Group #14565680 — subgroups

Subgroups — #14565680

Order 2432.

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

normal subgroups only

This group has 166 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×#10597284	C₂	1	2	yes	maximal
2	#11926924	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926347	C₂	1	2	yes	maximal, complemented
5	C₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₄×D₄×C₁₉	—	2	1	no	—
8	C₂×Dic₇₆	—	2	1	no	—
9	C₂×Dic₇₆	C₂²	1	2	yes	—
10	#10597315	—	2	1	no	—
11	C₁₉×#107	C₂²	1	1	yes	characteristic
12	C₁₉×#102	—	2	1	no	—
13	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	#10597284	—	2	4	no	—
15	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
16	C₂×D₄×C₁₉	—	2	1	no	—
17	C₂²×C₄×C₁₉	—	4	1	no	—
18	C₂×Dic₃₈	—	2	2	no	—
19	D₈×C₁₉	—	2	1	no	—
20	D₈×C₁₉	D₄	1	2	yes	—
21	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₁₉	—	2	1	no	—
24	C₂²⋊C₄×C₁₉	—	4	1	no	—
25	C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₄⋊Dic₁₉	—	4	1	no	—
27	C₄⋊Dic₁₉	—	4	1	no	—
28	Dic₇₆	—	2	2	no	—
29	Dic₇₆	—	2	2	no	—
30	Dic₇₆	—	4	2	no	—
31	C₁₉⋊C₁₆	—	2	2	no	—
32	C₂³×C₁₉	—	4	1	no	—
33	D₄×C₁₉	—	2	2	no	—
34	D₄×C₁₉	—	4	1	no	—
35	C₂×C₄×C₁₉	—	4	1	no	—
36	C₂×C₄×C₁₉	—	8	2	no	—
37	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
38	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₁₉	—	4	2	no	—
41	Dic₃₈	—	4	2	no	—
42	Dic₃₈	—	4	2	no	—
43	C₈×C₁₉	—	2	1	no	—
44	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₈×C₁₉	#41	1	1	yes	characteristic
46	#2208	—	19	1	no	maximal, Sylow
47	C₂²×C₁₉	—	4	2	no	—
48	C₂²×C₁₉	—	8	1	no	—
49	C₂²×C₁₉	—	8	1	no	—
50	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
51	C₄×C₁₉	—	2	1	no	—
52	C₄×C₁₉	—	8	1	no	—
53	C₄×C₁₉	SD₃₂	1	2	yes	complemented
54	C₄×C₁₉	#121	1	1	yes	characteristic
55	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
56	Dic₁₉	—	8	2	no	—
57	C₂×SD₃₂	—	19	2	no	—
58	#494	—	19	1	no	—
59	C₄×D₈	D₁₉	1	1	yes	characteristic
60	C₄⋊C₁₆	—	19	1	no	—
61	#358	—	19	2	no	—
62	C₂×C₁₉	—	8	2	no	—
63	C₂×C₁₉	#459	1	1	yes	characteristic
64	C₂×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
65	C₂×C₁₉	#510	1	1	yes	characteristic
66	C₂×Q₁₆	—	19	2	no	—
67	C₂×Q₁₆	—	38	1	no	—
68	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
69	C₄⋊Q₈	—	38	1	no	—
70	C₄×D₄	—	2	1	no	—
71	SD₃₂	—	38	4	no	—
72	C₂×C₁₆	—	19	2	no	—
73	#107	C₂×D₁₉	1	1	yes	characteristic
74	#102	—	2	1	no	—
75	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
76	C₁₉	#2208	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₈	—	38	2	no	—
78	C₂×D₄	—	2	1	no	—
79	C₂²×C₄	—	4	1	no	—
80	Q₁₆	—	38	2	no	—
81	Q₁₆	—	38	2	no	—
82	Q₁₆	—	76	2	no	—
83	D₈	—	2	1	no	—
84	D₈	D₇₆	1	2	yes	—
85	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
86	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
87	C₄⋊C₄	—	2	1	no	—
88	C₄⋊C₄	—	76	1	no	—
89	C₄⋊C₄	—	76	1	no	—
90	C₂²⋊C₄	—	4	1	no	—
91	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
92	C₁₆	—	38	2	no	—
93	C₂³	—	4	1	no	—
94	Q₈	—	76	2	no	—
95	Q₈	—	76	2	no	—
96	D₄	—	2	2	no	—
97	D₄	—	4	1	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	—	8	2	no	—
100	C₂×C₄	—	76	2	no	—
101	C₂×C₄	#64525	1	1	yes	characteristic
102	C₂×C₄	#64525	1	1	yes	characteristic
103	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
104	C₈	—	2	1	no	—
105	C₈	C₂×D₇₆	1	1	yes	characteristic
106	C₈	#64541	1	1	yes	characteristic
107	C₂²	—	4	2	no	—
108	C₂²	—	8	1	no	—
109	C₂²	—	8	1	no	—
110	C₂²	C₂×#64525	1	1	yes	characteristic
111	C₄	—	2	1	no	—
112	C₄	—	8	1	no	—
113	C₄	—	152	2	no	—
114	C₄	#10597284	1	2	yes	complemented
115	C₄	#10597376	1	1	yes	characteristic
116	C₄	#10597395	1	1	yes	characteristic
117	C₂	—	8	2	no	—
118	C₂	#11926739	1	1	yes	characteristic
119	C₂	C₂×#10597284	1	1	yes	characteristic
120	C₂	#11926984	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597284

C₂

yes

maximal

#11926924

C₂

yes

maximal, characteristic, complemented

C₄⋊(C₁₉⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

#11926347

C₂

yes

maximal, complemented

C₄×D₈×C₁₉

C₂

yes

maximal, characteristic

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₄×D₄×C₁₉

—

C₂×Dic₇₆

—

C₂×Dic₇₆

C₂²

yes

—

#10597315

—

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#102

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597284

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂×Dic₃₈

—

D₈×C₁₉

—

D₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₇₆

—

Dic₇₆

—

Dic₇₆

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

C₂×D₄

yes

C₈×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

SD₃₂

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×SD₃₂

—

#494

—

C₄×D₈

D₁₉

yes

characteristic

C₄⋊C₁₆

—

#358

—

C₂×C₁₉

—

C₂×C₁₉

#459

yes

characteristic

C₂×C₁₉

C₂×SD₃₂

yes

characteristic

C₂×C₁₉

#510

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×D₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

C₄×D₄

—

SD₃₂

—

C₂×C₁₆

—

#107

C₂×D₁₉

yes

characteristic

#102

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2208

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

D₈

—

D₈

D₇₆

yes

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

#64525

yes

characteristic

102

C₂×C₄

#64525

yes

characteristic

103

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

104

C₈

—

105

C₈

C₂×D₇₆

yes

characteristic

106

C₈

#64541

yes

characteristic

107

C₂²

—

108

C₂²

—

109

C₂²

—

110

C₂²

C₂×#64525

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

152

—

114

C₄

#10597284

yes

complemented

115

C₄

#10597376

yes

characteristic

116

C₄

#10597395

yes

characteristic

117

C₂

—

118

C₂

#11926739

yes

characteristic

119

C₂

C₂×#10597284

yes

characteristic

120

C₂

#11926984

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#64525
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₄×D₈×C₁₉	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂×D₈×C₁₉	C₂²
hypercenter	C₄×D₈	D₁₉
hypocenter	C₁₉	#2208
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

subgroup

G/H

center

C₂²

C₂×#64525

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₄×D₈×C₁₉

C₂

socle

C₂²×C₁₉

C₂×D₈

prime radical

C₂×D₈×C₁₉

C₂²

hypercenter

C₄×D₈

D₁₉

hypocenter

C₁₉

#2208

LCS

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

N	H ≅ G/N	type
2. #11926924	C₂	semidirect
3. C₄⋊(C₁₉⋊C₁₆)	C₂	semidirect
4. #11926347	C₂	semidirect
53. C₄×C₁₉	SD₃₂	semidirect
76. C₁₉	#2208	semidirect
114. C₄	#10597284	semidirect

H ≅ G/N

type

2. #11926924

C₂

semidirect

3. C₄⋊(C₁₉⋊C₁₆)

C₂

semidirect

4. #11926347

C₂

semidirect

53. C₄×C₁₉

SD₃₂

semidirect

76. C₁₉

#2208

semidirect

114. C₄

#10597284

semidirect

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

subgroup	index
C₂×#10597284	2
#11926924	2
C₄⋊(C₁₉⋊C₁₆)	2
#11926347	2
C₄×D₈×C₁₉	2
#2208	19

subgroup

index

C₄⋊(C₁₉⋊C₁₆)

C₄×D₈×C₁₉

Subgroups — #14565680

Conjugacy classes of subgroups

Complements

Maximal subgroups