Group #18069932 — subgroups

Subgroups — #18069932

Order 4864.

176 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14561579	C₂	1	2	yes	maximal
2	C₁₉×#1991	C₂	1	1	yes	maximal, characteristic
3	#11926270	—	2	2	no	—
4	C₂×C₁₉×#125	C₄	1	1	yes	characteristic
5	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
6	C₁₉×#382	C₂²	1	1	yes	characteristic
7	C₁₉×#340	—	2	2	no	—
8	C₂²×C₈×C₁₉	—	2	1	no	—
9	C₁₉×#125	—	2	1	no	—
10	C₁₉×#125	—	4	1	no	—
11	C₁₉×#125	C₈	1	2	yes	complemented
12	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
13	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
14	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₄×C₈×C₁₉	—	4	1	no	—
17	C₁₉×#95	—	4	1	no	—
18	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
19	C₂²×C₄×C₁₉	—	2	1	no	—
20	C₂²×C₄×C₁₉	—	2	2	no	—
21	C₂²×C₄×C₁₉	—	4	1	no	—
22	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₉	—	2	2	no	—
24	C₂×C₈×C₁₉	—	4	1	no	—
25	C₂×C₈×C₁₉	—	4	1	no	—
26	C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₄⋊C₄×C₁₉	—	4	2	no	—
28	C₄⋊C₄×C₁₉	—	4	2	no	—
29	C₄⋊C₄×C₁₉	—	4	2	no	—
30	C₄⋊C₄×C₁₉	—	4	1	no	—
31	C₄²×C₁₉	—	2	1	no	—
32	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
33	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
34	C₂×C₁₉⋊C₈	—	8	2	no	—
35	#7359	—	19	1	no	maximal, Sylow
36	C₂³×C₁₉	#99	1	1	yes	characteristic
37	C₂×C₄×C₁₉	—	2	1	no	—
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	2	1	no	—
41	C₂×C₄×C₁₉	—	4	2	no	—
42	C₂×C₄×C₁₉	—	4	2	no	—
43	C₂×C₄×C₁₉	—	4	2	no	—
44	C₂×C₄×C₁₉	—	8	2	no	—
45	C₂×C₄×C₁₉	—	8	2	no	—
46	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
47	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
48	C₈×C₁₉	—	4	2	no	—
49	C₁₉⋊C₈	—	16	2	no	—
50	#1991	D₁₉	1	1	yes	characteristic
51	#1324	—	19	2	no	—
52	C₂²×C₁₉	—	2	2	no	—
53	C₂²×C₁₉	#323	1	1	yes	characteristic
54	C₂²×C₁₉	#354	1	1	yes	characteristic
55	C₂²×C₁₉	#356	1	1	yes	characteristic
56	C₄×C₁₉	—	2	1	no	—
57	C₄×C₁₉	—	2	1	no	—
58	C₄×C₁₉	—	4	1	no	—
59	C₄×C₁₉	—	4	1	no	—
60	C₄×C₁₉	—	8	2	no	—
61	C₄×C₁₉	—	8	2	no	—
62	C₂×#125	Dic₁₉	1	1	yes	characteristic
63	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
64	#382	C₂×D₁₉	1	1	yes	characteristic
65	#340	—	2	2	no	—
66	#324	—	38	2	no	—
67	C₂×C₁₉	—	2	1	no	—
68	C₂×C₁₉	—	2	1	no	—
69	C₂×C₁₉	#1319	1	1	yes	characteristic
70	C₂×C₁₉	#1414	1	2	yes	—
71	C₂²×C₈	—	2	1	no	—
72	#125	—	2	1	no	—
73	#125	—	4	1	no	—
74	#125	C₁₉⋊C₈	1	2	yes	complemented
75	C₂×C₄⋊C₄	—	2	1	no	—
76	C₂×C₄⋊C₄	—	4	1	no	—
77	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
78	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
79	C₂²⋊C₈	—	76	2	no	—
80	C₄×C₈	—	4	1	no	—
81	#95	—	4	1	no	—
82	C₁₉	#7359	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₄	—	2	1	no	—
84	C₂²×C₄	—	2	2	no	—
85	C₂²×C₄	—	4	1	no	—
86	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	4	1	no	—
89	C₂×C₈	—	4	1	no	—
90	C₂×C₈	—	152	2	no	—
91	C₄⋊C₄	—	2	2	no	—
92	C₄⋊C₄	—	4	2	no	—
93	C₄⋊C₄	—	4	2	no	—
94	C₄⋊C₄	—	4	2	no	—
95	C₄⋊C₄	—	4	1	no	—
96	C₄²	—	2	1	no	—
97	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
98	C₄²	#64520	1	1	yes	characteristic
99	C₂³	#10597291	1	1	yes	characteristic
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	—	4	2	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	8	2	no	—
108	C₂×C₄	—	8	2	no	—
109	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
110	C₂×C₄	#10597290	1	1	yes	characteristic
111	C₈	—	4	2	no	—
112	C₈	—	304	2	no	—
113	C₂²	—	2	2	no	—
114	C₂²	#11926268	1	1	yes	characteristic
115	C₂²	#11926339	1	1	yes	characteristic
116	C₂²	#11926343	1	1	yes	characteristic
117	C₄	—	2	1	no	—
118	C₄	—	2	1	no	—
119	C₄	—	4	1	no	—
120	C₄	—	4	1	no	—
121	C₄	—	8	2	no	—
122	C₄	—	8	2	no	—
123	C₂	—	2	1	no	—
124	C₂	—	2	1	no	—
125	C₂	#14561569	1	1	yes	characteristic
126	C₂	#14561810	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14561579

C₂

yes

maximal

C₁₉×#1991

C₂

yes

maximal, characteristic

#11926270

—

C₂×C₁₉×#125

C₄

yes

characteristic

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₁₉×#382

C₂²

yes

characteristic

C₁₉×#340

—

C₂²×C₈×C₁₉

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

C₈

yes

complemented

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

#100

yes

characteristic

C₈×C₁₉

—

C₁₉⋊C₈

—

#1991

D₁₉

yes

characteristic

#1324

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×#125

Dic₁₉

yes

characteristic

C₂×C₄×C₈

Dic₁₉

yes

characteristic

#382

C₂×D₁₉

yes

characteristic

#340

—

#324

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1319

yes

characteristic

C₂×C₁₉

#1414

yes

—

C₂²×C₈

—

#125

—

#125

—

#125

C₁₉⋊C₈

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

C₂²⋊C₈

—

C₄×C₈

—

#95

—

C₁₉

#7359

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

152

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂×C₁₉⋊C₈

yes

C₄²

yes

C₂³

yes

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

110

C₂×C₄

#10597290

yes

characteristic

111

C₈

—

112

C₈

—

304

—

113

C₂²

—

114

C₂²

#11926268

yes

characteristic

115

C₂²

#11926339

yes

characteristic

116

C₂²

#11926343

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₂

—

124

C₂

—

125

C₂

#14561569

yes

characteristic

126

C₂

#14561810

yes

—

	subgroup	G/H
center	C₂²	#11926339
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#382	C₂×D₁₉
Fitting	C₁₉×#1991	C₂
socle	C₂²×C₁₉	#354
prime radical	C₂³×C₁₉	#99
cosocle	C₁₉×#382	C₂²
hypercenter	#1991	D₁₉
hypocenter	C₁₉	#7359
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #382 ◁ #1991

subgroup

G/H

center

C₂²

#11926339

commutator

C₄²×C₁₉

C₂×C₈

Frattini

#382

C₂×D₁₉

Fitting

C₁₉×#1991

C₂

C₂²×C₁₉

C₂³×C₁₉

C₁₉×#382

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #382 ◁ #1991

N	H ≅ G/N	type
11. C₁₉×#125	C₈	semidirect
74. #125	C₁₉⋊C₈	semidirect
82. C₁₉	#7359	semidirect

H ≅ G/N

type

11. C₁₉×#125

C₈

semidirect

74. #125

C₁₉⋊C₈

semidirect

82. C₁₉

#7359

semidirect

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

subgroup	index
#14561579	2
C₁₉×#1991	2
#7359	19

subgroup

index

#14561579

C₁₉×#1991

#7359

Subgroups — #18069932

Conjugacy classes of subgroups

Complements

Maximal subgroups