Group #14569586 — subgroups

Subgroups — #14569586

Order 2432.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597315	C₂	1	1	yes	maximal, characteristic
2	#11926483	C₂	1	8	yes	maximal
3	#11926449	C₂	1	4	yes	maximal
4	#11926390	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₈	C₂²	1	2	yes	—
7	C₁₉×#125	—	2	4	no	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
12	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
13	#10597315	—	2	4	no	—
14	C₁₉⋊#95	C₂²	1	4	yes	—
15	C₁₉⋊#95	C₂²	1	16	yes	—
16	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
17	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₁₉	C₂³	1	4	yes	—
20	C₂²×Dic₁₉	C₂³	1	4	yes	—
21	C₂×Dic₃₈	—	2	4	no	—
22	C₂×Dic₃₈	—	2	8	no	—
23	C₄⋊C₄×C₁₉	—	2	8	no	—
24	C₄⋊C₄×C₁₉	—	2	4	no	—
25	C₄²×C₁₉	D₄	1	4	yes	—
26	C₄⋊Dic₁₉	—	2	8	no	—
27	C₄×Dic₁₉	—	2	4	no	—
28	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
29	C₂×C₄×C₁₉	—	2	4	no	—
30	C₂×C₄×C₁₉	—	2	4	no	—
31	C₂×C₄×C₁₉	—	2	8	no	—
32	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
33	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₁₉	#41	1	4	yes	—
35	C₂×Dic₁₉	—	2	4	no	—
36	C₂×Dic₁₉	—	2	4	no	—
37	C₂×Dic₁₉	—	2	8	no	—
38	C₂×Dic₁₉	—	2	8	no	—
39	Dic₃₈	—	4	8	no	—
40	#2642	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
42	C₂²×C₁₉	C₂×#41	1	2	yes	—
43	C₂²×C₁₉	2₋¹⁺⁴	1	4	yes	—
44	C₄×C₁₉	—	2	4	no	—
45	C₄×C₁₉	—	4	4	no	—
46	C₄×C₁₉	#124	1	4	yes	—
47	Dic₁₉	—	4	4	no	—
48	Dic₁₉	—	4	4	no	—
49	C₂×C₄⋊Q₈	—	19	1	no	—
50	C₂×#125	D₁₉	1	1	yes	characteristic
51	#400	—	19	8	no	—
52	#391	—	19	4	no	—
53	#376	—	19	1	no	—
54	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
55	C₂×C₁₉	#536	1	2	yes	—
56	C₂×C₁₉	#541	1	4	yes	—
57	C₂²×Q₈	—	19	2	no	—
58	C₄⋊Q₈	—	38	4	no	—
59	#125	—	2	4	no	—
60	C₂×C₄⋊C₄	—	19	4	no	—
61	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
62	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
63	C₂×C₄²	—	19	2	no	—
64	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
65	#95	—	19	4	no	—
66	#95	—	19	16	no	—
67	C₁₉	#2642	1	1	yes	characteristic, complemented, Sylow
68	C₂×Q₈	—	38	8	no	—
69	C₂×Q₈	—	38	4	no	—
70	C₂²×C₄	—	19	4	no	—
71	C₂²×C₄	—	19	4	no	—
72	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
73	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
74	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
75	C₄⋊C₄	—	2	8	no	—
76	C₄⋊C₄	—	2	4	no	—
77	C₄⋊C₄	—	38	8	no	—
78	C₄²	—	38	4	no	—
79	C₄²	C₂²⋊D₁₉	1	4	yes	—
80	C₂³	C₂³×D₁₉	1	1	yes	characteristic
81	Q₈	—	76	8	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	2	8	no	—
84	C₂×C₄	—	2	4	no	—
85	C₂×C₄	—	38	4	no	—
86	C₂×C₄	—	38	8	no	—
87	C₂×C₄	—	38	8	no	—
88	C₂×C₄	—	38	4	no	—
89	C₂×C₄	#64545	1	4	yes	—
90	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
91	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
92	C₂²	C₂×#64545	1	2	yes	—
93	C₂²	#10597436	1	4	yes	—
94	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
95	C₄	—	2	4	no	—
96	C₄	—	4	4	no	—
97	C₄	—	76	4	no	—
98	C₄	—	76	4	no	—
99	C₄	#10597393	1	4	yes	—
100	C₂	C₂×#10597393	1	1	yes	characteristic
101	C₂	#11927115	1	2	yes	—
102	C₂	#11927157	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597315

C₂

yes

maximal, characteristic

#11926483

C₂

yes

maximal

#11926449

C₂

yes

maximal

#11926390

C₂

yes

maximal, characteristic

C₂×C₁₉×#125

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₁₉×#125

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#10597315

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

#2642

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

C₂×#125

D₁₉

yes

—

—

—

C₂×C₁₉

C₂×#124

yes

characteristic

C₂×C₁₉

#536

yes

—

C₂×C₁₉

#541

yes

—

C₂²×Q₈

—

C₄⋊Q₈

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#95

—

#95

—

C₁₉

#2642

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₁₉

yes

—

C₂³

C₂³×D₁₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#64545

yes

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

C₂²

C₂×#64545

yes

—

C₂²

#10597436

yes

—

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

#10597393

yes

—

100

C₂

C₂×#10597393

yes

characteristic

101

C₂

#11927115

yes

—

102

C₂

#11927157

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×#125	C₂
hypercenter	C₂×#125	D₁₉
hypocenter	C₁₉	#2642
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×#125

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
67. C₁₉	#2642	semidirect

H ≅ G/N

type

67. C₁₉

#2642

semidirect

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

subgroup	index
C₂×#10597315	2
#11926483	2
#11926449	2
#11926390	2
C₂×C₁₉×#125	2
#2642	19

subgroup

index

C₂×C₁₉×#125

Subgroups — #14569586

Conjugacy classes of subgroups

Complements

Maximal subgroups