Group #20267859 — subgroups

Subgroups — #20267859

Order 6592.

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

normal subgroups only

This group has 124 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×#13110088	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂²⋊D₁₀₃	C₂	1	1	yes	maximal, characteristic
4	Dic₁₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	(C₂×D₁₀₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#15692931	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²⋊C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂²⋊D₁₀₃	C₄	1	1	yes	characteristic
9	C₂×C₄×D₁₀₃	C₂²	1	1	yes	characteristic
10	#13110088	—	2	2	no	—
11	C₂×C₁₀₃⋊C₈	—	2	2	no	—
12	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
14	Dic₁₀₃⋊C₄	C₄	1	1	yes	characteristic
15	C₂²⋊Dic₁₀₃	C₄	1	1	yes	characteristic
16	(C₂×D₁₀₃)⋊C₄	C₄	1	1	yes	characteristic
17	C₄×Dic₁₀₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
19	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
20	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
21	C₂³×C₁₀₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₁₀₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₀₃	—	2	1	no	—
24	C₂×C₄×C₁₀₃	—	2	1	no	—
25	C₂×C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
27	C₂²⋊D₁₀₃	—	2	2	no	—
28	C₂×Dic₁₀₃	C₂×C₄	1	1	yes	characteristic
29	C₂×Dic₁₀₃	C₂×C₄	1	1	yes	characteristic
30	C₂×Dic₁₀₃	C₂×C₄	1	1	yes	characteristic
31	C₄×D₁₀₃	—	2	1	no	—
32	C₄×D₁₀₃	—	2	1	no	—
33	C₈×C₁₀₃	—	2	1	no	—
34	C₈×C₁₀₃	—	2	1	no	—
35	C₁₀₃⋊C₈	—	2	1	no	—
36	C₁₀₃⋊C₈	D₄	1	2	yes	complemented
37	C₂²×C₁₀₃	—	2	1	no	—
38	C₂²×C₁₀₃	—	2	1	no	—
39	C₂²×C₁₀₃	M₁₆	1	2	yes	complemented
40	C₂²×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×D₁₀₃	—	2	1	no	—
42	C₂×D₁₀₃	—	2	1	no	—
43	C₂×D₁₀₃	—	2	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	—	2	1	no	—
48	Dic₁₀₃	—	2	1	no	—
49	Dic₁₀₃	—	2	1	no	—
50	C₂×C₁₀₃	—	2	2	no	—
51	C₂×C₁₀₃	C₄×D₄	1	1	yes	characteristic
52	C₂×C₁₀₃	C₂×M₁₆	1	1	yes	characteristic
53	C₂×C₁₀₃	#131	1	1	yes	characteristic
54	D₁₀₃	—	4	1	no	—
55	C₁₀₃	#435	1	1	yes	characteristic, complemented, Sylow
56	#435	—	103	1	no	maximal, Sylow
57	C₂×M₁₆	—	103	1	no	—
58	C₂²×C₈	—	103	1	no	—
59	C₄×D₄	—	103	1	no	—
60	C₄⋊C₈	—	103	1	no	—
61	C₂²⋊C₈	—	103	1	no	—
62	C₂²⋊C₈	D₁₀₃	1	1	yes	characteristic, complemented
63	#97	—	103	1	no	—
64	C₂×D₄	—	103	1	no	—
65	C₂²×C₄	—	103	1	no	—
66	C₂²×C₄	C₂×D₁₀₃	1	1	yes	characteristic
67	M₁₆	—	206	2	no	—
68	C₂×C₈	—	103	1	no	—
69	C₂×C₈	—	103	1	no	—
70	C₂×C₈	—	206	2	no	—
71	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
72	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
73	C₄⋊C₄	—	103	1	no	—
74	C₂²⋊C₄	—	103	1	no	—
75	C₂²⋊C₄	—	103	1	no	—
76	C₄²	—	103	1	no	—
77	C₂³	—	103	1	no	—
78	C₂³	C₄×D₁₀₃	1	1	yes	characteristic
79	D₄	—	206	2	no	—
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	103	1	no	—
83	C₂×C₄	—	103	1	no	—
84	C₂×C₄	—	103	1	no	—
85	C₂×C₄	—	206	1	no	—
86	C₂×C₄	—	206	1	no	—
87	C₂×C₄	C₄×D₁₀₃	1	1	yes	characteristic
88	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	—	2	1	no	—
91	C₈	—	103	2	no	—
92	C₈	—	206	1	no	—
93	C₂²	—	2	1	no	—
94	C₂²	—	2	1	no	—
95	C₂²	—	206	1	no	—
96	C₂²	—	206	1	no	—
97	C₂²	—	206	1	no	—
98	C₂²	#13110088	1	2	yes	complemented
99	C₂²	C₂×C₄×D₁₀₃	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	206	1	no	—
102	C₄	—	206	1	no	—
103	C₄	—	206	1	no	—
104	C₄	D₄×D₁₀₃	1	1	yes	characteristic
105	C₄	#13110104	1	1	yes	characteristic
106	C₂	—	2	2	no	—
107	C₂	—	412	1	no	—
108	C₂	(C₂²⋊D₁₀₃)⋊C₄	1	1	yes	characteristic
109	C₂	C₂×#13110088	1	1	yes	characteristic
110	C₂	#15693029	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13110088

C₂

yes

maximal, characteristic, complemented

C₂²×C₁₀₃⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄×C₂²⋊D₁₀₃

C₂

yes

maximal, characteristic

Dic₁₀₃⋊C₈

C₂

yes

maximal, characteristic, complemented

(C₂×D₁₀₃)⋊C₈

C₂

yes

maximal, characteristic, complemented

#15692931

C₂

yes

maximal, characteristic, complemented

C₂²⋊C₈×C₁₀₃

C₂

yes

maximal, characteristic, complemented

C₂×C₂²⋊D₁₀₃

C₄

yes

characteristic

C₂×C₄×D₁₀₃

C₂²

yes

characteristic

#13110088

—

C₂×C₁₀₃⋊C₈

—

C₂×C₁₀₃⋊C₈

C₂²

yes

characteristic

C₂×C₁₀₃⋊C₈

C₂²

yes

characteristic

Dic₁₀₃⋊C₄

C₄

yes

characteristic

C₂²⋊Dic₁₀₃

C₄

yes

characteristic

(C₂×D₁₀₃)⋊C₄

C₄

yes

characteristic

C₄×Dic₁₀₃

C₂²

yes

characteristic

C₂²×C₄×C₁₀₃

C₂²

yes

characteristic

C₂×C₈×C₁₀₃

C₂²

yes

characteristic

C₂×C₈×C₁₀₃

C₂²

yes

characteristic

C₂³×C₁₀₃

C₂×C₄

yes

characteristic

C₂²×D₁₀₃

C₂×C₄

yes

characteristic

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

C₂×C₄

yes

characteristic

C₂×C₄×C₁₀₃

C₂³

yes

characteristic

C₂²⋊D₁₀₃

—

C₂×Dic₁₀₃

C₂×C₄

yes

characteristic

C₂×Dic₁₀₃

C₂×C₄

yes

characteristic

C₂×Dic₁₀₃

C₂×C₄

yes

characteristic

C₄×D₁₀₃

—

C₄×D₁₀₃

—

C₈×C₁₀₃

—

C₈×C₁₀₃

—

C₁₀₃⋊C₈

—

C₁₀₃⋊C₈

D₄

yes

complemented

C₂²×C₁₀₃

—

C₂²×C₁₀₃

—

C₂²×C₁₀₃

M₁₆

yes

complemented

C₂²×C₁₀₃

C₂²×C₄

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

C₄×D₄

yes

characteristic

C₂×C₁₀₃

C₂×M₁₆

yes

characteristic

C₂×C₁₀₃

#131

yes

characteristic

D₁₀₃

—

C₁₀₃

#435

yes

characteristic, complemented, Sylow

#435

—

103

maximal, Sylow

C₂×M₁₆

—

103

—

C₂²×C₈

—

103

—

C₄×D₄

—

103

—

C₄⋊C₈

—

103

—

C₂²⋊C₈

—

103

—

C₂²⋊C₈

D₁₀₃

yes

characteristic, complemented

#97

—

103

—

C₂×D₄

—

103

—

C₂²×C₄

—

103

—

C₂²×C₄

C₂×D₁₀₃

yes

characteristic

M₁₆

—

206

—

C₂×C₈

—

103

—

C₂×C₈

—

103

—

C₂×C₈

—

206

—

C₂×C₈

C₂×D₁₀₃

yes

characteristic

C₂×C₈

C₂×D₁₀₃

yes

characteristic

C₄⋊C₄

—

103

—

C₂²⋊C₄

—

103

—

C₂²⋊C₄

—

103

—

C₄²

—

103

—

C₂³

—

103

—

C₂³

C₄×D₁₀₃

yes

characteristic

D₄

—

206

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

103

—

C₂×C₄

—

103

—

C₂×C₄

—

103

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

C₄×D₁₀₃

yes

characteristic

C₂×C₄

C₂²×D₁₀₃

yes

characteristic

C₈

—

C₈

—

C₈

—

103

—

C₈

—

206

—

C₂²

—

C₂²

—

C₂²

—

206

—

C₂²

—

206

—

C₂²

—

206

—

C₂²

#13110088

yes

complemented

C₂²

C₂×C₄×D₁₀₃

yes

characteristic

100

C₄

—

101

C₄

—

206

—

102

C₄

—

206

—

103

C₄

—

206

—

104

C₄

D₄×D₁₀₃

yes

characteristic

105

C₄

#13110104

yes

characteristic

106

C₂

—

107

C₂

—

412

—

108

C₂

(C₂²⋊D₁₀₃)⋊C₄

yes

characteristic

109

C₂

C₂×#13110088

yes

characteristic

110

C₂

#15693029

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₀₃
commutator, socle	C₂²×C₁₀₃	C₂²×C₄
Fitting	C₂²⋊C₈×C₁₀₃	C₂
hypercenter	C₂²⋊C₈	D₁₀₃
hypocenter	C₁₀₃	#435
LCS	G ▷ C₂²×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×D₁₀₃

commutator, socle

C₂²×C₁₀₃

C₂²×C₄

Fitting

C₂²⋊C₈×C₁₀₃

C₂

hypercenter

C₂²⋊C₈

D₁₀₃

C₁₀₃

G ▷ C₂²×C₁₀₃ ▷ C₁₀₃

C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

N	H ≅ G/N	type
1. C₂×#13110088	C₂	semidirect
2. C₂²×C₁₀₃⋊C₈	C₂	semidirect
4. Dic₁₀₃⋊C₈	C₂	semidirect
5. (C₂×D₁₀₃)⋊C₈	C₂	semidirect
6. #15692931	C₂	semidirect
7. C₂²⋊C₈×C₁₀₃	C₂	semidirect
36. C₁₀₃⋊C₈	D₄	semidirect
39. C₂²×C₁₀₃	M₁₆	semidirect
55. C₁₀₃	#435	semidirect
62. C₂²⋊C₈	D₁₀₃	semidirect
98. C₂²	#13110088	semidirect

H ≅ G/N

type

1. C₂×#13110088

C₂

semidirect

2. C₂²×C₁₀₃⋊C₈

C₂

semidirect

4. Dic₁₀₃⋊C₈

C₂

semidirect

5. (C₂×D₁₀₃)⋊C₈

C₂

semidirect

6. #15692931

C₂

semidirect

7. C₂²⋊C₈×C₁₀₃

C₂

semidirect

36. C₁₀₃⋊C₈

D₄

semidirect

39. C₂²×C₁₀₃

M₁₆

semidirect

55. C₁₀₃

#435

semidirect

62. C₂²⋊C₈

D₁₀₃

semidirect

98. C₂²

#13110088

semidirect

Subgroups — #20267859

Conjugacy classes of subgroups

Complements