Group #18070396 — subgroups

Subgroups — #18070396

Order 4864.

186 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 25 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	#14563249	C₂	1	1	yes	maximal, characteristic
2	#14561798	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1408	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926921	C₄	1	1	yes	characteristic, complemented
5	#11926920	—	2	1	no	—
6	#11926920	—	2	1	no	—
7	#11926337	—	2	1	no	—
8	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic, complemented
9	C₁₉×#493	C₂²	1	1	yes	characteristic
10	C₁₉×#353	—	2	1	no	—
11	C₂×D₈×C₁₉	—	4	1	no	—
12	C₁₉×#127	D₄	1	1	yes	characteristic
13	C₁₉×#127	D₄	1	1	yes	characteristic
14	C₂×#64525	—	4	2	no	—
15	C₂×#64525	—	4	2	no	—
16	C₂×D₁₅₂	—	4	1	no	—
17	#10597320	—	2	1	no	—
18	C₁₉×#99	—	4	1	no	—
19	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	#10597291	—	4	1	no	—
21	C₄×C₁₉⋊C₈	—	2	1	no	—
22	C₂×D₄×C₁₉	—	2	1	no	—
23	C₂×D₄×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	4	1	no	—
25	C₂×D₄×C₁₉	—	4	1	no	—
26	C₂×D₇₆	—	4	1	no	—
27	C₂×D₇₆	—	4	1	no	—
28	C₂×D₇₆	—	4	1	no	—
29	D₈×C₁₉	—	8	2	no	—
30	C₂×C₈×C₁₉	—	2	1	no	—
31	C₂²⋊C₄×C₁₉	—	8	1	no	—
32	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂²⋊Dic₁₉	—	8	1	no	—
34	#64525	—	8	4	no	—
35	#64525	—	8	4	no	—
36	C₂×C₁₉⋊C₈	—	2	2	no	—
37	D₁₅₂	—	8	2	no	—
38	#7529	—	19	1	no	maximal, Sylow
39	C₂³×C₁₉	—	4	1	no	—
40	C₂³×C₁₉	—	4	1	no	—
41	C₂²×D₁₉	—	8	1	no	—
42	D₄×C₁₉	—	8	1	no	—
43	D₄×C₁₉	—	8	1	no	—
44	D₄×C₁₉	—	8	2	no	—
45	D₄×C₁₉	—	8	2	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	16	1	no	—
48	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
49	C₂×Dic₁₉	—	16	1	no	—
50	D₇₆	—	8	2	no	—
51	D₇₆	—	8	2	no	—
52	D₇₆	—	8	2	no	—
53	C₈×C₁₉	—	2	2	no	—
54	C₁₉⋊C₈	—	2	4	no	—
55	#1712	—	19	1	no	—
56	#1408	—	19	1	no	—
57	#1408	D₁₉	1	1	yes	characteristic, complemented
58	C₂²×C₁₉	—	8	1	no	—
59	C₂²×C₁₉	—	8	1	no	—
60	C₂²×C₁₉	—	16	1	no	—
61	C₂²×C₁₉	—	16	1	no	—
62	C₂²×C₁₉	#353	1	1	yes	characteristic
63	C₂×D₁₉	—	16	1	no	—
64	C₂×D₁₉	—	16	1	no	—
65	C₂×D₁₉	—	16	1	no	—
66	C₄×C₁₉	—	2	2	no	—
67	C₄×C₁₉	—	2	1	no	—
68	C₄×C₁₉	—	32	1	no	—
69	Dic₁₉	—	32	1	no	—
70	#493	—	19	1	no	—
71	#493	—	38	1	no	—
72	#493	—	38	1	no	—
73	#493	C₂×D₁₉	1	1	yes	characteristic
74	#353	—	2	1	no	—
75	#353	—	38	1	no	—
76	C₈²	—	19	1	no	—
77	C₂×C₁₉	—	2	1	no	—
78	C₂×C₁₉	—	16	1	no	—
79	C₂×C₁₉	—	16	1	no	—
80	C₂×C₁₉	#1408	1	1	yes	characteristic
81	D₁₉	—	32	1	no	—
82	C₂×D₈	—	4	1	no	—
83	C₂×D₈	—	76	1	no	—
84	C₂×D₈	—	76	2	no	—
85	C₂×D₈	—	76	2	no	—
86	#127	—	38	1	no	—
87	#127	D₇₆	1	1	yes	characteristic
88	#127	C₂²⋊D₁₉	1	1	yes	characteristic
89	#99	—	4	1	no	—
90	#99	—	76	1	no	—
91	C₄×C₈	—	38	1	no	—
92	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
93	C₁₉	#7529	1	1	yes	characteristic, complemented, Sylow
94	C₂×D₄	—	2	1	no	—
95	C₂×D₄	—	2	1	no	—
96	C₂×D₄	—	4	1	no	—
97	C₂×D₄	—	4	1	no	—
98	C₂×D₄	—	76	1	no	—
99	C₂×D₄	—	76	1	no	—
100	C₂×D₄	—	76	1	no	—
101	D₈	—	8	2	no	—
102	D₈	—	152	2	no	—
103	D₈	—	152	4	no	—
104	D₈	—	152	4	no	—
105	C₂×C₈	—	2	1	no	—
106	C₂×C₈	—	38	2	no	—
107	C₂²⋊C₄	—	8	1	no	—
108	C₂²⋊C₄	—	152	1	no	—
109	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
110	C₂³	—	4	1	no	—
111	C₂³	—	4	1	no	—
112	C₂³	—	152	1	no	—
113	D₄	—	8	1	no	—
114	D₄	—	8	1	no	—
115	D₄	—	8	2	no	—
116	D₄	—	8	2	no	—
117	D₄	—	152	2	no	—
118	D₄	—	152	2	no	—
119	D₄	—	152	2	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	16	1	no	—
122	C₂×C₄	—	304	1	no	—
123	C₂×C₄	#10597263	1	1	yes	characteristic
124	C₈	—	2	2	no	—
125	C₈	—	38	4	no	—
126	C₂²	—	8	1	no	—
127	C₂²	—	8	1	no	—
128	C₂²	—	16	1	no	—
129	C₂²	—	16	1	no	—
130	C₂²	—	304	1	no	—
131	C₂²	—	304	1	no	—
132	C₂²	—	304	1	no	—
133	C₂²	#11926336	1	1	yes	characteristic
134	C₄	—	2	2	no	—
135	C₄	—	2	1	no	—
136	C₄	—	32	1	no	—
137	C₄	—	608	1	no	—
138	C₂	—	2	1	no	—
139	C₂	—	16	1	no	—
140	C₂	—	16	1	no	—
141	C₂	—	608	1	no	—
142	C₂	#14561797	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563249

C₂

yes

maximal, characteristic

#14561798

C₂

yes

maximal, characteristic, complemented

C₁₉×#1408

C₂

yes

maximal, characteristic, complemented

#11926921

C₄

yes

characteristic, complemented

#11926920

—

#11926920

—

#11926337

—

C₈×C₁₉⋊C₈

C₄

yes

characteristic, complemented

C₁₉×#493

C₂²

yes

characteristic

C₁₉×#353

—

C₂×D₈×C₁₉

—

C₁₉×#127

D₄

yes

characteristic

C₁₉×#127

D₄

yes

characteristic

C₂×#64525

—

C₂×#64525

—

C₂×D₁₅₂

—

#10597320

—

C₁₉×#99

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

#10597291

—

C₄×C₁₉⋊C₈

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²⋊Dic₁₉

—

#64525

—

#64525

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

#7529

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂²×D₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

characteristic

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1712

—

#1408

—

#1408

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#353

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

—

—

—

C₂×D₁₉

yes

characteristic

#353

—

#353

—

C₈²

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1408

yes

characteristic

D₁₉

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

#127

—

#127

D₇₆

yes

characteristic

#127

C₂²⋊D₁₉

yes

characteristic

#99

—

#99

—

C₄×C₈

—

C₄×C₈

C₄×D₁₉

yes

characteristic

C₁₉

#7529

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

100

C₂×D₄

—

101

D₈

—

102

D₈

—

152

—

103

D₈

—

152

—

104

D₈

—

152

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂²⋊C₄

—

108

C₂²⋊C₄

—

152

—

109

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

110

C₂³

—

111

C₂³

—

112

C₂³

—

152

—

113

D₄

—

114

D₄

—

115

D₄

—

116

D₄

—

117

D₄

—

152

—

118

D₄

—

152

—

119

D₄

—

152

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

304

—

123

C₂×C₄

#10597263

yes

characteristic

124

C₈

—

125

C₈

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

304

—

131

C₂²

—

304

—

132

C₂²

—

304

—

133

C₂²

#11926336

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

608

—

138

C₂

—

139

C₂

—

140

C₂

—

141

C₂

—

608

—

142

C₂

#14561797

yes

characteristic

	subgroup	G/H
center	C₂	#14561797
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	#493	C₂×D₁₉
Fitting	C₁₉×#1408	C₂
socle	C₂×C₁₉	#1408
prime radical	#14563249	C₂
cosocle	C₁₉×#493	C₂²
hypercenter	#1408	D₁₉
hypocenter	C₁₉	#7529
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #493 ◁ #1408

subgroup

G/H

center

C₂

#14561797

commutator

C₄×C₈×C₁₉

C₂×C₄

Frattini

#493

C₂×D₁₉

Fitting

C₁₉×#1408

C₂

C₂×C₁₉

C₂

C₁₉×#493

C₂²

D₁₉

C₁₉

G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #493 ◁ #1408

N	H ≅ G/N	type
2. #14561798	C₂	semidirect
3. C₁₉×#1408	C₂	semidirect
4. #11926921	C₄	semidirect
8. C₈×C₁₉⋊C₈	C₄	semidirect
57. #1408	D₁₉	semidirect
93. C₁₉	#7529	semidirect

H ≅ G/N

type

2. #14561798

C₂

semidirect

3. C₁₉×#1408

C₂

semidirect

4. #11926921

C₄

semidirect

8. C₈×C₁₉⋊C₈

C₄

semidirect

57. #1408

D₁₉

semidirect

93. C₁₉

#7529

semidirect

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

subgroup	index
#14563249	2
#14561798	2
C₁₉×#1408	2
#7529	19

subgroup

index

#14563249

#14561798

C₁₉×#1408

#7529

Subgroups — #18070396

Conjugacy classes of subgroups

Complements

Maximal subgroups