Group #14568113 — subgroups

Subgroups — #14568113

Order 2432.

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

normal subgroups only

This group has 544 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×#10597370	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	#11926476	C₂	1	4	yes	maximal, complemented
4	#11926450	C₂	1	2	yes	maximal, complemented
5	#11926419	C₂	1	4	yes	maximal
6	#11926414	C₂	1	2	yes	maximal, complemented
7	C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×Dic₁₉	C₂²	1	2	yes	—
10	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
13	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂×C₄⋊Dic₁₉	—	2	4	no	—
15	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
17	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
18	C₂×C₄⋊Dic₁₉	C₂²	1	8	yes	—
19	#10597370	—	2	4	no	—
20	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
21	C₁₉×#95	C₂²	1	2	yes	—
22	C₁₉⋊#95	C₂²	1	8	yes	—
23	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	—	2	4	no	—
25	C₂²×C₄×C₁₉	D₄	1	4	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₁₉	—	2	4	no	—
30	C₂²×Dic₁₉	—	4	4	no	—
31	C₂²×Dic₁₉	C₂³	1	2	yes	—
32	C₂²×Dic₁₉	C₂³	1	2	yes	—
33	C₂²×Dic₁₉	C₂³	1	4	yes	—
34	C₂×Dic₃₈	—	2	2	no	—
35	C₂×Dic₃₈	—	2	4	no	—
36	C₂²⋊C₄×C₁₉	Q₈	1	8	yes	complemented
37	C₄²×C₁₉	—	2	4	no	—
38	C₂²⋊Dic₁₉	—	2	4	no	—
39	C₄⋊Dic₁₉	—	2	2	no	—
40	C₄⋊Dic₁₉	—	2	4	no	—
41	C₄⋊Dic₁₉	—	2	4	no	—
42	C₄⋊Dic₁₉	—	4	8	no	—
43	Dic₁₉⋊C₄	—	2	4	no	—
44	C₂³×C₁₉	—	2	2	no	—
45	C₂³×C₁₉	—	2	2	no	—
46	C₂³×C₁₉	C₂×D₄	1	2	yes	—
47	C₂³×C₁₉	C₂×Q₈	1	4	yes	—
48	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
49	C₂×C₄×C₁₉	—	2	4	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	4	no	—
52	C₂×C₄×C₁₉	—	2	8	no	—
53	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
55	C₂×C₄×C₁₉	C₂×Q₈	1	8	yes	—
56	C₂×C₄×C₁₉	#41	1	4	yes	—
57	C₂×Dic₁₉	—	2	2	no	—
58	C₂×Dic₁₉	—	2	2	no	—
59	C₂×Dic₁₉	—	2	4	no	—
60	C₂×Dic₁₉	—	2	4	no	—
61	C₂×Dic₁₉	—	2	4	no	—
62	C₂×Dic₁₉	—	2	8	no	—
63	C₂×Dic₁₉	—	4	8	no	—
64	Dic₃₈	—	4	4	no	—
65	#2502	—	19	1	no	maximal, Sylow
66	C₂²×C₁₉	—	2	2	no	—
67	C₂²×C₁₉	—	2	2	no	—
68	C₂²×C₁₉	—	2	8	no	—
69	C₂²×C₁₉	C₄⋊Q₈	1	4	yes	—
70	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
71	C₂²×C₁₉	C₂²×Q₈	1	2	yes	—
72	C₂²×C₁₉	C₂×#41	1	2	yes	—
73	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
74	C₄×C₁₉	—	2	2	no	—
75	C₄×C₁₉	—	2	8	no	—
76	C₄×C₁₉	#123	1	4	yes	—
77	Dic₁₉	—	4	2	no	—
78	Dic₁₉	—	4	2	no	—
79	Dic₁₉	—	4	4	no	—
80	C₂×C₂²⋊Q₈	—	19	1	no	—
81	C₂²×C₄⋊C₄	—	19	1	no	—
82	#398	—	19	4	no	—
83	#391	—	19	2	no	—
84	#385	—	19	4	no	—
85	#384	—	19	2	no	—
86	C₄×C₂²⋊C₄	D₁₉	1	1	yes	characteristic
87	C₂×C₁₉	—	2	4	no	—
88	C₂×C₁₉	C₂×#123	1	1	yes	characteristic
89	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
90	C₂×C₁₉	#535	1	1	yes	characteristic
91	C₂×C₁₉	#554	1	4	yes	—
92	C₂²×Q₈	—	19	1	no	—
93	C₂³×C₄	—	19	2	no	—
94	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
95	C₂²⋊Q₈	—	38	4	no	—
96	C₂×C₄⋊C₄	—	19	2	no	—
97	C₂×C₄⋊C₄	—	19	2	no	—
98	C₂×C₄⋊C₄	—	19	1	no	—
99	C₂×C₄⋊C₄	—	19	2	no	—
100	C₂×C₄⋊C₄	—	19	8	no	—
101	C₂×C₄⋊C₄	—	38	4	no	—
102	C₂×C₂²⋊C₄	—	19	2	no	—
103	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
104	C₂×C₄²	C₂×D₁₉	1	2	yes	—
105	#95	—	19	8	no	—
106	#95	C₂×D₁₉	1	2	yes	—
107	C₁₉	#2502	1	1	yes	characteristic, complemented, Sylow
108	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
109	C₂×Q₈	—	38	2	no	—
110	C₂×Q₈	—	38	4	no	—
111	C₂²×C₄	—	2	4	no	—
112	C₂²×C₄	—	19	2	no	—
113	C₂²×C₄	—	19	4	no	—
114	C₂²×C₄	—	19	2	no	—
115	C₂²×C₄	—	38	4	no	—
116	C₂²×C₄	—	76	4	no	—
117	C₂²×C₄	D₇₆	1	4	yes	—
118	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
119	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
120	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
121	C₄⋊C₄	—	38	4	no	—
122	C₄⋊C₄	—	38	4	no	—
123	C₄⋊C₄	—	38	4	no	—
124	C₄⋊C₄	—	38	2	no	—
125	C₄⋊C₄	—	76	8	no	—
126	C₂²⋊C₄	—	38	4	no	—
127	C₂²⋊C₄	Dic₃₈	1	8	yes	complemented
128	C₄²	—	2	4	no	—
129	C₂³	—	2	2	no	—
130	C₂³	—	2	2	no	—
131	C₂³	C₂×Dic₃₈	1	4	yes	—
132	C₂³	C₂×D₇₆	1	2	yes	—
133	C₂³	C₂³×D₁₉	1	1	yes	characteristic
134	Q₈	—	76	4	no	—
135	C₂×C₄	—	2	4	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	2	8	no	—
139	C₂×C₄	—	38	2	no	—
140	C₂×C₄	—	38	2	no	—
141	C₂×C₄	—	38	4	no	—
142	C₂×C₄	—	38	4	no	—
143	C₂×C₄	—	38	4	no	—
144	C₂×C₄	—	38	8	no	—
145	C₂×C₄	—	76	8	no	—
146	C₂×C₄	C₂×Dic₃₈	1	8	yes	—
147	C₂×C₄	C₂×D₇₆	1	2	yes	—
148	C₂×C₄	C₂×D₇₆	1	2	yes	—
149	C₂×C₄	#64543	1	4	yes	—
150	C₂²	—	2	2	no	—
151	C₂²	—	2	2	no	—
152	C₂²	—	2	8	no	—
153	C₂²	#10597315	1	4	yes	—
154	C₂²	C₂²×Dic₃₈	1	2	yes	—
155	C₂²	C₂²×D₇₆	1	1	yes	characteristic
156	C₂²	C₂×#64543	1	2	yes	—
157	C₂²	#10597435	1	2	yes	—
158	C₄	—	2	2	no	—
159	C₄	—	2	8	no	—
160	C₄	—	76	2	no	—
161	C₄	—	76	4	no	—
162	C₄	—	76	2	no	—
163	C₄	#10597332	1	4	yes	—
164	C₂	—	2	4	no	—
165	C₂	C₂×#10597332	1	1	yes	characteristic
166	C₂	C₂×#10597315	1	1	yes	characteristic
167	C₂	#11927113	1	1	yes	characteristic
168	C₂	#11927251	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597370

C₂

yes

maximal, characteristic

C₂²×C₄⋊Dic₁₉

C₂

yes

maximal, characteristic

#11926476

C₂

yes

maximal, complemented

#11926450

C₂

yes

maximal, complemented

#11926419

C₂

yes

maximal

#11926414

C₂

yes

maximal, complemented

C₄×C₂²⋊C₄×C₁₉

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂³×Dic₁₉

C₂²

yes

—

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597370

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂²⋊C₄×C₁₉

Q₈

yes

complemented

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

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

—

Dic₃₈

—

#2502

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄⋊Q₈

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

—

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#123

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₂²⋊Q₈

—

C₂²×C₄⋊C₄

—

—

—

—

—

C₄×C₂²⋊C₄

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

C₂×#123

yes

characteristic

C₂×C₁₉

C₂×C₄⋊Q₈

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂²×Q₈

—

C₂³×C₄

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

100

C₂×C₄⋊C₄

—

101

C₂×C₄⋊C₄

—

102

C₂×C₂²⋊C₄

—

103

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

104

C₂×C₄²

C₂×D₁₉

yes

—

105

#95

—

106

#95

C₂×D₁₉

yes

—

107

C₁₉

#2502

yes

characteristic, complemented, Sylow

108

C₂⁴

C₂²×D₁₉

yes

characteristic

109

C₂×Q₈

—

110

C₂×Q₈

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

D₇₆

yes

—

118

C₂²×C₄

C₂²×D₁₉

yes

—

119

C₂²×C₄

C₂²×D₁₉

yes

characteristic

120

C₂²×C₄

C₂²×D₁₉

yes

characteristic

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₂²⋊C₄

—

127

C₂²⋊C₄

Dic₃₈

yes

complemented

128

C₄²

—

129

C₂³

—

130

C₂³

—

131

C₂³

C₂×Dic₃₈

yes

—

132

C₂³

C₂×D₇₆

yes

—

133

C₂³

C₂³×D₁₉

yes

characteristic

134

Q₈

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

C₂×Dic₃₈

yes

—

147

C₂×C₄

C₂×D₇₆

yes

—

148

C₂×C₄

C₂×D₇₆

yes

—

149

C₂×C₄

#64543

yes

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

#10597315

yes

—

154

C₂²

C₂²×Dic₃₈

yes

—

155

C₂²

C₂²×D₇₆

yes

characteristic

156

C₂²

C₂×#64543

yes

—

157

C₂²

#10597435

yes

—

158

C₄

—

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

#10597332

yes

—

164

C₂

—

165

C₂

C₂×#10597332

yes

characteristic

166

C₂

C₂×#10597315

yes

characteristic

167

C₂

#11927113

yes

characteristic

168

C₂

#11927251

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₄×C₂²⋊C₄×C₁₉	C₂
prime radical	C₂⁴×C₁₉	C₂³
hypercenter	C₄×C₂²⋊C₄	D₁₉
hypocenter	C₁₉	#2502
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₄×C₂²⋊C₄×C₁₉

C₂

prime radical

C₂⁴×C₁₉

C₂³

hypercenter

C₄×C₂²⋊C₄

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄

N	H ≅ G/N	type
3. #11926476	C₂	semidirect
4. #11926450	C₂	semidirect
6. #11926414	C₂	semidirect
36. C₂²⋊C₄×C₁₉	Q₈	semidirect
107. C₁₉	#2502	semidirect
127. C₂²⋊C₄	Dic₃₈	semidirect

H ≅ G/N

type

3. #11926476

C₂

semidirect

4. #11926450

C₂

semidirect

6. #11926414

C₂

semidirect

36. C₂²⋊C₄×C₁₉

Q₈

semidirect

107. C₁₉

#2502

semidirect

127. C₂²⋊C₄

Dic₃₈

semidirect

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

subgroup	index
C₂×#10597370	2
C₂²×C₄⋊Dic₁₉	2
#11926476	2
#11926450	2
#11926419	2
#11926414	2
C₄×C₂²⋊C₄×C₁₉	2
#2502	19

subgroup

index

C₂²×C₄⋊Dic₁₉

C₄×C₂²⋊C₄×C₁₉

Subgroups — #14568113

Conjugacy classes of subgroups

Complements

Maximal subgroups