Group #21429338 — subgroups

Subgroups — #21429338

Order 7552.

380 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 165 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	#16837341	C₂	1	4	yes	maximal
2	#16837301	C₂	1	4	yes	maximal
3	#16837267	C₂	1	4	yes	maximal
4	C₄×C₄⋊Dic₅₉	C₂	1	2	yes	maximal
5	C₅₉×#384	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×C₄×Dic₅₉	C₂²	1	4	yes	—
10	C₅₉⋊#95	C₂²	1	4	yes	—
11	C₅₉⋊#95	C₂²	1	4	yes	—
12	C₅₉⋊#95	C₂²	1	8	yes	—
13	C₂×C₄⋊C₄×C₅₉	C₂²	1	4	yes	—
14	C₂×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
15	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₅₉	C₂³	1	4	yes	—
17	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
19	C₂²×Dic₅₉	C₂³	1	4	yes	—
20	C₂²×Dic₅₉	C₂³	1	4	yes	—
21	C₄⋊C₄×C₅₉	—	2	8	no	—
22	C₄⋊C₄×C₅₉	—	4	2	no	—
23	C₄²×C₅₉	Q₈	1	4	yes	—
24	C₄⋊Dic₅₉	—	2	4	no	—
25	C₄⋊Dic₅₉	—	2	4	no	—
26	C₄⋊Dic₅₉	—	4	4	no	—
27	C₄×Dic₅₉	—	2	8	no	—
28	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
29	C₂×C₄×C₅₉	—	2	1	no	—
30	C₂×C₄×C₅₉	—	2	1	no	—
31	C₂×C₄×C₅₉	—	2	8	no	—
32	C₂×C₄×C₅₉	—	2	4	no	—
33	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
34	C₂×C₄×C₅₉	C₂×Q₈	1	4	yes	—
35	C₂×C₄×C₅₉	#41	1	4	yes	—
36	C₂×C₄×C₅₉	#41	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	4	no	—
41	C₂×Dic₅₉	—	2	4	no	—
42	C₂×Dic₅₉	—	2	4	no	—
43	C₂²×C₅₉	C₂²×Q₈	1	1	yes	characteristic
44	C₂²×C₅₉	C₂×#41	1	2	yes	—
45	C₂²×C₅₉	C₂×#41	1	2	yes	—
46	C₂²×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
47	C₂²×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
48	C₄×C₅₉	—	2	2	no	—
49	C₄×C₅₉	—	4	4	no	—
50	C₄×C₅₉	#125	1	8	yes	—
51	Dic₅₉	—	4	4	no	—
52	Dic₅₉	—	4	4	no	—
53	#2571	—	59	1	no	maximal, Sylow
54	C₂×C₅₉	C₂×#125	1	2	yes	—
55	C₂×C₅₉	#544	1	1	yes	characteristic
56	C₂×C₅₉	#555	1	1	yes	characteristic
57	C₂×C₅₉	#556	1	2	yes	—
58	C₂×C₅₉	#559	1	1	yes	characteristic
59	#400	—	59	4	no	—
60	#389	—	59	4	no	—
61	#384	D₅₉	1	1	yes	characteristic
62	#382	—	59	4	no	—
63	C₄×C₄⋊C₄	—	59	2	no	—
64	C₅₉	#2571	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₄⋊C₄	—	59	2	no	—
66	C₂×C₄⋊C₄	—	59	2	no	—
67	C₂×C₄⋊C₄	—	59	4	no	—
68	C₂×C₄⋊C₄	C₂×D₅₉	1	4	yes	—
69	C₂×C₄⋊C₄	C₂×D₅₉	1	2	yes	—
70	C₂×C₄²	—	59	4	no	—
71	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
72	#95	—	59	4	no	—
73	#95	—	59	4	no	—
74	#95	—	59	8	no	—
75	C₂²×C₄	—	59	4	no	—
76	C₂²×C₄	—	59	4	no	—
77	C₂²×C₄	C₂²×D₅₉	1	4	yes	—
78	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
79	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
80	C₄⋊C₄	—	2	8	no	—
81	C₄⋊C₄	—	4	2	no	—
82	C₄⋊C₄	—	118	4	no	—
83	C₄⋊C₄	—	118	4	no	—
84	C₄⋊C₄	—	236	4	no	—
85	C₄²	—	118	8	no	—
86	C₄²	Dic₁₁₈	1	4	yes	—
87	C₂³	C₂³×D₅₉	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	8	no	—
91	C₂×C₄	—	2	4	no	—
92	C₂×C₄	—	118	4	no	—
93	C₂×C₄	—	118	4	no	—
94	C₂×C₄	—	118	4	no	—
95	C₂×C₄	—	118	4	no	—
96	C₂×C₄	—	118	4	no	—
97	C₂×C₄	—	118	4	no	—
98	C₂×C₄	C₂×Dic₁₁₈	1	2	yes	—
99	C₂×C₄	C₂×Dic₁₁₈	1	4	yes	—
100	C₂×C₄	#11745687	1	4	yes	—
101	C₂×C₄	#11745689	1	4	yes	—
102	C₂²	C₂²×Dic₁₁₈	1	1	yes	characteristic
103	C₂²	C₂×#11745687	1	2	yes	—
104	C₂²	C₂×#11745689	1	2	yes	—
105	C₂²	#14273772	1	1	yes	characteristic
106	C₂²	#14273775	1	1	yes	characteristic
107	C₄	—	2	2	no	—
108	C₄	—	4	4	no	—
109	C₄	—	236	4	no	—
110	C₄	—	236	4	no	—
111	C₄	#14273718	1	8	yes	—
112	C₂	C₂×#14273718	1	2	yes	—
113	C₂	#16838033	1	1	yes	characteristic
114	C₂	#16838118	1	1	yes	characteristic
115	C₂	#16838126	1	2	yes	—
116	C₂	#16838138	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837341

C₂

yes

maximal

#16837301

C₂

yes

maximal

#16837267

C₂

yes

maximal

C₄×C₄⋊Dic₅₉

C₂

yes

maximal

C₅₉×#384

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×C₄×Dic₅₉

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₅₉

C₂²

yes

—

C₂×C₄⋊C₄×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×Dic₅₉

C₂³

yes

—

C₂²×Dic₅₉

C₂³

yes

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

Q₈

yes

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄×Dic₅₉

—

C₂³×C₅₉

C₂⁴

yes

characteristic

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×C₄×C₅₉

#41

yes

—

C₂×C₄×C₅₉

#41

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂²×C₅₉

C₂²×Q₈

yes

characteristic

C₂²×C₅₉

C₂×#41

yes

—

C₂²×C₅₉

C₂×#41

yes

—

C₂²×C₅₉

H(5,𝔽₂)

yes

characteristic

C₂²×C₅₉

2₋¹⁺⁴

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#125

yes

—

Dic₅₉

—

Dic₅₉

—

#2571

—

maximal, Sylow

C₂×C₅₉

C₂×#125

yes

—

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×C₅₉

yes

—

—

D₅₉

yes

characteristic

#382

—

C₄×C₄⋊C₄

—

C₅₉

#2571

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₅₉

yes

—

C₂×C₄⋊C₄

C₂×D₅₉

yes

—

C₂×C₄²

—

C₂×C₄²

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

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

236

—

C₄²

—

118

—

C₄²

Dic₁₁₈

yes

—

C₂³

C₂³×D₅₉

yes

characteristic

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

—

118

—

C₂×C₄

C₂×Dic₁₁₈

yes

—

C₂×C₄

C₂×Dic₁₁₈

yes

—

100

C₂×C₄

#11745687

yes

—

101

C₂×C₄

#11745689

yes

—

102

C₂²

C₂²×Dic₁₁₈

yes

characteristic

103

C₂²

C₂×#11745687

yes

—

104

C₂²

C₂×#11745689

yes

—

105

C₂²

#14273772

yes

characteristic

106

C₂²

#14273775

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

236

—

110

C₄

—

236

—

111

C₄

#14273718

yes

—

112

C₂

C₂×#14273718

yes

—

113

C₂

#16838033

yes

characteristic

114

C₂

#16838118

yes

characteristic

115

C₂

#16838126

yes

—

116

C₂

#16838138

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂⁴
Fitting	C₅₉×#384	C₂
hypercenter	#384	D₅₉
hypocenter	C₅₉	#2571
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₅₉

commutator, socle

C₂³×C₅₉

C₂⁴

Fitting

C₅₉×#384

C₂

D₅₉

C₅₉

G ▷ C₂³×C₅₉ ▷ C₅₉

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
64. C₅₉	#2571	semidirect

H ≅ G/N

type

64. C₅₉

#2571

semidirect

Subgroups — #21429338

Conjugacy classes of subgroups

Complements