Group #14571632 — subgroups

Subgroups — #14571632

Order 2432.

712 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597399	C₂	1	2	yes	maximal, complemented
2	#11926469	C₂	1	3	yes	maximal, complemented
3	#11926460	C₂	1	6	yes	maximal, complemented
4	#11926453	C₂	1	3	yes	maximal, complemented
5	C₁₉×#379	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂⁵×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₂²⋊D₁₉	C₂²	1	6	yes	—
8	C₂²×D₇₆	C₂²	1	1	yes	characteristic, complemented
9	C₂×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
10	C₂×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
11	#10597399	—	2	8	no	—
12	C₂×C₂²⋊Dic₁₉	C₂²	1	6	yes	—
13	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	6	yes	complemented
14	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	complemented
15	C₁₉⋊#95	C₂²	1	3	yes	complemented
16	C₁₉⋊#95	C₂²	1	3	yes	complemented
17	C₂⁴×C₁₉	—	4	3	no	—
18	C₂⁴×C₁₉	—	4	3	no	—
19	C₂⁴×C₁₉	D₄	1	4	yes	complemented
20	C₂⁴×C₁₉	C₂³	1	3	yes	—
21	C₂³×D₁₉	C₂³	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
24	C₂×C₂²⋊D₁₉	—	2	12	no	—
25	C₂×C₂²⋊D₁₉	—	4	6	no	—
26	C₂×C₂²⋊D₁₉	—	4	6	no	—
27	C₂²×Dic₁₉	C₂³	1	6	yes	—
28	C₂×D₇₆	—	4	3	no	—
29	C₂²⋊C₄×C₁₉	—	4	3	no	—
30	C₂²⋊C₄×C₁₉	—	4	3	no	—
31	C₂²⋊Dic₁₉	—	2	12	no	—
32	(C₂×D₁₉)⋊C₄	—	4	6	no	—
33	C₄⋊Dic₁₉	—	4	3	no	—
34	C₂³×C₁₉	—	2	3	no	—
35	C₂³×C₁₉	—	2	3	no	—
36	C₂³×C₁₉	—	2	6	no	—
37	C₂³×C₁₉	—	2	6	no	—
38	C₂³×C₁₉	—	4	12	no	—
39	C₂³×C₁₉	—	4	12	no	—
40	C₂³×C₁₉	—	4	4	no	—
41	C₂³×C₁₉	C₂×D₄	1	6	yes	—
42	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
43	C₂²×D₁₉	—	2	2	no	—
44	C₂²×D₁₉	—	2	6	no	—
45	C₂²×D₁₉	—	2	6	no	—
46	C₂×C₄×C₁₉	—	2	3	no	—
47	C₂×C₄×C₁₉	—	2	6	no	—
48	C₂×C₄×C₁₉	—	2	3	no	—
49	C₂²⋊D₁₉	—	4	24	no	—
50	C₂×Dic₁₉	—	2	6	no	—
51	C₂×Dic₁₉	—	2	6	no	—
52	C₂×Dic₁₉	—	2	6	no	—
53	D₇₆	—	4	4	no	—
54	#2812	—	19	1	no	maximal, Sylow
55	C₂²×C₁₉	—	2	12	no	—
56	C₂²×C₁₉	—	2	6	no	—
57	C₂²×C₁₉	—	4	16	no	—
58	C₂²×C₁₉	—	4	6	no	—
59	C₂²×C₁₉	—	4	3	no	—
60	C₂²×C₁₉	—	4	3	no	—
61	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
62	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
63	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
64	C₂×D₁₉	—	4	6	no	—
65	C₂×D₁₉	—	4	6	no	—
66	C₂×D₁₉	—	4	2	no	—
67	C₄×C₁₉	—	4	3	no	—
68	C₄×C₁₉	—	4	1	no	—
69	Dic₁₉	—	4	6	no	—
70	C₂×#120	—	19	2	no	—
71	#397	—	19	3	no	—
72	#394	—	19	6	no	—
73	#392	—	19	3	no	—
74	#379	D₁₉	1	1	yes	characteristic, complemented
75	C₂×C₁₉	—	4	6	no	—
76	C₂×C₁₉	#534	1	3	yes	—
77	C₂×C₁₉	#560	1	3	yes	—
78	C₂×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
79	D₁₉	—	8	2	no	—
80	C₂⁵	C₂×D₁₉	1	1	yes	characteristic
81	C₂²×D₄	—	19	6	no	—
82	C₂²×D₄	—	19	1	no	—
83	#120	—	38	8	no	—
84	C₂×C₄⋊C₄	—	19	3	no	—
85	C₂×C₂²⋊C₄	—	19	6	no	—
86	C₂×C₂²⋊C₄	—	19	6	no	—
87	C₂×C₂²⋊C₄	C₂×D₁₉	1	3	yes	—
88	C₂×C₂²⋊C₄	C₂×D₁₉	1	3	yes	—
89	#95	—	19	3	no	—
90	#95	—	19	3	no	—
91	C₁₉	#2812	1	1	yes	characteristic, complemented, Sylow
92	C₂⁴	—	4	3	no	—
93	C₂⁴	—	4	3	no	—
94	C₂⁴	—	19	2	no	—
95	C₂⁴	D₇₆	1	4	yes	complemented
96	C₂⁴	C₂²×D₁₉	1	3	yes	—
97	C₂×D₄	—	38	12	no	—
98	C₂×D₄	—	76	3	no	—
99	C₂×D₄	—	76	6	no	—
100	C₂×D₄	—	76	6	no	—
101	C₂²×C₄	—	19	6	no	—
102	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
103	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
104	C₄⋊C₄	—	76	3	no	—
105	C₂²⋊C₄	—	4	3	no	—
106	C₂²⋊C₄	—	4	3	no	—
107	C₂²⋊C₄	—	38	12	no	—
108	C₂²⋊C₄	—	76	6	no	—
109	C₂³	—	2	3	no	—
110	C₂³	—	2	3	no	—
111	C₂³	—	2	6	no	—
112	C₂³	—	2	6	no	—
113	C₂³	—	4	12	no	—
114	C₂³	—	4	12	no	—
115	C₂³	—	4	4	no	—
116	C₂³	—	38	2	no	—
117	C₂³	—	38	6	no	—
118	C₂³	—	38	6	no	—
119	C₂³	C₂×D₇₆	1	6	yes	—
120	C₂³	C₂³×D₁₉	1	1	yes	characteristic
121	D₄	—	76	4	no	—
122	D₄	—	76	24	no	—
123	C₂×C₄	—	2	6	no	—
124	C₂×C₄	—	2	3	no	—
125	C₂×C₄	—	2	3	no	—
126	C₂×C₄	—	38	6	no	—
127	C₂×C₄	—	38	6	no	—
128	C₂×C₄	—	38	6	no	—
129	C₂²	—	2	12	no	—
130	C₂²	—	2	6	no	—
131	C₂²	—	4	16	no	—
132	C₂²	—	4	6	no	—
133	C₂²	—	4	3	no	—
134	C₂²	—	4	3	no	—
135	C₂²	—	76	6	no	—
136	C₂²	—	76	6	no	—
137	C₂²	—	76	2	no	—
138	C₂²	C₂²×D₇₆	1	1	yes	characteristic
139	C₂²	#10597430	1	3	yes	—
140	C₂²	#10597430	1	3	yes	—
141	C₄	—	4	3	no	—
142	C₄	—	4	1	no	—
143	C₄	—	76	6	no	—
144	C₂	—	4	6	no	—
145	C₂	—	152	2	no	—
146	C₂	#11927106	1	3	yes	—
147	C₂	#11927283	1	3	yes	—
148	C₂	#11927287	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597399

C₂

yes

maximal, complemented

#11926469

C₂

yes

maximal, complemented

#11926460

C₂

yes

maximal, complemented

#11926453

C₂

yes

maximal, complemented

C₁₉×#379

C₂

yes

maximal, characteristic, complemented

C₂⁵×C₁₉

C₂²

yes

characteristic

C₂²×C₂²⋊D₁₉

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

characteristic, complemented

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

#10597399

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

complemented

C₂×C₄⋊Dic₁₉

C₂²

yes

complemented

C₁₉⋊#95

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

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

#2812

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

#534

yes

—

C₂×C₁₉

#560

yes

—

C₂×C₁₉

H(3,𝔽₄)

yes

characteristic

D₁₉

—

C₂⁵

C₂×D₁₉

yes

characteristic

C₂²×D₄

—

C₂²×D₄

—

#120

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

#95

—

#95

—

C₁₉

#2812

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

D₇₆

yes

complemented

C₂⁴

C₂²×D₁₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₂²×D₁₉

yes

characteristic

103

C₂²×C₄

C₂²×D₁₉

yes

—

104

C₄⋊C₄

—

105

C₂²⋊C₄

—

106

C₂²⋊C₄

—

107

C₂²⋊C₄

—

108

C₂²⋊C₄

—

109

C₂³

—

110

C₂³

—

111

C₂³

—

112

C₂³

—

113

C₂³

—

114

C₂³

—

115

C₂³

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

C₂×D₇₆

yes

—

120

C₂³

C₂³×D₁₉

yes

characteristic

121

D₄

—

122

D₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

C₂²×D₇₆

yes

characteristic

139

C₂²

#10597430

yes

—

140

C₂²

#10597430

yes

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₂

—

145

C₂

—

152

—

146

C₂

#11927106

yes

—

147

C₂

#11927283

yes

—

148

C₂

#11927287

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#379	C₂
hypercenter	#379	D₁₉
hypocenter	C₁₉	#2812
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #379

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#379

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #379

N	H ≅ G/N	type
1. C₂×#10597399	C₂	semidirect
2. #11926469	C₂	semidirect
3. #11926460	C₂	semidirect
4. #11926453	C₂	semidirect
5. C₁₉×#379	C₂	semidirect
8. C₂²×D₇₆	C₂²	semidirect
13. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
14. C₂×C₄⋊Dic₁₉	C₂²	semidirect
15. C₁₉⋊#95	C₂²	semidirect
16. C₁₉⋊#95	C₂²	semidirect
19. C₂⁴×C₁₉	D₄	semidirect
74. #379	D₁₉	semidirect
91. C₁₉	#2812	semidirect
95. C₂⁴	D₇₆	semidirect

H ≅ G/N

type

1. C₂×#10597399

C₂

semidirect

2. #11926469

C₂

semidirect

3. #11926460

C₂

semidirect

4. #11926453

C₂

semidirect

5. C₁₉×#379

C₂

semidirect

8. C₂²×D₇₆

C₂²

semidirect

13. C₂×(C₂×D₁₉)⋊C₄

C₂²

semidirect

14. C₂×C₄⋊Dic₁₉

C₂²

semidirect

15. C₁₉⋊#95

C₂²

semidirect

16. C₁₉⋊#95

C₂²

semidirect

19. C₂⁴×C₁₉

D₄

semidirect

74. #379

D₁₉

semidirect

91. C₁₉

#2812

semidirect

95. C₂⁴

D₇₆

semidirect

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

subgroup	index
C₂×#10597399	2
#11926469	2
#11926460	2
#11926453	2
C₁₉×#379	2
#2812	19

subgroup

index

C₁₉×#379

Subgroups — #14571632

Conjugacy classes of subgroups

Complements

Maximal subgroups