Group #21430041 — subgroups

Subgroups — #21430041

Order 7552.

584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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	1	yes	maximal, characteristic, complemented
2	#16837316	C₂	1	8	yes	maximal, complemented
3	#16837305	C₂	1	4	yes	maximal, complemented
4	#16837248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#127×C₅₉	C₂	1	1	yes	maximal, characteristic
6	#14273719	—	2	4	no	—
7	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
8	C₂×Dic₅₉⋊C₄	C₂²	1	4	yes	—
9	C₂×C₂²⋊Dic₅₉	C₂²	1	16	yes	—
10	C₂×C₄×Dic₅₉	C₂²	1	2	yes	—
11	C₅₉⋊#95	C₂²	1	4	yes	—
12	C₂²×D₄×C₅₉	C₂²	1	2	yes	—
13	C₂²×D₄×C₅₉	C₂²	1	4	yes	—
14	#127×C₅₉	—	2	4	no	—
15	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
16	C₂⁴×C₅₉	C₂³	1	4	yes	—
17	C₂×D₄×C₅₉	—	2	8	no	—
18	C₂×D₄×C₅₉	—	2	4	no	—
19	C₂×D₄×C₅₉	—	2	8	no	—
20	C₂×D₄×C₅₉	—	4	8	no	—
21	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
22	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₅₉	C₂³	1	4	yes	—
24	C₂²×Dic₅₉	C₂³	1	4	yes	—
25	C₄²×C₅₉	D₄	1	4	yes	—
26	C₂²⋊Dic₅₉	—	4	16	no	—
27	C₄⋊Dic₅₉	—	2	4	no	—
28	Dic₅₉⋊C₄	—	2	8	no	—
29	C₄×Dic₅₉	—	2	4	no	—
30	C₂³×C₅₉	—	2	4	no	—
31	C₂³×C₅₉	—	2	8	no	—
32	C₂³×C₅₉	—	2	16	no	—
33	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
34	D₄×C₅₉	—	4	16	no	—
35	D₄×C₅₉	—	4	8	no	—
36	C₂×C₄×C₅₉	—	2	4	no	—
37	C₂×C₄×C₅₉	C₂×D₄	1	4	yes	—
38	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
39	C₂×C₄×C₅₉	#41	1	4	yes	—
40	C₂×Dic₅₉	—	2	4	no	—
41	C₂×Dic₅₉	—	2	4	no	—
42	C₂×Dic₅₉	—	2	8	no	—
43	C₂×Dic₅₉	—	2	8	no	—
44	C₂²×C₅₉	—	4	4	no	—
45	C₂²×C₅₉	—	4	8	no	—
46	C₂²×C₅₉	—	4	16	no	—
47	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
48	C₂²×C₅₉	C₂×#41	1	2	yes	—
49	C₂²×C₅₉	H(5,𝔽₂)	1	4	yes	—
50	C₄×C₅₉	—	2	4	no	—
51	C₄×C₅₉	#124	1	4	yes	—
52	Dic₅₉	—	4	4	no	—
53	Dic₅₉	—	4	4	no	—
54	#2641	—	59	1	no	maximal, Sylow
55	C₂×C₅₉	—	8	4	no	—
56	C₂×C₅₉	C₂×#124	1	1	yes	characteristic
57	C₂×C₅₉	#535	1	2	yes	—
58	C₂×C₅₉	#540	1	4	yes	—
59	C₂×#127	D₅₉	1	1	yes	characteristic
60	C₂×#125	—	59	1	no	—
61	#394	—	59	8	no	—
62	#390	—	59	4	no	—
63	#376	—	59	1	no	—
64	C₅₉	#2641	1	1	yes	characteristic, complemented, Sylow
65	C₂²×D₄	C₂×D₅₉	1	2	yes	—
66	C₂²×D₄	C₂×D₅₉	1	4	yes	—
67	#127	—	2	4	no	—
68	#125	—	118	4	no	—
69	C₂×C₄⋊C₄	—	59	2	no	—
70	C₂×C₄⋊C₄	—	59	4	no	—
71	C₂×C₂²⋊C₄	—	59	16	no	—
72	C₂×C₄²	—	59	2	no	—
73	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
74	#95	—	59	4	no	—
75	C₂⁴	C₂²×D₅₉	1	4	yes	—
76	C₂×D₄	—	2	8	no	—
77	C₂×D₄	—	2	8	no	—
78	C₂×D₄	—	2	4	no	—
79	C₂×D₄	—	4	8	no	—
80	C₂²×C₄	—	59	4	no	—
81	C₂²×C₄	—	59	4	no	—
82	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
83	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
84	C₄⋊C₄	—	118	8	no	—
85	C₄⋊C₄	—	118	4	no	—
86	C₂²⋊C₄	—	236	16	no	—
87	C₄²	—	118	4	no	—
88	C₄²	C₂²⋊D₅₉	1	4	yes	—
89	C₂³	—	2	4	no	—
90	C₂³	—	2	8	no	—
91	C₂³	—	2	16	no	—
92	C₂³	C₂³×D₅₉	1	1	yes	characteristic
93	D₄	—	4	16	no	—
94	D₄	—	4	8	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	118	4	no	—
97	C₂×C₄	—	118	4	no	—
98	C₂×C₄	—	118	8	no	—
99	C₂×C₄	—	118	8	no	—
100	C₂×C₄	#11745687	1	4	yes	—
101	C₂×C₄	C₂×C₂²⋊D₅₉	1	4	yes	—
102	C₂×C₄	C₂×C₂²⋊D₅₉	1	2	yes	—
103	C₂²	—	4	4	no	—
104	C₂²	—	4	8	no	—
105	C₂²	—	4	16	no	—
106	C₂²	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
107	C₂²	C₂×#11745687	1	2	yes	—
108	C₂²	#14273772	1	4	yes	—
109	C₄	—	2	4	no	—
110	C₄	—	236	4	no	—
111	C₄	—	236	4	no	—
112	C₄	#14273714	1	4	yes	—
113	C₂	—	8	4	no	—
114	C₂	C₂×#14273714	1	1	yes	characteristic
115	C₂	#16837969	1	2	yes	—
116	C₂	#16838006	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273719

C₂

yes

maximal, characteristic, complemented

#16837316

C₂

yes

maximal, complemented

#16837305

C₂

yes

maximal, complemented

#16837248

C₂

yes

maximal, characteristic, complemented

C₂×#127×C₅₉

C₂

yes

maximal, characteristic

#14273719

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×Dic₅₉⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₅₉

C₂²

yes

—

C₂×C₄×Dic₅₉

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₂²×D₄×C₅₉

C₂²

yes

—

C₂²×D₄×C₅₉

C₂²

yes

—

#127×C₅₉

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂⁴×C₅₉

C₂³

yes

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

C₂³

yes

—

C₂²×Dic₅₉

C₂³

yes

—

C₄²×C₅₉

D₄

yes

—

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

C₂⁴

yes

characteristic

D₄×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

#41

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂²×D₄

yes

characteristic

C₂²×C₅₉

C₂×#41

yes

—

C₂²×C₅₉

H(5,𝔽₂)

yes

—

C₄×C₅₉

—

C₄×C₅₉

#124

yes

—

Dic₅₉

—

Dic₅₉

—

#2641

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

C₂×#124

yes

characteristic

C₂×C₅₉

#535

yes

—

C₂×C₅₉

#540

yes

—

C₂×#127

D₅₉

yes

—

—

—

—

C₅₉

#2641

yes

characteristic, complemented, Sylow

C₂²×D₄

C₂×D₅₉

yes

—

C₂²×D₄

C₂×D₅₉

yes

—

#127

—

#125

—

118

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

#95

—

C₂⁴

C₂²×D₅₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

118

—

C₄⋊C₄

—

118

—

C₂²⋊C₄

—

236

—

C₄²

—

118

—

C₄²

C₂²⋊D₅₉

yes

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₅₉

yes

characteristic

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

100

C₂×C₄

#11745687

yes

—

101

C₂×C₄

C₂×C₂²⋊D₅₉

yes

—

102

C₂×C₄

C₂×C₂²⋊D₅₉

yes

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₂²×C₂²⋊D₅₉

yes

characteristic

107

C₂²

C₂×#11745687

yes

—

108

C₂²

#14273772

yes

—

109

C₄

—

110

C₄

—

236

—

111

C₄

—

236

—

112

C₄

#14273714

yes

—

113

C₂

—

114

C₂

C₂×#14273714

yes

characteristic

115

C₂

#16837969

yes

—

116

C₂

#16838006

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂⁴
Fitting	C₂×#127×C₅₉	C₂
hypercenter	C₂×#127	D₅₉
hypocenter	C₅₉	#2641
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×#127

subgroup

G/H

center, Frattini

C₂³

C₂³×D₅₉

commutator, socle

C₂³×C₅₉

C₂⁴

Fitting

C₂×#127×C₅₉

C₂

D₅₉

C₅₉

G ▷ C₂³×C₅₉ ▷ C₅₉

C₁ ◁ C₂³ ◁ C₂×#127

N	H ≅ G/N	type
1. C₂×#14273719	C₂	semidirect
2. #16837316	C₂	semidirect
3. #16837305	C₂	semidirect
4. #16837248	C₂	semidirect
64. C₅₉	#2641	semidirect

H ≅ G/N

type

1. C₂×#14273719

C₂

semidirect

2. #16837316

C₂

semidirect

3. #16837305

C₂

semidirect

4. #16837248

C₂

semidirect

64. C₅₉

#2641

semidirect

Subgroups — #21430041

Conjugacy classes of subgroups

Complements