Group #21462036 — subgroups

Subgroups — #21462036

Order 7808.

168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 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	D₆₁⋊M₃₂	C₂	1	2	yes	maximal
2	#16840655	C₂	1	2	yes	maximal, complemented
3	#16840654	C₂	1	2	yes	maximal, complemented
4	#97×D₆₁	C₂	1	1	yes	maximal, characteristic
5	#14519852	C₄	1	4	yes	complemented
6	#14519851	C₂²	1	4	yes	—
7	D₆₁⋊C₁₆	C₄	1	4	yes	complemented
8	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
9	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
10	C₄²×D₆₁	C₄	1	1	yes	characteristic
11	#14519688	C₂²	1	1	yes	characteristic
12	#14519687	C₄	1	1	yes	characteristic
13	#14519687	C₂²	1	1	yes	characteristic
14	#97×C₆₁	C₄	1	1	yes	characteristic
15	C₂×C₄×D₆₁	—	2	1	no	—
16	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₆₁	—	2	1	no	—
21	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×#92418	C₂×C₄	1	1	yes	characteristic
23	C₂×#92418	C₂³	1	1	yes	characteristic
24	C₈×D₆₁	—	2	1	no	—
25	C₈×D₆₁	—	2	1	no	—
26	C₈×D₆₁	C₂×C₄	1	2	yes	—
27	C₈×D₆₁	C₂×C₄	1	2	yes	—
28	#11758187	C₂×C₄	1	8	yes	complemented
29	C₂²×D₆₁	M₁₆	1	1	yes	characteristic
30	C₂×C₄×C₆₁	—	2	1	no	—
31	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₆₁	—	2	1	no	—
33	C₂×Dic₆₁	M₁₆	1	1	yes	characteristic
34	C₄×D₆₁	—	4	2	no	—
35	C₄×D₆₁	C₄²	1	1	yes	characteristic
36	C₄×D₆₁	C₄²	1	1	yes	characteristic
37	C₄×D₆₁	M₁₆	1	1	yes	characteristic
38	C₄×D₆₁	M₁₆	1	1	yes	characteristic
39	C₈×C₆₁	—	2	1	no	—
40	C₈×C₆₁	C₄²	1	2	yes	—
41	#92418	—	2	1	no	—
42	#92418	C₂²×C₄	1	2	yes	—
43	C₂²×C₆₁	C₂×M₁₆	1	1	yes	characteristic
44	C₂×D₆₁	—	2	2	no	—
45	C₂×D₆₁	#97	1	1	yes	characteristic
46	C₂×D₆₁	#97	1	1	yes	characteristic
47	C₄×C₆₁	—	4	1	no	—
48	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
49	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
50	Dic₆₁	—	4	1	no	—
51	Dic₆₁	#97	1	1	yes	characteristic
52	Dic₆₁	#97	1	1	yes	characteristic
53	C₂×#347	—	61	1	no	maximal, Sylow
54	C₂×C₆₁	—	2	1	no	—
55	C₂×C₆₁	C₂×#97	1	1	yes	characteristic
56	D₆₁	—	2	1	no	—
57	D₆₁	#347	1	2	yes	complemented
58	C₂×M₃₂	—	61	2	no	—
59	C₂×#97	—	61	1	no	—
60	#347	—	61	2	no	—
61	#347	—	61	2	no	—
62	C₆₁	C₂×#347	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₈	—	61	1	no	—
64	C₂²×C₈	—	61	1	no	—
65	C₂×C₄²	—	61	1	no	—
66	M₃₂	—	61	4	no	—
67	M₃₂	—	61	4	no	—
68	C₂×C₁₆	—	61	4	no	—
69	#97	—	61	1	no	—
70	#97	—	61	1	no	—
71	#97	—	61	1	no	—
72	#97	#6923	1	1	yes	characteristic
73	C₂²×C₄	—	61	1	no	—
74	C₂²×C₄	—	122	1	no	—
75	C₂×C₈	—	61	1	no	—
76	C₂×C₈	—	61	2	no	—
77	C₂×C₈	—	61	2	no	—
78	C₂×C₈	—	61	1	no	—
79	C₂×C₈	—	122	1	no	—
80	C₂×C₈	—	122	1	no	—
81	C₂×C₈	C₂×#6923	1	1	yes	characteristic
82	C₂×C₈	C₂×#6923	1	1	yes	characteristic
83	C₄²	—	61	1	no	—
84	C₄²	—	122	1	no	—
85	C₄²	C₂×#6923	1	1	yes	characteristic
86	C₁₆	—	61	8	no	—
87	C₂³	—	61	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	61	1	no	—
90	C₂×C₄	—	61	1	no	—
91	C₂×C₄	—	61	1	no	—
92	C₂×C₄	—	61	1	no	—
93	C₂×C₄	—	61	1	no	—
94	C₂×C₄	—	122	1	no	—
95	C₂×C₄	—	244	2	no	—
96	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
97	C₈	—	2	1	no	—
98	C₈	—	61	2	no	—
99	C₈	—	122	1	no	—
100	C₈	C₄×#6923	1	2	yes	—
101	C₂²	—	61	1	no	—
102	C₂²	—	61	1	no	—
103	C₂²	—	122	2	no	—
104	C₂²	D₆₁⋊M₁₆	1	1	yes	characteristic
105	C₄	—	4	1	no	—
106	C₄	—	61	1	no	—
107	C₄	—	61	1	no	—
108	C₄	—	244	1	no	—
109	C₄	C₂×C₄×#6923	1	1	yes	characteristic
110	C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
111	C₂	—	2	1	no	—
112	C₂	—	61	2	no	—
113	C₂	—	122	1	no	—
114	C₂	#16840721	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₆₁⋊M₃₂

C₂

yes

maximal

#16840655

C₂

yes

maximal, complemented

#16840654

C₂

yes

maximal, complemented

#97×D₆₁

C₂

yes

maximal, characteristic

#14519852

C₄

yes

complemented

#14519851

C₂²

yes

—

D₆₁⋊C₁₆

C₄

yes

complemented

C₂×C₈×D₆₁

C₄

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

C₄²×D₆₁

C₄

yes

characteristic

#14519688

C₂²

yes

characteristic

#14519687

C₄

yes

characteristic

#14519687

C₂²

yes

characteristic

#97×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂³

yes

characteristic

C₈×D₆₁

—

C₈×D₆₁

—

C₈×D₆₁

C₂×C₄

yes

—

C₈×D₆₁

C₂×C₄

yes

—

#11758187

C₂×C₄

yes

complemented

C₂²×D₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

M₁₆

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

C₄²

yes

characteristic

C₄×D₆₁

C₄²

yes

characteristic

C₄×D₆₁

M₁₆

yes

characteristic

C₄×D₆₁

M₁₆

yes

characteristic

C₈×C₆₁

—

C₈×C₆₁

C₄²

yes

—

#92418

—

#92418

C₂²×C₄

yes

—

C₂²×C₆₁

C₂×M₁₆

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

yes

C₂×D₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

yes

Dic₆₁

yes

—

C₂×C₆₁

—

C₂×C₆₁

C₂×#97

yes

characteristic

D₆₁

—

D₆₁

#347

yes

complemented

C₂×M₃₂

—

C₂×#97

—

#347

—

#347

—

C₆₁

C₂×#347

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

—

—

—

yes

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

122

—

C₄²

C₂×#6923

yes

characteristic

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

122

—

100

C₈

C₄×#6923

yes

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

122

—

104

C₂²

D₆₁⋊M₁₆

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

244

—

109

C₄

C₂×C₄×#6923

yes

characteristic

110

C₄

D₆₁⋊M₁₆

yes

characteristic

111

C₂

—

112

C₂

—

113

C₂

—

122

—

114

C₂

#16840721

yes

characteristic

	subgroup	G/H
center	C₄	C₂×C₄×#6923
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₂×C₄	C₂²×#6923
Fitting	#97×C₆₁	C₄
socle	C₂×C₆₁	C₂×#97
hypercenter	#97	#6923
hypocenter	C₆₁	C₂×#347
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ #97

subgroup

G/H

center

C₄

C₂×C₄×#6923

commutator

C₄×C₆₁

C₂×C₄²

Frattini

C₂×C₄

C₂²×#6923

Fitting

#97×C₆₁

C₄

socle

C₂×C₆₁

C₂×#97

C₆₁

G ▷ C₄×C₆₁ ▷ C₆₁

C₁ ◁ C₄ ◁ #97

N	H ≅ G/N	type
2. #16840655	C₂	semidirect
3. #16840654	C₂	semidirect
5. #14519852	C₄	semidirect
7. D₆₁⋊C₁₆	C₄	semidirect
28. #11758187	C₂×C₄	semidirect
57. D₆₁	#347	semidirect
62. C₆₁	C₂×#347	semidirect

H ≅ G/N

type

2. #16840655

C₂

semidirect

3. #16840654

C₂

semidirect

5. #14519852

C₄

semidirect

7. D₆₁⋊C₁₆

C₄

semidirect

28. #11758187

C₂×C₄

semidirect

57. D₆₁

#347

semidirect

62. C₆₁

C₂×#347

semidirect

Subgroups — #21462036

Conjugacy classes of subgroups

Complements