Group #14574459 — subgroups

Subgroups — #14574459

Order 2432.

410 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10597370	C₂	1	2	yes	maximal
2	#11926875	C₂	1	4	yes	maximal, complemented
3	#11926802	C₂	1	4	yes	maximal, complemented
4	#11926702	C₂	1	4	yes	maximal, complemented
5	C₁₉×#407	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₈	C₂²	1	2	yes	—
8	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
9	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	#10597370	—	2	2	no	—
12	#10597370	—	2	2	no	—
13	#10597370	C₂²	1	4	yes	—
14	#10597370	C₂²	1	4	yes	—
15	C₂×Dic₁₉⋊C₄	—	2	2	no	—
16	C₂×Dic₇₆	C₂²	1	4	yes	complemented
17	C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
18	#10597274	C₂²	1	4	yes	complemented
19	#10597273	C₂²	1	8	yes	complemented
20	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	—	4	2	no	—
22	C₂²×C₄×C₁₉	D₄	1	2	yes	—
23	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
26	C₂²×Dic₁₉	—	2	2	no	—
27	C₂²×Dic₁₉	—	2	2	no	—
28	C₂×Dic₃₈	—	2	2	no	—
29	C₂×Dic₃₈	—	4	4	no	—
30	C₂×Dic₃₈	C₂³	1	4	yes	—
31	M₁₆×C₁₉	—	4	2	no	—
32	C₂×C₈×C₁₉	C₂³	1	4	yes	—
33	C₂²⋊Dic₁₉	—	2	4	no	—
34	C₂²⋊Dic₁₉	—	2	4	no	—
35	C₄⋊Dic₁₉	—	2	2	no	—
36	C₄⋊Dic₁₉	C₂³	1	4	yes	—
37	Dic₁₉⋊C₄	—	2	4	no	—
38	Dic₁₉⋊C₄	—	2	4	no	—
39	Dic₇₆	—	4	4	no	—
40	C₂³×C₁₉	—	2	4	no	—
41	C₂³×C₁₉	—	4	1	no	—
42	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂³×C₁₉	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	4	1	no	—
47	C₂×C₄×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
51	C₂×Dic₁₉	—	2	4	no	—
52	C₂×Dic₁₉	—	2	4	no	—
53	C₂×Dic₁₉	—	4	4	no	—
54	C₂×Dic₁₉	—	4	4	no	—
55	Dic₃₈	—	2	8	no	—
56	Dic₃₈	—	4	4	no	—
57	C₈×C₁₉	—	2	4	no	—
58	#3195	—	19	1	no	maximal, Sylow
59	C₂²×C₁₉	—	2	2	no	—
60	C₂²×C₁₉	—	2	2	no	—
61	C₂²×C₁₉	—	2	1	no	—
62	C₂²×C₁₉	—	2	2	no	—
63	C₂²×C₁₉	—	4	4	no	—
64	C₂²×C₁₉	#137	1	4	yes	—
65	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
66	C₄×C₁₉	—	2	2	no	—
67	C₄×C₁₉	—	2	1	no	—
68	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
69	Dic₁₉	—	4	4	no	—
70	Dic₁₉	—	4	4	no	—
71	C₂×C₂²⋊Q₈	—	19	2	no	—
72	#483	—	19	4	no	—
73	#470	—	19	4	no	—
74	#451	—	19	4	no	—
75	#407	D₁₉	1	1	yes	characteristic
76	C₂×C₁₉	—	2	4	no	—
77	C₂×C₁₉	—	4	1	no	—
78	C₂×C₁₉	#534	1	1	yes	characteristic
79	C₂×C₁₉	C₂×#137	1	2	yes	—
80	C₂²×Q₈	—	19	2	no	—
81	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
82	C₂×Q₁₆	—	19	4	no	—
83	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
84	C₂²⋊Q₈	—	19	4	no	—
85	C₂²⋊Q₈	—	19	4	no	—
86	C₂²⋊Q₈	—	38	2	no	—
87	C₂²⋊Q₈	—	38	2	no	—
88	C₂×C₄⋊C₄	—	19	2	no	—
89	C₂×C₄⋊C₄	—	38	2	no	—
90	C₂×C₂²⋊C₄	—	38	2	no	—
91	#106	—	19	4	no	—
92	#103	—	19	8	no	—
93	C₂²⋊C₈	C₂×D₁₉	1	4	yes	—
94	C₁₉	#3195	1	1	yes	characteristic, complemented, Sylow
95	C₂⁴	D₇₆	1	1	yes	characteristic
96	C₂×Q₈	—	19	4	no	—
97	C₂×Q₈	—	38	2	no	—
98	C₂×Q₈	—	76	4	no	—
99	C₂²×C₄	—	4	2	no	—
100	C₂²×C₄	—	38	2	no	—
101	C₂²×C₄	—	38	2	no	—
102	C₂²×C₄	D₇₆	1	2	yes	—
103	C₂²×C₄	D₇₆	1	1	yes	characteristic
104	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
105	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
106	Q₁₆	—	76	4	no	—
107	M₁₆	—	4	2	no	—
108	C₂×C₈	C₂²×D₁₉	1	4	yes	—
109	C₄⋊C₄	—	19	4	no	—
110	C₄⋊C₄	—	38	4	no	—
111	C₄⋊C₄	—	38	4	no	—
112	C₄⋊C₄	—	38	2	no	—
113	C₂²⋊C₄	—	38	4	no	—
114	C₂²⋊C₄	—	38	4	no	—
115	C₂³	—	2	4	no	—
116	C₂³	—	4	1	no	—
117	C₂³	C₂×D₇₆	1	1	yes	characteristic
118	C₂³	C₂×D₇₆	1	2	yes	—
119	Q₈	—	38	8	no	—
120	Q₈	—	76	4	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	—	38	4	no	—
126	C₂×C₄	—	38	4	no	—
127	C₂×C₄	—	76	4	no	—
128	C₂×C₄	—	76	4	no	—
129	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
130	C₂×C₄	C₂×D₇₆	1	2	yes	—
131	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
132	C₈	—	2	4	no	—
133	C₂²	—	2	2	no	—
134	C₂²	—	2	2	no	—
135	C₂²	—	2	2	no	—
136	C₂²	—	2	1	no	—
137	C₂²	—	4	4	no	—
138	C₂²	#10597355	1	4	yes	—
139	C₂²	C₂²×D₇₆	1	1	yes	characteristic
140	C₄	—	2	2	no	—
141	C₄	—	2	1	no	—
142	C₄	—	76	4	no	—
143	C₄	—	76	4	no	—
144	C₄	#10597430	1	2	yes	—
145	C₂	—	2	4	no	—
146	C₂	—	4	1	no	—
147	C₂	#11927106	1	1	yes	characteristic
148	C₂	C₂×#10597355	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597370

C₂

yes

maximal

#11926875

C₂

yes

maximal, complemented

#11926802

C₂

yes

maximal, complemented

#11926702

C₂

yes

maximal, complemented

C₁₉×#407

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597370

—

#10597370

—

#10597370

C₂²

yes

—

#10597370

C₂²

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×Dic₇₆

C₂²

yes

complemented

C₁₉×C₂²⋊C₈

C₂²

yes

—

#10597274

C₂²

yes

complemented

#10597273

C₂²

yes

complemented

C₂⁴×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₇₆

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂³×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

#3195

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#137

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

H(5,𝔽₂)

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×C₂²⋊Q₈

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#534

yes

characteristic

C₂×C₁₉

C₂×#137

yes

—

C₂²×Q₈

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂×Q₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

#106

—

#103

—

C₂²⋊C₈

C₂×D₁₉

yes

—

C₁₉

#3195

yes

characteristic, complemented, Sylow

C₂⁴

D₇₆

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

D₇₆

yes

—

103

C₂²×C₄

D₇₆

yes

characteristic

104

C₂²×C₄

C₂²×D₁₉

yes

—

105

C₂²×C₄

C₂²×D₁₉

yes

characteristic

106

Q₁₆

—

107

M₁₆

—

108

C₂×C₈

C₂²×D₁₉

yes

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₂²⋊C₄

—

114

C₂²⋊C₄

—

115

C₂³

—

116

C₂³

—

117

C₂³

C₂×D₇₆

yes

characteristic

118

C₂³

C₂×D₇₆

yes

—

119

Q₈

—

120

Q₈

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

C₂×D₇₆

yes

characteristic

130

C₂×C₄

C₂×D₇₆

yes

—

131

C₂×C₄

C₂³×D₁₉

yes

characteristic

132

C₈

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

#10597355

yes

—

139

C₂²

C₂²×D₇₆

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

#10597430

yes

—

145

C₂

—

146

C₂

—

147

C₂

#11927106

yes

characteristic

148

C₂

C₂×#10597355

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#407	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂⁴×C₁₉	D₄
hypercenter	#407	D₁₉
hypocenter	C₁₉	#3195
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #407

subgroup

G/H

center

C₂²

C₂²×D₇₆

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#407

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂⁴×C₁₉

D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #407

N	H ≅ G/N	type
2. #11926875	C₂	semidirect
3. #11926802	C₂	semidirect
4. #11926702	C₂	semidirect
16. C₂×Dic₇₆	C₂²	semidirect
18. #10597274	C₂²	semidirect
19. #10597273	C₂²	semidirect
94. C₁₉	#3195	semidirect

H ≅ G/N

type

2. #11926875

C₂

semidirect

3. #11926802

C₂

semidirect

4. #11926702

C₂

semidirect

16. C₂×Dic₇₆

C₂²

semidirect

18. #10597274

C₂²

semidirect

19. #10597273

C₂²

semidirect

94. C₁₉

#3195

semidirect

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

subgroup	index
C₂×#10597370	2
#11926875	2
#11926802	2
#11926702	2
C₁₉×#407	2
#3195	19

subgroup

index

C₁₉×#407

Subgroups — #14574459

Conjugacy classes of subgroups

Complements

Maximal subgroups