Group #18073709 — subgroups

Subgroups — #18073709

Order 4864.

366 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 179 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	#14562383	C₂	1	2	yes	maximal
2	#14561927	C₂	1	2	yes	maximal
3	#14561468	C₂	1	2	yes	maximal
4	C₄×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
5	#11926597	C₂²	1	4	yes	—
6	#11926297	C₄	1	4	yes	complemented
7	#11926295	C₄	1	4	yes	complemented
8	#11926266	—	2	4	no	—
9	C₂×C₁₉×#97	C₄	1	2	yes	—
10	C₂×C₁₉×#97	C₄	1	2	yes	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₄³×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
16	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	—	2	2	no	—
18	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
20	C₁₉×#97	—	2	4	no	—
21	C₁₉×#97	—	2	4	no	—
22	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₄×C₈×C₁₉	D₄	1	2	yes	—
25	C₄×C₈×C₁₉	Q₈	1	2	yes	—
26	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
27	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	8	yes	—
28	C₄×C₁₉⋊C₈	—	2	4	no	—
29	C₂²×C₄×C₁₉	—	2	2	no	—
30	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	#41	1	2	yes	—
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₂×C₈×C₁₉	—	2	2	no	—
34	C₂×C₈×C₁₉	—	2	2	no	—
35	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
36	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₄²	1	2	yes	—
38	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
39	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
40	C₄²×C₁₉	—	2	2	no	—
41	C₄²×C₁₉	—	4	4	no	—
42	C₄²×C₁₉	M₁₆	1	4	yes	—
43	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
44	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₁₉⋊C₈	—	2	8	no	—
47	#8269	—	19	1	no	maximal, Sylow
48	C₂³×C₁₉	#117	1	1	yes	characteristic
49	C₂×C₄×C₁₉	—	2	4	no	—
50	C₂×C₄×C₁₉	—	2	4	no	—
51	C₂×C₄×C₁₉	—	4	4	no	—
52	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
55	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
56	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
57	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
58	C₈×C₁₉	—	2	1	no	—
59	C₈×C₁₉	—	2	1	no	—
60	C₈×C₁₉	—	2	4	no	—
61	C₈×C₁₉	#97	1	4	yes	—
62	C₁₉⋊C₈	—	4	8	no	—
63	C₄×#97	D₁₉	1	1	yes	characteristic
64	#1564	—	19	2	no	—
65	#1452	—	19	2	no	—
66	#1276	—	19	2	no	—
67	C₂²×C₁₉	—	2	2	no	—
68	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₁₉	#432	1	2	yes	—
70	C₄×C₁₉	—	2	2	no	—
71	C₄×C₁₉	—	4	4	no	—
72	C₄×C₁₉	C₂×#97	1	1	yes	characteristic
73	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
74	C₄×C₁₉	#423	1	2	yes	—
75	C₄×C₁₉	#444	1	4	yes	—
76	#431	—	19	4	no	—
77	C₂×#97	Dic₁₉	1	2	yes	—
78	C₂×#97	Dic₁₉	1	2	yes	—
79	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
80	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
81	C₄³	C₂×D₁₉	1	1	yes	characteristic
82	#335	—	19	4	no	—
83	#334	—	19	4	no	—
84	#322	—	38	4	no	—
85	C₂×C₁₉	—	2	2	no	—
86	C₂×C₁₉	#1767	1	1	yes	characteristic
87	C₂×C₁₉	#1773	1	2	yes	—
88	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
89	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
90	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
91	C₂×C₄²	—	2	2	no	—
92	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
93	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
94	C₄⋊C₈	—	19	8	no	—
95	C₂²⋊C₈	—	38	4	no	—
96	#97	—	2	4	no	—
97	#97	—	2	4	no	—
98	C₄×C₈	—	38	4	no	—
99	C₄×C₈	Dic₃₈	1	2	yes	—
100	C₄×C₈	C₄×D₁₉	1	2	yes	—
101	C₄×C₈	C₄×D₁₉	1	2	yes	—
102	C₄×C₈	D₇₆	1	2	yes	—
103	C₁₉	#8269	1	1	yes	characteristic, complemented, Sylow
104	C₂²×C₄	—	2	2	no	—
105	C₂²×C₄	#64541	1	2	yes	—
106	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
107	C₂×C₈	—	2	2	no	—
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	—	2	2	no	—
110	C₂×C₈	—	38	8	no	—
111	C₂×C₈	#64520	1	4	yes	—
112	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
113	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
114	C₂×C₈	C₄×Dic₁₉	1	2	yes	—
115	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
116	C₄²	—	2	2	no	—
117	C₄²	—	4	4	no	—
118	C₄²	#64520	1	4	yes	—
119	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
120	C₄²	C₂×C₄×D₁₉	1	2	yes	—
121	C₄²	C₂×D₇₆	1	1	yes	characteristic
122	C₂³	#10597372	1	1	yes	characteristic
123	C₂×C₄	—	2	4	no	—
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	4	4	no	—
126	C₂×C₄	C₄×Dic₃₈	1	2	yes	—
127	C₂×C₄	C₄×D₇₆	1	2	yes	—
128	C₂×C₄	C₂×#64520	1	2	yes	—
129	C₂×C₄	C₂×#64520	1	2	yes	—
130	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
131	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
132	C₈	—	2	4	no	—
133	C₈	—	2	1	no	—
134	C₈	—	2	1	no	—
135	C₈	—	76	8	no	—
136	C₈	#10597260	1	4	yes	—
137	C₂²	—	2	2	no	—
138	C₂²	C₄×C₄⋊Dic₁₉	1	1	yes	characteristic
139	C₂²	#11926601	1	2	yes	—
140	C₄	—	2	2	no	—
141	C₄	—	4	4	no	—
142	C₄	C₂×#10597260	1	1	yes	characteristic
143	C₄	C₄×#64520	1	1	yes	characteristic
144	C₄	#11926568	1	2	yes	—
145	C₄	#11926667	1	4	yes	—
146	C₂	—	2	2	no	—
147	C₂	#14563488	1	1	yes	characteristic
148	C₂	#14563519	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14562383

C₂

yes

maximal

#14561927

C₂

yes

maximal

#14561468

C₂

yes

maximal

C₄×C₁₉×#97

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926297

C₄

yes

complemented

#11926295

C₄

yes

complemented

#11926266

—

C₂×C₁₉×#97

C₄

yes

—

C₂×C₁₉×#97

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#97

—

C₁₉×#97

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₄²

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

C₄×Q₈

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#97

yes

—

C₁₉⋊C₈

—

C₄×#97

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

#432

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×#97

yes

characteristic

C₄×C₁₉

C₄×M₁₆

yes

characteristic

C₄×C₁₉

#423

yes

—

C₄×C₁₉

#444

yes

—

#431

—

C₂×#97

Dic₁₉

yes

—

C₂×#97

Dic₁₉

yes

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄³

C₂×D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

#1767

yes

characteristic

C₂×C₁₉

#1773

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×Dic₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

Dic₃₈

yes

—

100

C₄×C₈

C₄×D₁₉

yes

—

101

C₄×C₈

C₄×D₁₉

yes

—

102

C₄×C₈

D₇₆

yes

—

103

C₁₉

#8269

yes

characteristic, complemented, Sylow

104

C₂²×C₄

—

105

C₂²×C₄

#64541

yes

—

106

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

#64520

yes

—

112

C₂×C₈

C₄×Dic₁₉

yes

characteristic

113

C₂×C₈

C₄×Dic₁₉

yes

characteristic

114

C₂×C₈

C₄×Dic₁₉

yes

—

115

C₂×C₈

C₄⋊Dic₁₉

yes

—

116

C₄²

—

117

C₄²

—

118

C₄²

#64520

yes

—

119

C₄²

C₂×Dic₃₈

yes

characteristic

120

C₄²

C₂×C₄×D₁₉

yes

—

121

C₄²

C₂×D₇₆

yes

characteristic

122

C₂³

#10597372

yes

characteristic

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

C₄×Dic₃₈

yes

—

127

C₂×C₄

C₄×D₇₆

yes

—

128

C₂×C₄

C₂×#64520

yes

—

129

C₂×C₄

C₂×#64520

yes

—

130

C₂×C₄

C₂×C₄×Dic₁₉

yes

characteristic

131

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

132

C₈

—

133

C₈

—

134

C₈

—

135

C₈

—

136

C₈

#10597260

yes

—

137

C₂²

—

138

C₂²

C₄×C₄⋊Dic₁₉

yes

characteristic

139

C₂²

#11926601

yes

—

140

C₄

—

141

C₄

—

142

C₄

C₂×#10597260

yes

characteristic

143

C₄

C₄×#64520

yes

characteristic

144

C₄

#11926568

yes

—

145

C₄

#11926667

yes

—

146

C₂

—

147

C₂

#14563488

yes

characteristic

148

C₂

#14563519

yes

—

	subgroup	G/H
center	C₄²	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#97	C₂
socle	C₂²×C₁₉	C₄×C₄⋊C₄
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#97	D₁₉
hypocenter	C₁₉	#8269
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ C₄×#97

subgroup

G/H

center

C₄²

C₂×D₇₆

commutator

C₂×C₄×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#97

C₂

socle

C₂²×C₁₉

C₄×C₄⋊C₄

prime radical

C₂³×C₁₉

#117

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₄×#97

D₁₉

hypocenter

C₁₉

#8269

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ C₄×#97

N	H ≅ G/N	type
6. #11926297	C₄	semidirect
7. #11926295	C₄	semidirect
103. C₁₉	#8269	semidirect

H ≅ G/N

type

6. #11926297

C₄

semidirect

7. #11926295

C₄

semidirect

103. C₁₉

#8269

semidirect

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

subgroup	index
#14562383	2
#14561927	2
#14561468	2
C₄×C₁₉×#97	2
#8269	19

subgroup

index

C₄×C₁₉×#97

Subgroups — #18073709

Conjugacy classes of subgroups

Complements

Maximal subgroups