Group #21426407 — subgroups

Subgroups — #21426407

Order 7552.

112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 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	#16837831	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₆×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#16837241	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837240	C₂	1	1	yes	maximal, characteristic, complemented
5	#16837237	C₂	1	1	yes	maximal, characteristic, complemented
6	#16837235	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
8	#14273746	—	2	1	no	—
9	D₈×D₅₉	—	2	1	no	—
10	Dic₄₇₂	C₂²	1	1	yes	characteristic, complemented
11	#14273671	—	2	1	no	—
12	D₉₄₄	C₂²	1	1	yes	characteristic
13	#14273668	—	2	1	no	—
14	C₁₆×D₅₉	C₂²	1	1	yes	characteristic
15	C₅₉⋊C₃₂	C₂²	1	1	yes	characteristic, complemented
16	D₁₆×C₅₉	C₂²	1	1	yes	characteristic
17	D₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
18	C₃₂×C₅₉	C₂²	1	1	yes	characteristic, complemented
19	#11745687	—	4	1	no	—
20	D₄×D₅₉	—	4	1	no	—
21	D₈×C₅₉	—	2	1	no	—
22	D₈×C₅₉	—	2	1	no	—
23	#11745670	—	4	1	no	—
24	#11745669	—	4	1	no	—
25	Dic₂₃₆	—	2	1	no	—
26	D₄₇₂	—	2	1	no	—
27	C₈×D₅₉	D₄	1	1	yes	characteristic
28	C₁₆×C₅₉	C₂³	1	1	yes	characteristic
29	C₅₉⋊C₁₆	D₄	1	1	yes	characteristic
30	C₂²×D₅₉	—	8	1	no	—
31	D₄×C₅₉	—	4	1	no	—
32	D₄×C₅₉	—	4	1	no	—
33	C₂²⋊D₅₉	—	8	1	no	—
34	C₂²⋊D₅₉	—	8	1	no	—
35	C₂×Dic₅₉	—	8	1	no	—
36	D₂₃₆	—	4	1	no	—
37	C₄×D₅₉	D₈	1	1	yes	characteristic
38	Dic₁₁₈	—	4	1	no	—
39	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
40	C₅₉⋊C₈	D₈	1	1	yes	characteristic
41	C₂²×C₅₉	—	8	1	no	—
42	C₂²×C₅₉	—	8	1	no	—
43	C₂×D₅₉	—	8	1	no	—
44	C₂×D₅₉	—	16	2	no	—
45	C₂×D₅₉	D₁₆	1	1	yes	characteristic
46	C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
47	Dic₅₉	—	8	1	no	—
48	Dic₅₉	D₁₆	1	1	yes	characteristic
49	#2263	—	59	1	no	maximal, Sylow
50	C₂×C₅₉	—	16	1	no	—
51	C₂×C₅₉	—	16	1	no	—
52	C₂×C₅₉	C₂×D₁₆	1	1	yes	characteristic
53	D₅₉	—	2	1	no	—
54	D₅₉	—	16	1	no	—
55	#508	—	59	1	no	—
56	C₂×D₁₆	—	59	1	no	—
57	SD₆₄	—	59	1	no	—
58	SD₆₄	—	59	1	no	—
59	D₃₂	—	59	1	no	—
60	D₃₂	D₅₉	1	1	yes	characteristic, complemented
61	M₆₄	—	59	1	no	—
62	C₅₉	#2263	1	1	yes	characteristic, complemented, Sylow
63	#135	—	118	1	no	—
64	C₂×D₈	—	118	1	no	—
65	Q₃₂	—	59	1	no	—
66	SD₃₂	—	118	1	no	—
67	D₁₆	—	59	1	no	—
68	D₁₆	—	118	1	no	—
69	D₁₆	C₂×D₅₉	1	1	yes	characteristic
70	D₁₆	C₂×D₅₉	1	1	yes	characteristic, complemented
71	C₂×C₁₆	—	59	1	no	—
72	C₃₂	—	59	1	no	—
73	C₃₂	C₂×D₅₉	1	1	yes	characteristic, complemented
74	#41	—	236	1	no	—
75	C₂×D₄	—	236	1	no	—
76	Q₁₆	—	118	1	no	—
77	SD₁₆	—	236	1	no	—
78	D₈	—	2	1	no	—
79	D₈	—	2	1	no	—
80	D₈	—	118	1	no	—
81	D₈	—	236	1	no	—
82	C₂×C₈	—	59	1	no	—
83	C₁₆	—	59	1	no	—
84	C₁₆	C₂²×D₅₉	1	1	yes	characteristic
85	C₂³	—	472	1	no	—
86	Q₈	—	236	1	no	—
87	D₄	—	4	1	no	—
88	D₄	—	4	1	no	—
89	D₄	—	472	1	no	—
90	D₄	—	472	1	no	—
91	D₄	—	236	1	no	—
92	C₂×C₄	—	59	1	no	—
93	C₂×C₄	—	472	1	no	—
94	C₈	—	59	1	no	—
95	C₈	D₄×D₅₉	1	1	yes	characteristic
96	C₂²	—	8	1	no	—
97	C₂²	—	8	1	no	—
98	C₂²	—	59	1	no	—
99	C₂²	—	944	2	no	—
100	C₂²	—	472	1	no	—
101	C₄	—	59	1	no	—
102	C₄	—	472	1	no	—
103	C₄	D₈×D₅₉	1	1	yes	characteristic
104	C₂	—	16	1	no	—
105	C₂	—	16	1	no	—
106	C₂	—	118	1	no	—
107	C₂	—	944	1	no	—
108	C₂	D₁₆×D₅₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837831

C₂

yes

maximal, characteristic, complemented

D₁₆×D₅₉

C₂

yes

maximal, characteristic, complemented

#16837241

C₂

yes

maximal, characteristic, complemented

#16837240

C₂

yes

maximal, characteristic, complemented

#16837237

C₂

yes

maximal, characteristic, complemented

#16837235

C₂

yes

maximal, characteristic, complemented

C₅₉×D₃₂

C₂

yes

maximal, characteristic, complemented

#14273746

—

D₈×D₅₉

—

Dic₄₇₂

C₂²

yes

characteristic, complemented

#14273671

—

D₉₄₄

C₂²

yes

characteristic

#14273668

—

C₁₆×D₅₉

C₂²

yes

characteristic

C₅₉⋊C₃₂

C₂²

yes

characteristic, complemented

D₁₆×C₅₉

C₂²

yes

characteristic

D₁₆×C₅₉

C₂²

yes

characteristic, complemented

C₃₂×C₅₉

C₂²

yes

characteristic, complemented

#11745687

—

D₄×D₅₉

—

D₈×C₅₉

—

D₈×C₅₉

—

#11745670

—

#11745669

—

Dic₂₃₆

—

D₄₇₂

—

C₈×D₅₉

D₄

yes

characteristic

C₁₆×C₅₉

C₂³

yes

characteristic

C₅₉⋊C₁₆

D₄

yes

characteristic

C₂²×D₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

C₂²⋊D₅₉

—

C₂²⋊D₅₉

—

C₂×Dic₅₉

—

D₂₃₆

—

C₄×D₅₉

D₈

yes

characteristic

Dic₁₁₈

—

C₈×C₅₉

C₂×D₄

yes

characteristic

C₅₉⋊C₈

D₈

yes

characteristic

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

D₁₆

yes

characteristic

C₄×C₅₉

C₂×D₈

yes

characteristic

Dic₅₉

—

Dic₅₉

D₁₆

yes

characteristic

#2263

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

C₂×D₁₆

yes

characteristic

D₅₉

—

D₅₉

—

#508

—

C₂×D₁₆

—

SD₆₄

—

SD₆₄

—

D₃₂

—

D₃₂

D₅₉

yes

characteristic, complemented

M₆₄

—

C₅₉

#2263

yes

characteristic, complemented, Sylow

#135

—

118

—

C₂×D₈

—

118

—

Q₃₂

—

SD₃₂

—

118

—

D₁₆

—

D₁₆

—

118

—

D₁₆

C₂×D₅₉

yes

characteristic

D₁₆

C₂×D₅₉

yes

characteristic, complemented

C₂×C₁₆

—

C₃₂

—

C₃₂

C₂×D₅₉

yes

characteristic, complemented

#41

—

236

—

C₂×D₄

—

236

—

Q₁₆

—

118

—

SD₁₆

—

236

—

D₈

—

D₈

—

D₈

—

118

—

D₈

—

236

—

C₂×C₈

—

C₁₆

—

C₁₆

C₂²×D₅₉

yes

characteristic

C₂³

—

472

—

Q₈

—

236

—

D₄

—

D₄

—

D₄

—

472

—

D₄

—

472

—

D₄

—

236

—

C₂×C₄

—

C₂×C₄

—

472

—

C₈

—

C₈

D₄×D₅₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

—

944

—

100

C₂²

—

472

—

101

C₄

—

102

C₄

—

472

—

103

C₄

D₈×D₅₉

yes

characteristic

104

C₂

—

105

C₂

—

106

C₂

—

118

—

107

C₂

—

944

—

108

C₂

D₁₆×D₅₉

yes

characteristic

	subgroup	G/H
center	C₂	D₁₆×D₅₉
commutator	C₁₆×C₅₉	C₂³
Frattini	C₁₆	C₂²×D₅₉
Fitting	C₅₉×D₃₂	C₂
socle	C₂×C₅₉	C₂×D₁₆
hypercenter	D₃₂	D₅₉
hypocenter	C₅₉	#2263
LCS	G ▷ C₁₆×C₅₉ ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

subgroup

G/H

center

C₂

D₁₆×D₅₉

commutator

C₁₆×C₅₉

C₂³

Frattini

C₁₆

C₂²×D₅₉

Fitting

C₅₉×D₃₂

C₂

socle

C₂×C₅₉

C₂×D₁₆

hypercenter

D₃₂

D₅₉

hypocenter

C₅₉

#2263

LCS

G ▷ C₁₆×C₅₉ ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

N	H ≅ G/N	type
1. #16837831	C₂	semidirect
2. D₁₆×D₅₉	C₂	semidirect
3. #16837241	C₂	semidirect
4. #16837240	C₂	semidirect
5. #16837237	C₂	semidirect
6. #16837235	C₂	semidirect
7. C₅₉×D₃₂	C₂	semidirect
10. Dic₄₇₂	C₂²	semidirect
15. C₅₉⋊C₃₂	C₂²	semidirect
17. D₁₆×C₅₉	C₂²	semidirect
18. C₃₂×C₅₉	C₂²	semidirect
60. D₃₂	D₅₉	semidirect
62. C₅₉	#2263	semidirect
70. D₁₆	C₂×D₅₉	semidirect
73. C₃₂	C₂×D₅₉	semidirect

H ≅ G/N

type

1. #16837831

C₂

semidirect

2. D₁₆×D₅₉

C₂

semidirect

3. #16837241

C₂

semidirect

4. #16837240

C₂

semidirect

5. #16837237

C₂

semidirect

6. #16837235

C₂

semidirect

7. C₅₉×D₃₂

C₂

semidirect

10. Dic₄₇₂

C₂²

semidirect

15. C₅₉⋊C₃₂

C₂²

semidirect

17. D₁₆×C₅₉

C₂²

semidirect

18. C₃₂×C₅₉

C₂²

semidirect

60. D₃₂

D₅₉

semidirect

62. C₅₉

#2263

semidirect

70. D₁₆

C₂×D₅₉

semidirect

73. C₃₂

C₂×D₅₉

semidirect

Subgroups — #21426407

Conjugacy classes of subgroups

Complements