Group #21461742 — subgroups

Subgroups — #21461742

Order 7808.

224 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 74 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	#16840708	C₂	1	1	yes	maximal, characteristic
2	#16840706	C₂	1	1	yes	maximal, characteristic
3	#16840636	C₂	1	4	yes	maximal
4	#97×D₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊#6923	—	2	2	no	—
6	C₂×C₄⋊#6923	C₂²	1	2	yes	—
7	C₂×C₄⋊#6923	C₂²	1	2	yes	—
8	(C₂×#6923)⋊C₄	—	2	2	no	—
9	C₂×C₈×D₆₁	C₂²	1	2	yes	—
10	C₄²×D₆₁	C₂²	1	1	yes	characteristic
11	#14519688	C₄	1	1	yes	characteristic, complemented
12	#14519687	C₄	1	2	yes	complemented
13	#97×C₆₁	C₄	1	1	yes	characteristic, complemented
14	C₂²×#6923	—	2	2	no	—
15	C₂²×#6923	—	2	2	no	—
16	C₂×C₄×D₆₁	D₄	1	2	yes	—
17	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
18	C₄⋊#6923	—	2	4	no	—
19	C₄⋊#6923	—	2	4	no	—
20	C₄⋊#6923	—	4	4	no	—
21	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
22	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₆₁	Q₈	1	2	yes	—
25	C₂×#92418	C₂×C₄	1	2	yes	—
26	C₈×D₆₁	—	2	2	no	—
27	C₈×D₆₁	—	2	2	no	—
28	C₂²×D₆₁	C₂×D₄	1	1	yes	characteristic
29	C₂×#6923	—	4	2	no	—
30	C₂×#6923	—	4	2	no	—
31	C₂×#6923	—	4	4	no	—
32	C₂×#6923	—	4	2	no	—
33	C₂×#6923	—	4	2	no	—
34	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
37	C₂×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
38	C₄×D₆₁	—	2	2	no	—
39	C₄×D₆₁	—	2	2	no	—
40	C₄×D₆₁	#41	1	2	yes	—
41	C₄×D₆₁	#41	1	2	yes	—
42	C₈×C₆₁	—	2	2	no	—
43	#92418	—	2	2	no	—
44	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂×D₆₁	#124	1	1	yes	characteristic
46	C₂×D₆₁	#124	1	1	yes	characteristic
47	C₂×D₆₁	AGL(1,ℤ/8)	1	2	yes	—
48	C₂×D₆₁	#137	1	2	yes	—
49	#6923	—	8	2	no	—
50	#6923	—	8	2	no	—
51	C₄×C₆₁	—	2	2	no	—
52	C₄×C₆₁	#117	1	2	yes	—
53	Dic₆₁	—	2	2	no	—
54	Dic₆₁	#125	1	2	yes	—
55	#1836	—	61	1	no	maximal, Sylow
56	C₂×C₆₁	#382	1	1	yes	characteristic
57	C₂×C₆₁	#428	1	2	yes	—
58	D₆₁	#489	1	2	yes	—
59	D₆₁	#490	1	1	yes	characteristic
60	D₆₁	#491	1	1	yes	characteristic
61	C₂×#97	—	61	1	no	—
62	#384	—	61	1	no	—
63	#382	—	61	1	no	—
64	#340	—	61	4	no	—
65	C₆₁	#1836	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₈	—	61	2	no	—
67	C₂×C₄⋊C₄	—	61	2	no	—
68	C₂×C₄⋊C₄	—	61	2	no	—
69	C₂×C₄⋊C₄	—	122	2	no	—
70	C₂×C₄²	—	61	1	no	—
71	#97	—	61	2	no	—
72	#97	—	61	1	no	—
73	#97	#6923	1	1	yes	characteristic, complemented
74	#95	—	122	2	no	—
75	C₂²×C₄	—	61	1	no	—
76	C₂²×C₄	—	61	2	no	—
77	C₂²×C₄	—	122	2	no	—
78	C₂²×C₄	—	122	2	no	—
79	C₂×C₈	—	61	2	no	—
80	C₂×C₈	—	122	2	no	—
81	C₂×C₈	—	122	2	no	—
82	C₂×C₈	C₂×#6923	1	2	yes	—
83	C₄⋊C₄	—	122	4	no	—
84	C₄⋊C₄	—	122	4	no	—
85	C₄⋊C₄	—	244	4	no	—
86	C₄²	—	61	2	no	—
87	C₄²	—	61	1	no	—
88	C₄²	C₂×#6923	1	1	yes	characteristic
89	C₂³	—	61	1	no	—
90	C₂×C₄	—	61	1	no	—
91	C₂×C₄	—	61	2	no	—
92	C₂×C₄	—	61	2	no	—
93	C₂×C₄	—	61	2	no	—
94	C₂×C₄	—	122	2	no	—
95	C₂×C₄	—	122	2	no	—
96	C₂×C₄	—	244	2	no	—
97	C₂×C₄	—	244	2	no	—
98	C₂×C₄	—	244	4	no	—
99	C₂×C₄	—	244	2	no	—
100	C₂×C₄	—	244	2	no	—
101	C₂×C₄	C₄⋊#6923	1	2	yes	—
102	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
103	C₈	—	2	2	no	—
104	C₈	—	122	2	no	—
105	C₂²	—	61	1	no	—
106	C₂²	—	61	1	no	—
107	C₂²	—	61	2	no	—
108	C₂²	—	61	2	no	—
109	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
110	C₄	—	2	2	no	—
111	C₄	—	61	2	no	—
112	C₄	—	122	2	no	—
113	C₄	—	488	2	no	—
114	C₄	—	488	2	no	—
115	C₄	#14519856	1	2	yes	—
116	C₂	—	61	1	no	—
117	C₂	—	61	2	no	—
118	C₂	—	61	1	no	—
119	C₂	#16840706	1	1	yes	characteristic
120	C₂	#16840773	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840708

C₂

yes

maximal, characteristic

#16840706

C₂

yes

maximal, characteristic

#16840636

C₂

yes

maximal

#97×D₆₁

C₂

yes

maximal, characteristic

C₂×C₄⋊#6923

—

C₂×C₄⋊#6923

C₂²

yes

—

C₂×C₄⋊#6923

C₂²

yes

—

(C₂×#6923)⋊C₄

—

C₂×C₈×D₆₁

C₂²

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

#14519688

C₄

yes

characteristic, complemented

#14519687

C₄

yes

complemented

#97×C₆₁

C₄

yes

characteristic, complemented

C₂²×#6923

—

C₂²×#6923

—

C₂×C₄×D₆₁

D₄

yes

—

C₂×C₄×D₆₁

C₂³

yes

—

—

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

—

C₂×#92418

C₂×C₄

yes

—

C₈×D₆₁

—

C₈×D₆₁

—

C₂²×D₆₁

C₂×D₄

yes

—

—

—

—

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

—

C₂×Dic₆₁

C₂×Q₈

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

#41

yes

—

C₄×D₆₁

#41

yes

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

C₂×D₆₁

yes

C₂×D₆₁

yes

C₂×D₆₁

yes

—

C₂×D₆₁

#137

yes

—

#6923

—

#6923

—

C₄×C₆₁

—

C₄×C₆₁

#117

yes

—

Dic₆₁

—

Dic₆₁

#125

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

#489

yes

—

D₆₁

yes

D₆₁

yes

C₂×#97

—

#384

—

#382

—

#340

—

C₆₁

#1836

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄²

—

—

—

yes

characteristic, complemented

#95

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

—

122

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

100

C₂×C₄

—

244

—

101

C₂×C₄

C₄⋊#6923

yes

—

102

C₂×C₄

C₂²×#6923

yes

characteristic

103

C₈

—

104

C₈

—

122

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₂×C₄⋊#6923

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

122

—

113

C₄

—

488

—

114

C₄

—

488

—

115

C₄

#14519856

yes

—

116

C₂

—

117

C₂

—

118

C₂

—

119

C₂

#16840706

yes

characteristic

120

C₂

#16840773

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	#97×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	#97	#6923
hypocenter	C₆₁	#1836
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

#97×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₄⋊C₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
11. #14519688	C₄	semidirect
12. #14519687	C₄	semidirect
13. #97×C₆₁	C₄	semidirect
65. C₆₁	#1836	semidirect
73. #97	#6923	semidirect

H ≅ G/N

type

11. #14519688

C₄

semidirect

12. #14519687

C₄

semidirect

13. #97×C₆₁

C₄

semidirect

65. C₆₁

#1836

semidirect

73. #97

#6923

semidirect

Subgroups — #21461742

Conjugacy classes of subgroups

Complements