Group #21448049 — subgroups

Subgroups — #21448049

Order 7808.

138 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 47 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	#16840163	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840145	C₂	1	1	yes	maximal, characteristic
3	#16839567	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839565	C₂	1	1	yes	maximal, characteristic, complemented
5	#16839563	C₂	1	1	yes	maximal, characteristic
6	C₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#357	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₄₄	C₂²	1	1	yes	characteristic
9	C₂×#11758200	—	2	1	no	—
10	#14519768	—	2	1	no	—
11	#14519764	—	2	1	no	—
12	C₂×#11758185	C₂²	1	1	yes	characteristic
13	#14519711	C₂²	1	1	yes	characteristic
14	#14519708	—	2	1	no	—
15	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
16	C₂×D₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	#107×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×D₄×C₆₁	—	2	1	no	—
20	C₂×Dic₁₂₂	—	2	1	no	—
21	D₈×C₆₁	—	2	1	no	—
22	D₈×C₆₁	—	2	1	no	—
23	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₆₁	—	2	1	no	—
25	C₂²⋊Dic₆₁	—	4	1	no	—
26	C₂²⋊Dic₆₁	—	4	1	no	—
27	#11758200	—	4	2	no	—
28	C₄⋊Dic₆₁	—	2	1	no	—
29	C₄⋊Dic₆₁	—	4	1	no	—
30	#11758196	—	4	1	no	—
31	C₄×Dic₆₁	D₄	1	1	yes	characteristic
32	C₂×#92418	D₄	1	1	yes	characteristic
33	Dic₂₄₄	—	2	1	no	—
34	Dic₂₄₄	—	2	1	no	—
35	C₁₆×C₆₁	—	2	1	no	—
36	#11758185	—	2	1	no	—
37	C₂³×C₆₁	—	4	1	no	—
38	D₄×C₆₁	—	4	1	no	—
39	D₄×C₆₁	—	4	1	no	—
40	C₂×C₄×C₆₁	—	4	1	no	—
41	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₆₁	—	4	1	no	—
43	C₂×Dic₆₁	—	4	1	no	—
44	C₂×Dic₆₁	D₈	1	1	yes	characteristic
45	C₂×Dic₆₁	D₈	1	1	yes	characteristic
46	Dic₁₂₂	—	4	1	no	—
47	Dic₁₂₂	—	4	1	no	—
48	C₈×C₆₁	#41	1	1	yes	characteristic
49	C₈×C₆₁	#41	1	1	yes	characteristic
50	#92418	SD₁₆	1	2	yes	—
51	C₂²×C₆₁	—	8	1	no	—
52	C₂²×C₆₁	—	8	1	no	—
53	C₂²×C₆₁	—	8	1	no	—
54	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
55	C₄×C₆₁	—	8	1	no	—
56	C₄×C₆₁	#124	1	1	yes	characteristic
57	C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
58	Dic₆₁	—	2	1	no	—
59	Dic₆₁	—	2	1	no	—
60	Dic₆₁	—	8	1	no	—
61	Dic₆₁	—	8	1	no	—
62	#2242	—	61	1	no	maximal, Sylow
63	C₂×C₆₁	—	16	1	no	—
64	C₂×C₆₁	#486	1	1	yes	characteristic
65	C₂×C₆₁	#508	1	1	yes	characteristic
66	C₂×C₆₁	#508	1	1	yes	characteristic
67	#499	—	61	1	no	—
68	#495	—	61	1	no	—
69	#358	—	61	1	no	—
70	#358	—	61	1	no	—
71	#357	—	61	1	no	—
72	#357	D₆₁	1	1	yes	characteristic
73	C₄×C₁₆	—	61	1	no	—
74	C₆₁	#2242	1	1	yes	characteristic, complemented, Sylow
75	C₂×Q₁₆	—	61	1	no	—
76	C₂×SD₁₆	—	122	1	no	—
77	C₂×D₈	C₂×D₆₁	1	1	yes	characteristic
78	#125	—	122	1	no	—
79	#124	—	122	1	no	—
80	C₂×C₁₆	—	61	1	no	—
81	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
82	#107	—	61	1	no	—
83	#107	C₂×D₆₁	1	1	yes	characteristic
84	#106	—	122	1	no	—
85	C₄×C₈	—	61	1	no	—
86	C₂×Q₈	—	122	1	no	—
87	C₂×D₄	—	2	1	no	—
88	Q₁₆	—	122	1	no	—
89	Q₁₆	—	122	1	no	—
90	SD₁₆	—	244	2	no	—
91	D₈	—	2	1	no	—
92	D₈	—	2	1	no	—
93	C₂×C₈	—	61	1	no	—
94	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
95	C₄⋊C₄	—	2	1	no	—
96	C₄⋊C₄	—	122	1	no	—
97	C₄⋊C₄	—	244	1	no	—
98	C₄⋊C₄	—	244	1	no	—
99	C₂²⋊C₄	—	244	1	no	—
100	C₂²⋊C₄	—	244	1	no	—
101	C₄²	—	61	1	no	—
102	C₁₆	—	2	1	no	—
103	C₁₆	—	122	1	no	—
104	C₂³	—	4	1	no	—
105	Q₈	—	244	1	no	—
106	Q₈	—	244	1	no	—
107	D₄	—	4	1	no	—
108	D₄	—	4	1	no	—
109	C₂×C₄	—	4	1	no	—
110	C₂×C₄	—	61	1	no	—
111	C₂×C₄	—	61	1	no	—
112	C₂×C₄	—	244	1	no	—
113	C₂×C₄	—	244	1	no	—
114	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
115	C₈	—	61	2	no	—
116	C₈	#11758222	1	1	yes	characteristic
117	C₈	#11758224	1	1	yes	characteristic
118	C₂²	—	8	1	no	—
119	C₂²	—	8	1	no	—
120	C₂²	—	8	1	no	—
121	C₂²	D₈×D₆₁	1	1	yes	characteristic
122	C₄	—	8	1	no	—
123	C₄	—	122	1	no	—
124	C₄	—	122	1	no	—
125	C₄	—	488	1	no	—
126	C₄	—	488	1	no	—
127	C₄	#14519763	1	1	yes	characteristic
128	C₄	SD₁₆×D₆₁	1	1	yes	characteristic
129	C₂	—	16	1	no	—
130	C₂	#16840107	1	1	yes	characteristic
131	C₂	#16840191	1	1	yes	characteristic
132	C₂	#16840193	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840163

C₂

yes

maximal, characteristic, complemented

#16840145

C₂

yes

maximal, characteristic

#16839567

C₂

yes

maximal, characteristic, complemented

#16839565

C₂

yes

maximal, characteristic, complemented

#16839563

C₂

yes

maximal, characteristic

C₁₆×Dic₆₁

C₂

yes

maximal, characteristic, complemented

C₆₁×#357

C₂

yes

maximal, characteristic

C₂×Dic₂₄₄

C₂²

yes

—

—

—

C₂²

yes

characteristic

#14519711

C₂²

yes

characteristic

#14519708

—

C₈×Dic₆₁

C₂²

yes

characteristic

C₂×D₈×C₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

#107×C₆₁

C₂²

yes

characteristic

C₂×D₄×C₆₁

—

C₂×Dic₁₂₂

—

D₈×C₆₁

—

D₈×C₆₁

—

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄⋊C₄×C₆₁

—

C₂²⋊Dic₆₁

—

C₂²⋊Dic₆₁

—

#11758200

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

#11758196

—

C₄×Dic₆₁

D₄

yes

characteristic

C₂×#92418

D₄

yes

characteristic

Dic₂₄₄

—

Dic₂₄₄

—

C₁₆×C₆₁

—

#11758185

—

C₂³×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

D₈

yes

characteristic

C₂×Dic₆₁

D₈

yes

characteristic

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

yes

C₈×C₆₁

yes

SD₁₆

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

#124

yes

characteristic

C₄×C₆₁

C₂×SD₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

#2242

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

—

—

—

D₆₁

yes

characteristic

C₄×C₁₆

—

C₆₁

#2242

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

122

—

C₂×D₈

C₂×D₆₁

yes

characteristic

#125

—

122

—

#124

—

122

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₆₁

yes

characteristic

#107

—

#107

C₂×D₆₁

yes

characteristic

#106

—

122

—

C₄×C₈

—

C₂×Q₈

—

122

—

C₂×D₄

—

Q₁₆

—

122

—

Q₁₆

—

122

—

SD₁₆

—

244

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₄⋊C₄

—

244

—

C₂²⋊C₄

—

244

—

100

C₂²⋊C₄

—

244

—

101

C₄²

—

102

C₁₆

—

103

C₁₆

—

122

—

104

C₂³

—

105

Q₈

—

244

—

106

Q₈

—

244

—

107

D₄

—

108

D₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

244

—

113

C₂×C₄

—

244

—

114

C₂×C₄

D₄×D₆₁

yes

characteristic

115

C₈

—

116

C₈

#11758222

yes

characteristic

117

C₈

#11758224

yes

characteristic

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

D₈×D₆₁

yes

characteristic

122

C₄

—

123

C₄

—

122

—

124

C₄

—

122

—

125

C₄

—

488

—

126

C₄

—

488

—

127

C₄

#14519763

yes

characteristic

128

C₄

SD₁₆×D₆₁

yes

characteristic

129

C₂

—

130

C₂

#16840107

yes

characteristic

131

C₂

#16840191

yes

characteristic

132

C₂

#16840193

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₆₁
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#357	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	#357	D₆₁
hypocenter	C₆₁	#2242
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₆₁

commutator

C₂×C₈×C₆₁

C₂³

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#357

C₂

socle

C₂²×C₆₁

C₂×D₈

D₆₁

C₆₁

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. #16840163	C₂	semidirect
3. #16839567	C₂	semidirect
4. #16839565	C₂	semidirect
6. C₁₆×Dic₆₁	C₂	semidirect
74. C₆₁	#2242	semidirect

H ≅ G/N

type

1. #16840163

C₂

semidirect

3. #16839567

C₂

semidirect

4. #16839565

C₂

semidirect

6. C₁₆×Dic₆₁

C₂

semidirect

74. C₆₁

#2242

semidirect

Subgroups — #21448049

Conjugacy classes of subgroups

Complements