Group #21460747 — subgroups

Subgroups — #21460747

Order 7808.

170 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 36 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	#16840607	C₂	1	2	yes	maximal, complemented
2	#16839665	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#92420	—	2	2	no	—
4	C₂×C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
5	C₂×C₂²⋊Dic₆₁	—	2	2	no	—
6	C₂×C₄×Dic₆₁	C₄	1	1	yes	characteristic
7	C₂²×D₄×C₆₁	C₄	1	1	yes	characteristic
8	C₂⁴×C₆₁	—	2	1	no	—
9	C₂×D₄×C₆₁	—	2	1	no	—
10	C₂×D₄×C₆₁	—	4	1	no	—
11	C₂×D₄×C₆₁	—	4	1	no	—
12	C₂×D₄×C₆₁	C₈	1	2	yes	complemented
13	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
14	C₂²×Dic₆₁	—	2	1	no	—
15	C₂²×Dic₆₁	D₄	1	2	yes	—
16	C₂×#92420	—	4	2	no	—
17	C₂²⋊Dic₆₁	—	4	4	no	—
18	C₄⋊Dic₆₁	—	4	1	no	—
19	C₄×Dic₆₁	—	4	1	no	—
20	C₂³×C₆₁	—	2	2	no	—
21	C₂³×C₆₁	—	4	2	no	—
22	C₂³×C₆₁	—	4	2	no	—
23	C₂³×C₆₁	—	4	1	no	—
24	C₂³×C₆₁	—	4	1	no	—
25	C₂³×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
26	D₄×C₆₁	—	4	2	no	—
27	D₄×C₆₁	—	4	2	no	—
28	C₂×C₄×C₆₁	—	2	1	no	—
29	C₂×C₄×C₆₁	—	2	1	no	—
30	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
32	C₂×Dic₆₁	—	2	2	no	—
33	C₂×Dic₆₁	—	2	2	no	—
34	C₂×Dic₆₁	—	4	1	no	—
35	C₂×Dic₆₁	—	4	1	no	—
36	C₂×Dic₆₁	—	4	2	no	—
37	#92420	—	8	2	no	—
38	C₂²×C₆₁	—	2	1	no	—
39	C₂²×C₆₁	—	2	1	no	—
40	C₂²×C₆₁	—	4	4	no	—
41	C₂²×C₆₁	—	4	2	no	—
42	C₂²×C₆₁	—	8	2	no	—
43	C₂²×C₆₁	—	8	1	no	—
44	C₂²×C₆₁	—	8	1	no	—
45	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
46	C₂²×C₆₁	#99	1	1	yes	characteristic
47	C₂²×C₆₁	#100	1	1	yes	characteristic
48	C₄×C₆₁	—	2	1	no	—
49	C₄×C₆₁	—	2	1	no	—
50	Dic₆₁	—	4	2	no	—
51	Dic₆₁	—	4	2	no	—
52	#1318	—	61	1	no	maximal, Sylow
53	C₂×C₆₁	—	2	1	no	—
54	C₂×C₆₁	—	2	1	no	—
55	C₂×C₆₁	—	8	2	no	—
56	C₂×C₆₁	#323	1	1	yes	characteristic
57	C₂×C₆₁	#353	1	1	yes	characteristic
58	C₂×C₆₁	#355	1	1	yes	characteristic
59	#390	—	61	1	no	—
60	#324	—	61	2	no	—
61	C₆₁	#1318	1	1	yes	characteristic, complemented, Sylow
62	C₂²×D₄	#6923	1	1	yes	characteristic
63	C₂×C₄⋊C₄	—	61	1	no	—
64	C₂×C₂²⋊C₄	—	122	2	no	—
65	C₂×C₄²	—	61	1	no	—
66	C₂²⋊C₈	—	122	2	no	—
67	C₂⁴	—	2	1	no	—
68	C₂×D₄	—	2	1	no	—
69	C₂×D₄	—	4	1	no	—
70	C₂×D₄	—	4	1	no	—
71	C₂×D₄	#92420	1	2	yes	complemented
72	C₂²×C₄	—	61	2	no	—
73	C₂²×C₄	—	122	1	no	—
74	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
75	C₂×C₈	—	244	2	no	—
76	C₄⋊C₄	—	244	1	no	—
77	C₂²⋊C₄	—	244	4	no	—
78	C₄²	—	244	1	no	—
79	C₂³	—	2	2	no	—
80	C₂³	—	4	2	no	—
81	C₂³	—	4	2	no	—
82	C₂³	—	4	1	no	—
83	C₂³	—	4	1	no	—
84	C₂³	C₂²⋊#6923	1	1	yes	characteristic
85	D₄	—	4	2	no	—
86	D₄	—	4	2	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	122	2	no	—
90	C₂×C₄	—	122	2	no	—
91	C₂×C₄	—	244	1	no	—
92	C₂×C₄	—	244	1	no	—
93	C₂×C₄	—	244	2	no	—
94	C₂×C₄	C₂×#92420	1	1	yes	characteristic
95	C₂×C₄	#11758217	1	1	yes	characteristic
96	C₈	—	488	2	no	—
97	C₂²	—	2	1	no	—
98	C₂²	—	2	1	no	—
99	C₂²	—	4	4	no	—
100	C₂²	—	4	2	no	—
101	C₂²	—	8	2	no	—
102	C₂²	—	8	1	no	—
103	C₂²	—	8	1	no	—
104	C₂²	C₂²⋊#92420	1	1	yes	characteristic
105	C₂²	#14519835	1	1	yes	characteristic
106	C₂²	#14519837	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	2	1	no	—
109	C₄	—	244	2	no	—
110	C₄	—	244	2	no	—
111	C₂	—	2	1	no	—
112	C₂	—	2	1	no	—
113	C₂	—	8	2	no	—
114	C₂	#16840605	1	1	yes	characteristic
115	C₂	#16840666	1	1	yes	characteristic
116	C₂	#16840670	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840607

C₂

yes

maximal, complemented

#16839665

C₂

yes

maximal, characteristic

C₂²⋊#92420

—

C₂×C₄⋊Dic₆₁

C₂²

yes

characteristic

C₂×C₂²⋊Dic₆₁

—

C₂×C₄×Dic₆₁

C₄

yes

characteristic

C₂²×D₄×C₆₁

C₄

yes

characteristic

C₂⁴×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

C₈

yes

complemented

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

—

C₂²×Dic₆₁

D₄

yes

—

C₂×#92420

—

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

C₂²⋊C₄

yes

characteristic

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

#92420

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂²⋊C₈

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

#1318

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

C₆₁

#1318

yes

characteristic, complemented, Sylow

C₂²×D₄

#6923

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

122

—

C₂×C₄²

—

C₂²⋊C₈

—

122

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

#92420

yes

complemented

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

244

—

C₄⋊C₄

—

244

—

C₂²⋊C₄

—

244

—

C₄²

—

244

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²⋊#6923

yes

characteristic

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

488

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₂²⋊#92420

yes

characteristic

105

C₂²

#14519835

yes

characteristic

106

C₂²

#14519837

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

244

—

110

C₄

—

244

—

111

C₂

—

112

C₂

—

113

C₂

—

114

C₂

#16840605

yes

characteristic

115

C₂

#16840666

yes

characteristic

116

C₂

#16840670

yes

characteristic

	subgroup	G/H
center	C₂²	#14519835
commutator	C₂×C₄×C₆₁	C₂×C₈
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂²×D₄×C₆₁	C₄
socle	C₂²×C₆₁	#99
hypercenter	C₂²×D₄	#6923
hypocenter	C₆₁	#1318
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×D₄

subgroup

G/H

center

C₂²

#14519835

commutator

C₂×C₄×C₆₁

C₂×C₈

Frattini

C₂²×C₄

C₂×#6923

Fitting

C₂²×D₄×C₆₁

C₄

C₂²×C₆₁

C₂²×D₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×D₄

N	H ≅ G/N	type
1. #16840607	C₂	semidirect
12. C₂×D₄×C₆₁	C₈	semidirect
61. C₆₁	#1318	semidirect
71. C₂×D₄	#92420	semidirect

H ≅ G/N

type

1. #16840607

C₂

semidirect

12. C₂×D₄×C₆₁

C₈

semidirect

61. C₆₁

#1318

semidirect

71. C₂×D₄

#92420

semidirect

Subgroups — #21460747

Conjugacy classes of subgroups

Complements