Group #21460886 — subgroups

Subgroups — #21460886

Order 7808.

132 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 48 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	D₆₁⋊M₃₂	C₂	1	1	yes	maximal, characteristic
2	#16840772	C₂	1	1	yes	maximal, characteristic
3	#16839797	C₂	1	1	yes	maximal, characteristic
4	#14519856	—	2	1	no	—
5	#14519852	—	2	1	no	—
6	#14519851	—	2	1	no	—
7	D₆₁⋊C₁₆	C₄	1	2	yes	complemented
8	#14519846	—	2	1	no	—
9	#14519845	C₄	1	2	yes	complemented
10	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
11	#14519735	—	2	1	no	—
12	#14519710	—	2	1	no	—
13	#14519709	C₄	1	1	yes	characteristic, complemented
14	#106×C₆₁	C₄	1	1	yes	characteristic, complemented
15	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
16	C₂²⋊#6923	—	4	1	no	—
17	C₄⋊#6923	—	2	2	no	—
18	C₄×#6923	—	4	1	no	—
19	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₄⋊C₄×C₆₁	—	2	1	no	—
21	#11758198	—	4	1	no	—
22	C₄⋊Dic₆₁	—	2	1	no	—
23	C₄×Dic₆₁	—	4	1	no	—
24	C₂×#92418	D₄	1	1	yes	characteristic
25	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
26	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
27	C₈×D₆₁	D₄	1	1	yes	characteristic
28	C₈×D₆₁	Q₈	1	1	yes	characteristic
29	#11758187	—	2	2	no	—
30	C₂²×D₆₁	D₈	1	1	yes	characteristic
31	C₂×#6923	—	4	2	no	—
32	C₂×C₄×C₆₁	—	4	1	no	—
33	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×Dic₆₁	—	4	1	no	—
35	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
36	C₄×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
37	C₄×D₆₁	C₄⋊C₄	1	1	yes	characteristic
38	C₄×D₆₁	SD₁₆	1	1	yes	characteristic
39	C₄×D₆₁	Q₁₆	1	1	yes	characteristic
40	C₈×C₆₁	C₄²	1	1	yes	characteristic
41	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
42	#92418	C₂²⋊C₄	1	1	yes	characteristic
43	#92418	C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₆₁	#102	1	1	yes	characteristic
45	C₂×D₆₁	—	4	1	no	—
46	C₂×D₆₁	#102	1	1	yes	characteristic
47	C₂×D₆₁	#107	1	1	yes	characteristic
48	#6923	—	8	2	no	—
49	C₄×C₆₁	—	8	1	no	—
50	C₄×C₆₁	#95	1	1	yes	characteristic
51	C₄×C₆₁	#103	1	1	yes	characteristic
52	Dic₆₁	—	8	1	no	—
53	Dic₆₁	#103	1	1	yes	characteristic
54	Dic₆₁	#106	1	1	yes	characteristic
55	#1384	—	61	1	no	maximal, Sylow
56	C₂×C₆₁	—	2	1	no	—
57	C₂×C₆₁	#340	1	1	yes	characteristic
58	D₆₁	—	2	1	no	—
59	D₆₁	—	2	1	no	—
60	C₂×M₃₂	—	61	1	no	—
61	#427	—	61	1	no	—
62	#427	—	61	1	no	—
63	C₆₁	#1384	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₈	—	61	1	no	—
65	#117	—	122	1	no	—
66	#117	—	122	1	no	—
67	M₃₂	—	122	1	no	—
68	M₃₂	—	122	1	no	—
69	C₂×C₁₆	—	61	2	no	—
70	#107	—	122	1	no	—
71	#107	—	122	1	no	—
72	#106	—	61	2	no	—
73	#106	—	61	1	no	—
74	#106	#6923	1	1	yes	characteristic, complemented
75	C₂²×C₄	—	61	1	no	—
76	C₂×C₈	—	61	1	no	—
77	C₂×C₈	—	61	1	no	—
78	C₂×C₈	—	61	1	no	—
79	C₂×C₈	—	61	1	no	—
80	C₂×C₈	—	61	1	no	—
81	C₂×C₈	C₂×#6923	1	1	yes	characteristic
82	C₄⋊C₄	—	2	1	no	—
83	C₄⋊C₄	—	122	2	no	—
84	C₄⋊C₄	—	122	1	no	—
85	C₂²⋊C₄	—	244	1	no	—
86	C₂²⋊C₄	—	244	1	no	—
87	C₄²	—	244	1	no	—
88	C₄²	—	244	1	no	—
89	C₁₆	—	122	2	no	—
90	C₂³	—	61	1	no	—
91	C₂×C₄	—	4	1	no	—
92	C₂×C₄	—	61	1	no	—
93	C₂×C₄	—	61	1	no	—
94	C₂×C₄	—	61	1	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	244	2	no	—
98	C₂×C₄	—	244	1	no	—
99	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
100	C₈	—	61	1	no	—
101	C₈	—	61	1	no	—
102	C₈	C₄×#6923	1	1	yes	characteristic
103	C₈	C₄⋊#6923	1	1	yes	characteristic
104	C₂²	—	61	1	no	—
105	C₂²	—	61	1	no	—
106	C₂²	—	244	1	no	—
107	C₂²	#14519839	1	1	yes	characteristic
108	C₄	—	8	1	no	—
109	C₄	—	61	1	no	—
110	C₄	—	61	1	no	—
111	C₄	—	488	1	no	—
112	C₄	—	488	2	no	—
113	C₄	(C₂×#6923)⋊C₄	1	1	yes	characteristic
114	C₄	#14519840	1	1	yes	characteristic
115	C₂	—	2	1	no	—
116	C₂	—	122	1	no	—
117	C₂	—	122	1	no	—
118	C₂	#16840635	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₆₁⋊M₃₂

C₂

yes

maximal, characteristic

#16840772

C₂

yes

maximal, characteristic

#16839797

C₂

yes

maximal, characteristic

#14519856

—

#14519852

—

#14519851

—

D₆₁⋊C₁₆

C₄

yes

complemented

#14519846

—

#14519845

C₄

yes

complemented

C₂×C₈×D₆₁

C₂²

yes

—

—

C₄

yes

characteristic, complemented

#106×C₆₁

C₄

yes

characteristic, complemented

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂²⋊#6923

—

C₄⋊#6923

—

C₄×#6923

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄⋊C₄×C₆₁

—

#11758198

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

C₂×#92418

D₄

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

characteristic

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

Q₈

yes

characteristic

#11758187

—

C₂²×D₆₁

D₈

yes

characteristic

C₂×#6923

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

C₂²⋊C₄

yes

characteristic

C₄×D₆₁

C₄⋊C₄

yes

characteristic

C₄×D₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

Q₁₆

yes

characteristic

C₈×C₆₁

C₄²

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

#92418

C₂²⋊C₄

yes

characteristic

#92418

C₄⋊C₄

yes

characteristic

C₂²×C₆₁

#102

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

yes

C₂×D₆₁

yes

—

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

yes

Dic₆₁

yes

—

C₂×C₆₁

—

C₂×C₆₁

#340

yes

characteristic

D₆₁

—

D₆₁

—

C₂×M₃₂

—

#427

—

#427

—

C₆₁

#1384

yes

characteristic, complemented, Sylow

C₂²×C₈

—

#117

—

122

—

#117

—

122

—

M₃₂

—

122

—

M₃₂

—

122

—

C₂×C₁₆

—

#107

—

122

—

#107

—

122

—

—

—

yes

characteristic, complemented

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

244

—

C₂²⋊C₄

—

244

—

C₄²

—

244

—

C₄²

—

244

—

C₁₆

—

122

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

C₂²⋊#6923

yes

characteristic

100

C₈

—

101

C₈

—

102

C₈

C₄×#6923

yes

characteristic

103

C₈

C₄⋊#6923

yes

characteristic

104

C₂²

—

105

C₂²

—

106

C₂²

—

244

—

107

C₂²

#14519839

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

488

—

112

C₄

—

488

—

113

C₄

(C₂×#6923)⋊C₄

yes

characteristic

114

C₄

#14519840

yes

characteristic

115

C₂

—

116

C₂

—

122

—

117

C₂

—

122

—

118

C₂

#16840635

yes

characteristic

	subgroup	G/H
center	C₂	#16840635
commutator	C₈×C₆₁	C₄²
Frattini	C₂×C₈	C₂×#6923
Fitting	#106×C₆₁	C₄
socle	C₂×C₆₁	#340
hypercenter	#106	#6923
hypocenter	C₆₁	#1384
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

subgroup

G/H

center

C₂

#16840635

commutator

C₈×C₆₁

C₄²

Frattini

C₂×C₈

C₂×#6923

Fitting

#106×C₆₁

C₄

C₂×C₆₁

C₆₁

G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

N	H ≅ G/N	type
7. D₆₁⋊C₁₆	C₄	semidirect
9. #14519845	C₄	semidirect
13. #14519709	C₄	semidirect
14. #106×C₆₁	C₄	semidirect
63. C₆₁	#1384	semidirect
74. #106	#6923	semidirect

H ≅ G/N

type

7. D₆₁⋊C₁₆

C₄

semidirect

9. #14519845

C₄

semidirect

13. #14519709

C₄

semidirect

14. #106×C₆₁

C₄

semidirect

63. C₆₁

#1384

semidirect

74. #106

#6923

semidirect

Subgroups — #21460886

Conjugacy classes of subgroups

Complements