Group #14563631 — subgroups

Subgroups — #14563631

Order 2432.

272 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 113 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	#11926568	C₂	1	2	yes	maximal
2	C₂×#10597293	C₂	1	2	yes	maximal
3	#11926313	C₂	1	2	yes	maximal
4	C₂×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
6	C₄×Q₈×C₁₉	—	2	2	no	—
7	C₄×Q₈×C₁₉	—	2	2	no	—
8	C₂×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₁₉	C₄	1	2	yes	—
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×#64520	C₂²	1	4	yes	—
13	#10597293	—	2	4	no	—
14	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
15	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
16	C₂×Q₈×C₁₉	—	2	2	no	—
17	C₂×Q₈×C₁₉	—	2	2	no	—
18	C₂×Q₈×C₁₉	D₄	1	2	yes	—
19	C₂×Q₈×C₁₉	Q₈	1	2	yes	—
20	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₁₉	—	2	4	no	—
26	C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₄²×C₁₉	—	2	2	no	—
28	C₄²×C₁₉	—	2	2	no	—
29	C₄²×C₁₉	D₄	1	2	yes	—
30	C₄²×C₁₉	D₄	1	2	yes	—
31	#64520	—	2	4	no	—
32	#64520	—	2	4	no	—
33	C₂×C₁₉⋊C₈	—	2	4	no	—
34	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	Q₈×C₁₉	—	2	4	no	—
36	Q₈×C₁₉	—	2	4	no	—
37	C₂×C₄×C₁₉	—	2	2	no	—
38	C₂×C₄×C₁₉	—	2	2	no	—
39	C₂×C₄×C₁₉	—	2	2	no	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	4	1	no	—
42	C₂×C₄×C₁₉	—	4	2	no	—
43	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
45	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
47	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₄×C₁₉	#41	1	2	yes	—
51	C₁₉⋊C₈	—	4	4	no	—
52	#1801	—	19	1	no	maximal, Sylow
53	C₂²×C₁₉	—	2	1	no	—
54	C₂²×C₁₉	—	2	1	no	—
55	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₁₉	#117	1	1	yes	characteristic
58	C₄×C₁₉	—	2	4	no	—
59	C₄×C₁₉	—	2	1	no	—
60	C₄×C₁₉	—	2	2	no	—
61	C₄×C₁₉	—	4	2	no	—
62	C₄×C₁₉	#101	1	2	yes	complemented
63	C₄×C₁₉	#121	1	2	yes	—
64	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
65	C₂×C₄×Q₈	D₁₉	1	1	yes	characteristic
66	#423	—	19	2	no	—
67	C₂×#101	—	19	2	no	—
68	#343	—	19	2	no	—
69	C₂×C₁₉	—	2	1	no	—
70	C₂×C₁₉	—	2	1	no	—
71	C₂×C₁₉	#380	1	1	yes	characteristic
72	C₂×C₁₉	C₂×#101	1	1	yes	characteristic
73	C₂×C₁₉	#413	1	1	yes	characteristic
74	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
75	C₂×M₁₆	—	19	4	no	—
76	C₄×Q₈	—	2	2	no	—
77	C₄×Q₈	—	2	2	no	—
78	C₂×C₄⋊C₄	Dic₁₉	1	2	yes	—
79	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
80	C₂×C₄²	Dic₁₉	1	2	yes	—
81	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
82	C₄⋊C₈	—	38	2	no	—
83	C₄⋊C₈	—	38	2	no	—
84	#101	—	38	4	no	—
85	C₁₉	#1801	1	1	yes	characteristic, complemented, Sylow
86	C₂×Q₈	—	2	2	no	—
87	C₂×Q₈	—	2	2	no	—
88	C₂×Q₈	Dic₃₈	1	2	yes	—
89	C₂×Q₈	D₇₆	1	2	yes	—
90	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
91	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
92	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
93	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
94	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
95	M₁₆	—	38	4	no	—
96	M₁₆	—	38	4	no	—
97	C₂×C₈	—	38	4	no	—
98	C₄⋊C₄	—	2	4	no	—
99	C₄⋊C₄	—	2	2	no	—
100	C₄²	—	2	2	no	—
101	C₄²	—	2	2	no	—
102	C₄²	C₂²⋊D₁₉	1	2	yes	—
103	C₄²	C₂²⋊D₁₉	1	2	yes	—
104	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
105	Q₈	—	2	4	no	—
106	Q₈	—	2	4	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	—	4	1	no	—
112	C₂×C₄	—	4	2	no	—
113	C₂×C₄	C₄⋊Dic₁₉	1	4	yes	—
114	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
115	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
116	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
117	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
118	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
119	C₂×C₄	#64541	1	2	yes	—
120	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
121	C₈	—	76	4	no	—
122	C₂²	—	2	1	no	—
123	C₂²	—	2	1	no	—
124	C₂²	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
125	C₂²	#10597372	1	1	yes	characteristic
126	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
127	C₄	—	2	2	no	—
128	C₄	—	2	4	no	—
129	C₄	—	2	1	no	—
130	C₄	—	4	2	no	—
131	C₄	#10597293	1	2	yes	complemented
132	C₄	#10597370	1	2	yes	—
133	C₄	#10597376	1	2	yes	—
134	C₂	—	2	1	no	—
135	C₂	—	2	1	no	—
136	C₂	#11926404	1	1	yes	characteristic
137	C₂	C₂×#10597293	1	1	yes	characteristic
138	C₂	#11926528	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926568

C₂

yes

maximal

C₂×#10597293

C₂

yes

maximal

#11926313

C₂

yes

maximal

C₂×C₄×Q₈×C₁₉

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₄

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

#10597293

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂×Q₈×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

D₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₁₉⋊C₈

—

#1801

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

#117

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#101

yes

complemented

C₄×C₁₉

#121

yes

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×Q₈

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂×M₁₆

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

Dic₁₉

yes

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

Dic₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

#101

—

C₁₉

#1801

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₃₈

yes

—

C₂×Q₈

D₇₆

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄²

—

101

C₄²

—

102

C₄²

C₂²⋊D₁₉

yes

—

103

C₄²

C₂²⋊D₁₉

yes

—

104

C₂³

C₂²×Dic₁₉

yes

characteristic

105

Q₈

—

106

Q₈

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₄⋊Dic₁₉

yes

—

114

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

115

C₂×C₄

C₂²⋊Dic₁₉

yes

—

116

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

117

C₂×C₄

C₂×Dic₃₈

yes

characteristic

118

C₂×C₄

C₂×D₇₆

yes

characteristic

119

C₂×C₄

#64541

yes

—

120

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

121

C₈

—

122

C₂²

—

123

C₂²

—

124

C₂²

C₂×C₄⋊Dic₁₉

yes

characteristic

125

C₂²

#10597372

yes

characteristic

126

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

#10597293

yes

complemented

132

C₄

#10597370

yes

—

133

C₄

#10597376

yes

—

134

C₂

—

135

C₂

—

136

C₂

#11926404

yes

characteristic

137

C₂

C₂×#10597293

yes

characteristic

138

C₂

#11926528

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₁₉
commutator, prime radical	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₄×Q₈×C₁₉	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×Q₈	D₁₉
hypocenter	C₁₉	#1801
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×Q₈

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₁₉

commutator, prime radical

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₄×Q₈×C₁₉

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂×C₄×Q₈

D₁₉

hypocenter

C₁₉

#1801

LCS

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×Q₈

N	H ≅ G/N	type
62. C₄×C₁₉	#101	semidirect
85. C₁₉	#1801	semidirect
131. C₄	#10597293	semidirect

H ≅ G/N

type

62. C₄×C₁₉

#101

semidirect

85. C₁₉

#1801

semidirect

131. C₄

#10597293

semidirect

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

subgroup	index
#11926568	2
C₂×#10597293	2
#11926313	2
C₂×C₄×Q₈×C₁₉	2
#1801	19

subgroup

index

C₂×C₄×Q₈×C₁₉

Subgroups — #14563631

Conjugacy classes of subgroups

Complements

Maximal subgroups