Group #20266050 — subgroups

Subgroups — #20266050

Order 6464.

114 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 46 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	1	yes	maximal, characteristic
2	C₂×C₄⋊#87938	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×#87938	—	2	1	no	—
5	D₁₀₁⋊C₈	—	2	1	no	—
6	D₁₀₁⋊C₈	C₄	1	2	yes	complemented
7	C₂×#11717581	—	2	1	no	—
8	C₄⋊#87938	—	2	1	no	—
9	C₄⋊#87938	C₄	1	2	yes	complemented
10	C₂×C₄×D₁₀₁	—	2	1	no	—
11	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₀₁	C₄	1	1	yes	characteristic, complemented
13	#13108053	—	2	1	no	—
14	C₄⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic, complemented
15	C₂²×D₁₀₁	D₄	1	1	yes	characteristic
16	C₂×#87938	—	2	2	no	—
17	C₂×#87938	—	4	1	no	—
18	C₂×#87938	—	4	1	no	—
19	C₂×C₄×C₁₀₁	—	2	1	no	—
20	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₁₀₁	—	2	1	no	—
22	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
23	C₄×D₁₀₁	—	4	1	no	—
24	C₄×D₁₀₁	—	4	1	no	—
25	C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
26	C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
27	C₄×D₁₀₁	D₄	1	1	yes	characteristic
28	C₄×D₁₀₁	Q₈	1	1	yes	characteristic
29	#11717581	—	2	2	no	—
30	C₂²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×D₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×D₁₀₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×D₁₀₁	D₈	1	1	yes	characteristic
34	C₂×D₁₀₁	SD₁₆	1	1	yes	characteristic
35	C₂×D₁₀₁	SD₁₆	1	1	yes	characteristic
36	C₂×D₁₀₁	Q₁₆	1	1	yes	characteristic
37	#87938	—	4	2	no	—
38	C₄×C₁₀₁	—	4	1	no	—
39	C₄×C₁₀₁	C₄²	1	1	yes	characteristic
40	C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
41	Dic₁₀₁	—	4	1	no	—
42	Dic₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
43	Dic₁₀₁	C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₁₀₁	#95	1	1	yes	characteristic
45	C₂×C₁₀₁	#102	1	1	yes	characteristic
46	C₂×C₁₀₁	#103	1	1	yes	characteristic
47	D₁₀₁	#102	1	1	yes	characteristic
48	D₁₀₁	#103	1	1	yes	characteristic
49	D₁₀₁	#106	1	1	yes	characteristic
50	D₁₀₁	#107	1	1	yes	characteristic
51	C₁₀₁	#340	1	1	yes	characteristic, complemented, Sylow
52	#340	—	101	1	no	maximal, Sylow
53	C₂²×C₈	—	101	1	no	—
54	C₂×C₄⋊C₄	—	101	1	no	—
55	C₂×C₄⋊C₄	—	101	1	no	—
56	C₂²×C₄	—	101	1	no	—
57	C₂²×C₄	—	202	1	no	—
58	C₂²×C₄	—	202	1	no	—
59	C₂×C₈	—	101	2	no	—
60	C₂×C₈	—	202	1	no	—
61	C₂×C₈	—	202	1	no	—
62	C₄⋊C₄	—	101	2	no	—
63	C₄⋊C₄	—	101	1	no	—
64	C₄⋊C₄	—	202	1	no	—
65	C₄⋊C₄	—	202	1	no	—
66	C₄⋊C₄	#87938	1	1	yes	characteristic, complemented
67	C₂³	—	101	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	101	1	no	—
70	C₂×C₄	—	101	1	no	—
71	C₂×C₄	—	101	1	no	—
72	C₂×C₄	—	101	1	no	—
73	C₂×C₄	—	101	1	no	—
74	C₂×C₄	—	404	1	no	—
75	C₂×C₄	—	404	1	no	—
76	C₂×C₄	—	404	1	no	—
77	C₂×C₄	—	404	1	no	—
78	C₂×C₄	—	202	2	no	—
79	C₂×C₄	—	202	1	no	—
80	C₂×C₄	C₂×#87938	1	1	yes	characteristic
81	C₈	—	202	2	no	—
82	C₂²	—	101	1	no	—
83	C₂²	—	101	1	no	—
84	C₂²	—	101	1	no	—
85	C₂²	—	101	1	no	—
86	C₂²	—	101	1	no	—
87	C₂²	—	101	1	no	—
88	C₂²	C₂²⋊#87938	1	1	yes	characteristic
89	C₄	—	4	1	no	—
90	C₄	—	101	1	no	—
91	C₄	—	101	1	no	—
92	C₄	—	404	2	no	—
93	C₄	—	404	1	no	—
94	C₄	C₄×#87938	1	1	yes	characteristic
95	C₄	C₄⋊#87938	1	1	yes	characteristic
96	C₂	—	101	1	no	—
97	C₂	—	101	1	no	—
98	C₂	—	101	1	no	—
99	C₂	—	101	1	no	—
100	C₂	(C₂×#87938)⋊C₄	1	1	yes	characteristic
101	C₂	#15692317	1	1	yes	characteristic
102	C₂	#15692318	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₁₀₁⋊C₈

C₂

yes

maximal, characteristic

C₂×C₄⋊#87938

C₂

yes

maximal, characteristic

C₄⋊C₄×D₁₀₁

C₂

yes

maximal, characteristic

C₂²×#87938

—

D₁₀₁⋊C₈

—

D₁₀₁⋊C₈

C₄

yes

—

—

C₄

yes

complemented

C₂×C₄×D₁₀₁

—

C₂×C₄×D₁₀₁

C₂²

yes

characteristic

C₄⋊Dic₁₀₁

C₄

yes

characteristic, complemented

#13108053

—

C₄⋊C₄×C₁₀₁

C₄

yes

characteristic, complemented

C₂²×D₁₀₁

D₄

yes

—

—

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

C₂×C₄

yes

characteristic

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

D₄

yes

characteristic

C₄×D₁₀₁

—

C₄×D₁₀₁

—

C₄×D₁₀₁

C₂×C₄

yes

characteristic

C₄×D₁₀₁

C₂×C₄

yes

characteristic

C₄×D₁₀₁

D₄

yes

characteristic

C₄×D₁₀₁

Q₈

yes

characteristic

#11717581

—

C₂²×C₁₀₁

C₂²⋊C₄

yes

characteristic

C₂×D₁₀₁

C₂²⋊C₄

yes

characteristic

C₂×D₁₀₁

C₄⋊C₄

yes

characteristic

C₂×D₁₀₁

D₈

yes

characteristic

C₂×D₁₀₁

SD₁₆

yes

characteristic

C₂×D₁₀₁

SD₁₆

yes

characteristic

C₂×D₁₀₁

Q₁₆

yes

characteristic

#87938

—

C₄×C₁₀₁

—

C₄×C₁₀₁

C₄²

yes

characteristic

C₄×C₁₀₁

C₄⋊C₄

yes

characteristic

Dic₁₀₁

—

Dic₁₀₁

C₂²⋊C₄

yes

characteristic

Dic₁₀₁

C₄⋊C₄

yes

C₂×C₁₀₁

yes

C₂×C₁₀₁

yes

C₂×C₁₀₁

yes

D₁₀₁

yes

D₁₀₁

yes

D₁₀₁

yes

D₁₀₁

yes

C₁₀₁

yes

characteristic, complemented, Sylow

#340

—

101

maximal, Sylow

C₂²×C₈

—

101

—

C₂×C₄⋊C₄

—

101

—

C₂×C₄⋊C₄

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

202

—

C₂²×C₄

—

202

—

C₂×C₈

—

101

—

C₂×C₈

—

202

—

C₂×C₈

—

202

—

C₄⋊C₄

—

101

—

C₄⋊C₄

—

101

—

C₄⋊C₄

—

202

—

C₄⋊C₄

—

202

—

C₄⋊C₄

#87938

yes

characteristic, complemented

C₂³

—

101

—

C₂×C₄

—

C₂×C₄

—

101

—

C₂×C₄

—

101

—

C₂×C₄

—

101

—

C₂×C₄

—

101

—

C₂×C₄

—

101

—

C₂×C₄

—

404

—

C₂×C₄

—

404

—

C₂×C₄

—

404

—

C₂×C₄

—

404

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

C₂×#87938

yes

characteristic

C₈

—

202

—

C₂²

—

101

—

C₂²

—

101

—

C₂²

—

101

—

C₂²

—

101

—

C₂²

—

101

—

C₂²

—

101

—

C₂²

C₂²⋊#87938

yes

characteristic

C₄

—

C₄

—

101

—

C₄

—

101

—

C₄

—

404

—

C₄

—

404

—

C₄

yes

C₄

yes

C₂

—

101

—

C₂

—

101

—

C₂

—

101

—

C₂

—

101

—

100

C₂

(C₂×#87938)⋊C₄

yes

characteristic

101

C₂

#15692317

yes

characteristic

102

C₂

#15692318

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#87938
commutator	C₄×C₁₀₁	C₄²
Frattini	C₂×C₄	C₂×#87938
Fitting	C₄⋊C₄×C₁₀₁	C₄
socle	C₂²×C₁₀₁	C₂²⋊C₄
hypercenter	C₄⋊C₄	#87938
hypocenter	C₁₀₁	#340
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

subgroup

G/H

center

C₂²

C₂²⋊#87938

commutator

C₄×C₁₀₁

C₄²

Frattini

C₂×C₄

C₂×#87938

Fitting

C₄⋊C₄×C₁₀₁

C₄

socle

C₂²×C₁₀₁

C₂²⋊C₄

C₄⋊C₄

C₁₀₁

G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

N	H ≅ G/N	type
6. D₁₀₁⋊C₈	C₄	semidirect
9. C₄⋊#87938	C₄	semidirect
12. C₄⋊Dic₁₀₁	C₄	semidirect
14. C₄⋊C₄×C₁₀₁	C₄	semidirect
51. C₁₀₁	#340	semidirect
66. C₄⋊C₄	#87938	semidirect

H ≅ G/N

type

6. D₁₀₁⋊C₈

C₄

semidirect

9. C₄⋊#87938

C₄

semidirect

12. C₄⋊Dic₁₀₁

C₄

semidirect

14. C₄⋊C₄×C₁₀₁

C₄

semidirect

51. C₁₀₁

#340

semidirect

66. C₄⋊C₄

#87938

semidirect

Subgroups — #20266050

Conjugacy classes of subgroups

Complements