Group #21448067 — subgroups

Subgroups — #21448067

Order 7808.

216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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×D₉₇₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14519718	C₂	1	2	yes	maximal, complemented
3	#16840137	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₈₈	C₂²	1	2	yes	—
7	C₂×#11758199	—	2	2	no	—
8	#14519773	—	2	2	no	—
9	D₉₇₆	—	2	2	no	—
10	#14519718	—	2	4	no	—
11	C₂×#11758185	C₂²	1	1	yes	characteristic
12	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
13	C₂×D₈×C₆₁	C₂²	1	2	yes	—
14	D₁₆×C₆₁	—	2	2	no	—
15	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×D₄×C₆₁	—	2	2	no	—
17	C₂×C₂²⋊D₆₁	—	4	4	no	—
18	C₂×D₂₄₄	—	2	2	no	—
19	D₈×C₆₁	—	2	2	no	—
20	D₈×C₆₁	—	2	2	no	—
21	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
22	#11758199	—	4	4	no	—
23	C₄×Dic₆₁	D₄	1	1	yes	characteristic
24	C₂×#92418	D₄	1	1	yes	characteristic
25	D₄₈₈	—	2	2	no	—
26	D₄₈₈	—	2	2	no	—
27	C₁₆×C₆₁	D₄	1	2	yes	complemented
28	#11758185	D₄	1	2	yes	complemented
29	C₂³×C₆₁	—	4	2	no	—
30	C₂²×D₆₁	—	4	2	no	—
31	D₄×C₆₁	—	4	2	no	—
32	D₄×C₆₁	—	4	2	no	—
33	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
34	C₂²⋊D₆₁	—	8	8	no	—
35	C₂×Dic₆₁	D₈	1	2	yes	—
36	D₂₄₄	—	4	2	no	—
37	D₂₄₄	—	4	2	no	—
38	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
39	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
40	#92418	D₈	1	2	yes	—
41	C₂²×C₆₁	—	8	2	no	—
42	C₂²×C₆₁	—	8	4	no	—
43	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
44	C₂×D₆₁	—	8	2	no	—
45	C₂×D₆₁	—	8	4	no	—
46	C₄×C₆₁	#127	1	1	yes	characteristic
47	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
48	Dic₆₁	D₁₆	1	4	yes	complemented
49	#2246	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	—	16	2	no	—
51	C₂×C₆₁	#493	1	1	yes	characteristic
52	C₂×C₆₁	C₂×D₁₆	1	2	yes	—
53	D₆₁	—	16	2	no	—
54	C₂×D₁₆	—	61	2	no	—
55	C₂×D₁₆	—	61	1	no	—
56	C₂×D₁₆	D₆₁	1	1	yes	characteristic, complemented
57	#493	—	61	2	no	—
58	C₄×C₁₆	—	61	1	no	—
59	C₆₁	#2246	1	1	yes	characteristic, complemented, Sylow
60	C₂×D₈	—	61	2	no	—
61	C₂×D₈	—	122	2	no	—
62	C₂×D₈	C₂×D₆₁	1	2	yes	—
63	#127	—	122	2	no	—
64	D₁₆	—	2	2	no	—
65	D₁₆	—	122	4	no	—
66	D₁₆	—	122	2	no	—
67	C₂×C₁₆	—	61	1	no	—
68	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
69	C₄×C₈	—	61	1	no	—
70	C₂×D₄	—	2	2	no	—
71	C₂×D₄	—	122	2	no	—
72	C₂×D₄	—	244	4	no	—
73	D₈	—	2	2	no	—
74	D₈	—	2	2	no	—
75	D₈	—	122	2	no	—
76	D₈	—	122	2	no	—
77	D₈	—	244	4	no	—
78	C₂×C₈	—	61	1	no	—
79	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
80	C₄²	—	61	1	no	—
81	C₁₆	—	61	2	no	—
82	C₁₆	C₂²⋊D₆₁	1	2	yes	complemented
83	C₂³	—	4	2	no	—
84	C₂³	—	244	2	no	—
85	D₄	—	4	2	no	—
86	D₄	—	4	2	no	—
87	D₄	—	488	8	no	—
88	D₄	—	244	2	no	—
89	D₄	—	244	2	no	—
90	C₂×C₄	—	61	2	no	—
91	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
92	C₈	—	61	2	no	—
93	C₈	D₄×D₆₁	1	1	yes	characteristic
94	C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
95	C₂²	—	8	2	no	—
96	C₂²	—	8	4	no	—
97	C₂²	—	488	2	no	—
98	C₂²	—	488	4	no	—
99	C₂²	D₈×D₆₁	1	1	yes	characteristic
100	C₄	—	61	4	no	—
101	C₄	#14519773	1	1	yes	characteristic
102	C₄	D₈×D₆₁	1	1	yes	characteristic
103	C₂	—	16	2	no	—
104	C₂	—	976	2	no	—
105	C₂	#16840137	1	1	yes	characteristic
106	C₂	D₁₆×D₆₁	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₉₇₆

C₂

yes

maximal, characteristic, complemented

C₂×#14519718

C₂

yes

maximal, complemented

#16840137

C₂

yes

maximal, complemented

C₁₆×Dic₆₁

C₂

yes

maximal, characteristic, complemented

C₂×D₁₆×C₆₁

C₂

yes

maximal, characteristic, complemented

C₂×D₄₈₈

C₂²

yes

—

C₂×#11758199

—

#14519773

—

D₉₇₆

—

#14519718

—

C₂×#11758185

C₂²

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₂×D₈×C₆₁

C₂²

yes

—

D₁₆×C₆₁

—

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

C₂×D₄×C₆₁

—

C₂×C₂²⋊D₆₁

—

C₂×D₂₄₄

—

D₈×C₆₁

—

D₈×C₆₁

—

C₂×C₈×C₆₁

C₂³

yes

characteristic

#11758199

—

C₄×Dic₆₁

D₄

yes

characteristic

C₂×#92418

D₄

yes

characteristic

D₄₈₈

—

D₄₈₈

—

C₁₆×C₆₁

D₄

yes

complemented

#11758185

D₄

yes

complemented

C₂³×C₆₁

—

C₂²×D₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂²⋊D₆₁

—

C₂×Dic₆₁

D₈

yes

—

D₂₄₄

—

D₂₄₄

—

C₈×C₆₁

C₂×D₄

yes

characteristic

C₈×C₆₁

C₂×D₄

yes

characteristic

#92418

D₈

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

#127

yes

characteristic

C₄×C₆₁

C₂×D₈

yes

characteristic

Dic₆₁

D₁₆

yes

complemented

#2246

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#493

yes

characteristic

C₂×C₆₁

C₂×D₁₆

yes

—

D₆₁

—

C₂×D₁₆

—

C₂×D₁₆

—

C₂×D₁₆

D₆₁

yes

characteristic, complemented

#493

—

C₄×C₁₆

—

C₆₁

#2246

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×D₈

—

122

—

C₂×D₈

C₂×D₆₁

yes

—

#127

—

122

—

D₁₆

—

D₁₆

—

122

—

D₁₆

—

122

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₆₁

yes

characteristic

C₄×C₈

—

C₂×D₄

—

C₂×D₄

—

122

—

C₂×D₄

—

244

—

D₈

—

D₈

—

D₈

—

122

—

D₈

—

122

—

D₈

—

244

—

C₂×C₈

—

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄²

—

C₁₆

—

C₁₆

C₂²⋊D₆₁

yes

complemented

C₂³

—

C₂³

—

244

—

D₄

—

D₄

—

D₄

—

488

—

D₄

—

244

—

D₄

—

244

—

C₂×C₄

—

C₂×C₄

D₄×D₆₁

yes

characteristic

C₈

—

C₈

D₄×D₆₁

yes

characteristic

C₈

C₂×C₂²⋊D₆₁

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

488

—

C₂²

—

488

—

C₂²

D₈×D₆₁

yes

characteristic

100

C₄

—

101

C₄

#14519773

yes

characteristic

102

C₄

D₈×D₆₁

yes

characteristic

103

C₂

—

104

C₂

—

976

—

105

C₂

#16840137

yes

characteristic

106

C₂

D₁₆×D₆₁

yes

—

	subgroup	G/H
center	C₂²	D₈×D₆₁
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₂×D₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	C₂×D₁₆	D₆₁
hypocenter	C₆₁	#2246
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

subgroup

G/H

center

C₂²

D₈×D₆₁

commutator

C₂×C₈×C₆₁

C₂³

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₂×D₁₆×C₆₁

C₂

socle

C₂²×C₆₁

C₂×D₈

hypercenter

C₂×D₁₆

D₆₁

hypocenter

C₆₁

#2246

LCS

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

N	H ≅ G/N	type
1. C₂×D₉₇₆	C₂	semidirect
2. C₂×#14519718	C₂	semidirect
3. #16840137	C₂	semidirect
4. C₁₆×Dic₆₁	C₂	semidirect
5. C₂×D₁₆×C₆₁	C₂	semidirect
27. C₁₆×C₆₁	D₄	semidirect
28. #11758185	D₄	semidirect
48. Dic₆₁	D₁₆	semidirect
56. C₂×D₁₆	D₆₁	semidirect
59. C₆₁	#2246	semidirect
82. C₁₆	C₂²⋊D₆₁	semidirect

H ≅ G/N

type

1. C₂×D₉₇₆

C₂

semidirect

2. C₂×#14519718

C₂

semidirect

3. #16840137

C₂

semidirect

4. C₁₆×Dic₆₁

C₂

semidirect

5. C₂×D₁₆×C₆₁

C₂

semidirect

27. C₁₆×C₆₁

D₄

semidirect

28. #11758185

D₄

semidirect

48. Dic₆₁

D₁₆

semidirect

56. C₂×D₁₆

D₆₁

semidirect

59. C₆₁

#2246

semidirect

82. C₁₆

C₂²⋊D₆₁

semidirect

Subgroups — #21448067

Conjugacy classes of subgroups

Complements