Group #18072975 — subgroups

Subgroups — #18072975

Order 4864.

478 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 203 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	C₄×#10597272	C₂	1	3	yes	maximal
2	C₁₉⋊#1273	C₂	1	3	yes	maximal
3	C₁₉×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597272	C₄	1	6	yes	—
5	C₂×#10597272	C₄	1	6	yes	—
6	C₂×C₄×C₁₉⋊C₈	C₂²	1	3	yes	—
7	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
9	C₂²×C₈×C₁₉	C₂×C₄	1	6	yes	—
10	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
11	C₂×C₄×Dic₁₉	C₂×C₄	1	3	yes	—
12	C₂×C₄×Dic₁₉	C₂×C₄	1	3	yes	—
13	C₂²×C₁₉⋊C₈	C₂×C₄	1	6	yes	—
14	C₄×C₈×C₁₉	—	2	6	no	—
15	#10597272	—	2	12	no	—
16	#10597272	—	2	12	no	—
17	C₄×C₁₉⋊C₈	—	2	3	no	—
18	C₄×C₁₉⋊C₈	—	2	3	no	—
19	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
20	C₂²×Dic₁₉	C₄²	1	1	yes	characteristic
21	C₂²×Dic₁₉	C₄²	1	3	yes	—
22	C₂×C₈×C₁₉	—	2	6	no	—
23	C₂×C₈×C₁₉	—	2	6	no	—
24	C₂×C₈×C₁₉	M₁₆	1	12	yes	—
25	C₄²×C₁₉	#41	1	3	yes	—
26	C₄²×C₁₉	#41	1	1	yes	characteristic
27	C₄×Dic₁₉	—	2	6	no	—
28	C₄×Dic₁₉	—	2	6	no	—
29	C₂×C₁₉⋊C₈	—	2	6	no	—
30	C₂×C₁₉⋊C₈	—	2	6	no	—
31	C₂×C₁₉⋊C₈	M₁₆	1	12	yes	—
32	#8136	—	19	1	no	maximal, Sylow
33	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
34	C₂×C₄×C₁₉	#117	1	3	yes	—
35	C₂×C₄×C₁₉	#117	1	3	yes	—
36	C₂×C₄×C₁₉	C₂×M₁₆	1	6	yes	—
37	C₂×C₄×C₁₉	C₂×M₁₆	1	6	yes	—
38	C₂×Dic₁₉	—	2	3	no	—
39	C₂×Dic₁₉	—	2	3	no	—
40	C₂×Dic₁₉	—	2	6	no	—
41	C₈×C₁₉	—	2	12	no	—
42	C₁₉⋊C₈	—	2	12	no	—
43	C₄×#97	—	19	3	no	—
44	#1273	—	19	3	no	—
45	#1273	D₁₉	1	1	yes	characteristic
46	C₂²×C₁₉	#376	1	1	yes	characteristic
47	C₂²×C₁₉	C₄×M₁₆	1	3	yes	—
48	C₂²×C₁₉	C₄×M₁₆	1	3	yes	—
49	C₄×C₁₉	#432	1	6	yes	—
50	C₄×C₁₉	#432	1	6	yes	—
51	Dic₁₉	—	4	1	no	—
52	Dic₁₉	—	4	3	no	—
53	C₂×#97	—	19	6	no	—
54	C₂×#97	—	19	6	no	—
55	C₂×C₄×C₈	—	19	3	no	—
56	C₂×C₄×C₈	C₂×D₁₉	1	3	yes	—
57	C₄³	—	19	1	no	—
58	C₂×C₁₉	#1455	1	1	yes	characteristic
59	C₂×C₁₉	#1455	1	3	yes	—
60	C₂×C₁₉	#1745	1	3	yes	—
61	C₂²×C₈	—	19	6	no	—
62	C₂²×C₈	C₄×D₁₉	1	6	yes	—
63	C₂×C₄²	—	19	3	no	—
64	C₂×C₄²	—	19	3	no	—
65	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
66	#97	—	38	12	no	—
67	#97	—	38	12	no	—
68	C₄×C₈	—	2	6	no	—
69	C₄×C₈	—	38	3	no	—
70	C₄×C₈	—	38	3	no	—
71	C₁₉	#8136	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₄	—	19	1	no	—
73	C₂²×C₄	—	19	3	no	—
74	C₂²×C₄	C₂×C₄×D₁₉	1	3	yes	—
75	C₂×C₈	—	2	6	no	—
76	C₂×C₈	—	2	6	no	—
77	C₂×C₈	—	19	12	no	—
78	C₂×C₈	—	38	6	no	—
79	C₂×C₈	—	38	6	no	—
80	C₂×C₈	#64515	1	12	yes	—
81	C₄²	—	38	6	no	—
82	C₄²	—	38	6	no	—
83	C₄²	#64543	1	3	yes	—
84	C₄²	#64545	1	1	yes	characteristic
85	C₂³	C₄²×D₁₉	1	1	yes	characteristic
86	C₂×C₄	—	38	3	no	—
87	C₂×C₄	—	38	3	no	—
88	C₂×C₄	—	38	6	no	—
89	C₂×C₄	#10597323	1	3	yes	—
90	C₂×C₄	#10597338	1	3	yes	—
91	C₂×C₄	C₂×#64515	1	6	yes	—
92	C₂×C₄	M₁₆×D₁₉	1	6	yes	—
93	C₈	—	2	12	no	—
94	C₈	—	38	12	no	—
95	C₂²	#11926389	1	1	yes	characteristic
96	C₂²	C₄×#64515	1	3	yes	—
97	C₂²	#11926496	1	3	yes	—
98	C₄	—	76	1	no	—
99	C₄	—	76	3	no	—
100	C₄	#11926598	1	6	yes	—
101	C₄	#11926600	1	6	yes	—
102	C₂	#14561937	1	1	yes	characteristic
103	C₂	#14561939	1	3	yes	—
104	C₂	#14563382	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597272

C₂

yes

maximal

C₁₉⋊#1273

C₂

yes

maximal

C₁₉×#1273

C₂

yes

maximal, characteristic

C₂×#10597272

C₄

yes

—

C₂×#10597272

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

C₄²×Dic₁₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₈×C₁₉

—

#10597272

—

#10597272

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

—

C₂²×Dic₁₉

C₄²

yes

characteristic

C₂²×Dic₁₉

C₄²

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

M₁₆

yes

—

#8136

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₄×#97

—

#1273

—

#1273

D₁₉

yes

characteristic

C₂²×C₁₉

#376

yes

characteristic

C₂²×C₁₉

C₄×M₁₆

yes

—

C₂²×C₁₉

C₄×M₁₆

yes

—

C₄×C₁₉

#432

yes

—

C₄×C₁₉

#432

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

C₄³

—

C₂×C₁₉

#1455

yes

characteristic

C₂×C₁₉

#1455

yes

—

C₂×C₁₉

#1745

yes

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₁₉

#8136

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×D₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#64515

yes

—

C₄²

—

C₄²

—

C₄²

#64543

yes

—

C₄²

#64545

yes

characteristic

C₂³

C₄²×D₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10597323

yes

—

C₂×C₄

#10597338

yes

—

C₂×C₄

C₂×#64515

yes

—

C₂×C₄

M₁₆×D₁₉

yes

—

C₈

—

C₈

—

C₂²

#11926389

yes

characteristic

C₂²

C₄×#64515

yes

—

C₂²

#11926496

yes

—

C₄

—

C₄

—

100

C₄

#11926598

yes

—

101

C₄

#11926600

yes

—

102

C₂

#14561937

yes

characteristic

103

C₂

#14561939

yes

—

104

C₂

#14563382

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator, socle, prime radical	C₂³×C₁₉	C₂×C₄²
Fitting	C₁₉×#1273	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1273	D₁₉
hypocenter	C₁₉	#8136
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₁₉

commutator, socle, prime radical

C₂³×C₁₉

C₂×C₄²

Fitting

C₁₉×#1273

C₂

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
71. C₁₉	#8136	semidirect

H ≅ G/N

type

71. C₁₉

#8136

semidirect

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

subgroup	index
C₄×#10597272	2
C₁₉⋊#1273	2
C₁₉×#1273	2
#8136	19

subgroup

index

C₄×#10597272

C₁₉⋊#1273

C₁₉×#1273

#8136

Subgroups — #18072975

Conjugacy classes of subgroups

Complements

Maximal subgroups