Group #14571623 — subgroups

Subgroups — #14571623

Order 2432.

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

normal subgroups only

This group has 368 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	#11926483	C₂	1	2	yes	maximal
2	#11926476	C₂	1	4	yes	maximal
3	#11926451	C₂	1	2	yes	maximal
4	#11926442	C₂	1	2	yes	maximal
5	#11926431	C₂	1	4	yes	maximal
6	C₁₉×#391	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
15	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
16	C₁₉×#95	C₂²	1	4	yes	—
17	C₁₉⋊#95	C₂²	1	2	yes	—
18	C₁₉⋊#95	C₂²	1	4	yes	—
19	C₁₉⋊#95	C₂²	1	4	yes	—
20	C₁₉⋊#95	C₂²	1	4	yes	—
21	C₂×Q₈×C₁₉	—	4	1	no	—
22	C₂×Q₈×C₁₉	—	4	1	no	—
23	C₂×Q₈×C₁₉	Q₈	1	4	yes	—
24	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
28	C₂²×Dic₁₉	C₂³	1	4	yes	—
29	C₂²×Dic₁₉	C₂³	1	4	yes	—
30	C₄⋊C₄×C₁₉	—	4	1	no	—
31	C₄²×C₁₉	—	4	1	no	—
32	C₄⋊Dic₁₉	—	2	4	no	—
33	C₄⋊Dic₁₉	—	4	2	no	—
34	C₄⋊Dic₁₉	—	4	2	no	—
35	C₄⋊Dic₁₉	—	4	2	no	—
36	Dic₁₉⋊C₄	—	2	8	no	—
37	C₄×Dic₁₉	—	4	2	no	—
38	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
39	Q₈×C₁₉	—	4	4	no	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	—	2	4	no	—
48	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
49	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
50	C₂×C₄×C₁₉	#41	1	4	yes	—
51	C₂×Dic₁₉	—	2	4	no	—
52	C₂×Dic₁₉	—	2	4	no	—
53	C₂×Dic₁₉	—	2	4	no	—
54	C₂×Dic₁₉	—	2	4	no	—
55	C₂×Dic₁₉	—	2	4	no	—
56	C₂×Dic₁₉	—	2	4	no	—
57	#2809	—	19	1	no	maximal, Sylow
58	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
59	C₂²×C₁₉	C₂×#41	1	2	yes	—
60	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
61	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
62	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
63	C₄×C₁₉	—	2	4	no	—
64	C₄×C₁₉	—	2	4	no	—
65	C₄×C₁₉	—	2	2	no	—
66	C₄×C₁₉	—	4	2	no	—
67	Dic₁₉	—	4	4	no	—
68	Dic₁₉	—	4	4	no	—
69	#400	—	19	2	no	—
70	#398	—	19	4	no	—
71	#391	—	19	2	no	—
72	#391	D₁₉	1	1	yes	characteristic
73	#389	—	19	2	no	—
74	#387	—	19	4	no	—
75	C₂×C₁₉	#539	1	2	yes	—
76	C₂×C₁₉	#543	1	1	yes	characteristic
77	C₂×C₁₉	#555	1	1	yes	characteristic
78	C₂×C₁₉	#557	1	2	yes	—
79	C₂×C₁₉	#563	1	1	yes	characteristic
80	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
81	C₂×C₄⋊C₄	—	19	4	no	—
82	C₂×C₄⋊C₄	—	19	2	no	—
83	C₂×C₄⋊C₄	—	19	2	no	—
84	C₂×C₄⋊C₄	—	19	2	no	—
85	C₂×C₄⋊C₄	—	19	2	no	—
86	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
87	C₂×C₄²	—	19	2	no	—
88	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
89	#95	—	19	2	no	—
90	#95	—	19	4	no	—
91	#95	—	19	4	no	—
92	#95	—	19	4	no	—
93	#95	C₂×D₁₉	1	4	yes	—
94	C₁₉	#2809	1	1	yes	characteristic, complemented, Sylow
95	C₂×Q₈	—	4	1	no	—
96	C₂×Q₈	—	4	1	no	—
97	C₂×Q₈	Dic₃₈	1	4	yes	—
98	C₂²×C₄	—	19	4	no	—
99	C₂²×C₄	—	19	4	no	—
100	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
101	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
102	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
103	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
104	C₄⋊C₄	—	4	1	no	—
105	C₄⋊C₄	—	38	8	no	—
106	C₄⋊C₄	—	38	4	no	—
107	C₄⋊C₄	—	76	2	no	—
108	C₄⋊C₄	—	76	2	no	—
109	C₄⋊C₄	—	76	2	no	—
110	C₄²	—	4	1	no	—
111	C₄²	—	76	2	no	—
112	C₂³	C₂³×D₁₉	1	1	yes	characteristic
113	Q₈	—	4	4	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	38	4	no	—
123	C₂×C₄	—	38	4	no	—
124	C₂×C₄	—	38	4	no	—
125	C₂×C₄	—	38	4	no	—
126	C₂×C₄	—	38	4	no	—
127	C₂×C₄	—	38	4	no	—
128	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
129	C₂×C₄	C₂×Dic₃₈	1	4	yes	—
130	C₂×C₄	#64545	1	4	yes	—
131	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
132	C₂²	#10597430	1	1	yes	characteristic
133	C₂²	#10597430	1	1	yes	characteristic
134	C₂²	C₂×#64545	1	2	yes	—
135	C₂²	#10597436	1	2	yes	—
136	C₄	—	2	4	no	—
137	C₄	—	2	2	no	—
138	C₄	—	2	4	no	—
139	C₄	—	4	2	no	—
140	C₄	—	76	4	no	—
141	C₄	—	76	4	no	—
142	C₂	#11927143	1	2	yes	—
143	C₂	#11927170	1	1	yes	characteristic
144	C₂	#11927260	1	1	yes	characteristic
145	C₂	#11927273	1	2	yes	—
146	C₂	#11927294	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926483

C₂

yes

maximal

#11926476

C₂

yes

maximal

#11926451

C₂

yes

maximal

#11926442

C₂

yes

maximal

#11926431

C₂

yes

maximal

C₁₉×#391

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2809

—

maximal, Sylow

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic

#389

—

#387

—

C₂×C₁₉

#539

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#563

yes

characteristic

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

—

C₂×D₁₉

yes

—

C₁₉

#2809

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₃₈

yes

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

C₂²×D₁₉

yes

—

101

C₂²×C₄

C₂²×D₁₉

yes

characteristic

102

C₂²×C₄

C₂²×D₁₉

yes

—

103

C₂²×C₄

C₂²×D₁₉

yes

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄²

—

111

C₄²

—

112

C₂³

C₂³×D₁₉

yes

characteristic

113

Q₈

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

C₂×Dic₃₈

yes

—

129

C₂×C₄

C₂×Dic₃₈

yes

—

130

C₂×C₄

#64545

yes

—

131

C₂²

C₂²×Dic₃₈

yes

characteristic

132

C₂²

#10597430

yes

characteristic

133

C₂²

#10597430

yes

characteristic

134

C₂²

C₂×#64545

yes

—

135

C₂²

#10597436

yes

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₂

#11927143

yes

—

143

C₂

#11927170

yes

characteristic

144

C₂

#11927260

yes

characteristic

145

C₂

#11927273

yes

—

146

C₂

#11927294

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#391	C₂
hypercenter	#391	D₁₉
hypocenter	C₁₉	#2809
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #391

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#391

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #391

N	H ≅ G/N	type
94. C₁₉	#2809	semidirect

H ≅ G/N

type

94. C₁₉

#2809

semidirect

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

subgroup	index
#11926483	2
#11926476	2
#11926451	2
#11926442	2
#11926431	2
C₁₉×#391	2
#2809	19

subgroup

index

C₁₉×#391

Subgroups — #14571623

Conjugacy classes of subgroups

Complements

Maximal subgroups