Group #18076305 — subgroups

Subgroups — #18076305

Order 4864.

486 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 235 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	#14563792	C₂	1	1	yes	maximal, characteristic
2	#14563791	C₂	1	4	yes	maximal
3	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1844	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597274	—	2	2	no	—
6	C₂×#10597265	—	2	8	no	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
8	#11926414	C₂²	1	2	yes	—
9	C₈×C₁₉⋊C₈	C₄	1	4	yes	complemented
10	C₂×C₁₉×#106	—	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×#106	—	4	4	no	—
21	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₉	Q₈	1	2	yes	—
23	#10597274	—	4	4	no	—
24	#10597265	—	4	16	no	—
25	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
26	C₄×C₁₉⋊C₈	Q₈	1	4	yes	—
27	C₂²×C₄×C₁₉	—	4	2	no	—
28	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
30	C₂²×Dic₁₉	—	4	2	no	—
31	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
32	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
33	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
34	C₄⋊C₄×C₁₉	—	4	8	no	—
35	C₄⋊C₄×C₁₉	—	4	4	no	—
36	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
38	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
39	C₄⋊Dic₁₉	—	4	8	no	—
40	C₄⋊Dic₁₉	—	4	4	no	—
41	C₂×C₁₉⋊C₈	C₄⋊C₄	1	8	yes	—
42	C₂×C₁₉⋊C₈	SD₁₆	1	16	yes	—
43	#8813	—	19	1	no	maximal, Sylow
44	C₂³×C₁₉	#127	1	1	yes	characteristic
45	C₂×C₄×C₁₉	—	8	4	no	—
46	C₂×C₄×C₁₉	—	8	2	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×SD₁₆	1	2	yes	—
52	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
53	C₂×C₄×C₁₉	C₂×SD₁₆	1	8	yes	—
54	C₂×Dic₁₉	—	8	4	no	—
55	C₂×Dic₁₉	—	8	2	no	—
56	C₈×C₁₉	#106	1	8	yes	complemented
57	C₁₉⋊C₈	#106	1	16	yes	complemented
58	#1844	—	19	1	no	—
59	#1844	—	19	4	no	—
60	#1844	D₁₉	1	1	yes	characteristic
61	C₂×C₈²	—	19	1	no	—
62	C₂²×C₁₉	#384	1	1	yes	characteristic
63	C₂²×C₁₉	#492	1	4	yes	—
64	C₂²×C₁₉	#492	1	1	yes	characteristic
65	C₂²×C₁₉	#492	1	1	yes	characteristic
66	C₄×C₁₉	—	16	2	no	—
67	C₄×C₁₉	C₂×#106	1	4	yes	—
68	C₄×C₁₉	C₂×#106	1	2	yes	—
69	C₄×C₁₉	#498	1	2	yes	—
70	C₄×C₁₉	#498	1	4	yes	—
71	Dic₁₉	—	16	2	no	—
72	C₂×#106	—	2	2	no	—
73	C₂×#106	—	38	8	no	—
74	C₂×#106	—	38	2	no	—
75	C₂×C₄×C₈	—	19	2	no	—
76	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
77	#384	—	19	2	no	—
78	#384	C₂×D₁₉	1	2	yes	—
79	C₈²	—	19	4	no	—
80	C₂×C₁₉	#1705	1	2	yes	—
81	C₂×C₁₉	#1705	1	2	yes	—
82	C₂×C₁₉	#1844	1	2	yes	—
83	C₂×C₁₉	#1844	1	1	yes	characteristic
84	C₂²×C₈	—	19	4	no	—
85	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
86	C₂×C₄⋊C₄	—	2	4	no	—
87	C₂×C₄⋊C₄	—	2	2	no	—
88	C₂×C₄⋊C₄	—	38	4	no	—
89	C₂×C₄⋊C₄	—	38	2	no	—
90	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
91	#106	—	4	4	no	—
92	#106	—	76	16	no	—
93	#106	—	76	4	no	—
94	C₄×C₈	—	19	4	no	—
95	C₄×C₈	—	19	4	no	—
96	C₄×C₈	Dic₃₈	1	2	yes	—
97	C₄×C₈	C₄×D₁₉	1	2	yes	—
98	C₁₉	#8813	1	1	yes	characteristic, complemented, Sylow
99	C₂²×C₄	—	4	2	no	—
100	C₂²×C₄	—	76	2	no	—
101	C₂²×C₄	D₄×D₁₉	1	2	yes	—
102	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
103	C₂×C₈	—	19	8	no	—
104	C₂×C₈	—	19	16	no	—
105	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
106	C₂×C₈	#64526	1	4	yes	—
107	C₂×C₈	#64527	1	4	yes	—
108	C₄⋊C₄	—	4	4	no	—
109	C₄⋊C₄	—	4	8	no	—
110	C₄⋊C₄	—	76	4	no	—
111	C₄⋊C₄	—	76	8	no	—
112	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
113	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
114	C₄²	Q₈×D₁₉	1	2	yes	—
115	C₂³	#10597386	1	1	yes	characteristic
116	C₂×C₄	—	8	4	no	—
117	C₂×C₄	—	8	2	no	—
118	C₂×C₄	—	152	4	no	—
119	C₂×C₄	—	152	2	no	—
120	C₂×C₄	#10597334	1	2	yes	—
121	C₂×C₄	C₄⋊C₄×D₁₉	1	2	yes	—
122	C₂×C₄	SD₁₆×D₁₉	1	8	yes	—
123	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
124	C₂×C₄	C₂×#64526	1	2	yes	—
125	C₂×C₄	C₂×#64527	1	2	yes	—
126	C₂×C₄	#10597390	1	1	yes	characteristic
127	C₈	—	19	16	no	—
128	C₈	#10597265	1	8	yes	complemented
129	C₂²	#11926413	1	1	yes	characteristic
130	C₂²	#11926915	1	4	yes	—
131	C₂²	#11926916	1	1	yes	characteristic
132	C₂²	#11926918	1	1	yes	characteristic
133	C₄	—	16	2	no	—
134	C₄	—	304	2	no	—
135	C₄	#106×D₁₉	1	4	yes	—
136	C₄	C₂×#10597265	1	2	yes	—
137	C₄	#11926940	1	2	yes	—
138	C₄	#11926941	1	4	yes	—
139	C₂	#14563221	1	2	yes	—
140	C₂	#14563223	1	2	yes	—
141	C₂	#14563790	1	2	yes	—
142	C₂	#14563791	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563792

C₂

yes

maximal, characteristic

#14563791

C₂

yes

maximal

C₂×C₈×C₁₉⋊C₈

C₂

yes

maximal, characteristic

C₁₉×#1844

C₂

yes

maximal, characteristic

C₂×#10597274

—

C₂×#10597265

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926414

C₂²

yes

—

C₈×C₁₉⋊C₈

C₄

yes

complemented

C₂×C₁₉×#106

—

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×#106

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

#10597274

—

#10597265

—

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

SD₁₆

yes

—

C₂×C₈×C₁₉

SD₁₆

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

C₄⋊C₄

yes

—

C₂×C₁₉⋊C₈

SD₁₆

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×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

yes

C₁₉⋊C₈

yes

—

—

D₁₉

yes

characteristic

C₂×C₈²

—

C₂²×C₁₉

#384

yes

characteristic

C₂²×C₁₉

#492

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

C₂×#106

yes

—

C₄×C₁₉

C₂×#106

yes

—

C₄×C₁₉

#498

yes

—

C₄×C₁₉

#498

yes

—

Dic₁₉

—

C₂×#106

—

C₂×#106

—

C₂×#106

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#384

—

#384

C₂×D₁₉

yes

—

C₈²

—

C₂×C₁₉

#1705

yes

—

C₂×C₁₉

#1705

yes

—

C₂×C₁₉

#1844

yes

—

C₂×C₁₉

#1844

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₉

yes

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

C₄×D₁₉

yes

—

C₁₉

#8813

yes

characteristic, complemented, Sylow

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

D₄×D₁₉

yes

—

102

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

Dic₁₉⋊C₄

yes

—

106

C₂×C₈

#64526

yes

—

107

C₂×C₈

#64527

yes

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄²

C₂×Dic₃₈

yes

characteristic

113

C₄²

C₂×C₄×D₁₉

yes

characteristic

114

C₄²

Q₈×D₁₉

yes

—

115

C₂³

#10597386

yes

characteristic

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

152

—

119

C₂×C₄

—

152

—

120

C₂×C₄

#10597334

yes

—

121

C₂×C₄

C₄⋊C₄×D₁₉

yes

—

122

C₂×C₄

SD₁₆×D₁₉

yes

—

123

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

124

C₂×C₄

C₂×#64526

yes

—

125

C₂×C₄

C₂×#64527

yes

—

126

C₂×C₄

#10597390

yes

characteristic

127

C₈

—

128

C₈

#10597265

yes

complemented

129

C₂²

#11926413

yes

characteristic

130

C₂²

#11926915

yes

—

131

C₂²

#11926916

yes

characteristic

132

C₂²

#11926918

yes

characteristic

133

C₄

—

134

C₄

—

304

—

135

C₄

#106×D₁₉

yes

—

136

C₄

C₂×#10597265

yes

—

137

C₄

#11926940

yes

—

138

C₄

#11926941

yes

—

139

C₂

#14563221

yes

—

140

C₂

#14563223

yes

—

141

C₂

#14563790

yes

—

142

C₂

#14563791

yes

characteristic

	subgroup	G/H
center	C₂³	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1844	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1844	D₁₉
hypocenter	C₁₉	#8813
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

subgroup

G/H

center

C₂³

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1844

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 ◁ #1844

N	H ≅ G/N	type
9. C₈×C₁₉⋊C₈	C₄	semidirect
56. C₈×C₁₉	#106	semidirect
57. C₁₉⋊C₈	#106	semidirect
98. C₁₉	#8813	semidirect
128. C₈	#10597265	semidirect

H ≅ G/N

type

9. C₈×C₁₉⋊C₈

C₄

semidirect

56. C₈×C₁₉

#106

semidirect

57. C₁₉⋊C₈

#106

semidirect

98. C₁₉

#8813

semidirect

128. C₈

#10597265

semidirect

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

subgroup	index
#14563792	2
#14563791	2
C₂×C₈×C₁₉⋊C₈	2
C₁₉×#1844	2
#8813	19

subgroup

index

#14563792

#14563791

C₂×C₈×C₁₉⋊C₈

C₁₉×#1844

#8813

Subgroups — #18076305

Conjugacy classes of subgroups

Complements

Maximal subgroups