Group #21448130 — subgroups

Subgroups — #21448130

Order 7808.

112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 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	#16840191	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#16839601	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839600	C₂	1	1	yes	maximal, characteristic, complemented
5	#16839597	C₂	1	1	yes	maximal, characteristic, complemented
6	#16839595	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
8	#14519796	—	2	1	no	—
9	D₈×D₆₁	—	2	1	no	—
10	Dic₄₈₈	C₂²	1	1	yes	characteristic, complemented
11	#14519721	—	2	1	no	—
12	D₉₇₆	C₂²	1	1	yes	characteristic
13	#14519718	—	2	1	no	—
14	C₁₆×D₆₁	C₂²	1	1	yes	characteristic
15	#14519683	C₂²	1	1	yes	characteristic, complemented
16	D₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	D₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
18	C₃₂×C₆₁	C₂²	1	1	yes	characteristic, complemented
19	#11758224	—	4	1	no	—
20	D₄×D₆₁	—	4	1	no	—
21	D₈×C₆₁	—	2	1	no	—
22	D₈×C₆₁	—	2	1	no	—
23	#11758200	—	4	1	no	—
24	#11758199	—	4	1	no	—
25	Dic₂₄₄	—	2	1	no	—
26	D₄₈₈	—	2	1	no	—
27	C₈×D₆₁	D₄	1	1	yes	characteristic
28	C₁₆×C₆₁	C₂³	1	1	yes	characteristic
29	#11758185	D₄	1	1	yes	characteristic
30	C₂²×D₆₁	—	8	1	no	—
31	D₄×C₆₁	—	4	1	no	—
32	D₄×C₆₁	—	4	1	no	—
33	C₂²⋊D₆₁	—	8	1	no	—
34	C₂²⋊D₆₁	—	8	1	no	—
35	C₂×Dic₆₁	—	8	1	no	—
36	D₂₄₄	—	4	1	no	—
37	C₄×D₆₁	D₈	1	1	yes	characteristic
38	Dic₁₂₂	—	4	1	no	—
39	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
40	#92418	D₈	1	1	yes	characteristic
41	C₂²×C₆₁	—	8	1	no	—
42	C₂²×C₆₁	—	8	1	no	—
43	C₂×D₆₁	—	8	1	no	—
44	C₂×D₆₁	—	16	2	no	—
45	C₂×D₆₁	D₁₆	1	1	yes	characteristic
46	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
47	Dic₆₁	—	8	1	no	—
48	Dic₆₁	D₁₆	1	1	yes	characteristic
49	#2263	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	—	16	1	no	—
51	C₂×C₆₁	—	16	1	no	—
52	C₂×C₆₁	C₂×D₁₆	1	1	yes	characteristic
53	D₆₁	—	2	1	no	—
54	D₆₁	—	16	1	no	—
55	#508	—	61	1	no	—
56	C₂×D₁₆	—	61	1	no	—
57	SD₆₄	—	61	1	no	—
58	SD₆₄	—	61	1	no	—
59	D₃₂	—	61	1	no	—
60	D₃₂	D₆₁	1	1	yes	characteristic, complemented
61	M₆₄	—	61	1	no	—
62	C₆₁	#2263	1	1	yes	characteristic, complemented, Sylow
63	#135	—	122	1	no	—
64	C₂×D₈	—	122	1	no	—
65	Q₃₂	—	61	1	no	—
66	SD₃₂	—	122	1	no	—
67	D₁₆	—	61	1	no	—
68	D₁₆	—	122	1	no	—
69	D₁₆	C₂×D₆₁	1	1	yes	characteristic
70	D₁₆	C₂×D₆₁	1	1	yes	characteristic, complemented
71	C₂×C₁₆	—	61	1	no	—
72	C₃₂	—	61	1	no	—
73	C₃₂	C₂×D₆₁	1	1	yes	characteristic, complemented
74	#41	—	244	1	no	—
75	C₂×D₄	—	244	1	no	—
76	Q₁₆	—	122	1	no	—
77	SD₁₆	—	244	1	no	—
78	D₈	—	2	1	no	—
79	D₈	—	2	1	no	—
80	D₈	—	122	1	no	—
81	D₈	—	244	1	no	—
82	C₂×C₈	—	61	1	no	—
83	C₁₆	—	61	1	no	—
84	C₁₆	C₂²×D₆₁	1	1	yes	characteristic
85	C₂³	—	488	1	no	—
86	Q₈	—	244	1	no	—
87	D₄	—	4	1	no	—
88	D₄	—	4	1	no	—
89	D₄	—	488	1	no	—
90	D₄	—	488	1	no	—
91	D₄	—	244	1	no	—
92	C₂×C₄	—	61	1	no	—
93	C₂×C₄	—	488	1	no	—
94	C₈	—	61	1	no	—
95	C₈	D₄×D₆₁	1	1	yes	characteristic
96	C₂²	—	8	1	no	—
97	C₂²	—	8	1	no	—
98	C₂²	—	61	1	no	—
99	C₂²	—	976	2	no	—
100	C₂²	—	488	1	no	—
101	C₄	—	61	1	no	—
102	C₄	—	488	1	no	—
103	C₄	D₈×D₆₁	1	1	yes	characteristic
104	C₂	—	16	1	no	—
105	C₂	—	16	1	no	—
106	C₂	—	122	1	no	—
107	C₂	—	976	1	no	—
108	C₂	D₁₆×D₆₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840191

C₂

yes

maximal, characteristic, complemented

D₁₆×D₆₁

C₂

yes

maximal, characteristic, complemented

#16839601

C₂

yes

maximal, characteristic, complemented

#16839600

C₂

yes

maximal, characteristic, complemented

#16839597

C₂

yes

maximal, characteristic, complemented

#16839595

C₂

yes

maximal, characteristic, complemented

C₆₁×D₃₂

C₂

yes

maximal, characteristic, complemented

#14519796

—

D₈×D₆₁

—

Dic₄₈₈

C₂²

yes

characteristic, complemented

#14519721

—

D₉₇₆

C₂²

yes

characteristic

#14519718

—

C₁₆×D₆₁

C₂²

yes

characteristic

#14519683

C₂²

yes

characteristic, complemented

D₁₆×C₆₁

C₂²

yes

characteristic

D₁₆×C₆₁

C₂²

yes

characteristic, complemented

C₃₂×C₆₁

C₂²

yes

characteristic, complemented

#11758224

—

D₄×D₆₁

—

D₈×C₆₁

—

D₈×C₆₁

—

#11758200

—

#11758199

—

Dic₂₄₄

—

D₄₈₈

—

C₈×D₆₁

D₄

yes

characteristic

C₁₆×C₆₁

C₂³

yes

characteristic

#11758185

D₄

yes

characteristic

C₂²×D₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂²⋊D₆₁

—

C₂²⋊D₆₁

—

C₂×Dic₆₁

—

D₂₄₄

—

C₄×D₆₁

D₈

yes

characteristic

Dic₁₂₂

—

C₈×C₆₁

C₂×D₄

yes

characteristic

#92418

D₈

yes

characteristic

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

D₁₆

yes

characteristic

C₄×C₆₁

C₂×D₈

yes

characteristic

Dic₆₁

—

Dic₆₁

D₁₆

yes

characteristic

#2263

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

C₂×D₁₆

yes

characteristic

D₆₁

—

D₆₁

—

#508

—

C₂×D₁₆

—

SD₆₄

—

SD₆₄

—

D₃₂

—

D₃₂

D₆₁

yes

characteristic, complemented

M₆₄

—

C₆₁

#2263

yes

characteristic, complemented, Sylow

#135

—

122

—

C₂×D₈

—

122

—

Q₃₂

—

SD₃₂

—

122

—

D₁₆

—

D₁₆

—

122

—

D₁₆

C₂×D₆₁

yes

characteristic

D₁₆

C₂×D₆₁

yes

characteristic, complemented

C₂×C₁₆

—

C₃₂

—

C₃₂

C₂×D₆₁

yes

characteristic, complemented

#41

—

244

—

C₂×D₄

—

244

—

Q₁₆

—

122

—

SD₁₆

—

244

—

D₈

—

D₈

—

D₈

—

122

—

D₈

—

244

—

C₂×C₈

—

C₁₆

—

C₁₆

C₂²×D₆₁

yes

characteristic

C₂³

—

488

—

Q₈

—

244

—

D₄

—

D₄

—

D₄

—

488

—

D₄

—

488

—

D₄

—

244

—

C₂×C₄

—

C₂×C₄

—

488

—

C₈

—

C₈

D₄×D₆₁

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

—

976

—

100

C₂²

—

488

—

101

C₄

—

102

C₄

—

488

—

103

C₄

D₈×D₆₁

yes

characteristic

104

C₂

—

105

C₂

—

106

C₂

—

122

—

107

C₂

—

976

—

108

C₂

D₁₆×D₆₁

yes

characteristic

	subgroup	G/H
center	C₂	D₁₆×D₆₁
commutator	C₁₆×C₆₁	C₂³
Frattini	C₁₆	C₂²×D₆₁
Fitting	C₆₁×D₃₂	C₂
socle	C₂×C₆₁	C₂×D₁₆
hypercenter	D₃₂	D₆₁
hypocenter	C₆₁	#2263
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

subgroup

G/H

center

C₂

D₁₆×D₆₁

commutator

C₁₆×C₆₁

C₂³

Frattini

C₁₆

C₂²×D₆₁

Fitting

C₆₁×D₃₂

C₂

socle

C₂×C₆₁

C₂×D₁₆

hypercenter

D₃₂

D₆₁

hypocenter

C₆₁

#2263

LCS

G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

N	H ≅ G/N	type
1. #16840191	C₂	semidirect
2. D₁₆×D₆₁	C₂	semidirect
3. #16839601	C₂	semidirect
4. #16839600	C₂	semidirect
5. #16839597	C₂	semidirect
6. #16839595	C₂	semidirect
7. C₆₁×D₃₂	C₂	semidirect
10. Dic₄₈₈	C₂²	semidirect
15. #14519683	C₂²	semidirect
17. D₁₆×C₆₁	C₂²	semidirect
18. C₃₂×C₆₁	C₂²	semidirect
60. D₃₂	D₆₁	semidirect
62. C₆₁	#2263	semidirect
70. D₁₆	C₂×D₆₁	semidirect
73. C₃₂	C₂×D₆₁	semidirect

H ≅ G/N

type

1. #16840191

C₂

semidirect

2. D₁₆×D₆₁

C₂

semidirect

3. #16839601

C₂

semidirect

4. #16839600

C₂

semidirect

5. #16839597

C₂

semidirect

6. #16839595

C₂

semidirect

7. C₆₁×D₃₂

C₂

semidirect

10. Dic₄₈₈

C₂²

semidirect

15. #14519683

C₂²

semidirect

17. D₁₆×C₆₁

C₂²

semidirect

18. C₃₂×C₆₁

C₂²

semidirect

60. D₃₂

D₆₁

semidirect

62. C₆₁

#2263

semidirect

70. D₁₆

C₂×D₆₁

semidirect

73. C₃₂

C₂×D₆₁

semidirect

Subgroups — #21448130

Conjugacy classes of subgroups

Complements