Group #20267766 — subgroups

Subgroups — #100×D₁₀₃ #20267766

Order 6592.

186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 53 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×D₄×D₁₀₃	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₁₀₃	C₂	1	2	yes	maximal, complemented
3	#15692938	C₂	1	1	yes	maximal, characteristic, complemented
4	#15692937	C₂	1	2	yes	maximal, complemented
5	#100×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₁₀₃	C₄	1	2	yes	—
7	C₂×D₄₁₂	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊D₁₀₃	C₄	1	2	yes	—
9	D₄×D₁₀₃	—	2	2	no	—
10	D₄×D₁₀₃	—	2	2	no	—
11	C₂×C₄×D₁₀₃	C₂²	1	1	yes	characteristic
12	#13110089	C₂²	1	2	yes	complemented
13	#13110088	—	2	2	no	—
14	C₈×D₁₀₃	—	2	2	no	—
15	C₂×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
16	M₁₆×C₁₀₃	C₂²	1	2	yes	complemented
17	C₂³×C₁₀₃	C₂×C₄	1	2	yes	—
18	C₂²×D₁₀₃	—	2	2	no	—
19	C₂²×D₁₀₃	—	2	2	no	—
20	C₂²×D₁₀₃	—	4	4	no	—
21	C₂²×D₁₀₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₁₀₃	C₂×C₄	1	2	yes	—
23	D₄×C₁₀₃	—	2	2	no	—
24	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
25	C₂²⋊D₁₀₃	—	2	4	no	—
26	C₂×Dic₁₀₃	C₂×C₄	1	1	yes	characteristic
27	D₄₁₂	—	2	2	no	—
28	C₄×D₁₀₃	D₄	1	2	yes	—
29	C₄×D₁₀₃	D₄	1	2	yes	—
30	C₈×C₁₀₃	—	2	2	no	—
31	C₁₀₃⋊C₈	—	2	2	no	—
32	C₂²×C₁₀₃	—	2	2	no	—
33	C₂²×C₁₀₃	—	4	2	no	—
34	C₂²×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×D₁₀₃	—	2	2	no	—
36	C₂×D₁₀₃	—	2	2	no	—
37	C₂×D₁₀₃	—	4	4	no	—
38	C₂×D₁₀₃	—	4	4	no	—
39	C₂×D₁₀₃	—	4	2	no	—
40	C₂×D₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
41	C₂×D₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
42	C₄×C₁₀₃	C₂×D₄	1	2	yes	—
43	Dic₁₀₃	C₂²⋊C₄	1	2	yes	—
44	C₂×C₁₀₃	—	2	1	no	—
45	C₂×C₁₀₃	—	4	2	no	—
46	C₂×C₁₀₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
47	D₁₀₃	—	2	1	no	—
48	D₁₀₃	—	4	2	no	—
49	D₁₀₃	#100	1	2	yes	direct product factor
50	C₁₀₃	C₂×#100	1	1	yes	characteristic, complemented, Sylow
51	C₂×#100	—	103	1	no	maximal, Sylow
52	C₂²×D₄	—	103	1	no	—
53	C₂×M₁₆	—	103	2	no	—
54	#100	—	103	1	no	—
55	#100	—	103	2	no	—
56	#100	D₁₀₃	1	1	yes	characteristic, direct product factor
57	C₂⁴	—	103	2	no	—
58	C₂×D₄	—	103	2	no	—
59	C₂×D₄	—	103	1	no	—
60	C₂×D₄	—	206	2	no	—
61	C₂×D₄	—	206	2	no	—
62	C₂×D₄	C₂×D₁₀₃	1	1	yes	characteristic
63	C₂²×C₄	—	103	1	no	—
64	M₁₆	—	103	2	no	—
65	M₁₆	—	206	2	no	—
66	M₁₆	C₂×D₁₀₃	1	2	yes	complemented
67	C₂×C₈	—	206	2	no	—
68	C₂³	—	103	1	no	—
69	C₂³	—	103	2	no	—
70	C₂³	—	412	4	no	—
71	C₂³	—	206	2	no	—
72	C₂³	—	206	2	no	—
73	C₂³	C₄×D₁₀₃	1	2	yes	—
74	D₄	—	2	2	no	—
75	D₄	—	206	4	no	—
76	D₄	—	206	2	no	—
77	C₂×C₄	—	103	1	no	—
78	C₂×C₄	—	103	2	no	—
79	C₂×C₄	—	103	2	no	—
80	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	206	2	no	—
83	C₂²	—	2	2	no	—
84	C₂²	—	4	2	no	—
85	C₂²	—	103	1	no	—
86	C₂²	—	103	1	no	—
87	C₂²	—	412	2	no	—
88	C₂²	—	412	4	no	—
89	C₂²	—	412	4	no	—
90	C₂²	—	206	2	no	—
91	C₂²	—	206	2	no	—
92	C₂²	C₂×C₄×D₁₀₃	1	1	yes	characteristic
93	C₄	—	103	2	no	—
94	C₄	D₄×D₁₀₃	1	2	yes	—
95	C₂	—	2	1	no	—
96	C₂	—	4	2	no	—
97	C₂	—	103	2	no	—
98	C₂	—	412	2	no	—
99	C₂	—	206	1	no	—
100	C₂	C₂²⋊C₄×D₁₀₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₄×D₁₀₃

C₂

yes

maximal, characteristic

M₁₆×D₁₀₃

C₂

yes

maximal, complemented

#15692938

C₂

yes

maximal, characteristic, complemented

#15692937

C₂

yes

maximal, complemented

#100×C₁₀₃

C₂

yes

maximal, characteristic, complemented

C₂³×D₁₀₃

C₄

yes

—

C₂×D₄₁₂

C₂²

yes

characteristic

C₂×C₂²⋊D₁₀₃

C₄

yes

—

D₄×D₁₀₃

—

D₄×D₁₀₃

—

C₂×C₄×D₁₀₃

C₂²

yes

characteristic

#13110089

C₂²

yes

complemented

#13110088

—

C₈×D₁₀₃

—

C₂×D₄×C₁₀₃

C₂²

yes

characteristic

M₁₆×C₁₀₃

C₂²

yes

complemented

C₂³×C₁₀₃

C₂×C₄

yes

—

C₂²×D₁₀₃

—

C₂²×D₁₀₃

—

C₂²×D₁₀₃

—

C₂²×D₁₀₃

C₂×C₄

yes

characteristic

C₂²×D₁₀₃

C₂×C₄

yes

—

D₄×C₁₀₃

—

C₂×C₄×C₁₀₃

C₂³

yes

characteristic

C₂²⋊D₁₀₃

—

C₂×Dic₁₀₃

C₂×C₄

yes

characteristic

D₄₁₂

—

C₄×D₁₀₃

D₄

yes

—

C₄×D₁₀₃

D₄

yes

—

C₈×C₁₀₃

—

C₁₀₃⋊C₈

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

C₂²×C₄

yes

characteristic

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

C₂²⋊C₄

yes

characteristic

C₂×D₁₀₃

C₂²⋊C₄

yes

characteristic

C₄×C₁₀₃

C₂×D₄

yes

—

Dic₁₀₃

C₂²⋊C₄

yes

—

C₂×C₁₀₃

—

C₂×C₁₀₃

—

C₂×C₁₀₃

C₂×C₂²⋊C₄

yes

characteristic

D₁₀₃

—

D₁₀₃

—

D₁₀₃

#100

yes

direct product factor

C₁₀₃

C₂×#100

yes

characteristic, complemented, Sylow

C₂×#100

—

103

maximal, Sylow

C₂²×D₄

—

103

—

C₂×M₁₆

—

103

—

#100

—

103

—

#100

—

103

—

#100

D₁₀₃

yes

characteristic, direct product factor

C₂⁴

—

103

—

C₂×D₄

—

103

—

C₂×D₄

—

103

—

C₂×D₄

—

206

—

C₂×D₄

—

206

—

C₂×D₄

C₂×D₁₀₃

yes

characteristic

C₂²×C₄

—

103

—

M₁₆

—

103

—

M₁₆

—

206

—

M₁₆

C₂×D₁₀₃

yes

complemented

C₂×C₈

—

206

—

C₂³

—

103

—

C₂³

—

103

—

C₂³

—

412

—

C₂³

—

206

—

C₂³

—

206

—

C₂³

C₄×D₁₀₃

yes

—

D₄

—

D₄

—

206

—

D₄

—

206

—

C₂×C₄

—

103

—

C₂×C₄

—

103

—

C₂×C₄

—

103

—

C₂×C₄

C₂²×D₁₀₃

yes

characteristic

C₈

—

C₈

—

206

—

C₂²

—

C₂²

—

C₂²

—

103

—

C₂²

—

103

—

C₂²

—

412

—

C₂²

—

412

—

C₂²

—

412

—

C₂²

—

206

—

C₂²

—

206

—

C₂²

C₂×C₄×D₁₀₃

yes

characteristic

C₄

—

103

—

C₄

D₄×D₁₀₃

yes

—

C₂

—

C₂

—

C₂

—

103

—

C₂

—

412

—

C₂

—

206

—

100

C₂

C₂²⋊C₄×D₁₀₃

yes

characteristic

	subgroup	G/H
center	C₂	C₂²⋊C₄×D₁₀₃
commutator	C₂²×C₁₀₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#100×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂×C₂²⋊C₄
hypercenter	#100	D₁₀₃
hypocenter	C₁₀₃	C₂×#100
LCS	G ▷ C₂²×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #100

subgroup

G/H

center

C₂

C₂²⋊C₄×D₁₀₃

commutator

C₂²×C₁₀₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×D₁₀₃

Fitting

#100×C₁₀₃

C₂

socle

C₂×C₁₀₃

C₂×C₂²⋊C₄

D₁₀₃

C₁₀₃

G ▷ C₂²×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #100

N	H ≅ G/N	type
2. M₁₆×D₁₀₃	C₂	semidirect
3. #15692938	C₂	semidirect
4. #15692937	C₂	semidirect
5. #100×C₁₀₃	C₂	semidirect
12. #13110089	C₂²	semidirect
16. M₁₆×C₁₀₃	C₂²	semidirect
49. D₁₀₃	#100	direct (N × H)
50. C₁₀₃	C₂×#100	semidirect
56. #100	D₁₀₃	direct (N × H)
66. M₁₆	C₂×D₁₀₃	semidirect

H ≅ G/N

type

2. M₁₆×D₁₀₃

C₂

semidirect

3. #15692938

C₂

semidirect

4. #15692937

C₂

semidirect

5. #100×C₁₀₃

C₂

semidirect

12. #13110089

C₂²

semidirect

16. M₁₆×C₁₀₃

C₂²

semidirect

49. D₁₀₃

#100

direct (N × H)

50. C₁₀₃

C₂×#100

semidirect

56. #100

D₁₀₃

direct (N × H)

66. M₁₆

C₂×D₁₀₃

semidirect

Subgroups — #100×D₁₀₃ #20267766

Conjugacy classes of subgroups

Complements

Subgroups — #100×D103 #20267766

Conjugacy classes of subgroups

Complements

Subgroups — #100×D₁₀₃ #20267766