Group #21432164 — subgroups

Subgroups — #21432164

Order 7552.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14273719	C₂	1	2	yes	maximal
2	#16837342	C₂	1	4	yes	maximal
3	#16837334	C₂	1	4	yes	maximal
4	#16837332	C₂	1	4	yes	maximal
5	C₅₉×#382	C₂	1	1	yes	maximal, characteristic
6	#14273719	—	2	8	no	—
7	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₅₉	C₂²	1	4	yes	—
10	C₂×Dic₅₉⋊C₄	C₂²	1	4	yes	—
11	C₂×Dic₅₉⋊C₄	C₂²	1	4	yes	—
12	C₅₉⋊#95	C₂²	1	8	yes	—
13	C₅₉⋊#95	C₂²	1	4	yes	—
14	C₂×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
15	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
16	#95×C₅₉	C₂²	1	4	yes	—
17	C₂²×C₄×C₅₉	C₂³	1	4	yes	—
18	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
19	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
20	C₂²×Dic₅₉	C₂³	1	4	yes	—
21	C₂²×Dic₅₉	C₂³	1	4	yes	—
22	C₄⋊C₄×C₅₉	—	4	2	no	—
23	C₄²×C₅₉	D₄	1	4	yes	—
24	C₄⋊Dic₅₉	—	2	4	no	—
25	C₄⋊Dic₅₉	—	2	4	no	—
26	C₄⋊Dic₅₉	—	4	4	no	—
27	Dic₅₉⋊C₄	—	2	8	no	—
28	Dic₅₉⋊C₄	—	2	8	no	—
29	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₅₉	—	2	1	no	—
31	C₂×C₄×C₅₉	—	2	4	no	—
32	C₂×C₄×C₅₉	—	2	1	no	—
33	C₂×C₄×C₅₉	—	2	4	no	—
34	C₂×C₄×C₅₉	—	2	8	no	—
35	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₅₉	C₂×D₄	1	4	yes	—
37	C₂×Dic₅₉	—	2	4	no	—
38	C₂×Dic₅₉	—	2	4	no	—
39	C₂×Dic₅₉	—	2	4	no	—
40	C₂×Dic₅₉	—	2	8	no	—
41	C₂×Dic₅₉	—	2	4	no	—
42	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
43	C₂²×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
44	C₂²×C₅₉	2₋¹⁺⁴	1	4	yes	—
45	C₂²×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
46	C₄×C₅₉	—	2	4	no	—
47	C₄×C₅₉	—	2	2	no	—
48	C₄×C₅₉	—	4	4	no	—
49	Dic₅₉	—	4	4	no	—
50	Dic₅₉	—	4	4	no	—
51	#2822	—	59	1	no	maximal, Sylow
52	C₂×C₅₉	#536	1	2	yes	—
53	C₂×C₅₉	#537	1	1	yes	characteristic
54	C₂×C₅₉	#563	1	2	yes	—
55	C₂×C₅₉	#564	1	2	yes	—
56	C₂×#125	—	59	2	no	—
57	#400	—	59	4	no	—
58	#398	—	59	4	no	—
59	#398	—	59	4	no	—
60	#382	D₅₉	1	1	yes	characteristic
61	C₅₉	#2822	1	1	yes	characteristic, complemented, Sylow
62	#125	—	118	8	no	—
63	C₂×C₄⋊C₄	—	59	4	no	—
64	C₂×C₄⋊C₄	—	59	2	no	—
65	C₂×C₄⋊C₄	—	59	4	no	—
66	C₂×C₄⋊C₄	—	59	2	no	—
67	C₂×C₄⋊C₄	—	59	4	no	—
68	C₂×C₄⋊C₄	C₂×D₅₉	1	2	yes	—
69	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
70	#95	—	59	8	no	—
71	#95	—	59	4	no	—
72	#95	C₂×D₅₉	1	4	yes	—
73	C₂²×C₄	—	59	4	no	—
74	C₂²×C₄	—	59	4	no	—
75	C₂²×C₄	C₂²×D₅₉	1	4	yes	—
76	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
77	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
78	C₄⋊C₄	—	4	2	no	—
79	C₄⋊C₄	—	118	8	no	—
80	C₄⋊C₄	—	118	8	no	—
81	C₄⋊C₄	—	118	4	no	—
82	C₄⋊C₄	—	118	4	no	—
83	C₄⋊C₄	—	236	4	no	—
84	C₄²	D₂₃₆	1	4	yes	—
85	C₂³	C₂³×D₅₉	1	1	yes	characteristic
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	—	2	8	no	—
91	C₂×C₄	—	118	4	no	—
92	C₂×C₄	—	118	4	no	—
93	C₂×C₄	—	118	4	no	—
94	C₂×C₄	—	118	8	no	—
95	C₂×C₄	—	118	4	no	—
96	C₂×C₄	C₂×D₂₃₆	1	4	yes	—
97	C₂×C₄	C₂×D₂₃₆	1	2	yes	—
98	C₂²	C₂²×D₂₃₆	1	1	yes	characteristic
99	C₂²	#14273772	1	1	yes	characteristic
100	C₂²	#14273774	1	4	yes	—
101	C₂²	#14273775	1	1	yes	characteristic
102	C₄	—	2	4	no	—
103	C₄	—	2	2	no	—
104	C₄	—	4	4	no	—
105	C₄	—	236	4	no	—
106	C₄	—	236	4	no	—
107	C₂	#16837978	1	2	yes	—
108	C₂	#16837983	1	1	yes	characteristic
109	C₂	#16838152	1	2	yes	—
110	C₂	C₅₉⋊#564	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273719

C₂

yes

maximal

#16837342

C₂

yes

maximal

#16837334

C₂

yes

maximal

#16837332

C₂

yes

maximal

C₅₉×#382

C₂

yes

maximal, characteristic

#14273719

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×Dic₅₉⋊C₄

C₂²

yes

—

C₂×Dic₅₉⋊C₄

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

#95×C₅₉

C₂²

yes

—

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

C₂³

yes

—

C₂²×Dic₅₉

C₂³

yes

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

D₄

yes

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₂³×C₅₉

C₂⁴

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂²×C₅₉

C₂²×D₄

yes

characteristic

C₂²×C₅₉

H(5,𝔽₂)

yes

characteristic

C₂²×C₅₉

2₋¹⁺⁴

yes

—

C₂²×C₅₉

2₋¹⁺⁴

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

Dic₅₉

—

Dic₅₉

—

#2822

—

maximal, Sylow

C₂×C₅₉

#536

yes

—

C₂×C₅₉

#537

yes

characteristic

C₂×C₅₉

#563

yes

—

C₂×C₅₉

#564

yes

—

—

—

—

—

D₅₉

yes

characteristic

C₅₉

#2822

yes

characteristic, complemented, Sylow

#125

—

118

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₅₉

yes

—

C₂×C₄²

C₂×D₅₉

yes

—

—

C₂×D₅₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

236

—

C₄²

D₂₃₆

yes

—

C₂³

C₂³×D₅₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

C₂×D₂₃₆

yes

—

C₂×C₄

C₂×D₂₃₆

yes

—

C₂²

C₂²×D₂₃₆

yes

characteristic

C₂²

#14273772

yes

characteristic

100

C₂²

#14273774

yes

—

101

C₂²

#14273775

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

236

—

106

C₄

—

236

—

107

C₂

#16837978

yes

—

108

C₂

#16837983

yes

characteristic

109

C₂

#16838152

yes

—

110

C₂

C₅₉⋊#564

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂⁴
Fitting	C₅₉×#382	C₂
hypercenter	#382	D₅₉
hypocenter	C₅₉	#2822
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₅₉

commutator, socle

C₂³×C₅₉

C₂⁴

Fitting

C₅₉×#382

C₂

D₅₉

C₅₉

G ▷ C₂³×C₅₉ ▷ C₅₉

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
61. C₅₉	#2822	semidirect

H ≅ G/N

type

61. C₅₉

#2822

semidirect

Subgroups — #21432164

Conjugacy classes of subgroups

Complements