Group #14569359 — subgroups

Subgroups — #14569359

Order 2432.

932 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 181 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×#10597376	C₂	1	3	yes	maximal, complemented
2	#11926455	C₂	1	2	yes	maximal, complemented
3	#11926452	C₂	1	6	yes	maximal, complemented
4	#11926404	C₂	1	3	yes	maximal, complemented
5	C₂²×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#41×C₁₉	—	2	12	no	—
7	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×D₄×C₁₉	C₂²	1	3	yes	—
9	C₂³×C₄×C₁₉	C₂²	1	3	yes	—
10	C₂²×C₂²⋊D₁₉	C₂²	1	6	yes	—
11	C₂²×D₇₆	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊Dic₁₉	C₂²	1	6	yes	—
13	#10597376	—	2	12	no	—
14	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	6	yes	—
15	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	—
16	C₁₉⋊#95	C₂²	1	6	yes	—
17	C₂⁴×C₁₉	C₂³	1	3	yes	—
18	C₂³×D₁₉	C₂³	1	2	yes	—
19	#41×C₁₉	—	2	32	no	—
20	C₂×Q₈×C₁₉	—	2	6	no	—
21	C₂×D₄×C₁₉	—	2	12	no	—
22	C₂×D₄×C₁₉	—	2	6	no	—
23	C₂²×C₄×C₁₉	—	2	12	no	—
24	C₂²×C₄×C₁₉	D₄	1	12	yes	complemented
25	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₂²⋊D₁₉	—	2	12	no	—
28	C₂×C₂²⋊D₁₉	—	4	12	no	—
29	C₂²×Dic₁₉	C₂³	1	6	yes	—
30	C₂×D₇₆	—	2	6	no	—
31	C₂²⋊Dic₁₉	—	4	6	no	—
32	(C₂×D₁₉)⋊C₄	—	2	12	no	—
33	C₄⋊Dic₁₉	—	2	6	no	—
34	C₂³×C₁₉	—	2	6	no	—
35	C₂³×C₁₉	—	2	3	no	—
36	C₂³×C₁₉	—	2	6	no	—
37	C₂³×C₁₉	—	2	3	no	—
38	C₂³×C₁₉	C₂×D₄	1	6	yes	—
39	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
40	C₂²×D₁₉	—	2	6	no	—
41	C₂²×D₁₉	—	2	6	no	—
42	C₂²×D₁₉	—	2	2	no	—
43	Q₈×C₁₉	—	2	8	no	—
44	D₄×C₁₉	—	2	24	no	—
45	C₂×C₄×C₁₉	—	2	6	no	—
46	C₂×C₄×C₁₉	—	2	24	no	—
47	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
48	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
49	C₂²⋊D₁₉	—	4	24	no	—
50	C₂×Dic₁₉	—	2	6	no	—
51	C₂×Dic₁₉	—	2	12	no	—
52	D₇₆	—	4	4	no	—
53	#2615	—	19	1	no	maximal, Sylow
54	C₂²×C₁₉	—	2	6	no	—
55	C₂²×C₁₉	—	2	6	no	—
56	C₂²×C₁₉	—	2	6	no	—
57	C₂²×C₁₉	—	4	6	no	—
58	C₂²×C₁₉	—	4	6	no	—
59	C₂²×C₁₉	C₂²×D₄	1	3	yes	—
60	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
61	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
62	C₂×D₁₉	—	4	2	no	—
63	C₂×D₁₉	—	4	6	no	—
64	C₂×D₁₉	—	4	6	no	—
65	C₄×C₁₉	—	2	6	no	—
66	C₄×C₁₉	#120	1	4	yes	—
67	Dic₁₉	—	4	6	no	—
68	C₂²×#41	D₁₉	1	1	yes	characteristic, complemented
69	C₂×#121	—	19	3	no	—
70	#393	—	19	2	no	—
71	#392	—	19	6	no	—
72	#380	—	19	3	no	—
73	C₂×C₁₉	—	4	6	no	—
74	C₂×C₁₉	C₂×#120	1	1	yes	characteristic
75	C₂×C₁₉	#535	1	3	yes	—
76	C₂×C₁₉	#537	1	3	yes	—
77	D₁₉	—	8	2	no	—
78	C₂×#41	—	2	12	no	—
79	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
80	C₂²×D₄	—	19	6	no	—
81	C₂²×D₄	—	19	1	no	—
82	C₂²×D₄	C₂×D₁₉	1	3	yes	—
83	C₂³×C₄	C₂×D₁₉	1	3	yes	—
84	#121	—	38	12	no	—
85	C₂×C₄⋊C₄	—	19	3	no	—
86	C₂×C₂²⋊C₄	—	19	6	no	—
87	C₂×C₂²⋊C₄	—	19	6	no	—
88	#95	—	19	6	no	—
89	C₁₉	#2615	1	1	yes	characteristic, complemented, Sylow
90	C₂⁴	—	19	2	no	—
91	C₂⁴	C₂²×D₁₉	1	3	yes	—
92	#41	—	2	32	no	—
93	C₂×Q₈	—	2	6	no	—
94	C₂×D₄	—	2	12	no	—
95	C₂×D₄	—	2	6	no	—
96	C₂×D₄	—	38	12	no	—
97	C₂×D₄	—	38	6	no	—
98	C₂×D₄	—	76	12	no	—
99	C₂²×C₄	—	2	12	no	—
100	C₂²×C₄	—	19	6	no	—
101	C₂²×C₄	C₂²⋊D₁₉	1	12	yes	complemented
102	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
103	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
104	C₄⋊C₄	—	38	6	no	—
105	C₂²⋊C₄	—	38	12	no	—
106	C₂²⋊C₄	—	76	6	no	—
107	C₂³	—	2	3	no	—
108	C₂³	—	2	6	no	—
109	C₂³	—	2	3	no	—
110	C₂³	—	2	6	no	—
111	C₂³	—	38	6	no	—
112	C₂³	—	38	2	no	—
113	C₂³	—	38	6	no	—
114	C₂³	C₂×C₂²⋊D₁₉	1	6	yes	—
115	C₂³	C₂³×D₁₉	1	1	yes	characteristic
116	Q₈	—	2	8	no	—
117	D₄	—	2	24	no	—
118	D₄	—	76	24	no	—
119	D₄	—	76	4	no	—
120	C₂×C₄	—	2	6	no	—
121	C₂×C₄	—	2	24	no	—
122	C₂×C₄	—	38	12	no	—
123	C₂×C₄	—	38	6	no	—
124	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
125	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
126	C₂²	—	2	6	no	—
127	C₂²	—	2	6	no	—
128	C₂²	—	2	6	no	—
129	C₂²	—	4	6	no	—
130	C₂²	—	4	6	no	—
131	C₂²	—	76	6	no	—
132	C₂²	—	76	6	no	—
133	C₂²	—	76	2	no	—
134	C₂²	#10597435	1	3	yes	—
135	C₂²	#10597436	1	1	yes	characteristic
136	C₂²	C₂²×C₂²⋊D₁₉	1	3	yes	—
137	C₄	—	2	6	no	—
138	C₄	—	76	6	no	—
139	C₄	#10597399	1	4	yes	—
140	C₂	—	4	6	no	—
141	C₂	—	152	2	no	—
142	C₂	C₂×#10597399	1	1	yes	characteristic
143	C₂	#11927108	1	3	yes	—
144	C₂	#11927122	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597376

C₂

yes

maximal, complemented

#11926455

C₂

yes

maximal, complemented

#11926452

C₂

yes

maximal, complemented

#11926404

C₂

yes

maximal, complemented

C₂²×#41×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×#41×C₁₉

—

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

C₂²

yes

—

C₂³×C₄×C₁₉

C₂²

yes

—

C₂²×C₂²⋊D₁₉

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

#10597376

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

—

C₂³×D₁₉

C₂³

yes

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

complemented

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

#2615

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

—

Dic₁₉

—

C₂²×#41

D₁₉

yes

characteristic, complemented

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#120

yes

characteristic

C₂×C₁₉

#535

yes

—

C₂×C₁₉

#537

yes

—

D₁₉

—

C₂×#41

—

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂²×D₄

—

C₂²×D₄

—

C₂²×D₄

C₂×D₁₉

yes

—

C₂³×C₄

C₂×D₁₉

yes

—

#121

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

C₁₉

#2615

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

C₂²×D₁₉

yes

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₂²⋊D₁₉

yes

complemented

102

C₂²×C₄

C₂²×D₁₉

yes

—

103

C₂²×C₄

C₂²×D₁₉

yes

characteristic

104

C₄⋊C₄

—

105

C₂²⋊C₄

—

106

C₂²⋊C₄

—

107

C₂³

—

108

C₂³

—

109

C₂³

—

110

C₂³

—

111

C₂³

—

112

C₂³

—

113

C₂³

—

114

C₂³

C₂×C₂²⋊D₁₉

yes

—

115

C₂³

C₂³×D₁₉

yes

characteristic

116

Q₈

—

117

D₄

—

118

D₄

—

119

D₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

125

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

#10597435

yes

—

135

C₂²

#10597436

yes

characteristic

136

C₂²

C₂²×C₂²⋊D₁₉

yes

—

137

C₄

—

138

C₄

—

139

C₄

#10597399

yes

—

140

C₂

—

141

C₂

—

152

—

142

C₂

C₂×#10597399

yes

characteristic

143

C₂

#11927108

yes

—

144

C₂

#11927122

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂²×#41×C₁₉	C₂
hypercenter	C₂²×#41	D₁₉
hypocenter	C₁₉	#2615
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×#41

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂²×#41×C₁₉

C₂

hypercenter

C₂²×#41

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂²×#41

N	H ≅ G/N	type
1. C₂×#10597376	C₂	semidirect
2. #11926455	C₂	semidirect
3. #11926452	C₂	semidirect
4. #11926404	C₂	semidirect
5. C₂²×#41×C₁₉	C₂	semidirect
24. C₂²×C₄×C₁₉	D₄	semidirect
68. C₂²×#41	D₁₉	semidirect
89. C₁₉	#2615	semidirect
101. C₂²×C₄	C₂²⋊D₁₉	semidirect

H ≅ G/N

type

1. C₂×#10597376

C₂

semidirect

2. #11926455

C₂

semidirect

3. #11926452

C₂

semidirect

4. #11926404

C₂

semidirect

5. C₂²×#41×C₁₉

C₂

semidirect

24. C₂²×C₄×C₁₉

D₄

semidirect

68. C₂²×#41

D₁₉

semidirect

89. C₁₉

#2615

semidirect

101. C₂²×C₄

C₂²⋊D₁₉

semidirect

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

subgroup	index
C₂×#10597376	2
#11926455	2
#11926452	2
#11926404	2
C₂²×#41×C₁₉	2
#2615	19

subgroup

index

C₂²×#41×C₁₉

Subgroups — #14569359

Conjugacy classes of subgroups

Complements

Maximal subgroups