Group #20268020 — subgroups

Subgroups — #20268020

Order 6592.

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

normal subgroups only

This group has 124 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	#15693000	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692995	C₂	1	1	yes	maximal, characteristic
4	#15692953	C₂	1	1	yes	maximal, characteristic, complemented
5	#15692946	C₂	1	1	yes	maximal, characteristic, complemented
6	#15692943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₈×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	1	no	—
11	#13110094	—	2	2	no	—
12	C₄⋊Dic₁₀₃	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₁₀₃	C₂²	1	1	yes	characteristic
14	Dic₁₀₃⋊C₄	—	2	1	no	—
15	C₂²⋊Dic₁₀₃	—	2	1	no	—
16	(C₂×D₁₀₃)⋊C₄	—	2	1	no	—
17	C₂²×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
18	C₂×C₈×C₁₀₃	—	2	2	no	—
19	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
20	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
21	C₂³×C₁₀₃	D₄	1	1	yes	characteristic
22	C₂²×D₁₀₃	—	2	1	no	—
23	C₂×C₄×C₁₀₃	—	2	1	no	—
24	C₂×C₄×C₁₀₃	—	2	1	no	—
25	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
26	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
27	C₂²⋊D₁₀₃	—	4	2	no	—
28	C₂×Dic₁₀₃	—	2	1	no	—
29	C₂×Dic₁₀₃	—	2	1	no	—
30	C₂×Dic₁₀₃	—	2	1	no	—
31	D₄₁₂	—	2	1	no	—
32	D₄₁₂	—	2	1	no	—
33	Dic₂₀₆	—	2	1	no	—
34	Dic₂₀₆	—	2	1	no	—
35	C₈×C₁₀₃	—	2	1	no	—
36	C₈×C₁₀₃	D₄	1	2	yes	complemented
37	C₂²×C₁₀₃	—	2	1	no	—
38	C₂²×C₁₀₃	—	2	1	no	—
39	C₂²×C₁₀₃	SD₁₆	1	2	yes	complemented
40	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
41	C₂×D₁₀₃	—	4	1	no	—
42	C₂×D₁₀₃	—	4	1	no	—
43	C₂×D₁₀₃	—	4	1	no	—
44	C₄×C₁₀₃	—	2	1	no	—
45	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
46	C₄×C₁₀₃	#41	1	1	yes	characteristic
47	Dic₁₀₃	—	4	1	no	—
48	Dic₁₀₃	—	4	1	no	—
49	Dic₁₀₃	—	4	1	no	—
50	C₂×C₁₀₃	—	2	2	no	—
51	C₂×C₁₀₃	#121	1	1	yes	characteristic
52	C₂×C₁₀₃	C₂×SD₁₆	1	1	yes	characteristic
53	C₂×C₁₀₃	#135	1	1	yes	characteristic
54	D₁₀₃	—	8	1	no	—
55	C₁₀₃	#465	1	1	yes	characteristic, complemented, Sylow
56	#465	—	103	1	no	maximal, Sylow
57	C₂×SD₁₆	—	103	1	no	—
58	C₂²×C₈	D₁₀₃	1	1	yes	characteristic, complemented
59	C₂²⋊Q₈	—	103	1	no	—
60	#121	—	103	1	no	—
61	#106	—	103	1	no	—
62	#103	—	103	1	no	—
63	#102	—	103	1	no	—
64	C₂×Q₈	—	103	1	no	—
65	C₂×D₄	—	103	1	no	—
66	C₂×D₄	—	206	1	no	—
67	C₂²×C₄	C₂×D₁₀₃	1	1	yes	characteristic
68	SD₁₆	—	206	2	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
71	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
72	C₄⋊C₄	—	103	1	no	—
73	C₄⋊C₄	—	103	1	no	—
74	C₄⋊C₄	—	206	1	no	—
75	C₂²⋊C₄	—	206	1	no	—
76	C₂²⋊C₄	—	206	1	no	—
77	C₂³	—	206	1	no	—
78	C₂³	D₄₁₂	1	1	yes	characteristic
79	Q₈	—	206	1	no	—
80	Q₈	—	206	1	no	—
81	D₄	—	412	2	no	—
82	D₄	—	206	1	no	—
83	D₄	—	206	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	206	1	no	—
87	C₂×C₄	—	206	1	no	—
88	C₂×C₄	—	206	1	no	—
89	C₂×C₄	D₄₁₂	1	1	yes	characteristic
90	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
91	C₈	—	2	1	no	—
92	C₈	C₂²⋊D₁₀₃	1	2	yes	complemented
93	C₂²	—	2	1	no	—
94	C₂²	—	2	1	no	—
95	C₂²	—	412	1	no	—
96	C₂²	—	412	1	no	—
97	C₂²	—	412	1	no	—
98	C₂²	#13110094	1	2	yes	complemented
99	C₂²	C₂×D₄₁₂	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	412	1	no	—
102	C₄	—	412	1	no	—
103	C₄	—	412	1	no	—
104	C₄	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
105	C₄	#13110105	1	1	yes	characteristic
106	C₂	—	2	2	no	—
107	C₂	—	824	1	no	—
108	C₂	#15692995	1	1	yes	characteristic
109	C₂	C₂×#13110094	1	1	yes	characteristic
110	C₂	#15693043	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13110094

C₂

yes

maximal, characteristic, complemented

#15693000

C₂

yes

maximal, characteristic, complemented

#15692995

C₂

yes

maximal, characteristic

#15692953

C₂

yes

maximal, characteristic, complemented

#15692946

C₂

yes

maximal, characteristic, complemented

#15692943

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×C₁₀₃

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₀₆

C₂²

yes

characteristic

C₂×D₄₁₂

C₂²

yes

characteristic

C₂×C₂²⋊D₁₀₃

—

#13110094

—

C₄⋊Dic₁₀₃

C₂²

yes

characteristic

C₄⋊Dic₁₀₃

C₂²

yes

characteristic

Dic₁₀₃⋊C₄

—

C₂²⋊Dic₁₀₃

—

(C₂×D₁₀₃)⋊C₄

—

C₂²×C₄×C₁₀₃

C₂²

yes

characteristic

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

C₂²

yes

characteristic

C₂×C₈×C₁₀₃

C₂²

yes

characteristic

C₂³×C₁₀₃

D₄

yes

characteristic

C₂²×D₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

D₄

yes

characteristic

C₂×C₄×C₁₀₃

C₂³

yes

characteristic

C₂²⋊D₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

D₄₁₂

—

D₄₁₂

—

Dic₂₀₆

—

Dic₂₀₆

—

C₈×C₁₀₃

—

C₈×C₁₀₃

D₄

yes

complemented

C₂²×C₁₀₃

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

SD₁₆

yes

complemented

C₂²×C₁₀₃

C₂×D₄

yes

characteristic

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₄×C₁₀₃

—

C₄×C₁₀₃

C₂×D₄

yes

characteristic

C₄×C₁₀₃

#41

yes

characteristic

Dic₁₀₃

—

Dic₁₀₃

—

Dic₁₀₃

—

C₂×C₁₀₃

—

C₂×C₁₀₃

#121

yes

characteristic

C₂×C₁₀₃

C₂×SD₁₆

yes

characteristic

C₂×C₁₀₃

#135

yes

characteristic

D₁₀₃

—

C₁₀₃

#465

yes

characteristic, complemented, Sylow

#465

—

103

maximal, Sylow

C₂×SD₁₆

—

103

—

C₂²×C₈

D₁₀₃

yes

characteristic, complemented

C₂²⋊Q₈

—

103

—

#121

—

103

—

#106

—

103

—

#103

—

103

—

#102

—

103

—

C₂×Q₈

—

103

—

C₂×D₄

—

103

—

C₂×D₄

—

206

—

C₂²×C₄

C₂×D₁₀₃

yes

characteristic

SD₁₆

—

206

—

C₂×C₈

—

C₂×C₈

C₂×D₁₀₃

yes

characteristic

C₂×C₈

C₂×D₁₀₃

yes

characteristic

C₄⋊C₄

—

103

—

C₄⋊C₄

—

103

—

C₄⋊C₄

—

206

—

C₂²⋊C₄

—

206

—

C₂²⋊C₄

—

206

—

C₂³

—

206

—

C₂³

D₄₁₂

yes

characteristic

Q₈

—

206

—

Q₈

—

206

—

D₄

—

412

—

D₄

—

206

—

D₄

—

206

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

D₄₁₂

yes

characteristic

C₂×C₄

C₂²×D₁₀₃

yes

characteristic

C₈

—

C₈

C₂²⋊D₁₀₃

yes

complemented

C₂²

—

C₂²

—

C₂²

—

412

—

C₂²

—

412

—

C₂²

—

412

—

C₂²

#13110094

yes

complemented

C₂²

C₂×D₄₁₂

yes

characteristic

100

C₄

—

101

C₄

—

412

—

102

C₄

—

412

—

103

C₄

—

412

—

104

C₄

C₂×C₂²⋊D₁₀₃

yes

characteristic

105

C₄

#13110105

yes

characteristic

106

C₂

—

107

C₂

—

824

—

108

C₂

#15692995

yes

characteristic

109

C₂

C₂×#13110094

yes

characteristic

110

C₂

#15693043

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄₁₂
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₂²×C₈×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	C₂²×C₈	D₁₀₃
hypocenter	C₁₀₃	#465
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂²

C₂×D₄₁₂

commutator

C₂×C₄×C₁₀₃

C₂³

Frattini

C₂×C₄

C₂²×D₁₀₃

Fitting

C₂²×C₈×C₁₀₃

C₂

socle

C₂²×C₁₀₃

C₂×D₄

hypercenter

C₂²×C₈

D₁₀₃

hypocenter

C₁₀₃

#465

LCS

G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
1. C₂×#13110094	C₂	semidirect
2. #15693000	C₂	semidirect
4. #15692953	C₂	semidirect
5. #15692946	C₂	semidirect
6. #15692943	C₂	semidirect
7. C₂²×C₈×C₁₀₃	C₂	semidirect
36. C₈×C₁₀₃	D₄	semidirect
39. C₂²×C₁₀₃	SD₁₆	semidirect
55. C₁₀₃	#465	semidirect
58. C₂²×C₈	D₁₀₃	semidirect
92. C₈	C₂²⋊D₁₀₃	semidirect
98. C₂²	#13110094	semidirect

H ≅ G/N

type

1. C₂×#13110094

C₂

semidirect

2. #15693000

C₂

semidirect

4. #15692953

C₂

semidirect

5. #15692946

C₂

semidirect

6. #15692943

C₂

semidirect

7. C₂²×C₈×C₁₀₃

C₂

semidirect

36. C₈×C₁₀₃

D₄

semidirect

39. C₂²×C₁₀₃

SD₁₆

semidirect

55. C₁₀₃

#465

semidirect

58. C₂²×C₈

D₁₀₃

semidirect

92. C₈

C₂²⋊D₁₀₃

semidirect

98. C₂²

#13110094

semidirect

Subgroups — #20268020

Conjugacy classes of subgroups

Complements