Group #20268162 — subgroups

Subgroups — #20268162

Order 6592.

142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 47 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×#13110094	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13110093	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13110092	C₂	1	1	yes	maximal, characteristic, complemented
4	#15693019	C₂	1	1	yes	maximal, characteristic, complemented
5	#15693017	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×SD₁₆×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₀₆	C₂²	1	1	yes	characteristic
9	C₂×D₄₁₂	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊D₁₀₃	—	2	2	no	—
11	#13110094	—	2	2	no	—
12	#13110093	—	2	2	no	—
13	#13110092	—	2	2	no	—
14	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
15	Dic₁₀₃⋊C₄	—	2	2	no	—
16	C₄×Dic₁₀₃	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
18	C₂×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
19	SD₁₆×C₁₀₃	—	2	2	no	—
20	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
21	C₂³×C₁₀₃	—	2	1	no	—
22	C₂²×D₁₀₃	—	2	1	no	—
23	Q₈×C₁₀₃	—	2	1	no	—
24	Q₈×C₁₀₃	—	2	1	no	—
25	D₄×C₁₀₃	—	2	1	no	—
26	D₄×C₁₀₃	—	2	1	no	—
27	C₂×C₄×C₁₀₃	—	2	1	no	—
28	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
29	C₂²⋊D₁₀₃	—	4	4	no	—
30	C₂×Dic₁₀₃	—	2	1	no	—
31	C₂×Dic₁₀₃	D₄	1	2	yes	—
32	D₄₁₂	—	2	1	no	—
33	D₄₁₂	—	2	1	no	—
34	Dic₂₀₆	—	2	1	no	—
35	Dic₂₀₆	—	2	1	no	—
36	C₈×C₁₀₃	D₄	1	2	yes	complemented
37	C₁₀₃⋊C₈	D₄	1	2	yes	complemented
38	C₂²×C₁₀₃	—	4	1	no	—
39	C₂²×C₁₀₃	—	4	2	no	—
40	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
41	C₂×D₁₀₃	—	4	1	no	—
42	C₂×D₁₀₃	—	4	2	no	—
43	C₄×C₁₀₃	—	4	1	no	—
44	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
45	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
46	Dic₁₀₃	—	4	1	no	—
47	Dic₁₀₃	SD₁₆	1	4	yes	complemented
48	C₂×C₁₀₃	—	8	1	no	—
49	C₂×C₁₀₃	#127	1	1	yes	characteristic
50	C₂×C₁₀₃	C₂×SD₁₆	1	2	yes	—
51	D₁₀₃	—	8	1	no	—
52	C₁₀₃	#492	1	1	yes	characteristic, complemented, Sylow
53	#492	—	103	1	no	maximal, Sylow
54	C₂×SD₁₆	—	103	1	no	—
55	C₂×SD₁₆	—	103	1	no	—
56	C₂×SD₁₆	—	103	1	no	—
57	C₂×SD₁₆	D₁₀₃	1	1	yes	characteristic, complemented
58	C₄⋊Q₈	—	103	1	no	—
59	#127	—	103	1	no	—
60	C₄×C₈	—	103	1	no	—
61	C₂×Q₈	—	103	1	no	—
62	C₂×Q₈	C₂×D₁₀₃	1	1	yes	characteristic
63	C₂×D₄	—	103	1	no	—
64	C₂×D₄	—	206	2	no	—
65	C₂×D₄	C₂×D₁₀₃	1	1	yes	characteristic
66	SD₁₆	—	2	2	no	—
67	SD₁₆	—	206	2	no	—
68	SD₁₆	—	206	2	no	—
69	SD₁₆	—	206	2	no	—
70	C₂×C₈	—	103	1	no	—
71	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
72	C₄⋊C₄	—	206	2	no	—
73	C₄²	—	103	1	no	—
74	C₂³	—	2	1	no	—
75	C₂³	—	206	1	no	—
76	Q₈	—	2	1	no	—
77	Q₈	—	2	1	no	—
78	Q₈	—	206	1	no	—
79	Q₈	—	206	1	no	—
80	D₄	—	2	1	no	—
81	D₄	—	2	1	no	—
82	D₄	—	412	4	no	—
83	D₄	—	206	1	no	—
84	D₄	—	206	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	103	2	no	—
87	C₂×C₄	—	206	1	no	—
88	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
89	C₈	—	103	2	no	—
90	C₈	C₂²⋊D₁₀₃	1	2	yes	complemented
91	C₂²	—	4	1	no	—
92	C₂²	—	4	2	no	—
93	C₂²	—	412	1	no	—
94	C₂²	—	412	2	no	—
95	C₂²	D₄×D₁₀₃	1	1	yes	characteristic
96	C₄	—	4	1	no	—
97	C₄	—	103	4	no	—
98	C₄	—	412	1	no	—
99	C₄	D₄×D₁₀₃	1	1	yes	characteristic
100	C₄	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
101	C₂	—	8	1	no	—
102	C₂	—	824	1	no	—
103	C₂	#15693017	1	1	yes	characteristic
104	C₂	SD₁₆×D₁₀₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13110094

C₂

yes

maximal, characteristic, complemented

C₂×#13110093

C₂

yes

maximal, characteristic, complemented

C₂×#13110092

C₂

yes

maximal, characteristic, complemented

#15693019

C₂

yes

maximal, characteristic, complemented

#15693017

C₂

yes

maximal, characteristic

C₈×Dic₁₀₃

C₂

yes

maximal, characteristic, complemented

C₂×SD₁₆×C₁₀₃

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₀₆

C₂²

yes

characteristic

C₂×D₄₁₂

C₂²

yes

characteristic

C₂×C₂²⋊D₁₀₃

—

#13110094

—

#13110093

—

#13110092

—

C₂×C₁₀₃⋊C₈

C₂²

yes

characteristic

Dic₁₀₃⋊C₄

—

C₄×Dic₁₀₃

C₂²

yes

characteristic

C₂×Q₈×C₁₀₃

C₂²

yes

characteristic

C₂×D₄×C₁₀₃

C₂²

yes

characteristic

SD₁₆×C₁₀₃

—

C₂×C₈×C₁₀₃

C₂²

yes

characteristic

C₂³×C₁₀₃

—

C₂²×D₁₀₃

—

Q₈×C₁₀₃

—

Q₈×C₁₀₃

—

D₄×C₁₀₃

—

D₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

C₂³

yes

characteristic

C₂²⋊D₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

D₄

yes

—

D₄₁₂

—

D₄₁₂

—

Dic₂₀₆

—

Dic₂₀₆

—

C₈×C₁₀₃

D₄

yes

complemented

C₁₀₃⋊C₈

D₄

yes

complemented

C₂²×C₁₀₃

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

C₂×D₄

yes

characteristic

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₄×C₁₀₃

—

C₄×C₁₀₃

C₂×D₄

yes

characteristic

C₄×C₁₀₃

C₂×D₄

yes

characteristic

Dic₁₀₃

—

Dic₁₀₃

SD₁₆

yes

complemented

C₂×C₁₀₃

—

C₂×C₁₀₃

#127

yes

characteristic

C₂×C₁₀₃

C₂×SD₁₆

yes

—

D₁₀₃

—

C₁₀₃

#492

yes

characteristic, complemented, Sylow

#492

—

103

maximal, Sylow

C₂×SD₁₆

—

103

—

C₂×SD₁₆

—

103

—

C₂×SD₁₆

—

103

—

C₂×SD₁₆

D₁₀₃

yes

characteristic, complemented

C₄⋊Q₈

—

103

—

#127

—

103

—

C₄×C₈

—

103

—

C₂×Q₈

—

103

—

C₂×Q₈

C₂×D₁₀₃

yes

characteristic

C₂×D₄

—

103

—

C₂×D₄

—

206

—

C₂×D₄

C₂×D₁₀₃

yes

characteristic

SD₁₆

—

SD₁₆

—

206

—

SD₁₆

—

206

—

SD₁₆

—

206

—

C₂×C₈

—

103

—

C₂×C₈

C₂×D₁₀₃

yes

characteristic

C₄⋊C₄

—

206

—

C₄²

—

103

—

C₂³

—

C₂³

—

206

—

Q₈

—

Q₈

—

Q₈

—

206

—

Q₈

—

206

—

D₄

—

D₄

—

D₄

—

412

—

D₄

—

206

—

D₄

—

206

—

C₂×C₄

—

C₂×C₄

—

103

—

C₂×C₄

—

206

—

C₂×C₄

C₂²×D₁₀₃

yes

characteristic

C₈

—

103

—

C₈

C₂²⋊D₁₀₃

yes

complemented

C₂²

—

C₂²

—

C₂²

—

412

—

C₂²

—

412

—

C₂²

D₄×D₁₀₃

yes

characteristic

C₄

—

C₄

—

103

—

C₄

—

412

—

C₄

D₄×D₁₀₃

yes

characteristic

100

C₄

C₂×C₂²⋊D₁₀₃

yes

characteristic

101

C₂

—

102

C₂

—

824

—

103

C₂

#15693017

yes

characteristic

104

C₂

SD₁₆×D₁₀₃

yes

—

	subgroup	G/H
center	C₂²	D₄×D₁₀₃
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₂×SD₁₆×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	C₂×SD₁₆	D₁₀₃
hypocenter	C₁₀₃	#492
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×SD₁₆

subgroup

G/H

center

C₂²

D₄×D₁₀₃

commutator

C₂×C₄×C₁₀₃

C₂³

Frattini

C₂×C₄

C₂²×D₁₀₃

Fitting

C₂×SD₁₆×C₁₀₃

C₂

socle

C₂²×C₁₀₃

C₂×D₄

hypercenter

C₂×SD₁₆

D₁₀₃

hypocenter

C₁₀₃

#492

LCS

G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×SD₁₆

N	H ≅ G/N	type
1. C₂×#13110094	C₂	semidirect
2. C₂×#13110093	C₂	semidirect
3. C₂×#13110092	C₂	semidirect
4. #15693019	C₂	semidirect
6. C₈×Dic₁₀₃	C₂	semidirect
7. C₂×SD₁₆×C₁₀₃	C₂	semidirect
36. C₈×C₁₀₃	D₄	semidirect
37. C₁₀₃⋊C₈	D₄	semidirect
47. Dic₁₀₃	SD₁₆	semidirect
52. C₁₀₃	#492	semidirect
57. C₂×SD₁₆	D₁₀₃	semidirect
90. C₈	C₂²⋊D₁₀₃	semidirect

H ≅ G/N

type

1. C₂×#13110094

C₂

semidirect

2. C₂×#13110093

C₂

semidirect

3. C₂×#13110092

C₂

semidirect

4. #15693019

C₂

semidirect

6. C₈×Dic₁₀₃

C₂

semidirect

7. C₂×SD₁₆×C₁₀₃

C₂

semidirect

36. C₈×C₁₀₃

D₄

semidirect

37. C₁₀₃⋊C₈

D₄

semidirect

47. Dic₁₀₃

SD₁₆

semidirect

52. C₁₀₃

#492

semidirect

57. C₂×SD₁₆

D₁₀₃

semidirect

90. C₈

C₂²⋊D₁₀₃

semidirect

Subgroups — #20268162

Conjugacy classes of subgroups

Complements