Group #21461376 — subgroups

Subgroups — #21461376

Order 7808.

184 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 78 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	#16840765	C₂	1	2	yes	maximal
2	#16840626	C₂	1	2	yes	maximal, complemented
3	#16840625	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11758217	—	2	2	no	—
6	#14519844	—	2	2	no	—
7	C₄⋊#92420	C₂²	1	4	yes	—
8	C₂²×#92418	C₄	1	1	yes	characteristic
9	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
10	C₈×Dic₆₁	C₄	1	1	yes	characteristic
11	C₈×Dic₆₁	C₄	1	1	yes	characteristic
12	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
13	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
17	C₂²×Dic₆₁	Q₈	1	1	yes	characteristic
18	#11758217	—	4	4	no	—
19	C₂×#92420	—	2	4	no	—
20	C₂×C₈×C₆₁	—	2	2	no	—
21	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₆₁	D₄	1	1	yes	characteristic
25	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
26	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
27	C₂×#92418	—	2	2	no	—
28	C₂×#92418	C₂×C₄	1	1	yes	characteristic
29	C₂×#92418	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₆₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₆₁	—	2	1	no	—
32	C₂×C₄×C₆₁	—	2	1	no	—
33	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₆₁	—	2	2	no	—
36	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
37	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₆₁	D₈	1	2	yes	—
39	C₂×Dic₆₁	Q₁₆	1	2	yes	—
40	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
42	#92420	—	4	4	no	—
43	C₈×C₆₁	—	2	1	no	—
44	C₈×C₆₁	M₁₆	1	2	yes	complemented
45	#92418	—	2	1	no	—
46	#92418	M₁₆	1	2	yes	complemented
47	C₂²×C₆₁	—	2	1	no	—
48	C₂²×C₆₁	—	2	1	no	—
49	C₂²×C₆₁	#107	1	2	yes	—
50	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₄×C₆₁	—	2	1	no	—
52	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
53	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
54	Dic₆₁	—	2	1	no	—
55	Dic₆₁	#107	1	2	yes	—
56	Dic₆₁	#108	1	2	yes	—
57	Dic₆₁	C₂×D₈	1	1	yes	characteristic
58	Dic₆₁	C₂×Q₁₆	1	1	yes	characteristic
59	#1567	—	61	1	no	maximal, Sylow
60	C₂×C₆₁	—	2	2	no	—
61	C₂×C₆₁	#423	1	1	yes	characteristic
62	C₂×C₆₁	C₂×#107	1	1	yes	characteristic
63	C₂×C₆₁	C₂×#108	1	1	yes	characteristic
64	#423	—	61	2	no	—
65	C₂×C₄×C₈	—	61	1	no	—
66	#335	—	61	2	no	—
67	#335	—	61	2	no	—
68	C₆₁	#1567	1	1	yes	characteristic, complemented, Sylow
69	C₂×M₁₆	—	122	2	no	—
70	C₂²×C₈	—	61	1	no	—
71	C₂²×C₈	#6923	1	1	yes	characteristic
72	C₂×C₄²	—	61	1	no	—
73	C₄⋊C₈	—	61	4	no	—
74	C₄⋊C₈	—	122	2	no	—
75	C₄×C₈	—	61	1	no	—
76	C₄×C₈	—	61	1	no	—
77	C₄×C₈	—	61	1	no	—
78	C₄×C₈	—	61	1	no	—
79	C₂²×C₄	—	61	1	no	—
80	C₂²×C₄	—	61	1	no	—
81	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
82	M₁₆	—	244	4	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	61	1	no	—
85	C₂×C₈	—	61	1	no	—
86	C₂×C₈	—	122	2	no	—
87	C₂×C₈	—	122	4	no	—
88	C₂×C₈	C₂×#6923	1	1	yes	characteristic
89	C₂×C₈	C₂×#6923	1	1	yes	characteristic
90	C₄²	—	61	1	no	—
91	C₄²	—	61	1	no	—
92	C₄²	—	61	1	no	—
93	C₄²	—	61	1	no	—
94	C₂³	C₄⋊#6923	1	1	yes	characteristic
95	C₂×C₄	—	2	1	no	—
96	C₂×C₄	—	2	1	no	—
97	C₂×C₄	—	61	2	no	—
98	C₂×C₄	—	61	2	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	2	no	—
104	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
105	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
106	C₈	—	2	1	no	—
107	C₈	—	61	2	no	—
108	C₈	—	122	1	no	—
109	C₈	—	244	4	no	—
110	C₈	#11758217	1	2	yes	complemented
111	C₂²	—	2	1	no	—
112	C₂²	—	2	1	no	—
113	C₂²	#14519846	1	2	yes	—
114	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
115	C₄	—	2	1	no	—
116	C₄	—	61	2	no	—
117	C₄	—	61	1	no	—
118	C₄	—	61	1	no	—
119	C₄	—	61	2	no	—
120	C₄	—	122	1	no	—
121	C₄	C₂×#11758217	1	1	yes	characteristic
122	C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	#16840765	1	1	yes	characteristic
125	C₂	C₂×#14519846	1	1	yes	characteristic
126	C₂	D₆₁⋊#108	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840765

C₂

yes

maximal

#16840626

C₂

yes

maximal, complemented

#16840625

C₂

yes

maximal, complemented

C₂×C₈×Dic₆₁

C₂

yes

maximal, characteristic

C₂×#11758217

—

#14519844

—

C₄⋊#92420

C₂²

yes

—

C₂²×#92418

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

C₈×Dic₆₁

C₄

yes

characteristic

C₈×Dic₆₁

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₂²×C₈×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

D₄

yes

characteristic

C₂²×Dic₆₁

Q₈

yes

characteristic

#11758217

—

C₂×#92420

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₄×Dic₆₁

C₂³

yes

characteristic

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂³×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

D₈

yes

—

C₂×Dic₆₁

Q₁₆

yes

—

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

C₂×Q₈

yes

characteristic

#92420

—

C₈×C₆₁

—

C₈×C₆₁

M₁₆

yes

complemented

#92418

—

#92418

M₁₆

yes

complemented

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#107

yes

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

#107

yes

—

Dic₆₁

#108

yes

—

Dic₆₁

C₂×D₈

yes

characteristic

Dic₆₁

C₂×Q₁₆

yes

characteristic

#1567

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₄×C₈

—

#335

—

#335

—

C₆₁

#1567

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

122

—

C₂²×C₈

—

C₂²×C₈

#6923

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄⋊#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

C₄⋊#6923

yes

characteristic

105

C₂×C₄

C₂²×#6923

yes

characteristic

106

C₈

—

107

C₈

—

108

C₈

—

122

—

109

C₈

—

244

—

110

C₈

#11758217

yes

complemented

111

C₂²

—

112

C₂²

—

113

C₂²

#14519846

yes

—

114

C₂²

C₂×C₄⋊#6923

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

122

—

121

C₄

C₂×#11758217

yes

characteristic

122

C₄

D₆₁⋊M₁₆

yes

characteristic

123

C₂

—

124

C₂

#16840765

yes

characteristic

125

C₂

C₂×#14519846

yes

characteristic

126

C₂

D₆₁⋊#108

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₂²×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	C₂²×C₈	#6923
hypocenter	C₆₁	#1567
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₂²×C₈×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₄⋊C₄

C₂²×C₈

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
2. #16840626	C₂	semidirect
3. #16840625	C₂	semidirect
44. C₈×C₆₁	M₁₆	semidirect
46. #92418	M₁₆	semidirect
68. C₆₁	#1567	semidirect
110. C₈	#11758217	semidirect

H ≅ G/N

type

2. #16840626

C₂

semidirect

3. #16840625

C₂

semidirect

44. C₈×C₆₁

M₁₆

semidirect

46. #92418

M₁₆

semidirect

68. C₆₁

#1567

semidirect

110. C₈

#11758217

semidirect

Subgroups — #21461376

Conjugacy classes of subgroups

Complements