Group #14574011 — subgroups

Subgroups — #14574011

Order 2432.

484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10597320	C₂	1	1	yes	maximal, characteristic
2	#11926910	C₂	1	4	yes	maximal, complemented
3	#11926892	C₂	1	4	yes	maximal, complemented
4	#11926548	C₂	1	4	yes	maximal, complemented
5	C₄×#64520	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₇₆	—	2	2	no	—
8	C₂²×D₇₆	C₂²	1	2	yes	—
9	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
10	C₁₉×#125	C₂²	1	2	yes	complemented
11	C₁₉×C₂²⋊Q₈	—	2	2	no	—
12	C₄×Q₈×C₁₉	—	2	2	no	—
13	C₁₉×#117	C₂²	1	2	yes	—
14	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×#64520	C₂²	1	2	yes	—
16	#10597320	—	2	2	no	—
17	#10597320	C₂²	1	2	yes	—
18	#10597320	C₂²	1	2	yes	—
19	#10597266	C₂²	1	16	yes	complemented
20	#10597260	C₂²	1	2	yes	complemented
21	C₄×C₁₉⋊C₈	C₂²	1	2	yes	complemented
22	C₂³×D₁₉	—	2	2	no	—
23	C₂×Q₈×C₁₉	—	2	2	no	—
24	C₂²×C₄×C₁₉	D₄	1	2	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×D₇₆	—	2	8	no	—
27	C₂×D₇₆	—	2	4	no	—
28	C₂×D₇₆	—	2	4	no	—
29	C₂×D₇₆	—	2	2	no	—
30	C₂×D₇₆	—	4	8	no	—
31	C₂×D₇₆	C₂³	1	4	yes	—
32	C₄⋊C₄×C₁₉	—	2	4	no	—
33	C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
35	C₂²⋊C₄×C₁₉	—	2	2	no	—
36	C₄²×C₁₉	—	2	2	no	—
37	C₄²×C₁₉	D₄	1	2	yes	—
38	C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	#64520	—	2	4	no	—
41	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
42	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂²×D₁₉	—	2	4	no	—
44	C₂²×D₁₉	—	4	8	no	—
45	C₂²×D₁₉	—	4	4	no	—
46	Q₈×C₁₉	—	4	4	no	—
47	C₂×C₄×C₁₉	—	2	4	no	—
48	C₂×C₄×C₁₉	—	2	4	no	—
49	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
52	C₂×C₄×C₁₉	#41	1	4	yes	—
53	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
54	D₇₆	—	2	8	no	—
55	D₇₆	—	4	8	no	—
56	D₇₆	—	4	4	no	—
57	D₇₆	—	4	8	no	—
58	C₁₉⋊C₈	—	2	4	no	—
59	#3138	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	—	2	2	no	—
61	C₂²×C₁₉	#124	1	2	yes	—
62	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
63	C₂×D₁₉	—	4	4	no	—
64	C₂×D₁₉	—	4	8	no	—
65	C₂×D₁₉	—	8	8	no	—
66	C₄×C₁₉	—	2	2	no	—
67	C₄×C₁₉	—	4	4	no	—
68	C₄×C₁₉	#124	1	2	yes	—
69	C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
70	C₄×C₁₉	C₂×#41	1	2	yes	—
71	#533	D₁₉	1	1	yes	characteristic, complemented
72	C₂×#127	—	19	1	no	—
73	#490	—	19	4	no	—
74	#486	—	19	4	no	—
75	#418	—	19	4	no	—
76	C₄×M₁₆	—	19	1	no	—
77	C₂×C₁₉	—	2	2	no	—
78	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
79	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
80	D₁₉	—	8	4	no	—
81	C₂²×D₄	—	19	2	no	—
82	C₂²×D₄	—	38	2	no	—
83	C₂×M₁₆	—	19	2	no	—
84	C₄⋊Q₈	C₂×D₁₉	1	2	yes	complemented
85	#127	—	19	2	no	—
86	#127	—	19	2	no	—
87	#127	—	38	2	no	—
88	#125	C₂×D₁₉	1	2	yes	complemented
89	C₂²⋊Q₈	—	2	2	no	—
90	C₄×Q₈	—	2	2	no	—
91	#117	C₂×D₁₉	1	2	yes	—
92	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
93	#102	—	19	16	no	—
94	#97	—	19	2	no	—
95	C₄×C₈	—	19	2	no	—
96	C₁₉	#3138	1	1	yes	characteristic, complemented, Sylow
97	C₂⁴	—	38	2	no	—
98	C₂×Q₈	—	2	2	no	—
99	C₂×D₄	—	19	4	no	—
100	C₂×D₄	—	38	8	no	—
101	C₂×D₄	—	38	4	no	—
102	C₂×D₄	—	38	4	no	—
103	C₂×D₄	—	38	2	no	—
104	C₂×D₄	—	76	8	no	—
105	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
106	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
107	M₁₆	—	38	4	no	—
108	C₂×C₈	—	19	4	no	—
109	C₄⋊C₄	—	2	4	no	—
110	C₄⋊C₄	—	2	2	no	—
111	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
112	C₂²⋊C₄	—	2	2	no	—
113	C₄²	—	2	2	no	—
114	C₄²	C₂²⋊D₁₉	1	2	yes	—
115	C₄²	C₂²×D₁₉	1	1	yes	characteristic
116	C₄²	C₂²×D₁₉	1	1	yes	characteristic
117	C₂³	—	38	4	no	—
118	C₂³	—	76	8	no	—
119	C₂³	—	76	4	no	—
120	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
121	Q₈	—	4	4	no	—
122	D₄	—	38	8	no	—
123	D₄	—	76	8	no	—
124	D₄	—	76	4	no	—
125	D₄	—	76	8	no	—
126	C₂×C₄	—	2	4	no	—
127	C₂×C₄	—	2	4	no	—
128	C₂×C₄	#64545	1	4	yes	—
129	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
130	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
131	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
132	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
133	C₈	—	38	4	no	—
134	C₂²	—	2	2	no	—
135	C₂²	—	76	4	no	—
136	C₂²	—	76	8	no	—
137	C₂²	—	152	8	no	—
138	C₂²	#10597393	1	2	yes	—
139	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
140	C₄	—	2	2	no	—
141	C₄	—	4	4	no	—
142	C₄	#10597393	1	2	yes	—
143	C₄	#10597395	1	4	yes	—
144	C₄	C₂×#64545	1	2	yes	—
145	C₂	—	2	2	no	—
146	C₂	—	152	4	no	—
147	C₂	C₂×#10597393	1	1	yes	characteristic
148	C₂	C₂×#10597395	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597320

C₂

yes

maximal, characteristic

#11926910

C₂

yes

maximal, complemented

#11926892

C₂

yes

maximal, complemented

#11926548

C₂

yes

maximal, complemented

C₄×#64520

C₂

yes

maximal, characteristic, complemented

C₁₉×#533

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

—

C₂²×D₇₆

C₂²

yes

—

C₁₉×C₄⋊Q₈

C₂²

yes

complemented

C₁₉×#125

C₂²

yes

complemented

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

#10597320

—

#10597320

C₂²

yes

—

#10597320

C₂²

yes

—

#10597266

C₂²

yes

complemented

#10597260

C₂²

yes

complemented

C₄×C₁₉⋊C₈

C₂²

yes

complemented

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₁₉⋊C₈

—

#3138

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#124

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

C₂×#41

yes

—

#533

D₁₉

yes

characteristic, complemented

—

—

—

—

C₄×M₁₆

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#124

yes

characteristic

C₂×C₁₉

C₂×AGL(1,ℤ/8)

yes

—

D₁₉

—

C₂²×D₄

—

C₂²×D₄

—

C₂×M₁₆

—

C₄⋊Q₈

C₂×D₁₉

yes

—

—

—

C₂×D₁₉

yes

complemented

C₂²⋊Q₈

—

C₄×Q₈

—

#117

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#102

—

#97

—

C₄×C₈

—

C₁₉

#3138

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×Q₈

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂²×C₄

C₂²⋊D₁₉

yes

—

106

C₂²×C₄

C₂²×D₁₉

yes

characteristic

107

M₁₆

—

108

C₂×C₈

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

C₂²×D₁₉

yes

—

112

C₂²⋊C₄

—

113

C₄²

—

114

C₄²

C₂²⋊D₁₉

yes

—

115

C₄²

C₂²×D₁₉

yes

characteristic

116

C₄²

C₂²×D₁₉

yes

characteristic

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

121

Q₈

—

122

D₄

—

123

D₄

—

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

#64545

yes

—

129

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

130

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

131

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

132

C₂×C₄

C₂³×D₁₉

yes

characteristic

133

C₈

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

152

—

138

C₂²

#10597393

yes

—

139

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

#10597393

yes

—

143

C₄

#10597395

yes

—

144

C₄

C₂×#64545

yes

—

145

C₂

—

146

C₂

—

152

—

147

C₂

C₂×#10597393

yes

characteristic

148

C₂

C₂×#10597395

yes

—

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#533	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂×#10597320	C₂
hypercenter	#533	D₁₉
hypocenter	C₁₉	#3138
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#533

C₂

socle

C₂²×C₁₉

C₂²×D₄

C₂

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

N	H ≅ G/N	type
2. #11926910	C₂	semidirect
3. #11926892	C₂	semidirect
4. #11926548	C₂	semidirect
5. C₄×#64520	C₂	semidirect
6. C₁₉×#533	C₂	semidirect
9. C₁₉×C₄⋊Q₈	C₂²	semidirect
10. C₁₉×#125	C₂²	semidirect
19. #10597266	C₂²	semidirect
20. #10597260	C₂²	semidirect
21. C₄×C₁₉⋊C₈	C₂²	semidirect
71. #533	D₁₉	semidirect
84. C₄⋊Q₈	C₂×D₁₉	semidirect
88. #125	C₂×D₁₉	semidirect
96. C₁₉	#3138	semidirect

H ≅ G/N

type

2. #11926910

C₂

semidirect

3. #11926892

C₂

semidirect

4. #11926548

C₂

semidirect

5. C₄×#64520

C₂

semidirect

6. C₁₉×#533

C₂

semidirect

9. C₁₉×C₄⋊Q₈

C₂²

semidirect

10. C₁₉×#125

C₂²

semidirect

19. #10597266

C₂²

semidirect

20. #10597260

C₂²

semidirect

21. C₄×C₁₉⋊C₈

C₂²

semidirect

71. #533

D₁₉

semidirect

84. C₄⋊Q₈

C₂×D₁₉

semidirect

88. #125

C₂×D₁₉

semidirect

96. C₁₉

#3138

semidirect

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

subgroup	index
C₂×#10597320	2
#11926910	2
#11926892	2
#11926548	2
C₄×#64520	2
C₁₉×#533	2
#3138	19

subgroup

index

C₁₉×#533

Subgroups — #14574011

Conjugacy classes of subgroups

Complements

Maximal subgroups