Group #18076267 — subgroups

Subgroups — #18076267

Order 4864.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14561480	C₂	1	2	yes	maximal
2	#14561468	C₂	1	2	yes	maximal
3	#14561466	C₂	1	2	yes	maximal
4	C₁₉×#1745	C₂	1	1	yes	maximal, characteristic
5	#11926597	C₂²	1	4	yes	—
6	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
8	C₄³×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#336	C₄	1	4	yes	—
10	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
11	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
12	C₂×C₄²×C₁₉	—	2	2	no	—
13	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
14	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
15	C₁₉×#97	—	2	2	no	—
16	C₁₉×#97	—	2	2	no	—
17	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
18	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
19	C₄×C₁₉⋊C₈	—	2	4	no	—
20	C₂²×C₄×C₁₉	—	2	2	no	—
21	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	#41	1	2	yes	—
23	C₂×C₈×C₁₉	—	2	2	no	—
24	C₂×C₈×C₁₉	—	2	2	no	—
25	C₂×C₈×C₁₉	—	2	4	no	—
26	C₂×C₈×C₁₉	—	2	4	no	—
27	C₄²×C₁₉	—	2	4	no	—
28	C₄²×C₁₉	—	4	4	no	—
29	C₄²×C₁₉	#41	1	2	yes	—
30	C₄²×C₁₉	#41	1	2	yes	—
31	C₂×C₁₉⋊C₈	—	4	4	no	—
32	#8802	—	19	1	no	maximal, Sylow
33	C₂³×C₁₉	#117	1	1	yes	characteristic
34	C₂×C₄×C₁₉	—	2	4	no	—
35	C₂×C₄×C₁₉	—	4	2	no	—
36	C₂×C₄×C₁₉	—	4	2	no	—
37	C₂×C₄×C₁₉	—	4	2	no	—
38	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
39	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
40	C₂×C₄×C₁₉	#126	1	4	yes	—
41	C₂×C₄×C₁₉	#131	1	4	yes	—
42	C₈×C₁₉	—	4	2	no	—
43	C₈×C₁₉	—	4	2	no	—
44	C₁₉⋊C₈	—	8	4	no	—
45	#1745	D₁₉	1	1	yes	characteristic
46	#1281	—	19	2	no	—
47	#1276	—	19	2	no	—
48	#1275	—	19	2	no	—
49	C₂²×C₁₉	—	2	2	no	—
50	C₂²×C₁₉	#383	1	1	yes	characteristic
51	C₂²×C₁₉	#433	1	2	yes	—
52	C₄×C₁₉	—	2	4	no	—
53	C₄×C₁₉	—	4	4	no	—
54	C₄×C₁₉	#433	1	2	yes	—
55	C₄×C₁₉	#433	1	2	yes	—
56	#431	—	19	4	no	—
57	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
58	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
59	C₄³	C₂×D₁₉	1	1	yes	characteristic
60	#336	Dic₁₉	1	4	yes	—
61	C₂×C₁₉	—	2	2	no	—
62	C₂×C₁₉	#1840	1	1	yes	characteristic
63	C₂×C₁₉	#1841	1	2	yes	—
64	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
65	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
66	C₂×C₄²	—	2	2	no	—
67	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
68	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
69	C₄⋊C₈	—	38	4	no	—
70	C₂²⋊C₈	—	38	4	no	—
71	#97	—	2	2	no	—
72	#97	—	2	2	no	—
73	C₄×C₈	—	38	4	no	—
74	C₁₉	#8802	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	—	2	2	no	—
76	C₂²×C₄	#64541	1	2	yes	—
77	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
78	C₂×C₈	—	2	4	no	—
79	C₂×C₈	—	2	4	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	76	4	no	—
83	C₄²	—	2	4	no	—
84	C₄²	—	4	4	no	—
85	C₄²	#64541	1	2	yes	—
86	C₄²	#64541	1	2	yes	—
87	C₂³	#10597372	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	4	2	no	—
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	#10597322	1	4	yes	—
93	C₂×C₄	#10597372	1	1	yes	characteristic
94	C₂×C₄	#10597372	1	1	yes	characteristic
95	C₂×C₄	#10597394	1	4	yes	—
96	C₈	—	4	2	no	—
97	C₈	—	4	2	no	—
98	C₈	—	152	4	no	—
99	C₂²	—	2	2	no	—
100	C₂²	#11926412	1	1	yes	characteristic
101	C₂²	#11926605	1	2	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	4	4	no	—
104	C₄	#11926605	1	2	yes	—
105	C₄	#11926605	1	2	yes	—
106	C₂	—	2	2	no	—
107	C₂	#14563780	1	1	yes	characteristic
108	C₂	#14563784	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14561480

C₂

yes

maximal

#14561468

C₂

yes

maximal

#14561466

C₂

yes

maximal

C₁₉×#1745

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂×C₁₉×#97

C₂²

yes

characteristic

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#97

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1745

D₁₉

yes

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

#383

yes

characteristic

C₂²×C₁₉

#433

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#433

yes

—

C₄×C₁₉

#433

yes

—

#431

—

C₂×#97

C₂×D₁₉

yes

characteristic

C₂×#97

C₂×D₁₉

yes

characteristic

C₄³

C₂×D₁₉

yes

characteristic

#336

Dic₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

#1840

yes

characteristic

C₂×C₁₉

#1841

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×Dic₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₁₉

#8802

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

#64541

yes

—

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

#64541

yes

—

C₄²

#64541

yes

—

C₂³

#10597372

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10597322

yes

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

—

C₈

—

C₈

—

C₈

—

152

—

C₂²

—

100

C₂²

#11926412

yes

characteristic

101

C₂²

#11926605

yes

—

102

C₄

—

103

C₄

—

104

C₄

#11926605

yes

—

105

C₄

#11926605

yes

—

106

C₂

—

107

C₂

#14563780

yes

characteristic

108

C₂

#14563784

yes

—

	subgroup	G/H
center	C₂×C₄	#10597372
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1745	C₂
socle	C₂²×C₁₉	#383
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1745	D₁₉
hypocenter	C₁₉	#8802
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1745

subgroup

G/H

center

C₂×C₄

#10597372

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1745

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1745

N	H ≅ G/N	type
74. C₁₉	#8802	semidirect

H ≅ G/N

type

74. C₁₉

#8802

semidirect

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

subgroup	index
#14561480	2
#14561468	2
#14561466	2
C₁₉×#1745	2
#8802	19

subgroup

index

C₁₉×#1745

Subgroups — #18076267

Conjugacy classes of subgroups

Complements

Maximal subgroups