Group #14562108 — subgroups

Subgroups — #14562108

Order 2432.

202 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 81 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	#11926601	C₂	1	1	yes	maximal, characteristic
2	#11926597	C₂	1	1	yes	maximal, characteristic
3	Q₈⋊(C₁₉⋊C₈)	C₂	1	4	yes	maximal, complemented
4	C₁₉×#533	C₂	1	1	yes	maximal, characteristic
5	C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
6	C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
7	C₁₉×#125	—	2	1	no	—
8	C₁₉×C₂²⋊Q₈	—	2	1	no	—
9	C₁₉×C₂²⋊Q₈	C₄	1	2	yes	—
10	C₄×Q₈×C₁₉	—	2	1	no	—
11	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
12	C₁₉×#117	—	2	1	no	—
13	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
15	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
16	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
17	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
18	#10597260	—	2	1	no	—
19	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
20	C₂×Q₈×C₁₉	—	2	1	no	—
21	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
31	C₂²⋊C₄×C₁₉	—	2	2	no	—
32	C₄²×C₁₉	—	2	2	no	—
33	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₄²×C₁₉	D₄	1	1	yes	characteristic
35	C₄²×C₁₉	D₄	1	1	yes	characteristic
36	C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×C₁₉⋊C₈	—	2	2	no	—
38	C₂×C₁₉⋊C₈	—	2	2	no	—
39	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
40	Q₈×C₁₉	—	2	4	no	—
41	Q₈×C₁₉	—	4	2	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	4	1	no	—
47	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₁₉⋊C₈	—	4	2	no	—
54	C₁₉⋊C₈	—	4	2	no	—
55	#1497	—	19	1	no	maximal, Sylow
56	C₂²×C₁₉	—	2	1	no	—
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	C₂×C₂²⋊C₄	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	—	2	1	no	—
64	C₄×C₁₉	—	4	2	no	—
65	C₄×C₁₉	—	4	2	no	—
66	C₄×C₁₉	#131	1	2	yes	—
67	C₄×C₁₉	#137	1	2	yes	—
68	#533	D₁₉	1	1	yes	characteristic
69	#432	—	19	1	no	—
70	#431	—	19	1	no	—
71	Q₈⋊C₈	—	19	4	no	—
72	C₂×C₁₉	—	4	1	no	—
73	C₂×C₁₉	#408	1	1	yes	characteristic
74	C₂×C₁₉	#419	1	1	yes	characteristic
75	C₂×C₁₉	#421	1	1	yes	characteristic
76	C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic
77	C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic
78	#125	—	2	1	no	—
79	C₂²⋊Q₈	—	2	1	no	—
80	C₂²⋊Q₈	Dic₁₉	1	2	yes	—
81	C₄×Q₈	—	2	1	no	—
82	C₄×Q₈	C₂×D₁₉	1	2	yes	—
83	#117	—	2	1	no	—
84	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
85	C₄⋊C₈	—	19	2	no	—
86	C₄⋊C₈	—	38	1	no	—
87	C₂²⋊C₈	—	38	1	no	—
88	C₂²⋊C₈	—	38	1	no	—
89	#97	—	38	1	no	—
90	C₄×C₈	—	19	2	no	—
91	C₁₉	#1497	1	1	yes	characteristic, complemented, Sylow
92	C₂×Q₈	—	2	1	no	—
93	C₂×Q₈	C₂×Dic₁₉	1	2	yes	—
94	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
95	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
96	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
97	C₂×C₈	—	38	2	no	—
98	C₂×C₈	—	38	2	no	—
99	C₄⋊C₄	—	2	1	no	—
100	C₄⋊C₄	—	2	1	no	—
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	2	2	no	—
103	C₄⋊C₄	—	2	2	no	—
104	C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
105	C₂²⋊C₄	—	2	2	no	—
106	C₄²	—	2	2	no	—
107	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
108	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
109	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
110	C₄²	C₂²×D₁₉	1	1	yes	characteristic
111	C₂³	C₂²⋊Dic₁₉	1	1	yes	characteristic
112	Q₈	—	2	4	no	—
113	Q₈	—	4	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
120	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
121	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
122	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
123	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
124	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
125	C₈	—	76	2	no	—
126	C₈	—	76	2	no	—
127	C₂²	—	2	1	no	—
128	C₂²	—	2	1	no	—
129	C₂²	—	2	1	no	—
130	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
131	C₄	—	2	1	no	—
132	C₄	—	2	1	no	—
133	C₄	—	2	1	no	—
134	C₄	—	2	1	no	—
135	C₄	—	4	2	no	—
136	C₄	—	4	2	no	—
137	C₄	#10597388	1	2	yes	—
138	C₄	#10597394	1	2	yes	—
139	C₂	—	4	1	no	—
140	C₂	#11926511	1	1	yes	characteristic
141	C₂	#11926553	1	1	yes	characteristic
142	C₂	#11926561	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926601

C₂

yes

maximal, characteristic

#11926597

C₂

yes

maximal, characteristic

Q₈⋊(C₁₉⋊C₈)

C₂

yes

maximal, complemented

C₁₉×#533

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

C₄

yes

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

C₂²

yes

—

C₁₉×#117

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597260

—

C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

—

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

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×C₄×C₁₉

C₂×D₄

yes

characteristic

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1497

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#131

yes

—

C₄×C₁₉

#137

yes

—

#533

D₁₉

yes

characteristic

#432

—

#431

—

Q₈⋊C₈

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₄⋊Q₈

Dic₁₉

yes

characteristic

C₄⋊Q₈

Dic₁₉

yes

characteristic

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

Dic₁₉

yes

—

C₄×Q₈

—

C₄×Q₈

C₂×D₁₉

yes

—

#117

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₁₉

#1497

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

C₂×Dic₁₉

yes

—

105

C₂²⋊C₄

—

106

C₄²

—

107

C₄²

C₂×Dic₁₉

yes

characteristic

108

C₄²

C₂²⋊D₁₉

yes

characteristic

109

C₄²

C₂²⋊D₁₉

yes

characteristic

110

C₄²

C₂²×D₁₉

yes

characteristic

111

C₂³

C₂²⋊Dic₁₉

yes

characteristic

112

Q₈

—

113

Q₈

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

120

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

121

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

122

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

123

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

124

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

125

C₈

—

126

C₈

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

#10597388

yes

—

138

C₄

#10597394

yes

—

139

C₂

—

140

C₂

#11926511

yes

characteristic

141

C₂

#11926553

yes

characteristic

142

C₂

#11926561

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#533	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₉	C₂²⋊C₄
cosocle	C₄²×C₁₉	C₂³
hypercenter	#533	D₁₉
hypocenter	C₁₉	#1497
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#533

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂³×C₁₉

C₂²⋊C₄

cosocle

C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

N	H ≅ G/N	type
3. Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
91. C₁₉	#1497	semidirect

H ≅ G/N

type

3. Q₈⋊(C₁₉⋊C₈)

C₂

semidirect

91. C₁₉

#1497

semidirect

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

subgroup	index
#11926601	2
#11926597	2
Q₈⋊(C₁₉⋊C₈)	2
C₁₉×#533	2
#1497	19

subgroup

index

#11926601

#11926597

Q₈⋊(C₁₉⋊C₈)

C₁₉×#533

#1497

Subgroups — #14562108

Conjugacy classes of subgroups

Complements

Maximal subgroups