Group #14564981 — subgroups

Subgroups — #14564981

Order 2432.

246 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 75 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	#11927175	C₂	1	1	yes	maximal, characteristic
2	#11926586	C₂	1	2	yes	maximal
3	#11926413	C₂	1	1	yes	maximal, characteristic
4	#11926305	C₂	1	2	yes	maximal
5	C₁₉×#343	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
8	#10597372	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
10	#10597370	—	2	2	no	—
11	C₂×Dic₁₉⋊C₄	—	2	2	no	—
12	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
13	#10597336	—	2	2	no	—
14	#10597334	—	2	2	no	—
15	#10597275	—	2	2	no	—
16	#10597274	—	2	2	no	—
17	C₂²×C₄×C₁₉	D₄	1	2	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₁₉	—	2	1	no	—
20	C₂²×Dic₁₉	—	2	1	no	—
21	C₂×Dic₃₈	—	2	2	no	—
22	M₁₆×C₁₉	—	2	2	no	—
23	M₁₆×C₁₉	Q₈	1	4	yes	complemented
24	C₂×C₈×C₁₉	—	2	2	no	—
25	C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂²⋊Dic₁₉	—	2	2	no	—
27	C₄⋊Dic₁₉	—	2	2	no	—
28	C₄⋊Dic₁₉	—	2	2	no	—
29	C₄⋊Dic₁₉	D₄	1	2	yes	—
30	C₄⋊Dic₁₉	D₄	1	2	yes	—
31	Dic₁₉⋊C₄	—	2	4	no	—
32	Dic₁₉⋊C₄	—	4	4	no	—
33	C₄×Dic₁₉	—	2	2	no	—
34	C₄×Dic₁₉	—	2	1	no	—
35	C₄×Dic₁₉	Q₈	1	2	yes	complemented
36	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	—	2	2	no	—
38	C₂×C₄×C₁₉	—	4	2	no	—
39	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
41	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
43	C₂×Dic₁₉	—	2	2	no	—
44	C₂×Dic₁₉	—	2	2	no	—
45	C₂×Dic₁₉	—	2	2	no	—
46	C₂×Dic₁₉	—	2	2	no	—
47	C₂×Dic₁₉	—	2	2	no	—
48	C₂×Dic₁₉	—	4	2	no	—
49	C₂×Dic₁₉	—	4	1	no	—
50	Dic₃₈	—	8	2	no	—
51	C₈×C₁₉	—	2	4	no	—
52	#2060	—	19	1	no	maximal, Sylow
53	C₂²×C₁₉	—	2	1	no	—
54	C₂²×C₁₉	—	2	1	no	—
55	C₂²×C₁₉	#120	1	1	yes	characteristic
56	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
57	C₂²×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
58	C₄×C₁₉	—	4	2	no	—
59	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
60	C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
61	Dic₁₉	—	2	4	no	—
62	Dic₁₉	—	4	2	no	—
63	Dic₁₉	—	4	2	no	—
64	Dic₁₉	—	8	1	no	—
65	#544	—	19	1	no	—
66	#428	—	19	2	no	—
67	#384	—	19	1	no	—
68	#343	D₁₉	1	1	yes	characteristic
69	#339	—	19	2	no	—
70	C₂×C₁₉	—	2	1	no	—
71	C₂×C₁₉	—	2	1	no	—
72	C₂×C₁₉	#395	1	1	yes	characteristic
73	C₂×C₁₉	#453	1	1	yes	characteristic
74	C₂×C₁₉	#456	1	1	yes	characteristic
75	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
76	C₄⋊Q₈	—	38	2	no	—
77	#125	—	38	2	no	—
78	C₂²⋊Q₈	—	38	2	no	—
79	#117	—	19	2	no	—
80	C₂×C₄⋊C₄	—	19	1	no	—
81	C₂×C₄⋊C₄	—	38	2	no	—
82	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
83	C₂×C₄²	—	19	1	no	—
84	#107	—	38	2	no	—
85	#106	—	38	2	no	—
86	C₁₉	#2060	1	1	yes	characteristic, complemented, Sylow
87	C₂×Q₈	—	38	2	no	—
88	C₂²×C₄	—	38	1	no	—
89	C₂²×C₄	—	38	1	no	—
90	C₂²×C₄	D₇₆	1	2	yes	—
91	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
92	M₁₆	—	2	2	no	—
93	M₁₆	Dic₃₈	1	4	yes	complemented
94	C₂×C₈	—	2	2	no	—
95	C₄⋊C₄	—	2	2	no	—
96	C₄⋊C₄	—	19	2	no	—
97	C₄⋊C₄	—	19	2	no	—
98	C₄⋊C₄	—	38	4	no	—
99	C₄⋊C₄	—	38	2	no	—
100	C₄⋊C₄	—	38	2	no	—
101	C₄⋊C₄	—	76	4	no	—
102	C₂²⋊C₄	—	38	2	no	—
103	C₄²	—	19	2	no	—
104	C₄²	—	38	2	no	—
105	C₄²	—	38	1	no	—
106	C₂³	C₂×D₇₆	1	1	yes	characteristic
107	Q₈	—	152	2	no	—
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	4	2	no	—
110	C₂×C₄	—	38	2	no	—
111	C₂×C₄	—	38	2	no	—
112	C₂×C₄	—	38	2	no	—
113	C₂×C₄	—	38	2	no	—
114	C₂×C₄	—	38	2	no	—
115	C₂×C₄	—	76	2	no	—
116	C₂×C₄	—	76	1	no	—
117	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
118	C₂×C₄	D₄×D₁₉	1	2	yes	—
119	C₂×C₄	#64543	1	1	yes	characteristic
120	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
121	C₈	—	2	4	no	—
122	C₂²	—	2	1	no	—
123	C₂²	—	2	1	no	—
124	C₂²	#10597315	1	1	yes	characteristic
125	C₂²	#10597328	1	1	yes	characteristic
126	C₂²	#10597343	1	1	yes	characteristic
127	C₄	—	4	2	no	—
128	C₄	—	38	4	no	—
129	C₄	—	76	2	no	—
130	C₄	—	76	2	no	—
131	C₄	—	152	1	no	—
132	C₄	#10597324	1	2	yes	—
133	C₄	#10597334	1	2	yes	—
134	C₂	—	2	1	no	—
135	C₂	—	2	1	no	—
136	C₂	#11926465	1	1	yes	characteristic
137	C₂	#11926714	1	1	yes	characteristic
138	C₂	#11926729	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927175

C₂

yes

maximal, characteristic

#11926586

C₂

yes

maximal

#11926413

C₂

yes

maximal, characteristic

#11926305

C₂

yes

maximal

C₁₉×#343

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

#10597370

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

—

—

—

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

Q₈

yes

complemented

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

C₄⋊Dic₁₉

D₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

Q₈

yes

complemented

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

C₈×C₁₉

—

#2060

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

C₄⋊Q₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

C₄⋊Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic

#339

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

C₂×D₁₉

yes

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

—

#107

—

#106

—

C₁₉

#2060

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

Dic₃₈

yes

complemented

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

103

C₄²

—

104

C₄²

—

105

C₄²

—

106

C₂³

C₂×D₇₆

yes

characteristic

107

Q₈

—

152

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

C₂×Dic₃₈

yes

—

118

C₂×C₄

D₄×D₁₉

yes

—

119

C₂×C₄

#64543

yes

characteristic

120

C₂×C₄

Q₈×D₁₉

yes

characteristic

121

C₈

—

122

C₂²

—

123

C₂²

—

124

C₂²

#10597315

yes

characteristic

125

C₂²

#10597328

yes

characteristic

126

C₂²

#10597343

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

152

—

132

C₄

#10597324

yes

—

133

C₄

#10597334

yes

—

134

C₂

—

135

C₂

—

136

C₂

#11926465

yes

characteristic

137

C₂

#11926714

yes

characteristic

138

C₂

#11926729

yes

characteristic

	subgroup	G/H
center	C₂²	#10597328
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#343	C₂
socle	C₂²×C₁₉	#120
prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#343	D₁₉
hypocenter	C₁₉	#2060
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #343

subgroup

G/H

center

C₂²

#10597328

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#343

C₂

socle

C₂²×C₁₉

#120

prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #343

N	H ≅ G/N	type
23. M₁₆×C₁₉	Q₈	semidirect
35. C₄×Dic₁₉	Q₈	semidirect
86. C₁₉	#2060	semidirect
93. M₁₆	Dic₃₈	semidirect

H ≅ G/N

type

23. M₁₆×C₁₉

Q₈

semidirect

35. C₄×Dic₁₉

Q₈

semidirect

86. C₁₉

#2060

semidirect

93. M₁₆

Dic₃₈

semidirect

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

subgroup	index
#11927175	2
#11926586	2
#11926413	2
#11926305	2
C₁₉×#343	2
#2060	19

subgroup

index

C₁₉×#343

Subgroups — #14564981

Conjugacy classes of subgroups

Complements

Maximal subgroups