Group #21460678 — subgroups

Subgroups — #21460678

Order 7808.

152 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 44 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	#16840783	C₂	1	1	yes	maximal, characteristic
2	C₄×#11758217	C₂	1	1	yes	maximal, characteristic
3	#16839629	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758217	—	2	1	no	—
5	C₄⋊#92420	—	2	1	no	—
6	C₂²⋊#92420	—	2	1	no	—
7	#14519832	—	2	1	no	—
8	#14519832	C₄	1	2	yes	complemented
9	C₄×#92420	C₄	1	2	yes	complemented
10	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
11	#14519684	—	2	1	no	—
12	#14519684	—	2	1	no	—
13	#14519684	C₄	1	1	yes	characteristic
14	#95×C₆₁	C₄	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	—	2	1	no	—
16	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₆₁	—	2	1	no	—
18	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
19	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
20	#11758217	—	2	2	no	—
21	#11758217	—	2	2	no	—
22	C₂×#92420	—	2	2	no	—
23	C₂×#92420	—	2	2	no	—
24	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₆₁	D₄	1	1	yes	characteristic
27	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
28	C₂³×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	—	4	1	no	—
30	C₂×C₄×C₆₁	—	4	1	no	—
31	C₂×C₄×C₆₁	—	4	1	no	—
32	C₂×C₄×C₆₁	—	4	1	no	—
33	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
35	C₂×Dic₆₁	—	2	1	no	—
36	C₂×Dic₆₁	—	2	1	no	—
37	C₂×Dic₆₁	—	4	1	no	—
38	C₂×Dic₆₁	—	4	1	no	—
39	C₂×Dic₆₁	—	4	1	no	—
40	C₂×Dic₆₁	—	4	1	no	—
41	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
44	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
45	#92420	—	2	4	no	—
46	#92420	—	4	2	no	—
47	C₂²×C₆₁	—	2	1	no	—
48	C₂²×C₆₁	—	2	1	no	—
49	C₂²×C₆₁	#95	1	1	yes	characteristic
50	C₂²×C₆₁	#104	1	1	yes	characteristic
51	C₂²×C₆₁	#104	1	1	yes	characteristic
52	C₄×C₆₁	—	2	1	no	—
53	C₄×C₆₁	—	2	1	no	—
54	C₄×C₆₁	—	8	1	no	—
55	Dic₆₁	—	2	1	no	—
56	Dic₆₁	—	2	1	no	—
57	Dic₆₁	—	2	1	no	—
58	Dic₆₁	—	2	1	no	—
59	Dic₆₁	—	8	1	no	—
60	#1288	—	61	1	no	maximal, Sylow
61	C₂×C₆₁	—	2	1	no	—
62	C₂×C₆₁	—	2	1	no	—
63	C₂×C₆₁	H(3,ℤ/4)	1	1	yes	characteristic
64	C₂×C₆₁	#339	1	1	yes	characteristic
65	C₂×C₆₁	#344	1	1	yes	characteristic
66	#432	—	61	1	no	—
67	C₄×M₁₆	—	61	1	no	—
68	#383	—	61	1	no	—
69	C₆₁	#1288	1	1	yes	characteristic, complemented, Sylow
70	C₂×M₁₆	—	122	1	no	—
71	C₂×C₄²	—	61	1	no	—
72	C₄⋊C₈	—	122	1	no	—
73	C₂²⋊C₈	—	122	1	no	—
74	#97	—	61	2	no	—
75	#97	—	122	1	no	—
76	C₄×C₈	—	61	2	no	—
77	#95	—	61	1	no	—
78	#95	—	122	1	no	—
79	#95	—	122	1	no	—
80	#95	#6923	1	1	yes	characteristic
81	C₂²×C₄	—	2	1	no	—
82	C₂²×C₄	—	61	1	no	—
83	C₂²×C₄	—	61	1	no	—
84	C₂²×C₄	—	122	1	no	—
85	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
86	M₁₆	—	122	2	no	—
87	M₁₆	—	122	2	no	—
88	C₂×C₈	—	122	2	no	—
89	C₂×C₈	—	122	2	no	—
90	C₄²	—	61	1	no	—
91	C₄²	—	61	1	no	—
92	C₄²	—	61	1	no	—
93	C₄²	—	61	1	no	—
94	C₂³	C₂²⋊#6923	1	1	yes	characteristic
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	4	1	no	—
98	C₂×C₄	—	4	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	—	122	1	no	—
104	C₂×C₄	—	122	1	no	—
105	C₂×C₄	—	244	1	no	—
106	C₂×C₄	—	244	1	no	—
107	C₂×C₄	—	244	1	no	—
108	C₂×C₄	—	244	1	no	—
109	C₂×C₄	C₄×#6923	1	1	yes	characteristic
110	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
111	C₈	—	122	4	no	—
112	C₈	—	244	2	no	—
113	C₂²	—	2	1	no	—
114	C₂²	—	2	1	no	—
115	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
116	C₂²	#14519841	1	1	yes	characteristic
117	C₂²	#14519842	1	1	yes	characteristic
118	C₄	—	2	1	no	—
119	C₄	—	2	1	no	—
120	C₄	—	8	1	no	—
121	C₄	—	122	1	no	—
122	C₄	—	122	1	no	—
123	C₄	—	122	1	no	—
124	C₄	—	122	1	no	—
125	C₄	—	488	1	no	—
126	C₂	—	2	1	no	—
127	C₂	—	2	1	no	—
128	C₂	#16840629	1	1	yes	characteristic
129	C₂	#16840632	1	1	yes	characteristic
130	C₂	#16840643	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840783

C₂

yes

maximal, characteristic

C₄×#11758217

C₂

yes

maximal, characteristic

#16839629

C₂

yes

maximal, characteristic

—

—

—

—

C₄

yes

complemented

C₄×#92420

C₄

yes

complemented

C₂×C₄×Dic₆₁

C₂²

yes

—

—

C₄

yes

characteristic

#95×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

—

C₂²×Dic₆₁

D₄

yes

characteristic

C₂²×Dic₆₁

D₄

yes

—

—

—

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₂³×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

#92420

—

#92420

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

#1288

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₄×M₁₆

—

#383

—

C₆₁

#1288

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

122

—

C₂×C₄²

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

#97

—

#97

—

122

—

C₄×C₈

—

#95

—

#95

—

122

—

#95

—

122

—

#95

#6923

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂²⋊#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

122

—

104

C₂×C₄

—

122

—

105

C₂×C₄

—

244

—

106

C₂×C₄

—

244

—

107

C₂×C₄

—

244

—

108

C₂×C₄

—

244

—

109

C₂×C₄

C₄×#6923

yes

characteristic

110

C₂×C₄

C₄⋊#6923

yes

characteristic

111

C₈

—

122

—

112

C₈

—

244

—

113

C₂²

—

114

C₂²

—

115

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

116

C₂²

#14519841

yes

characteristic

117

C₂²

#14519842

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

—

122

C₄

—

122

—

123

C₄

—

122

—

124

C₄

—

122

—

125

C₄

—

488

—

126

C₂

—

127

C₂

—

128

C₂

#16840629

yes

characteristic

129

C₂

#16840632

yes

characteristic

130

C₂

#16840643

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#6923)⋊C₄
commutator	C₂×C₄×C₆₁	C₄²
Frattini	C₂²×C₄	C₂×#6923
Fitting	#95×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	#95	#6923
hypocenter	C₆₁	#1288
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #95

subgroup

G/H

center

C₂²

(C₂×#6923)⋊C₄

commutator

C₂×C₄×C₆₁

C₄²

Frattini

C₂²×C₄

C₂×#6923

Fitting

#95×C₆₁

C₄

C₂²×C₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #95

N	H ≅ G/N	type
8. #14519832	C₄	semidirect
9. C₄×#92420	C₄	semidirect
69. C₆₁	#1288	semidirect

H ≅ G/N

type

8. #14519832

C₄

semidirect

9. C₄×#92420

C₄

semidirect

69. C₆₁

#1288

semidirect

Subgroups — #21460678

Conjugacy classes of subgroups

Complements