Group #21432371 — subgroups

Subgroups — #21432371

Order 7552.

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

normal subgroups only

This group has 340 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	#16837336	C₂	1	4	yes	maximal
2	#16837335	C₂	1	4	yes	maximal
3	#16837334	C₂	1	4	yes	maximal
4	#16837268	C₂	1	2	yes	maximal
5	C₅₉×#382	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₅₉	C₂²	1	4	yes	—
9	C₂×Dic₅₉⋊C₄	C₂²	1	4	yes	—
10	C₂×Dic₅₉⋊C₄	C₂²	1	4	yes	—
11	C₅₉⋊#95	C₂²	1	4	yes	—
12	C₅₉⋊#95	C₂²	1	4	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	Q₈	1	4	yes	—
24	C₄⋊Dic₅₉	—	4	2	no	—
25	C₄⋊Dic₅₉	—	4	4	no	—
26	C₄⋊Dic₅₉	—	4	2	no	—
27	Dic₅₉⋊C₄	—	4	4	no	—
28	Dic₅₉⋊C₄	—	4	4	no	—
29	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₅₉	—	2	2	no	—
31	C₂×C₄×C₅₉	—	2	1	no	—
32	C₂×C₄×C₅₉	—	2	2	no	—
33	C₂×C₄×C₅₉	—	2	1	no	—
34	C₂×C₄×C₅₉	—	2	4	no	—
35	C₂×C₄×C₅₉	—	2	4	no	—
36	C₂×C₄×C₅₉	—	2	4	no	—
37	C₂×C₄×C₅₉	C₂×Q₈	1	4	yes	—
38	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
39	C₂×Dic₅₉	—	2	4	no	—
40	C₂×Dic₅₉	—	2	4	no	—
41	C₂×Dic₅₉	—	2	4	no	—
42	C₂×Dic₅₉	—	2	4	no	—
43	C₂×Dic₅₉	—	2	4	no	—
44	C₂×Dic₅₉	—	2	4	no	—
45	C₂²×C₅₉	C₂²×Q₈	1	1	yes	characteristic
46	C₂²×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
47	C₂²×C₅₉	H(5,𝔽₂)	1	2	yes	—
48	C₂²×C₅₉	2₋¹⁺⁴	1	2	yes	—
49	C₂²×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
50	C₄×C₅₉	—	2	4	no	—
51	C₄×C₅₉	—	2	2	no	—
52	C₄×C₅₉	—	4	4	no	—
53	Dic₅₉	—	4	4	no	—
54	Dic₅₉	—	4	4	no	—
55	#2845	—	59	1	no	maximal, Sylow
56	C₂×C₅₉	#544	1	2	yes	—
57	C₂×C₅₉	#544	1	1	yes	characteristic
58	C₂×C₅₉	#562	1	2	yes	—
59	C₂×C₅₉	#562	1	1	yes	characteristic
60	C₂×C₅₉	#564	1	1	yes	characteristic
61	#398	—	59	4	no	—
62	#398	—	59	4	no	—
63	#398	—	59	4	no	—
64	#382	—	59	2	no	—
65	#382	D₅₉	1	1	yes	characteristic
66	C₅₉	#2845	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₄⋊C₄	—	59	2	no	—
68	C₂×C₄⋊C₄	—	59	2	no	—
69	C₂×C₄⋊C₄	—	59	4	no	—
70	C₂×C₄⋊C₄	—	59	4	no	—
71	C₂×C₄⋊C₄	—	59	4	no	—
72	C₂×C₄⋊C₄	C₂×D₅₉	1	2	yes	—
73	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
74	#95	—	59	4	no	—
75	#95	—	59	4	no	—
76	#95	—	59	4	no	—
77	#95	C₂×D₅₉	1	4	yes	—
78	C₂²×C₄	—	59	4	no	—
79	C₂²×C₄	—	59	4	no	—
80	C₂²×C₄	C₂²×D₅₉	1	4	yes	—
81	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
82	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
83	C₄⋊C₄	—	4	2	no	—
84	C₄⋊C₄	—	236	4	no	—
85	C₄⋊C₄	—	236	4	no	—
86	C₄⋊C₄	—	236	2	no	—
87	C₄⋊C₄	—	236	2	no	—
88	C₄⋊C₄	—	236	4	no	—
89	C₄²	Dic₁₁₈	1	4	yes	—
90	C₂³	C₂³×D₅₉	1	1	yes	characteristic
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	2	4	no	—
98	C₂×C₄	—	118	4	no	—
99	C₂×C₄	—	118	4	no	—
100	C₂×C₄	—	118	4	no	—
101	C₂×C₄	—	118	4	no	—
102	C₂×C₄	—	118	4	no	—
103	C₂×C₄	—	118	4	no	—
104	C₂×C₄	C₂×Dic₁₁₈	1	4	yes	—
105	C₂×C₄	C₂×Dic₁₁₈	1	2	yes	—
106	C₂²	C₂²×Dic₁₁₈	1	1	yes	characteristic
107	C₂²	#14273772	1	1	yes	characteristic
108	C₂²	#14273773	1	2	yes	—
109	C₂²	#14273774	1	2	yes	—
110	C₂²	#14273775	1	1	yes	characteristic
111	C₄	—	2	4	no	—
112	C₄	—	2	2	no	—
113	C₄	—	4	4	no	—
114	C₄	—	236	4	no	—
115	C₄	—	236	4	no	—
116	C₂	#16838030	1	2	yes	—
117	C₂	#16838033	1	1	yes	characteristic
118	C₂	#16838146	1	2	yes	—
119	C₂	#16838150	1	1	yes	characteristic
120	C₂	C₅₉⋊#564	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837336

C₂

yes

maximal

#16837335

C₂

yes

maximal

#16837334

C₂

yes

maximal

#16837268

C₂

yes

maximal

C₅₉×#382

C₂

yes

maximal, characteristic

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

—

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

Q₈

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×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×Q₈

yes

—

C₂×C₄×C₅₉

C₂×Q₈

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂²×C₅₉

C₂²×Q₈

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

—

C₂²×C₅₉

2₋¹⁺⁴

yes

—

C₂²×C₅₉

2₋¹⁺⁴

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

Dic₅₉

—

Dic₅₉

—

#2845

—

maximal, Sylow

C₂×C₅₉

#544

yes

—

C₂×C₅₉

#544

yes

characteristic

C₂×C₅₉

#562

yes

—

C₂×C₅₉

yes

C₂×C₅₉

yes

—

—

—

—

D₅₉

yes

characteristic

C₅₉

#2845

yes

characteristic, complemented, Sylow

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

characteristic

C₂²×C₄

C₂²×D₅₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

236

—

C₄⋊C₄

—

236

—

C₄⋊C₄

—

236

—

C₄⋊C₄

—

236

—

C₄⋊C₄

—

236

—

C₄²

Dic₁₁₈

yes

—

C₂³

C₂³×D₅₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

100

C₂×C₄

—

118

—

101

C₂×C₄

—

118

—

102

C₂×C₄

—

118

—

103

C₂×C₄

—

118

—

104

C₂×C₄

C₂×Dic₁₁₈

yes

—

105

C₂×C₄

C₂×Dic₁₁₈

yes

—

106

C₂²

C₂²×Dic₁₁₈

yes

characteristic

107

C₂²

#14273772

yes

characteristic

108

C₂²

#14273773

yes

—

109

C₂²

#14273774

yes

—

110

C₂²

#14273775

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

236

—

115

C₄

—

236

—

116

C₂

#16838030

yes

—

117

C₂

#16838033

yes

characteristic

118

C₂

#16838146

yes

—

119

C₂

#16838150

yes

characteristic

120

C₂

C₅₉⋊#564

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂⁴
Fitting	C₅₉×#382	C₂
hypercenter	#382	D₅₉
hypocenter	C₅₉	#2845
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
66. C₅₉	#2845	semidirect

H ≅ G/N

type

66. C₅₉

#2845

semidirect

Subgroups — #21432371

Conjugacy classes of subgroups

Complements