Group #18076338 — subgroups

Subgroups — #18076338

Order 4864.

354 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 171 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	#14563807	C₂	1	1	yes	maximal, characteristic
2	#14562390	C₂	1	4	yes	maximal
3	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1848	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597276	—	2	2	no	—
6	#11926568	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
8	#11926294	—	2	8	no	—
9	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
10	C₈×C₁₉⋊C₈	C₄	1	2	yes	—
11	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₁₉×#108	—	2	2	no	—
13	C₁₉×#423	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×M₁₆×C₁₉	—	2	2	no	—
16	C₂²×C₈×C₁₉	D₄	1	2	yes	—
17	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
18	C₂×#64520	—	2	2	no	—
19	C₂²×C₁₉⋊C₈	Q₈	1	4	yes	—
20	C₁₉×#108	—	4	4	no	—
21	C₁₉×C₄⋊C₈	—	2	4	no	—
22	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₉	Q₈	1	2	yes	—
25	#10597276	—	4	4	no	—
26	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
27	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
28	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
29	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
30	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
32	M₁₆×C₁₉	—	4	4	no	—
33	C₂×C₈×C₁₉	—	4	2	no	—
34	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
35	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
36	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
37	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
38	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₄²×C₁₉	C₂×D₄	1	2	yes	—
40	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	#64520	—	4	4	no	—
42	C₂×C₁₉⋊C₈	—	2	8	no	—
43	C₂×C₁₉⋊C₈	—	4	2	no	—
44	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
45	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
46	#8822	—	19	1	no	maximal, Sylow
47	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
48	C₂×C₄×C₁₉	—	2	4	no	—
49	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
50	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
53	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
54	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
55	C₈×C₁₉	—	8	2	no	—
56	C₈×C₁₉	#106	1	4	yes	—
57	C₈×C₁₉	#106	1	4	yes	—
58	C₁₉⋊C₈	—	2	4	no	—
59	C₁₉⋊C₈	—	8	2	no	—
60	C₁₉⋊C₈	#108	1	8	yes	complemented
61	#1848	—	19	1	no	—
62	#1848	D₁₉	1	1	yes	characteristic
63	#1566	—	19	4	no	—
64	C₂×C₈²	—	19	1	no	—
65	C₂²×C₁₉	—	2	2	no	—
66	C₂²×C₁₉	#384	1	1	yes	characteristic
67	C₂²×C₁₉	#498	1	2	yes	—
68	C₄×C₁₉	—	2	2	no	—
69	C₄×C₁₉	C₂×#106	1	2	yes	—
70	C₄×C₁₉	C₂×#108	1	4	yes	—
71	C₄×C₁₉	#492	1	1	yes	characteristic
72	C₄×C₁₉	#492	1	1	yes	characteristic
73	C₂×#108	—	2	2	no	—
74	C₂×#108	—	38	2	no	—
75	#423	—	19	2	no	—
76	#423	C₂×D₁₉	1	2	yes	—
77	C₂×C₄×C₈	—	19	2	no	—
78	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
79	#334	—	38	8	no	—
80	C₈²	—	19	1	no	—
81	C₈²	—	19	2	no	—
82	C₈²	—	19	1	no	—
83	C₂×C₁₉	—	2	2	no	—
84	C₂×C₁₉	#1844	1	1	yes	characteristic
85	C₂×C₁₉	#1848	1	2	yes	—
86	C₂×M₁₆	—	2	2	no	—
87	C₂×M₁₆	—	38	2	no	—
88	C₂²×C₈	—	19	4	no	—
89	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
90	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
91	#108	—	4	4	no	—
92	#108	—	76	4	no	—
93	C₄⋊C₈	—	2	4	no	—
94	C₄⋊C₈	—	38	4	no	—
95	C₄×C₈	—	19	2	no	—
96	C₄×C₈	—	19	2	no	—
97	C₄×C₈	—	19	4	no	—
98	C₄×C₈	Dic₃₈	1	2	yes	—
99	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
100	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
101	C₁₉	#8822	1	1	yes	characteristic, complemented, Sylow
102	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
103	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
104	M₁₆	—	4	4	no	—
105	M₁₆	—	76	4	no	—
106	C₂×C₈	—	4	2	no	—
107	C₂×C₈	—	19	4	no	—
108	C₂×C₈	—	19	4	no	—
109	C₂×C₈	—	38	8	no	—
110	C₂×C₈	—	76	2	no	—
111	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
112	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
113	C₂×C₈	#64526	1	4	yes	—
114	C₂×C₈	#64527	1	4	yes	—
115	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
116	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
117	C₄²	D₄×D₁₉	1	2	yes	—
118	C₂³	#10597390	1	1	yes	characteristic
119	C₂×C₄	—	2	4	no	—
120	C₂×C₄	#10597334	1	2	yes	—
121	C₂×C₄	C₄⋊C₄×D₁₉	1	2	yes	—
122	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
123	C₂×C₄	C₂×#64526	1	2	yes	—
124	C₂×C₄	#10597386	1	1	yes	characteristic
125	C₂×C₄	C₂×#64527	1	2	yes	—
126	C₈	—	8	2	no	—
127	C₈	—	19	8	no	—
128	C₈	—	38	4	no	—
129	C₈	—	152	2	no	—
130	C₈	#10597265	1	4	yes	—
131	C₈	#10597265	1	4	yes	—
132	C₂²	—	2	2	no	—
133	C₂²	#11926413	1	1	yes	characteristic
134	C₂²	#11926940	1	2	yes	—
135	C₄	—	2	2	no	—
136	C₄	C₂×#10597265	1	2	yes	—
137	C₄	#108×D₁₉	1	4	yes	—
138	C₄	#11926916	1	1	yes	characteristic
139	C₄	#11926918	1	1	yes	characteristic
140	C₂	—	2	2	no	—
141	C₂	#14563791	1	1	yes	characteristic
142	C₂	#14563805	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563807

C₂

yes

maximal, characteristic

#14562390

C₂

yes

maximal

C₂×C₈×C₁₉⋊C₈

C₂

yes

maximal, characteristic

C₁₉×#1848

C₂

yes

maximal, characteristic

C₂×#10597276

—

#11926568

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926294

—

C₈×C₁₉⋊C₈

C₄

yes

characteristic

C₈×C₁₉⋊C₈

C₄

yes

—

C₈×C₁₉⋊C₈

C₄

yes

characteristic

C₂×C₁₉×#108

—

C₁₉×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

Q₈

yes

—

C₁₉×#108

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

Q₈

yes

—

#10597276

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

#8822

—

maximal, Sylow

C₂³×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₈×C₁₉

—

C₈×C₁₉

#106

yes

—

C₈×C₁₉

#106

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

yes

—

D₁₉

yes

characteristic

#1566

—

C₂×C₈²

—

C₂²×C₁₉

—

C₂²×C₁₉

#384

yes

characteristic

C₂²×C₁₉

#498

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×#106

yes

—

C₄×C₁₉

C₂×#108

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

—

—

C₂×D₁₉

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#334

—

C₈²

—

C₈²

—

C₈²

—

C₂×C₁₉

—

C₂×C₁₉

#1844

yes

characteristic

C₂×C₁₉

#1848

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#108

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

C₄×D₁₉

yes

characteristic

100

C₄×C₈

C₄×D₁₉

yes

characteristic

101

C₁₉

#8822

yes

characteristic, complemented, Sylow

102

C₂²×C₄

Q₈×D₁₉

yes

—

103

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

104

M₁₆

—

105

M₁₆

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

Dic₁₉⋊C₄

yes

—

112

C₂×C₈

Dic₁₉⋊C₄

yes

—

113

C₂×C₈

#64526

yes

—

114

C₂×C₈

#64527

yes

—

115

C₄²

C₂×Dic₃₈

yes

characteristic

116

C₄²

C₂×C₄×D₁₉

yes

characteristic

117

C₄²

D₄×D₁₉

yes

—

118

C₂³

#10597390

yes

characteristic

119

C₂×C₄

—

120

C₂×C₄

#10597334

yes

—

121

C₂×C₄

C₄⋊C₄×D₁₉

yes

—

122

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

123

C₂×C₄

C₂×#64526

yes

—

124

C₂×C₄

#10597386

yes

characteristic

125

C₂×C₄

C₂×#64527

yes

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₈

—

152

—

130

C₈

#10597265

yes

—

131

C₈

#10597265

yes

—

132

C₂²

—

133

C₂²

#11926413

yes

characteristic

134

C₂²

#11926940

yes

—

135

C₄

—

136

C₄

C₂×#10597265

yes

—

137

C₄

#108×D₁₉

yes

—

138

C₄

#11926916

yes

characteristic

139

C₄

#11926918

yes

characteristic

140

C₂

—

141

C₂

#14563791

yes

characteristic

142

C₂

#14563805

yes

—

	subgroup	G/H
center	C₂×C₄	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1848	C₂
socle	C₂²×C₁₉	#384
prime radical	C₂³×C₁₉	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1848	D₁₉
hypocenter	C₁₉	#8822
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

subgroup

G/H

center

C₂×C₄

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1848

C₂

socle

C₂²×C₁₉

#384

prime radical

C₂³×C₁₉

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

N	H ≅ G/N	type
60. C₁₉⋊C₈	#108	semidirect
101. C₁₉	#8822	semidirect

H ≅ G/N

type

60. C₁₉⋊C₈

#108

semidirect

101. C₁₉

#8822

semidirect

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

subgroup	index
#14563807	2
#14562390	2
C₂×C₈×C₁₉⋊C₈	2
C₁₉×#1848	2
#8822	19

subgroup

index

#14563807

#14562390

C₂×C₈×C₁₉⋊C₈

C₁₉×#1848

#8822

Subgroups — #18076338

Conjugacy classes of subgroups

Complements

Maximal subgroups