Group #20266145 — subgroups

Subgroups — D₁₀₁⋊(C₂²⋊C₈) #20266145

Order 6464.

202 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 70 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×D₁₀₁⋊C₈	C₂	1	2	yes	maximal, complemented
2	#15692312	C₂	1	2	yes	maximal, complemented
3	C₂²⋊#11717581	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic
5	D₁₀₁⋊C₈	—	2	4	no	—
6	C₂×#11717581	C₂²	1	4	yes	complemented
7	C₂³×D₁₀₁	C₄	1	1	yes	characteristic
8	C₂²×Dic₁₀₁	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₀₁	—	2	4	no	—
10	C₂×C₄×D₁₀₁	C₄	1	1	yes	characteristic
11	C₂×C₄×D₁₀₁	C₄	1	1	yes	characteristic
12	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₁₀₁	C₄	1	1	yes	characteristic
15	C₂³×C₁₀₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×D₁₀₁	—	2	2	no	—
17	C₂²×D₁₀₁	—	2	2	no	—
18	C₂²×D₁₀₁	C₈	1	4	yes	complemented
19	C₂²×D₁₀₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×D₁₀₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₀₁	—	2	2	no	—
22	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₁₀₁	—	2	2	no	—
25	C₂×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
26	C₂×Dic₁₀₁	C₂³	1	1	yes	characteristic
27	C₄×D₁₀₁	—	2	2	no	—
28	C₄×D₁₀₁	—	2	2	no	—
29	C₄×D₁₀₁	—	2	2	no	—
30	C₄×D₁₀₁	D₄	1	4	yes	—
31	#11717581	—	2	4	no	—
32	C₂²×C₁₀₁	—	2	1	no	—
33	C₂²×C₁₀₁	—	2	1	no	—
34	C₂²×C₁₀₁	C₂×C₈	1	2	yes	complemented
35	C₂²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×D₁₀₁	—	2	1	no	—
37	C₂×D₁₀₁	—	2	1	no	—
38	C₂×D₁₀₁	—	2	8	no	—
39	C₂×D₁₀₁	C₂²⋊C₄	1	2	yes	—
40	C₂×D₁₀₁	C₂×C₈	1	2	yes	—
41	C₂×D₁₀₁	C₂×C₈	1	2	yes	complemented
42	C₂×D₁₀₁	M₁₆	1	2	yes	—
43	C₄×C₁₀₁	—	2	1	no	—
44	C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
45	Dic₁₀₁	—	2	1	no	—
46	Dic₁₀₁	C₂×D₄	1	2	yes	—
47	C₂×C₁₀₁	—	2	2	no	—
48	C₂×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₁₀₁	C₂²×C₈	1	1	yes	characteristic
50	C₂×C₁₀₁	C₂×M₁₆	1	1	yes	characteristic
51	D₁₀₁	—	2	2	no	—
52	D₁₀₁	C₂²⋊C₈	1	4	yes	complemented
53	C₁₀₁	C₂×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₂²⋊C₈	—	101	1	no	maximal, Sylow
55	C₂³×C₄	—	101	1	no	—
56	C₂²×C₈	—	101	2	no	—
57	C₂²⋊C₈	—	101	2	no	—
58	C₂²⋊C₈	—	101	2	no	—
59	C₂⁴	—	101	1	no	—
60	C₂²×C₄	—	101	1	no	—
61	C₂²×C₄	—	101	1	no	—
62	C₂²×C₄	—	101	1	no	—
63	C₂²×C₄	—	101	1	no	—
64	C₂²×C₄	—	101	1	no	—
65	C₂²×C₄	—	202	4	no	—
66	C₂²×C₄	#87938	1	1	yes	characteristic
67	C₂×C₈	—	101	4	no	—
68	C₂×C₈	—	202	4	no	—
69	C₂³	—	101	1	no	—
70	C₂³	—	101	4	no	—
71	C₂³	—	101	1	no	—
72	C₂³	—	202	2	no	—
73	C₂³	—	202	2	no	—
74	C₂³	C₂×#87938	1	1	yes	characteristic
75	C₂×C₄	—	2	2	no	—
76	C₂×C₄	—	101	1	no	—
77	C₂×C₄	—	101	4	no	—
78	C₂×C₄	—	101	1	no	—
79	C₂×C₄	—	202	2	no	—
80	C₂×C₄	—	202	2	no	—
81	C₂×C₄	—	202	2	no	—
82	C₂×C₄	—	202	2	no	—
83	C₂×C₄	C₂×#87938	1	1	yes	characteristic
84	C₂×C₄	C₂×#87938	1	1	yes	characteristic
85	C₈	—	202	4	no	—
86	C₂²	—	2	1	no	—
87	C₂²	—	2	1	no	—
88	C₂²	—	101	2	no	—
89	C₂²	—	101	2	no	—
90	C₂²	—	101	2	no	—
91	C₂²	—	101	2	no	—
92	C₂²	—	202	8	no	—
93	C₂²	—	202	1	no	—
94	C₂²	—	202	1	no	—
95	C₂²	D₁₀₁⋊C₈	1	2	yes	complemented
96	C₂²	C₂²×#87938	1	1	yes	characteristic
97	C₄	—	2	1	no	—
98	C₄	—	101	2	no	—
99	C₄	—	202	1	no	—
100	C₄	C₂²⋊#87938	1	2	yes	—
101	C₂	—	2	2	no	—
102	C₂	—	101	4	no	—
103	C₂	—	202	2	no	—
104	C₂	C₂×C₂²⋊#87938	1	1	yes	characteristic
105	C₂	C₂×D₁₀₁⋊C₈	1	1	yes	characteristic
106	C₂	D₁₀₁⋊M₁₆	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₁₀₁⋊C₈

C₂

yes

maximal, complemented

#15692312

C₂

yes

maximal, complemented

C₂²⋊#11717581

C₂

yes

maximal, complemented

C₂²×C₄×D₁₀₁

C₂

yes

maximal, characteristic

D₁₀₁⋊C₈

—

C₂×#11717581

C₂²

yes

complemented

C₂³×D₁₀₁

C₄

yes

characteristic

C₂²×Dic₁₀₁

C₂²

yes

characteristic

C₂×C₄×D₁₀₁

—

C₂×C₄×D₁₀₁

C₄

yes

characteristic

C₂×C₄×D₁₀₁

C₄

yes

characteristic

C₂×C₄×D₁₀₁

C₂²

yes

characteristic

C₂×C₄×D₁₀₁

C₂²

yes

characteristic

C₂²×C₄×C₁₀₁

C₄

yes

characteristic

C₂³×C₁₀₁

C₂×C₄

yes

characteristic

C₂²×D₁₀₁

—

C₂²×D₁₀₁

—

C₂²×D₁₀₁

C₈

yes

complemented

C₂²×D₁₀₁

C₂×C₄

yes

characteristic

C₂²×D₁₀₁

C₂×C₄

yes

characteristic

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

C₂×C₄

yes

characteristic

C₂×C₄×C₁₀₁

C₂×C₄

yes

characteristic

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

C₂×C₄

yes

characteristic

C₂×Dic₁₀₁

C₂³

yes

characteristic

C₄×D₁₀₁

—

C₄×D₁₀₁

—

C₄×D₁₀₁

—

C₄×D₁₀₁

D₄

yes

—

#11717581

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

C₂×C₈

yes

complemented

C₂²×C₁₀₁

C₂²×C₄

yes

characteristic

C₂×D₁₀₁

—

C₂×D₁₀₁

—

C₂×D₁₀₁

—

C₂×D₁₀₁

C₂²⋊C₄

yes

—

C₂×D₁₀₁

C₂×C₈

yes

—

C₂×D₁₀₁

C₂×C₈

yes

complemented

C₂×D₁₀₁

M₁₆

yes

—

C₄×C₁₀₁

—

C₄×C₁₀₁

C₂²⋊C₄

yes

—

Dic₁₀₁

—

Dic₁₀₁

C₂×D₄

yes

—

C₂×C₁₀₁

—

C₂×C₁₀₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₁₀₁

C₂²×C₈

yes

characteristic

C₂×C₁₀₁

C₂×M₁₆

yes

characteristic

D₁₀₁

—

D₁₀₁

C₂²⋊C₈

yes

complemented

C₁₀₁

C₂×C₂²⋊C₈

yes

characteristic, complemented, Sylow

C₂×C₂²⋊C₈

—

101

maximal, Sylow

C₂³×C₄

—

101

—

C₂²×C₈

—

101

—

C₂²⋊C₈

—

101

—

C₂²⋊C₈

—

101

—

C₂⁴

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

202

—

C₂²×C₄

#87938

yes

characteristic

C₂×C₈

—

101

—

C₂×C₈

—

202

—

C₂³

—

101

—

C₂³

—

101

—

C₂³

—

101

—

C₂³

—

202

—

C₂³

—

202

—

C₂³

C₂×#87938

yes

characteristic

C₂×C₄

—

C₂×C₄

—

101

—

C₂×C₄

—

101

—

C₂×C₄

—

101

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

202

—

C₂²

—

C₂²

—

C₂²

—

101

—

C₂²

—

101

—

C₂²

—

101

—

C₂²

—

101

—

C₂²

—

202

—

C₂²

—

202

—

C₂²

—

202

—

C₂²

D₁₀₁⋊C₈

yes

complemented

C₂²

C₂²×#87938

yes

characteristic

C₄

—

C₄

—

101

—

C₄

—

202

—

100

C₄

C₂²⋊#87938

yes

—

101

C₂

—

102

C₂

—

101

—

103

C₂

—

202

—

104

C₂

C₂×C₂²⋊#87938

yes

characteristic

105

C₂

C₂×D₁₀₁⋊C₈

yes

characteristic

106

C₂

D₁₀₁⋊M₁₆

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#87938
commutator	C₂×C₁₀₁	C₂²×C₈
Frattini	C₂²	C₂²×#87938
Fitting	C₂²×C₄×C₁₀₁	C₄
socle	C₂²×C₁₀₁	C₂²×C₄
hypercenter	C₂²×C₄	#87938
hypocenter	C₁₀₁	C₂×C₂²⋊C₈
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

subgroup

G/H

center

C₂×C₄

C₂×#87938

commutator

C₂×C₁₀₁

C₂²×C₈

Frattini

C₂²

C₂²×#87938

Fitting

C₂²×C₄×C₁₀₁

C₄

socle

C₂²×C₁₀₁

C₂²×C₄

hypercenter

C₂²×C₄

#87938

hypocenter

C₁₀₁

C₂×C₂²⋊C₈

LCS

G ▷ C₂×C₁₀₁ ▷ C₁₀₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄

N	H ≅ G/N	type
1. C₂×D₁₀₁⋊C₈	C₂	semidirect
2. #15692312	C₂	semidirect
3. C₂²⋊#11717581	C₂	semidirect
6. C₂×#11717581	C₂²	semidirect
18. C₂²×D₁₀₁	C₈	semidirect
34. C₂²×C₁₀₁	C₂×C₈	semidirect
41. C₂×D₁₀₁	C₂×C₈	semidirect
52. D₁₀₁	C₂²⋊C₈	semidirect
53. C₁₀₁	C₂×C₂²⋊C₈	semidirect
95. C₂²	D₁₀₁⋊C₈	semidirect

H ≅ G/N

type

1. C₂×D₁₀₁⋊C₈

C₂

semidirect

2. #15692312

C₂

semidirect

3. C₂²⋊#11717581

C₂

semidirect

6. C₂×#11717581

C₂²

semidirect

18. C₂²×D₁₀₁

C₈

semidirect

34. C₂²×C₁₀₁

C₂×C₈

semidirect

41. C₂×D₁₀₁

C₂×C₈

semidirect

52. D₁₀₁

C₂²⋊C₈

semidirect

53. C₁₀₁

C₂×C₂²⋊C₈

semidirect

95. C₂²

D₁₀₁⋊C₈

semidirect

Subgroups — D₁₀₁⋊(C₂²⋊C₈) #20266145

Conjugacy classes of subgroups

Complements

Subgroups — D101⋊(C22⋊C8) #20266145

Conjugacy classes of subgroups

Complements

Subgroups — D₁₀₁⋊(C₂²⋊C₈) #20266145