Group #14571998 — subgroups

Subgroups — #14571998

Order 2432.

472 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 213 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×#10597316	C₂	1	2	yes	maximal
2	#11926442	C₂	1	8	yes	maximal
3	#11926414	C₂	1	2	yes	maximal
4	#11926410	C₂	1	2	yes	maximal
5	C₄³×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄²×C₁₉	C₂²	1	4	yes	—
7	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	8	yes	—
12	C₂×Dic₁₉⋊C₄	C₂²	1	8	yes	—
13	#10597316	—	2	8	no	—
14	C₁₉⋊#95	C₂²	1	8	yes	—
15	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
16	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
19	C₂²×Dic₁₉	C₂³	1	8	yes	—
20	C₄²×C₁₉	—	2	8	no	—
21	C₄²×C₁₉	D₄	1	4	yes	—
22	C₄²×C₁₉	Q₈	1	4	yes	—
23	C₄²×C₁₉	Q₈	1	4	yes	—
24	C₄⋊Dic₁₉	—	2	8	no	—
25	C₄⋊Dic₁₉	—	2	16	no	—
26	Dic₁₉⋊C₄	—	2	16	no	—
27	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
28	C₂×C₄×C₁₉	—	2	4	no	—
29	C₂×C₄×C₁₉	—	2	4	no	—
30	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
31	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
33	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
34	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
36	C₂×C₄×C₁₉	#41	1	8	yes	—
37	C₂×Dic₁₉	—	2	8	no	—
38	C₂×Dic₁₉	—	2	16	no	—
39	#2859	—	19	1	no	maximal, Sylow
40	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
41	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
42	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
43	C₂²×C₁₉	C₂×#41	1	4	yes	—
44	C₄×C₁₉	—	2	4	no	—
45	C₄×C₁₉	—	2	4	no	—
46	C₄×C₁₉	#125	1	8	yes	complemented
47	C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
48	Dic₁₉	—	4	8	no	—
49	C₂×#125	—	19	2	no	—
50	#389	—	19	8	no	—
51	#384	—	19	2	no	—
52	#382	—	19	2	no	—
53	C₄³	D₁₉	1	1	yes	characteristic
54	C₂×C₁₉	C₂×#125	1	2	yes	—
55	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
56	C₂×C₁₉	#532	1	2	yes	—
57	C₂×C₁₉	#533	1	2	yes	—
58	#125	—	38	8	no	—
59	C₂×C₄⋊C₄	—	19	4	no	—
60	C₂×C₄⋊C₄	—	19	8	no	—
61	C₂×C₄⋊C₄	—	19	8	no	—
62	C₂×C₄²	C₂×D₁₉	1	4	yes	—
63	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
64	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
65	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
66	#95	—	19	8	no	—
67	C₁₉	#2859	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₄	—	19	8	no	—
69	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
70	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
71	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
73	C₄⋊C₄	—	38	16	no	—
74	C₄⋊C₄	—	38	8	no	—
75	C₄⋊C₄	—	38	16	no	—
76	C₄²	—	2	8	no	—
77	C₄²	Dic₃₈	1	4	yes	—
78	C₄²	Dic₃₈	1	4	yes	—
79	C₄²	D₇₆	1	4	yes	—
80	C₂³	C₂³×D₁₉	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	38	8	no	—
84	C₂×C₄	—	38	16	no	—
85	C₂×C₄	C₂×Dic₃₈	1	4	yes	—
86	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
87	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
88	C₂×C₄	C₂×Dic₃₈	1	4	yes	—
89	C₂×C₄	C₂×D₇₆	1	4	yes	—
90	C₂×C₄	C₂×D₇₆	1	2	yes	—
91	C₂×C₄	#64541	1	8	yes	—
92	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
93	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
94	C₂²	C₂²×D₇₆	1	1	yes	characteristic
95	C₂²	C₂×#64541	1	4	yes	—
96	C₄	—	2	4	no	—
97	C₄	—	2	4	no	—
98	C₄	—	76	8	no	—
99	C₄	#10597315	1	4	yes	—
100	C₄	#10597316	1	8	yes	complemented
101	C₂	C₂×#10597316	1	2	yes	—
102	C₂	C₂×#10597315	1	1	yes	characteristic
103	C₂	#11927094	1	2	yes	—
104	C₂	#11927101	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597316

C₂

yes

maximal

#11926442

C₂

yes

maximal

#11926414

C₂

yes

maximal

#11926410

C₂

yes

maximal

C₄³×C₁₉

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

#10597316

—

C₁₉⋊#95

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

Q₈

yes

—

C₄²×C₁₉

Q₈

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2859

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#125

yes

complemented

C₄×C₁₉

C₄⋊Q₈

yes

—

Dic₁₉

—

—

—

—

—

C₄³

D₁₉

yes

characteristic

C₂×C₁₉

C₂×#125

yes

—

C₂×C₁₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₁₉

#532

yes

—

C₂×C₁₉

#533

yes

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

characteristic

#95

—

C₁₉

#2859

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

Dic₃₈

yes

—

C₄²

Dic₃₈

yes

—

C₄²

D₇₆

yes

—

C₂³

C₂³×D₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₃₈

yes

—

C₂×C₄

C₂×Dic₃₈

yes

—

C₂×C₄

C₂×Dic₃₈

yes

—

C₂×C₄

C₂×Dic₃₈

yes

—

C₂×C₄

C₂×D₇₆

yes

—

C₂×C₄

C₂×D₇₆

yes

—

C₂×C₄

#64541

yes

—

C₂²

C₂²×Dic₃₈

yes

characteristic

C₂²

C₂²×Dic₃₈

yes

characteristic

C₂²

C₂²×D₇₆

yes

characteristic

C₂²

C₂×#64541

yes

—

C₄

—

C₄

—

C₄

—

C₄

#10597315

yes

—

100

C₄

#10597316

yes

complemented

101

C₂

C₂×#10597316

yes

—

102

C₂

C₂×#10597315

yes

characteristic

103

C₂

#11927094

yes

—

104

C₂

#11927101

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₄³×C₁₉	C₂
hypercenter	C₄³	D₁₉
hypocenter	C₁₉	#2859
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₄³×C₁₉

C₂

hypercenter

C₄³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
46. C₄×C₁₉	#125	semidirect
67. C₁₉	#2859	semidirect
100. C₄	#10597316	semidirect

H ≅ G/N

type

46. C₄×C₁₉

#125

semidirect

67. C₁₉

#2859

semidirect

100. C₄

#10597316

semidirect

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

subgroup	index
C₂×#10597316	2
#11926442	2
#11926414	2
#11926410	2
C₄³×C₁₉	2
#2859	19

subgroup

index

C₄³×C₁₉

Subgroups — #14571998

Conjugacy classes of subgroups

Complements

Maximal subgroups