Group #21447571 — subgroups

Subgroups — C₂×#16839580 #21447571

Order 7808.

184 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 117 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	C₂²×#11758185	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic
3	#16839580	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92418	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₆₁	C₄	1	1	yes	characteristic
7	C₂×#11758185	—	2	2	no	—
8	C₂×#11758185	C₂²	1	2	yes	—
9	C₈×Dic₆₁	C₄	1	2	yes	—
10	C₈×Dic₆₁	C₂²	1	2	yes	—
11	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₆₁	—	2	2	no	—
13	C₂×C₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₆₁	C₈	1	1	yes	characteristic
16	C₂²×Dic₆₁	C₈	1	1	yes	characteristic
17	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	D₄	1	2	yes	—
19	C₂×C₈×C₆₁	Q₈	1	2	yes	—
20	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
21	C₄×Dic₆₁	C₈	1	2	yes	—
22	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
23	C₂×#92418	—	2	2	no	—
24	C₂×#92418	C₂×C₄	1	2	yes	—
25	C₁₆×C₆₁	—	2	2	no	—
26	#11758185	—	2	2	no	—
27	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
31	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₆₁	—	2	2	no	—
33	C₂×Dic₆₁	C₁₆	1	4	yes	complemented
34	C₂×Dic₆₁	C₂×C₈	1	2	yes	—
35	C₂×Dic₆₁	C₂×C₈	1	2	yes	—
36	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
37	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
38	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
39	#92418	—	2	2	no	—
40	C₂²×C₆₁	C₄⋊C₈	1	2	yes	—
41	C₂²×C₆₁	C₂×C₁₆	1	2	yes	—
42	C₂²×C₆₁	M₃₂	1	2	yes	—
43	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
44	C₄×C₆₁	C₄⋊C₈	1	2	yes	—
45	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
47	Dic₆₁	—	2	2	no	—
48	Dic₆₁	C₂×C₁₆	1	4	yes	complemented
49	C₂×C₄⋊C₁₆	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	C₄⋊C₁₆	1	4	yes	complemented
51	C₂×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
52	C₂×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
53	C₂×C₆₁	C₂×M₃₂	1	1	yes	characteristic
54	C₂²×C₁₆	—	61	1	no	—
55	C₂²×C₁₆	D₆₁	1	1	yes	characteristic
56	C₂×C₄×C₈	—	61	1	no	—
57	C₄⋊C₁₆	—	61	4	no	—
58	C₆₁	C₂×C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₈	—	61	1	no	—
60	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
61	C₂×C₄²	—	61	1	no	—
62	C₂×C₁₆	—	2	2	no	—
63	C₂×C₁₆	—	61	2	no	—
64	C₂×C₁₆	—	122	2	no	—
65	C₂×C₁₆	C₂×D₆₁	1	2	yes	—
66	C₄×C₈	—	61	2	no	—
67	C₄×C₈	—	61	2	no	—
68	C₂²×C₄	—	61	1	no	—
69	C₂²×C₄	—	61	1	no	—
70	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
71	C₂×C₈	—	61	2	no	—
72	C₂×C₈	—	122	2	no	—
73	C₂×C₈	Dic₁₂₂	1	2	yes	—
74	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
75	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
76	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
77	C₄²	—	61	2	no	—
78	C₄²	—	61	2	no	—
79	C₁₆	—	2	2	no	—
80	C₁₆	—	122	2	no	—
81	C₂³	C₈×D₆₁	1	1	yes	characteristic
82	C₂×C₄	—	61	4	no	—
83	C₂×C₄	—	61	2	no	—
84	C₂×C₄	—	61	2	no	—
85	C₂×C₄	—	122	2	no	—
86	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
87	C₂×C₄	#11758189	1	2	yes	—
88	C₂×C₄	#11758196	1	2	yes	—
89	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
90	C₈	—	122	2	no	—
91	C₈	#11758196	1	2	yes	—
92	C₈	C₂×Dic₁₂₂	1	1	yes	characteristic
93	C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
94	C₂²	#14519706	1	2	yes	—
95	C₂²	C₁₆×D₆₁	1	2	yes	—
96	C₂²	#14519716	1	2	yes	—
97	C₂²	C₂×C₈×D₆₁	1	1	yes	characteristic
98	C₄	—	61	4	no	—
99	C₄	—	122	2	no	—
100	C₄	#14519706	1	2	yes	—
101	C₄	C₂×#11758196	1	1	yes	characteristic
102	C₄	C₂×#11758189	1	1	yes	characteristic
103	C₂	#16839580	1	4	yes	direct product factor
104	C₂	C₂×#14519706	1	1	yes	characteristic
105	C₂	C₂×C₁₆×D₆₁	1	1	yes	characteristic
106	C₂	C₂×#14519716	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11758185

C₂

yes

maximal, characteristic

C₂×C₈×Dic₆₁

C₂

yes

maximal, characteristic

#16839580

C₂

yes

maximal, direct product factor

C₂²×C₁₆×C₆₁

C₂

yes

maximal, characteristic

C₂²×#92418

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₄

yes

characteristic

C₂×#11758185

—

C₂×#11758185

C₂²

yes

—

C₈×Dic₆₁

C₄

yes

—

C₈×Dic₆₁

C₂²

yes

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

—

C₂×C₁₆×C₆₁

C₂²

yes

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₈

yes

characteristic

C₂²×Dic₆₁

C₈

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

—

C₂×C₈×C₆₁

Q₈

yes

—

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄×Dic₆₁

C₈

yes

—

C₄×Dic₆₁

C₂×C₄

yes

—

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

—

C₁₆×C₆₁

—

#11758185

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₁₆

yes

complemented

C₂×Dic₆₁

C₂×C₈

yes

—

C₂×Dic₆₁

C₂×C₈

yes

—

C₈×C₆₁

C₄⋊C₄

yes

—

C₈×C₆₁

C₂×D₄

yes

characteristic

C₈×C₆₁

C₂×Q₈

yes

characteristic

#92418

—

C₂²×C₆₁

C₄⋊C₈

yes

—

C₂²×C₆₁

C₂×C₁₆

yes

—

C₂²×C₆₁

M₃₂

yes

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

C₂×C₁₆

yes

complemented

C₂×C₄⋊C₁₆

—

maximal, Sylow

C₂×C₆₁

C₄⋊C₁₆

yes

complemented

C₂×C₆₁

C₂×C₄⋊C₈

yes

characteristic

C₂×C₆₁

C₂²×C₁₆

yes

characteristic

C₂×C₆₁

C₂×M₃₂

yes

characteristic

C₂²×C₁₆

—

C₂²×C₁₆

D₆₁

yes

characteristic

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₆₁

C₂×C₄⋊C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

C₂×C₁₆

C₂×D₆₁

yes

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

Dic₁₂₂

yes

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

—

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

122

—

C₂³

C₈×D₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

C₈×D₆₁

yes

characteristic

C₂×C₄

#11758189

yes

—

C₂×C₄

#11758196

yes

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₈

—

122

—

C₈

#11758196

yes

—

C₈

C₂×Dic₁₂₂

yes

characteristic

C₈

C₂×C₂²⋊D₆₁

yes

characteristic

C₂²

#14519706

yes

—

C₂²

C₁₆×D₆₁

yes

—

C₂²

#14519716

yes

—

C₂²

C₂×C₈×D₆₁

yes

characteristic

C₄

—

C₄

—

122

—

100

C₄

#14519706

yes

—

101

C₄

C₂×#11758196

yes

characteristic

102

C₄

C₂×#11758189

yes

characteristic

103

C₂

#16839580

yes

direct product factor

104

C₂

C₂×#14519706

yes

characteristic

105

C₂

C₂×C₁₆×D₆₁

yes

characteristic

106

C₂

C₂×#14519716

yes

characteristic

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

subgroup

G/H

center

C₂²×C₈

C₂×D₆₁

commutator

C₂×C₆₁

C₂²×C₁₆

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₂²×C₁₆×C₆₁

C₂

socle

C₂³×C₆₁

C₂×C₈

hypercenter

C₂²×C₁₆

D₆₁

hypocenter

C₆₁

C₂×C₄⋊C₁₆

LCS

G ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂²×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
3. #16839580	C₂	direct (N × H)
33. C₂×Dic₆₁	C₁₆	semidirect
48. Dic₆₁	C₂×C₁₆	semidirect
50. C₂×C₆₁	C₄⋊C₁₆	semidirect
58. C₆₁	C₂×C₄⋊C₁₆	semidirect
103. C₂	#16839580	direct (N × H)

H ≅ G/N

type

3. #16839580

C₂

direct (N × H)

33. C₂×Dic₆₁

C₁₆

semidirect

48. Dic₆₁

C₂×C₁₆

semidirect

50. C₂×C₆₁

C₄⋊C₁₆

semidirect

58. C₆₁

C₂×C₄⋊C₁₆

semidirect

103. C₂

#16839580

direct (N × H)

Subgroups — C₂×#16839580 #21447571

Conjugacy classes of subgroups

Complements

Subgroups — C2×#16839580 #21447571

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16839580 #21447571