Group #21451779 — subgroups

Subgroups — #21451779

Order 7808.

420 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 133 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	#16839691	C₂	1	6	yes	maximal, complemented
2	#16839686	C₂	1	2	yes	maximal, complemented
3	#16839664	C₂	1	3	yes	maximal
4	#16839660	C₂	1	3	yes	maximal, complemented
5	C₆₁×#376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₂₄₄	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₆₁	C₂²	1	3	yes	—
8	C₂×#11758196	C₂²	1	6	yes	—
9	C₂×#11758198	C₂²	1	6	yes	—
10	C₂×#11758198	C₂²	1	6	yes	—
11	#14519684	C₂²	1	6	yes	—
12	C₂×C₄²×C₆₁	C₂²	1	3	yes	—
13	#95×C₆₁	C₂²	1	1	yes	characteristic
14	#95×C₆₁	C₂²	1	3	yes	—
15	C₂³×D₆₁	C₂³	1	2	yes	—
16	C₂²×C₄×C₆₁	C₂³	1	3	yes	—
17	C₂²×C₄×C₆₁	C₂³	1	3	yes	—
18	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
19	C₂²×Dic₆₁	C₂³	1	6	yes	—
20	C₂×D₂₄₄	—	2	6	no	—
21	C₄²×C₆₁	—	2	6	no	—
22	#11758198	—	4	6	no	—
23	#11758198	—	4	6	no	—
24	C₄⋊Dic₆₁	—	2	6	no	—
25	#11758196	—	4	6	no	—
26	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
27	C₂²×D₆₁	—	2	6	no	—
28	C₂²×D₆₁	—	2	6	no	—
29	C₂²×D₆₁	—	2	2	no	—
30	C₂×C₄×C₆₁	—	2	3	no	—
31	C₂×C₄×C₆₁	—	2	3	no	—
32	C₂×C₄×C₆₁	—	2	3	no	—
33	C₂×C₄×C₆₁	—	2	3	no	—
34	C₂×C₄×C₆₁	—	2	3	no	—
35	C₂×C₄×C₆₁	—	2	3	no	—
36	C₂×C₄×C₆₁	#41	1	6	yes	—
37	C₂×Dic₆₁	—	2	6	no	—
38	C₂×Dic₆₁	—	2	6	no	—
39	C₂×Dic₆₁	—	2	6	no	—
40	D₂₄₄	—	4	4	no	—
41	C₂²×C₆₁	C₂×#41	1	3	yes	—
42	C₂²×C₆₁	H(5,𝔽₂)	1	3	yes	—
43	C₂²×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
44	C₂×D₆₁	—	4	2	no	—
45	C₂×D₆₁	—	4	6	no	—
46	C₂×D₆₁	—	4	6	no	—
47	C₄×C₆₁	—	4	3	no	—
48	C₄×C₆₁	—	4	3	no	—
49	C₄×C₆₁	#126	1	4	yes	—
50	Dic₆₁	—	4	6	no	—
51	#2644	—	61	1	no	maximal, Sylow
52	C₂×C₆₁	C₂×#126	1	1	yes	characteristic
53	C₂×C₆₁	#540	1	3	yes	—
54	C₂×C₆₁	#542	1	3	yes	—
55	D₆₁	—	8	2	no	—
56	#397	—	61	6	no	—
57	#396	—	61	2	no	—
58	#390	—	61	3	no	—
59	#389	—	61	3	no	—
60	#376	D₆₁	1	1	yes	characteristic, complemented
61	C₆₁	#2644	1	1	yes	characteristic, complemented, Sylow
62	C₂²×D₄	—	61	1	no	—
63	C₂×C₄⋊C₄	—	61	3	no	—
64	C₂×C₄⋊C₄	—	61	6	no	—
65	C₂×C₂²⋊C₄	—	61	6	no	—
66	C₂×C₂²⋊C₄	—	61	6	no	—
67	C₂×C₄²	C₂×D₆₁	1	3	yes	—
68	#95	—	61	6	no	—
69	#95	C₂×D₆₁	1	1	yes	characteristic
70	#95	C₂×D₆₁	1	3	yes	—
71	C₂⁴	—	61	2	no	—
72	C₂×D₄	—	122	6	no	—
73	C₂²×C₄	—	61	6	no	—
74	C₂²×C₄	C₂²×D₆₁	1	3	yes	—
75	C₂²×C₄	C₂²×D₆₁	1	3	yes	—
76	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
77	C₄⋊C₄	—	122	6	no	—
78	C₄⋊C₄	—	244	6	no	—
79	C₂²⋊C₄	—	244	6	no	—
80	C₂²⋊C₄	—	244	6	no	—
81	C₄²	—	2	6	no	—
82	C₂³	—	122	6	no	—
83	C₂³	—	122	6	no	—
84	C₂³	—	122	2	no	—
85	C₂³	C₂³×D₆₁	1	1	yes	characteristic
86	D₄	—	244	4	no	—
87	C₂×C₄	—	2	3	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	3	no	—
90	C₂×C₄	—	2	3	no	—
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	2	3	no	—
93	C₂×C₄	—	122	6	no	—
94	C₂×C₄	—	122	6	no	—
95	C₂×C₄	—	122	6	no	—
96	C₂×C₄	#11758222	1	6	yes	—
97	C₂²	—	244	2	no	—
98	C₂²	—	244	6	no	—
99	C₂²	—	244	6	no	—
100	C₂²	C₂×#11758222	1	3	yes	—
101	C₂²	#14519823	1	3	yes	—
102	C₂²	#14519824	1	1	yes	characteristic
103	C₄	—	4	3	no	—
104	C₄	—	4	3	no	—
105	C₄	—	244	6	no	—
106	C₄	#14519771	1	4	yes	—
107	C₂	—	488	2	no	—
108	C₂	C₂×#14519771	1	1	yes	characteristic
109	C₂	#16840367	1	3	yes	—
110	C₂	#16840383	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16839691

C₂

yes

maximal, complemented

#16839686

C₂

yes

maximal, complemented

#16839664

C₂

yes

maximal

#16839660

C₂

yes

maximal, complemented

C₆₁×#376

C₂

yes

maximal, characteristic, complemented

C₂²×D₂₄₄

C₂²

yes

characteristic

C₂×C₄⋊Dic₆₁

C₂²

yes

—

C₂×#11758196

C₂²

yes

—

C₂×#11758198

C₂²

yes

—

C₂×#11758198

C₂²

yes

—

#14519684

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

—

#95×C₆₁

C₂²

yes

characteristic

#95×C₆₁

C₂²

yes

—

C₂³×D₆₁

C₂³

yes

—

C₂²×C₄×C₆₁

C₂³

yes

—

C₂²×C₄×C₆₁

C₂³

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

C₂³

yes

—

C₂×D₂₄₄

—

C₄²×C₆₁

—

#11758198

—

#11758198

—

C₄⋊Dic₆₁

—

#11758196

—

C₂³×C₆₁

C₂⁴

yes

characteristic

C₂²×D₆₁

—

C₂²×D₆₁

—

C₂²×D₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

D₂₄₄

—

C₂²×C₆₁

C₂×#41

yes

—

C₂²×C₆₁

H(5,𝔽₂)

yes

—

C₂²×C₆₁

2₋¹⁺⁴

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#126

yes

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₆₁

#542

yes

—

D₆₁

—

—

—

—

—

D₆₁

yes

characteristic, complemented

C₆₁

#2644

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₆₁

yes

—

#95

—

#95

C₂×D₆₁

yes

characteristic

#95

C₂×D₆₁

yes

—

C₂⁴

—

C₂×D₄

—

122

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₂²⋊C₄

—

244

—

C₂²⋊C₄

—

244

—

C₄²

—

C₂³

—

122

—

C₂³

—

122

—

C₂³

—

122

—

C₂³

C₂³×D₆₁

yes

characteristic

D₄

—

244

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

#11758222

yes

—

C₂²

—

244

—

C₂²

—

244

—

C₂²

—

244

—

100

C₂²

C₂×#11758222

yes

—

101

C₂²

#14519823

yes

—

102

C₂²

#14519824

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

244

—

106

C₄

#14519771

yes

—

107

C₂

—

488

—

108

C₂

C₂×#14519771

yes

characteristic

109

C₂

#16840367

yes

—

110

C₂

#16840383

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₆₁
commutator, socle	C₂³×C₆₁	C₂⁴
Fitting	C₆₁×#376	C₂
hypercenter	#376	D₆₁
hypocenter	C₆₁	#2644
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₆₁

commutator, socle

C₂³×C₆₁

C₂⁴

Fitting

C₆₁×#376

C₂

D₆₁

C₆₁

G ▷ C₂³×C₆₁ ▷ C₆₁

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
1. #16839691	C₂	semidirect
2. #16839686	C₂	semidirect
4. #16839660	C₂	semidirect
5. C₆₁×#376	C₂	semidirect
60. #376	D₆₁	semidirect
61. C₆₁	#2644	semidirect

H ≅ G/N

type

1. #16839691

C₂

semidirect

2. #16839686

C₂

semidirect

4. #16839660

C₂

semidirect

5. C₆₁×#376

C₂

semidirect

60. #376

D₆₁

semidirect

61. C₆₁

#2644

semidirect

Subgroups — #21451779

Conjugacy classes of subgroups

Complements