Group #21447402 — subgroups

Subgroups — #21447402

Order 7808.

148 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 59 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	#16839810	C₂	1	1	yes	maximal, characteristic
2	#16839789	C₂	1	1	yes	maximal, characteristic
3	#16839532	C₂	1	1	yes	maximal, characteristic
4	#16839526	C₂	1	1	yes	maximal, characteristic
5	#16839526	C₂	1	1	yes	maximal, characteristic
6	#16839520	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#344	C₂	1	1	yes	maximal, characteristic
8	C₂×#11758194	C₂²	1	1	yes	characteristic
9	C₂×#11758194	C₂²	1	1	yes	characteristic
10	C₂×#11758194	C₂²	1	1	yes	characteristic
11	C₂²×#92418	C₂²	1	1	yes	characteristic
12	#14519712	—	2	2	no	—
13	C₄⋊#92418	—	2	2	no	—
14	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
16	#117×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
18	M₁₆×C₆₁	—	2	1	no	—
19	M₁₆×C₆₁	—	2	1	no	—
20	M₁₆×C₆₁	—	2	1	no	—
21	M₁₆×C₆₁	—	2	1	no	—
22	C₂×C₈×C₆₁	—	2	1	no	—
23	C₂×C₈×C₆₁	—	2	1	no	—
24	C₄⋊C₄×C₆₁	—	2	1	no	—
25	C₂²⋊C₄×C₆₁	Q₈	1	2	yes	—
26	C₄²×C₆₁	—	2	1	no	—
27	#11758194	—	2	1	no	—
28	#11758194	—	2	1	no	—
29	#11758194	—	2	1	no	—
30	#11758194	—	2	1	no	—
31	#11758194	—	2	1	no	—
32	#11758194	—	2	1	no	—
33	C₂×#92418	—	2	1	no	—
34	C₂×#92418	—	2	1	no	—
35	C₂×#92418	—	2	1	no	—
36	C₂×#92418	—	2	1	no	—
37	C₂×#92418	—	2	1	no	—
38	C₂×#92418	D₄	1	2	yes	—
39	C₂³×C₆₁	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₆₁	—	2	2	no	—
41	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
43	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
44	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
45	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
46	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
47	C₈×C₆₁	—	4	1	no	—
48	C₈×C₆₁	—	4	1	no	—
49	#92418	—	2	2	no	—
50	#92418	—	4	1	no	—
51	#92418	—	4	1	no	—
52	#92418	—	4	1	no	—
53	C₂²×C₆₁	—	4	1	no	—
54	C₂²×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
55	C₂²×C₆₁	#125	1	1	yes	characteristic
56	C₂²×C₆₁	#125	1	1	yes	characteristic
57	C₄×C₆₁	—	4	2	no	—
58	C₄×C₆₁	#123	1	1	yes	characteristic
59	C₄×C₆₁	#124	1	1	yes	characteristic
60	C₄×C₆₁	#126	1	1	yes	characteristic
61	C₄×C₆₁	#126	1	1	yes	characteristic
62	#2103	—	61	1	no	maximal, Sylow
63	C₂×C₆₁	—	2	1	no	—
64	C₂×C₆₁	—	2	1	no	—
65	C₂×C₆₁	—	2	1	no	—
66	C₂×C₆₁	#400	1	1	yes	characteristic
67	#430	—	61	1	no	—
68	#424	—	61	1	no	—
69	#344	—	61	1	no	—
70	#344	D₆₁	1	1	yes	characteristic
71	#341	—	61	1	no	—
72	#341	—	61	1	no	—
73	#338	—	61	1	no	—
74	C₆₁	#2103	1	1	yes	characteristic, complemented, Sylow
75	C₂×M₁₆	—	61	1	no	—
76	C₂×M₁₆	—	61	1	no	—
77	C₂×M₁₆	—	61	1	no	—
78	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
79	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
80	C₂²×C₈	—	61	1	no	—
81	#117	C₂×D₆₁	1	1	yes	characteristic
82	#108	—	122	2	no	—
83	C₄⋊C₈	—	122	2	no	—
84	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
85	M₁₆	—	2	1	no	—
86	M₁₆	—	2	1	no	—
87	M₁₆	—	2	1	no	—
88	M₁₆	—	2	1	no	—
89	M₁₆	—	122	1	no	—
90	M₁₆	—	122	1	no	—
91	M₁₆	—	122	1	no	—
92	M₁₆	—	122	1	no	—
93	M₁₆	—	122	1	no	—
94	M₁₆	—	122	1	no	—
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	2	1	no	—
97	C₂×C₈	—	61	2	no	—
98	C₂×C₈	—	122	1	no	—
99	C₂×C₈	—	122	1	no	—
100	C₂×C₈	—	122	1	no	—
101	C₂×C₈	—	122	1	no	—
102	C₂×C₈	—	122	1	no	—
103	C₄⋊C₄	—	2	1	no	—
104	C₂²⋊C₄	Dic₁₂₂	1	2	yes	—
105	C₄²	—	2	1	no	—
106	C₂³	C₂×Dic₁₂₂	1	1	yes	characteristic
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	#11758222	1	1	yes	characteristic
109	C₂×C₄	#11758222	1	1	yes	characteristic
110	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
111	C₂×C₄	#11758224	1	1	yes	characteristic
112	C₂×C₄	#11758224	1	1	yes	characteristic
113	C₂×C₄	#11758226	1	1	yes	characteristic
114	C₈	—	4	1	no	—
115	C₈	—	4	1	no	—
116	C₈	—	122	2	no	—
117	C₈	—	244	1	no	—
118	C₈	—	244	1	no	—
119	C₈	—	244	1	no	—
120	C₂²	—	4	1	no	—
121	C₂²	#14519754	1	1	yes	characteristic
122	C₂²	#14519768	1	1	yes	characteristic
123	C₂²	#14519769	1	1	yes	characteristic
124	C₄	—	4	2	no	—
125	C₄	#14519762	1	1	yes	characteristic
126	C₄	#14519763	1	1	yes	characteristic
127	C₄	#14519770	1	1	yes	characteristic
128	C₄	#14519772	1	1	yes	characteristic
129	C₂	—	2	1	no	—
130	C₂	—	2	1	no	—
131	C₂	—	2	1	no	—
132	C₂	#16839704	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839810

C₂

yes

maximal, characteristic

#16839789

C₂

yes

maximal, characteristic

#16839532

C₂

yes

maximal, characteristic

#16839526

C₂

yes

maximal, characteristic

#16839526

C₂

yes

maximal, characteristic

#16839520

C₂

yes

maximal, characteristic

C₆₁×#344

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

characteristic

C₂×#11758194

C₂²

yes

characteristic

C₂×#11758194

C₂²

yes

characteristic

C₂²×#92418

C₂²

yes

characteristic

#14519712

—

C₄⋊#92418

—

C₂×M₁₆×C₆₁

C₂²

yes

characteristic

C₂×M₁₆×C₆₁

C₂²

yes

characteristic

#117×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

C₂³

yes

characteristic

M₁₆×C₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₄⋊C₄×C₆₁

—

C₂²⋊C₄×C₆₁

Q₈

yes

—

C₄²×C₆₁

—

—

—

—

—

—

—

—

—

—

—

—

D₄

yes

—

C₂³×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₈×C₆₁

—

C₈×C₆₁

—

—

—

—

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂²⋊Q₈

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

—

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

—

—

—

D₆₁

yes

—

—

—

C₆₁

#2103

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

characteristic

C₂×M₁₆

C₂×D₆₁

yes

characteristic

C₂²×C₈

—

#117

C₂×D₆₁

yes

characteristic

#108

—

122

—

C₄⋊C₈

—

122

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

100

C₂×C₈

—

122

—

101

C₂×C₈

—

122

—

102

C₂×C₈

—

122

—

103

C₄⋊C₄

—

104

C₂²⋊C₄

Dic₁₂₂

yes

—

105

C₄²

—

106

C₂³

C₂×Dic₁₂₂

yes

characteristic

107

C₂×C₄

—

108

C₂×C₄

#11758222

yes

characteristic

109

C₂×C₄

#11758222

yes

characteristic

110

C₂×C₄

D₄×D₆₁

yes

characteristic

111

C₂×C₄

#11758224

yes

characteristic

112

C₂×C₄

#11758224

yes

characteristic

113

C₂×C₄

#11758226

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

—

122

—

117

C₈

—

244

—

118

C₈

—

244

—

119

C₈

—

244

—

120

C₂²

—

121

C₂²

#14519754

yes

characteristic

122

C₂²

#14519768

yes

characteristic

123

C₂²

#14519769

yes

characteristic

124

C₄

—

125

C₄

#14519762

yes

characteristic

126

C₄

#14519763

yes

characteristic

127

C₄

#14519770

yes

characteristic

128

C₄

#14519772

yes

characteristic

129

C₂

—

130

C₂

—

131

C₂

—

132

C₂

#16839704

yes

characteristic

	subgroup	G/H
center	C₄	#14519763
commutator	C₂²×C₄×C₆₁	C₂³
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#344	C₂
socle	C₂×C₆₁	#400
hypercenter	#344	D₆₁
hypocenter	C₆₁	#2103
LCS	G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #344

subgroup

G/H

center

C₄

#14519763

commutator

C₂²×C₄×C₆₁

C₂³

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#344

C₂

C₂×C₆₁

D₆₁

C₆₁

G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #344

N	H ≅ G/N	type
74. C₆₁	#2103	semidirect

H ≅ G/N

type

74. C₆₁

#2103

semidirect

Subgroups — #21447402

Conjugacy classes of subgroups

Complements