Group #14563089 — subgroups

Subgroups — #14563089

Order 2432.

160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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	#11926896	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926831	C₂	1	1	yes	maximal, characteristic
3	#11926825	C₂	1	1	yes	maximal, characteristic
4	#11926609	C₂	1	1	yes	maximal, characteristic
5	#11926296	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926291	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₁₉	—	2	1	no	—
10	C₄×D₇₆	C₂²	1	1	yes	characteristic
11	#10597315	C₂²	1	1	yes	characteristic
12	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	#10597278	—	2	1	no	—
15	(C₂×D₁₉)⋊C₈	—	2	1	no	—
16	#10597275	—	2	1	no	—
17	#10597267	—	2	1	no	—
18	#10597267	—	2	1	no	—
19	#10597266	—	2	1	no	—
20	#10597265	—	2	1	no	—
21	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×D₇₆	D₄	1	1	yes	characteristic
25	C₂×C₄×D₁₉	—	2	1	no	—
26	C₂×Dic₃₈	—	2	1	no	—
27	C₂×C₈×C₁₉	—	2	1	no	—
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	(C₂×D₁₉)⋊C₄	—	2	1	no	—
33	C₄⋊Dic₁₉	—	2	1	no	—
34	C₄⋊Dic₁₉	—	2	1	no	—
35	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
36	C₂×C₁₉⋊C₈	—	2	1	no	—
37	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
38	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
39	C₈×D₁₉	—	4	2	no	—
40	C₂²×D₁₉	—	2	1	no	—
41	Q₈×C₁₉	—	8	1	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
46	C₂×Dic₁₉	—	2	1	no	—
47	C₂×Dic₁₉	—	4	1	no	—
48	D₇₆	—	2	1	no	—
49	D₇₆	Q₁₆	1	2	yes	—
50	C₄×D₁₉	—	4	1	no	—
51	C₄×D₁₉	—	4	1	no	—
52	Dic₃₈	—	4	1	no	—
53	Dic₃₈	—	4	1	no	—
54	C₈×C₁₉	—	4	1	no	—
55	C₈×C₁₉	—	4	1	no	—
56	C₁₉⋊C₈	—	2	1	no	—
57	C₁₉⋊C₈	—	2	1	no	—
58	C₁₉⋊C₈	—	4	1	no	—
59	#1683	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	#121	1	1	yes	characteristic
61	C₂×D₁₉	—	2	2	no	—
62	C₂×D₁₉	—	4	1	no	—
63	C₂×D₁₉	—	4	1	no	—
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	—	8	1	no	—
66	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
67	C₄×C₁₉	#135	1	1	yes	characteristic
68	C₄×C₁₉	#135	1	1	yes	characteristic
69	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
70	Dic₁₉	—	4	1	no	—
71	Dic₁₉	—	8	1	no	—
72	#487	—	19	1	no	—
73	#476	—	19	1	no	—
74	#474	—	19	1	no	—
75	C₈×D₄	—	19	1	no	—
76	#335	—	19	1	no	—
77	#333	D₁₉	1	1	yes	characteristic, complemented
78	#332	—	19	1	no	—
79	C₂×C₁₉	#463	1	1	yes	characteristic
80	C₂×C₁₉	#467	1	1	yes	characteristic
81	C₂×C₁₉	#471	1	1	yes	characteristic
82	D₁₉	—	4	2	no	—
83	C₂²×C₈	—	38	1	no	—
84	C₄⋊Q₈	—	19	1	no	—
85	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
86	C₄×D₄	—	19	1	no	—
87	#107	—	38	1	no	—
88	#106	—	38	1	no	—
89	C₄⋊C₈	—	19	1	no	—
90	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
91	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
92	#103	—	38	1	no	—
93	#103	—	38	1	no	—
94	#102	—	38	1	no	—
95	#102	—	38	1	no	—
96	C₂²⋊C₈	—	38	1	no	—
97	C₄×C₈	—	19	1	no	—
98	C₁₉	#1683	1	1	yes	characteristic, complemented, Sylow
99	C₂×Q₈	—	2	1	no	—
100	C₂×Q₈	—	38	1	no	—
101	C₂×D₄	—	19	1	no	—
102	C₂²×C₄	—	38	1	no	—
103	C₂×C₈	—	2	1	no	—
104	C₂×C₈	—	2	1	no	—
105	C₂×C₈	—	19	1	no	—
106	C₂×C₈	—	19	1	no	—
107	C₂×C₈	—	38	1	no	—
108	C₂×C₈	—	76	2	no	—
109	C₄⋊C₄	—	2	1	no	—
110	C₄⋊C₄	—	2	1	no	—
111	C₄⋊C₄	—	19	1	no	—
112	C₄⋊C₄	—	38	1	no	—
113	C₄⋊C₄	—	38	1	no	—
114	C₂²⋊C₄	—	38	1	no	—
115	C₄²	C₂²×D₁₉	1	1	yes	characteristic
116	C₂³	—	38	1	no	—
117	Q₈	—	8	1	no	—
118	Q₈	—	76	1	no	—
119	Q₈	—	76	1	no	—
120	D₄	—	19	2	no	—
121	D₄	—	38	1	no	—
122	C₂×C₄	—	4	1	no	—
123	C₂×C₄	—	38	1	no	—
124	C₂×C₄	—	76	1	no	—
125	C₂×C₄	—	76	1	no	—
126	C₂×C₄	—	76	1	no	—
127	C₂×C₄	#64541	1	1	yes	characteristic
128	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
129	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
130	C₈	—	4	1	no	—
131	C₈	—	4	1	no	—
132	C₈	—	38	1	no	—
133	C₈	—	38	1	no	—
134	C₈	—	76	1	no	—
135	C₂²	—	38	2	no	—
136	C₂²	—	76	1	no	—
137	C₂²	—	76	1	no	—
138	C₂²	#10597330	1	1	yes	characteristic
139	C₄	—	2	1	no	—
140	C₄	—	8	1	no	—
141	C₄	—	76	1	no	—
142	C₄	—	152	1	no	—
143	C₄	#10597360	1	1	yes	characteristic
144	C₄	#10597362	1	1	yes	characteristic
145	C₄	Q₁₆×D₁₉	1	1	yes	characteristic
146	C₄	#10597365	1	1	yes	characteristic
147	C₂	—	76	2	no	—
148	C₂	#11926762	1	1	yes	characteristic
149	C₂	#11926784	1	1	yes	characteristic
150	C₂	#11926806	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926896

C₂

yes

maximal, characteristic, complemented

#11926831

C₂

yes

maximal, characteristic

#11926825

C₂

yes

maximal, characteristic

#11926609

C₂

yes

maximal, characteristic

#11926296

C₂

yes

maximal, characteristic, complemented

#11926291

C₂

yes

maximal, characteristic, complemented

C₁₉×#333

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₈×D₁₉

—

C₄×D₇₆

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

#10597278

—

(C₂×D₁₉)⋊C₈

—

—

—

—

—

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×D₇₆

D₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₈×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

Q₁₆

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×Q₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

#487

—

#476

—

#474

—

C₈×D₄

—

#335

—

#333

D₁₉

yes

characteristic, complemented

#332

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄×D₄

—

#107

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

characteristic

C₄⋊C₈

C₂×D₁₉

yes

—

—

—

—

C₂²⋊C₈

—

C₄×C₈

—

C₁₉

#1683

yes

characteristic, complemented, Sylow

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×D₄

—

102

C₂²×C₄

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₂²⋊C₄

—

115

C₄²

C₂²×D₁₉

yes

characteristic

116

C₂³

—

117

Q₈

—

118

Q₈

—

119

Q₈

—

120

D₄

—

121

D₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

#64541

yes

characteristic

128

C₂×C₄

D₄×D₁₉

yes

characteristic

129

C₂×C₄

D₄×D₁₉

yes

characteristic

130

C₈

—

131

C₈

—

132

C₈

—

133

C₈

—

134

C₈

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

#10597330

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

152

—

143

C₄

#10597360

yes

characteristic

144

C₄

#10597362

yes

characteristic

145

C₄

Q₁₆×D₁₉

yes

characteristic

146

C₄

#10597365

yes

characteristic

147

C₂

—

148

C₂

#11926762

yes

characteristic

149

C₂

#11926784

yes

characteristic

150

C₂

#11926806

yes

characteristic

	subgroup	G/H
center	C₂²	#10597330
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#333	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂×D₇₆	D₄
hypercenter	#333	D₁₉
hypocenter	C₁₉	#1683
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

#10597330

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#333

C₂

socle

C₂²×C₁₉

#121

prime radical

C₂×D₇₆

D₄

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
1. #11926896	C₂	semidirect
5. #11926296	C₂	semidirect
6. #11926291	C₂	semidirect
7. C₁₉×#333	C₂	semidirect
77. #333	D₁₉	semidirect
98. C₁₉	#1683	semidirect

H ≅ G/N

type

1. #11926896

C₂

semidirect

5. #11926296

C₂

semidirect

6. #11926291

C₂

semidirect

7. C₁₉×#333

C₂

semidirect

77. #333

D₁₉

semidirect

98. C₁₉

#1683

semidirect

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

subgroup	index
#11926896	2
#11926831	2
#11926825	2
#11926609	2
#11926296	2
#11926291	2
C₁₉×#333	2
#1683	19

subgroup

index

C₁₉×#333

Subgroups — #14563089

Conjugacy classes of subgroups

Complements

Maximal subgroups