Group #14565788 — subgroups

Subgroups — #14565788

Order 2432.

130 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 55 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	#11926949	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₇₆	C₂	1	1	yes	maximal, characteristic
3	#11926370	C₂	1	2	yes	maximal
4	#11926349	C₂	1	2	yes	maximal
5	C₁₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
7	#10597315	—	2	1	no	—
8	C₄×Dic₃₈	—	2	1	no	—
9	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
10	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	#10597275	—	2	1	no	—
12	#10597275	C₂²	1	2	yes	—
13	#10597275	C₂²	1	1	yes	characteristic
14	#10597273	—	2	1	no	—
15	C₂×Dic₃₈	—	2	1	no	—
16	C₂×Dic₃₈	—	4	1	no	—
17	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
19	C₄²×C₁₉	D₄	1	1	yes	characteristic
20	C₄⋊Dic₁₉	—	2	1	no	—
21	C₄⋊Dic₁₉	—	2	2	no	—
22	C₄⋊Dic₁₉	—	4	1	no	—
23	Dic₁₉⋊C₄	—	4	1	no	—
24	C₄×Dic₁₉	—	4	1	no	—
25	Dic₇₆	—	2	1	no	—
26	Dic₇₆	Q₈	1	2	yes	complemented
27	C₁₆×C₁₉	—	2	2	no	—
28	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
30	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₁₉	—	4	1	no	—
32	C₂×Dic₁₉	—	4	1	no	—
33	C₂×Dic₁₉	—	4	2	no	—
34	Dic₃₈	—	2	2	no	—
35	Dic₃₈	—	4	1	no	—
36	Dic₃₈	—	8	2	no	—
37	C₈×C₁₉	—	2	1	no	—
38	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
39	C₈×C₁₉	#41	1	1	yes	characteristic
40	#2227	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
42	C₄×C₁₉	—	2	1	no	—
43	C₄×C₁₉	Q₃₂	1	2	yes	—
44	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
45	C₄×C₁₉	#137	1	1	yes	characteristic
46	Dic₁₉	—	4	2	no	—
47	Dic₁₉	—	8	2	no	—
48	Dic₁₉	—	8	1	no	—
49	#500	—	19	1	no	—
50	C₄×Q₁₆	—	19	1	no	—
51	#366	—	19	2	no	—
52	C₄⋊C₁₆	D₁₉	1	1	yes	characteristic
53	#358	—	19	2	no	—
54	C₂×C₁₉	#474	1	1	yes	characteristic
55	C₂×C₁₉	C₂×Q₃₂	1	1	yes	characteristic
56	C₂×C₁₉	#509	1	1	yes	characteristic
57	C₂×Q₁₆	—	19	1	no	—
58	C₄⋊Q₈	—	38	1	no	—
59	C₄×Q₈	—	38	1	no	—
60	C₂×C₁₆	C₂×D₁₉	1	2	yes	—
61	#107	—	19	2	no	—
62	#107	—	19	1	no	—
63	#107	—	38	1	no	—
64	#103	—	38	1	no	—
65	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
66	C₁₉	#2227	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₈	—	38	1	no	—
68	C₂×Q₈	—	76	1	no	—
69	Q₁₆	—	19	2	no	—
70	Q₁₆	—	38	1	no	—
71	C₂×C₈	D₇₆	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
73	C₄⋊C₄	—	38	1	no	—
74	C₄⋊C₄	—	38	2	no	—
75	C₄⋊C₄	—	76	1	no	—
76	C₄⋊C₄	—	76	1	no	—
77	C₄²	—	76	1	no	—
78	C₄²	D₇₆	1	1	yes	characteristic
79	C₁₆	—	2	2	no	—
80	Q₈	—	38	2	no	—
81	Q₈	—	76	1	no	—
82	Q₈	—	152	2	no	—
83	C₂×C₄	—	76	1	no	—
84	C₂×C₄	—	76	1	no	—
85	C₂×C₄	—	76	2	no	—
86	C₂×C₄	D₁₅₂	1	1	yes	characteristic
87	C₂×C₄	D₁₅₂	1	1	yes	characteristic
88	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	#64543	1	1	yes	characteristic
91	C₈	Q₈×D₁₉	1	1	yes	characteristic
92	C₂²	C₂×D₁₅₂	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	76	2	no	—
95	C₄	—	152	2	no	—
96	C₄	—	152	1	no	—
97	C₄	Dic₁₅₂	1	2	yes	—
98	C₄	#10597343	1	1	yes	characteristic
99	C₄	#10597355	1	1	yes	characteristic
100	C₂	#11926825	1	1	yes	characteristic
101	C₂	C₂×Dic₁₅₂	1	1	yes	characteristic
102	C₂	#11926982	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926949

C₂

yes

maximal, characteristic

C₄×Dic₇₆

C₂

yes

maximal, characteristic

#11926370

C₂

yes

maximal

#11926349

C₂

yes

maximal

C₁₉×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₂×Dic₇₆

C₂²

yes

characteristic

#10597315

—

C₄×Dic₃₈

—

C₂×C₁₆×C₁₉

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597275

—

#10597275

C₂²

yes

—

#10597275

C₂²

yes

characteristic

#10597273

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

Dic₇₆

—

Dic₇₆

Q₈

yes

complemented

C₁₆×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

C₂×Q₈

yes

C₈×C₁₉

yes

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

Q₃₂

yes

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

#137

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

#500

—

C₄×Q₁₆

—

#366

—

C₄⋊C₁₆

D₁₉

yes

characteristic

#358

—

C₂×C₁₉

#474

yes

characteristic

C₂×C₁₉

C₂×Q₃₂

yes

characteristic

C₂×C₁₉

#509

yes

characteristic

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

—

C₂×C₁₆

C₂×D₁₉

yes

—

—

—

—

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2227

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

D₇₆

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

Q₈

—

152

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₁₅₂

yes

characteristic

C₂×C₄

D₁₅₂

yes

characteristic

C₂×C₄

C₂×D₇₆

yes

characteristic

C₈

—

C₈

#64543

yes

characteristic

C₈

Q₈×D₁₉

yes

characteristic

C₂²

C₂×D₁₅₂

yes

characteristic

C₄

—

C₄

—

C₄

—

152

—

C₄

—

152

—

C₄

Dic₁₅₂

yes

—

C₄

yes

C₄

yes

100

C₂

#11926825

yes

characteristic

101

C₂

C₂×Dic₁₅₂

yes

characteristic

102

C₂

#11926982

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₅₂
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×C₄⋊C₁₆	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₈
hypercenter	C₄⋊C₁₆	D₁₉
hypocenter	C₁₉	#2227
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center

C₂²

C₂×D₁₅₂

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×C₄⋊C₁₆

C₂

socle, prime radical

C₂²×C₁₉

C₂×D₈

hypercenter

C₄⋊C₁₆

D₁₉

hypocenter

C₁₉

#2227

LCS

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
26. Dic₇₆	Q₈	semidirect
66. C₁₉	#2227	semidirect

H ≅ G/N

type

26. Dic₇₆

Q₈

semidirect

66. C₁₉

#2227

semidirect

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

subgroup	index
#11926949	2
C₄×Dic₇₆	2
#11926370	2
#11926349	2
C₁₉×C₄⋊C₁₆	2
#2227	19

subgroup

index

C₄×Dic₇₆

C₁₉×C₄⋊C₁₆

Subgroups — #14565788

Conjugacy classes of subgroups

Complements

Maximal subgroups