Group #18069202 — subgroups

Subgroups — #18069202

Order 4864.

132 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 55 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	#14562533	C₂	1	1	yes	maximal, characteristic
2	#14561553	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1370	C₂	1	1	yes	maximal, characteristic
4	#11926674	—	2	1	no	—
5	C₄×Dic₇₆	C₄	1	1	yes	characteristic
6	C₄×C₁₉⋊C₁₆	—	2	1	no	—
7	#11926297	C₄	1	1	yes	characteristic
8	#11926276	—	2	1	no	—
9	C₁₉×C₄⋊C₁₆	—	2	1	no	—
10	C₈²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₆	C₈	1	1	yes	characteristic
12	C₄×Dic₃₈	—	2	1	no	—
13	C₂×C₁₆×C₁₉	—	4	1	no	—
14	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
17	#10597275	C₈	1	1	yes	characteristic
18	#10597273	—	2	1	no	—
19	#10597272	—	4	1	no	—
20	Dic₁₉⋊C₈	—	4	1	no	—
21	C₂×C₁₉⋊C₁₆	—	2	2	no	—
22	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
23	C₂×Dic₃₈	—	2	1	no	—
24	C₂×C₈×C₁₉	—	2	1	no	—
25	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
26	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
27	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
28	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
29	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₄⋊Dic₁₉	—	2	1	no	—
31	Dic₁₉⋊C₄	—	4	1	no	—
32	C₄×Dic₁₉	—	4	1	no	—
33	C₂×C₁₉⋊C₈	—	4	1	no	—
34	Dic₇₆	—	4	1	no	—
35	C₁₆×C₁₉	—	8	1	no	—
36	C₁₉⋊C₁₆	—	4	2	no	—
37	#7073	—	19	1	no	maximal, Sylow
38	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
39	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
40	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
41	C₂×Dic₁₉	—	4	1	no	—
42	C₂×Dic₁₉	—	4	1	no	—
43	Dic₃₈	—	4	1	no	—
44	Dic₃₈	—	4	1	no	—
45	C₈×C₁₉	—	2	2	no	—
46	C₈×C₁₉	—	2	1	no	—
47	C₈×C₁₉	—	2	1	no	—
48	C₈×C₁₉	—	2	1	no	—
49	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
50	C₈×C₁₉	Q₃₂	1	1	yes	characteristic
51	C₁₉⋊C₈	—	8	1	no	—
52	#1591	—	19	1	no	—
53	#1370	D₁₉	1	1	yes	characteristic
54	#1312	—	19	1	no	—
55	C₂²×C₁₉	D₄⋊C₈	1	1	yes	characteristic
56	C₄×C₁₉	—	2	1	no	—
57	C₄×C₁₉	#349	1	1	yes	characteristic
58	C₄×C₁₉	#350	1	1	yes	characteristic
59	C₄×C₁₉	#358	1	1	yes	characteristic
60	C₄×C₁₉	#359	1	1	yes	characteristic
61	Dic₁₉	—	8	1	no	—
62	Dic₁₉	—	8	1	no	—
63	#446	—	38	1	no	—
64	C₄×Q₁₆	—	19	1	no	—
65	C₄⋊C₁₆	—	2	1	no	—
66	C₄×C₁₆	—	38	1	no	—
67	#335	—	19	1	no	—
68	Q₈⋊C₈	—	38	1	no	—
69	C₈²	C₂×D₁₉	1	1	yes	characteristic
70	C₂×C₁₉	#1330	1	1	yes	characteristic
71	C₂×C₁₉	#1332	1	1	yes	characteristic
72	C₂×C₁₉	#1336	1	1	yes	characteristic
73	C₂×Q₁₆	—	19	1	no	—
74	C₄×Q₈	—	38	1	no	—
75	C₂×C₁₆	—	4	1	no	—
76	C₂×C₁₆	—	38	2	no	—
77	#107	—	19	1	no	—
78	C₄⋊C₈	—	38	1	no	—
79	C₄⋊C₈	—	76	1	no	—
80	#103	—	38	1	no	—
81	#97	—	76	1	no	—
82	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
83	C₄×C₈	D₇₆	1	1	yes	characteristic
84	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
85	C₁₉	#7073	1	1	yes	characteristic, complemented, Sylow
86	C₂×Q₈	—	38	1	no	—
87	Q₁₆	—	76	1	no	—
88	C₂×C₈	—	2	1	no	—
89	C₂×C₈	—	76	1	no	—
90	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
91	C₂×C₈	#64515	1	1	yes	characteristic
92	C₂×C₈	#64525	1	1	yes	characteristic
93	C₂×C₈	#64527	1	1	yes	characteristic
94	C₄⋊C₄	—	38	1	no	—
95	C₄⋊C₄	—	76	1	no	—
96	C₄²	—	76	1	no	—
97	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
98	C₁₆	—	8	1	no	—
99	C₁₆	—	76	2	no	—
100	Q₈	—	76	1	no	—
101	Q₈	—	76	1	no	—
102	C₂×C₄	—	76	1	no	—
103	C₂×C₄	—	76	1	no	—
104	C₂×C₄	#10597266	1	1	yes	characteristic
105	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
106	C₂×C₄	#10597282	1	1	yes	characteristic
107	C₈	—	2	2	no	—
108	C₈	—	2	1	no	—
109	C₈	—	2	1	no	—
110	C₈	—	2	1	no	—
111	C₈	—	152	1	no	—
112	C₈	#10597284	1	1	yes	characteristic
113	C₈	#10597286	1	1	yes	characteristic
114	C₂²	#11926271	1	1	yes	characteristic
115	C₄	—	2	1	no	—
116	C₄	—	152	1	no	—
117	C₄	—	152	1	no	—
118	C₄	#11926325	1	1	yes	characteristic
119	C₄	#11926327	1	1	yes	characteristic
120	C₄	#11926347	1	1	yes	characteristic
121	C₄	#11926350	1	1	yes	characteristic
122	C₂	#14561592	1	1	yes	characteristic
123	C₂	#14561598	1	1	yes	characteristic
124	C₂	#14561610	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14562533

C₂

yes

maximal, characteristic

#14561553

C₂

yes

maximal, characteristic

C₁₉×#1370

C₂

yes

maximal, characteristic

#11926674

—

C₄×Dic₇₆

C₄

yes

characteristic

C₄×C₁₉⋊C₁₆

—

#11926297

C₄

yes

characteristic

#11926276

—

C₁₉×C₄⋊C₁₆

—

C₈²×C₁₉

C₂²

yes

characteristic

C₂×Dic₇₆

C₈

yes

characteristic

C₄×Dic₃₈

—

C₂×C₁₆×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597275

C₈

yes

characteristic

#10597273

—

#10597272

—

Dic₁₉⋊C₈

—

C₂×C₁₉⋊C₁₆

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₈

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7073

—

maximal, Sylow

C₂×C₄×C₁₉

C₂²⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

SD₃₂

yes

characteristic

C₈×C₁₉

Q₃₂

yes

characteristic

C₁₉⋊C₈

—

#1591

—

#1370

D₁₉

yes

characteristic

#1312

—

C₂²×C₁₉

D₄⋊C₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

#446

—

C₄×Q₁₆

—

C₄⋊C₁₆

—

C₄×C₁₆

—

#335

—

Q₈⋊C₈

—

C₈²

C₂×D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#97

—

C₄×C₈

C₄×D₁₉

yes

characteristic

C₄×C₈

D₇₆

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₁₉

#7073

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₈×D₁₉

yes

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

C₁₆

—

C₁₆

—

100

Q₈

—

101

Q₈

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

#10597266

yes

characteristic

105

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

106

C₂×C₄

#10597282

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

110

C₈

—

111

C₈

—

152

—

112

C₈

#10597284

yes

characteristic

113

C₈

#10597286

yes

characteristic

114

C₂²

#11926271

yes

characteristic

115

C₄

—

116

C₄

—

152

—

117

C₄

—

152

—

118

C₄

#11926325

yes

characteristic

119

C₄

#11926327

yes

characteristic

120

C₄

#11926347

yes

characteristic

121

C₄

#11926350

yes

characteristic

122

C₂

#14561592

yes

characteristic

123

C₂

#14561598

yes

characteristic

124

C₂

#14561610

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597266
commutator	C₂×C₈×C₁₉	C₂×C₈
Frattini	C₈²	C₂×D₁₉
Fitting	C₁₉×#1370	C₂
socle, prime radical	C₂²×C₁₉	D₄⋊C₈
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1370	D₁₉
hypocenter	C₁₉	#7073
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈² ◁ #1370

subgroup

G/H

center

C₂×C₄

#10597266

commutator

C₂×C₈×C₁₉

C₂×C₈

Frattini

C₈²

C₂×D₁₉

Fitting

C₁₉×#1370

C₂

socle, prime radical

C₂²×C₁₉

D₄⋊C₈

cosocle

C₈²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈² ◁ #1370

N	H ≅ G/N	type
85. C₁₉	#7073	semidirect

H ≅ G/N

type

85. C₁₉

#7073

semidirect

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

subgroup	index
#14562533	2
#14561553	2
C₁₉×#1370	2
#7073	19

subgroup

index

#14562533

#14561553

C₁₉×#1370

#7073

Subgroups — #18069202

Conjugacy classes of subgroups

Complements

Maximal subgroups