Group #14569755 — subgroups

Subgroups — #14569755

Order 2432.

448 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10597316	C₂	1	1	yes	maximal, characteristic
2	#11926475	C₂	1	4	yes	maximal
3	#11926463	C₂	1	4	yes	maximal
4	#11926413	C₂	1	2	yes	maximal
5	#11926409	C₂	1	2	yes	maximal
6	#11926390	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
9	C₁₉×C₄⋊Q₈	—	2	4	no	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
16	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
17	C₂×Dic₁₉⋊C₄	C₂²	1	8	yes	—
18	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
19	#10597316	—	2	4	no	—
20	C₁₉⋊#95	C₂²	1	2	yes	—
21	C₁₉⋊#95	C₂²	1	2	yes	—
22	C₁₉⋊#95	C₂²	1	8	yes	—
23	C₂×Q₈×C₁₉	—	2	4	no	—
24	C₂×Q₈×C₁₉	—	4	4	no	—
25	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₁₉	C₂³	1	2	yes	—
30	C₂²×Dic₁₉	C₂³	1	2	yes	—
31	C₂²×Dic₁₉	C₂³	1	4	yes	—
32	C₄⋊C₄×C₁₉	—	2	4	no	—
33	C₄⋊C₄×C₁₉	—	2	4	no	—
34	C₄²×C₁₉	D₄	1	4	yes	—
35	C₄⋊Dic₁₉	—	2	2	no	—
36	C₄⋊Dic₁₉	—	2	2	no	—
37	Dic₁₉⋊C₄	—	2	4	no	—
38	Dic₁₉⋊C₄	—	2	4	no	—
39	Dic₁₉⋊C₄	—	4	8	no	—
40	C₄×Dic₁₉	Q₈	1	8	yes	complemented
41	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
42	Q₈×C₁₉	—	4	8	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	2	8	no	—
47	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
48	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
51	C₂×Dic₁₉	—	2	4	no	—
52	C₂×Dic₁₉	—	2	4	no	—
53	C₂×Dic₁₉	—	2	2	no	—
54	C₂×Dic₁₉	—	2	2	no	—
55	C₂×Dic₁₉	—	2	4	no	—
56	C₂×Dic₁₉	—	2	4	no	—
57	C₂×Dic₁₉	C₂×Q₈	1	8	yes	—
58	#2660	—	19	1	no	maximal, Sylow
59	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
60	C₂²×C₁₉	C₂²×Q₈	1	2	yes	—
61	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
62	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
63	C₄×C₁₉	—	2	2	no	—
64	C₄×C₁₉	—	2	2	no	—
65	C₄×C₁₉	—	4	4	no	—
66	C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
67	Dic₁₉	—	2	8	no	—
68	Dic₁₉	—	4	2	no	—
69	Dic₁₉	—	4	2	no	—
70	C₂×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
71	C₂×#125	—	19	1	no	—
72	#398	—	19	4	no	—
73	#395	—	19	4	no	—
74	#384	—	19	2	no	—
75	#382	—	19	2	no	—
76	#376	—	19	1	no	—
77	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
78	C₂×C₁₉	#535	1	1	yes	characteristic
79	C₂×C₁₉	#536	1	1	yes	characteristic
80	C₂×C₁₉	#544	1	4	yes	—
81	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
82	C₄⋊Q₈	—	2	4	no	—
83	#125	—	38	4	no	—
84	C₂×C₄⋊C₄	—	19	1	no	—
85	C₂×C₄⋊C₄	—	19	1	no	—
86	C₂×C₄⋊C₄	—	19	2	no	—
87	C₂×C₄⋊C₄	—	19	2	no	—
88	C₂×C₄⋊C₄	—	19	8	no	—
89	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
90	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
91	C₂×C₄²	—	19	2	no	—
92	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
93	#95	—	19	2	no	—
94	#95	—	19	2	no	—
95	#95	—	19	8	no	—
96	C₁₉	#2660	1	1	yes	characteristic, complemented, Sylow
97	C₂×Q₈	—	2	4	no	—
98	C₂×Q₈	—	4	4	no	—
99	C₂²×C₄	—	19	4	no	—
100	C₂²×C₄	—	19	2	no	—
101	C₂²×C₄	—	19	2	no	—
102	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
103	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
104	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
105	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
106	C₄⋊C₄	—	2	4	no	—
107	C₄⋊C₄	—	2	4	no	—
108	C₄⋊C₄	—	38	4	no	—
109	C₄⋊C₄	—	38	4	no	—
110	C₄⋊C₄	—	38	2	no	—
111	C₄⋊C₄	—	38	2	no	—
112	C₄⋊C₄	—	76	8	no	—
113	C₄²	—	19	8	no	—
114	C₄²	C₂²⋊D₁₉	1	4	yes	—
115	C₂³	C₂³×D₁₉	1	1	yes	characteristic
116	Q₈	—	4	8	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	8	no	—
120	C₂×C₄	—	2	4	no	—
121	C₂×C₄	—	19	8	no	—
122	C₂×C₄	—	38	4	no	—
123	C₂×C₄	—	38	4	no	—
124	C₂×C₄	—	38	4	no	—
125	C₂×C₄	—	38	4	no	—
126	C₂×C₄	—	38	2	no	—
127	C₂×C₄	—	38	2	no	—
128	C₂×C₄	Q₈×D₁₉	1	4	yes	—
129	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
130	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
131	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
132	C₂²	#10597430	1	2	yes	—
133	C₂²	C₂×Q₈×D₁₉	1	2	yes	—
134	C₂²	#10597433	1	2	yes	—
135	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
136	C₄	—	2	2	no	—
137	C₄	—	2	2	no	—
138	C₄	—	4	4	no	—
139	C₄	—	38	8	no	—
140	C₄	—	76	2	no	—
141	C₄	—	76	2	no	—
142	C₄	#10597390	1	4	yes	—
143	C₂	C₂×#10597390	1	1	yes	characteristic
144	C₂	#11927111	1	1	yes	characteristic
145	C₂	#11927118	1	1	yes	characteristic
146	C₂	#11927171	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597316

C₂

yes

maximal, characteristic

#11926475

C₂

yes

maximal

#11926463

C₂

yes

maximal

#11926413

C₂

yes

maximal

#11926409

C₂

yes

maximal

#11926390

C₂

yes

maximal, characteristic

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#10597316

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

Q₈

yes

complemented

C₂³×C₁₉

C₂⁴

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×Q₈

yes

—

#2660

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄⋊Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

D₁₉

yes

—

—

—

—

—

—

C₂×C₁₉

C₂×C₄⋊Q₈

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂²×Q₈

C₂×D₁₉

yes

—

C₄⋊Q₈

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

C₁₉

#2660

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₂²×D₁₉

yes

—

103

C₂²×C₄

C₂²×D₁₉

yes

characteristic

104

C₂²×C₄

C₂²×D₁₉

yes

characteristic

105

C₂²×C₄

C₂²×D₁₉

yes

characteristic

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄²

—

114

C₄²

C₂²⋊D₁₉

yes

—

115

C₂³

C₂³×D₁₉

yes

characteristic

116

Q₈

—

117

C₂×C₄

—

118

C₂×C₄

—

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

Q₈×D₁₉

yes

—

129

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

130

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

131

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

132

C₂²

#10597430

yes

—

133

C₂²

C₂×Q₈×D₁₉

yes

—

134

C₂²

#10597433

yes

—

135

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

#10597390

yes

—

143

C₂

C₂×#10597390

yes

characteristic

144

C₂

#11927111

yes

characteristic

145

C₂

#11927118

yes

characteristic

146

C₂

#11927171

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×C₄⋊Q₈	C₂
hypercenter	C₂×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#2660
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×C₄⋊Q₈

C₂

hypercenter

C₂×C₄⋊Q₈

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
40. C₄×Dic₁₉	Q₈	semidirect
96. C₁₉	#2660	semidirect

H ≅ G/N

type

40. C₄×Dic₁₉

Q₈

semidirect

96. C₁₉

#2660

semidirect

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

subgroup	index
C₂×#10597316	2
#11926475	2
#11926463	2
#11926413	2
#11926409	2
#11926390	2
C₂×C₁₉×C₄⋊Q₈	2
#2660	19

subgroup

index

C₂×C₁₉×C₄⋊Q₈

Subgroups — #14569755

Conjugacy classes of subgroups

Complements

Maximal subgroups