Group #18069269 — subgroups

Subgroups — #18069269

Order 4864.

186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14563250	C₂	1	1	yes	maximal, characteristic
2	#14561705	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1370	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926921	—	2	1	no	—
5	#11926921	—	2	1	no	—
6	#11926921	C₄	1	2	yes	—
7	C₄⋊(C₁₉⋊C₁₆)	—	2	1	no	—
8	C₁₉×C₄⋊C₁₆	—	2	1	no	—
9	C₈²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×D₁₅₂	—	4	2	no	—
11	C₂×D₁₅₂	—	4	1	no	—
12	C₂×D₁₅₂	—	4	1	no	—
13	C₂×D₁₅₂	—	4	1	no	—
14	C₂×D₁₅₂	—	4	1	no	—
15	#10597320	—	2	2	no	—
16	C₂×C₁₆×C₁₉	—	4	1	no	—
17	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
19	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₁₉⋊C₁₆	—	4	1	no	—
21	C₂×D₇₆	—	4	2	no	—
22	C₂×D₇₆	—	4	2	no	—
23	C₂×D₇₆	—	4	2	no	—
24	C₂×C₈×C₁₉	—	2	1	no	—
25	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
26	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
27	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
28	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
29	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	D₁₅₂	—	8	4	no	—
31	D₁₅₂	—	8	2	no	—
32	D₁₅₂	—	8	2	no	—
33	D₁₅₂	—	8	1	no	—
34	D₁₅₂	—	8	1	no	—
35	D₁₅₂	—	8	1	no	—
36	D₁₅₂	—	8	1	no	—
37	C₁₆×C₁₉	—	8	1	no	—
38	C₁₉⋊C₁₆	—	8	1	no	—
39	#7096	—	19	1	no	maximal, Sylow
40	C₂²×D₁₉	—	8	2	no	—
41	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
42	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
44	D₇₆	—	8	4	no	—
45	D₇₆	—	8	2	no	—
46	D₇₆	—	8	2	no	—
47	D₇₆	—	8	2	no	—
48	D₇₆	—	8	2	no	—
49	C₈×C₁₉	—	2	2	no	—
50	C₈×C₁₉	—	2	1	no	—
51	C₈×C₁₉	—	2	1	no	—
52	C₈×C₁₉	D₁₆	1	1	yes	characteristic
53	C₈×C₁₉	D₁₆	1	1	yes	characteristic
54	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
55	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
56	#1712	—	19	1	no	—
57	#1370	—	19	1	no	—
58	#1370	D₁₉	1	1	yes	characteristic, complemented
59	C₂²×C₁₉	#331	1	1	yes	characteristic
60	C₂×D₁₉	—	16	2	no	—
61	C₂×D₁₉	—	16	2	no	—
62	C₂×D₁₉	—	16	2	no	—
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	#357	1	1	yes	characteristic
65	C₄×C₁₉	#357	1	1	yes	characteristic
66	C₄×C₁₉	#361	1	1	yes	characteristic
67	C₄×C₁₉	#361	1	1	yes	characteristic
68	#493	—	19	2	no	—
69	#493	—	38	1	no	—
70	#493	—	38	1	no	—
71	C₄⋊C₁₆	—	2	1	no	—
72	C₄⋊C₁₆	—	38	1	no	—
73	C₈²	C₂×D₁₉	1	1	yes	characteristic
74	C₂×C₁₉	#1357	1	1	yes	characteristic
75	C₂×C₁₉	#1361	1	1	yes	characteristic
76	C₂×C₁₉	#1361	1	1	yes	characteristic
77	D₁₉	—	32	2	no	—
78	C₂×D₈	—	76	2	no	—
79	C₂×D₈	—	76	1	no	—
80	C₂×D₈	—	76	1	no	—
81	C₂×D₈	—	76	1	no	—
82	C₂×D₈	—	76	1	no	—
83	#127	—	38	2	no	—
84	C₂×C₁₆	—	4	1	no	—
85	C₂×C₁₆	—	76	1	no	—
86	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
87	C₄×C₈	D₇₆	1	1	yes	characteristic
88	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
89	C₁₉	#7096	1	1	yes	characteristic, complemented, Sylow
90	C₂×D₄	—	76	2	no	—
91	C₂×D₄	—	76	2	no	—
92	C₂×D₄	—	76	2	no	—
93	D₈	—	152	4	no	—
94	D₈	—	152	2	no	—
95	D₈	—	152	2	no	—
96	D₈	—	152	1	no	—
97	D₈	—	152	1	no	—
98	D₈	—	152	1	no	—
99	D₈	—	152	1	no	—
100	C₂×C₈	—	2	1	no	—
101	C₂×C₈	#64516	1	1	yes	characteristic
102	C₂×C₈	D₁₅₂	1	1	yes	characteristic
103	C₂×C₈	#64525	1	1	yes	characteristic
104	C₂×C₈	#64527	1	1	yes	characteristic
105	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
106	C₁₆	—	8	1	no	—
107	C₁₆	—	152	1	no	—
108	C₂³	—	152	2	no	—
109	D₄	—	152	4	no	—
110	D₄	—	152	2	no	—
111	D₄	—	152	2	no	—
112	D₄	—	152	2	no	—
113	D₄	—	152	2	no	—
114	C₂×C₄	#10597266	1	1	yes	characteristic
115	C₂×C₄	#10597278	1	1	yes	characteristic
116	C₂×C₄	#10597280	1	1	yes	characteristic
117	C₈	—	2	2	no	—
118	C₈	—	2	1	no	—
119	C₈	—	2	1	no	—
120	C₈	D₃₀₄	1	1	yes	characteristic
121	C₈	#10597257	1	1	yes	characteristic
122	C₈	#10597283	1	1	yes	characteristic
123	C₈	#10597285	1	1	yes	characteristic
124	C₂²	—	304	2	no	—
125	C₂²	—	304	2	no	—
126	C₂²	—	304	2	no	—
127	C₂²	#11926287	1	1	yes	characteristic
128	C₄	—	2	1	no	—
129	C₄	#11926344	1	1	yes	characteristic
130	C₄	#11926346	1	1	yes	characteristic
131	C₄	#11926356	1	1	yes	characteristic
132	C₄	#11926358	1	1	yes	characteristic
133	C₂	—	608	2	no	—
134	C₂	#14561671	1	1	yes	characteristic
135	C₂	#14561680	1	1	yes	characteristic
136	C₂	#14561682	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563250

C₂

yes

maximal, characteristic

#14561705

C₂

yes

maximal, characteristic, complemented

C₁₉×#1370

C₂

yes

maximal, characteristic, complemented

#11926921

—

#11926921

—

#11926921

C₄

yes

—

C₄⋊(C₁₉⋊C₁₆)

—

C₁₉×C₄⋊C₁₆

—

C₈²×C₁₉

C₂²

yes

characteristic

C₂×D₁₅₂

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

#10597320

—

C₂×C₁₆×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₁₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

D₁₅₂

—

D₁₅₂

—

D₁₅₂

—

D₁₅₂

—

D₁₅₂

—

D₁₅₂

—

D₁₅₂

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7096

—

maximal, Sylow

C₂²×D₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

D₁₆

yes

characteristic

C₈×C₁₉

D₁₆

yes

characteristic

C₈×C₁₉

SD₃₂

yes

characteristic

C₈×C₁₉

SD₃₂

yes

—

—

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

#331

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

—

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₈²

C₂×D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

#127

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

C₄×D₁₉

yes

characteristic

C₄×C₈

D₇₆

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₁₉

#7096

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

D₈

—

152

—

D₈

—

152

—

D₈

—

152

—

D₈

—

152

—

D₈

—

152

—

D₈

—

152

—

D₈

—

152

—

100

C₂×C₈

—

101

C₂×C₈

#64516

yes

characteristic

102

C₂×C₈

D₁₅₂

yes

characteristic

103

C₂×C₈

#64525

yes

characteristic

104

C₂×C₈

#64527

yes

characteristic

105

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

106

C₁₆

—

107

C₁₆

—

152

—

108

C₂³

—

152

—

109

D₄

—

152

—

110

D₄

—

152

—

111

D₄

—

152

—

112

D₄

—

152

—

113

D₄

—

152

—

114

C₂×C₄

#10597266

yes

characteristic

115

C₂×C₄

#10597278

yes

characteristic

116

C₂×C₄

#10597280

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

—

120

C₈

D₃₀₄

yes

characteristic

121

C₈

#10597257

yes

characteristic

122

C₈

#10597283

yes

characteristic

123

C₈

#10597285

yes

characteristic

124

C₂²

—

304

—

125

C₂²

—

304

—

126

C₂²

—

304

—

127

C₂²

#11926287

yes

characteristic

128

C₄

—

129

C₄

#11926344

yes

characteristic

130

C₄

#11926346

yes

characteristic

131

C₄

#11926356

yes

characteristic

132

C₄

#11926358

yes

characteristic

133

C₂

—

608

—

134

C₂

#14561671

yes

characteristic

135

C₂

#14561680

yes

characteristic

136

C₂

#14561682

yes

characteristic

	subgroup	G/H
center	C₂²	#11926287
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	C₈²	C₂×D₁₉
Fitting	C₁₉×#1370	C₂
socle	C₂²×C₁₉	#331
prime radical	#14563250	C₂
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1370	D₁₉
hypocenter	C₁₉	#7096
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1370

subgroup

G/H

center

C₂²

#11926287

commutator

C₄×C₈×C₁₉

C₂×C₄

Frattini

C₈²

C₂×D₁₉

Fitting

C₁₉×#1370

C₂

C₂²×C₁₉

C₂

C₈²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1370

N	H ≅ G/N	type
2. #14561705	C₂	semidirect
3. C₁₉×#1370	C₂	semidirect
58. #1370	D₁₉	semidirect
89. C₁₉	#7096	semidirect

H ≅ G/N

type

2. #14561705

C₂

semidirect

3. C₁₉×#1370

C₂

semidirect

58. #1370

D₁₉

semidirect

89. C₁₉

#7096

semidirect

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

subgroup	index
#14563250	2
#14561705	2
C₁₉×#1370	2
#7096	19

subgroup

index

#14563250

#14561705

C₁₉×#1370

#7096

Subgroups — #18069269

Conjugacy classes of subgroups

Complements

Maximal subgroups