Group #14565726 — subgroups

Subgroups — #14565726

Order 2432.

154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 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×Dic₁₅₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926785	C₂	1	2	yes	maximal
3	#11926370	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926349	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	#10597370	—	2	2	no	—
8	C₂×Dic₇₆	C₂²	1	2	yes	—
9	C₂×C₁₆×C₁₉	—	2	2	no	—
10	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	#10597275	C₂²	1	2	yes	—
13	#10597273	—	2	2	no	—
14	Dic₁₅₂	—	2	2	no	—
15	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂×Dic₃₈	—	2	2	no	—
17	C₂×C₈×C₁₉	—	2	1	no	—
18	C₂×C₈×C₁₉	—	2	1	no	—
19	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
21	C₂²⋊Dic₁₉	—	4	2	no	—
22	C₄⋊Dic₁₉	—	2	2	no	—
23	Dic₁₉⋊C₄	—	4	2	no	—
24	Dic₇₆	—	2	2	no	—
25	Dic₇₆	—	2	2	no	—
26	C₁₆×C₁₉	—	2	1	no	—
27	C₁₆×C₁₉	D₄	1	2	yes	—
28	C₂³×C₁₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₁₉	—	2	1	no	—
30	C₂×C₄×C₁₉	—	2	1	no	—
31	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
32	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₁₉	—	4	2	no	—
34	C₂×Dic₁₉	—	4	2	no	—
35	Dic₃₈	—	4	2	no	—
36	Dic₃₈	—	4	2	no	—
37	C₈×C₁₉	—	2	1	no	—
38	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₁₉	#41	1	1	yes	characteristic
40	#2216	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	—	2	1	no	—
42	C₂²×C₁₉	—	2	1	no	—
43	C₂²×C₁₉	Q₃₂	1	2	yes	complemented
44	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
45	C₄×C₁₉	—	2	1	no	—
46	C₄×C₁₉	#121	1	1	yes	characteristic
47	C₄×C₁₉	#135	1	1	yes	characteristic
48	Dic₁₉	—	8	2	no	—
49	Dic₁₉	—	8	2	no	—
50	C₂×Q₃₂	—	19	1	no	—
51	C₂²×C₁₆	D₁₉	1	1	yes	characteristic
52	#467	—	19	2	no	—
53	#366	—	19	1	no	—
54	#358	—	19	2	no	—
55	C₂×C₁₉	—	2	2	no	—
56	C₂×C₁₉	#466	1	1	yes	characteristic
57	C₂×C₁₉	C₂×Q₃₂	1	1	yes	characteristic
58	C₂×C₁₉	#508	1	1	yes	characteristic
59	C₂×Q₁₆	—	19	2	no	—
60	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
61	C₂²⋊Q₈	—	38	2	no	—
62	Q₃₂	—	38	2	no	—
63	C₂×C₁₆	—	2	2	no	—
64	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
65	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
66	#107	—	19	2	no	—
67	#103	—	38	2	no	—
68	C₁₉	#2216	1	1	yes	characteristic, complemented, Sylow
69	C₂×Q₈	—	38	2	no	—
70	C₂²×C₄	D₇₆	1	1	yes	characteristic
71	Q₁₆	—	38	2	no	—
72	Q₁₆	—	38	2	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	—	2	1	no	—
75	C₂×C₈	D₇₆	1	1	yes	characteristic
76	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
77	C₄⋊C₄	—	38	2	no	—
78	C₄⋊C₄	—	76	2	no	—
79	C₂²⋊C₄	—	76	2	no	—
80	C₁₆	—	2	1	no	—
81	C₁₆	C₂²⋊D₁₉	1	2	yes	—
82	C₂³	D₁₅₂	1	1	yes	characteristic
83	Q₈	—	76	2	no	—
84	Q₈	—	76	2	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	76	2	no	—
88	C₂×C₄	—	76	2	no	—
89	C₂×C₄	D₁₅₂	1	1	yes	characteristic
90	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
91	C₈	—	2	1	no	—
92	C₈	#64541	1	1	yes	characteristic
93	C₈	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
94	C₂²	—	2	1	no	—
95	C₂²	—	2	1	no	—
96	C₂²	Dic₁₅₂	1	2	yes	complemented
97	C₂²	C₂×D₁₅₂	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	152	2	no	—
100	C₄	—	152	2	no	—
101	C₄	#10597350	1	1	yes	characteristic
102	C₄	#10597376	1	1	yes	characteristic
103	C₂	—	2	2	no	—
104	C₂	#11926780	1	1	yes	characteristic
105	C₂	C₂×Dic₁₅₂	1	1	yes	characteristic
106	C₂	#11926976	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₁₅₂

C₂

yes

maximal, characteristic, complemented

#11926785

C₂

yes

maximal

#11926370

C₂

yes

maximal, characteristic, complemented

#11926349

C₂

yes

maximal, complemented

C₂²×C₁₆×C₁₉

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

#10597370

—

C₂×Dic₇₆

C₂²

yes

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

#10597275

C₂²

yes

—

#10597273

—

Dic₁₅₂

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₇₆

—

Dic₇₆

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₄

yes

—

C₂³×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

C₂×D₄

yes

C₈×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

Q₃₂

yes

complemented

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×Q₃₂

—

C₂²×C₁₆

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

#466

yes

characteristic

C₂×C₁₉

C₂×Q₃₂

yes

characteristic

C₂×C₁₉

#508

yes

characteristic

C₂×Q₁₆

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂²⋊Q₈

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic

C₂×C₁₆

C₂×D₁₉

yes

characteristic

#107

—

#103

—

C₁₉

#2216

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

D₇₆

yes

characteristic

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₁₆

C₂²⋊D₁₉

yes

—

C₂³

D₁₅₂

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₁₅₂

yes

characteristic

C₂×C₄

C₂×D₇₆

yes

characteristic

C₈

—

C₈

#64541

yes

characteristic

C₈

C₂×C₂²⋊D₁₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

Dic₁₅₂

yes

complemented

C₂²

C₂×D₁₅₂

yes

characteristic

C₄

—

C₄

—

152

—

100

C₄

—

152

—

101

C₄

#10597350

yes

characteristic

102

C₄

#10597376

yes

characteristic

103

C₂

—

104

C₂

#11926780

yes

characteristic

105

C₂

C₂×Dic₁₅₂

yes

characteristic

106

C₂

#11926976

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₅₂
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₂²×C₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂³×C₁₉	D₈
hypercenter	C₂²×C₁₆	D₁₉
hypocenter	C₁₉	#2216
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center

C₂²

C₂×D₁₅₂

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₂²×C₁₆×C₁₉

C₂

socle

C₂²×C₁₉

C₂×D₈

prime radical

C₂³×C₁₉

D₈

hypercenter

C₂²×C₁₆

D₁₉

hypocenter

C₁₉

#2216

LCS

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
1. C₂×Dic₁₅₂	C₂	semidirect
3. #11926370	C₂	semidirect
4. #11926349	C₂	semidirect
43. C₂²×C₁₉	Q₃₂	semidirect
68. C₁₉	#2216	semidirect
96. C₂²	Dic₁₅₂	semidirect

H ≅ G/N

type

1. C₂×Dic₁₅₂

C₂

semidirect

3. #11926370

C₂

semidirect

4. #11926349

C₂

semidirect

43. C₂²×C₁₉

Q₃₂

semidirect

68. C₁₉

#2216

semidirect

96. C₂²

Dic₁₅₂

semidirect

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

subgroup	index
C₂×Dic₁₅₂	2
#11926785	2
#11926370	2
#11926349	2
C₂²×C₁₆×C₁₉	2
#2216	19

subgroup

index

C₂×Dic₁₅₂

C₂²×C₁₆×C₁₉

Subgroups — #14565726

Conjugacy classes of subgroups

Complements

Maximal subgroups