Group #14562964 — subgroups

Subgroups — #14562964

Order 2432.

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

normal subgroups only

This group has 172 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	C₁₉⋊#564	C₂	1	1	yes	maximal, characteristic
2	#11926953	C₂	1	2	yes	maximal
3	#11926914	C₂	1	1	yes	maximal, characteristic
4	#11926285	C₂	1	2	yes	maximal
5	C₁₉×#330	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#125	C₂²	1	1	yes	characteristic
7	#10597336	—	2	2	no	—
8	#10597335	—	2	2	no	—
9	#10597335	—	2	2	no	—
10	#10597316	C₂²	1	2	yes	—
11	#10597315	C₂²	1	1	yes	characteristic
12	C₁₉×#97	C₂²	1	2	yes	—
13	#10597275	—	2	2	no	—
14	#10597274	—	2	2	no	—
15	#10597267	—	2	2	no	—
16	#10597260	C₂²	1	1	yes	characteristic
17	C₂×Dic₃₈	—	2	1	no	—
18	C₂×C₈×C₁₉	—	2	2	no	—
19	C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
21	C₄²×C₁₉	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₁₉	—	2	2	no	—
23	C₄⋊Dic₁₉	—	2	2	no	—
24	C₄⋊Dic₁₉	D₄	1	2	yes	—
25	C₄⋊Dic₁₉	D₄	1	2	yes	—
26	Dic₁₉⋊C₄	—	2	2	no	—
27	Dic₁₉⋊C₄	—	2	2	no	—
28	Dic₁₉⋊C₄	—	2	2	no	—
29	Dic₁₉⋊C₄	—	2	2	no	—
30	C₄×Dic₁₉	—	2	2	no	—
31	C₂×C₁₉⋊C₈	—	2	1	no	—
32	C₂×C₄×C₁₉	—	2	2	no	—
33	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
35	C₂×Dic₁₉	—	2	2	no	—
36	C₂×Dic₁₉	—	2	2	no	—
37	C₂×Dic₁₉	—	4	1	no	—
38	Dic₃₈	—	4	2	no	—
39	C₈×C₁₉	—	2	4	no	—
40	C₁₉⋊C₈	—	4	1	no	—
41	#1663	—	19	1	no	maximal, Sylow
42	C₂²×C₁₉	#120	1	1	yes	characteristic
43	C₄×C₁₉	—	2	1	no	—
44	C₄×C₁₉	—	2	2	no	—
45	C₄×C₁₉	—	4	2	no	—
46	Dic₁₉	—	4	2	no	—
47	Dic₁₉	—	4	2	no	—
48	Dic₁₉	—	8	1	no	—
49	#564	—	19	1	no	—
50	#501	—	19	2	no	—
51	#491	—	19	1	no	—
52	#330	—	19	2	no	—
53	#330	D₁₉	1	1	yes	characteristic
54	C₂×C₁₉	#454	1	1	yes	characteristic
55	C₂×C₁₉	#456	1	2	yes	—
56	C₄⋊Q₈	—	19	1	no	—
57	#125	—	19	2	no	—
58	#125	—	38	2	no	—
59	#125	—	38	2	no	—
60	#125	—	38	2	no	—
61	#125	C₂×D₁₉	1	1	yes	characteristic
62	#107	—	38	2	no	—
63	#106	—	38	2	no	—
64	#103	—	38	2	no	—
65	#97	—	19	1	no	—
66	#97	C₂×D₁₉	1	2	yes	—
67	C₁₉	#1663	1	1	yes	characteristic, complemented, Sylow
68	C₂×Q₈	—	38	1	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	38	1	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	19	2	no	—
73	C₄⋊C₄	—	19	2	no	—
74	C₄⋊C₄	—	38	2	no	—
75	C₄⋊C₄	—	38	2	no	—
76	C₄⋊C₄	—	38	2	no	—
77	C₄⋊C₄	—	38	2	no	—
78	C₄⋊C₄	—	38	2	no	—
79	C₄⋊C₄	—	38	2	no	—
80	C₄⋊C₄	D₇₆	1	2	yes	—
81	C₄²	—	38	2	no	—
82	C₄²	C₂²×D₁₉	1	1	yes	characteristic
83	Q₈	—	76	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	38	2	no	—
86	C₂×C₄	—	38	2	no	—
87	C₂×C₄	—	76	1	no	—
88	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
89	C₂×C₄	D₄×D₁₉	1	2	yes	—
90	C₈	—	2	4	no	—
91	C₈	—	76	1	no	—
92	C₂²	#10597328	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	4	2	no	—
96	C₄	—	76	2	no	—
97	C₄	—	76	2	no	—
98	C₄	—	152	1	no	—
99	C₂	#11926719	1	1	yes	characteristic
100	C₂	#11926728	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉⋊#564

C₂

yes

maximal, characteristic

#11926953

C₂

yes

maximal

#11926914

C₂

yes

maximal, characteristic

#11926285

C₂

yes

maximal

C₁₉×#330

C₂

yes

maximal, characteristic

C₁₉×#125

C₂²

yes

—

—

—

C₂²

yes

—

#10597315

C₂²

yes

characteristic

C₁₉×#97

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

C₄⋊Dic₁₉

D₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₄⋊Q₈

—

—

—

—

—

C₂×D₁₉

yes

—

—

—

—

C₂×D₁₉

yes

—

C₁₉

#1663

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₇₆

yes

—

C₄²

—

C₄²

C₂²×D₁₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₇₆

yes

characteristic

C₂×C₄

D₄×D₁₉

yes

—

C₈

—

C₈

—

C₂²

#10597328

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

152

—

C₂

#11926719

yes

characteristic

100

C₂

#11926728

yes

—

	subgroup	G/H
center	C₂²	#10597328
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#330	C₂
socle, prime radical	C₂²×C₁₉	#120
hypercenter	#330	D₁₉
hypocenter	C₁₉	#1663
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

#10597328

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#330

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
67. C₁₉	#1663	semidirect

H ≅ G/N

type

67. C₁₉

#1663

semidirect

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

subgroup	index
C₁₉⋊#564	2
#11926953	2
#11926914	2
#11926285	2
C₁₉×#330	2
#1663	19

subgroup

index

C₁₉⋊#564

C₁₉×#330

Subgroups — #14562964

Conjugacy classes of subgroups

Complements

Maximal subgroups