Group #21446789 — subgroups

Subgroups — #21446789

Order 7808.

260 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14519688	C₂	1	1	yes	maximal, characteristic
2	#16839632	C₂	1	1	yes	maximal, characteristic
3	#16839524	C₂	1	4	yes	maximal
4	C₂×#125×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92418	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₆₁	—	2	2	no	—
7	C₂×C₄⋊Dic₆₁	C₂²	1	2	yes	—
8	#14519688	—	2	2	no	—
9	#125×C₆₁	—	2	2	no	—
10	#125×C₆₁	C₄	1	4	yes	complemented
11	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
12	C₂×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
13	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₆₁	—	2	2	no	—
15	C₂²×C₄×C₆₁	D₄	1	2	yes	—
16	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
17	C₂²×Dic₆₁	—	2	2	no	—
18	C₄⋊C₄×C₆₁	—	2	8	no	—
19	C₄⋊C₄×C₆₁	—	2	2	no	—
20	C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
21	C₄²×C₆₁	C₂×C₄	1	2	yes	—
22	C₄²×C₆₁	D₄	1	2	yes	—
23	C₄⋊Dic₆₁	—	2	4	no	—
24	C₄⋊Dic₆₁	—	4	4	no	—
25	C₂×#92418	—	2	2	no	—
26	C₂×#92418	—	2	2	no	—
27	C₂×#92418	Q₈	1	4	yes	—
28	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	—	2	2	no	—
30	C₂×C₄×C₆₁	—	2	2	no	—
31	C₂×C₄×C₆₁	—	2	4	no	—
32	C₂×C₄×C₆₁	—	4	2	no	—
33	C₂×C₄×C₆₁	—	4	2	no	—
34	C₂×C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
35	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₆₁	C₂×Q₈	1	2	yes	—
38	C₂×C₄×C₆₁	#41	1	2	yes	—
39	C₂×Dic₆₁	—	4	2	no	—
40	C₂×Dic₆₁	—	4	4	no	—
41	#92418	—	2	4	no	—
42	C₂²×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×C₆₁	#124	1	1	yes	characteristic
44	C₂²×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
45	C₂²×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
46	C₂²×C₆₁	#137	1	2	yes	—
47	C₄×C₆₁	—	2	4	no	—
48	C₄×C₆₁	—	4	4	no	—
49	C₄×C₆₁	C₄×Q₈	1	2	yes	—
50	C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
51	Dic₆₁	—	8	2	no	—
52	#1992	—	61	1	no	maximal, Sylow
53	C₂×C₆₁	#391	1	1	yes	characteristic
54	C₂×C₆₁	#417	1	2	yes	—
55	C₂×C₆₁	#490	1	1	yes	characteristic
56	C₂×C₆₁	#491	1	1	yes	characteristic
57	C₂×C₆₁	#501	1	2	yes	—
58	C₂×#125	D₆₁	1	1	yes	characteristic
59	C₂×#97	—	61	1	no	—
60	#384	—	61	1	no	—
61	#340	—	61	4	no	—
62	C₆₁	#1992	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₈	—	61	2	no	—
64	#125	—	2	2	no	—
65	#125	Dic₆₁	1	4	yes	complemented
66	C₂×C₄⋊C₄	—	2	2	no	—
67	C₂×C₄⋊C₄	—	61	2	no	—
68	C₂×C₄⋊C₄	—	122	2	no	—
69	C₂×C₄⋊C₄	C₂×D₆₁	1	2	yes	—
70	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
71	#97	—	122	2	no	—
72	C₂²×C₄	—	2	2	no	—
73	C₂²×C₄	—	122	2	no	—
74	C₂²×C₄	C₂²⋊D₆₁	1	2	yes	—
75	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
76	C₂×C₈	—	61	4	no	—
77	C₂×C₈	—	122	2	no	—
78	C₂×C₈	—	122	2	no	—
79	C₄⋊C₄	—	2	8	no	—
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	—	122	4	no	—
82	C₄⋊C₄	—	244	4	no	—
83	C₄⋊C₄	C₂×Dic₆₁	1	4	yes	—
84	C₄²	C₂×Dic₆₁	1	2	yes	—
85	C₄²	C₂²⋊D₆₁	1	2	yes	—
86	C₂³	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
87	C₂×C₄	—	2	2	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	—	4	2	no	—
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	—	244	2	no	—
93	C₂×C₄	—	244	4	no	—
94	C₂×C₄	C₂²⋊Dic₆₁	1	4	yes	—
95	C₂×C₄	Q₈×D₆₁	1	2	yes	—
96	C₂×C₄	#11758226	1	2	yes	—
97	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
99	C₈	—	122	4	no	—
100	C₂²	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
101	C₂²	#14519766	1	1	yes	characteristic
102	C₂²	#14519775	1	1	yes	characteristic
103	C₂²	#14519802	1	2	yes	—
104	C₂²	#14519807	1	2	yes	—
105	C₄	—	2	4	no	—
106	C₄	—	4	4	no	—
107	C₄	—	488	2	no	—
108	C₄	Q₈×Dic₆₁	1	2	yes	—
109	C₄	#14519753	1	2	yes	—
110	C₂	#16839669	1	1	yes	characteristic
111	C₂	#16839763	1	2	yes	—
112	C₂	#16840128	1	1	yes	characteristic
113	C₂	#16840132	1	1	yes	characteristic
114	C₂	#16840172	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519688

C₂

yes

maximal, characteristic

#16839632

C₂

yes

maximal, characteristic

#16839524

C₂

yes

maximal

C₂×#125×C₆₁

C₂

yes

maximal, characteristic

C₂²×#92418

C₂²

yes

—

C₂×C₄⋊Dic₆₁

—

C₂×C₄⋊Dic₆₁

C₂²

yes

—

#14519688

—

#125×C₆₁

—

#125×C₆₁

C₄

yes

complemented

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

D₄

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

D₄

yes

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₂×#92418

—

C₂×#92418

—

C₂×#92418

Q₈

yes

—

C₂³×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

—

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

#92418

—

C₂²×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₆₁

#124

yes

characteristic

C₂²×C₆₁

C₄⋊Q₈

yes

characteristic

C₂²×C₆₁

AGL(1,ℤ/8)

yes

—

C₂²×C₆₁

#137

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₄×Q₈

yes

—

C₄×C₆₁

C₂²⋊Q₈

yes

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×#125

D₆₁

yes

characteristic

C₂×#97

—

#384

—

#340

—

C₆₁

#1992

yes

characteristic, complemented, Sylow

C₂²×C₈

—

#125

—

#125

Dic₆₁

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄⋊C₄

C₂×D₆₁

yes

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

#97

—

122

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂²⋊D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₄⋊C₄

C₂×Dic₆₁

yes

—

C₄²

C₂×Dic₆₁

yes

—

C₄²

C₂²⋊D₆₁

yes

—

C₂³

C₂×C₂²⋊D₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

C₂²⋊Dic₆₁

yes

—

C₂×C₄

Q₈×D₆₁

yes

—

C₂×C₄

#11758226

yes

—

C₂×C₄

C₂²×Dic₆₁

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

122

—

100

C₂²

C₂×C₂²⋊Dic₆₁

yes

characteristic

101

C₂²

#14519766

yes

characteristic

102

C₂²

#14519775

yes

characteristic

103

C₂²

#14519802

yes

—

104

C₂²

#14519807

yes

—

105

C₄

—

106

C₄

—

107

C₄

—

488

—

108

C₄

Q₈×Dic₆₁

yes

—

109

C₄

#14519753

yes

—

110

C₂

#16839669

yes

characteristic

111

C₂

#16839763

yes

—

112

C₂

#16840128

yes

characteristic

113

C₂

#16840132

yes

characteristic

114

C₂

#16840172

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×#125×C₆₁	C₂
socle	C₂³×C₆₁	C₂×D₄
hypercenter	C₂×#125	D₆₁
hypocenter	C₆₁	#1992
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₆₁

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₂×#125×C₆₁

C₂

socle

C₂³×C₆₁

C₂×D₄

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
10. #125×C₆₁	C₄	semidirect
62. C₆₁	#1992	semidirect
65. #125	Dic₆₁	semidirect

H ≅ G/N

type

10. #125×C₆₁

C₄

semidirect

62. C₆₁

#1992

semidirect

65. #125

Dic₆₁

semidirect

Subgroups — #21446789

Conjugacy classes of subgroups

Complements