Group #14572702 — subgroups

Subgroups — #14572702

Order 2432.

410 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 205 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	#11926622	C₂	1	4	yes	maximal, complemented
2	D₄×C₁₉⋊C₈	C₂	1	4	yes	maximal, complemented
3	#11926597	C₂	1	2	yes	maximal, complemented
4	#11926511	C₂	1	4	yes	maximal, complemented
5	C₁₉×#532	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	C₂²	1	2	yes	—
7	C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
8	C₁₉×#127	C₄	1	1	yes	characteristic
9	C₁₉×#124	C₄	1	2	yes	—
10	C₁₉×#121	C₄	1	4	yes	—
11	C₄×D₄×C₁₉	C₂²	1	4	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×#64520	C₂²	1	4	yes	—
14	C₂²×C₁₉⋊C₈	C₂²	1	4	yes	—
15	C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
16	C₂²⋊(C₁₉⋊C₈)	C₂²	1	8	yes	—
17	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
18	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
19	C₄×C₁₉⋊C₈	C₂²	1	4	yes	—
20	#41×C₁₉	—	4	2	no	—
21	#41×C₁₉	—	4	2	no	—
22	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×D₄×C₁₉	C₂×C₄	1	4	yes	—
24	C₂×D₄×C₁₉	C₂×C₄	1	4	yes	—
25	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
29	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
30	C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
31	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₄²×C₁₉	C₂³	1	2	yes	—
34	#64520	—	4	4	no	—
35	C₂×C₁₉⋊C₈	—	4	4	no	—
36	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
37	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
38	C₂³×C₁₉	C₂²×C₄	1	4	yes	—
39	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	Q₈×C₁₉	—	4	2	no	—
41	D₄×C₁₉	—	2	8	no	—
42	D₄×C₁₉	—	4	2	no	—
43	D₄×C₁₉	—	4	4	no	—
44	C₂×C₄×C₁₉	—	2	4	no	—
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	2	4	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
49	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
51	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
52	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
53	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
54	C₁₉⋊C₈	—	2	4	no	—
55	C₁₉⋊C₈	—	2	4	no	—
56	#2979	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	—	2	4	no	—
59	C₂²×C₁₉	—	2	2	no	—
60	C₂²×C₁₉	—	2	8	no	—
61	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	—	2	4	no	—
64	C₄×C₁₉	—	2	2	no	—
65	C₄×C₁₉	#131	1	4	yes	—
66	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
67	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
68	#532	D₁₉	1	1	yes	characteristic
69	#436	—	19	4	no	—
70	C₈×D₄	—	19	4	no	—
71	#431	—	19	2	no	—
72	#408	—	19	4	no	—
73	C₂×C₁₉	—	4	1	no	—
74	C₂×C₁₉	—	4	4	no	—
75	C₂×C₁₉	#518	1	1	yes	characteristic
76	C₂×C₁₉	C₂×#131	1	2	yes	—
77	C₂×#41	C₂×D₁₉	1	2	yes	—
78	C₂×M₁₆	—	19	4	no	—
79	C₂²×C₈	—	19	4	no	—
80	C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic
81	#127	Dic₁₉	1	1	yes	characteristic
82	#124	Dic₁₉	1	2	yes	—
83	#121	Dic₁₉	1	4	yes	—
84	C₄×D₄	C₂×D₁₉	1	4	yes	—
85	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
86	C₄⋊C₈	—	19	2	no	—
87	C₄⋊C₈	—	19	2	no	—
88	C₂²⋊C₈	—	19	4	no	—
89	C₂²⋊C₈	—	19	8	no	—
90	C₄×C₈	—	19	4	no	—
91	C₁₉	#2979	1	1	yes	characteristic, complemented, Sylow
92	#41	—	4	2	no	—
93	#41	—	4	2	no	—
94	C₂×Q₈	C₂×Dic₁₉	1	2	yes	—
95	C₂×D₄	C₂×Dic₁₉	1	4	yes	—
96	C₂×D₄	C₂×Dic₁₉	1	4	yes	—
97	C₂×D₄	C₂×Dic₁₉	1	2	yes	—
98	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
99	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
100	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
101	M₁₆	—	76	4	no	—
102	C₂×C₈	—	19	4	no	—
103	C₂×C₈	—	19	4	no	—
104	C₂×C₈	—	76	4	no	—
105	C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
106	C₂²⋊C₄	C₂×Dic₁₉	1	8	yes	—
107	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
108	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
109	C₄²	C₂²×D₁₉	1	2	yes	—
110	C₂³	C₂²×Dic₁₉	1	4	yes	—
111	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
112	Q₈	—	4	2	no	—
113	D₄	—	2	8	no	—
114	D₄	—	4	2	no	—
115	D₄	—	4	4	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	2	4	no	—
118	C₂×C₄	—	2	4	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
122	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
123	C₂×C₄	C₂²×Dic₁₉	1	4	yes	—
124	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
125	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
126	C₈	—	38	4	no	—
127	C₈	—	38	4	no	—
128	C₂²	—	2	2	no	—
129	C₂²	—	2	8	no	—
130	C₂²	—	2	1	no	—
131	C₂²	—	2	4	no	—
132	C₂²	C₂³×Dic₁₉	1	1	yes	characteristic
133	C₄	—	2	2	no	—
134	C₄	—	2	1	no	—
135	C₄	—	2	4	no	—
136	C₄	#10597394	1	4	yes	—
137	C₄	#10597430	1	1	yes	characteristic
138	C₄	#10597430	1	1	yes	characteristic
139	C₂	—	4	1	no	—
140	C₂	—	4	4	no	—
141	C₂	#11927019	1	1	yes	characteristic
142	C₂	C₂×#10597394	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926622

C₂

yes

maximal, complemented

D₄×C₁₉⋊C₈

C₂

yes

maximal, complemented

#11926597

C₂

yes

maximal, complemented

#11926511

C₂

yes

maximal, complemented

C₁₉×#532

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₁₉×#127

C₄

yes

characteristic

C₁₉×#124

C₄

yes

—

C₁₉×#121

C₄

yes

—

C₄×D₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂²×C₄

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2979

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#131

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

D₁₉

yes

characteristic

#436

—

C₈×D₄

—

#431

—

#408

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#518

yes

characteristic

C₂×C₁₉

C₂×#131

yes

—

C₂×#41

C₂×D₁₉

yes

—

C₂×M₁₆

—

C₂²×C₈

—

C₄⋊Q₈

Dic₁₉

yes

characteristic

#127

Dic₁₉

yes

characteristic

#124

Dic₁₉

yes

—

#121

Dic₁₉

yes

—

C₄×D₄

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₁₉

#2979

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

C₂×Dic₁₉

yes

—

C₂×D₄

C₂×Dic₁₉

yes

—

C₂×D₄

C₂×Dic₁₉

yes

—

C₂×D₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

100

C₂²×C₄

C₂²×D₁₉

yes

—

101

M₁₆

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₄⋊C₄

C₂×Dic₁₉

yes

—

106

C₂²⋊C₄

C₂×Dic₁₉

yes

—

107

C₄²

C₂×Dic₁₉

yes

characteristic

108

C₄²

C₂×Dic₁₉

yes

characteristic

109

C₄²

C₂²×D₁₉

yes

—

110

C₂³

C₂²×Dic₁₉

yes

—

111

C₂³

C₂²×Dic₁₉

yes

characteristic

112

Q₈

—

113

D₄

—

114

D₄

—

115

D₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

122

C₂×C₄

C₂²×Dic₁₉

yes

—

123

C₂×C₄

C₂²×Dic₁₉

yes

—

124

C₂×C₄

C₂²×Dic₁₉

yes

—

125

C₂×C₄

C₂³×D₁₉

yes

characteristic

126

C₈

—

127

C₈

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

C₂³×Dic₁₉

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

#10597394

yes

—

137

C₄

#10597430

yes

characteristic

138

C₄

#10597430

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

#11927019

yes

characteristic

142

C₂

C₂×#10597394

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting, prime radical	C₁₉×#532	C₂
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#532	D₁₉
hypocenter	C₁₉	#2979
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #532

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₁₉

commutator, socle

C₂²×C₁₉

C₂³×C₄

Fitting, prime radical

C₁₉×#532

C₂

cosocle

C₂×C₄×C₁₉

C₂⁴

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄ ◁ #532

N	H ≅ G/N	type
1. #11926622	C₂	semidirect
2. D₄×C₁₉⋊C₈	C₂	semidirect
3. #11926597	C₂	semidirect
4. #11926511	C₂	semidirect
91. C₁₉	#2979	semidirect

H ≅ G/N

type

1. #11926622

C₂

semidirect

2. D₄×C₁₉⋊C₈

C₂

semidirect

3. #11926597

C₂

semidirect

4. #11926511

C₂

semidirect

91. C₁₉

#2979

semidirect

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

subgroup	index
#11926622	2
D₄×C₁₉⋊C₈	2
#11926597	2
#11926511	2
C₁₉×#532	2
#2979	19

subgroup

index

D₄×C₁₉⋊C₈

C₁₉×#532

Subgroups — #14572702

Conjugacy classes of subgroups

Complements

Maximal subgroups