Group #18069355 — subgroups

Subgroups — #18069355

Order 4864.

206 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 71 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	#14561715	C₂	1	2	yes	maximal
2	C₁₉×#1992	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597269	—	2	2	no	—
4	C₂×C₁₉×#125	C₄	1	1	yes	characteristic
5	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
6	C₁₉×#384	C₄	1	1	yes	characteristic
7	C₁₉×#340	—	2	2	no	—
8	C₂²×C₈×C₁₉	D₄	1	2	yes	—
9	C₁₉×#125	—	2	1	no	—
10	C₁₉×#125	—	4	1	no	—
11	C₁₉×#125	C₈	1	2	yes	—
12	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
13	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
14	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
15	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₁₉×#97	—	4	1	no	—
18	#10597269	—	4	2	no	—
19	#10597269	—	4	2	no	—
20	C₂×C₁₉⋊C₁₆	—	2	4	no	—
21	C₂²×C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	—	4	1	no	—
23	C₂²×C₄×C₁₉	—	4	1	no	—
24	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₈×C₁₉	—	2	2	no	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
28	C₂×C₈×C₁₉	Q₁₆	1	2	yes	—
29	C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₄⋊C₄×C₁₉	—	4	2	no	—
31	C₄⋊C₄×C₁₉	—	4	2	no	—
32	C₄⋊C₄×C₁₉	—	4	1	no	—
33	C₄⋊C₄×C₁₉	—	4	2	no	—
34	C₄⋊C₄×C₁₉	—	8	2	no	—
35	C₄²×C₁₉	—	2	1	no	—
36	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
37	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
38	C₁₉⋊C₁₆	—	4	4	no	—
39	#7130	—	19	1	no	maximal, Sylow
40	C₂³×C₁₉	#100	1	1	yes	characteristic
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	4	1	no	—
44	C₂×C₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	—	4	2	no	—
46	C₂×C₄×C₁₉	—	8	1	no	—
47	C₂×C₄×C₁₉	—	8	1	no	—
48	C₂×C₄×C₁₉	—	8	2	no	—
49	C₂×C₄×C₁₉	—	8	1	no	—
50	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
51	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
52	C₂×C₄×C₁₉	#103	1	2	yes	—
53	C₂×C₄×C₁₉	#104	1	2	yes	—
54	C₈×C₁₉	—	2	2	no	—
55	C₈×C₁₉	—	2	2	no	—
56	#1992	D₁₉	1	1	yes	characteristic
57	#1375	—	19	2	no	—
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	—	2	1	no	—
60	C₂²×C₁₉	#323	1	1	yes	characteristic
61	C₂²×C₁₉	#329	1	1	yes	characteristic
62	C₂²×C₁₉	#333	1	1	yes	characteristic
63	C₄×C₁₉	—	4	1	no	—
64	C₄×C₁₉	—	4	1	no	—
65	C₄×C₁₉	—	8	2	no	—
66	C₄×C₁₉	—	16	1	no	—
67	C₄×C₁₉	Q₈⋊C₈	1	2	yes	—
68	C₄×C₁₉	#328	1	2	yes	—
69	C₂×#125	Dic₁₉	1	1	yes	characteristic
70	C₂×M₃₂	—	38	2	no	—
71	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
72	#384	Dic₁₉	1	1	yes	characteristic
73	#340	—	2	2	no	—
74	C₂×C₁₉	—	2	1	no	—
75	C₂×C₁₉	—	2	1	no	—
76	C₂×C₁₉	#1272	1	1	yes	characteristic
77	C₂×C₁₉	#1355	1	1	yes	characteristic
78	C₂×C₁₉	#1356	1	1	yes	characteristic
79	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
80	#125	—	2	1	no	—
81	#125	—	4	1	no	—
82	#125	C₁₉⋊C₈	1	2	yes	—
83	C₂×C₄⋊C₄	—	2	1	no	—
84	C₂×C₄⋊C₄	—	2	1	no	—
85	C₂×C₄⋊C₄	—	4	1	no	—
86	C₂×C₄⋊C₄	—	4	1	no	—
87	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
88	M₃₂	—	76	2	no	—
89	M₃₂	—	76	2	no	—
90	C₂×C₁₆	—	38	4	no	—
91	#97	—	4	1	no	—
92	C₁₉	#7130	1	1	yes	characteristic, complemented, Sylow
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	—	4	1	no	—
95	C₂²×C₄	—	4	1	no	—
96	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	#64527	1	2	yes	—
100	C₂×C₈	#64528	1	2	yes	—
101	C₄⋊C₄	—	2	2	no	—
102	C₄⋊C₄	—	4	2	no	—
103	C₄⋊C₄	—	4	2	no	—
104	C₄⋊C₄	—	4	1	no	—
105	C₄⋊C₄	—	4	2	no	—
106	C₄⋊C₄	—	8	2	no	—
107	C₄²	—	2	1	no	—
108	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
109	C₄²	#64520	1	1	yes	characteristic
110	C₁₆	—	76	4	no	—
111	C₂³	#10597290	1	1	yes	characteristic
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	4	1	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	8	1	no	—
118	C₂×C₄	—	8	1	no	—
119	C₂×C₄	—	8	2	no	—
120	C₂×C₄	—	8	1	no	—
121	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
122	C₂×C₄	#10597291	1	1	yes	characteristic
123	C₂×C₄	#10597292	1	2	yes	—
124	C₂×C₄	#10597294	1	2	yes	—
125	C₈	—	2	2	no	—
126	C₈	—	2	2	no	—
127	C₂²	—	2	1	no	—
128	C₂²	—	2	1	no	—
129	C₂²	#11926268	1	1	yes	characteristic
130	C₂²	#11926284	1	1	yes	characteristic
131	C₂²	#11926293	1	1	yes	characteristic
132	C₄	—	4	1	no	—
133	C₄	—	4	1	no	—
134	C₄	—	8	2	no	—
135	C₄	—	16	1	no	—
136	C₄	Q₈⋊(C₁₉⋊C₈)	1	2	yes	—
137	C₄	#11926281	1	2	yes	—
138	C₂	—	2	1	no	—
139	C₂	—	2	1	no	—
140	C₂	#14561461	1	1	yes	characteristic
141	C₂	#14561668	1	1	yes	characteristic
142	C₂	#14561670	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561715

C₂

yes

maximal

C₁₉×#1992

C₂

yes

maximal, characteristic

C₂×#10597269

—

C₂×C₁₉×#125

C₄

yes

characteristic

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#384

C₄

yes

characteristic

C₁₉×#340

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

C₈

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#97

—

#10597269

—

#10597269

—

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₂×C₈×C₁₉

Q₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

#1992

D₁₉

yes

characteristic

#1375

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

Q₈⋊C₈

yes

—

C₄×C₁₉

#328

yes

—

C₂×#125

Dic₁₉

yes

characteristic

C₂×M₃₂

—

C₂×#97

C₂×D₁₉

yes

characteristic

#384

Dic₁₉

yes

characteristic

#340

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

C₂²⋊D₁₉

yes

—

#125

—

#125

—

#125

C₁₉⋊C₈

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#97

—

C₁₉

#7130

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#64527

yes

—

100

C₂×C₈

#64528

yes

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄²

—

108

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

109

C₄²

#64520

yes

characteristic

110

C₁₆

—

111

C₂³

#10597290

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

122

C₂×C₄

#10597291

yes

characteristic

123

C₂×C₄

#10597292

yes

—

124

C₂×C₄

#10597294

yes

—

125

C₈

—

126

C₈

—

127

C₂²

—

128

C₂²

—

129

C₂²

#11926268

yes

characteristic

130

C₂²

#11926284

yes

characteristic

131

C₂²

#11926293

yes

characteristic

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

Q₈⋊(C₁₉⋊C₈)

yes

—

137

C₄

#11926281

yes

—

138

C₂

—

139

C₂

—

140

C₂

#14561461

yes

characteristic

141

C₂

#14561668

yes

characteristic

142

C₂

#14561670

yes

characteristic

	subgroup	G/H
center	C₂²	#11926284
commutator	C₄²×C₁₉	C₂×C₈
Frattini	C₂×#97	C₂×D₁₉
Fitting	C₁₉×#1992	C₂
socle	C₂²×C₁₉	#329
prime radical	C₂³×C₁₉	#100
cosocle	C₂×C₁₉×#97	C₂²
hypercenter	#1992	D₁₉
hypocenter	C₁₉	#7130
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1992

subgroup

G/H

center

C₂²

#11926284

commutator

C₄²×C₁₉

C₂×C₈

Frattini

C₂×#97

C₂×D₁₉

Fitting

C₁₉×#1992

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₁₉×#97

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1992

N	H ≅ G/N	type
92. C₁₉	#7130	semidirect

H ≅ G/N

type

92. C₁₉

#7130

semidirect

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

subgroup	index
#14561715	2
C₁₉×#1992	2
#7130	19

subgroup

index

#14561715

C₁₉×#1992

#7130

Subgroups — #18069355

Conjugacy classes of subgroups

Complements

Maximal subgroups