Group #18070112 — subgroups

Subgroups — #18070112

Order 4864.

146 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 43 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	#14561775	C₂	1	1	yes	maximal, characteristic, complemented
2	#14561739	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2218	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597276	—	2	1	no	—
5	#11926378	—	2	1	no	—
6	C₂×C₁₉×D₁₆	C₄	1	1	yes	characteristic
7	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
8	C₁₉×#466	—	2	1	no	—
9	C₁₉×#367	C₄	1	1	yes	characteristic
10	C₁₉×#357	—	2	1	no	—
11	C₂×D₈×C₁₉	—	2	1	no	—
12	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₁₉×#121	—	4	1	no	—
14	C₂×#64520	—	4	1	no	—
15	C₁₉×D₁₆	—	4	1	no	—
16	C₁₉×M₃₂	—	4	1	no	—
17	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
19	C₁₉×#107	—	2	1	no	—
20	C₁₉×#102	—	4	1	no	—
21	#10597276	—	2	2	no	—
22	#10597276	—	4	1	no	—
23	C₁₉⋊C₃₂	—	4	1	no	—
24	C₂×D₄×C₁₉	—	4	1	no	—
25	C₂×D₄×C₁₉	—	8	1	no	—
26	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
27	D₈×C₁₉	—	4	1	no	—
28	D₈×C₁₉	—	4	1	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₂×C₈×C₁₉	—	2	1	no	—
31	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
33	C₄⋊C₄×C₁₉	—	4	1	no	—
34	C₂²⋊C₄×C₁₉	—	8	1	no	—
35	#64520	—	4	2	no	—
36	#64520	—	8	1	no	—
37	C₂×C₁₉⋊C₈	—	8	1	no	—
38	C₁₆×C₁₉	—	2	1	no	—
39	C₁₆×C₁₉	—	2	1	no	—
40	#7424	—	19	1	no	maximal, Sylow
41	C₂³×C₁₉	—	8	1	no	—
42	C₂³×C₁₉	SD₃₂	1	1	yes	characteristic
43	D₄×C₁₉	—	8	1	no	—
44	D₄×C₁₉	—	8	1	no	—
45	D₄×C₁₉	—	16	2	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	8	1	no	—
49	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
50	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
51	C₈×C₁₉	—	2	1	no	—
52	C₈×C₁₉	#99	1	1	yes	characteristic
53	C₈×C₁₉	#104	1	1	yes	characteristic
54	C₁₉⋊C₈	—	8	2	no	—
55	#2218	D₁₉	1	1	yes	characteristic
56	#1400	—	19	1	no	—
57	#1385	—	19	1	no	—
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	—	4	1	no	—
60	C₂²×C₁₉	—	16	1	no	—
61	C₂²×C₁₉	—	16	1	no	—
62	C₂²×C₁₉	—	16	1	no	—
63	C₂²×C₁₉	#357	1	1	yes	characteristic
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	—	16	1	no	—
66	C₄×C₁₉	#327	1	1	yes	characteristic
67	C₄×C₁₉	#360	1	1	yes	characteristic
68	C₂×D₁₆	Dic₁₉	1	1	yes	characteristic
69	C₂×M₃₂	C₂×D₁₉	1	1	yes	characteristic
70	#466	—	2	1	no	—
71	C₂×#108	—	38	1	no	—
72	M₆₄	—	38	1	no	—
73	#367	Dic₁₉	1	1	yes	characteristic
74	#357	—	2	1	no	—
75	C₂×C₁₉	—	2	1	no	—
76	C₂×C₁₉	—	4	1	no	—
77	C₂×C₁₉	—	32	1	no	—
78	C₂×C₁₉	#1347	1	1	yes	characteristic
79	C₂×D₈	—	2	1	no	—
80	C₂×M₁₆	—	76	1	no	—
81	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
82	#121	—	4	1	no	—
83	D₁₆	—	4	1	no	—
84	M₃₂	—	4	1	no	—
85	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
86	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
87	#108	—	38	2	no	—
88	#108	—	76	1	no	—
89	#107	—	2	1	no	—
90	#102	—	4	1	no	—
91	C₃₂	—	76	1	no	—
92	C₁₉	#7424	1	1	yes	characteristic, complemented, Sylow
93	C₂×D₄	—	4	1	no	—
94	C₂×D₄	—	8	1	no	—
95	C₂²×C₄	#64525	1	1	yes	characteristic
96	D₈	—	4	1	no	—
97	D₈	—	4	1	no	—
98	M₁₆	—	76	2	no	—
99	M₁₆	—	152	1	no	—
100	C₂×C₈	—	2	1	no	—
101	C₂×C₈	—	2	1	no	—
102	C₂×C₈	—	152	1	no	—
103	C₂×C₈	#64526	1	1	yes	characteristic
104	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
105	C₄⋊C₄	—	4	1	no	—
106	C₂²⋊C₄	—	8	1	no	—
107	C₁₆	—	2	1	no	—
108	C₁₆	—	2	1	no	—
109	C₂³	—	8	1	no	—
110	C₂³	#10597284	1	1	yes	characteristic
111	D₄	—	8	1	no	—
112	D₄	—	8	1	no	—
113	D₄	—	16	2	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	8	1	no	—
117	C₂×C₄	#10597283	1	1	yes	characteristic
118	C₂×C₄	#10597289	1	1	yes	characteristic
119	C₈	—	2	1	no	—
120	C₈	—	152	2	no	—
121	C₈	#10597291	1	1	yes	characteristic
122	C₈	#10597294	1	1	yes	characteristic
123	C₂²	—	2	1	no	—
124	C₂²	—	4	1	no	—
125	C₂²	—	16	1	no	—
126	C₂²	—	16	1	no	—
127	C₂²	—	16	1	no	—
128	C₂²	#11926345	1	1	yes	characteristic
129	C₄	—	2	1	no	—
130	C₄	—	16	1	no	—
131	C₄	#11926278	1	1	yes	characteristic
132	C₄	#11926354	1	1	yes	characteristic
133	C₂	—	2	1	no	—
134	C₂	—	4	1	no	—
135	C₂	—	32	1	no	—
136	C₂	#14561644	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561775

C₂

yes

maximal, characteristic, complemented

#14561739

C₂

yes

maximal, characteristic, complemented

C₁₉×#2218

C₂

yes

maximal, characteristic

C₂×#10597276

—

#11926378

—

C₂×C₁₉×D₁₆

C₄

yes

characteristic

C₂×C₁₉×M₃₂

C₂²

yes

characteristic

C₁₉×#466

—

C₁₉×#367

C₄

yes

characteristic

C₁₉×#357

—

C₂×D₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₁₉×#121

—

C₂×#64520

—

C₁₉×D₁₆

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×#107

—

C₁₉×#102

—

#10597276

—

#10597276

—

C₁₉⋊C₃₂

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

D₈

yes

characteristic

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

#7424

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

SD₃₂

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₁₉⋊C₈

—

#2218

D₁₉

yes

characteristic

#1400

—

#1385

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#357

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×D₁₆

Dic₁₉

yes

characteristic

C₂×M₃₂

C₂×D₁₉

yes

characteristic

#466

—

C₂×#108

—

M₆₄

—

#367

Dic₁₉

yes

characteristic

#357

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1347

yes

characteristic

C₂×D₈

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

#121

—

D₁₆

—

M₃₂

—

C₂×C₁₆

C₂×Dic₁₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

—

—

—

—

C₃₂

—

C₁₉

#7424

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

#64525

yes

characteristic

D₈

—

D₈

—

M₁₆

—

M₁₆

—

152

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

152

—

103

C₂×C₈

#64526

yes

characteristic

104

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

105

C₄⋊C₄

—

106

C₂²⋊C₄

—

107

C₁₆

—

108

C₁₆

—

109

C₂³

—

110

C₂³

#10597284

yes

characteristic

111

D₄

—

112

D₄

—

113

D₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

#10597283

yes

characteristic

118

C₂×C₄

#10597289

yes

characteristic

119

C₈

—

120

C₈

—

152

—

121

C₈

#10597291

yes

characteristic

122

C₈

#10597294

yes

characteristic

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

#11926345

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

#11926278

yes

characteristic

132

C₄

#11926354

yes

characteristic

133

C₂

—

134

C₂

—

135

C₂

—

136

C₂

#14561644

yes

characteristic

	subgroup	G/H
center	C₂	#14561644
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₂×M₃₂	C₂×D₁₉
Fitting, prime radical	C₁₉×#2218	C₂
socle	C₂×C₁₉	#1347
cosocle	C₂×C₁₉×M₃₂	C₂²
hypercenter	#2218	D₁₉
hypocenter	C₁₉	#7424
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂ ◁ #2218

subgroup

G/H

center

C₂

#14561644

commutator

C₂×C₁₆×C₁₉

C₂×C₄

Frattini

C₂×M₃₂

C₂×D₁₉

Fitting, prime radical

C₁₉×#2218

C₂

socle

C₂×C₁₉

#1347

cosocle

C₂×C₁₉×M₃₂

C₂²

D₁₉

C₁₉

G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂ ◁ #2218

N	H ≅ G/N	type
1. #14561775	C₂	semidirect
2. #14561739	C₂	semidirect
92. C₁₉	#7424	semidirect

H ≅ G/N

type

1. #14561775

C₂

semidirect

2. #14561739

C₂

semidirect

92. C₁₉

#7424

semidirect

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

subgroup	index
#14561775	2
#14561739	2
C₁₉×#2218	2
#7424	19

subgroup

index

#14561775

#14561739

C₁₉×#2218

#7424

Subgroups — #18070112

Conjugacy classes of subgroups

Complements

Maximal subgroups