Group #14565685 — subgroups

Subgroups — #14565685

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×#10597286	C₂	1	2	yes	maximal
2	#11926924	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
4	#11926347	C₂	1	2	yes	maximal
5	C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₄×Q₈×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×#103	—	2	1	no	—
13	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	#10597286	—	2	4	no	—
15	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
16	C₂×Q₈×C₁₉	—	2	1	no	—
17	C₂×Dic₃₈	—	2	2	no	—
18	Q₁₆×C₁₉	—	2	1	no	—
19	Q₁₆×C₁₉	D₄	1	2	yes	—
20	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₄⋊C₄×C₁₉	—	4	1	no	—
24	C₄²×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	Q₈×C₁₉	—	2	2	no	—
33	Q₈×C₁₉	—	4	1	no	—
34	C₂×C₄×C₁₉	—	4	1	no	—
35	C₂×C₄×C₁₉	—	4	1	no	—
36	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
37	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₁₉	—	4	2	no	—
40	Dic₃₈	—	4	2	no	—
41	Dic₃₈	—	4	2	no	—
42	C₈×C₁₉	—	2	1	no	—
43	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₈×C₁₉	#41	1	1	yes	characteristic
45	#2209	—	19	1	no	maximal, Sylow
46	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
47	C₄×C₁₉	—	2	1	no	—
48	C₄×C₁₉	—	4	2	no	—
49	C₄×C₁₉	—	8	1	no	—
50	C₄×C₁₉	Q₃₂	1	2	yes	complemented
51	C₄×C₁₉	#121	1	1	yes	characteristic
52	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
53	Dic₁₉	—	8	2	no	—
54	C₂×Q₃₂	—	19	2	no	—
55	#494	—	19	1	no	—
56	C₄×Q₁₆	D₁₉	1	1	yes	characteristic
57	C₄⋊C₁₆	—	19	1	no	—
58	#358	—	19	2	no	—
59	C₂×C₁₉	#459	1	1	yes	characteristic
60	C₂×C₁₉	C₂×Q₃₂	1	1	yes	characteristic
61	C₂×C₁₉	#510	1	1	yes	characteristic
62	C₂×Q₁₆	—	19	2	no	—
63	C₂×Q₁₆	—	38	1	no	—
64	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
65	C₄⋊Q₈	—	38	1	no	—
66	C₄×Q₈	—	2	1	no	—
67	Q₃₂	—	38	4	no	—
68	C₂×C₁₆	—	19	2	no	—
69	#107	C₂×D₁₉	1	1	yes	characteristic
70	#103	—	2	1	no	—
71	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
72	C₁₉	#2209	1	1	yes	characteristic, complemented, Sylow
73	C₂×Q₈	—	2	1	no	—
74	C₂×Q₈	—	38	2	no	—
75	Q₁₆	—	2	1	no	—
76	Q₁₆	—	38	2	no	—
77	Q₁₆	—	38	2	no	—
78	Q₁₆	—	76	2	no	—
79	Q₁₆	D₇₆	1	2	yes	—
80	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
81	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
82	C₄⋊C₄	—	2	1	no	—
83	C₄⋊C₄	—	4	1	no	—
84	C₄⋊C₄	—	76	1	no	—
85	C₄⋊C₄	—	76	1	no	—
86	C₄²	—	4	1	no	—
87	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
88	C₁₆	—	38	2	no	—
89	Q₈	—	2	2	no	—
90	Q₈	—	4	1	no	—
91	Q₈	—	76	2	no	—
92	Q₈	—	76	2	no	—
93	C₂×C₄	—	4	1	no	—
94	C₂×C₄	—	4	1	no	—
95	C₂×C₄	—	76	2	no	—
96	C₂×C₄	#64525	1	1	yes	characteristic
97	C₂×C₄	#64525	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	C₂×D₇₆	1	1	yes	characteristic
101	C₈	#64541	1	1	yes	characteristic
102	C₂²	C₂×#64525	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	4	2	no	—
105	C₄	—	8	1	no	—
106	C₄	—	152	2	no	—
107	C₄	#10597286	1	2	yes	complemented
108	C₄	#10597376	1	1	yes	characteristic
109	C₄	#10597395	1	1	yes	characteristic
110	C₂	#11926739	1	1	yes	characteristic
111	C₂	C₂×#10597286	1	1	yes	characteristic
112	C₂	#11926984	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597286

C₂

yes

maximal

#11926924

C₂

yes

maximal, characteristic

C₄⋊(C₁₉⋊C₁₆)

C₂

yes

maximal, characteristic

#11926347

C₂

yes

maximal

C₄×Q₁₆×C₁₉

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₄×Q₈×C₁₉

—

C₂×Dic₇₆

—

C₂×Dic₇₆

C₂²

yes

—

#10597315

—

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#103

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597286

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×Dic₃₈

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₇₆

—

Dic₇₆

—

Dic₇₆

—

C₁₉⋊C₁₆

—

Q₈×C₁₉

—

Q₈×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

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

Q₃₂

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×Q₃₂

—

#494

—

C₄×Q₁₆

D₁₉

yes

characteristic

C₄⋊C₁₆

—

#358

—

C₂×C₁₉

#459

yes

characteristic

C₂×C₁₉

C₂×Q₃₂

yes

characteristic

C₂×C₁₉

#510

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

C₄×Q₈

—

Q₃₂

—

C₂×C₁₆

—

#107

C₂×D₁₉

yes

characteristic

#103

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2209

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

D₇₆

yes

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

100

C₈

C₂×D₇₆

yes

characteristic

101

C₈

#64541

yes

characteristic

102

C₂²

C₂×#64525

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

152

—

107

C₄

#10597286

yes

complemented

108

C₄

#10597376

yes

characteristic

109

C₄

#10597395

yes

characteristic

110

C₂

#11926739

yes

characteristic

111

C₂

C₂×#10597286

yes

characteristic

112

C₂

#11926984

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#64525
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₄×Q₁₆×C₁₉	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₈
hypercenter	C₄×Q₁₆	D₁₉
hypocenter	C₁₉	#2209
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

subgroup

G/H

center

C₂²

C₂×#64525

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₄×Q₁₆×C₁₉

C₂

socle, prime radical

C₂²×C₁₉

C₂×D₈

hypercenter

C₄×Q₁₆

D₁₉

hypocenter

C₁₉

#2209

LCS

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

N	H ≅ G/N	type
50. C₄×C₁₉	Q₃₂	semidirect
72. C₁₉	#2209	semidirect
107. C₄	#10597286	semidirect

H ≅ G/N

type

50. C₄×C₁₉

Q₃₂

semidirect

72. C₁₉

#2209

semidirect

107. C₄

#10597286

semidirect

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

subgroup	index
C₂×#10597286	2
#11926924	2
C₄⋊(C₁₉⋊C₁₆)	2
#11926347	2
C₄×Q₁₆×C₁₉	2
#2209	19

subgroup

index

C₄⋊(C₁₉⋊C₁₆)

C₄×Q₁₆×C₁₉

Subgroups — #14565685

Conjugacy classes of subgroups

Complements

Maximal subgroups