Group #21445726 — subgroups

Subgroups — #21445726

Order 7808.

220 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14519712	C₂	1	2	yes	maximal
2	C₄×#11758194	C₂	1	1	yes	maximal, characteristic
3	C₂×#14519688	C₂	1	1	yes	maximal, characteristic
4	#16839526	C₂	1	2	yes	maximal
5	C₄×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758194	C₂²	1	2	yes	—
7	C₂²×#92418	C₂²	1	1	yes	characteristic
8	C₂²×#92418	C₂²	1	1	yes	characteristic
9	#14519712	C₄	1	8	yes	complemented
10	#14519688	—	2	1	no	—
11	#14519688	C₄	1	4	yes	—
12	C₄×#92418	—	2	1	no	—
13	C₂×M₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
15	#97×C₆₁	—	2	1	no	—
16	C₄×C₈×C₆₁	—	2	1	no	—
17	C₂²×C₄×C₆₁	Q₈	1	2	yes	—
18	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
19	M₁₆×C₆₁	—	2	2	no	—
20	M₁₆×C₆₁	C₂×C₄	1	4	yes	—
21	C₂×C₈×C₆₁	—	2	2	no	—
22	C₄²×C₆₁	C₂×C₄	1	2	yes	—
23	C₄²×C₆₁	D₄	1	1	yes	characteristic
24	C₄²×C₆₁	D₄	1	1	yes	characteristic
25	#11758194	—	2	2	no	—
26	#11758194	C₂×C₄	1	4	yes	—
27	C₂×#92418	—	2	2	no	—
28	C₂×#92418	—	2	2	no	—
29	C₂×#92418	C₂×C₄	1	2	yes	—
30	C₂×#92418	C₂×C₄	1	2	yes	—
31	C₂×#92418	C₂×C₄	1	4	yes	—
32	C₂³×C₆₁	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₆₁	—	4	2	no	—
34	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
36	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
38	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₆₁	#41	1	2	yes	—
40	C₈×C₆₁	—	2	4	no	—
41	#92418	—	2	2	no	—
42	#92418	—	2	4	no	—
43	#92418	C₄²	1	4	yes	—
44	C₂²×C₆₁	—	2	2	no	—
45	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₆₁	C₄×Q₈	1	2	yes	—
47	C₄×C₆₁	—	2	2	no	—
48	C₄×C₆₁	—	2	2	no	—
49	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
50	C₄×C₆₁	#117	1	1	yes	characteristic
51	C₄×C₆₁	C₄×D₄	1	2	yes	—
52	#1778	—	61	1	no	maximal, Sylow
53	C₂×C₆₁	—	2	2	no	—
54	C₂×C₆₁	C₄×C₄⋊C₄	1	1	yes	characteristic
55	C₂×C₆₁	#430	1	2	yes	—
56	C₂×#108	—	61	2	no	—
57	C₄×M₁₆	—	61	1	no	—
58	C₄×M₁₆	D₆₁	1	1	yes	characteristic
59	C₂×#97	—	61	1	no	—
60	#341	—	61	2	no	—
61	C₆₁	#1778	1	1	yes	characteristic, complemented, Sylow
62	C₂×M₁₆	—	61	2	no	—
63	C₂×M₁₆	C₂×D₆₁	1	2	yes	—
64	C₂²×C₈	—	61	1	no	—
65	C₂²×C₈	—	61	1	no	—
66	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
67	#108	—	61	8	no	—
68	#97	—	2	1	no	—
69	#97	—	61	4	no	—
70	#97	—	122	1	no	—
71	C₄×C₈	—	2	1	no	—
72	C₄×C₈	—	122	1	no	—
73	C₂²×C₄	Dic₁₂₂	1	2	yes	—
74	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
75	M₁₆	—	2	2	no	—
76	M₁₆	—	61	4	no	—
77	M₁₆	—	122	2	no	—
78	M₁₆	C₄×D₆₁	1	4	yes	—
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	61	2	no	—
81	C₂×C₈	—	61	4	no	—
82	C₂×C₈	—	61	2	no	—
83	C₂×C₈	—	122	2	no	—
84	C₂×C₈	—	122	2	no	—
85	C₄²	C₄×D₆₁	1	2	yes	—
86	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
87	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
88	C₂³	C₂×Dic₁₂₂	1	1	yes	characteristic
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	#11758196	1	2	yes	—
91	C₂×C₄	#11758196	1	2	yes	—
92	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
93	C₂×C₄	C₂×C₄×D₆₁	1	2	yes	—
94	C₂×C₄	#11758222	1	2	yes	—
95	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
96	C₈	—	2	4	no	—
97	C₈	—	61	4	no	—
98	C₈	—	122	2	no	—
99	C₈	—	122	4	no	—
100	C₂²	—	2	2	no	—
101	C₂²	C₂×#11758196	1	1	yes	characteristic
102	C₂²	C₄×Dic₁₂₂	1	2	yes	—
103	C₄	—	2	2	no	—
104	C₄	—	2	2	no	—
105	C₄	C₄²×D₆₁	1	1	yes	characteristic
106	C₄	#14519734	1	1	yes	characteristic
107	C₄	C₄×C₂²⋊D₆₁	1	2	yes	—
108	C₂	—	2	2	no	—
109	C₂	C₄×#11758196	1	1	yes	characteristic
110	C₂	#16839810	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519712

C₂

yes

maximal

C₄×#11758194

C₂

yes

maximal, characteristic

C₂×#14519688

C₂

yes

maximal, characteristic

#16839526

C₂

yes

maximal

C₄×M₁₆×C₆₁

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

—

C₂²×#92418

C₂²

yes

characteristic

C₂²×#92418

C₂²

yes

characteristic

#14519712

C₄

yes

complemented

#14519688

—

#14519688

C₄

yes

—

C₄×#92418

—

C₂×M₁₆×C₆₁

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

#97×C₆₁

—

C₄×C₈×C₆₁

—

C₂²×C₄×C₆₁

Q₈

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

M₁₆×C₆₁

—

M₁₆×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

—

C₄²×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

D₄

yes

characteristic

C₄²×C₆₁

D₄

yes

characteristic

#11758194

—

#11758194

C₂×C₄

yes

—

C₂×#92418

—

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

—

C₂³×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₈×C₆₁

—

#92418

—

#92418

—

#92418

C₄²

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₆₁

C₄×Q₈

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

#117

yes

characteristic

C₄×C₆₁

C₄×D₄

yes

—

#1778

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₄×C₄⋊C₄

yes

characteristic

C₂×C₆₁

#430

yes

—

C₂×#108

—

C₄×M₁₆

—

C₄×M₁₆

D₆₁

yes

characteristic

C₂×#97

—

#341

—

C₆₁

#1778

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

C₂×D₆₁

yes

—

—

—

—

122

—

C₄×C₈

—

C₄×C₈

—

122

—

C₂²×C₄

Dic₁₂₂

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

122

—

M₁₆

C₄×D₆₁

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄²

C₄×D₆₁

yes

—

C₄²

C₂²⋊D₆₁

yes

characteristic

C₄²

C₂²⋊D₆₁

yes

characteristic

C₂³

C₂×Dic₁₂₂

yes

characteristic

C₂×C₄

—

C₂×C₄

#11758196

yes

—

C₂×C₄

#11758196

yes

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₂×C₄

C₂×C₄×D₆₁

yes

—

C₂×C₄

#11758222

yes

—

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

C₈

—

C₈

—

122

—

C₈

—

122

—

100

C₂²

—

101

C₂²

C₂×#11758196

yes

characteristic

102

C₂²

C₄×Dic₁₂₂

yes

—

103

C₄

—

104

C₄

—

105

C₄

C₄²×D₆₁

yes

characteristic

106

C₄

#14519734

yes

characteristic

107

C₄

C₄×C₂²⋊D₆₁

yes

—

108

C₂

—

109

C₂

C₄×#11758196

yes

characteristic

110

C₂

#16839810

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₆₁
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₄×M₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	C₄×M₁₆	D₆₁
hypocenter	C₆₁	#1778
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₆₁

commutator

C₄×C₆₁

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₄×M₁₆×C₆₁

C₂

socle

C₂²×C₆₁

C₂×C₄⋊C₄

hypercenter

C₄×M₁₆

D₆₁

hypocenter

C₆₁

#1778

LCS

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
9. #14519712	C₄	semidirect
61. C₆₁	#1778	semidirect

H ≅ G/N

type

9. #14519712

C₄

semidirect

61. C₆₁

#1778

semidirect

Subgroups — #21445726

Conjugacy classes of subgroups

Complements