Group #14566374 — subgroups

Subgroups — #14566374

Order 2432.

444 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 197 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×#10597316	C₂	1	1	yes	maximal, characteristic
2	#11926440	C₂	1	2	yes	maximal
3	#11926439	C₂	1	4	yes	maximal
4	#11926425	C₂	1	4	yes	maximal
5	C₄⋊C₄×Dic₁₉	C₂	1	2	yes	maximal
6	#11926390	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#384	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
12	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
13	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
14	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
16	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
17	#10597316	C₄	1	8	yes	complemented
18	C₁₉⋊#95	C₂²	1	2	yes	—
19	C₁₉⋊#95	C₂²	1	2	yes	—
20	C₁₉⋊#95	C₂²	1	4	yes	—
21	C₁₉⋊#95	C₂²	1	4	yes	—
22	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
24	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
27	C₂²×Dic₁₉	C₂³	1	4	yes	—
28	C₂²×Dic₁₉	C₂³	1	2	yes	—
29	C₄⋊C₄×C₁₉	—	2	4	no	—
30	C₄⋊C₄×C₁₉	—	4	4	no	—
31	C₄²×C₁₉	C₂×C₄	1	4	yes	—
32	C₄⋊Dic₁₉	C₂×C₄	1	8	yes	—
33	Dic₁₉⋊C₄	—	4	4	no	—
34	Dic₁₉⋊C₄	C₂×C₄	1	16	yes	—
35	C₄×Dic₁₉	—	2	2	no	—
36	C₄×Dic₁₉	—	4	4	no	—
37	C₄×Dic₁₉	Q₈	1	4	yes	—
38	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
39	C₂×C₄×C₁₉	—	2	2	no	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	4	no	—
42	C₂×C₄×C₁₉	—	2	4	no	—
43	C₂×C₄×C₁₉	—	2	4	no	—
44	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
45	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
46	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
47	C₂×C₄×C₁₉	#41	1	2	yes	—
48	C₂×Dic₁₉	—	2	2	no	—
49	C₂×Dic₁₉	—	2	4	no	—
50	C₂×Dic₁₉	—	2	4	no	—
51	C₂×Dic₁₉	—	2	2	no	—
52	C₂×Dic₁₉	—	2	1	no	—
53	C₂×Dic₁₉	—	2	1	no	—
54	C₂×Dic₁₉	—	2	2	no	—
55	C₂×Dic₁₉	—	2	2	no	—
56	C₂×Dic₁₉	C₂²×C₄	1	8	yes	—
57	C₂×Dic₁₉	C₂×Q₈	1	4	yes	—
58	#2330	—	19	1	no	maximal, Sylow
59	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
60	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
61	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
62	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
63	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
64	C₄×C₁₉	—	2	4	no	—
65	C₄×C₁₉	—	4	4	no	—
66	C₄×C₁₉	C₄×Q₈	1	4	yes	—
67	Dic₁₉	—	2	8	no	—
68	Dic₁₉	—	2	4	no	—
69	Dic₁₉	—	4	1	no	—
70	Dic₁₉	—	4	1	no	—
71	C₂×#125	—	19	1	no	—
72	#389	—	19	4	no	—
73	#389	—	19	2	no	—
74	#387	—	19	4	no	—
75	#384	D₁₉	1	1	yes	characteristic
76	C₄×C₄⋊C₄	—	19	2	no	—
77	#376	—	19	1	no	—
78	C₂×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
79	C₂×C₁₉	#520	1	2	yes	—
80	C₂×C₁₉	#540	1	1	yes	characteristic
81	C₂×C₁₉	#541	1	1	yes	characteristic
82	C₂×C₁₉	#544	1	2	yes	—
83	#125	—	19	8	no	—
84	C₂×C₄⋊C₄	—	19	2	no	—
85	C₂×C₄⋊C₄	—	19	4	no	—
86	C₂×C₄⋊C₄	—	19	4	no	—
87	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
88	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
89	C₂×C₄²	—	19	1	no	—
90	C₂×C₄²	—	19	1	no	—
91	C₂×C₄²	—	19	4	no	—
92	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
93	#95	—	19	2	no	—
94	#95	—	19	2	no	—
95	#95	—	19	4	no	—
96	#95	—	19	4	no	—
97	C₁₉	#2330	1	1	yes	characteristic, complemented, Sylow
98	C₂²×C₄	—	19	2	no	—
99	C₂²×C₄	—	19	4	no	—
100	C₂²×C₄	—	19	1	no	—
101	C₂²×C₄	—	19	1	no	—
102	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
103	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
104	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
105	C₄⋊C₄	—	2	4	no	—
106	C₄⋊C₄	—	4	4	no	—
107	C₄⋊C₄	—	19	16	no	—
108	C₄⋊C₄	—	19	8	no	—
109	C₄⋊C₄	—	76	4	no	—
110	C₄²	—	19	4	no	—
111	C₄²	—	38	2	no	—
112	C₄²	—	76	4	no	—
113	C₄²	C₄×D₁₉	1	4	yes	—
114	C₂³	C₂³×D₁₉	1	1	yes	characteristic
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	4	no	—
118	C₂×C₄	—	2	4	no	—
119	C₂×C₄	—	2	4	no	—
120	C₂×C₄	—	19	8	no	—
121	C₂×C₄	—	19	4	no	—
122	C₂×C₄	—	38	2	no	—
123	C₂×C₄	—	38	4	no	—
124	C₂×C₄	—	38	2	no	—
125	C₂×C₄	—	38	4	no	—
126	C₂×C₄	—	38	1	no	—
127	C₂×C₄	—	38	1	no	—
128	C₂×C₄	—	38	2	no	—
129	C₂×C₄	—	38	2	no	—
130	C₂×C₄	C₂×C₄×D₁₉	1	4	yes	—
131	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
132	C₂×C₄	#64543	1	2	yes	—
133	C₂×C₄	Q₈×D₁₉	1	2	yes	—
134	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
135	C₂²	C₂×#64543	1	1	yes	characteristic
136	C₂²	#10597430	1	2	yes	—
137	C₂²	C₂×Q₈×D₁₉	1	1	yes	characteristic
138	C₂²	#10597433	1	2	yes	—
139	C₄	—	2	4	no	—
140	C₄	—	4	4	no	—
141	C₄	—	38	4	no	—
142	C₄	—	38	8	no	—
143	C₄	—	76	1	no	—
144	C₄	—	76	1	no	—
145	C₄	#10597333	1	4	yes	—
146	C₂	C₂×#10597333	1	1	yes	characteristic
147	C₂	#11927025	1	2	yes	—
148	C₂	#11927148	1	1	yes	characteristic
149	C₂	#11927155	1	1	yes	characteristic
150	C₂	#11927171	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597316

C₂

yes

maximal, characteristic

#11926440

C₂

yes

maximal

#11926439

C₂

yes

maximal

#11926425

C₂

yes

maximal

C₄⋊C₄×Dic₁₉

C₂

yes

maximal

#11926390

C₂

yes

maximal, characteristic

C₁₉×#384

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

#10597316

C₄

yes

complemented

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

C₂×C₄

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

Q₈

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

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

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂²×C₄

yes

—

C₂×Dic₁₉

C₂×Q₈

yes

—

#2330

—

maximal, Sylow

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic

C₄×C₄⋊C₄

—

#376

—

C₂×C₁₉

C₂×C₄×Q₈

yes

characteristic

C₂×C₁₉

#520

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

—

C₁₉

#2330

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₂²×D₁₉

yes

—

103

C₂²×C₄

C₂²×D₁₉

yes

—

104

C₂²×C₄

C₂²×D₁₉

yes

characteristic

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

113

C₄²

C₄×D₁₉

yes

—

114

C₂³

C₂³×D₁₉

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

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

C₂×C₄×D₁₉

yes

—

131

C₂×C₄

C₂×C₄×D₁₉

yes

—

132

C₂×C₄

#64543

yes

—

133

C₂×C₄

Q₈×D₁₉

yes

—

134

C₂²

C₂²×C₄×D₁₉

yes

characteristic

135

C₂²

C₂×#64543

yes

characteristic

136

C₂²

#10597430

yes

—

137

C₂²

C₂×Q₈×D₁₉

yes

characteristic

138

C₂²

#10597433

yes

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

#10597333

yes

—

146

C₂

C₂×#10597333

yes

characteristic

147

C₂

#11927025

yes

—

148

C₂

#11927148

yes

characteristic

149

C₂

#11927155

yes

characteristic

150

C₂

#11927171

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#384	C₂
socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
hypercenter	#384	D₁₉
hypocenter	C₁₉	#2330
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator

C₂²×C₁₉

C₂³×C₄

Fitting

C₁₉×#384

C₂

socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
17. #10597316	C₄	semidirect
97. C₁₉	#2330	semidirect

H ≅ G/N

type

17. #10597316

C₄

semidirect

97. C₁₉

#2330

semidirect

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

subgroup	index
C₂×#10597316	2
#11926440	2
#11926439	2
#11926425	2
C₄⋊C₄×Dic₁₉	2
#11926390	2
C₁₉×#384	2
#2330	19

subgroup

index

C₄⋊C₄×Dic₁₉

C₁₉×#384

Subgroups — #14566374

Conjugacy classes of subgroups

Complements

Maximal subgroups