Group #14562187 — subgroups

Subgroups — #14562187

Order 2432.

208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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	#11927101	C₂	1	1	yes	maximal, characteristic
2	#11926412	C₂	1	1	yes	maximal, characteristic
3	#11926282	C₂	1	4	yes	maximal
4	C₁₉×#432	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
6	#10597372	—	2	1	no	—
7	#10597370	—	2	1	no	—
8	#10597370	C₂²	1	2	yes	—
9	#10597316	—	2	1	no	—
10	#10597315	C₄	1	1	yes	characteristic, complemented
11	#10597315	C₄	1	1	yes	characteristic, complemented
12	C₄×Dic₃₈	—	2	1	no	—
13	C₄×Dic₃₈	C₄	1	2	yes	complemented
14	C₁₉×C₄⋊C₈	—	2	1	no	—
15	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₁₉×#97	—	2	1	no	—
17	C₁₉⋊#95	—	2	1	no	—
18	C₁₉⋊#95	—	2	1	no	—
19	C₁₉⋊#95	C₂²	1	2	yes	—
20	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₁₉	—	2	2	no	—
24	C₂×Dic₃₈	—	2	1	no	—
25	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₄²×C₁₉	D₄	1	1	yes	characteristic
30	C₄²×C₁₉	D₄	1	1	yes	characteristic
31	C₂²⋊Dic₁₉	—	2	2	no	—
32	C₄⋊Dic₁₉	—	2	1	no	—
33	C₄⋊Dic₁₉	—	2	1	no	—
34	C₄⋊Dic₁₉	—	2	1	no	—
35	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
36	Dic₁₉⋊C₄	—	2	2	no	—
37	Dic₁₉⋊C₄	—	2	2	no	—
38	C₄×Dic₁₉	—	2	2	no	—
39	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	4	1	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×Dic₁₉	—	2	2	no	—
50	C₂×Dic₁₉	—	2	2	no	—
51	C₂×Dic₁₉	—	4	2	no	—
52	C₂×Dic₁₉	—	4	2	no	—
53	C₂×Dic₁₉	—	4	2	no	—
54	Dic₃₈	—	4	2	no	—
55	Dic₃₈	—	4	2	no	—
56	C₈×C₁₉	—	4	2	no	—
57	#1515	—	19	1	no	maximal, Sylow
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	—	2	1	no	—
60	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₁₉	#137	1	2	yes	—
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	—	2	1	no	—
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	2	1	no	—
68	Dic₁₉	—	4	2	no	—
69	Dic₁₉	—	4	2	no	—
70	Dic₁₉	—	8	2	no	—
71	#533	—	19	1	no	—
72	#432	D₁₉	1	1	yes	characteristic
73	#383	—	19	1	no	—
74	#328	—	19	4	no	—
75	C₂×C₁₉	—	2	2	no	—
76	C₂×C₁₉	#410	1	1	yes	characteristic
77	C₂×C₁₉	#419	1	1	yes	characteristic
78	C₂×C₁₉	#421	1	1	yes	characteristic
79	C₄⋊Q₈	—	19	1	no	—
80	C₄⋊Q₈	—	19	1	no	—
81	#125	—	38	1	no	—
82	C₂²⋊Q₈	—	19	2	no	—
83	C₂²⋊Q₈	—	38	1	no	—
84	C₄×Q₈	—	19	2	no	—
85	C₄×Q₈	—	38	1	no	—
86	#117	—	38	1	no	—
87	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
88	C₄⋊C₈	—	2	1	no	—
89	C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
90	#97	—	2	1	no	—
91	#95	—	19	2	no	—
92	#95	—	38	1	no	—
93	#95	—	38	1	no	—
94	C₁₉	#1515	1	1	yes	characteristic, complemented, Sylow
95	C₂×Q₈	—	19	2	no	—
96	C₂×Q₈	—	38	1	no	—
97	C₂²×C₄	—	38	2	no	—
98	C₂²×C₄	D₇₆	1	1	yes	characteristic
99	C₂²×C₄	D₇₆	1	1	yes	characteristic
100	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
101	C₂×C₈	—	2	2	no	—
102	C₄⋊C₄	—	19	2	no	—
103	C₄⋊C₄	—	38	2	no	—
104	C₄⋊C₄	—	38	1	no	—
105	C₄⋊C₄	—	38	1	no	—
106	C₄⋊C₄	—	38	1	no	—
107	C₄⋊C₄	—	38	2	no	—
108	C₂²⋊C₄	—	38	2	no	—
109	C₄²	—	38	2	no	—
110	C₄²	C₄×D₁₉	1	1	yes	characteristic
111	C₄²	C₄×D₁₉	1	1	yes	characteristic
112	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
113	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
114	C₂³	C₂×D₇₆	1	1	yes	characteristic
115	Q₈	—	76	2	no	—
116	Q₈	—	76	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	38	2	no	—
121	C₂×C₄	—	38	2	no	—
122	C₂×C₄	—	76	2	no	—
123	C₂×C₄	—	76	2	no	—
124	C₂×C₄	—	76	2	no	—
125	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
126	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
127	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
128	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
129	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
130	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
131	C₈	—	4	2	no	—
132	C₂²	—	2	1	no	—
133	C₂²	—	2	1	no	—
134	C₂²	#10597355	1	2	yes	—
135	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
136	C₄	—	2	1	no	—
137	C₄	—	2	1	no	—
138	C₄	—	2	1	no	—
139	C₄	—	2	1	no	—
140	C₄	—	2	1	no	—
141	C₄	—	2	1	no	—
142	C₄	—	76	2	no	—
143	C₄	—	76	2	no	—
144	C₄	—	152	2	no	—
145	C₂	—	2	2	no	—
146	C₂	#11926517	1	1	yes	characteristic
147	C₂	#11926554	1	1	yes	characteristic
148	C₂	#11926560	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927101

C₂

yes

maximal, characteristic

#11926412

C₂

yes

maximal, characteristic

#11926282

C₂

yes

maximal

C₁₉×#432

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₉

C₂²

yes

—

—

C₂²

yes

—

#10597316

—

#10597315

C₄

yes

characteristic, complemented

#10597315

C₄

yes

characteristic, complemented

C₄×Dic₃₈

—

C₄×Dic₃₈

C₄

yes

complemented

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

C₂²

yes

—

C₁₉×#97

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂²

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

#1515

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

#533

—

#432

D₁₉

yes

characteristic

#383

—

#328

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

C₂×D₁₉

yes

—

—

—

—

—

C₁₉

#1515

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

D₇₆

yes

characteristic

100

C₂²×C₄

C₂²×D₁₉

yes

characteristic

101

C₂×C₈

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₄²

—

110

C₄²

C₄×D₁₉

yes

characteristic

111

C₄²

C₄×D₁₉

yes

characteristic

112

C₄²

C₂²⋊D₁₉

yes

characteristic

113

C₄²

C₂²⋊D₁₉

yes

characteristic

114

C₂³

C₂×D₇₆

yes

characteristic

115

Q₈

—

116

Q₈

—

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

(C₂×D₁₉)⋊C₄

yes

characteristic

126

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

127

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

128

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

129

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

130

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

131

C₈

—

132

C₂²

—

133

C₂²

—

134

C₂²

#10597355

yes

—

135

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

152

—

145

C₂

—

146

C₂

#11926517

yes

characteristic

147

C₂

#11926554

yes

characteristic

148

C₂

#11926560

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#432	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#432	D₁₉
hypocenter	C₁₉	#1515
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #432

subgroup

G/H

center

C₂²

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#432

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #432

N	H ≅ G/N	type
10. #10597315	C₄	semidirect
11. #10597315	C₄	semidirect
13. C₄×Dic₃₈	C₄	semidirect
94. C₁₉	#1515	semidirect

H ≅ G/N

type

10. #10597315

C₄

semidirect

11. #10597315

C₄

semidirect

13. C₄×Dic₃₈

C₄

semidirect

94. C₁₉

#1515

semidirect

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

subgroup	index
#11927101	2
#11926412	2
#11926282	2
C₁₉×#432	2
#1515	19

subgroup

index

C₁₉×#432

Subgroups — #14562187

Conjugacy classes of subgroups

Complements

Maximal subgroups