Group #21445486 — subgroups

Subgroups — #21445486

Order 7808.

242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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	#16840138	C₂	1	2	yes	maximal, complemented
2	#16840135	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840108	C₂	1	2	yes	maximal, complemented
4	#16839483	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11758190	—	2	2	no	—
7	C₂×#11758199	—	2	4	no	—
8	#14519777	C₂²	1	1	yes	characteristic
9	#14519774	C₂²	1	1	yes	characteristic
10	#14519698	—	2	4	no	—
11	C₄×#92418	C₂²	1	2	yes	—
12	C₂×D₈×C₆₁	—	2	2	no	—
13	#127×C₆₁	C₂²	1	2	yes	—
14	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×D₄×C₆₁	—	2	2	no	—
16	C₂×D₄×C₆₁	—	2	2	no	—
17	C₂×D₄×C₆₁	—	2	2	no	—
18	C₂×D₂₄₄	—	2	2	no	—
19	C₂×D₂₄₄	—	2	1	no	—
20	C₂×Dic₁₂₂	—	2	1	no	—
21	D₈×C₆₁	—	4	4	no	—
22	C₂×C₈×C₆₁	D₄	1	2	yes	—
23	C₄²×C₆₁	C₂³	1	1	yes	characteristic
24	#11758199	—	4	8	no	—
25	C₄⋊Dic₆₁	—	2	2	no	—
26	C₂×#92418	D₄	1	4	yes	—
27	#11758190	—	4	4	no	—
28	C₂³×C₆₁	—	4	2	no	—
29	C₂²×D₆₁	—	4	1	no	—
30	D₄×C₆₁	—	4	4	no	—
31	D₄×C₆₁	—	4	4	no	—
32	D₄×C₆₁	—	4	4	no	—
33	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
35	C₂×Dic₆₁	—	4	1	no	—
36	D₂₄₄	—	4	2	no	—
37	D₂₄₄	—	4	4	no	—
38	Dic₁₂₂	—	4	2	no	—
39	C₈×C₆₁	D₈	1	4	yes	complemented
40	#92418	—	2	4	no	—
41	C₂²×C₆₁	—	8	2	no	—
42	C₂²×C₆₁	—	8	2	no	—
43	C₂²×C₆₁	—	8	2	no	—
44	C₂²×C₆₁	#127	1	1	yes	characteristic
45	C₂×D₆₁	—	8	1	no	—
46	C₂×D₆₁	—	8	2	no	—
47	C₄×C₆₁	C₂×D₈	1	2	yes	—
48	C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
49	Dic₆₁	—	8	1	no	—
50	#1721	—	61	1	no	maximal, Sylow
51	C₂×C₆₁	—	16	2	no	—
52	C₂×C₆₁	#493	1	1	yes	characteristic
53	C₂×C₆₁	#496	1	2	yes	—
54	D₆₁	—	16	1	no	—
55	#493	—	61	2	no	—
56	#493	D₆₁	1	1	yes	characteristic, complemented
57	#492	—	61	1	no	—
58	#486	—	61	2	no	—
59	#322	—	61	1	no	—
60	C₆₁	#1721	1	1	yes	characteristic, complemented, Sylow
61	C₂×SD₁₆	—	122	2	no	—
62	C₂×D₈	—	2	2	no	—
63	C₂×D₈	—	122	4	no	—
64	C₄⋊Q₈	—	61	1	no	—
65	#127	—	61	1	no	—
66	#127	C₂×D₆₁	1	2	yes	—
67	#102	—	122	4	no	—
68	C₄×C₈	—	61	2	no	—
69	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
70	C₂×Q₈	—	122	1	no	—
71	C₂×D₄	—	2	2	no	—
72	C₂×D₄	—	2	2	no	—
73	C₂×D₄	—	2	2	no	—
74	C₂×D₄	—	122	2	no	—
75	C₂×D₄	—	122	1	no	—
76	SD₁₆	—	244	4	no	—
77	D₈	—	4	4	no	—
78	D₈	—	244	8	no	—
79	C₂×C₈	—	61	4	no	—
80	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
81	C₄⋊C₄	—	122	2	no	—
82	C₄²	C₂²×D₆₁	1	1	yes	characteristic
83	C₂³	—	4	2	no	—
84	C₂³	—	244	1	no	—
85	Q₈	—	244	2	no	—
86	D₄	—	4	4	no	—
87	D₄	—	4	4	no	—
88	D₄	—	4	4	no	—
89	D₄	—	244	2	no	—
90	D₄	—	244	4	no	—
91	C₂×C₄	—	244	1	no	—
92	C₂×C₄	D₄×D₆₁	1	2	yes	—
93	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
94	C₈	—	122	4	no	—
95	C₈	#11758199	1	4	yes	complemented
96	C₂²	—	8	2	no	—
97	C₂²	—	8	2	no	—
98	C₂²	—	8	2	no	—
99	C₂²	—	488	1	no	—
100	C₂²	—	488	2	no	—
101	C₂²	#14519773	1	1	yes	characteristic
102	C₄	—	488	1	no	—
103	C₄	C₂×#11758199	1	2	yes	—
104	C₄	#14519801	1	4	yes	—
105	C₂	—	16	2	no	—
106	C₂	—	976	1	no	—
107	C₂	#16840138	1	1	yes	characteristic
108	C₂	#16840150	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840138

C₂

yes

maximal, complemented

#16840135

C₂

yes

maximal, characteristic, complemented

#16840108

C₂

yes

maximal, complemented

#16839483

C₂

yes

maximal, characteristic, complemented

C₆₁×#493

C₂

yes

maximal, characteristic, complemented

C₂×#11758190

—

C₂×#11758199

—

#14519777

C₂²

yes

characteristic

#14519774

C₂²

yes

characteristic

#14519698

—

C₄×#92418

C₂²

yes

—

C₂×D₈×C₆₁

—

#127×C₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₂₄₄

—

C₂×D₂₄₄

—

C₂×Dic₁₂₂

—

D₈×C₆₁

—

C₂×C₈×C₆₁

D₄

yes

—

C₄²×C₆₁

C₂³

yes

characteristic

#11758199

—

C₄⋊Dic₆₁

—

C₂×#92418

D₄

yes

—

#11758190

—

C₂³×C₆₁

—

C₂²×D₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×Dic₆₁

—

D₂₄₄

—

D₂₄₄

—

Dic₁₂₂

—

C₈×C₆₁

D₈

yes

complemented

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#127

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

C₂×D₈

yes

—

C₄×C₆₁

AGL(1,ℤ/8)

yes

—

Dic₆₁

—

#1721

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#493

yes

characteristic

C₂×C₆₁

#496

yes

—

D₆₁

—

#493

—

#493

D₆₁

yes

characteristic, complemented

#492

—

#486

—

#322

—

C₆₁

#1721

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

122

—

C₂×D₈

—

C₂×D₈

—

122

—

C₄⋊Q₈

—

#127

—

#127

C₂×D₆₁

yes

—

#102

—

122

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

122

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

122

—

C₂×D₄

—

122

—

SD₁₆

—

244

—

D₈

—

D₈

—

244

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₆₁

yes

—

C₄⋊C₄

—

122

—

C₄²

C₂²×D₆₁

yes

characteristic

C₂³

—

C₂³

—

244

—

Q₈

—

244

—

D₄

—

D₄

—

D₄

—

D₄

—

244

—

D₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

D₄×D₆₁

yes

—

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

122

—

C₈

#11758199

yes

complemented

C₂²

—

C₂²

—

C₂²

—

C₂²

—

488

—

100

C₂²

—

488

—

101

C₂²

#14519773

yes

characteristic

102

C₄

—

488

—

103

C₄

C₂×#11758199

yes

—

104

C₄

#14519801

yes

—

105

C₂

—

106

C₂

—

976

—

107

C₂

#16840138

yes

characteristic

108

C₂

#16840150

yes

—

	subgroup	G/H
center	C₂²	#14519773
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#493	C₂
socle	C₂²×C₆₁	#127
hypercenter	#493	D₆₁
hypocenter	C₆₁	#1721
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

#14519773

commutator

C₄²×C₆₁

C₂³

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#493

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
1. #16840138	C₂	semidirect
2. #16840135	C₂	semidirect
3. #16840108	C₂	semidirect
4. #16839483	C₂	semidirect
5. C₆₁×#493	C₂	semidirect
39. C₈×C₆₁	D₈	semidirect
56. #493	D₆₁	semidirect
60. C₆₁	#1721	semidirect
95. C₈	#11758199	semidirect

H ≅ G/N

type

1. #16840138

C₂

semidirect

2. #16840135

C₂

semidirect

3. #16840108

C₂

semidirect

4. #16839483

C₂

semidirect

5. C₆₁×#493

C₂

semidirect

39. C₈×C₆₁

D₈

semidirect

56. #493

D₆₁

semidirect

60. C₆₁

#1721

semidirect

95. C₈

#11758199

semidirect

Subgroups — #21445486

Conjugacy classes of subgroups

Complements