Group #21445952 — subgroups

Subgroups — #21445952

Order 7808.

224 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14519688	C₂	1	1	yes	maximal, characteristic
2	#16839632	C₂	1	1	yes	maximal, characteristic
3	#16839524	C₂	1	4	yes	maximal
4	C₆₁×#382	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92418	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₆₁	—	2	2	no	—
7	C₂×C₄⋊Dic₆₁	C₂²	1	2	yes	—
8	#14519688	C₄	1	4	yes	complemented
9	C₂×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
10	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
11	#95×C₆₁	—	2	2	no	—
12	C₂²×C₄×C₆₁	—	2	2	no	—
13	C₂²×C₄×C₆₁	D₄	1	2	yes	—
14	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
15	C₂²×Dic₆₁	—	2	2	no	—
16	C₄⋊C₄×C₆₁	—	2	4	no	—
17	C₄²×C₆₁	C₂×C₄	1	2	yes	—
18	C₄²×C₆₁	Q₈	1	2	yes	—
19	C₄⋊Dic₆₁	—	2	4	no	—
20	C₄⋊Dic₆₁	—	4	4	no	—
21	C₂×#92418	—	2	2	no	—
22	C₂×#92418	—	2	2	no	—
23	C₂×#92418	C₂×C₄	1	4	yes	—
24	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	—	2	2	no	—
26	C₂×C₄×C₆₁	—	2	2	no	—
27	C₂×C₄×C₆₁	—	4	2	no	—
28	C₂×C₄×C₆₁	—	4	2	no	—
29	C₂×C₄×C₆₁	—	4	2	no	—
30	C₂×C₄×C₆₁	C₄⋊C₄	1	4	yes	—
31	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₆₁	#41	1	2	yes	—
34	C₂×C₄×C₆₁	#41	1	2	yes	—
35	C₂×Dic₆₁	—	4	2	no	—
36	C₂×Dic₆₁	—	4	4	no	—
37	#92418	—	2	4	no	—
38	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₆₁	#124	1	1	yes	characteristic
40	C₂²×C₆₁	#124	1	1	yes	characteristic
41	C₂²×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
42	C₂²×C₆₁	#137	1	2	yes	—
43	C₄×C₆₁	—	2	4	no	—
44	C₄×C₆₁	—	8	2	no	—
45	C₄×C₆₁	#117	1	2	yes	—
46	C₄×C₆₁	#125	1	2	yes	—
47	Dic₆₁	—	8	2	no	—
48	#1836	—	61	1	no	maximal, Sylow
49	C₂×C₆₁	#382	1	1	yes	characteristic
50	C₂×C₆₁	#428	1	2	yes	—
51	C₂×C₆₁	#489	1	2	yes	—
52	C₂×C₆₁	#490	1	1	yes	characteristic
53	C₂×C₆₁	#491	1	1	yes	characteristic
54	C₂×#97	—	61	1	no	—
55	#384	—	61	1	no	—
56	#382	D₆₁	1	1	yes	characteristic
57	#340	—	61	4	no	—
58	C₆₁	#1836	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₈	—	61	2	no	—
60	C₂×C₄⋊C₄	—	61	2	no	—
61	C₂×C₄⋊C₄	—	122	2	no	—
62	C₂×C₄⋊C₄	C₂×D₆₁	1	2	yes	—
63	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
64	#97	—	61	4	no	—
65	#95	—	2	2	no	—
66	C₂²×C₄	—	2	2	no	—
67	C₂²×C₄	—	122	2	no	—
68	C₂²×C₄	C₂²⋊D₆₁	1	2	yes	—
69	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
70	C₂×C₈	—	61	4	no	—
71	C₂×C₈	—	122	2	no	—
72	C₂×C₈	—	122	2	no	—
73	C₄⋊C₄	—	2	4	no	—
74	C₄⋊C₄	—	122	4	no	—
75	C₄⋊C₄	—	244	4	no	—
76	C₄²	Dic₁₂₂	1	2	yes	—
77	C₄²	C₄×D₆₁	1	2	yes	—
78	C₂³	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	—	244	2	no	—
85	C₂×C₄	—	244	4	no	—
86	C₂×C₄	#11758196	1	4	yes	—
87	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
88	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
89	C₂×C₄	#11758224	1	2	yes	—
90	C₂×C₄	#11758226	1	2	yes	—
91	C₈	—	122	4	no	—
92	C₂²	C₂×#11758196	1	1	yes	characteristic
93	C₂²	#14519764	1	1	yes	characteristic
94	C₂²	#14519766	1	1	yes	characteristic
95	C₂²	#14519802	1	2	yes	—
96	C₂²	#14519807	1	2	yes	—
97	C₄	—	2	4	no	—
98	C₄	—	8	2	no	—
99	C₄	—	488	2	no	—
100	C₄	#14519735	1	2	yes	—
101	C₄	#14519768	1	2	yes	—
102	C₂	#16839627	1	1	yes	characteristic
103	C₂	#16839805	1	2	yes	—
104	C₂	#16840121	1	2	yes	—
105	C₂	#16840128	1	1	yes	characteristic
106	C₂	#16840132	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519688

C₂

yes

maximal, characteristic

#16839632

C₂

yes

maximal, characteristic

#16839524

C₂

yes

maximal

C₆₁×#382

C₂

yes

maximal, characteristic

C₂²×#92418

C₂²

yes

—

C₂×C₄⋊Dic₆₁

—

C₂×C₄⋊Dic₆₁

C₂²

yes

—

#14519688

C₄

yes

complemented

C₂×C₄⋊C₄×C₆₁

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

#95×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

D₄

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

Q₈

yes

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₂×#92418

—

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

—

C₂³×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

#92418

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

—

C₂²×C₆₁

#137

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#117

yes

—

C₄×C₆₁

#125

yes

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₆₁

#489

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×#97

—

#384

—

#382

D₆₁

yes

characteristic

#340

—

C₆₁

#1836

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄⋊C₄

C₂×D₆₁

yes

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

#97

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂²⋊D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₄²

Dic₁₂₂

yes

—

C₄²

C₄×D₆₁

yes

—

C₂³

C₂×C₂²⋊D₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

#11758196

yes

—

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₂×C₄

#11758224

yes

—

C₂×C₄

#11758226

yes

—

C₈

—

122

—

C₂²

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

#14519807

yes

—

C₄

—

C₄

—

C₄

—

488

—

100

C₄

#14519735

yes

—

101

C₄

#14519768

yes

—

102

C₂

#16839627

yes

characteristic

103

C₂

#16839805

yes

—

104

C₂

#16840121

yes

—

105

C₂

#16840128

yes

characteristic

106

C₂

#16840132

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#382	C₂
socle	C₂³×C₆₁	C₂×D₄
hypercenter	#382	D₆₁
hypocenter	C₆₁	#1836
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₆₁

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#382

C₂

socle

C₂³×C₆₁

C₂×D₄

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

N	H ≅ G/N	type
8. #14519688	C₄	semidirect
58. C₆₁	#1836	semidirect

H ≅ G/N

type

8. #14519688

C₄

semidirect

58. C₆₁

#1836

semidirect

Subgroups — #21445952

Conjugacy classes of subgroups

Complements