Group #21446104 — subgroups

Subgroups — #21446104

Order 7808.

260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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	#16840529	C₂	1	1	yes	maximal, characteristic
2	#16839788	C₂	1	2	yes	maximal, complemented
3	#16839736	C₂	1	1	yes	maximal, characteristic
4	#16839534	C₂	1	2	yes	maximal, complemented
5	C₆₁×#408	C₂	1	1	yes	maximal, characteristic
6	#14519784	—	2	4	no	—
7	C₂×#11758194	—	2	2	no	—
8	C₂×#11758194	C₂²	1	2	yes	—
9	#14519736	C₂²	1	2	yes	—
10	#14519706	—	2	4	no	—
11	#14519692	C₄	1	4	yes	—
12	C₂×#41×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²⋊C₈×C₆₁	—	2	2	no	—
16	#41×C₆₁	—	2	2	no	—
17	#41×C₆₁	—	2	2	no	—
18	C₂×Q₈×C₆₁	Q₈	1	1	yes	characteristic
19	C₂×D₄×C₆₁	C₂×C₄	1	2	yes	—
20	C₂×D₄×C₆₁	Q₈	1	1	yes	characteristic
21	C₂²×C₄×C₆₁	D₄	1	2	yes	—
22	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
23	M₁₆×C₆₁	—	2	2	no	—
24	C₂×C₈×C₆₁	—	2	1	no	—
25	C₂×C₈×C₆₁	—	2	1	no	—
26	C₂×C₈×C₆₁	—	2	2	no	—
27	C₂²⋊Dic₆₁	C₂×C₄	1	4	yes	—
28	C₄⋊Dic₆₁	—	2	2	no	—
29	C₄×Dic₆₁	—	2	2	no	—
30	#11758194	—	2	4	no	—
31	#11758194	—	2	2	no	—
32	#11758194	—	2	2	no	—
33	C₂×#92418	—	2	4	no	—
34	C₂×#92418	D₄	1	4	yes	—
35	C₂³×C₆₁	C₄⋊C₄	1	2	yes	—
36	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
37	Q₈×C₆₁	—	2	2	no	—
38	D₄×C₆₁	—	2	4	no	—
39	D₄×C₆₁	—	2	2	no	—
40	C₂×C₄×C₆₁	—	2	2	no	—
41	C₂×C₄×C₆₁	—	2	2	no	—
42	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
43	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₄×C₆₁	#41	1	2	yes	—
47	C₂×Dic₆₁	—	2	4	no	—
48	C₈×C₆₁	—	4	1	no	—
49	C₈×C₆₁	—	4	1	no	—
50	#92418	—	2	4	no	—
51	C₂²×C₆₁	—	2	2	no	—
52	C₂²×C₆₁	—	4	1	no	—
53	C₂²×C₆₁	—	4	2	no	—
54	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₂²×C₆₁	C₄×D₄	1	2	yes	—
56	C₄×C₆₁	—	2	2	no	—
57	C₄×C₆₁	#120	1	1	yes	characteristic
58	C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
59	C₄×C₆₁	#123	1	1	yes	characteristic
60	Dic₆₁	—	4	4	no	—
61	#1868	—	61	1	no	maximal, Sylow
62	C₂×C₆₁	—	2	2	no	—
63	C₂×C₆₁	—	2	1	no	—
64	C₂×C₆₁	—	4	2	no	—
65	C₂×C₆₁	#385	1	1	yes	characteristic
66	#568	—	61	1	no	—
67	#424	—	61	2	no	—
68	#410	—	61	1	no	—
69	#408	D₆₁	1	1	yes	characteristic
70	#344	—	61	2	no	—
71	C₆₁	#1868	1	1	yes	characteristic, complemented, Sylow
72	C₂×#41	C₂×D₆₁	1	1	yes	characteristic
73	#131	—	122	4	no	—
74	C₂×M₁₆	—	61	2	no	—
75	C₂×M₁₆	—	122	2	no	—
76	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
77	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
78	#117	—	61	2	no	—
79	C₄⋊C₈	—	122	4	no	—
80	#99	—	61	4	no	—
81	C₂²⋊C₈	—	2	2	no	—
82	#41	—	2	2	no	—
83	#41	—	2	2	no	—
84	C₂×Q₈	Dic₁₂₂	1	1	yes	characteristic
85	C₂×D₄	Dic₁₂₂	1	1	yes	characteristic
86	C₂×D₄	C₄×D₆₁	1	2	yes	—
87	C₂²×C₄	C₂²⋊D₆₁	1	2	yes	—
88	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
89	M₁₆	—	2	2	no	—
90	M₁₆	—	122	4	no	—
91	M₁₆	—	122	2	no	—
92	M₁₆	—	122	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	2	1	no	—
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	61	4	no	—
97	C₂×C₈	—	122	4	no	—
98	C₄⋊C₄	—	122	2	no	—
99	C₂²⋊C₄	—	61	4	no	—
100	C₄²	—	122	2	no	—
101	C₂³	#11758196	1	2	yes	—
102	C₂³	C₂×C₄×D₆₁	1	1	yes	characteristic
103	Q₈	—	2	2	no	—
104	D₄	—	2	4	no	—
105	D₄	—	2	2	no	—
106	C₂×C₄	—	2	2	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	122	4	no	—
109	C₂×C₄	#11758196	1	2	yes	—
110	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
111	C₂×C₄	D₄×D₆₁	1	2	yes	—
112	C₂×C₄	#11758224	1	2	yes	—
113	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
114	C₈	—	4	1	no	—
115	C₈	—	4	1	no	—
116	C₈	—	122	4	no	—
117	C₂²	—	2	2	no	—
118	C₂²	—	4	1	no	—
119	C₂²	—	4	2	no	—
120	C₂²	C₂×#11758196	1	1	yes	characteristic
121	C₂²	#14519737	1	2	yes	—
122	C₄	—	2	2	no	—
123	C₄	—	244	4	no	—
124	C₄	#14519745	1	1	yes	characteristic
125	C₄	#14519754	1	2	yes	—
126	C₄	#14519758	1	1	yes	characteristic
127	C₂	—	2	2	no	—
128	C₂	—	2	1	no	—
129	C₂	—	4	2	no	—
130	C₂	#16839634	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840529

C₂

yes

maximal, characteristic

#16839788

C₂

yes

maximal, complemented

#16839736

C₂

yes

maximal, characteristic

#16839534

C₂

yes

maximal, complemented

C₆₁×#408

C₂

yes

maximal, characteristic

#14519784

—

C₂×#11758194

—

C₂×#11758194

C₂²

yes

—

#14519736

C₂²

yes

—

#14519706

—

#14519692

C₄

yes

—

C₂×#41×C₆₁

C₂²

yes

characteristic

C₂×M₁₆×C₆₁

C₂²

yes

characteristic

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂²⋊C₈×C₆₁

—

#41×C₆₁

—

#41×C₆₁

—

C₂×Q₈×C₆₁

Q₈

yes

characteristic

C₂×D₄×C₆₁

C₂×C₄

yes

—

C₂×D₄×C₆₁

Q₈

yes

characteristic

C₂²×C₄×C₆₁

D₄

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂²⋊Dic₆₁

C₂×C₄

yes

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

—

—

—

—

D₄

yes

—

C₂³×C₆₁

C₄⋊C₄

yes

—

C₂³×C₆₁

C₂²×C₄

yes

characteristic

Q₈×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₈×C₆₁

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₆₁

C₄×D₄

yes

—

C₄×C₆₁

—

C₄×C₆₁

#120

yes

characteristic

C₄×C₆₁

C₂²⋊Q₈

yes

—

C₄×C₆₁

#123

yes

characteristic

Dic₆₁

—

#1868

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

—

—

—

D₆₁

yes

characteristic

#344

—

C₆₁

#1868

yes

characteristic, complemented, Sylow

C₂×#41

C₂×D₆₁

yes

characteristic

#131

—

122

—

C₂×M₁₆

—

C₂×M₁₆

—

122

—

C₂×M₁₆

C₂×D₆₁

yes

characteristic

C₂²×C₈

C₂×D₆₁

yes

characteristic

#117

—

C₄⋊C₈

—

122

—

#99

—

C₂²⋊C₈

—

#41

—

#41

—

C₂×Q₈

Dic₁₂₂

yes

characteristic

C₂×D₄

Dic₁₂₂

yes

characteristic

C₂×D₄

C₄×D₆₁

yes

—

C₂²×C₄

C₂²⋊D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

100

C₄²

—

122

—

101

C₂³

#11758196

yes

—

102

C₂³

C₂×C₄×D₆₁

yes

characteristic

103

Q₈

—

104

D₄

—

105

D₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

122

—

109

C₂×C₄

#11758196

yes

—

110

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

111

C₂×C₄

D₄×D₆₁

yes

—

112

C₂×C₄

#11758224

yes

—

113

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

—

122

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

C₂×#11758196

yes

characteristic

121

C₂²

#14519737

yes

—

122

C₄

—

123

C₄

—

244

—

124

C₄

#14519745

yes

characteristic

125

C₄

#14519754

yes

—

126

C₄

#14519758

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

130

C₂

#16839634

yes

characteristic

	subgroup	G/H
center	C₄	#14519745
commutator	C₂³×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#408	C₂
socle	C₂×C₆₁	#385
hypercenter	#408	D₆₁
hypocenter	C₆₁	#1868
LCS	G ▷ C₂³×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #408

subgroup

G/H

center

C₄

#14519745

commutator

C₂³×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#408

C₂

C₂×C₆₁

D₆₁

C₆₁

G ▷ C₂³×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #408

N	H ≅ G/N	type
2. #16839788	C₂	semidirect
4. #16839534	C₂	semidirect
71. C₆₁	#1868	semidirect

H ≅ G/N

type

2. #16839788

C₂

semidirect

4. #16839534

C₂

semidirect

71. C₆₁

#1868

semidirect

Subgroups — #21446104

Conjugacy classes of subgroups

Complements