Group #20267789 — subgroups

Subgroups — #20267789

Order 6592.

162 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 55 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×#13110104	C₂	1	1	yes	maximal, characteristic
2	C₂×#13110088	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₄×D₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#15692946	C₂	1	1	yes	maximal, characteristic, complemented
5	#15692944	C₂	1	1	yes	maximal, characteristic, complemented
6	#15692942	C₂	1	1	yes	maximal, characteristic, complemented
7	#102×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#13110104	—	2	2	no	—
9	#13110104	C₄	1	4	yes	complemented
10	C₂×Dic₂₀₆	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊D₁₀₃	—	2	1	no	—
12	C₂²×Dic₁₀₃	—	2	1	no	—
13	C₂×C₄×D₁₀₃	—	2	1	no	—
14	C₂×C₄×D₁₀₃	C₂²	1	1	yes	characteristic
15	#13110088	—	2	2	no	—
16	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₄⋊Dic₁₀₃	C₂²	1	1	yes	characteristic
18	Dic₁₀₃⋊C₄	—	2	1	no	—
19	C₂×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
20	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
21	C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
22	C₂³×C₁₀₃	—	2	1	no	—
23	C₂²×D₁₀₃	D₄	1	1	yes	characteristic
24	D₄×C₁₀₃	—	2	1	no	—
25	D₄×C₁₀₃	C₂×C₄	1	2	yes	complemented
26	C₂×C₄×C₁₀₃	—	2	1	no	—
27	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
28	C₂²⋊D₁₀₃	—	2	4	no	—
29	C₂×Dic₁₀₃	—	2	1	no	—
30	C₂×Dic₁₀₃	—	2	4	no	—
31	C₂×Dic₁₀₃	—	2	1	no	—
32	C₂×Dic₁₀₃	D₄	1	1	yes	characteristic
33	C₄×D₁₀₃	—	4	2	no	—
34	C₄×D₁₀₃	C₂×C₄	1	2	yes	—
35	C₄×D₁₀₃	D₄	1	2	yes	—
36	Dic₂₀₆	—	2	1	no	—
37	Dic₂₀₆	C₂×C₄	1	2	yes	complemented
38	C₈×C₁₀₃	—	2	1	no	—
39	C₁₀₃⋊C₈	—	2	1	no	—
40	C₂²×C₁₀₃	—	2	2	no	—
41	C₂²×C₁₀₃	—	4	1	no	—
42	C₂²×C₁₀₃	—	4	1	no	—
43	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
44	C₂×D₁₀₃	—	2	1	no	—
45	C₂×D₁₀₃	—	2	1	no	—
46	C₂×D₁₀₃	C₂²⋊C₄	1	2	yes	—
47	C₄×C₁₀₃	—	4	1	no	—
48	C₄×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
49	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
50	Dic₁₀₃	—	2	2	no	—
51	Dic₁₀₃	—	4	1	no	—
52	Dic₁₀₃	C₂²⋊C₄	1	2	yes	—
53	C₂×C₁₀₃	—	4	2	no	—
54	C₂×C₁₀₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₁₀₃	AGL(1,ℤ/8)	1	1	yes	characteristic
56	C₂×C₁₀₃	#137	1	1	yes	characteristic
57	D₁₀₃	—	2	2	no	—
58	C₁₀₃	#417	1	1	yes	characteristic, complemented, Sylow
59	#417	—	103	1	no	maximal, Sylow
60	C₂×#41	—	103	1	no	—
61	C₂×M₁₆	—	103	1	no	—
62	C₂×C₄⋊C₄	—	103	1	no	—
63	#103	—	103	1	no	—
64	#103	—	103	1	no	—
65	#102	—	103	1	no	—
66	#102	D₁₀₃	1	1	yes	characteristic, complemented
67	#41	—	103	4	no	—
68	#41	—	206	2	no	—
69	C₂×Q₈	—	103	1	no	—
70	C₂×D₄	—	206	1	no	—
71	C₂×D₄	C₂×D₁₀₃	1	1	yes	characteristic
72	C₂²×C₄	—	103	1	no	—
73	C₂²×C₄	—	206	1	no	—
74	C₂²×C₄	—	206	1	no	—
75	M₁₆	—	206	2	no	—
76	C₂×C₈	—	103	1	no	—
77	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
78	C₄⋊C₄	—	103	1	no	—
79	C₄⋊C₄	—	206	1	no	—
80	C₄⋊C₄	C₂×D₁₀₃	1	1	yes	characteristic
81	C₂³	—	2	1	no	—
82	C₂³	—	103	1	no	—
83	Q₈	—	103	2	no	—
84	Q₈	—	206	1	no	—
85	D₄	—	2	1	no	—
86	D₄	—	206	4	no	—
87	D₄	C₄×D₁₀₃	1	2	yes	complemented
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	103	1	no	—
90	C₂×C₄	—	103	2	no	—
91	C₂×C₄	—	103	2	no	—
92	C₂×C₄	—	412	2	no	—
93	C₂×C₄	—	206	4	no	—
94	C₂×C₄	—	206	1	no	—
95	C₂×C₄	—	206	1	no	—
96	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
97	C₈	—	2	1	no	—
98	C₈	—	206	1	no	—
99	C₂²	—	2	2	no	—
100	C₂²	—	4	1	no	—
101	C₂²	—	4	1	no	—
102	C₂²	—	103	2	no	—
103	C₂²	—	206	1	no	—
104	C₂²	—	206	1	no	—
105	C₂²	D₄×D₁₀₃	1	1	yes	characteristic
106	C₄	—	4	1	no	—
107	C₄	—	103	2	no	—
108	C₄	—	412	1	no	—
109	C₄	—	206	2	no	—
110	C₄	C₂×C₄×D₁₀₃	1	1	yes	characteristic
111	C₄	D₄×D₁₀₃	1	1	yes	characteristic
112	C₂	—	4	2	no	—
113	C₂	—	206	2	no	—
114	C₂	C₂²⋊C₄×D₁₀₃	1	1	yes	characteristic
115	C₂	#15693045	1	1	yes	characteristic
116	C₂	#15693050	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13110104

C₂

yes

maximal, characteristic

C₂×#13110088

C₂

yes

maximal, characteristic, complemented

C₄⋊C₄×D₁₀₃

C₂

yes

maximal, characteristic, complemented

#15692946

C₂

yes

maximal, characteristic, complemented

#15692944

C₂

yes

maximal, characteristic, complemented

#15692942

C₂

yes

maximal, characteristic, complemented

#102×C₁₀₃

C₂

yes

maximal, characteristic, complemented

#13110104

—

#13110104

C₄

yes

complemented

C₂×Dic₂₀₆

C₂²

yes

characteristic

C₂×C₂²⋊D₁₀₃

—

C₂²×Dic₁₀₃

—

C₂×C₄×D₁₀₃

—

C₂×C₄×D₁₀₃

C₂²

yes

characteristic

#13110088

—

C₂×C₁₀₃⋊C₈

C₂²

yes

characteristic

C₄⋊Dic₁₀₃

C₂²

yes

characteristic

Dic₁₀₃⋊C₄

—

C₂×D₄×C₁₀₃

C₂²

yes

characteristic

C₂×C₈×C₁₀₃

C₂²

yes

characteristic

C₄⋊C₄×C₁₀₃

C₂²

yes

characteristic

C₂³×C₁₀₃

—

C₂²×D₁₀₃

D₄

yes

characteristic

D₄×C₁₀₃

—

D₄×C₁₀₃

C₂×C₄

yes

complemented

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

C₂³

yes

characteristic

C₂²⋊D₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

D₄

yes

characteristic

C₄×D₁₀₃

—

C₄×D₁₀₃

C₂×C₄

yes

—

C₄×D₁₀₃

D₄

yes

—

Dic₂₀₆

—

Dic₂₀₆

C₂×C₄

yes

complemented

C₈×C₁₀₃

—

C₁₀₃⋊C₈

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

C₂×D₄

yes

characteristic

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

C₂²⋊C₄

yes

—

C₄×C₁₀₃

—

C₄×C₁₀₃

C₂²×C₄

yes

characteristic

C₄×C₁₀₃

C₂×D₄

yes

characteristic

Dic₁₀₃

—

Dic₁₀₃

—

Dic₁₀₃

C₂²⋊C₄

yes

—

C₂×C₁₀₃

—

C₂×C₁₀₃

C₂×C₂²⋊C₄

yes

C₂×C₁₀₃

yes

C₂×C₁₀₃

yes

D₁₀₃

—

C₁₀₃

#417

yes

characteristic, complemented, Sylow

#417

—

103

maximal, Sylow

C₂×#41

—

103

—

C₂×M₁₆

—

103

—

C₂×C₄⋊C₄

—

103

—

#103

—

103

—

#103

—

103

—

#102

—

103

—

#102

D₁₀₃

yes

characteristic, complemented

#41

—

103

—

#41

—

206

—

C₂×Q₈

—

103

—

C₂×D₄

—

206

—

C₂×D₄

C₂×D₁₀₃

yes

characteristic

C₂²×C₄

—

103

—

C₂²×C₄

—

206

—

C₂²×C₄

—

206

—

M₁₆

—

206

—

C₂×C₈

—

103

—

C₂×C₈

C₂×D₁₀₃

yes

characteristic

C₄⋊C₄

—

103

—

C₄⋊C₄

—

206

—

C₄⋊C₄

C₂×D₁₀₃

yes

characteristic

C₂³

—

C₂³

—

103

—

Q₈

—

103

—

Q₈

—

206

—

D₄

—

D₄

—

206

—

D₄

C₄×D₁₀₃

yes

complemented

C₂×C₄

—

C₂×C₄

—

103

—

C₂×C₄

—

103

—

C₂×C₄

—

103

—

C₂×C₄

—

412

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

C₂²×D₁₀₃

yes

characteristic

C₈

—

C₈

—

206

—

C₂²

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

103

—

103

C₂²

—

206

—

104

C₂²

—

206

—

105

C₂²

D₄×D₁₀₃

yes

characteristic

106

C₄

—

107

C₄

—

103

—

108

C₄

—

412

—

109

C₄

—

206

—

110

C₄

C₂×C₄×D₁₀₃

yes

characteristic

111

C₄

D₄×D₁₀₃

yes

characteristic

112

C₂

—

113

C₂

—

206

—

114

C₂

C₂²⋊C₄×D₁₀₃

yes

characteristic

115

C₂

#15693045

yes

characteristic

116

C₂

#15693050

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₃
commutator	C₄×C₁₀₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#102×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	#102	D₁₀₃
hypocenter	C₁₀₃	#417
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

subgroup

G/H

center

C₂²

D₄×D₁₀₃

commutator

C₄×C₁₀₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×D₁₀₃

Fitting

#102×C₁₀₃

C₂

socle

C₂²×C₁₀₃

C₂×D₄

D₁₀₃

C₁₀₃

G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

N	H ≅ G/N	type
2. C₂×#13110088	C₂	semidirect
3. C₄⋊C₄×D₁₀₃	C₂	semidirect
4. #15692946	C₂	semidirect
5. #15692944	C₂	semidirect
6. #15692942	C₂	semidirect
7. #102×C₁₀₃	C₂	semidirect
9. #13110104	C₄	semidirect
25. D₄×C₁₀₃	C₂×C₄	semidirect
37. Dic₂₀₆	C₂×C₄	semidirect
58. C₁₀₃	#417	semidirect
66. #102	D₁₀₃	semidirect
87. D₄	C₄×D₁₀₃	semidirect

H ≅ G/N

type

2. C₂×#13110088

C₂

semidirect

3. C₄⋊C₄×D₁₀₃

C₂

semidirect

4. #15692946

C₂

semidirect

5. #15692944

C₂

semidirect

6. #15692942

C₂

semidirect

7. #102×C₁₀₃

C₂

semidirect

9. #13110104

C₄

semidirect

25. D₄×C₁₀₃

C₂×C₄

semidirect

37. Dic₂₀₆

C₂×C₄

semidirect

58. C₁₀₃

#417

semidirect

66. #102

D₁₀₃

semidirect

87. D₄

C₄×D₁₀₃

semidirect

Subgroups — #20267789

Conjugacy classes of subgroups

Complements