Group #18069206 — subgroups

Subgroups — #18069206

Order 4864.

148 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 55 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	#14561699	C₂	1	1	yes	maximal, characteristic, complemented
2	#14561552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1589	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₁₉⋊C₁₆)	—	2	1	no	—
5	C₄×C₁₉⋊C₁₆	—	2	1	no	—
6	C₄×D₈×C₁₉	C₄	1	1	yes	characteristic
7	C₁₉×#436	—	2	1	no	—
8	C₁₉×#335	C₄	1	1	yes	characteristic
9	C₁₉×D₄⋊C₈	—	2	1	no	—
10	C₈²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×D₈×C₁₉	C₈	1	1	yes	characteristic
12	C₂×M₁₆×C₁₉	—	4	1	no	—
13	C₄×D₄×C₁₉	—	2	1	no	—
14	C₁₉×#107	C₈	1	1	yes	characteristic
15	C₁₉×C₄⋊C₈	—	2	1	no	—
16	C₁₉×#102	—	2	1	no	—
17	C₁₉×C₂²⋊C₈	—	4	1	no	—
18	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₁₉⋊C₁₆	—	2	2	no	—
22	C₂×C₁₉⋊C₁₆	—	4	1	no	—
23	C₂×D₄×C₁₉	—	2	1	no	—
24	C₂²×C₄×C₁₉	—	4	1	no	—
25	D₈×C₁₉	—	4	1	no	—
26	M₁₆×C₁₉	—	8	2	no	—
27	C₂×C₈×C₁₉	—	2	1	no	—
28	C₂×C₈×C₁₉	—	4	1	no	—
29	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
30	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
31	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
32	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
33	C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂²⋊C₄×C₁₉	—	4	1	no	—
35	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₁₉⋊C₁₆	—	2	4	no	—
37	C₁₉⋊C₁₆	—	8	1	no	—
38	#7074	—	19	1	no	maximal, Sylow
39	C₂³×C₁₉	—	4	1	no	—
40	D₄×C₁₉	—	4	1	no	—
41	D₄×C₁₉	—	4	1	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	—	8	1	no	—
44	C₂×C₄×C₁₉	—	8	1	no	—
45	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
47	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
48	C₈×C₁₉	—	2	2	no	—
49	C₈×C₁₉	—	2	1	no	—
50	C₈×C₁₉	—	2	1	no	—
51	C₈×C₁₉	—	2	1	no	—
52	C₈×C₁₉	—	2	1	no	—
53	C₈×C₁₉	—	8	1	no	—
54	#1589	D₁₉	1	1	yes	characteristic
55	#1367	—	19	1	no	—
56	#1311	—	19	1	no	—
57	C₂²×C₁₉	—	8	1	no	—
58	C₂²×C₁₉	—	8	1	no	—
59	C₂²×C₁₉	—	8	1	no	—
60	C₂²×C₁₉	D₄⋊C₈	1	1	yes	characteristic
61	C₄×C₁₉	—	2	1	no	—
62	C₄×C₁₉	—	8	1	no	—
63	C₄×C₁₉	#349	1	1	yes	characteristic
64	C₄×C₁₉	#350	1	1	yes	characteristic
65	C₄×C₁₉	#360	1	1	yes	characteristic
66	C₄×C₁₉	#361	1	1	yes	characteristic
67	C₄×D₈	Dic₁₉	1	1	yes	characteristic
68	#436	—	2	1	no	—
69	C₄⋊C₁₆	—	38	1	no	—
70	C₄×C₁₆	—	38	1	no	—
71	#335	Dic₁₉	1	1	yes	characteristic
72	D₄⋊C₈	—	2	1	no	—
73	C₈²	C₂×D₁₉	1	1	yes	characteristic
74	C₂×C₁₉	—	16	1	no	—
75	C₂×C₁₉	#1330	1	1	yes	characteristic
76	C₂×C₁₉	#1333	1	1	yes	characteristic
77	C₂×C₁₉	#1335	1	1	yes	characteristic
78	C₂×D₈	C₁₉⋊C₈	1	1	yes	characteristic
79	C₂×M₁₆	—	4	1	no	—
80	C₄×D₄	—	2	1	no	—
81	C₂×C₁₆	—	38	2	no	—
82	C₂×C₁₆	—	76	1	no	—
83	#107	C₁₉⋊C₈	1	1	yes	characteristic
84	C₄⋊C₈	—	2	1	no	—
85	#102	—	2	1	no	—
86	C₂²⋊C₈	—	4	1	no	—
87	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
88	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
89	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
90	C₁₉	#7074	1	1	yes	characteristic, complemented, Sylow
91	C₂×D₄	—	2	1	no	—
92	C₂²×C₄	—	4	1	no	—
93	D₈	—	4	1	no	—
94	M₁₆	—	8	2	no	—
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	4	1	no	—
97	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
98	C₂×C₈	#64520	1	1	yes	characteristic
99	C₂×C₈	#64525	1	1	yes	characteristic
100	C₂×C₈	#64526	1	1	yes	characteristic
101	C₄⋊C₄	—	2	1	no	—
102	C₂²⋊C₄	—	4	1	no	—
103	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
104	C₁₆	—	38	4	no	—
105	C₁₆	—	152	1	no	—
106	C₂³	—	4	1	no	—
107	D₄	—	4	1	no	—
108	D₄	—	4	1	no	—
109	C₂×C₄	—	4	1	no	—
110	C₂×C₄	—	8	1	no	—
111	C₂×C₄	—	8	1	no	—
112	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
113	C₂×C₄	#10597289	1	1	yes	characteristic
114	C₂×C₄	#10597294	1	1	yes	characteristic
115	C₈	—	2	2	no	—
116	C₈	—	2	1	no	—
117	C₈	—	2	1	no	—
118	C₈	—	2	1	no	—
119	C₈	—	2	1	no	—
120	C₈	—	8	1	no	—
121	C₂²	—	8	1	no	—
122	C₂²	—	8	1	no	—
123	C₂²	—	8	1	no	—
124	C₂²	D₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
125	C₄	—	2	1	no	—
126	C₄	—	8	1	no	—
127	C₄	#11926326	1	1	yes	characteristic
128	C₄	#11926328	1	1	yes	characteristic
129	C₄	#11926354	1	1	yes	characteristic
130	C₄	#11926357	1	1	yes	characteristic
131	C₂	—	16	1	no	—
132	C₂	#14561593	1	1	yes	characteristic
133	C₂	#14561602	1	1	yes	characteristic
134	C₂	#14561608	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561699

C₂

yes

maximal, characteristic, complemented

#14561552

C₂

yes

maximal, characteristic, complemented

C₁₉×#1589

C₂

yes

maximal, characteristic

C₄⋊(C₁₉⋊C₁₆)

—

C₄×C₁₉⋊C₁₆

—

C₄×D₈×C₁₉

C₄

yes

characteristic

C₁₉×#436

—

C₁₉×#335

C₄

yes

characteristic

C₁₉×D₄⋊C₈

—

C₈²×C₁₉

C₂²

yes

characteristic

C₂×D₈×C₁₉

C₈

yes

characteristic

C₂×M₁₆×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×#107

C₈

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×#102

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

D₈×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₈

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₁₉⋊C₁₆

—

C₁₉⋊C₁₆

—

#7074

—

maximal, Sylow

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#1589

D₁₉

yes

characteristic

#1367

—

#1311

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

D₄⋊C₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×D₈

Dic₁₉

yes

characteristic

#436

—

C₄⋊C₁₆

—

C₄×C₁₆

—

#335

Dic₁₉

yes

characteristic

D₄⋊C₈

—

C₈²

C₂×D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×D₈

C₁₉⋊C₈

yes

characteristic

C₂×M₁₆

—

C₄×D₄

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

C₁₉⋊C₈

yes

characteristic

C₄⋊C₈

—

#102

—

C₂²⋊C₈

—

C₄×C₈

C₂×Dic₁₉

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₁₉

#7074

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂²×C₄

—

D₈

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×C₁₉⋊C₈

yes

C₂×C₈

yes

C₂×C₈

yes

100

C₂×C₈

#64526

yes

characteristic

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

103

C₄²

C₂²⋊Dic₁₉

yes

characteristic

104

C₁₆

—

105

C₁₆

—

152

—

106

C₂³

—

107

D₄

—

108

D₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

113

C₂×C₄

#10597289

yes

characteristic

114

C₂×C₄

#10597294

yes

characteristic

115

C₈

—

116

C₈

—

117

C₈

—

118

C₈

—

119

C₈

—

120

C₈

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

D₄⋊(C₁₉⋊C₈)

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

#11926326

yes

characteristic

128

C₄

#11926328

yes

characteristic

129

C₄

#11926354

yes

characteristic

130

C₄

#11926357

yes

characteristic

131

C₂

—

132

C₂

#14561593

yes

characteristic

133

C₂

#14561602

yes

characteristic

134

C₂

#14561608

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597289
commutator	C₂×C₈×C₁₉	C₂×C₈
Frattini	C₈²	C₂×D₁₉
Fitting	C₁₉×#1589	C₂
socle	C₂²×C₁₉	D₄⋊C₈
prime radical	C₂×D₈×C₁₉	C₈
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1589	D₁₉
hypocenter	C₁₉	#7074
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈² ◁ #1589

subgroup

G/H

center

C₂×C₄

#10597289

commutator

C₂×C₈×C₁₉

C₂×C₈

Frattini

C₈²

C₂×D₁₉

Fitting

C₁₉×#1589

C₂

socle

C₂²×C₁₉

D₄⋊C₈

prime radical

C₂×D₈×C₁₉

C₈

cosocle

C₈²×C₁₉

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈² ◁ #1589

N	H ≅ G/N	type
1. #14561699	C₂	semidirect
2. #14561552	C₂	semidirect
90. C₁₉	#7074	semidirect

H ≅ G/N

type

1. #14561699

C₂

semidirect

2. #14561552

C₂

semidirect

90. C₁₉

#7074

semidirect

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

subgroup	index
#14561699	2
#14561552	2
C₁₉×#1589	2
#7074	19

subgroup

index

#14561699

#14561552

C₁₉×#1589

#7074

Subgroups — #18069206

Conjugacy classes of subgroups

Complements

Maximal subgroups