Group #21444444 — subgroups

Subgroups — #21444444

Order 7808.

196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 59 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	#125×D₆₁	C₂	1	1	yes	maximal, characteristic
2	#16839817	C₂	1	2	yes	maximal
3	#16839504	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839503	C₂	1	2	yes	maximal, complemented
5	C₆₁×#330	C₂	1	1	yes	maximal, characteristic, complemented
6	#14519769	C₂²	1	1	yes	characteristic
7	#14519768	C₄	1	2	yes	—
8	#14519767	—	2	2	no	—
9	C₄⋊C₄×D₆₁	—	2	2	no	—
10	C₄⋊C₄×D₆₁	C₄	1	2	yes	—
11	C₄²×D₆₁	C₂²	1	1	yes	characteristic
12	#14519706	—	2	2	no	—
13	#14519689	—	2	2	no	—
14	#14519688	C₂²	1	2	yes	—
15	#125×C₆₁	C₂²	1	1	yes	characteristic
16	#97×C₆₁	C₂²	1	2	yes	—
17	C₂×C₄×D₆₁	—	2	2	no	—
18	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×D₆₁	D₄	1	2	yes	—
20	C₂×C₈×C₆₁	—	2	2	no	—
21	C₄⋊C₄×C₆₁	—	2	2	no	—
22	C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
23	C₄²×C₆₁	C₂³	1	1	yes	characteristic
24	C₄⋊Dic₆₁	—	2	2	no	—
25	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
26	#11758196	—	2	2	no	—
27	#11758196	—	2	2	no	—
28	#11758196	—	2	2	no	—
29	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₆₁	D₄	1	2	yes	—
31	C₂×#92418	—	2	2	no	—
32	C₂²×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₆₁	—	2	2	no	—
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
36	C₂×Dic₆₁	—	2	2	no	—
37	C₂×Dic₆₁	C₂²⋊C₄	1	2	yes	—
38	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
39	C₄×D₆₁	—	2	2	no	—
40	C₄×D₆₁	—	4	2	no	—
41	C₄×D₆₁	—	4	4	no	—
42	C₈×C₆₁	—	4	2	no	—
43	#92418	—	4	2	no	—
44	C₂²×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×D₆₁	—	2	2	no	—
46	C₂×D₆₁	#101	1	2	yes	—
47	C₄×C₆₁	—	2	1	no	—
48	C₄×C₆₁	—	2	2	no	—
49	C₄×C₆₁	—	4	2	no	—
50	Dic₆₁	—	2	1	no	—
51	Dic₆₁	—	2	2	no	—
52	Dic₆₁	—	4	2	no	—
53	#1534	—	61	1	no	maximal, Sylow
54	C₂×C₆₁	C₂×#101	1	1	yes	characteristic
55	C₂×C₆₁	#421	1	2	yes	—
56	D₆₁	—	2	2	no	—
57	C₂×#125	—	61	1	no	—
58	#432	—	61	2	no	—
59	#330	—	61	1	no	—
60	#330	—	61	2	no	—
61	#330	D₆₁	1	1	yes	characteristic, complemented
62	C₆₁	#1534	1	1	yes	characteristic, complemented, Sylow
63	#125	—	61	2	no	—
64	#125	—	61	1	no	—
65	#125	—	122	2	no	—
66	#125	C₂×D₆₁	1	1	yes	characteristic
67	C₂×C₄⋊C₄	—	61	2	no	—
68	C₂×C₄⋊C₄	—	122	2	no	—
69	C₂×C₄²	—	61	1	no	—
70	C₄⋊C₈	—	122	2	no	—
71	C₂²⋊C₈	—	122	2	no	—
72	#97	—	61	2	no	—
73	#97	C₂×D₆₁	1	2	yes	—
74	C₂²×C₄	—	61	1	no	—
75	C₂²×C₄	—	61	2	no	—
76	C₂²×C₄	—	122	2	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	122	2	no	—
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	61	2	no	—
81	C₄⋊C₄	—	122	2	no	—
82	C₄⋊C₄	—	122	2	no	—
83	C₄⋊C₄	—	122	2	no	—
84	C₄⋊C₄	—	122	2	no	—
85	C₄⋊C₄	C₄×D₆₁	1	2	yes	—
86	C₄²	—	61	1	no	—
87	C₄²	—	61	2	no	—
88	C₄²	C₂²×D₆₁	1	1	yes	characteristic
89	C₂³	—	61	1	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	61	1	no	—
92	C₂×C₄	—	61	2	no	—
93	C₂×C₄	—	122	2	no	—
94	C₂×C₄	—	122	2	no	—
95	C₂×C₄	—	244	2	no	—
96	C₂×C₄	—	244	4	no	—
97	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
98	C₂×C₄	D₄×D₆₁	1	2	yes	—
99	C₈	—	4	2	no	—
100	C₈	—	244	2	no	—
101	C₂²	—	61	2	no	—
102	C₂²	—	122	2	no	—
103	C₂²	C₂²⋊C₄×D₆₁	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	2	no	—
106	C₄	—	4	2	no	—
107	C₄	—	122	1	no	—
108	C₄	—	122	2	no	—
109	C₄	—	244	2	no	—
110	C₂	—	122	2	no	—
111	C₂	#101×D₆₁	1	1	yes	characteristic
112	C₂	#16839777	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#125×D₆₁

C₂

yes

maximal, characteristic

#16839817

C₂

yes

maximal

#16839504

C₂

yes

maximal, characteristic, complemented

#16839503

C₂

yes

maximal, complemented

C₆₁×#330

C₂

yes

maximal, characteristic, complemented

#14519769

C₂²

yes

characteristic

#14519768

C₄

yes

—

#14519767

—

C₄⋊C₄×D₆₁

—

C₄⋊C₄×D₆₁

C₄

yes

—

C₄²×D₆₁

C₂²

yes

—

—

C₂²

yes

—

#125×C₆₁

C₂²

yes

characteristic

#97×C₆₁

C₂²

yes

—

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

—

C₂×C₈×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂³

yes

characteristic

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

C₂×C₄

yes

—

#11758196

—

#11758196

—

#11758196

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

—

C₂×#92418

—

C₂²×D₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂²⋊C₄

yes

—

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

#101

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

—

—

—

—

—

D₆₁

yes

characteristic, complemented

C₆₁

#1534

yes

characteristic, complemented, Sylow

#125

—

#125

—

#125

—

122

—

#125

C₂×D₆₁

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄²

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

#97

—

#97

C₂×D₆₁

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂×C₈

—

C₂×C₈

—

122

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

C₄×D₆₁

yes

—

C₄²

—

C₄²

—

C₄²

C₂²×D₆₁

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₂×C₄

D₄×D₆₁

yes

—

C₈

—

100

C₈

—

244

—

101

C₂²

—

102

C₂²

—

122

—

103

C₂²

C₂²⋊C₄×D₆₁

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

122

—

108

C₄

—

122

—

109

C₄

—

244

—

110

C₂

—

122

—

111

C₂

#101×D₆₁

yes

characteristic

112

C₂

#16839777

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#330	C₂
socle	C₂²×C₆₁	C₂×C₂²⋊C₄
hypercenter	#330	D₆₁
hypocenter	C₆₁	#1534
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₆₁

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#330

C₂

socle

C₂²×C₆₁

C₂×C₂²⋊C₄

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
3. #16839504	C₂	semidirect
4. #16839503	C₂	semidirect
5. C₆₁×#330	C₂	semidirect
61. #330	D₆₁	semidirect
62. C₆₁	#1534	semidirect

H ≅ G/N

type

3. #16839504

C₂

semidirect

4. #16839503

C₂

semidirect

5. C₆₁×#330

C₂

semidirect

61. #330

D₆₁

semidirect

62. C₆₁

#1534

semidirect

Subgroups — #21444444

Conjugacy classes of subgroups

Complements