Group #18069862 — subgroups

Subgroups — #18069862

Order 4864.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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	#14561969	C₂	1	2	yes	maximal
2	C₁₉×#1818	C₂	1	1	yes	maximal, characteristic
3	#11926601	—	2	2	no	—
4	#11926270	C₄	1	4	yes	—
5	#11926268	—	2	2	no	—
6	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×C₂²⋊C₈	C₄	1	2	yes	—
8	C₁₉×#336	—	2	2	no	—
9	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	—	2	2	no	—
11	C₁₉×#117	—	4	2	no	—
12	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
13	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
14	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
15	C₂×C₄²×C₁₉	D₄	1	2	yes	—
16	C₁₉×C₂²⋊C₈	—	4	2	no	—
17	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
18	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
19	#10597260	—	4	2	no	—
20	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	—	2	2	no	—
22	C₂²×C₄×C₁₉	—	4	2	no	—
23	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
25	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
27	C₂×C₈×C₁₉	—	4	4	no	—
28	C₂×C₈×C₁₉	—	4	2	no	—
29	C₄⋊C₄×C₁₉	—	4	2	no	—
30	C₂²⋊C₄×C₁₉	—	4	1	no	—
31	C₂²⋊C₄×C₁₉	—	4	1	no	—
32	C₄²×C₁₉	—	2	2	no	—
33	C₄²×C₁₉	—	2	2	no	—
34	C₂×C₁₉⋊C₈	—	4	4	no	—
35	#7327	—	19	1	no	maximal, Sylow
36	C₂³×C₁₉	—	2	1	no	—
37	C₂³×C₁₉	—	2	2	no	—
38	C₂³×C₁₉	—	4	2	no	—
39	C₂³×C₁₉	#95	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	4	4	no	—
46	C₂×C₄×C₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	#99	1	2	yes	—
49	C₈×C₁₉	—	8	2	no	—
50	C₁₉⋊C₈	—	8	4	no	—
51	#1818	D₁₉	1	1	yes	characteristic
52	#1464	—	19	2	no	—
53	C₂²×C₁₉	—	2	2	no	—
54	C₂²×C₁₉	—	4	1	no	—
55	C₂²×C₁₉	—	4	2	no	—
56	C₂²×C₁₉	—	8	2	no	—
57	C₂²×C₁₉	#342	1	1	yes	characteristic
58	C₂²×C₁₉	#344	1	2	yes	—
59	C₄×C₁₉	—	2	2	no	—
60	C₄×C₁₉	—	4	1	no	—
61	C₄×C₁₉	—	4	2	no	—
62	C₄×C₁₉	—	4	2	no	—
63	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
64	#432	—	38	2	no	—
65	C₂×C₂²⋊C₈	Dic₁₉	1	2	yes	—
66	#336	—	2	2	no	—
67	#324	—	19	4	no	—
68	#323	—	38	2	no	—
69	C₂×C₁₉	—	2	2	no	—
70	C₂×C₁₉	—	8	1	no	—
71	C₂×C₁₉	#1306	1	1	yes	characteristic
72	C₂×C₁₉	#1395	1	2	yes	—
73	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
74	C₂²×C₈	—	2	2	no	—
75	#117	—	4	2	no	—
76	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
77	C₂×C₂²⋊C₄	Dic₃₈	1	1	yes	characteristic
78	C₂×C₂²⋊C₄	D₇₆	1	1	yes	characteristic
79	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
80	C₄⋊C₈	—	76	2	no	—
81	C₂²⋊C₈	—	4	2	no	—
82	C₂²⋊C₈	—	38	4	no	—
83	#97	—	76	2	no	—
84	C₁₉	#7327	1	1	yes	characteristic, complemented, Sylow
85	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
86	C₂²×C₄	—	2	2	no	—
87	C₂²×C₄	—	4	2	no	—
88	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
89	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
90	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
91	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
92	C₂×C₈	—	4	4	no	—
93	C₂×C₈	—	4	2	no	—
94	C₂×C₈	—	76	4	no	—
95	C₄⋊C₄	—	4	2	no	—
96	C₂²⋊C₄	—	4	1	no	—
97	C₂²⋊C₄	—	4	1	no	—
98	C₄²	—	2	2	no	—
99	C₄²	—	2	2	no	—
100	C₂³	—	2	1	no	—
101	C₂³	—	2	2	no	—
102	C₂³	—	4	2	no	—
103	C₂³	C₁₉⋊#95	1	1	yes	characteristic
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	2	2	no	—
107	C₂×C₄	—	2	1	no	—
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	4	4	no	—
110	C₂×C₄	—	4	2	no	—
111	C₂×C₄	—	4	2	no	—
112	C₂×C₄	#10597291	1	2	yes	—
113	C₈	—	8	2	no	—
114	C₈	—	152	4	no	—
115	C₂²	—	2	2	no	—
116	C₂²	—	4	1	no	—
117	C₂²	—	4	2	no	—
118	C₂²	—	8	2	no	—
119	C₂²	#11926311	1	1	yes	characteristic
120	C₂²	#11926314	1	2	yes	—
121	C₄	—	2	2	no	—
122	C₄	—	4	1	no	—
123	C₄	—	4	2	no	—
124	C₄	—	4	2	no	—
125	C₂	—	2	2	no	—
126	C₂	—	8	1	no	—
127	C₂	#14561543	1	1	yes	characteristic
128	C₂	#14561764	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14561969

C₂

yes

maximal

C₁₉×#1818

C₂

yes

maximal, characteristic

#11926601

—

#11926270

C₄

yes

—

#11926268

—

C₂×C₁₉×#117

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

C₄

yes

—

C₁₉×#336

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

#7327

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#95

yes

characteristic

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

#99

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1818

D₁₉

yes

characteristic

#1464

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#342

yes

characteristic

C₂²×C₁₉

#344

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×#117

C₂×D₁₉

yes

characteristic

#432

—

C₂×C₂²⋊C₈

Dic₁₉

yes

—

#336

—

#324

—

#323

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1306

yes

characteristic

C₂×C₁₉

#1395

yes

—

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

C₂²×C₈

—

#117

—

C₂×C₄⋊C₄

C₄×D₁₉

yes

—

C₂×C₂²⋊C₄

Dic₃₈

yes

characteristic

C₂×C₂²⋊C₄

D₇₆

yes

characteristic

C₂×C₄²

C₂²⋊D₁₉

yes

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₁₉

#7327

yes

characteristic, complemented, Sylow

C₂⁴

C₄⋊Dic₁₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

C₂²×C₄

Dic₁₉⋊C₄

yes

—

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

100

C₂³

—

101

C₂³

—

102

C₂³

—

103

C₂³

C₁₉⋊#95

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

#10597291

yes

—

113

C₈

—

114

C₈

—

152

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

#11926311

yes

characteristic

120

C₂²

#11926314

yes

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₂

—

126

C₂

—

127

C₂

#14561543

yes

characteristic

128

C₂

#14561764

yes

—

	subgroup	G/H
center	C₂²	#11926311
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₂×#117	C₂×D₁₉
Fitting	C₁₉×#1818	C₂
socle	C₂²×C₁₉	#342
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂×C₁₉×#117	C₂²
hypercenter	#1818	D₁₉
hypocenter	C₁₉	#7327
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#117 ◁ #1818

subgroup

G/H

center

C₂²

#11926311

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₂×#117

C₂×D₁₉

Fitting

C₁₉×#1818

C₂

socle

C₂²×C₁₉

#342

prime radical

C₂⁴×C₁₉

C₄⋊C₄

cosocle

C₂×C₁₉×#117

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#117 ◁ #1818

N	H ≅ G/N	type
84. C₁₉	#7327	semidirect

H ≅ G/N

type

84. C₁₉

#7327

semidirect

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

subgroup	index
#14561969	2
C₁₉×#1818	2
#7327	19

subgroup

index

#14561969

C₁₉×#1818

#7327

Subgroups — #18069862

Conjugacy classes of subgroups

Complements

Maximal subgroups