Group #21445931 — subgroups

Subgroups — #21445931

Order 7808.

236 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 81 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	#16840240	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519696	C₂	1	1	yes	maximal, characteristic
3	#16839534	C₂	1	2	yes	maximal
4	#16839533	C₂	1	2	yes	maximal
5	C₂×#101×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758194	C₂²	1	2	yes	—
7	Q₈×Dic₆₁	—	2	2	no	—
8	Q₈×Dic₆₁	—	2	2	no	—
9	#14519736	C₄	1	4	yes	—
10	#14519736	C₂²	1	1	yes	characteristic
11	#14519736	C₂²	1	1	yes	characteristic
12	#14519696	—	2	2	no	—
13	C₂²×Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×C₆₁	C₂²	1	2	yes	—
15	#101×C₆₁	—	2	2	no	—
16	C₂×Q₈×C₆₁	—	2	2	no	—
17	C₂×Q₈×C₆₁	—	2	2	no	—
18	C₂×Q₈×C₆₁	D₄	1	2	yes	—
19	C₂×Q₈×C₆₁	D₄	1	2	yes	—
20	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
22	M₁₆×C₆₁	—	2	2	no	—
23	M₁₆×C₆₁	—	2	2	no	—
24	C₂×C₈×C₆₁	—	2	2	no	—
25	C₂²⋊Dic₆₁	C₂×C₄	1	2	yes	—
26	C₂²⋊Dic₆₁	C₂×C₄	1	2	yes	—
27	C₄⋊Dic₆₁	—	2	4	no	—
28	C₄⋊Dic₆₁	—	2	1	no	—
29	C₄⋊Dic₆₁	—	2	1	no	—
30	C₄×Dic₆₁	—	2	4	no	—
31	C₄×Dic₆₁	—	2	1	no	—
32	C₄×Dic₆₁	—	2	1	no	—
33	#11758194	—	2	2	no	—
34	#11758194	—	2	2	no	—
35	C₂×#92418	—	2	2	no	—
36	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
37	Q₈×C₆₁	—	2	4	no	—
38	Q₈×C₆₁	—	2	4	no	—
39	C₂×C₄×C₆₁	—	2	2	no	—
40	C₂×C₄×C₆₁	—	2	2	no	—
41	C₂×C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
42	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₆₁	#41	1	2	yes	—
45	C₂×C₄×C₆₁	#41	1	2	yes	—
46	C₂×Dic₆₁	—	2	2	no	—
47	C₂×Dic₆₁	—	2	2	no	—
48	C₈×C₆₁	—	4	2	no	—
49	#92418	—	4	2	no	—
50	C₂²×C₆₁	—	4	1	no	—
51	C₂²×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₆₁	#117	1	1	yes	characteristic
53	C₂²×C₆₁	#117	1	1	yes	characteristic
54	C₄×C₆₁	—	2	4	no	—
55	C₄×C₆₁	#123	1	2	yes	—
56	C₄×C₆₁	#123	1	2	yes	—
57	Dic₆₁	—	4	2	no	—
58	Dic₆₁	—	4	2	no	—
59	#1830	—	61	1	no	maximal, Sylow
60	C₂×C₆₁	—	2	1	no	—
61	C₂×C₆₁	—	2	1	no	—
62	C₂×C₆₁	—	2	1	no	—
63	C₂×C₆₁	#381	1	1	yes	characteristic
64	#519	—	61	1	no	—
65	C₂×#101	—	61	1	no	—
66	C₂×#101	D₆₁	1	1	yes	characteristic
67	#344	—	61	2	no	—
68	#344	—	61	2	no	—
69	C₆₁	#1830	1	1	yes	characteristic, complemented, Sylow
70	C₂²×Q₈	C₂×D₆₁	1	1	yes	characteristic
71	C₂×M₁₆	—	61	2	no	—
72	C₂×M₁₆	C₂×D₆₁	1	2	yes	—
73	C₄×Q₈	—	122	2	no	—
74	C₄×Q₈	—	122	2	no	—
75	#117	—	61	4	no	—
76	#117	—	61	1	no	—
77	#117	—	61	1	no	—
78	#101	—	2	2	no	—
79	#101	—	122	2	no	—
80	C₂×Q₈	—	2	2	no	—
81	C₂×Q₈	—	2	2	no	—
82	C₂×Q₈	D₂₄₄	1	2	yes	—
83	C₂×Q₈	C₂²⋊D₆₁	1	2	yes	—
84	C₂²×C₄	C₄×D₆₁	1	2	yes	—
85	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
86	M₁₆	—	2	2	no	—
87	M₁₆	—	2	2	no	—
88	M₁₆	—	122	2	no	—
89	M₁₆	—	122	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	122	2	no	—
92	C₄⋊C₄	—	122	4	no	—
93	C₄⋊C₄	—	122	1	no	—
94	C₄⋊C₄	—	122	1	no	—
95	C₂²⋊C₄	—	61	2	no	—
96	C₂²⋊C₄	—	61	2	no	—
97	C₄²	—	122	4	no	—
98	C₄²	—	122	1	no	—
99	C₄²	—	122	1	no	—
100	C₂³	C₂×C₄×D₆₁	1	1	yes	characteristic
101	Q₈	—	2	4	no	—
102	Q₈	—	2	4	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	122	2	no	—
106	C₂×C₄	—	122	2	no	—
107	C₂×C₄	#11758198	1	4	yes	—
108	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
109	C₂×C₄	#11758224	1	2	yes	—
110	C₂×C₄	#11758224	1	2	yes	—
111	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
112	C₈	—	4	2	no	—
113	C₈	—	244	2	no	—
114	C₂²	—	4	1	no	—
115	C₂²	C₂×#11758198	1	1	yes	characteristic
116	C₂²	#14519733	1	1	yes	characteristic
117	C₂²	#14519733	1	1	yes	characteristic
118	C₄	—	2	4	no	—
119	C₄	—	244	2	no	—
120	C₄	—	244	2	no	—
121	C₄	#14519758	1	2	yes	—
122	C₄	#14519761	1	2	yes	—
123	C₂	—	2	1	no	—
124	C₂	—	2	1	no	—
125	C₂	—	2	1	no	—
126	C₂	#16839623	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840240

C₂

yes

maximal, characteristic

C₂×#14519696

C₂

yes

maximal, characteristic

#16839534

C₂

yes

maximal

#16839533

C₂

yes

maximal

C₂×#101×C₆₁

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

—

Q₈×Dic₆₁

—

Q₈×Dic₆₁

—

#14519736

C₄

yes

—

#14519736

C₂²

yes

characteristic

#14519736

C₂²

yes

characteristic

#14519696

—

C₂²×Q₈×C₆₁

C₂²

yes

characteristic

C₂×M₁₆×C₆₁

C₂²

yes

—

#101×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

D₄

yes

—

C₂×Q₈×C₆₁

D₄

yes

—

C₂²×C₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂²⋊Dic₆₁

C₂×C₄

yes

—

C₂²⋊Dic₆₁

C₂×C₄

yes

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

#11758194

—

#11758194

—

C₂×#92418

—

C₂³×C₆₁

C₂²×C₄

yes

characteristic

Q₈×C₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×C₂²⋊C₄

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

#123

yes

—

C₄×C₆₁

#123

yes

—

Dic₆₁

—

Dic₆₁

—

#1830

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

—

—

D₆₁

yes

characteristic

#344

—

#344

—

C₆₁

#1830

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₆₁

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

—

C₄×Q₈

—

122

—

C₄×Q₈

—

122

—

—

—

—

—

—

122

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₂₄₄

yes

—

C₂×Q₈

C₂²⋊D₆₁

yes

—

C₂²×C₄

C₄×D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

122

—

C₄²

—

122

—

C₄²

—

122

—

100

C₂³

C₂×C₄×D₆₁

yes

characteristic

101

Q₈

—

102

Q₈

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

122

—

106

C₂×C₄

—

122

—

107

C₂×C₄

#11758198

yes

—

108

C₂×C₄

C₂×D₂₄₄

yes

characteristic

109

C₂×C₄

#11758224

yes

—

110

C₂×C₄

#11758224

yes

—

111

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

112

C₈

—

113

C₈

—

244

—

114

C₂²

—

115

C₂²

C₂×#11758198

yes

characteristic

116

C₂²

#14519733

yes

characteristic

117

C₂²

#14519733

yes

characteristic

118

C₄

—

119

C₄

—

244

—

120

C₄

—

244

—

121

C₄

#14519758

yes

—

122

C₄

#14519761

yes

—

123

C₂

—

124

C₂

—

125

C₂

—

126

C₂

#16839623

yes

characteristic

	subgroup	G/H
center	C₂	#16839623
commutator	C₂³×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×#101×C₆₁	C₂
socle	C₂×C₆₁	#381
hypercenter	C₂×#101	D₆₁
hypocenter	C₆₁	#1830
LCS	G ▷ C₂³×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#101

subgroup

G/H

center

C₂

#16839623

commutator

C₂³×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₂×#101×C₆₁

C₂

C₂×C₆₁

D₆₁

C₆₁

G ▷ C₂³×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#101

N	H ≅ G/N	type
69. C₆₁	#1830	semidirect

H ≅ G/N

type

69. C₆₁

#1830

semidirect

Subgroups — #21445931

Conjugacy classes of subgroups

Complements