Group #18069622 — subgroups

Subgroups — #18069622

Order 4864.

264 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 83 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	#14563673	C₂	1	2	yes	maximal
2	C₁₉×#2112	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597276	—	2	2	no	—
4	#11926508	—	2	2	no	—
5	#11926309	C₄	1	4	yes	—
6	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×M₃₂	C₄	1	2	yes	—
8	C₁₉×C₂²⋊C₁₆	—	2	2	no	—
9	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	—	4	2	no	—
11	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
13	C₂²×C₈×C₁₉	D₄	1	2	yes	—
14	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
15	C₂×#64520	—	2	4	no	—
16	C₁₉×M₃₂	—	4	2	no	—
17	C₂×C₁₆×C₁₉	—	2	2	no	—
18	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
19	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
20	#10597276	—	4	4	no	—
21	C₂⁴×C₁₉	Q₁₆	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	—	4	1	no	—
23	C₂²×C₄×C₁₉	—	4	1	no	—
24	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
25	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₂×C₈×C₁₉	—	2	4	no	—
30	C₂×C₈×C₁₉	—	4	2	no	—
31	C₂×C₈×C₁₉	—	4	1	no	—
32	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
33	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
35	#64520	—	4	4	no	—
36	#64520	—	4	4	no	—
37	C₂×C₁₉⋊C₈	—	4	4	no	—
38	C₁₆×C₁₉	—	4	2	no	—
39	#7234	—	19	1	no	maximal, Sylow
40	C₂³×C₁₉	—	4	1	no	—
41	C₂³×C₁₉	—	4	2	no	—
42	C₂³×C₁₉	#103	1	2	yes	—
43	C₂³×C₁₉	#107	1	1	yes	characteristic
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	4	1	no	—
49	C₂×C₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
51	C₂×C₄×C₁₉	#102	1	2	yes	—
52	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
53	C₈×C₁₉	—	2	1	no	—
54	C₈×C₁₉	—	2	2	no	—
55	C₈×C₁₉	#99	1	2	yes	—
56	C₁₉⋊C₈	—	8	4	no	—
57	#2112	D₁₉	1	1	yes	characteristic
58	#1810	—	19	2	no	—
59	C₂²×C₁₉	—	2	2	no	—
60	C₂²×C₁₉	—	2	1	no	—
61	C₂²×C₁₉	—	2	4	no	—
62	C₂²×C₁₉	—	2	2	no	—
63	C₂²×C₁₉	—	4	4	no	—
64	C₂²×C₁₉	#340	1	1	yes	characteristic
65	C₄×C₁₉	—	2	2	no	—
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
68	C₄×C₁₉	#342	1	1	yes	characteristic
69	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
70	C₂×M₃₂	Dic₁₉	1	2	yes	—
71	C₂×#108	—	38	2	no	—
72	#407	—	38	2	no	—
73	C₂²⋊C₁₆	—	2	2	no	—
74	#341	—	19	4	no	—
75	C₂×C₁₉	—	4	2	no	—
76	C₂×C₁₉	—	4	1	no	—
77	C₂×C₁₉	#1289	1	1	yes	characteristic
78	C₂×C₁₉	#1388	1	2	yes	—
79	C₂³×C₄	D₇₆	1	1	yes	characteristic
80	C₂×M₁₆	—	38	4	no	—
81	C₂²×C₈	—	4	2	no	—
82	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
83	C₂²×C₈	C₄×D₁₉	1	2	yes	—
84	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
85	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
86	M₃₂	—	4	2	no	—
87	C₂×C₁₆	—	2	2	no	—
88	#108	—	76	4	no	—
89	C₂²⋊C₈	—	76	2	no	—
90	C₂²⋊C₈	—	76	2	no	—
91	C₁₉	#7234	1	1	yes	characteristic, complemented, Sylow
92	C₂⁴	Dic₇₆	1	1	yes	characteristic
93	C₂²×C₄	—	4	1	no	—
94	C₂²×C₄	—	4	1	no	—
95	C₂²×C₄	#64516	1	2	yes	—
96	C₂²×C₄	D₁₅₂	1	1	yes	characteristic
97	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
98	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
99	M₁₆	—	76	4	no	—
100	M₁₆	—	76	4	no	—
101	C₂×C₈	—	2	4	no	—
102	C₂×C₈	—	2	2	no	—
103	C₂×C₈	—	4	1	no	—
104	C₂×C₈	—	4	2	no	—
105	C₂×C₈	—	76	4	no	—
106	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
107	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
108	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
109	C₁₆	—	4	2	no	—
110	C₂³	—	4	1	no	—
111	C₂³	—	4	2	no	—
112	C₂³	#10597273	1	2	yes	—
113	C₂³	#10597275	1	1	yes	characteristic
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	#10597274	1	1	yes	characteristic
121	C₂×C₄	#10597278	1	2	yes	—
122	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	2	2	no	—
125	C₈	—	152	4	no	—
126	C₈	#10597291	1	2	yes	—
127	C₂²	—	2	4	no	—
128	C₂²	—	2	2	no	—
129	C₂²	—	2	2	no	—
130	C₂²	—	2	1	no	—
131	C₂²	—	4	4	no	—
132	C₂²	#11926307	1	1	yes	characteristic
133	C₄	—	2	2	no	—
134	C₄	—	2	1	no	—
135	C₄	#11926301	1	1	yes	characteristic
136	C₄	#11926311	1	1	yes	characteristic
137	C₂	—	4	2	no	—
138	C₂	—	4	1	no	—
139	C₂	#14561503	1	1	yes	characteristic
140	C₂	#14561747	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563673

C₂

yes

maximal

C₁₉×#2112

C₂

yes

maximal, characteristic

C₂×#10597276

—

#11926508

—

#11926309

C₄

yes

—

C₂³×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×M₃₂

C₄

yes

—

C₁₉×C₂²⋊C₁₆

—

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×#64520

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

#10597276

—

C₂⁴×C₁₉

Q₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

#7234

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#103

yes

—

C₂³×C₁₉

#107

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

#102

yes

—

C₂×C₄×C₁₉

#106

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#99

yes

—

C₁₉⋊C₈

—

#2112

D₁₉

yes

characteristic

#1810

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#340

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂³×C₈

C₂×D₁₉

yes

characteristic

C₂×M₃₂

Dic₁₉

yes

—

C₂×#108

—

#407

—

C₂²⋊C₁₆

—

#341

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1289

yes

characteristic

C₂×C₁₉

#1388

yes

—

C₂³×C₄

D₇₆

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

Dic₃₈

yes

characteristic

C₂²×C₈

C₄×D₁₉

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

C₂²×C₈

C₂²⋊D₁₉

yes

—

M₃₂

—

C₂×C₁₆

—

#108

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₁₉

#7234

yes

characteristic, complemented, Sylow

C₂⁴

Dic₇₆

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

#64516

yes

—

C₂²×C₄

D₁₅₂

yes

characteristic

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

M₁₆

—

100

M₁₆

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

C₄×Dic₁₉

yes

characteristic

107

C₂×C₈

Dic₁₉⋊C₄

yes

—

108

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

109

C₁₆

—

110

C₂³

—

111

C₂³

—

112

C₂³

#10597273

yes

—

113

C₂³

#10597275

yes

characteristic

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

#10597274

yes

characteristic

121

C₂×C₄

#10597278

yes

—

122

C₂×C₄

C₁₉⋊#95

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

152

—

126

C₈

#10597291

yes

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

#11926307

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

#11926301

yes

characteristic

136

C₄

#11926311

yes

characteristic

137

C₂

—

138

C₂

—

139

C₂

#14561503

yes

characteristic

140

C₂

#14561747

yes

—

	subgroup	G/H
center	C₂²	#11926307
commutator	C₂×C₈×C₁₉	C₄²
Frattini	C₂³×C₈	C₂×D₁₉
Fitting	C₁₉×#2112	C₂
socle	C₂²×C₁₉	#340
prime radical	C₂⁴×C₁₉	Q₁₆
cosocle	C₂³×C₈×C₁₉	C₂²
hypercenter	#2112	D₁₉
hypocenter	C₁₉	#7234
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #2112

subgroup

G/H

center

C₂²

#11926307

commutator

C₂×C₈×C₁₉

C₄²

Frattini

C₂³×C₈

C₂×D₁₉

Fitting

C₁₉×#2112

C₂

socle

C₂²×C₁₉

#340

prime radical

C₂⁴×C₁₉

Q₁₆

cosocle

C₂³×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #2112

N	H ≅ G/N	type
91. C₁₉	#7234	semidirect

H ≅ G/N

type

91. C₁₉

#7234

semidirect

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

subgroup	index
#14563673	2
C₁₉×#2112	2
#7234	19

subgroup

index

#14563673

C₁₉×#2112

#7234

Subgroups — #18069622

Conjugacy classes of subgroups

Complements

Maximal subgroups