Group #21447422 — subgroups

Subgroups — #21447422

Order 7808.

160 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 85 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	M₃₂×D₆₁	C₂	1	2	yes	maximal
2	#16839719	C₂	1	1	yes	maximal, characteristic
3	#16839540	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839539	C₂	1	2	yes	maximal, complemented
5	C₆₁×#347	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11758189	C₄	1	1	yes	characteristic
7	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
8	#14519734	C₄	1	1	yes	characteristic
9	#14519717	C₂²	1	2	yes	—
10	#14519716	C₄	1	4	yes	complemented
11	C₁₆×D₆₁	C₄	1	4	yes	complemented
12	#14519687	C₂²	1	1	yes	characteristic
13	C₄×#92418	C₄	1	1	yes	characteristic
14	C₈×Dic₆₁	C₄	1	1	yes	characteristic
15	M₃₂×C₆₁	C₂²	1	2	yes	—
16	#97×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
20	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
21	#11758198	—	2	1	no	—
22	#11758196	—	2	1	no	—
23	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×#92418	C₂×C₄	1	1	yes	characteristic
25	C₂×#92418	C₂×C₄	1	1	yes	characteristic
26	#11758189	—	2	2	no	—
27	C₈×D₆₁	C₂×C₄	1	2	yes	—
28	C₈×D₆₁	C₂×C₄	1	2	yes	—
29	C₁₆×C₆₁	C₂×C₄	1	4	yes	—
30	#11758185	C₂×C₄	1	4	yes	—
31	C₂²×D₆₁	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₆₁	—	2	1	no	—
33	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₆₁	—	2	1	no	—
35	C₂×Dic₆₁	M₁₆	1	1	yes	characteristic
36	C₄×D₆₁	C₄²	1	2	yes	—
37	C₄×D₆₁	M₁₆	1	2	yes	—
38	C₈×C₆₁	—	2	1	no	—
39	C₈×C₆₁	C₂²×C₄	1	2	yes	—
40	#92418	—	2	1	no	—
41	#92418	C₄²	1	1	yes	characteristic
42	#92418	C₄²	1	1	yes	characteristic
43	C₂²×C₆₁	C₂×M₁₆	1	1	yes	characteristic
44	C₂×D₆₁	—	4	1	no	—
45	C₂×D₆₁	#97	1	2	yes	—
46	C₄×C₆₁	—	4	1	no	—
47	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
48	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
49	Dic₆₁	—	4	1	no	—
50	Dic₆₁	#97	1	2	yes	—
51	#2110	—	61	1	no	maximal, Sylow
52	C₂×C₆₁	—	2	1	no	—
53	C₂×C₆₁	C₂×#97	1	1	yes	characteristic
54	D₆₁	—	2	2	no	—
55	C₂×M₃₂	—	61	2	no	—
56	#405	—	61	1	no	—
57	#347	—	61	2	no	—
58	#347	—	61	1	no	—
59	#347	D₆₁	1	1	yes	characteristic, complemented
60	C₆₁	#2110	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	61	1	no	—
62	C₂²×C₈	—	61	1	no	—
63	#117	—	61	1	no	—
64	M₃₂	—	61	2	no	—
65	M₃₂	—	61	4	no	—
66	M₃₂	C₂×D₆₁	1	2	yes	—
67	C₂×C₁₆	—	61	4	no	—
68	#97	—	61	1	no	—
69	#97	C₂×D₆₁	1	1	yes	characteristic
70	C₄×C₈	—	61	1	no	—
71	C₄×C₈	—	61	1	no	—
72	C₂²×C₄	—	61	1	no	—
73	M₁₆	—	122	2	no	—
74	C₂×C₈	—	61	1	no	—
75	C₂×C₈	—	61	2	no	—
76	C₂×C₈	—	61	2	no	—
77	C₂×C₈	—	61	1	no	—
78	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
79	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
80	C₄⋊C₄	—	122	1	no	—
81	C₂²⋊C₄	—	122	1	no	—
82	C₄²	—	61	1	no	—
83	C₄²	C₄×D₆₁	1	1	yes	characteristic
84	C₁₆	—	61	4	no	—
85	C₁₆	C₄×D₆₁	1	4	yes	—
86	C₂³	—	61	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	61	1	no	—
89	C₂×C₄	—	61	2	no	—
90	C₂×C₄	—	61	2	no	—
91	C₂×C₄	—	122	1	no	—
92	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	61	1	no	—
95	C₈	—	61	1	no	—
96	C₈	—	122	1	no	—
97	C₈	C₂×C₄×D₆₁	1	2	yes	—
98	C₂²	—	61	2	no	—
99	C₂²	—	244	1	no	—
100	C₂²	M₁₆×D₆₁	1	1	yes	characteristic
101	C₄	—	4	1	no	—
102	C₄	—	61	2	no	—
103	C₄	—	244	1	no	—
104	C₄	C₄²×D₆₁	1	1	yes	characteristic
105	C₄	M₁₆×D₆₁	1	1	yes	characteristic
106	C₂	—	2	1	no	—
107	C₂	—	122	2	no	—
108	C₂	#97×D₆₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

M₃₂×D₆₁

C₂

yes

maximal

#16839719

C₂

yes

maximal, characteristic

#16839540

C₂

yes

maximal, characteristic, complemented

#16839539

C₂

yes

maximal, complemented

C₆₁×#347

C₂

yes

maximal, characteristic, complemented

C₂×#11758189

C₄

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519734

C₄

yes

characteristic

#14519717

C₂²

yes

—

#14519716

C₄

yes

complemented

C₁₆×D₆₁

C₄

yes

complemented

#14519687

C₂²

yes

characteristic

C₄×#92418

C₄

yes

characteristic

C₈×Dic₆₁

C₄

yes

characteristic

M₃₂×C₆₁

C₂²

yes

—

#97×C₆₁

C₂²

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

#11758198

—

#11758196

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

#11758189

—

C₈×D₆₁

C₂×C₄

yes

—

C₈×D₆₁

C₂×C₄

yes

—

C₁₆×C₆₁

C₂×C₄

yes

—

#11758185

C₂×C₄

yes

—

C₂²×D₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

M₁₆

yes

characteristic

C₄×D₆₁

C₄²

yes

—

C₄×D₆₁

M₁₆

yes

—

C₈×C₆₁

—

C₈×C₆₁

C₂²×C₄

yes

—

#92418

—

#92418

C₄²

yes

characteristic

#92418

C₄²

yes

characteristic

C₂²×C₆₁

C₂×M₁₆

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

#97

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

#97

yes

—

#2110

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×#97

yes

characteristic

D₆₁

—

C₂×M₃₂

—

—

—

—

D₆₁

yes

characteristic, complemented

C₆₁

#2110

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

M₃₂

C₂×D₆₁

yes

—

C₂×C₁₆

—

#97

—

#97

C₂×D₆₁

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

122

—

C₄²

—

C₄²

C₄×D₆₁

yes

characteristic

C₁₆

—

C₁₆

C₄×D₆₁

yes

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

122

—

C₈

C₂×C₄×D₆₁

yes

—

C₂²

—

C₂²

—

244

—

100

C₂²

M₁₆×D₆₁

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

244

—

104

C₄

C₄²×D₆₁

yes

characteristic

105

C₄

M₁₆×D₆₁

yes

characteristic

106

C₂

—

107

C₂

—

122

—

108

C₂

#97×D₆₁

yes

characteristic

	subgroup	G/H
center	C₄	C₄²×D₆₁
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#347	C₂
socle	C₂×C₆₁	C₂×#97
hypercenter	#347	D₆₁
hypocenter	C₆₁	#2110
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ #347

subgroup

G/H

center

C₄

C₄²×D₆₁

commutator

C₄×C₆₁

C₂×C₄²

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#347

C₂

socle

C₂×C₆₁

C₂×#97

D₆₁

C₆₁

G ▷ C₄×C₆₁ ▷ C₆₁

C₁ ◁ C₄ ◁ #347

N	H ≅ G/N	type
3. #16839540	C₂	semidirect
4. #16839539	C₂	semidirect
5. C₆₁×#347	C₂	semidirect
10. #14519716	C₄	semidirect
11. C₁₆×D₆₁	C₄	semidirect
59. #347	D₆₁	semidirect
60. C₆₁	#2110	semidirect

H ≅ G/N

type

3. #16839540

C₂

semidirect

4. #16839539

C₂

semidirect

5. C₆₁×#347

C₂

semidirect

10. #14519716

C₄

semidirect

11. C₁₆×D₆₁

C₄

semidirect

59. #347

D₆₁

semidirect

60. C₆₁

#2110

semidirect

Subgroups — #21447422

Conjugacy classes of subgroups

Complements