Group #18069943 — subgroups

Subgroups — #18069943

Order 4864.

120 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 45 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	#14565395	C₂	1	1	yes	maximal, characteristic
2	#14561775	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1400	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉⋊C₁₆	C₄	1	1	yes	characteristic
5	#11926499	C₄	1	1	yes	characteristic
6	#11926378	—	2	1	no	—
7	Dic₁₉⋊C₁₆	—	2	1	no	—
8	Dic₁₉⋊C₁₆	—	2	1	no	—
9	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
10	C₁₉×M₆₄	—	2	1	no	—
11	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	#10597372	C₈	1	1	yes	characteristic
13	C₂×#64520	C₈	1	1	yes	characteristic
14	C₁₉×M₃₂	—	4	1	no	—
15	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
17	#10597272	—	2	1	no	—
18	C₈×Dic₁₉	—	2	1	no	—
19	C₂×C₁₉⋊C₁₆	—	2	1	no	—
20	C₂×C₁₉⋊C₁₆	—	4	1	no	—
21	C₁₉×C₃₂	—	4	1	no	—
22	C₁₉⋊C₃₂	—	4	1	no	—
23	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
24	C₂×C₈×C₁₉	—	2	1	no	—
25	C₂×C₈×C₁₉	—	2	1	no	—
26	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
28	C₂²⋊Dic₁₉	C₁₆	1	2	yes	—
29	C₄⋊Dic₁₉	—	2	1	no	—
30	C₄×Dic₁₉	—	2	1	no	—
31	#64520	—	4	1	no	—
32	C₂×C₁₉⋊C₈	—	2	1	no	—
33	C₁₆×C₁₉	—	2	1	no	—
34	C₁₆×C₁₉	—	2	1	no	—
35	C₁₉⋊C₁₆	—	4	1	no	—
36	#7365	—	19	1	no	maximal, Sylow
37	C₂³×C₁₉	C₂×C₁₆	1	1	yes	characteristic
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
41	C₂×C₄×C₁₉	M₃₂	1	1	yes	characteristic
42	C₂×Dic₁₉	—	2	2	no	—
43	C₈×C₁₉	—	2	1	no	—
44	C₈×C₁₉	#99	1	1	yes	characteristic
45	C₈×C₁₉	#101	1	1	yes	characteristic
46	C₁₉⋊C₈	—	4	1	no	—
47	#2151	—	19	1	no	—
48	#1400	—	19	1	no	—
49	#1400	D₁₉	1	1	yes	characteristic
50	C₂²×C₁₉	—	2	1	no	—
51	C₂²×C₁₉	—	4	1	no	—
52	C₂²×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
53	C₄×C₁₉	—	2	1	no	—
54	C₄×C₁₉	#324	1	1	yes	characteristic
55	C₄×C₁₉	#349	1	1	yes	characteristic
56	Dic₁₉	—	4	2	no	—
57	C₂×M₃₂	C₂×D₁₉	1	1	yes	characteristic
58	C₂²×C₁₆	—	19	1	no	—
59	#405	—	19	1	no	—
60	M₆₄	—	2	1	no	—
61	M₆₄	—	38	1	no	—
62	C₄⋊C₁₆	—	38	1	no	—
63	C₄⋊C₁₆	—	38	1	no	—
64	C₂×C₁₉	—	2	1	no	—
65	C₂×C₁₉	—	4	1	no	—
66	C₂×C₁₉	#1322	1	1	yes	characteristic
67	C₂×M₁₆	—	19	1	no	—
68	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
69	#117	—	19	1	no	—
70	M₃₂	—	4	1	no	—
71	C₂×C₁₆	—	38	1	no	—
72	C₂×C₁₆	—	76	1	no	—
73	C₂×C₁₆	D₇₆	1	1	yes	characteristic
74	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
75	#97	—	38	1	no	—
76	C₄×C₈	—	38	1	no	—
77	C₃₂	—	4	1	no	—
78	C₃₂	—	76	1	no	—
79	C₁₉	#7365	1	1	yes	characteristic, complemented, Sylow
80	C₂²×C₄	C₈×D₁₉	1	1	yes	characteristic
81	M₁₆	—	76	1	no	—
82	C₂×C₈	—	2	1	no	—
83	C₂×C₈	—	2	1	no	—
84	C₂×C₈	—	38	1	no	—
85	C₂×C₈	#64515	1	1	yes	characteristic
86	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
87	C₄⋊C₄	—	38	1	no	—
88	C₂²⋊C₄	—	19	2	no	—
89	C₄²	—	38	1	no	—
90	C₁₆	—	2	1	no	—
91	C₁₆	—	2	1	no	—
92	C₁₆	—	76	1	no	—
93	C₂³	C₁₆×D₁₉	1	1	yes	characteristic
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	2	1	no	—
96	C₂×C₄	—	38	2	no	—
97	C₂×C₄	#10597255	1	1	yes	characteristic
98	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	76	1	no	—
101	C₈	#10597263	1	1	yes	characteristic
102	C₈	#10597281	1	1	yes	characteristic
103	C₂²	—	2	1	no	—
104	C₂²	—	4	1	no	—
105	C₂²	(C₂×D₁₉)⋊C₁₆	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	76	2	no	—
108	C₄	#11926269	1	1	yes	characteristic
109	C₄	#11926325	1	1	yes	characteristic
110	C₂	—	2	1	no	—
111	C₂	—	4	1	no	—
112	C₂	#14561574	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565395

C₂

yes

maximal, characteristic

#14561775

C₂

yes

maximal, characteristic

C₁₉×#1400

C₂

yes

maximal, characteristic

C₂²×C₁₉⋊C₁₆

C₄

yes

characteristic

#11926499

C₄

yes

characteristic

#11926378

—

Dic₁₉⋊C₁₆

—

Dic₁₉⋊C₁₆

—

C₂×C₁₉×M₃₂

C₂²

yes

characteristic

C₁₉×M₆₄

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

#10597372

C₈

yes

characteristic

C₂×#64520

C₈

yes

characteristic

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

#10597272

—

C₈×Dic₁₉

—

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

—

C₁₉×C₃₂

—

C₁₉⋊C₃₂

—

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₂²⋊Dic₁₉

C₁₆

yes

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7365

—

maximal, Sylow

C₂³×C₁₉

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

M₃₂

yes

characteristic

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₁₉⋊C₈

—

#2151

—

#1400

—

#1400

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊C₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×M₃₂

C₂×D₁₉

yes

characteristic

C₂²×C₁₆

—

#405

—

M₆₄

—

M₆₄

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1322

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

C₄×D₁₉

yes

characteristic

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

D₇₆

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

characteristic

#97

—

C₄×C₈

—

C₃₂

—

C₃₂

—

C₁₉

#7365

yes

characteristic, complemented, Sylow

C₂²×C₄

C₈×D₁₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#64515

yes

characteristic

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

C₂³

C₁₆×D₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10597255

yes

characteristic

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

C₈

—

100

C₈

—

101

C₈

#10597263

yes

characteristic

102

C₈

#10597281

yes

characteristic

103

C₂²

—

104

C₂²

—

105

C₂²

(C₂×D₁₉)⋊C₁₆

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

#11926269

yes

characteristic

109

C₄

#11926325

yes

characteristic

110

C₂

—

111

C₂

—

112

C₂

#14561574

yes

characteristic

	subgroup	G/H
center	C₈	#10597263
commutator, prime radical	C₂³×C₁₉	C₂×C₁₆
Frattini	C₂×M₃₂	C₂×D₁₉
Fitting	C₁₉×#1400	C₂
socle	C₂×C₁₉	#1322
cosocle	C₂×C₁₉×M₃₂	C₂²
hypercenter	#1400	D₁₉
hypocenter	C₁₉	#7365
LCS	G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×M₃₂ ◁ #1400

subgroup

G/H

center

C₈

#10597263

commutator, prime radical

C₂³×C₁₉

C₂×C₁₆

Frattini

C₂×M₃₂

C₂×D₁₉

Fitting

C₁₉×#1400

C₂

socle

C₂×C₁₉

#1322

cosocle

C₂×C₁₉×M₃₂

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×M₃₂ ◁ #1400

N	H ≅ G/N	type
79. C₁₉	#7365	semidirect

H ≅ G/N

type

79. C₁₉

#7365

semidirect

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

subgroup	index
#14565395	2
#14561775	2
C₁₉×#1400	2
#7365	19

subgroup

index

#14565395

#14561775

C₁₉×#1400

#7365

Subgroups — #18069943

Conjugacy classes of subgroups

Complements

Maximal subgroups