Group #14564408 — subgroups

Subgroups — #14564408

Order 2432.

200 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10597279	C₂	1	2	yes	maximal
2	C₂×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₄×#64520	C₂	1	1	yes	maximal, characteristic
4	#11926308	C₂	1	2	yes	maximal
5	C₁₉×#423	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×#64520	C₂²	1	1	yes	characteristic
9	C₂×#64520	C₂²	1	1	yes	characteristic
10	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
11	C₁₉×C₄⋊C₈	—	2	1	no	—
12	C₁₉×C₄⋊C₈	—	2	1	no	—
13	#10597279	—	2	4	no	—
14	C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
15	C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
16	#10597260	—	2	1	no	—
17	C₄×C₁₉⋊C₈	—	2	1	no	—
18	C₂²×C₄×C₁₉	Q₈	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	Q₈	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	M₁₆×C₁₉	—	2	2	no	—
22	M₁₆×C₁₉	—	2	2	no	—
23	C₂×C₈×C₁₉	—	2	2	no	—
24	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₄²×C₁₉	D₄	1	1	yes	characteristic
28	#64520	—	2	1	no	—
29	#64520	—	2	1	no	—
30	#64520	D₄	1	2	yes	—
31	#64520	Q₈	1	2	yes	—
32	C₂×C₁₉⋊C₈	—	2	1	no	—
33	C₂×C₁₉⋊C₈	—	2	1	no	—
34	C₂×C₁₉⋊C₈	—	2	2	no	—
35	C₂×C₁₉⋊C₈	—	2	2	no	—
36	C₂×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
37	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₁₉	—	2	2	no	—
39	C₂×C₄×C₁₉	—	4	1	no	—
40	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
50	C₈×C₁₉	—	4	2	no	—
51	C₁₉⋊C₈	—	2	4	no	—
52	C₁₉⋊C₈	—	2	2	no	—
53	C₁₉⋊C₈	—	2	2	no	—
54	#1950	—	19	1	no	maximal, Sylow
55	C₂²×C₁₉	—	2	1	no	—
56	C₂²×C₁₉	—	2	1	no	—
57	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₁₉	#125	1	1	yes	characteristic
59	C₂²×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
60	C₄×C₁₉	—	2	1	no	—
61	C₄×C₁₉	—	2	1	no	—
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	#108	1	2	yes	complemented
64	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
65	C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
66	C₄×C₁₉	#121	1	1	yes	characteristic
67	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
68	C₂×#108	—	19	2	no	—
69	#423	D₁₉	1	1	yes	characteristic
70	C₂×C₄⋊C₈	—	19	1	no	—
71	C₄×M₁₆	—	19	1	no	—
72	#341	—	19	2	no	—
73	C₂×C₁₉	—	2	1	no	—
74	C₂×C₁₉	—	2	1	no	—
75	C₂×C₁₉	#389	1	1	yes	characteristic
76	C₂×C₁₉	C₂×#108	1	1	yes	characteristic
77	C₂×C₁₉	#430	1	1	yes	characteristic
78	C₂×M₁₆	—	19	1	no	—
79	C₂×M₁₆	—	19	1	no	—
80	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
81	C₂²×C₈	—	19	2	no	—
82	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
83	#108	—	38	4	no	—
84	C₄⋊C₈	—	2	1	no	—
85	C₄⋊C₈	—	2	1	no	—
86	C₄⋊C₈	—	19	2	no	—
87	C₄⋊C₈	—	19	2	no	—
88	#97	—	38	1	no	—
89	C₄×C₈	—	38	1	no	—
90	C₁₉	#1950	1	1	yes	characteristic, complemented, Sylow
91	C₂²×C₄	Dic₃₈	1	1	yes	characteristic
92	C₂²×C₄	Dic₃₈	1	1	yes	characteristic
93	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
94	M₁₆	—	2	2	no	—
95	M₁₆	—	2	2	no	—
96	M₁₆	—	19	2	no	—
97	M₁₆	—	19	2	no	—
98	M₁₆	—	38	1	no	—
99	M₁₆	—	38	1	no	—
100	C₂×C₈	—	2	2	no	—
101	C₂×C₈	—	19	4	no	—
102	C₂×C₈	—	38	2	no	—
103	C₂×C₈	—	38	2	no	—
104	C₂×C₈	—	38	1	no	—
105	C₂×C₈	—	38	1	no	—
106	C₄²	C₄×D₁₉	1	1	yes	characteristic
107	C₄²	C₄×D₁₉	1	1	yes	characteristic
108	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
109	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
110	C₂³	C₂×Dic₃₈	1	1	yes	characteristic
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	4	1	no	—
113	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
114	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
115	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
116	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
117	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
118	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
119	C₂×C₄	#64543	1	1	yes	characteristic
120	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
121	C₂×C₄	#64545	1	1	yes	characteristic
122	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
123	C₈	—	4	2	no	—
124	C₈	—	38	2	no	—
125	C₈	—	38	2	no	—
126	C₈	—	38	4	no	—
127	C₂²	—	2	1	no	—
128	C₂²	—	2	1	no	—
129	C₂²	#10597334	1	1	yes	characteristic
130	C₂²	#10597336	1	1	yes	characteristic
131	C₂²	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
132	C₄	—	2	1	no	—
133	C₄	—	2	1	no	—
134	C₄	—	2	1	no	—
135	C₄	#10597279	1	2	yes	complemented
136	C₄	#10597333	1	1	yes	characteristic
137	C₄	#10597339	1	1	yes	characteristic
138	C₄	#10597384	1	1	yes	characteristic
139	C₄	#10597392	1	1	yes	characteristic
140	C₂	—	2	1	no	—
141	C₂	—	2	1	no	—
142	C₂	#11926440	1	1	yes	characteristic
143	C₂	C₂×#10597279	1	1	yes	characteristic
144	C₂	#11926592	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597279

C₂

yes

maximal

C₂×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic

C₄×#64520

C₂

yes

maximal, characteristic

#11926308

C₂

yes

maximal

C₁₉×#423

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

#10597279

—

C₄⋊(C₁₉⋊C₈)

C₄

yes

—

C₄⋊(C₁₉⋊C₈)

C₄

yes

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

Q₈

yes

characteristic

C₂²×C₄×C₁₉

Q₈

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

—

—

D₄

yes

—

#64520

Q₈

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1950

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

#125

yes

characteristic

C₂²×C₁₉

C₄⋊Q₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#108

yes

complemented

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

C₄×Q₈

yes

characteristic

C₄×C₁₉

#121

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×#108

—

#423

D₁₉

yes

characteristic

C₂×C₄⋊C₈

—

C₄×M₁₆

—

#341

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂²×C₈

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

C₄×C₈

—

C₁₉

#1950

yes

characteristic, complemented, Sylow

C₂²×C₄

Dic₃₈

yes

characteristic

C₂²×C₄

Dic₃₈

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₄²

C₄×D₁₉

yes

characteristic

107

C₄²

C₄×D₁₉

yes

characteristic

108

C₄²

C₂²⋊D₁₉

yes

characteristic

109

C₄²

C₂²⋊D₁₉

yes

characteristic

110

C₂³

C₂×Dic₃₈

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

114

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

115

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

116

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

117

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

118

C₂×C₄

D₄×D₁₉

yes

characteristic

119

C₂×C₄

#64543

yes

characteristic

120

C₂×C₄

Q₈×D₁₉

yes

characteristic

121

C₂×C₄

#64545

yes

characteristic

122

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

127

C₂²

—

128

C₂²

—

129

C₂²

#10597334

yes

characteristic

130

C₂²

#10597336

yes

characteristic

131

C₂²

C₂×Dic₁₉⋊C₄

yes

characteristic

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

#10597279

yes

complemented

136

C₄

#10597333

yes

characteristic

137

C₄

#10597339

yes

characteristic

138

C₄

#10597384

yes

characteristic

139

C₄

#10597392

yes

characteristic

140

C₂

—

141

C₂

—

142

C₂

#11926440

yes

characteristic

143

C₂

C₂×#10597279

yes

characteristic

144

C₂

#11926592

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#423	C₂
socle	C₂²×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×C₁₉	C₂×Q₈
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#423	D₁₉
hypocenter	C₁₉	#1950
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#423

C₂

socle

C₂²×C₁₉

C₂×C₄⋊C₄

prime radical

C₂³×C₁₉

C₂×Q₈

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
63. C₄×C₁₉	#108	semidirect
90. C₁₉	#1950	semidirect
135. C₄	#10597279	semidirect

H ≅ G/N

type

63. C₄×C₁₉

#108

semidirect

90. C₁₉

#1950

semidirect

135. C₄

#10597279

semidirect

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

subgroup	index
C₂×#10597279	2
C₂×C₄⋊(C₁₉⋊C₈)	2
C₄×#64520	2
#11926308	2
C₁₉×#423	2
#1950	19

subgroup

index

C₂×C₄⋊(C₁₉⋊C₈)

C₁₉×#423

Subgroups — #14564408

Conjugacy classes of subgroups

Complements

Maximal subgroups