Group #21447584 — subgroups

Subgroups — #21447584

Order 7808.

152 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 89 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	C₂×#14519717	C₂	1	1	yes	maximal, characteristic
2	#16839717	C₂	1	1	yes	maximal, characteristic
3	#16839582	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11758194	C₄	1	1	yes	characteristic
6	#14519736	C₄	1	1	yes	characteristic
7	#14519717	—	2	1	no	—
8	#14519717	C₂²	1	2	yes	—
9	C₂×#11758185	—	2	1	no	—
10	#14519687	C₄	1	2	yes	—
11	C₈×Dic₆₁	C₂²	1	2	yes	—
12	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	M₃₂×C₆₁	—	2	1	no	—
14	M₃₂×C₆₁	C₂²	1	2	yes	—
15	C₂×C₁₆×C₆₁	—	2	1	no	—
16	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
21	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
22	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
23	C₂²⋊Dic₆₁	—	2	1	no	—
24	C₄⋊Dic₆₁	—	2	1	no	—
25	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
26	#11758194	C₈	1	2	yes	—
27	#11758194	C₈	1	2	yes	—
28	C₂×#92418	C₂×C₄	1	2	yes	—
29	C₁₆×C₆₁	—	2	2	no	—
30	#11758185	—	2	2	no	—
31	C₂³×C₆₁	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
37	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
38	C₂×Dic₆₁	—	2	2	no	—
39	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
40	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
41	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
42	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
43	#92418	C₂×C₈	1	4	yes	—
44	C₂²×C₆₁	—	4	1	no	—
45	C₂²×C₆₁	C₄⋊C₈	1	1	yes	characteristic
46	C₂²×C₆₁	C₄⋊C₈	1	1	yes	characteristic
47	C₂²×C₆₁	C₂×M₁₆	1	1	yes	characteristic
48	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
49	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
50	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
52	Dic₆₁	—	4	2	no	—
53	#2153	—	61	1	no	maximal, Sylow
54	C₂×C₆₁	—	2	1	no	—
55	C₂×C₆₁	—	2	1	no	—
56	C₂×C₆₁	—	2	1	no	—
57	C₂×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
58	C₂×M₃₂	—	61	1	no	—
59	C₂×M₃₂	D₆₁	1	1	yes	characteristic
60	#405	—	61	1	no	—
61	#364	—	61	4	no	—
62	C₆₁	#2153	1	1	yes	characteristic, complemented, Sylow
63	C₂×M₁₆	—	61	1	no	—
64	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
65	#117	—	61	1	no	—
66	M₃₂	—	2	1	no	—
67	M₃₂	—	61	2	no	—
68	M₃₂	—	122	1	no	—
69	M₃₂	C₂×D₆₁	1	2	yes	—
70	C₂×C₁₆	—	2	1	no	—
71	C₂×C₁₆	—	122	1	no	—
72	#97	—	61	2	no	—
73	C₄×C₈	—	61	2	no	—
74	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
75	M₁₆	—	61	2	no	—
76	M₁₆	—	61	2	no	—
77	C₂×C₈	—	61	2	no	—
78	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
79	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
80	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
81	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
82	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
83	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
84	C₄⋊C₄	—	122	1	no	—
85	C₂²⋊C₄	—	122	1	no	—
86	C₄²	—	61	2	no	—
87	C₁₆	—	2	2	no	—
88	C₁₆	—	122	2	no	—
89	C₂³	#11758189	1	1	yes	characteristic
90	C₂×C₄	—	122	2	no	—
91	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
92	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
93	C₂×C₄	#11758189	1	1	yes	characteristic
94	C₂×C₄	#11758196	1	1	yes	characteristic
95	C₂×C₄	#11758196	1	1	yes	characteristic
96	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
97	C₈	—	61	4	no	—
98	C₈	#11758196	1	1	yes	characteristic
99	C₈	#11758196	1	1	yes	characteristic
100	C₈	C₂×Dic₁₂₂	1	1	yes	characteristic
101	C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
102	C₂²	—	4	1	no	—
103	C₂²	#14519706	1	1	yes	characteristic
104	C₂²	#14519706	1	1	yes	characteristic
105	C₂²	C₂×#11758189	1	1	yes	characteristic
106	C₄	—	244	2	no	—
107	C₄	#14519706	1	1	yes	characteristic
108	C₄	#14519706	1	1	yes	characteristic
109	C₄	C₂×#11758196	1	1	yes	characteristic
110	C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
111	C₂	—	2	1	no	—
112	C₂	—	2	1	no	—
113	C₂	—	2	1	no	—
114	C₂	C₂×#14519706	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519717

C₂

yes

maximal, characteristic

#16839717

C₂

yes

maximal, characteristic

#16839582

C₂

yes

maximal, complemented

C₂×M₃₂×C₆₁

C₂

yes

maximal, characteristic

C₂×#11758194

C₄

yes

characteristic

#14519736

C₄

yes

characteristic

#14519717

—

#14519717

C₂²

yes

—

C₂×#11758185

—

#14519687

C₄

yes

—

C₈×Dic₆₁

C₂²

yes

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

M₃₂×C₆₁

—

M₃₂×C₆₁

C₂²

yes

—

C₂×C₁₆×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

Q₈

yes

characteristic

C₂×C₈×C₆₁

Q₈

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

C₂×C₄

yes

—

#11758194

C₈

yes

—

#11758194

C₈

yes

—

C₂×#92418

C₂×C₄

yes

—

C₁₆×C₆₁

—

#11758185

—

C₂³×C₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₂×D₄

yes

characteristic

C₈×C₆₁

C₂×Q₈

yes

characteristic

#92418

C₂×C₈

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

C₄⋊C₈

yes

characteristic

C₂²×C₆₁

C₄⋊C₈

yes

characteristic

C₂²×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

characteristic

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₂²×C₈

yes

characteristic

Dic₆₁

—

#2153

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

C₂×C₄⋊C₈

yes

characteristic

C₂×M₃₂

—

C₂×M₃₂

D₆₁

yes

characteristic

#405

—

#364

—

C₆₁

#2153

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

#117

—

M₃₂

—

M₃₂

—

M₃₂

—

122

—

M₃₂

C₂×D₆₁

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

#97

—

C₄×C₈

—

C₂²×C₄

C₄×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

Dic₁₂₂

yes

characteristic

C₂×C₈

Dic₁₂₂

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

122

—

C₄²

—

C₁₆

—

C₁₆

—

122

—

C₂³

#11758189

yes

characteristic

C₂×C₄

—

122

—

C₂×C₄

C₈×D₆₁

yes

characteristic

C₂×C₄

C₈×D₆₁

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₈

—

C₈

yes

C₈

yes

100

C₈

C₂×Dic₁₂₂

yes

characteristic

101

C₈

C₂×C₂²⋊D₆₁

yes

characteristic

102

C₂²

—

103

C₂²

#14519706

yes

characteristic

104

C₂²

#14519706

yes

characteristic

105

C₂²

C₂×#11758189

yes

characteristic

106

C₄

—

244

—

107

C₄

#14519706

yes

characteristic

108

C₄

#14519706

yes

characteristic

109

C₄

C₂×#11758196

yes

characteristic

110

C₄

C₂×C₈×D₆₁

yes

characteristic

111

C₂

—

112

C₂

—

113

C₂

—

114

C₂

C₂×#14519706

yes

characteristic

	subgroup	G/H
center	C₈	C₂×C₂²⋊D₆₁
commutator	C₄×C₆₁	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₂×M₃₂×C₆₁	C₂
socle	C₂×C₆₁	C₂×C₄⋊C₈
hypercenter	C₂×M₃₂	D₆₁
hypocenter	C₆₁	#2153
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₈

C₂×C₂²⋊D₆₁

commutator

C₄×C₆₁

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₂×M₃₂×C₆₁

C₂

socle

C₂×C₆₁

C₂×C₄⋊C₈

hypercenter

C₂×M₃₂

D₆₁

hypocenter

C₆₁

#2153

LCS

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #16839582	C₂	semidirect
62. C₆₁	#2153	semidirect

H ≅ G/N

type

3. #16839582

C₂

semidirect

62. C₆₁

#2153

semidirect

Subgroups — #21447584

Conjugacy classes of subgroups

Complements