Group #21460648 — subgroups

Subgroups — #21460648

Order 7808.

180 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 74 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	D₆₁⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₄×D₆₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×D₆₁⋊C₈	—	2	1	no	—
5	C₂×D₆₁⋊C₈	C₄	1	2	yes	—
6	#14519844	—	2	1	no	—
7	C₄⋊#92420	C₄	1	2	yes	—
8	C₄×#92420	—	2	1	no	—
9	C₄×#92420	—	2	1	no	—
10	C₂×C₈×D₆₁	—	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	—	2	2	no	—
21	D₆₁⋊C₈	—	4	1	no	—
22	D₆₁⋊C₈	—	4	1	no	—
23	D₆₁⋊C₈	C₈	1	4	yes	complemented
24	C₂×C₈×C₆₁	—	2	1	no	—
25	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₆₁	D₄	1	1	yes	characteristic
28	C₄×Dic₆₁	D₄	1	1	yes	characteristic
29	C₂×#92418	—	2	1	no	—
30	C₈×D₆₁	—	4	1	no	—
31	C₈×D₆₁	—	4	1	no	—
32	C₂²×D₆₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
36	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
39	C₄×D₆₁	—	2	2	no	—
40	C₄×D₆₁	C₂×C₈	1	2	yes	—
41	C₄×D₆₁	M₁₆	1	2	yes	—
42	C₄×D₆₁	D₈	1	1	yes	characteristic
43	C₄×D₆₁	SD₁₆	1	1	yes	characteristic
44	C₄×D₆₁	SD₁₆	1	1	yes	characteristic
45	C₄×D₆₁	Q₁₆	1	1	yes	characteristic
46	#92420	—	2	4	no	—
47	#92420	—	4	2	no	—
48	C₈×C₆₁	—	4	1	no	—
49	#92418	—	4	1	no	—
50	C₂²×C₆₁	#95	1	1	yes	characteristic
51	C₂×D₆₁	C₄⋊C₈	1	2	yes	—
52	C₂×D₆₁	#106	1	1	yes	characteristic
53	C₂×D₆₁	#107	1	1	yes	characteristic
54	C₂×D₆₁	#108	1	2	yes	—
55	C₄×C₆₁	—	2	1	no	—
56	C₄×C₆₁	C₄×C₈	1	1	yes	characteristic
57	C₄×C₆₁	#97	1	1	yes	characteristic
58	C₄×C₆₁	#102	1	1	yes	characteristic
59	C₄×C₆₁	#103	1	1	yes	characteristic
60	Dic₆₁	—	2	1	no	—
61	Dic₆₁	C₂²⋊C₈	1	2	yes	—
62	Dic₆₁	#102	1	1	yes	characteristic
63	Dic₆₁	#103	1	1	yes	characteristic
64	#1277	—	61	1	no	maximal, Sylow
65	C₂×C₆₁	#336	1	1	yes	characteristic
66	C₂×C₆₁	#340	1	1	yes	characteristic
67	C₂×C₆₁	#341	1	1	yes	characteristic
68	D₆₁	#334	1	2	yes	—
69	D₆₁	#335	1	2	yes	—
70	C₂×C₄⋊C₈	—	61	1	no	—
71	C₂×C₄⋊C₈	—	61	1	no	—
72	C₂×C₄×C₈	—	61	1	no	—
73	C₆₁	#1277	1	1	yes	characteristic, complemented, Sylow
74	C₂²×C₈	—	61	2	no	—
75	C₂²×C₈	—	122	1	no	—
76	C₂²×C₈	—	122	1	no	—
77	C₂×C₄²	—	61	1	no	—
78	C₄⋊C₈	—	61	2	no	—
79	C₄⋊C₈	—	61	1	no	—
80	C₄⋊C₈	—	122	1	no	—
81	C₄⋊C₈	—	122	1	no	—
82	C₄⋊C₈	#6923	1	1	yes	characteristic
83	C₄×C₈	—	122	1	no	—
84	C₄×C₈	—	122	1	no	—
85	C₂²×C₄	—	61	1	no	—
86	C₂²×C₄	—	61	1	no	—
87	C₂²×C₄	—	61	1	no	—
88	C₂×C₈	—	2	1	no	—
89	C₂×C₈	—	61	4	no	—
90	C₂×C₈	—	122	2	no	—
91	C₂×C₈	—	122	2	no	—
92	C₂×C₈	—	122	2	no	—
93	C₂×C₈	—	122	1	no	—
94	C₂×C₈	—	244	1	no	—
95	C₂×C₈	—	244	1	no	—
96	C₂×C₈	—	244	1	no	—
97	C₂×C₈	—	244	1	no	—
98	C₄²	—	61	1	no	—
99	C₄²	—	61	1	no	—
100	C₄²	—	61	1	no	—
101	C₄²	C₂×#6923	1	1	yes	characteristic
102	C₂³	—	61	1	no	—
103	C₂×C₄	—	61	1	no	—
104	C₂×C₄	—	61	1	no	—
105	C₂×C₄	—	61	2	no	—
106	C₂×C₄	—	61	2	no	—
107	C₂×C₄	—	61	1	no	—
108	C₂×C₄	—	61	1	no	—
109	C₂×C₄	—	61	1	no	—
110	C₂×C₄	—	61	1	no	—
111	C₂×C₄	—	61	1	no	—
112	C₂×C₄	—	122	2	no	—
113	C₂×C₄	C₄×#6923	1	1	yes	characteristic
114	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
115	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
116	C₈	—	4	1	no	—
117	C₈	—	122	4	no	—
118	C₈	—	244	2	no	—
119	C₈	—	244	1	no	—
120	C₂²	—	61	2	no	—
121	C₂²	—	61	1	no	—
122	C₂²	—	61	1	no	—
123	C₂²	—	61	2	no	—
124	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
125	C₄	—	2	1	no	—
126	C₄	—	61	2	no	—
127	C₄	—	61	1	no	—
128	C₄	—	61	1	no	—
129	C₄	—	122	1	no	—
130	C₄	C₈×#6923	1	1	yes	characteristic
131	C₄	#14519831	1	1	yes	characteristic
132	C₄	#14519839	1	1	yes	characteristic
133	C₄	#14519840	1	1	yes	characteristic
134	C₂	—	61	2	no	—
135	C₂	—	61	2	no	—
136	C₂	(C₂×#6923)⋊C₈	1	1	yes	characteristic
137	C₂	#16840635	1	1	yes	characteristic
138	C₂	#16840637	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₆₁⋊(C₄⋊C₈)

C₂

yes

maximal, characteristic

C₄×D₆₁⋊C₈

C₂

yes

maximal, characteristic

C₄⋊C₈×D₆₁

C₂

yes

maximal, characteristic

C₂×D₆₁⋊C₈

—

C₂×D₆₁⋊C₈

C₄

yes

—

#14519844

—

C₄⋊#92420

C₄

yes

—

C₄×#92420

—

C₄×#92420

—

C₂×C₈×D₆₁

—

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

—

D₆₁⋊C₈

—

D₆₁⋊C₈

C₈

yes

complemented

C₂×C₈×C₆₁

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₂×#92418

—

C₈×D₆₁

—

C₈×D₆₁

—

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

C₂×C₈

yes

—

C₄×D₆₁

M₁₆

yes

—

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

C₄⋊C₈

yes

—

C₂×D₆₁

yes

C₂×D₆₁

yes

C₂×D₆₁

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₄×C₈

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

C₂²⋊C₈

yes

—

Dic₆₁

yes

Dic₆₁

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

yes

—

D₆₁

#335

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

C₆₁

#1277

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

122

—

C₂²×C₈

—

122

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₄⋊C₈

#6923

yes

characteristic

C₄×C₈

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

244

—

C₂×C₈

—

244

—

C₂×C₈

—

244

—

C₂×C₈

—

244

—

C₄²

—

C₄²

—

100

C₄²

—

101

C₄²

C₂×#6923

yes

characteristic

102

C₂³

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

122

—

113

C₂×C₄

C₄×#6923

yes

characteristic

114

C₂×C₄

C₄⋊#6923

yes

characteristic

115

C₂×C₄

C₂²⋊#6923

yes

characteristic

116

C₈

—

117

C₈

—

122

—

118

C₈

—

244

—

119

C₈

—

244

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

122

—

130

C₄

C₈×#6923

yes

characteristic

131

C₄

#14519831

yes

characteristic

132

C₄

#14519839

yes

characteristic

133

C₄

#14519840

yes

characteristic

134

C₂

—

135

C₂

—

136

C₂

(C₂×#6923)⋊C₈

yes

characteristic

137

C₂

#16840635

yes

characteristic

138

C₂

#16840637

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#6923
commutator	C₄×C₆₁	C₄×C₈
Frattini	C₄²	C₂×#6923
Fitting	C₄⋊C₈×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	C₄⋊C₈	#6923
hypocenter	C₆₁	#1277
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

subgroup

G/H

center

C₂×C₄

C₂²⋊#6923

commutator

C₄×C₆₁

C₄×C₈

Frattini

C₄²

C₂×#6923

Fitting

C₄⋊C₈×C₆₁

C₄

C₂²×C₆₁

C₄⋊C₈

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

N	H ≅ G/N	type
23. D₆₁⋊C₈	C₈	semidirect
73. C₆₁	#1277	semidirect

H ≅ G/N

type

23. D₆₁⋊C₈

C₈

semidirect

73. C₆₁

#1277

semidirect

Subgroups — #21460648

Conjugacy classes of subgroups

Complements