Group #21447259 — subgroups

Subgroups — #21447259

Order 7808.

198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 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	C₂×#14519711	C₂	1	1	yes	maximal, characteristic, complemented
2	#16839763	C₂	1	2	yes	maximal
3	#16839530	C₂	1	2	yes	maximal, complemented
4	#16839527	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#408	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758194	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₆₁	C₂²	1	2	yes	—
8	#14519711	—	2	2	no	—
9	#14519701	—	2	2	no	—
10	#14519698	—	2	2	no	—
11	C₂×#41×C₆₁	C₂²	1	1	yes	characteristic
12	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²⋊C₈×C₆₁	—	2	2	no	—
15	#41×C₆₁	—	2	2	no	—
16	#41×C₆₁	—	2	2	no	—
17	C₂×Q₈×C₆₁	D₄	1	1	yes	characteristic
18	C₂×D₄×C₆₁	—	2	1	no	—
19	C₂×D₄×C₆₁	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₆₁	—	2	1	no	—
21	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
22	C₂²×Dic₆₁	—	2	2	no	—
23	M₁₆×C₆₁	—	2	2	no	—
24	C₂×C₈×C₆₁	—	2	2	no	—
25	C₂×C₈×C₆₁	—	2	1	no	—
26	C₂×C₈×C₆₁	D₄	1	2	yes	—
27	C₄⋊Dic₆₁	—	2	2	no	—
28	C₄⋊Dic₆₁	—	2	2	no	—
29	#11758194	—	2	2	no	—
30	#11758194	—	2	2	no	—
31	C₂×#92418	—	2	2	no	—
32	C₂³×C₆₁	—	2	1	no	—
33	C₂³×C₆₁	#41	1	1	yes	characteristic
34	Q₈×C₆₁	—	2	2	no	—
35	D₄×C₆₁	—	2	2	no	—
36	D₄×C₆₁	—	4	2	no	—
37	C₂×C₄×C₆₁	—	2	1	no	—
38	C₂×C₄×C₆₁	—	4	1	no	—
39	C₂×C₄×C₆₁	—	4	1	no	—
40	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₆₁	#41	1	2	yes	—
43	C₂×C₄×C₆₁	#41	1	2	yes	—
44	C₂×Dic₆₁	—	4	2	no	—
45	C₂×Dic₆₁	—	8	2	no	—
46	C₈×C₆₁	—	2	2	no	—
47	C₈×C₆₁	—	4	1	no	—
48	#92418	—	4	2	no	—
49	C₂²×C₆₁	—	2	1	no	—
50	C₂²×C₆₁	—	2	1	no	—
51	C₂²×C₆₁	—	4	1	no	—
52	C₂²×C₆₁	—	4	1	no	—
53	C₂²×C₆₁	—	4	1	no	—
54	C₂²×C₆₁	#121	1	1	yes	characteristic
55	C₂²×C₆₁	#126	1	2	yes	—
56	C₄×C₆₁	—	4	1	no	—
57	C₄×C₆₁	#123	1	1	yes	characteristic
58	C₄×C₆₁	#123	1	2	yes	—
59	C₄×C₆₁	#124	1	1	yes	characteristic
60	Dic₆₁	—	8	2	no	—
61	#2078	—	61	1	no	maximal, Sylow
62	C₂×C₆₁	—	2	2	no	—
63	C₂×C₆₁	—	8	1	no	—
64	C₂×C₆₁	#397	1	1	yes	characteristic
65	C₂×C₆₁	#472	1	1	yes	characteristic
66	C₂×C₆₁	#473	1	1	yes	characteristic
67	C₂×#107	—	61	1	no	—
68	#417	—	61	2	no	—
69	#408	D₆₁	1	1	yes	characteristic
70	#343	—	61	2	no	—
71	#341	—	61	1	no	—
72	C₆₁	#2078	1	1	yes	characteristic, complemented, Sylow
73	C₂×#41	C₂×D₆₁	1	1	yes	characteristic
74	C₂×M₁₆	—	61	2	no	—
75	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
76	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
77	C₂×C₄⋊C₄	—	61	2	no	—
78	#107	—	122	2	no	—
79	#103	—	122	2	no	—
80	#102	—	122	2	no	—
81	C₂²⋊C₈	—	2	2	no	—
82	#41	—	2	2	no	—
83	#41	—	2	2	no	—
84	C₂×Q₈	D₂₄₄	1	1	yes	characteristic
85	C₂×D₄	—	2	1	no	—
86	C₂×D₄	D₂₄₄	1	1	yes	characteristic
87	C₂²×C₄	—	2	1	no	—
88	C₂²×C₄	—	122	2	no	—
89	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
90	M₁₆	—	2	2	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	—	122	2	no	—
96	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
97	C₄⋊C₄	—	122	2	no	—
98	C₄⋊C₄	—	122	2	no	—
99	C₂³	—	2	1	no	—
100	C₂³	#11758222	1	1	yes	characteristic
101	Q₈	—	2	2	no	—
102	D₄	—	2	2	no	—
103	D₄	—	4	2	no	—
104	C₂×C₄	—	2	1	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	488	2	no	—
108	C₂×C₄	—	244	2	no	—
109	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
110	C₂×C₄	#11758224	1	2	yes	—
111	C₂×C₄	#11758224	1	2	yes	—
112	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
113	C₈	—	2	2	no	—
114	C₈	—	4	1	no	—
115	C₈	—	244	2	no	—
116	C₂²	—	2	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	4	1	no	—
119	C₂²	—	4	1	no	—
120	C₂²	—	4	1	no	—
121	C₂²	#14519751	1	1	yes	characteristic
122	C₂²	#14519770	1	2	yes	—
123	C₄	—	4	1	no	—
124	C₄	—	488	2	no	—
125	C₄	#14519758	1	1	yes	characteristic
126	C₄	#14519761	1	2	yes	—
127	C₄	#14519764	1	1	yes	characteristic
128	C₂	—	2	2	no	—
129	C₂	—	8	1	no	—
130	C₂	#16839687	1	1	yes	characteristic
131	C₂	#16840032	1	1	yes	characteristic
132	C₂	#16840037	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519711

C₂

yes

maximal, characteristic, complemented

#16839763

C₂

yes

maximal

#16839530

C₂

yes

maximal, complemented

#16839527

C₂

yes

maximal, characteristic, complemented

C₆₁×#408

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

—

C₂×C₄⋊Dic₆₁

C₂²

yes

—

#14519711

—

#14519701

—

#14519698

—

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

D₄

yes

characteristic

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

D₄

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

D₄

yes

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

#11758194

—

#11758194

—

C₂×#92418

—

C₂³×C₆₁

—

C₂³×C₆₁

#41

yes

characteristic

Q₈×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

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

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#121

yes

characteristic

C₂²×C₆₁

#126

yes

—

C₄×C₆₁

—

C₄×C₆₁

#123

yes

characteristic

C₄×C₆₁

#123

yes

—

C₄×C₆₁

#124

yes

characteristic

Dic₆₁

—

#2078

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

D₆₁

yes

characteristic

#343

—

#341

—

C₆₁

#2078

yes

characteristic, complemented, Sylow

C₂×#41

C₂×D₆₁

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

characteristic

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂×C₄⋊C₄

—

#107

—

122

—

#103

—

122

—

#102

—

122

—

C₂²⋊C₈

—

#41

—

#41

—

C₂×Q₈

D₂₄₄

yes

characteristic

C₂×D₄

—

C₂×D₄

D₂₄₄

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₂²⋊D₆₁

yes

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₂³

—

100

C₂³

#11758222

yes

characteristic

101

Q₈

—

102

D₄

—

103

D₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

488

—

108

C₂×C₄

—

244

—

109

C₂×C₄

C₂×D₂₄₄

yes

characteristic

110

C₂×C₄

#11758224

yes

—

111

C₂×C₄

#11758224

yes

—

112

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

—

244

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

#14519751

yes

characteristic

122

C₂²

#14519770

yes

—

123

C₄

—

124

C₄

—

488

—

125

C₄

#14519758

yes

characteristic

126

C₄

#14519761

yes

—

127

C₄

#14519764

yes

characteristic

128

C₂

—

129

C₂

—

130

C₂

#16839687

yes

characteristic

131

C₂

#16840032

yes

characteristic

132

C₂

#16840037

yes

characteristic

	subgroup	G/H
center	C₂²	#14519751
commutator	C₂²×C₄×C₆₁	C₂³
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#408	C₂
socle	C₂²×C₆₁	#121
hypercenter	#408	D₆₁
hypocenter	C₆₁	#2078
LCS	G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #408

subgroup

G/H

center

C₂²

#14519751

commutator

C₂²×C₄×C₆₁

C₂³

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#408

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #408

N	H ≅ G/N	type
1. C₂×#14519711	C₂	semidirect
3. #16839530	C₂	semidirect
4. #16839527	C₂	semidirect
72. C₆₁	#2078	semidirect

H ≅ G/N

type

1. C₂×#14519711

C₂

semidirect

3. #16839530

C₂

semidirect

4. #16839527

C₂

semidirect

72. C₆₁

#2078

semidirect

Subgroups — #21447259

Conjugacy classes of subgroups

Complements