Group #21460709 — subgroups

Subgroups — #21460709

Order 7808.

148 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 54 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	#16840780	C₂	1	1	yes	maximal, characteristic
2	D₆₁⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#16839784	C₂	1	1	yes	maximal, characteristic
4	C₂×D₆₁⋊C₈	—	2	1	no	—
5	#14519844	—	2	1	no	—
6	#14519844	C₄	1	2	yes	—
7	C₄⋊#92420	—	2	1	no	—
8	#14519834	C₄	1	2	yes	—
9	C₄×#92420	—	2	1	no	—
10	C₂×#11758189	—	2	1	no	—
11	C₄²×D₆₁	C₂²	1	1	yes	characteristic
12	C₄⋊#92418	C₄	1	1	yes	characteristic
13	#14519706	—	2	1	no	—
14	C₄⋊C₈×C₆₁	C₄	1	1	yes	characteristic
15	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
17	C₂×C₄×D₆₁	Q₈	1	1	yes	characteristic
18	C₂×#92420	—	2	2	no	—
19	C₂×#92420	—	2	2	no	—
20	D₆₁⋊C₈	—	4	1	no	—
21	D₆₁⋊C₈	—	4	1	no	—
22	C₂×C₈×C₆₁	—	2	1	no	—
23	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₆₁	D₄	1	1	yes	characteristic
26	C₄×Dic₆₁	D₄	1	1	yes	characteristic
27	C₂×#92418	—	2	1	no	—
28	#11758189	—	4	1	no	—
29	#11758189	—	4	1	no	—
30	C₂²×D₆₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
34	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
37	C₄×D₆₁	—	2	2	no	—
38	C₄×D₆₁	—	4	1	no	—
39	C₄×D₆₁	D₈	1	1	yes	characteristic
40	C₄×D₆₁	SD₁₆	1	1	yes	characteristic
41	C₄×D₆₁	SD₁₆	1	1	yes	characteristic
42	C₄×D₆₁	Q₁₆	1	1	yes	characteristic
43	#92420	—	4	2	no	—
44	#92420	—	4	2	no	—
45	C₈×C₆₁	—	4	1	no	—
46	#92418	—	4	1	no	—
47	C₂²×C₆₁	#95	1	1	yes	characteristic
48	C₂×D₆₁	—	2	1	no	—
49	C₂×D₆₁	—	2	1	no	—
50	C₂×D₆₁	#106	1	1	yes	characteristic
51	C₂×D₆₁	#107	1	1	yes	characteristic
52	C₄×C₆₁	—	2	1	no	—
53	C₄×C₆₁	—	2	1	no	—
54	C₄×C₆₁	#102	1	1	yes	characteristic
55	C₄×C₆₁	#103	1	1	yes	characteristic
56	Dic₆₁	—	2	1	no	—
57	Dic₆₁	#102	1	1	yes	characteristic
58	Dic₆₁	#103	1	1	yes	characteristic
59	Dic₆₁	#108	1	2	yes	—
60	#1301	—	61	1	no	maximal, Sylow
61	C₂×C₆₁	#340	1	1	yes	characteristic
62	C₂×C₆₁	#341	1	1	yes	characteristic
63	C₂×C₆₁	#344	1	1	yes	characteristic
64	D₆₁	—	2	1	no	—
65	D₆₁	—	2	1	no	—
66	#431	—	61	1	no	—
67	#423	—	61	1	no	—
68	C₂×C₄⋊C₈	—	61	1	no	—
69	C₆₁	#1301	1	1	yes	characteristic, complemented, Sylow
70	C₂×M₁₆	—	122	1	no	—
71	C₂²×C₈	—	122	1	no	—
72	C₂×C₄²	—	61	1	no	—
73	C₄⋊C₈	—	61	2	no	—
74	C₄⋊C₈	—	61	1	no	—
75	C₄⋊C₈	—	122	1	no	—
76	C₄⋊C₈	—	122	1	no	—
77	C₄⋊C₈	—	122	1	no	—
78	C₄⋊C₈	#6923	1	1	yes	characteristic
79	C₂²⋊C₈	—	61	2	no	—
80	C₄×C₈	—	122	1	no	—
81	C₂²×C₄	—	61	1	no	—
82	C₂²×C₄	—	61	1	no	—
83	C₂²×C₄	—	61	1	no	—
84	M₁₆	—	244	1	no	—
85	M₁₆	—	244	1	no	—
86	C₂×C₈	—	2	1	no	—
87	C₂×C₈	—	122	2	no	—
88	C₂×C₈	—	122	2	no	—
89	C₂×C₈	—	122	1	no	—
90	C₂×C₈	—	244	1	no	—
91	C₂×C₈	—	244	1	no	—
92	C₄²	—	61	1	no	—
93	C₄²	—	61	1	no	—
94	C₄²	—	61	1	no	—
95	C₄²	C₂×#6923	1	1	yes	characteristic
96	C₂³	—	61	1	no	—
97	C₂×C₄	—	61	1	no	—
98	C₂×C₄	—	61	1	no	—
99	C₂×C₄	—	61	1	no	—
100	C₂×C₄	—	61	1	no	—
101	C₂×C₄	—	61	1	no	—
102	C₂×C₄	—	61	1	no	—
103	C₂×C₄	—	61	1	no	—
104	C₂×C₄	—	122	2	no	—
105	C₂×C₄	—	244	1	no	—
106	C₂×C₄	C₄×#6923	1	1	yes	characteristic
107	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
108	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
109	C₈	—	4	1	no	—
110	C₈	—	244	2	no	—
111	C₈	—	244	2	no	—
112	C₈	—	244	1	no	—
113	C₂²	—	61	1	no	—
114	C₂²	—	61	1	no	—
115	C₂²	—	122	1	no	—
116	C₂²	—	122	1	no	—
117	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
118	C₄	—	2	1	no	—
119	C₄	—	2	1	no	—
120	C₄	—	61	1	no	—
121	C₄	—	61	1	no	—
122	C₄	—	61	2	no	—
123	C₄	—	122	1	no	—
124	C₄	#14519839	1	1	yes	characteristic
125	C₄	#14519840	1	1	yes	characteristic
126	C₂	—	122	1	no	—
127	C₂	—	122	1	no	—
128	C₂	#16840635	1	1	yes	characteristic
129	C₂	#16840637	1	1	yes	characteristic
130	C₂	#16840644	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840780

C₂

yes

maximal, characteristic

D₆₁⋊(C₄⋊C₈)

C₂

yes

maximal, characteristic

#16839784

C₂

yes

maximal, characteristic

C₂×D₆₁⋊C₈

—

#14519844

—

#14519844

C₄

yes

—

C₄⋊#92420

—

#14519834

C₄

yes

—

C₄×#92420

—

C₂×#11758189

—

C₄²×D₆₁

C₂²

yes

characteristic

C₄⋊#92418

C₄

yes

characteristic

#14519706

—

C₄⋊C₈×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂×C₄×D₆₁

Q₈

yes

characteristic

C₂×#92420

—

C₂×#92420

—

D₆₁⋊C₈

—

D₆₁⋊C₈

—

C₂×C₈×C₆₁

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

—

—

—

C₂²×D₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

D₈

yes

characteristic

C₄×D₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

Q₁₆

yes

characteristic

#92420

—

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

#95

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

yes

C₂×D₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

yes

Dic₆₁

yes

Dic₆₁

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

D₆₁

—

#431

—

#423

—

C₂×C₄⋊C₈

—

C₆₁

#1301

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

122

—

C₂²×C₈

—

122

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₄⋊C₈

#6923

yes

characteristic

C₂²⋊C₈

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

244

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

244

—

C₂×C₈

—

244

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

122

—

105

C₂×C₄

—

244

—

106

C₂×C₄

C₄×#6923

yes

characteristic

107

C₂×C₄

C₄⋊#6923

yes

characteristic

108

C₂×C₄

C₂²⋊#6923

yes

characteristic

109

C₈

—

110

C₈

—

244

—

111

C₈

—

244

—

112

C₈

—

244

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

122

—

116

C₂²

—

122

—

117

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

122

—

124

C₄

#14519839

yes

characteristic

125

C₄

#14519840

yes

characteristic

126

C₂

—

122

—

127

C₂

—

122

—

128

C₂

#16840635

yes

characteristic

129

C₂

#16840637

yes

characteristic

130

C₂

#16840644

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#6923
commutator	C₂×C₄×C₆₁	C₄²
Frattini	C₄²	C₂×#6923
Fitting	C₄⋊C₈×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	C₄⋊C₈	#6923
hypocenter	C₆₁	#1301
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

subgroup

G/H

center

C₂×C₄

C₂²⋊#6923

commutator

C₂×C₄×C₆₁

C₄²

Frattini

C₄²

C₂×#6923

Fitting

C₄⋊C₈×C₆₁

C₄

C₂²×C₆₁

C₄⋊C₈

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

N	H ≅ G/N	type
69. C₆₁	#1301	semidirect

H ≅ G/N

type

69. C₆₁

#1301

semidirect

Subgroups — #21460709

Conjugacy classes of subgroups

Complements