Group #21438908 — subgroups

Subgroups — #21438908

Order 7552.

5796 conjugacy classes of subgroups; only the 3201 normal subgroups are shown.

normal subgroups only

This group has 5796 conjugacy classes of subgroups — too many to draw. Only its 3201 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	#16838239	C₂	1	16	yes	maximal, complemented
2	#16838238	C₂	1	20	yes	maximal, complemented
3	C₂×#14273775	C₂	1	10	yes	maximal, complemented
4	2₋¹⁺⁴×D₅₉	C₂	1	16	yes	maximal, complemented
5	C₂×2₋¹⁺⁴×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#14273775	C₂²	1	80	yes	complemented
7	#14273775	C₂²	1	40	yes	complemented
8	#14273774	C₂²	1	80	yes	complemented
9	#14273773	C₂²	1	80	yes	complemented
10	#14273772	C₂²	1	40	yes	complemented
11	C₂×#11745689	C₂²	1	40	yes	complemented
12	C₂×#11745685	C₂²	1	60	yes	complemented
13	#41×D₅₉	C₂²	1	160	yes	complemented
14	C₂×Q₈×D₅₉	C₂²	1	40	yes	complemented
15	2₋¹⁺⁴×C₅₉	C₂²	1	16	yes	complemented
16	C₂×#41×C₅₉	C₂²	1	10	yes	complemented
17	C₂²×Q₈×C₅₉	C₂²	1	5	yes	complemented
18	#41×C₅₉	C₂³	1	80	yes	—
19	C₂×Q₈×C₅₉	C₂³	1	10	yes	—
20	C₂×Q₈×C₅₉	C₂³	1	40	yes	—
21	C₂×D₄×C₅₉	C₂³	1	10	yes	—
22	C₂²×C₄×C₅₉	C₂³	1	15	yes	—
23	C₂×C₂²⋊D₅₉	C₂³	1	40	yes	—
24	#11745689	C₂³	1	160	yes	—
25	Q₈×D₅₉	C₂³	1	160	yes	—
26	#11745687	C₂³	1	160	yes	—
27	D₄×D₅₉	C₂³	1	160	yes	—
28	#11745685	C₂³	1	240	yes	—
29	#11745685	C₂³	1	80	yes	—
30	C₂×D₂₃₆	C₂³	1	60	yes	—
31	C₂×C₄×D₅₉	C₂³	1	120	yes	—
32	C₂×Dic₁₁₈	C₂³	1	60	yes	—
33	C₂³×C₅₉	C₂⁴	1	5	yes	—
34	C₂²×D₅₉	C₂⁴	1	40	yes	—
35	Q₈×C₅₉	C₂⁴	1	40	yes	—
36	D₄×C₅₉	C₂⁴	1	40	yes	—
37	C₂×C₄×C₅₉	C₂⁴	1	60	yes	—
38	C₂×C₄×C₅₉	C₂⁴	1	10	yes	—
39	C₂²⋊D₅₉	C₂⁴	1	16	yes	—
40	C₂²⋊D₅₉	C₂⁴	1	80	yes	—
41	C₂×Dic₅₉	C₂⁴	1	40	yes	—
42	D₂₃₆	C₂⁴	1	80	yes	—
43	C₄×D₅₉	C₂⁴	1	160	yes	—
44	Dic₁₁₈	C₂⁴	1	80	yes	—
45	C₂²×C₅₉	—	4	5	no	—
46	C₂²×C₅₉	C₂⁵	1	10	yes	—
47	C₂²×C₅₉	C₂⁵	1	1	yes	characteristic
48	C₂×D₅₉	—	4	40	no	—
49	C₂×D₅₉	C₂⁵	1	16	yes	—
50	C₄×C₅₉	C₂⁵	1	20	yes	—
51	Dic₅₉	C₂⁵	1	16	yes	—
52	2₋¹⁺⁶	—	59	1	no	maximal, Sylow
53	C₂×C₅₉	—	2	10	no	—
54	C₂×C₅₉	—	2	1	no	—
55	C₂×C₅₉	C₂⁶	1	1	yes	characteristic
56	D₅₉	—	2	16	no	—
57	#585	—	59	16	no	—
58	#585	—	59	20	no	—
59	C₂×2₋¹⁺⁴	—	59	16	no	—
60	C₂×2₋¹⁺⁴	—	59	10	no	—
61	C₂×2₋¹⁺⁴	D₅₉	1	1	yes	characteristic, complemented
62	C₅₉	2₋¹⁺⁶	1	1	yes	characteristic, complemented, Sylow
63	2₋¹⁺⁴	—	59	80	no	—
64	2₋¹⁺⁴	—	59	80	no	—
65	2₋¹⁺⁴	—	59	40	no	—
66	2₋¹⁺⁴	C₂×D₅₉	1	16	yes	complemented
67	H(5,𝔽₂)	—	59	80	no	—
68	H(5,𝔽₂)	—	59	40	no	—
69	C₂×#41	—	59	160	no	—
70	C₂×#41	—	59	40	no	—
71	C₂×#41	—	59	60	no	—
72	C₂×#41	C₂×D₅₉	1	10	yes	complemented
73	C₂²×Q₈	—	59	40	no	—
74	C₂²×Q₈	C₂×D₅₉	1	5	yes	complemented
75	#41	—	59	160	no	—
76	#41	—	59	160	no	—
77	#41	—	59	240	no	—
78	#41	—	59	80	no	—
79	#41	C₂²×D₅₉	1	80	yes	—
80	C₂×Q₈	—	59	160	no	—
81	C₂×Q₈	—	59	60	no	—
82	C₂×Q₈	C₂²×D₅₉	1	40	yes	—
83	C₂×Q₈	C₂²×D₅₉	1	10	yes	—
84	C₂×D₄	—	59	40	no	—
85	C₂×D₄	—	59	160	no	—
86	C₂×D₄	—	59	60	no	—
87	C₂×D₄	C₂²×D₅₉	1	10	yes	—
88	C₂²×C₄	—	59	120	no	—
89	C₂²×C₄	C₂²×D₅₉	1	15	yes	—
90	C₂³	—	59	40	no	—
91	C₂³	C₂³×D₅₉	1	5	yes	—
92	Q₈	—	59	80	no	—
93	Q₈	C₂³×D₅₉	1	40	yes	—
94	D₄	—	59	80	no	—
95	D₄	—	59	16	no	—
96	D₄	—	59	80	no	—
97	D₄	C₂³×D₅₉	1	40	yes	—
98	C₂×C₄	—	59	40	no	—
99	C₂×C₄	—	59	160	no	—
100	C₂×C₄	C₂³×D₅₉	1	60	yes	—
101	C₂×C₄	C₂³×D₅₉	1	10	yes	—
102	C₂²	—	4	5	no	—
103	C₂²	—	59	16	no	—
104	C₂²	—	236	40	no	—
105	C₂²	C₂⁴×D₅₉	1	10	yes	—
106	C₂²	C₂⁴×D₅₉	1	1	yes	characteristic
107	C₄	—	59	16	no	—
108	C₄	C₂⁴×D₅₉	1	20	yes	—
109	C₂	—	2	1	no	—
110	C₂	—	2	10	no	—
111	C₂	—	118	16	no	—
112	C₂	C₂⁵×D₅₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16838239

C₂

yes

maximal, complemented

#16838238

C₂

yes

maximal, complemented

C₂×#14273775

C₂

yes

maximal, complemented

2₋¹⁺⁴×D₅₉

C₂

yes

maximal, complemented

C₂×2₋¹⁺⁴×C₅₉

C₂

yes

maximal, characteristic, complemented

#14273775

C₂²

yes

complemented

#14273775

C₂²

yes

complemented

#14273774

C₂²

yes

complemented

#14273773

C₂²

yes

complemented

#14273772

C₂²

yes

complemented

C₂×#11745689

C₂²

yes

complemented

C₂×#11745685

C₂²

yes

complemented

#41×D₅₉

C₂²

160

yes

complemented

C₂×Q₈×D₅₉

C₂²

yes

complemented

2₋¹⁺⁴×C₅₉

C₂²

yes

complemented

C₂×#41×C₅₉

C₂²

yes

complemented

C₂²×Q₈×C₅₉

C₂²

yes

complemented

#41×C₅₉

C₂³

yes

—

C₂×Q₈×C₅₉

C₂³

yes

—

C₂×Q₈×C₅₉

C₂³

yes

—

C₂×D₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

—

C₂×C₂²⋊D₅₉

C₂³

yes

—

#11745689

C₂³

160

yes

—

Q₈×D₅₉

C₂³

160

yes

—

#11745687

C₂³

160

yes

—

D₄×D₅₉

C₂³

160

yes

—

#11745685

C₂³

240

yes

—

#11745685

C₂³

yes

—

C₂×D₂₃₆

C₂³

yes

—

C₂×C₄×D₅₉

C₂³

120

yes

—

C₂×Dic₁₁₈

C₂³

yes

—

C₂³×C₅₉

C₂⁴

yes

—

C₂²×D₅₉

C₂⁴

yes

—

Q₈×C₅₉

C₂⁴

yes

—

D₄×C₅₉

C₂⁴

yes

—

C₂×C₄×C₅₉

C₂⁴

yes

—

C₂×C₄×C₅₉

C₂⁴

yes

—

C₂²⋊D₅₉

C₂⁴

yes

—

C₂²⋊D₅₉

C₂⁴

yes

—

C₂×Dic₅₉

C₂⁴

yes

—

D₂₃₆

C₂⁴

yes

—

C₄×D₅₉

C₂⁴

160

yes

—

Dic₁₁₈

C₂⁴

yes

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂⁵

yes

—

C₂²×C₅₉

C₂⁵

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

C₂⁵

yes

—

C₄×C₅₉

C₂⁵

yes

—

Dic₅₉

C₂⁵

yes

—

2₋¹⁺⁶

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

C₂⁶

yes

characteristic

D₅₉

—

#585

—

#585

—

C₂×2₋¹⁺⁴

—

C₂×2₋¹⁺⁴

—

C₂×2₋¹⁺⁴

D₅₉

yes

characteristic, complemented

C₅₉

2₋¹⁺⁶

yes

characteristic, complemented, Sylow

2₋¹⁺⁴

—

2₋¹⁺⁴

—

2₋¹⁺⁴

—

2₋¹⁺⁴

C₂×D₅₉

yes

complemented

H(5,𝔽₂)

—

H(5,𝔽₂)

—

C₂×#41

—

160

—

C₂×#41

—

C₂×#41

—

C₂×#41

C₂×D₅₉

yes

complemented

C₂²×Q₈

—

C₂²×Q₈

C₂×D₅₉

yes

complemented

#41

—

160

—

#41

—

160

—

#41

—

240

—

#41

—

#41

C₂²×D₅₉

yes

—

C₂×Q₈

—

160

—

C₂×Q₈

—

C₂×Q₈

C₂²×D₅₉

yes

—

C₂×Q₈

C₂²×D₅₉

yes

—

C₂×D₄

—

C₂×D₄

—

160

—

C₂×D₄

—

C₂×D₄

C₂²×D₅₉

yes

—

C₂²×C₄

—

120

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₂³

—

C₂³

C₂³×D₅₉

yes

—

Q₈

—

Q₈

C₂³×D₅₉

yes

—

D₄

—

D₄

—

D₄

—

D₄

C₂³×D₅₉

yes

—

C₂×C₄

—

C₂×C₄

—

160

—

100

C₂×C₄

C₂³×D₅₉

yes

—

101

C₂×C₄

C₂³×D₅₉

yes

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

236

—

105

C₂²

C₂⁴×D₅₉

yes

—

106

C₂²

C₂⁴×D₅₉

yes

characteristic

107

C₄

—

108

C₄

C₂⁴×D₅₉

yes

—

109

C₂

—

110

C₂

—

111

C₂

—

118

—

112

C₂

C₂⁵×D₅₉

yes

characteristic

	subgroup	G/H
center, Frattini	C₂	C₂⁵×D₅₉
commutator, socle	C₂×C₅₉	C₂⁶
Fitting	C₂×2₋¹⁺⁴×C₅₉	C₂
hypercenter	C₂×2₋¹⁺⁴	D₅₉
hypocenter	C₅₉	2₋¹⁺⁶
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×2₋¹⁺⁴

subgroup

G/H

center, Frattini

C₂

C₂⁵×D₅₉

commutator, socle

C₂×C₅₉

C₂⁶

Fitting

C₂×2₋¹⁺⁴×C₅₉

C₂

hypercenter

C₂×2₋¹⁺⁴

D₅₉

hypocenter

C₅₉

2₋¹⁺⁶

LCS

G ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂ ◁ C₂×2₋¹⁺⁴

N	H ≅ G/N	type
1. #16838239	C₂	semidirect
2. #16838238	C₂	semidirect
3. C₂×#14273775	C₂	semidirect
4. 2₋¹⁺⁴×D₅₉	C₂	semidirect
5. C₂×2₋¹⁺⁴×C₅₉	C₂	semidirect
6. #14273775	C₂²	semidirect
7. #14273775	C₂²	semidirect
8. #14273774	C₂²	semidirect
9. #14273773	C₂²	semidirect
10. #14273772	C₂²	semidirect
11. C₂×#11745689	C₂²	semidirect
12. C₂×#11745685	C₂²	semidirect
13. #41×D₅₉	C₂²	semidirect
14. C₂×Q₈×D₅₉	C₂²	semidirect
15. 2₋¹⁺⁴×C₅₉	C₂²	semidirect
16. C₂×#41×C₅₉	C₂²	semidirect
17. C₂²×Q₈×C₅₉	C₂²	semidirect
61. C₂×2₋¹⁺⁴	D₅₉	semidirect
62. C₅₉	2₋¹⁺⁶	semidirect
66. 2₋¹⁺⁴	C₂×D₅₉	semidirect
72. C₂×#41	C₂×D₅₉	semidirect
74. C₂²×Q₈	C₂×D₅₉	semidirect

H ≅ G/N

type

1. #16838239

C₂

semidirect

2. #16838238

C₂

semidirect

3. C₂×#14273775

C₂

semidirect

4. 2₋¹⁺⁴×D₅₉

C₂

semidirect

5. C₂×2₋¹⁺⁴×C₅₉

C₂

semidirect

6. #14273775

C₂²

semidirect

7. #14273775

C₂²

semidirect

8. #14273774

C₂²

semidirect

9. #14273773

C₂²

semidirect

10. #14273772

C₂²

semidirect

11. C₂×#11745689

C₂²

semidirect

12. C₂×#11745685

C₂²

semidirect

13. #41×D₅₉

C₂²

semidirect

14. C₂×Q₈×D₅₉

C₂²

semidirect

15. 2₋¹⁺⁴×C₅₉

C₂²

semidirect

16. C₂×#41×C₅₉

C₂²

semidirect

17. C₂²×Q₈×C₅₉

C₂²

semidirect

61. C₂×2₋¹⁺⁴

D₅₉

semidirect

62. C₅₉

2₋¹⁺⁶

semidirect

66. 2₋¹⁺⁴

C₂×D₅₉

semidirect

72. C₂×#41

C₂×D₅₉

semidirect

74. C₂²×Q₈

C₂×D₅₉

semidirect

Subgroups — #21438908

Conjugacy classes of subgroups

Complements