
9	C₂³×C₄×C₁₉	C₂²	1	3	yes	—
10	C₂²×C₂²⋊D₁₉	C₂²	1	6	yes	—
11	C₂²×D₇₆	C₂²	1	1	yes	characteristic, complemented
12	#10597399	—	2	8	no	—
13	C₂×C₂²⋊Dic₁₉	C₂²	1	6	yes	—
14	#10597376	—	2	12	no	—
15	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	6	yes	complemented
16	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	complemented
17	C₁₉⋊#95	C₂²	1	6	yes	complemented
18	C₂⁴×C₁₉	—	2	6	no	—
19	C₂⁴×C₁₉	—	2	6	no	—
20	C₂⁴×C₁₉	D₄	1	4	yes	complemented
21	C₂⁴×C₁₉	C₂³	1	3	yes	—
22	C₂³×D₁₉	C₂³	1	2	yes	—
23	C₂²×C₄×C₁₉	—	2	32	no	—
24	C₂²×C₄×C₁₉	—	2	6	no	—
25	C₂²×C₄×C₁₉	—	2	12	no	—
26	C₂²×C₄×C₁₉	—	2	12	no	—
27	C₂²×C₄×C₁₉	D₄	1	12	yes	complemented
28	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
29	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×C₂²⋊D₁₉	—	2	12	no	—
31	C₂×C₂²⋊D₁₉	—	2	12	no	—
32	C₂×C₂²⋊D₁₉	—	2	12	no	—
33	C₂²×Dic₁₉	C₂³	1	6	yes	—
34	C₂×D₇₆	—	2	6	no	—
35	C₂²⋊Dic₁₉	—	2	12	no	—
36	(C₂×D₁₉)⋊C₄	—	2	12	no	—
37	C₄⋊Dic₁₉	—	2	6	no	—
38	C₂³×C₁₉	—	2	8	no	—
39	C₂³×C₁₉	—	2	24	no	—
40	C₂³×C₁₉	—	2	24	no	—
41	C₂³×C₁₉	—	2	6	no	—
42	C₂³×C₁₉	—	2	6	no	—
43	C₂³×C₁₉	C₂×D₄	1	6	yes	—
44	C₂³×C₁₉	C₂×D₄	1	6	yes	—
45	C₂³×C₁₉	#41	1	6	yes	—
46	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
47	C₂²×D₁₉	—	2	6	no	—
48	C₂²×D₁₉	—	2	2	no	—
49	C₂²×D₁₉	—	2	6	no	—
50	C₂×C₄×C₁₉	—	2	24	no	—
51	C₂×C₄×C₁₉	—	2	6	no	—
52	C₂×C₄×C₁₉	—	2	24	no	—
53	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
54	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
55	C₂²⋊D₁₉	—	4	24	no	—
56	C₂×Dic₁₉	—	2	6	no	—
57	C₂×Dic₁₉	—	2	6	no	—
58	C₂×Dic₁₉	—	2	6	no	—
59	D₇₆	—	4	4	no	—
60	#2847	—	19	1	no	maximal, Sylow
61	C₂²×C₁₉	—	2	32	no	—
62	C₂²×C₁₉	—	2	6	no	—
63	C₂²×C₁₉	—	2	12	no	—
64	C₂²×C₁₉	—	2	6	no	—
65	C₂²×C₁₉	—	2	12	no	—
66	C₂²×C₁₉	#121	1	12	yes	complemented
67	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
68	C₂²×C₁₉	C₂²×D₄	1	3	yes	—
69	C₂²×C₁₉	C₂×#41	1	3	yes	—
70	C₂×D₁₉	—	4	2	no	—
71	C₂×D₁₉	—	4	6	no	—
72	C₂×D₁₉	—	4	6	no	—
73	C₄×C₁₉	—	2	6	no	—
74	C₄×C₁₉	#120	1	4	yes	complemented
75	Dic₁₉	—	4	6	no	—
76	C₂⁴×C₄	D₁₉	1	1	yes	characteristic, complemented
77	C₂×#121	—	19	3	no	—
78	C₂×#120	—	19	2	no	—
79	#386	—	19	6	no	—
80	#380	—	19	3	no	—
81	C₂×C₁₉	—	2	12	no	—
82	C₂×C₁₉	C₂×#120	1	1	yes	characteristic
83	C₂×C₁₉	C₂×#121	1	3	yes	—
84	C₂×C₁₉	#525	1	3	yes	—
85	D₁₉	—	8	2	no	—
86	C₂⁵	C₂×D₁₉	1	1	yes	characteristic
87	C₂²×D₄	—	19	6	no	—
88	C₂²×D₄	—	19	1	no	—
89	C₂³×C₄	—	2	12	no	—
90	C₂³×C₄	C₂×D₁₉	1	3	yes	—
91	C₂³×C₄	C₂×D₁₉	1	3	yes	—
92	#121	—	38	12	no	—
93	#120	—	38	8	no	—
94	C₂×C₄⋊C₄	—	19	3	no	—
95	C₂×C₂²⋊C₄	—	19	6	no	—
96	C₂×C₂²⋊C₄	—	19	6	no	—
97	#95	—	19	6	no	—
98	C₁₉	#2847	1	1	yes	characteristic, complemented, Sylow
99	C₂⁴	—	2	6	no	—
100	C₂⁴	—	2	6	no	—
101	C₂⁴	—	19	2	no	—
102	C₂⁴	D₇₆	1	4	yes	complemented
103	C₂⁴	C₂²×D₁₉	1	3	yes	—
104	C₂×D₄	—	38	12	no	—
105	C₂×D₄	—	38	12	no	—
106	C₂×D₄	—	38	12	no	—
107	C₂×D₄	—	38	6	no	—
108	C₂²×C₄	—	2	32	no	—
109	C₂²×C₄	—	2	6	no	—
110	C₂²×C₄	—	2	12	no	—
111	C₂²×C₄	—	2	12	no	—
112	C₂²×C₄	—	19	6	no	—
113	C₂²×C₄	C₂²⋊D₁₉	1	12	yes	complemented
114	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
115	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
116	C₄⋊C₄	—	38	6	no	—
117	C₂²⋊C₄	—	38	12	no	—
118	C₂²⋊C₄	—	38	12	no	—
119	C₂³	—	2	8	no	—
120	C₂³	—	2	24	no	—
121	C₂³	—	2	24	no	—
122	C₂³	—	2	6	no	—
123	C₂³	—	2	6	no	—
124	C₂³	—	38	2	no	—
125	C₂³	—	38	6	no	—
126	C₂³	—	38	6	no	—
127	C₂³	C₂×D₇₆	1	6	yes	—
128	C₂³	#64541	1	6	yes	—
129	C₂³	C₂×C₂²⋊D₁₉	1	6	yes	—
130	C₂³	C₂³×D₁₉	1	1	yes	characteristic
131	D₄	—	76	24	no	—
132	D₄	—	76	4	no	—
133	C₂×C₄	—	2	24	no	—
134	C₂×C₄	—	2	6	no	—
135	C₂×C₄	—	2	24	no	—
136	C₂×C₄	—	38	6	no	—
137	C₂×C₄	—	38	6	no	—
138	C₂×C₄	—	38	6	no	—
139	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
140	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
141	C₂²	—	2	32	no	—
142	C₂²	—	2	12	no	—
143	C₂²	—	2	6	no	—
144	C₂²	—	2	6	no	—
145	C₂²	—	2	12	no	—
146	C₂²	—	76	6	no	—
147	C₂²	—	76	2	no	—
148	C₂²	—	76	6	no	—
149	C₂²	#10597376	1	12	yes	complemented
150	C₂²	C₂²×D₇₆	1	1	yes	characteristic
151	C₂²	C₂×#64541	1	3	yes	—
152	C₂²	C₂²×C₂²⋊D₁₉	1	3	yes	—
153	C₄	—	2	6	no	—
154	C₄	—	76	6	no	—
155	C₄	#10597399	1	4	yes	complemented
156	C₂	—	2	12	no	—
157	C₂	—	152	2	no	—
158	C₂	C₂×#10597399	1	1	yes	characteristic
159	C₂	C₂×#10597376	1	3	yes	—
160	C₂	#11927055	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597376

C₂

yes

maximal, complemented

C₂×#10597399

C₂

yes

maximal, complemented

#11926423

C₂

yes

maximal, complemented

#11926404

C₂

yes

maximal, complemented

C₂⁴×C₄×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂⁵×C₁₉

C₂²

yes

characteristic

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂²

yes

—

C₂³×C₄×C₁₉

C₂²

yes

—

C₂²×C₂²⋊D₁₉

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

characteristic, complemented

#10597399

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

#10597376

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

complemented

C₂×C₄⋊Dic₁₉

C₂²

yes

complemented

C₁₉⋊#95

C₂²

yes

complemented

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

D₄

yes

complemented

C₂⁴×C₁₉

C₂³

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

complemented

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

#41

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

#2847

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

complemented

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

C₂×#41

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

complemented

Dic₁₉

—

C₂⁴×C₄

D₁₉

yes

characteristic, complemented

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#120

yes

characteristic

C₂×C₁₉

C₂×#121

yes

—

C₂×C₁₉

#525

yes

—

D₁₉

—

C₂⁵

C₂×D₁₉

yes

characteristic

C₂²×D₄

—

C₂²×D₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₁₉

yes

—

C₂³×C₄

C₂×D₁₉

yes

—

#121

—

#120

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

C₁₉

#2847

yes

characteristic, complemented, Sylow

C₂⁴

—

100

C₂⁴

—

101

C₂⁴

—

102

C₂⁴

D₇₆

yes

complemented

103

C₂⁴

C₂²×D₁₉

yes

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

C₂²⋊D₁₉

yes

complemented

114

C₂²×C₄

C₂²×D₁₉

yes

—

115

C₂²×C₄

C₂²×D₁₉

yes

characteristic

116

C₄⋊C₄

—

117

C₂²⋊C₄

—

118

C₂²⋊C₄

—

119

C₂³

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

123

C₂³

—

124

C₂³

—

125

C₂³

—

126

C₂³

—

127

C₂³

C₂×D₇₆

yes

—

128

C₂³

#64541

yes

—

129

C₂³

C₂×C₂²⋊D₁₉

yes

—

130

C₂³

C₂³×D₁₉

yes

characteristic

131

D₄

—

132

D₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

140

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

#10597376

yes

complemented

150

C₂²

C₂²×D₇₆

yes

characteristic

151

C₂²

C₂×#64541

yes

—

152

C₂²

C₂²×C₂²⋊D₁₉

yes

—

153

C₄

—

154

C₄

—

155

C₄

#10597399

yes

complemented

156

C₂

—

157

C₂

—

152

—

158

C₂

C₂×#10597399

yes

characteristic

159

C₂

C₂×#10597376

yes

—

160

C₂

#11927055

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂⁴×C₄×C₁₉	C₂
hypercenter	C₂⁴×C₄	D₁₉
hypocenter	C₁₉	#2847
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂⁴×C₄×C₁₉

C₂

hypercenter

C₂⁴×C₄

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂⁴×C₄

N	H ≅ G/N	type
1. C₂×#10597376	C₂	semidirect
2. C₂×#10597399	C₂	semidirect
3. #11926423	C₂	semidirect
4. #11926404	C₂	semidirect
5. C₂⁴×C₄×C₁₉	C₂	semidirect
11. C₂²×D₇₆	C₂²	semidirect
15. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
16. C₂×C₄⋊Dic₁₉	C₂²	semidirect
17. C₁₉⋊#95	C₂²	semidirect
20. C₂⁴×C₁₉	D₄	semidirect
27. C₂²×C₄×C₁₉	D₄	semidirect
66. C₂²×C₁₉	#121	semidirect
74. C₄×C₁₉	#120	semidirect
76. C₂⁴×C₄	D₁₉	semidirect
98. C₁₉	#2847	semidirect
102. C₂⁴	D₇₆	semidirect
113. C₂²×C₄	C₂²⋊D₁₉	semidirect
149. C₂²	#10597376	semidirect
155. C₄	#10597399	semidirect

H ≅ G/N

type

1. C₂×#10597376

C₂

semidirect

2. C₂×#10597399

C₂

semidirect

3. #11926423

C₂

semidirect

4. #11926404

C₂

semidirect

5. C₂⁴×C₄×C₁₉

C₂

semidirect

11. C₂²×D₇₆

C₂²

semidirect

15. C₂×(C₂×D₁₉)⋊C₄

C₂²

semidirect

16. C₂×C₄⋊Dic₁₉

C₂²

semidirect

17. C₁₉⋊#95

C₂²

semidirect

20. C₂⁴×C₁₉

D₄

semidirect

27. C₂²×C₄×C₁₉

D₄

semidirect

66. C₂²×C₁₉

#121

semidirect

74. C₄×C₁₉

#120

semidirect

76. C₂⁴×C₄

D₁₉

semidirect

98. C₁₉

#2847

semidirect

102. C₂⁴

D₇₆

semidirect

113. C₂²×C₄

C₂²⋊D₁₉

semidirect

149. C₂²

#10597376

semidirect

155. C₄

#10597399

semidirect

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

subgroup	index
C₂×#10597376	2
C₂×#10597399	2
#11926423	2
#11926404	2
C₂⁴×C₄×C₁₉	2
#2847	19

subgroup

index

C₂⁴×C₄×C₁₉

Subgroups — #14571917

Conjugacy classes of subgroups

Complements

Maximal subgroups