Group #18076315 — subgroups

Subgroups — #18076315

Order 4864.

422 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 203 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	#14563795	C₂	1	1	yes	maximal, characteristic
2	#14563762	C₂	1	4	yes	maximal
3	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1845	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597275	—	2	2	no	—
6	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
7	#11926414	C₂²	1	2	yes	—
8	#11926306	—	2	8	no	—
9	C₈×C₁₉⋊C₈	C₄	1	4	yes	complemented
10	C₂×C₁₉×#107	—	2	2	no	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#384	C₂²	1	2	yes	—
13	C₂²×C₈×C₁₉	D₄	1	2	yes	—
14	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
15	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
16	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₉	—	2	4	no	—
18	C₂×C₄⋊Dic₁₉	—	2	2	no	—
19	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
20	C₁₉×#107	—	4	4	no	—
21	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₉	Q₈	1	2	yes	—
23	#10597275	—	4	4	no	—
24	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
25	C₄×C₁₉⋊C₈	Q₈	1	4	yes	—
26	C₂²×C₄×C₁₉	—	4	2	no	—
27	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
28	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
29	C₂²×Dic₁₉	—	4	2	no	—
30	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
31	C₂×C₈×C₁₉	D₈	1	4	yes	—
32	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
33	C₄⋊C₄×C₁₉	—	4	4	no	—
34	C₄⋊C₄×C₁₉	—	4	8	no	—
35	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
37	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
38	C₄⋊Dic₁₉	—	4	4	no	—
39	C₄⋊Dic₁₉	—	4	8	no	—
40	C₂×C₁₉⋊C₈	—	2	4	no	—
41	C₂×C₁₉⋊C₈	—	2	4	no	—
42	C₂×C₁₉⋊C₈	C₄⋊C₄	1	8	yes	—
43	#8816	—	19	1	no	maximal, Sylow
44	C₂³×C₁₉	#127	1	1	yes	characteristic
45	C₂×C₄×C₁₉	—	8	2	no	—
46	C₂×C₄×C₁₉	—	8	4	no	—
47	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
48	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
51	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
52	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
53	C₂×C₄×C₁₉	#135	1	4	yes	—
54	C₂×C₄×C₁₉	#135	1	4	yes	—
55	C₂×Dic₁₉	—	8	2	no	—
56	C₂×Dic₁₉	—	8	4	no	—
57	C₈×C₁₉	#107	1	8	yes	—
58	C₁₉⋊C₈	—	2	8	no	—
59	#1845	—	19	1	no	—
60	#1845	D₁₉	1	1	yes	characteristic
61	#1834	—	19	4	no	—
62	C₂×C₈²	—	19	1	no	—
63	C₂²×C₁₉	#384	1	1	yes	characteristic
64	C₂²×C₁₉	#493	1	1	yes	characteristic
65	C₂²×C₁₉	#494	1	1	yes	characteristic
66	C₂²×C₁₉	#495	1	2	yes	—
67	C₂²×C₁₉	#495	1	2	yes	—
68	C₄×C₁₉	—	16	2	no	—
69	C₄×C₁₉	C₂×#107	1	2	yes	—
70	C₄×C₁₉	#427	1	4	yes	—
71	C₄×C₁₉	#499	1	4	yes	—
72	C₄×C₁₉	#500	1	2	yes	—
73	Dic₁₉	—	16	2	no	—
74	C₂×#107	—	2	2	no	—
75	C₂×#107	—	38	2	no	—
76	C₂×C₄×C₈	—	19	2	no	—
77	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
78	#384	—	19	2	no	—
79	#384	C₂×D₁₉	1	2	yes	—
80	#340	—	38	8	no	—
81	C₈²	—	19	4	no	—
82	C₂×C₁₉	#1709	1	1	yes	characteristic
83	C₂×C₁₉	#1709	1	1	yes	characteristic
84	C₂×C₁₉	#1710	1	2	yes	—
85	C₂×C₁₉	#1845	1	1	yes	characteristic
86	C₂×C₁₉	#1846	1	2	yes	—
87	C₂²×C₈	—	19	4	no	—
88	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
89	C₂×C₄⋊C₄	—	2	4	no	—
90	C₂×C₄⋊C₄	—	2	2	no	—
91	C₂×C₄⋊C₄	—	38	4	no	—
92	C₂×C₄⋊C₄	—	38	2	no	—
93	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
94	#107	—	4	4	no	—
95	#107	—	76	4	no	—
96	C₄×C₈	—	19	4	no	—
97	C₄×C₈	—	19	4	no	—
98	C₄×C₈	Dic₃₈	1	2	yes	—
99	C₄×C₈	C₄×D₁₉	1	2	yes	—
100	C₁₉	#8816	1	1	yes	characteristic, complemented, Sylow
101	C₂²×C₄	—	4	2	no	—
102	C₂²×C₄	—	76	2	no	—
103	C₂²×C₄	D₄×D₁₉	1	2	yes	—
104	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
105	C₂×C₈	—	19	8	no	—
106	C₂×C₈	—	38	4	no	—
107	C₂×C₈	—	38	4	no	—
108	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
109	C₂×C₈	#64525	1	4	yes	—
110	C₂×C₈	#64528	1	4	yes	—
111	C₄⋊C₄	—	4	4	no	—
112	C₄⋊C₄	—	4	8	no	—
113	C₄⋊C₄	—	76	4	no	—
114	C₄⋊C₄	—	76	8	no	—
115	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
116	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
117	C₄²	Q₈×D₁₉	1	2	yes	—
118	C₂³	#10597386	1	1	yes	characteristic
119	C₂×C₄	—	8	2	no	—
120	C₂×C₄	—	8	4	no	—
121	C₂×C₄	—	152	2	no	—
122	C₂×C₄	—	152	4	no	—
123	C₂×C₄	#10597334	1	2	yes	—
124	C₂×C₄	C₄⋊C₄×D₁₉	1	2	yes	—
125	C₂×C₄	#10597358	1	4	yes	—
126	C₂×C₄	#10597365	1	4	yes	—
127	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
128	C₂×C₄	C₂×#64525	1	2	yes	—
129	C₂×C₄	C₂×#64528	1	2	yes	—
130	C₂×C₄	#10597390	1	1	yes	characteristic
131	C₈	—	38	8	no	—
132	C₈	#10597264	1	8	yes	—
133	C₂²	#11926413	1	1	yes	characteristic
134	C₂²	#11926920	1	1	yes	characteristic
135	C₂²	#11926923	1	1	yes	characteristic
136	C₂²	#11926927	1	2	yes	—
137	C₂²	#11926929	1	2	yes	—
138	C₄	—	16	2	no	—
139	C₄	—	304	2	no	—
140	C₄	C₂×#10597264	1	2	yes	—
141	C₄	#11926581	1	4	yes	—
142	C₄	#11926945	1	4	yes	—
143	C₄	#11926947	1	2	yes	—
144	C₂	#14563240	1	1	yes	characteristic
145	C₂	#14563242	1	1	yes	characteristic
146	C₂	#14563244	1	2	yes	—
147	C₂	#14563794	1	1	yes	characteristic
148	C₂	#14563798	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563795

C₂

yes

maximal, characteristic

#14563762

C₂

yes

maximal

C₂×C₈×C₁₉⋊C₈

C₂

yes

maximal, characteristic

C₁₉×#1845

C₂

yes

maximal, characteristic

C₂×#10597275

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926414

C₂²

yes

—

#11926306

—

C₈×C₁₉⋊C₈

C₄

yes

complemented

C₂×C₁₉×#107

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₁₉×#107

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

#10597275

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

Q₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

Q₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

#107

yes

—

C₁₉⋊C₈

—

#1845

—

#1845

D₁₉

yes

characteristic

#1834

—

C₂×C₈²

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#495

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×#107

yes

—

C₄×C₁₉

#427

yes

—

C₄×C₁₉

#499

yes

—

C₄×C₁₉

#500

yes

—

Dic₁₉

—

C₂×#107

—

C₂×#107

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#384

—

#384

C₂×D₁₉

yes

—

#340

—

C₈²

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#1845

yes

characteristic

C₂×C₁₉

#1846

yes

—

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#107

—

#107

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

C₄×D₁₉

yes

—

100

C₁₉

#8816

yes

characteristic, complemented, Sylow

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

D₄×D₁₉

yes

—

104

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

Dic₁₉⋊C₄

yes

—

109

C₂×C₈

#64525

yes

—

110

C₂×C₈

#64528

yes

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄²

C₂×Dic₃₈

yes

characteristic

116

C₄²

C₂×C₄×D₁₉

yes

characteristic

117

C₄²

Q₈×D₁₉

yes

—

118

C₂³

#10597386

yes

characteristic

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

152

—

122

C₂×C₄

—

152

—

123

C₂×C₄

#10597334

yes

—

124

C₂×C₄

C₄⋊C₄×D₁₉

yes

—

125

C₂×C₄

#10597358

yes

—

126

C₂×C₄

#10597365

yes

—

127

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

128

C₂×C₄

C₂×#64525

yes

—

129

C₂×C₄

C₂×#64528

yes

—

130

C₂×C₄

#10597390

yes

characteristic

131

C₈

—

132

C₈

#10597264

yes

—

133

C₂²

#11926413

yes

characteristic

134

C₂²

#11926920

yes

characteristic

135

C₂²

#11926923

yes

characteristic

136

C₂²

#11926927

yes

—

137

C₂²

#11926929

yes

—

138

C₄

—

139

C₄

—

304

—

140

C₄

C₂×#10597264

yes

—

141

C₄

#11926581

yes

—

142

C₄

#11926945

yes

—

143

C₄

#11926947

yes

—

144

C₂

#14563240

yes

characteristic

145

C₂

#14563242

yes

characteristic

146

C₂

#14563244

yes

—

147

C₂

#14563794

yes

characteristic

148

C₂

#14563798

yes

—

	subgroup	G/H
center	C₂³	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1845	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1845	D₁₉
hypocenter	C₁₉	#8816
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

subgroup

G/H

center

C₂³

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1845

C₂

socle, prime radical

C₂³×C₁₉

#127

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

N	H ≅ G/N	type
9. C₈×C₁₉⋊C₈	C₄	semidirect
100. C₁₉	#8816	semidirect

H ≅ G/N

type

9. C₈×C₁₉⋊C₈

C₄

semidirect

100. C₁₉

#8816

semidirect

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

subgroup	index
#14563795	2
#14563762	2
C₂×C₈×C₁₉⋊C₈	2
C₁₉×#1845	2
#8816	19

subgroup

index

#14563795

#14563762

C₂×C₈×C₁₉⋊C₈

C₁₉×#1845

#8816

Subgroups — #18076315

Conjugacy classes of subgroups

Complements

Maximal subgroups