Group #14565738 — subgroups

Subgroups — #14565738

Order 2432.

170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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×D₃₀₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926780	C₂	1	2	yes	maximal, complemented
3	#11926372	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926346	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	#10597376	—	2	2	no	—
8	C₂×D₁₅₂	C₂²	1	2	yes	—
9	C₁₉×M₃₂	—	2	2	no	—
10	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	#10597278	—	2	2	no	—
13	#10597275	C₂²	1	2	yes	—
14	D₃₀₄	—	2	2	no	—
15	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₂²⋊D₁₉	—	4	2	no	—
17	C₂×D₇₆	—	2	2	no	—
18	C₂×C₈×C₁₉	—	2	1	no	—
19	C₂×C₈×C₁₉	—	2	1	no	—
20	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
22	(C₂×D₁₉)⋊C₄	—	4	2	no	—
23	C₄⋊Dic₁₉	—	2	2	no	—
24	D₁₅₂	—	2	2	no	—
25	D₁₅₂	—	2	2	no	—
26	C₁₆×C₁₉	—	2	1	no	—
27	C₁₆×C₁₉	D₄	1	2	yes	complemented
28	C₂³×C₁₉	D₈	1	1	yes	characteristic
29	C₂²×D₁₉	—	4	2	no	—
30	C₂×C₄×C₁₉	—	2	1	no	—
31	C₂×C₄×C₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
33	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂²⋊D₁₉	—	8	4	no	—
35	C₂×Dic₁₉	—	4	2	no	—
36	D₇₆	—	4	2	no	—
37	D₇₆	—	4	2	no	—
38	C₈×C₁₉	—	2	1	no	—
39	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₈×C₁₉	#41	1	1	yes	characteristic
41	#2218	—	19	1	no	maximal, Sylow
42	C₂²×C₁₉	—	2	1	no	—
43	C₂²×C₁₉	—	2	2	no	—
44	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
45	C₂×D₁₉	—	8	2	no	—
46	C₂×D₁₉	—	8	2	no	—
47	C₂×D₁₉	—	8	2	no	—
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	#121	1	1	yes	characteristic
50	C₄×C₁₉	#135	1	1	yes	characteristic
51	Dic₁₉	—	8	2	no	—
52	C₂×D₁₆	—	19	1	no	—
53	C₂×M₃₂	D₁₉	1	1	yes	characteristic, complemented
54	#466	—	19	2	no	—
55	#367	—	19	1	no	—
56	#357	—	19	2	no	—
57	C₂×C₁₉	—	4	1	no	—
58	C₂×C₁₉	#466	1	1	yes	characteristic
59	C₂×C₁₉	#509	1	2	yes	—
60	D₁₉	—	16	2	no	—
61	C₂×D₈	—	19	2	no	—
62	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
63	#121	—	38	2	no	—
64	D₁₆	—	38	2	no	—
65	M₃₂	—	2	2	no	—
66	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
67	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
68	#107	—	19	2	no	—
69	#102	—	38	2	no	—
70	C₁₉	#2218	1	1	yes	characteristic, complemented, Sylow
71	C₂×D₄	—	38	2	no	—
72	C₂×D₄	—	76	2	no	—
73	C₂²×C₄	D₇₆	1	1	yes	characteristic
74	D₈	—	38	2	no	—
75	D₈	—	38	2	no	—
76	C₂×C₈	—	2	1	no	—
77	C₂×C₈	—	2	1	no	—
78	C₂×C₈	D₇₆	1	1	yes	characteristic
79	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
80	C₄⋊C₄	—	38	2	no	—
81	C₂²⋊C₄	—	76	2	no	—
82	C₁₆	—	2	1	no	—
83	C₁₆	C₂²⋊D₁₉	1	2	yes	complemented
84	C₂³	—	76	2	no	—
85	C₂³	D₁₅₂	1	1	yes	characteristic
86	D₄	—	76	2	no	—
87	D₄	—	76	2	no	—
88	D₄	—	152	4	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	76	2	no	—
92	C₂×C₄	D₁₅₂	1	1	yes	characteristic
93	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	#64541	1	1	yes	characteristic
96	C₈	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
97	C₂²	—	2	2	no	—
98	C₂²	—	2	1	no	—
99	C₂²	—	152	2	no	—
100	C₂²	—	152	2	no	—
101	C₂²	—	152	2	no	—
102	C₂²	C₂×D₁₅₂	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	152	2	no	—
105	C₄	#10597350	1	1	yes	characteristic
106	C₄	#10597376	1	1	yes	characteristic
107	C₂	—	4	1	no	—
108	C₂	—	304	2	no	—
109	C₂	#11926780	1	1	yes	characteristic
110	C₂	#11926982	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₃₀₄

C₂

yes

maximal, characteristic, complemented

#11926780

C₂

yes

maximal, complemented

#11926372

C₂

yes

maximal, characteristic, complemented

#11926346

C₂

yes

maximal, complemented

C₂×C₁₉×M₃₂

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×C₁₉

C₂²

yes

characteristic

#10597376

—

C₂×D₁₅₂

C₂²

yes

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

#10597278

—

#10597275

C₂²

yes

—

D₃₀₄

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×D₇₆

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

D₁₅₂

—

D₁₅₂

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₄

yes

complemented

C₂³×C₁₉

D₈

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₈×C₁₉

C₂×D₄

yes

C₈×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×D₁₆

—

C₂×M₃₂

D₁₉

yes

characteristic, complemented

#466

—

#367

—

#357

—

C₂×C₁₉

—

C₂×C₁₉

#466

yes

characteristic

C₂×C₁₉

#509

yes

—

D₁₉

—

C₂×D₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

#121

—

D₁₆

—

M₃₂

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic

C₂×C₁₆

C₂×D₁₉

yes

characteristic

#107

—

#102

—

C₁₉

#2218

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

D₇₆

yes

characteristic

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₁₆

C₂²⋊D₁₉

yes

complemented

C₂³

—

C₂³

D₁₅₂

yes

characteristic

D₄

—

D₄

—

D₄

—

152

—

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

—

152

—

100

C₂²

—

152

—

101

C₂²

—

152

—

102

C₂²

C₂×D₁₅₂

yes

characteristic

103

C₄

—

104

C₄

—

152

—

105

C₄

#10597350

yes

characteristic

106

C₄

#10597376

yes

characteristic

107

C₂

—

108

C₂

—

304

—

109

C₂

#11926780

yes

characteristic

110

C₂

#11926982

yes

—

	subgroup	G/H
center	C₂²	C₂×D₁₅₂
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₂×C₁₉×M₃₂	C₂
socle	C₂²×C₁₉	C₂×D₈
hypercenter	C₂×M₃₂	D₁₉
hypocenter	C₁₉	#2218
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂²

C₂×D₁₅₂

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₂×C₁₉×M₃₂

C₂

socle

C₂²×C₁₉

C₂×D₈

hypercenter

C₂×M₃₂

D₁₉

hypocenter

C₁₉

#2218

LCS

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
1. C₂×D₃₀₄	C₂	semidirect
2. #11926780	C₂	semidirect
3. #11926372	C₂	semidirect
4. #11926346	C₂	semidirect
5. C₂×C₁₉×M₃₂	C₂	semidirect
27. C₁₆×C₁₉	D₄	semidirect
53. C₂×M₃₂	D₁₉	semidirect
70. C₁₉	#2218	semidirect
83. C₁₆	C₂²⋊D₁₉	semidirect

H ≅ G/N

type

1. C₂×D₃₀₄

C₂

semidirect

2. #11926780

C₂

semidirect

3. #11926372

C₂

semidirect

4. #11926346

C₂

semidirect

5. C₂×C₁₉×M₃₂

C₂

semidirect

27. C₁₆×C₁₉

D₄

semidirect

53. C₂×M₃₂

D₁₉

semidirect

70. C₁₉

#2218

semidirect

83. C₁₆

C₂²⋊D₁₉

semidirect

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

subgroup	index
C₂×D₃₀₄	2
#11926780	2
#11926372	2
#11926346	2
C₂×C₁₉×M₃₂	2
#2218	19

subgroup

index

C₂×D₃₀₄

C₂×C₁₉×M₃₂

Subgroups — #14565738

Conjugacy classes of subgroups

Complements

Maximal subgroups