Group #14566133 — subgroups

Subgroups — #14566133

Order 2432.

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

normal subgroups only

This group has 524 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	#11926437	C₂	1	4	yes	maximal
2	#11926430	C₂	1	4	yes	maximal, complemented
3	C₄×C₄⋊Dic₁₉	C₂	1	2	yes	maximal, complemented
4	C₄×C₂²⋊Dic₁₉	C₂	1	2	yes	maximal
5	#11926390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄²×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#117	C₄	1	8	yes	complemented
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
15	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
16	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
17	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
18	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
19	C₁₉⋊#95	C₂²	1	4	yes	—
20	C₁₉⋊#95	C₂²	1	4	yes	—
21	C₁₉⋊#95	C₂²	1	4	yes	—
22	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	—	2	4	no	—
24	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₁₉	C₂³	1	4	yes	—
30	C₂²×Dic₁₉	C₂³	1	4	yes	—
31	C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
32	C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
33	C₄²×C₁₉	C₂×C₄	1	4	yes	—
34	C₄²×C₁₉	C₂×C₄	1	4	yes	—
35	C₂²⋊Dic₁₉	—	2	8	no	—
36	C₄⋊Dic₁₉	—	2	8	no	—
37	C₄×Dic₁₉	—	2	4	no	—
38	C₄×Dic₁₉	—	2	4	no	—
39	C₄×Dic₁₉	—	2	8	no	—
40	C₂³×C₁₉	—	2	4	no	—
41	C₂³×C₁₉	—	2	2	no	—
42	C₂³×C₁₉	C₂²×C₄	1	2	yes	—
43	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
44	C₂×C₄×C₁₉	—	2	4	no	—
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	—	2	8	no	—
48	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
49	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
50	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
51	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
52	C₂×C₄×C₁₉	#41	1	4	yes	—
53	C₂×Dic₁₉	—	2	4	no	—
54	C₂×Dic₁₉	—	2	4	no	—
55	C₂×Dic₁₉	—	2	4	no	—
56	C₂×Dic₁₉	—	2	4	no	—
57	C₂×Dic₁₉	—	2	4	no	—
58	C₂×Dic₁₉	#41	1	8	yes	—
59	#2298	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	—	2	2	no	—
61	C₂²×C₁₉	—	2	4	no	—
62	C₂²×C₁₉	—	4	4	no	—
63	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
64	C₂²×C₁₉	C₂×#41	1	2	yes	—
65	C₂²×C₁₉	C₂×#41	1	4	yes	—
66	C₄×C₁₉	—	2	2	no	—
67	C₄×C₁₉	—	2	4	no	—
68	C₄×C₁₉	—	2	4	no	—
69	C₄×C₁₉	#117	1	4	yes	—
70	Dic₁₉	—	2	8	no	—
71	Dic₁₉	—	4	4	no	—
72	C₂×#117	D₁₉	1	1	yes	characteristic
73	#388	—	19	4	no	—
74	#387	—	19	4	no	—
75	C₄×C₄⋊C₄	—	19	2	no	—
76	C₄×C₂²⋊C₄	—	19	2	no	—
77	#376	—	19	1	no	—
78	C₄³	—	19	1	no	—
79	C₂×C₁₉	—	4	2	no	—
80	C₂×C₁₉	C₂×#117	1	1	yes	characteristic
81	C₂×C₁₉	C₄×#41	1	2	yes	—
82	C₂×C₁₉	#529	1	4	yes	—
83	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
84	#117	Dic₁₉	1	8	yes	complemented
85	C₂×C₄⋊C₄	—	19	4	no	—
86	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
87	C₂×C₂²⋊C₄	—	19	4	no	—
88	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
89	C₂×C₄²	—	19	4	no	—
90	C₂×C₄²	—	19	2	no	—
91	C₂×C₄²	—	19	2	no	—
92	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
93	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
94	#95	—	19	4	no	—
95	#95	—	19	4	no	—
96	#95	—	19	4	no	—
97	C₁₉	#2298	1	1	yes	characteristic, complemented, Sylow
98	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
99	C₂²×C₄	—	2	4	no	—
100	C₂²×C₄	—	19	4	no	—
101	C₂²×C₄	—	19	4	no	—
102	C₂²×C₄	C₂×Dic₁₉	1	4	yes	—
103	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
104	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
105	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
106	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
107	C₄⋊C₄	—	38	8	no	—
108	C₄⋊C₄	C₂×Dic₁₉	1	8	yes	—
109	C₂²⋊C₄	—	38	8	no	—
110	C₂²⋊C₄	C₂×Dic₁₉	1	8	yes	—
111	C₄²	—	38	8	no	—
112	C₄²	—	38	4	no	—
113	C₄²	—	38	4	no	—
114	C₄²	C₂×Dic₁₉	1	4	yes	—
115	C₄²	C₂×Dic₁₉	1	4	yes	—
116	C₂³	—	2	2	no	—
117	C₂³	—	2	4	no	—
118	C₂³	C₂²×Dic₁₉	1	2	yes	—
119	C₂³	C₂³×D₁₉	1	1	yes	characteristic
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	—	2	8	no	—
124	C₂×C₄	—	19	8	no	—
125	C₂×C₄	—	38	4	no	—
126	C₂×C₄	—	38	4	no	—
127	C₂×C₄	—	38	4	no	—
128	C₂×C₄	—	38	4	no	—
129	C₂×C₄	—	38	4	no	—
130	C₂×C₄	#64541	1	4	yes	—
131	C₂×C₄	C₂²×Dic₁₉	1	4	yes	—
132	C₂×C₄	C₂²×Dic₁₉	1	4	yes	—
133	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
134	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
135	C₂²	—	2	2	no	—
136	C₂²	—	2	4	no	—
137	C₂²	—	4	4	no	—
138	C₂²	C₂×#64541	1	2	yes	—
139	C₂²	#41×D₁₉	1	4	yes	—
140	C₂²	C₂³×Dic₁₉	1	1	yes	characteristic
141	C₄	—	2	2	no	—
142	C₄	—	2	4	no	—
143	C₄	—	2	4	no	—
144	C₄	—	38	8	no	—
145	C₄	—	76	4	no	—
146	C₄	#10597372	1	4	yes	—
147	C₂	—	4	2	no	—
148	C₂	C₂×#10597372	1	1	yes	characteristic
149	C₂	#41×Dic₁₉	1	2	yes	—
150	C₂	#11927072	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926437

C₂

yes

maximal

#11926430

C₂

yes

maximal, complemented

C₄×C₄⋊Dic₁₉

C₂

yes

maximal, complemented

C₄×C₂²⋊Dic₁₉

C₂

yes

maximal

#11926390

C₂

yes

maximal, characteristic, complemented

C₄²×Dic₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#117

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₄

yes

complemented

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂×C₄

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²×C₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#41

yes

—

#2298

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

C₂×#41

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#117

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×#117

D₁₉

yes

characteristic

#388

—

#387

—

C₄×C₄⋊C₄

—

C₄×C₂²⋊C₄

—

#376

—

C₄³

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#117

yes

characteristic

C₂×C₁₉

C₄×#41

yes

—

C₂×C₁₉

#529

yes

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

#117

Dic₁₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

—

—

—

C₁₉

#2298

yes

characteristic, complemented, Sylow

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₂×Dic₁₉

yes

—

103

C₂²×C₄

C₂²×D₁₉

yes

characteristic

104

C₂²×C₄

C₂²×D₁₉

yes

—

105

C₂²×C₄

C₂²×D₁₉

yes

—

106

C₂²×C₄

C₂²×D₁₉

yes

characteristic

107

C₄⋊C₄

—

108

C₄⋊C₄

C₂×Dic₁₉

yes

—

109

C₂²⋊C₄

—

110

C₂²⋊C₄

C₂×Dic₁₉

yes

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

C₂×Dic₁₉

yes

—

115

C₄²

C₂×Dic₁₉

yes

—

116

C₂³

—

117

C₂³

—

118

C₂³

C₂²×Dic₁₉

yes

—

119

C₂³

C₂³×D₁₉

yes

characteristic

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

#64541

yes

—

131

C₂×C₄

C₂²×Dic₁₉

yes

—

132

C₂×C₄

C₂²×Dic₁₉

yes

—

133

C₂×C₄

C₂²×Dic₁₉

yes

—

134

C₂×C₄

C₂²×Dic₁₉

yes

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

C₂×#64541

yes

—

139

C₂²

#41×D₁₉

yes

—

140

C₂²

C₂³×Dic₁₉

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

#10597372

yes

—

147

C₂

—

148

C₂

C₂×#10597372

yes

characteristic

149

C₂

#41×Dic₁₉

yes

—

150

C₂

#11927072

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂³×C₄
Frattini	C₂³	C₂³×D₁₉
Fitting	C₂×C₁₉×#117	C₂
socle, cosocle	C₂³×C₁₉	C₂⁴
prime radical	C₂⁴×C₁₉	C₂³
hypercenter	C₂×#117	D₁₉
hypocenter	C₁₉	#2298
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#117

subgroup

G/H

center

C₂²×C₄

C₂²×D₁₉

commutator

C₂²×C₁₉

C₂³×C₄

Frattini

C₂³

C₂³×D₁₉

Fitting

C₂×C₁₉×#117

C₂

socle, cosocle

C₂³×C₁₉

C₂⁴

prime radical

C₂⁴×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂²×C₄ ◁ C₂×#117

N	H ≅ G/N	type
2. #11926430	C₂	semidirect
3. C₄×C₄⋊Dic₁₉	C₂	semidirect
5. #11926390	C₂	semidirect
6. C₄²×Dic₁₉	C₂	semidirect
9. C₁₉×#117	C₄	semidirect
84. #117	Dic₁₉	semidirect
97. C₁₉	#2298	semidirect

H ≅ G/N

type

2. #11926430

C₂

semidirect

3. C₄×C₄⋊Dic₁₉

C₂

semidirect

5. #11926390

C₂

semidirect

6. C₄²×Dic₁₉

C₂

semidirect

9. C₁₉×#117

C₄

semidirect

84. #117

Dic₁₉

semidirect

97. C₁₉

#2298

semidirect

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

subgroup	index
#11926437	2
#11926430	2
C₄×C₄⋊Dic₁₉	2
C₄×C₂²⋊Dic₁₉	2
#11926390	2
C₄²×Dic₁₉	2
C₂×C₁₉×#117	2
#2298	19

subgroup

index

#11926437

#11926430

C₄×C₄⋊Dic₁₉

C₄×C₂²⋊Dic₁₉

#11926390

C₄²×Dic₁₉

C₂×C₁₉×#117

#2298

Subgroups — #14566133

Conjugacy classes of subgroups

Complements

Maximal subgroups