Group #14564959 — subgroups

Subgroups — #14564959

Order 2432.

288 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂²×Dic₇₆	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597267	C₂	1	2	yes	maximal
4	#11926449	C₂	1	2	yes	maximal
5	C₁₉×#340	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₈	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₆	—	2	4	no	—
12	C₂×Dic₇₆	—	2	2	no	—
13	C₁₉⋊#95	—	2	2	no	—
14	C₁₉⋊#95	—	2	2	no	—
15	Dic₁₉⋊C₈	—	2	2	no	—
16	#10597267	—	2	4	no	—
17	C₂²×C₄×C₁₉	—	2	2	no	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₁₉	—	2	2	no	—
20	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
21	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
22	C₂×Dic₃₈	—	2	2	no	—
23	C₂×Dic₃₈	—	2	2	no	—
24	C₂×Dic₃₈	—	2	2	no	—
25	C₂×Dic₃₈	—	2	2	no	—
26	C₂×Dic₃₈	—	2	2	no	—
27	C₂×Dic₃₈	D₄	1	4	yes	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₂×C₈×C₁₉	D₄	1	2	yes	—
30	C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₄×Dic₁₉	—	2	1	no	—
33	C₄×Dic₁₉	—	2	1	no	—
34	C₂×C₁₉⋊C₈	—	2	2	no	—
35	C₂×C₁₉⋊C₈	—	2	1	no	—
36	Dic₇₆	—	2	8	no	—
37	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	—	4	2	no	—
39	C₂×C₄×C₁₉	—	4	2	no	—
40	C₂×C₄×C₁₉	—	4	2	no	—
41	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₁₉	#41	1	2	yes	—
44	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
45	C₂×Dic₁₉	—	2	1	no	—
46	C₂×Dic₁₉	—	2	1	no	—
47	C₂×Dic₁₉	—	2	1	no	—
48	C₂×Dic₁₉	—	2	4	no	—
49	C₂×Dic₁₉	—	2	2	no	—
50	C₂×Dic₁₉	—	4	2	no	—
51	C₂×Dic₁₉	—	4	2	no	—
52	C₂×Dic₁₉	Q₁₆	1	2	yes	complemented
53	Dic₃₈	—	2	4	no	—
54	Dic₃₈	—	2	4	no	—
55	Dic₃₈	—	4	2	no	—
56	Dic₃₈	—	4	2	no	—
57	C₈×C₁₉	—	2	2	no	—
58	C₁₉⋊C₈	—	4	1	no	—
59	#2056	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	#121	1	2	yes	—
61	C₂²×C₁₉	#121	1	1	yes	characteristic
62	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
63	C₂²×C₁₉	#135	1	1	yes	characteristic
64	C₂²×C₁₉	#137	1	2	yes	—
65	C₄×C₁₉	—	8	2	no	—
66	C₄×C₁₉	#120	1	1	yes	characteristic
67	C₄×C₁₉	#123	1	2	yes	—
68	C₄×C₁₉	#124	1	1	yes	characteristic
69	Dic₁₉	—	2	2	no	—
70	Dic₁₉	—	4	4	no	—
71	Dic₁₉	—	4	1	no	—
72	C₂²×Q₁₆	—	19	1	no	—
73	C₂×C₄⋊C₈	—	19	1	no	—
74	C₂×#103	—	19	2	no	—
75	#391	—	19	2	no	—
76	#340	D₁₉	1	1	yes	characteristic
77	C₂×C₁₉	#394	1	1	yes	characteristic
78	C₂×C₁₉	#462	1	2	yes	—
79	C₂×C₁₉	#464	1	2	yes	—
80	C₂×C₁₉	#467	1	1	yes	characteristic
81	C₂×C₁₉	#470	1	1	yes	characteristic
82	C₂²×Q₈	—	19	2	no	—
83	C₂×Q₁₆	—	38	4	no	—
84	C₂×Q₁₆	—	38	2	no	—
85	C₂²×C₈	—	19	1	no	—
86	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
87	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
88	C₂×C₄²	—	19	1	no	—
89	C₄⋊C₈	—	38	2	no	—
90	#103	—	38	4	no	—
91	#95	—	38	2	no	—
92	#95	—	38	2	no	—
93	C₁₉	#2056	1	1	yes	characteristic, complemented, Sylow
94	C₂×Q₈	—	19	4	no	—
95	C₂×Q₈	—	38	2	no	—
96	C₂×Q₈	—	38	2	no	—
97	C₂×Q₈	—	38	2	no	—
98	C₂×Q₈	—	38	2	no	—
99	C₂×Q₈	—	38	2	no	—
100	C₂²×C₄	—	2	2	no	—
101	C₂²×C₄	—	19	1	no	—
102	C₂²×C₄	—	19	1	no	—
103	C₂²×C₄	—	38	2	no	—
104	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
105	Q₁₆	—	38	8	no	—
106	C₂×C₈	—	2	2	no	—
107	C₂×C₈	—	38	1	no	—
108	C₂×C₈	—	38	2	no	—
109	C₂×C₈	D₇₆	1	2	yes	—
110	C₄⋊C₄	—	2	2	no	—
111	C₄⋊C₄	—	2	2	no	—
112	C₄²	—	38	1	no	—
113	C₄²	—	38	1	no	—
114	C₂³	D₄×D₁₉	1	1	yes	characteristic
115	Q₈	—	38	4	no	—
116	Q₈	—	38	4	no	—
117	Q₈	—	76	2	no	—
118	Q₈	—	76	2	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	4	2	no	—
121	C₂×C₄	—	4	2	no	—
122	C₂×C₄	—	19	2	no	—
123	C₂×C₄	—	38	1	no	—
124	C₂×C₄	—	38	1	no	—
125	C₂×C₄	—	38	4	no	—
126	C₂×C₄	—	38	1	no	—
127	C₂×C₄	—	38	2	no	—
128	C₂×C₄	—	76	2	no	—
129	C₂×C₄	—	76	2	no	—
130	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
131	C₂×C₄	#64541	1	2	yes	—
132	C₂×C₄	D₄×D₁₉	1	2	yes	—
133	C₂×C₄	#64545	1	1	yes	characteristic
134	C₈	—	2	2	no	—
135	C₈	—	76	1	no	—
136	C₂²	#10597330	1	2	yes	—
137	C₂²	#10597341	1	1	yes	characteristic
138	C₂²	#10597358	1	1	yes	characteristic
139	C₂²	#10597361	1	2	yes	—
140	C₂²	Q₁₆×D₁₉	1	1	yes	characteristic
141	C₄	—	8	2	no	—
142	C₄	—	38	2	no	—
143	C₄	—	76	1	no	—
144	C₄	—	76	4	no	—
145	C₄	#10597321	1	1	yes	characteristic
146	C₄	#10597328	1	1	yes	characteristic
147	C₄	#10597340	1	2	yes	—
148	C₂	#11926462	1	1	yes	characteristic
149	C₂	#11926753	1	2	yes	—
150	C₂	#11926765	1	2	yes	—
151	C₂	#11926786	1	1	yes	characteristic
152	C₂	#11926803	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₇₆

C₂

yes

maximal, characteristic

C₂×Dic₁₉⋊C₈

C₂

yes

maximal, characteristic

C₂×#10597267

C₂

yes

maximal

#11926449

C₂

yes

maximal

C₁₉×#340

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₁₉⋊#95

—

C₁₉⋊#95

—

Dic₁₉⋊C₈

—

#10597267

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

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

#41

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

Q₁₆

yes

complemented

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2056

—

maximal, Sylow

C₂²×C₁₉

#121

yes

—

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

C₂×Q₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

characteristic

C₄×C₁₉

#123

yes

—

C₄×C₁₉

#124

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂²×Q₁₆

—

C₂×C₄⋊C₈

—

C₂×#103

—

#391

—

#340

D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#464

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₄⋊C₈

—

#103

—

#95

—

#95

—

C₁₉

#2056

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

C₂²×D₁₉

yes

characteristic

105

Q₁₆

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

D₇₆

yes

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄²

—

113

C₄²

—

114

C₂³

D₄×D₁₉

yes

characteristic

115

Q₈

—

116

Q₈

—

117

Q₈

—

118

Q₈

—

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

—

129

C₂×C₄

—

130

C₂×C₄

C₂×D₇₆

yes

characteristic

131

C₂×C₄

#64541

yes

—

132

C₂×C₄

D₄×D₁₉

yes

—

133

C₂×C₄

#64545

yes

characteristic

134

C₈

—

135

C₈

—

136

C₂²

#10597330

yes

—

137

C₂²

#10597341

yes

characteristic

138

C₂²

#10597358

yes

characteristic

139

C₂²

#10597361

yes

—

140

C₂²

Q₁₆×D₁₉

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

#10597321

yes

characteristic

146

C₄

#10597328

yes

characteristic

147

C₄

#10597340

yes

—

148

C₂

#11926462

yes

characteristic

149

C₂

#11926753

yes

—

150

C₂

#11926765

yes

—

151

C₂

#11926786

yes

characteristic

152

C₂

#11926803

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#340	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#340	D₁₉
hypocenter	C₁₉	#2056
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#340

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
52. C₂×Dic₁₉	Q₁₆	semidirect
93. C₁₉	#2056	semidirect

H ≅ G/N

type

52. C₂×Dic₁₉

Q₁₆

semidirect

93. C₁₉

#2056

semidirect

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

subgroup	index
C₂²×Dic₇₆	2
C₂×Dic₁₉⋊C₈	2
C₂×#10597267	2
#11926449	2
C₁₉×#340	2
#2056	19

subgroup

index

C₂²×Dic₇₆

C₂×Dic₁₉⋊C₈

C₂×#10597267

#11926449

C₁₉×#340

#2056

Subgroups — #14564959

Conjugacy classes of subgroups

Complements

Maximal subgroups