Group #18069413 — subgroups

Subgroups — #18069413

Order 4864.

234 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 135 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	C₂×#11926295	C₂	1	2	yes	maximal
2	C₂×C₁₉×#346	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
4	#11926295	—	2	2	no	—
5	#11926295	C₄	1	4	yes	—
6	C₂²×C₁₆×C₁₉	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#346	—	2	2	no	—
9	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
11	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
12	C₂²×C₁₉⋊C₈	—	4	2	no	—
13	C₂×C₁₆×C₁₉	—	2	2	no	—
14	C₂×C₁₆×C₁₉	—	2	2	no	—
15	C₂×C₁₆×C₁₉	C₈	1	4	yes	complemented
16	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
17	C₄×C₈×C₁₉	D₄	1	2	yes	—
18	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
19	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
20	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
22	C₂×C₈×C₁₉	—	2	2	no	—
23	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
24	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
26	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
27	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
28	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
29	C₄²×C₁₉	D₈	1	1	yes	characteristic
30	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
31	C₂×C₁₉⋊C₈	—	4	4	no	—
32	C₂×C₁₉⋊C₈	—	8	4	no	—
33	C₁₆×C₁₉	—	2	4	no	—
34	#7156	—	19	1	no	maximal, Sylow
35	C₂³×C₁₉	#106	1	1	yes	characteristic
36	C₂×C₄×C₁₉	—	2	4	no	—
37	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
38	C₂×C₄×C₁₉	#102	1	2	yes	—
39	C₂×C₄×C₁₉	#103	1	2	yes	—
40	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
41	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
42	C₂×C₄×C₁₉	#108	1	2	yes	—
43	C₈×C₁₉	—	2	2	no	—
44	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
45	C₈×C₁₉	#97	1	1	yes	characteristic
46	C₈×C₁₉	C₂²⋊C₈	1	2	yes	—
47	C₁₉⋊C₈	—	8	4	no	—
48	C₂×#346	D₁₉	1	1	yes	characteristic
49	C₂×#334	—	19	2	no	—
50	C₂²×C₁₉	#334	1	2	yes	—
51	C₂²×C₁₉	#340	1	1	yes	characteristic
52	C₂²×C₁₉	#365	1	4	yes	—
53	C₄×C₁₉	—	2	2	no	—
54	C₄×C₁₉	—	2	2	no	—
55	C₄×C₁₉	#335	1	2	yes	—
56	C₄×C₁₉	#336	1	1	yes	characteristic
57	C₄×C₁₉	#341	1	1	yes	characteristic
58	C₂²×C₁₆	Dic₁₉	1	2	yes	—
59	C₂×C₄⋊C₈	—	38	2	no	—
60	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
61	#346	—	2	2	no	—
62	#334	—	19	4	no	—
63	#334	—	38	2	no	—
64	C₂×C₁₉	#1277	1	1	yes	characteristic
65	C₂×C₁₉	#1368	1	4	yes	—
66	C₂×C₁₉	#1383	1	2	yes	—
67	C₂²×C₈	—	76	2	no	—
68	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
69	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
70	C₂×C₄²	D₇₆	1	1	yes	characteristic
71	C₂×C₁₆	—	2	2	no	—
72	C₂×C₁₆	—	2	2	no	—
73	C₂×C₁₆	C₁₉⋊C₈	1	4	yes	complemented
74	C₄⋊C₈	—	38	4	no	—
75	C₄⋊C₈	—	76	2	no	—
76	C₄×C₈	C₄×D₁₉	1	2	yes	—
77	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
78	C₁₉	#7156	1	1	yes	characteristic, complemented, Sylow
79	C₂²×C₄	#64516	1	2	yes	—
80	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	76	4	no	—
83	C₂×C₈	—	152	4	no	—
84	C₂×C₈	C₂×C₁₉⋊C₈	1	2	yes	—
85	C₂×C₈	#64520	1	2	yes	—
86	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
87	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
88	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
89	C₄²	D₁₅₂	1	1	yes	characteristic
90	C₄²	Dic₇₆	1	1	yes	characteristic
91	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
92	C₁₆	—	2	4	no	—
93	C₂³	#10597274	1	1	yes	characteristic
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
96	C₂×C₄	#10597273	1	2	yes	—
97	C₂×C₄	#10597275	1	1	yes	characteristic
98	C₂×C₄	#10597276	1	2	yes	—
99	C₂×C₄	#10597278	1	2	yes	—
100	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
101	C₈	—	2	2	no	—
102	C₈	—	152	4	no	—
103	C₈	C₄×C₁₉⋊C₈	1	1	yes	characteristic
104	C₈	#10597260	1	1	yes	characteristic
105	C₈	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
106	C₂²	#11926295	1	2	yes	—
107	C₂²	#11926307	1	1	yes	characteristic
108	C₂²	#11926367	1	4	yes	—
109	C₄	—	2	2	no	—
110	C₄	—	2	2	no	—
111	C₄	#11926297	1	2	yes	—
112	C₄	#11926299	1	1	yes	characteristic
113	C₄	#11926309	1	1	yes	characteristic
114	C₂	#14561470	1	1	yes	characteristic
115	C₂	#14561701	1	4	yes	—
116	C₂	#14561734	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926295

C₂

yes

maximal

C₂×C₁₉×#346

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

#11926295

—

#11926295

C₄

yes

—

C₂²×C₁₆×C₁₉

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#346

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

C₈

yes

complemented

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

Q₁₆

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

#102

yes

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

C₄⋊C₈

yes

—

C₂×C₄×C₁₉

#107

yes

characteristic

C₂×C₄×C₁₉

#108

yes

—

C₈×C₁₉

—

C₈×C₁₉

C₄×C₈

yes

characteristic

C₈×C₁₉

#97

yes

characteristic

C₈×C₁₉

C₂²⋊C₈

yes

—

C₁₉⋊C₈

—

C₂×#346

D₁₉

yes

characteristic

C₂×#334

—

C₂²×C₁₉

#334

yes

—

C₂²×C₁₉

#340

yes

characteristic

C₂²×C₁₉

#365

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#335

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂²×C₁₆

Dic₁₉

yes

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

—

C₂×C₁₉

#1277

yes

characteristic

C₂×C₁₉

#1368

yes

—

C₂×C₁₉

#1383

yes

—

C₂²×C₈

—

C₂²×C₈

Dic₃₈

yes

characteristic

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₄²

D₇₆

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₁₉⋊C₈

yes

complemented

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

C₄×D₁₉

yes

—

C₄×C₈

C₂²⋊D₁₉

yes

—

C₁₉

#7156

yes

characteristic, complemented, Sylow

C₂²×C₄

#64516

yes

—

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

152

—

C₂×C₈

C₂×C₁₉⋊C₈

yes

—

C₂×C₈

#64520

yes

—

C₂×C₈

C₄×Dic₁₉

yes

characteristic

C₂×C₈

Dic₁₉⋊C₄

yes

—

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

C₄²

D₁₅₂

yes

characteristic

C₄²

Dic₇₆

yes

characteristic

C₄²

(C₂×D₁₉)⋊C₄

yes

—

C₁₆

—

C₂³

#10597274

yes

characteristic

C₂×C₄

—

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

—

C₂×C₄

#10597273

yes

—

C₂×C₄

#10597275

yes

characteristic

C₂×C₄

#10597276

yes

—

C₂×C₄

#10597278

yes

—

100

C₂×C₄

C₁₉⋊#95

yes

characteristic

101

C₈

—

102

C₈

—

152

—

103

C₈

C₄×C₁₉⋊C₈

yes

characteristic

104

C₈

#10597260

yes

characteristic

105

C₈

C₂²⋊(C₁₉⋊C₈)

yes

—

106

C₂²

#11926295

yes

—

107

C₂²

#11926307

yes

characteristic

108

C₂²

#11926367

yes

—

109

C₄

—

110

C₄

—

111

C₄

#11926297

yes

—

112

C₄

#11926299

yes

characteristic

113

C₄

#11926309

yes

characteristic

114

C₂

#14561470

yes

characteristic

115

C₂

#14561701

yes

—

116

C₂

#14561734

yes

—

	subgroup	G/H
center	C₂³	#10597274
commutator	C₈×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×#346	C₂
socle, prime radical	C₂³×C₁₉	#106
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₂×#346	D₁₉
hypocenter	C₁₉	#7156
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂³

#10597274

commutator

C₈×C₁₉

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₂×C₁₉×#346

C₂

socle, prime radical

C₂³×C₁₉

#106

cosocle

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
15. C₂×C₁₆×C₁₉	C₈	semidirect
73. C₂×C₁₆	C₁₉⋊C₈	semidirect
78. C₁₉	#7156	semidirect

H ≅ G/N

type

15. C₂×C₁₆×C₁₉

C₈

semidirect

73. C₂×C₁₆

C₁₉⋊C₈

semidirect

78. C₁₉

#7156

semidirect

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

subgroup	index
C₂×#11926295	2
C₂×C₁₉×#346	2
#7156	19

subgroup

index

C₂×#11926295

C₂×C₁₉×#346

#7156

Subgroups — #18069413

Conjugacy classes of subgroups

Complements

Maximal subgroups