Group #21432287 — subgroups

Subgroups — #21432287

Order 7552.

380 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 117 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	#16837344	C₂	1	6	yes	maximal, complemented
2	#16837327	C₂	1	3	yes	maximal
3	#16837321	C₂	1	2	yes	maximal, complemented
4	#16837274	C₂	1	3	yes	maximal
5	C₅₉×#393	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₅₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₅₉	C₂²	1	3	yes	—
8	C₂×Dic₅₉⋊C₄	C₂²	1	6	yes	—
9	C₂×C₂²⋊Dic₅₉	C₂²	1	3	yes	—
10	C₅₉⋊#95	C₂²	1	6	yes	—
11	C₅₉⋊#95	C₂²	1	6	yes	—
12	C₅₉⋊#95	C₂²	1	3	yes	—
13	C₂²×Q₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊C₄×C₅₉	C₂²	1	3	yes	—
15	#95×C₅₉	C₂²	1	3	yes	—
16	C₂⁴×C₅₉	C₂³	1	1	yes	characteristic
17	C₂×Q₈×C₅₉	—	4	3	no	—
18	C₂²×C₄×C₅₉	C₂³	1	3	yes	—
19	C₂²×C₄×C₅₉	C₂³	1	3	yes	—
20	C₂²×Dic₅₉	—	4	3	no	—
21	C₂²×Dic₅₉	C₂³	1	6	yes	—
22	C₂²×Dic₅₉	C₂³	1	2	yes	—
23	C₂²⋊C₄×C₅₉	—	4	3	no	—
24	C₂²⋊Dic₅₉	—	2	6	no	—
25	C₄⋊Dic₅₉	—	4	3	no	—
26	Dic₅₉⋊C₄	—	4	6	no	—
27	C₂³×C₅₉	—	2	3	no	—
28	C₂³×C₅₉	—	2	3	no	—
29	C₂³×C₅₉	#41	1	2	yes	—
30	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
31	Q₈×C₅₉	—	4	4	no	—
32	C₂×C₄×C₅₉	—	2	6	no	—
33	C₂×C₄×C₅₉	—	2	3	no	—
34	C₂×C₄×C₅₉	—	2	3	no	—
35	C₂×C₄×C₅₉	—	2	6	no	—
36	C₂×Dic₅₉	—	2	6	no	—
37	C₂×Dic₅₉	—	2	6	no	—
38	C₂×Dic₅₉	—	2	6	no	—
39	C₂×Dic₅₉	—	2	6	no	—
40	C₂×Dic₅₉	—	4	4	no	—
41	C₂²×C₅₉	—	2	6	no	—
42	C₂²×C₅₉	—	4	1	no	—
43	C₂²×C₅₉	—	4	3	no	—
44	C₂²×C₅₉	C₂×#41	1	1	yes	characteristic
45	C₂²×C₅₉	H(5,𝔽₂)	1	3	yes	—
46	C₂²×C₅₉	2₋¹⁺⁴	1	3	yes	—
47	C₄×C₅₉	—	4	3	no	—
48	C₄×C₅₉	—	4	3	no	—
49	Dic₅₉	—	4	6	no	—
50	Dic₅₉	—	4	2	no	—
51	#2835	—	59	1	no	maximal, Sylow
52	C₂×C₅₉	—	4	2	no	—
53	C₂×C₅₉	#539	1	3	yes	—
54	C₂×C₅₉	H(3,𝔽₄)	1	1	yes	characteristic
55	C₂×C₅₉	#563	1	3	yes	—
56	#400	—	59	6	no	—
57	#397	—	59	3	no	—
58	#395	—	59	2	no	—
59	#393	D₅₉	1	1	yes	characteristic
60	#385	—	59	3	no	—
61	C₅₉	#2835	1	1	yes	characteristic, complemented, Sylow
62	C₂²×Q₈	C₂×D₅₉	1	1	yes	characteristic
63	C₂³×C₄	—	59	1	no	—
64	C₂×C₄⋊C₄	—	59	6	no	—
65	C₂×C₄⋊C₄	—	59	3	no	—
66	C₂×C₂²⋊C₄	—	59	3	no	—
67	C₂×C₂²⋊C₄	C₂×D₅₉	1	3	yes	—
68	#95	—	59	6	no	—
69	#95	—	59	6	no	—
70	#95	—	59	3	no	—
71	#95	C₂×D₅₉	1	3	yes	—
72	C₂⁴	C₂²×D₅₉	1	1	yes	characteristic
73	C₂×Q₈	—	4	3	no	—
74	C₂²×C₄	—	59	6	no	—
75	C₂²×C₄	—	59	2	no	—
76	C₂²×C₄	—	236	3	no	—
77	C₂²×C₄	C₂²×D₅₉	1	3	yes	—
78	C₂²×C₄	C₂²×D₅₉	1	3	yes	—
79	C₄⋊C₄	—	236	6	no	—
80	C₄⋊C₄	—	236	3	no	—
81	C₂²⋊C₄	—	4	3	no	—
82	C₂²⋊C₄	—	118	6	no	—
83	C₂³	—	2	3	no	—
84	C₂³	—	2	3	no	—
85	C₂³	#11745689	1	2	yes	—
86	C₂³	C₂³×D₅₉	1	1	yes	characteristic
87	Q₈	—	4	4	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	3	no	—
90	C₂×C₄	—	2	6	no	—
91	C₂×C₄	—	2	6	no	—
92	C₂×C₄	—	118	6	no	—
93	C₂×C₄	—	118	6	no	—
94	C₂×C₄	—	118	6	no	—
95	C₂×C₄	—	118	6	no	—
96	C₂×C₄	—	236	4	no	—
97	C₂²	—	2	6	no	—
98	C₂²	—	4	1	no	—
99	C₂²	—	4	3	no	—
100	C₂²	C₂×#11745689	1	1	yes	characteristic
101	C₂²	#14273772	1	3	yes	—
102	C₂²	#14273774	1	3	yes	—
103	C₄	—	4	3	no	—
104	C₄	—	4	3	no	—
105	C₄	—	236	2	no	—
106	C₄	—	236	6	no	—
107	C₂	—	4	2	no	—
108	C₂	#16838001	1	3	yes	—
109	C₂	#16838145	1	1	yes	characteristic
110	C₂	#16838152	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16837344

C₂

yes

maximal, complemented

#16837327

C₂

yes

maximal

#16837321

C₂

yes

maximal, complemented

#16837274

C₂

yes

maximal

C₅₉×#393

C₂

yes

maximal, characteristic

C₂³×Dic₅₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×Dic₅₉⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₅₉

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₂²×Q₈×C₅₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₅₉

C₂²

yes

—

#95×C₅₉

C₂²

yes

—

C₂⁴×C₅₉

C₂³

yes

characteristic

C₂×Q₈×C₅₉

—

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×Dic₅₉

—

C₂²×Dic₅₉

C₂³

yes

—

C₂²×Dic₅₉

C₂³

yes

—

C₂²⋊C₄×C₅₉

—

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

#41

yes

—

C₂³×C₅₉

C₂⁴

yes

characteristic

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂×#41

yes

characteristic

C₂²×C₅₉

H(5,𝔽₂)

yes

—

C₂²×C₅₉

2₋¹⁺⁴

yes

—

C₄×C₅₉

—

C₄×C₅₉

—

Dic₅₉

—

Dic₅₉

—

#2835

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

#539

yes

—

C₂×C₅₉

H(3,𝔽₄)

yes

characteristic

C₂×C₅₉

#563

yes

—

—

—

—

D₅₉

yes

characteristic

#385

—

C₅₉

#2835

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₅₉

yes

characteristic

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₅₉

yes

—

—

—

—

C₂×D₅₉

yes

—

C₂⁴

C₂²×D₅₉

yes

characteristic

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

236

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₄⋊C₄

—

236

—

C₄⋊C₄

—

236

—

C₂²⋊C₄

—

C₂²⋊C₄

—

118

—

C₂³

—

C₂³

—

C₂³

#11745689

yes

—

C₂³

C₂³×D₅₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

236

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

C₂×#11745689

yes

characteristic

101

C₂²

#14273772

yes

—

102

C₂²

#14273774

yes

—

103

C₄

—

104

C₄

—

105

C₄

—

236

—

106

C₄

—

236

—

107

C₂

—

108

C₂

#16838001

yes

—

109

C₂

#16838145

yes

characteristic

110

C₂

#16838152

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂⁴
Fitting	C₅₉×#393	C₂
hypercenter	#393	D₅₉
hypocenter	C₅₉	#2835
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ #393

subgroup

G/H

center, Frattini

C₂³

C₂³×D₅₉

commutator, socle

C₂³×C₅₉

C₂⁴

Fitting

C₅₉×#393

C₂

D₅₉

C₅₉

G ▷ C₂³×C₅₉ ▷ C₅₉

C₁ ◁ C₂³ ◁ #393

N	H ≅ G/N	type
1. #16837344	C₂	semidirect
3. #16837321	C₂	semidirect
61. C₅₉	#2835	semidirect

H ≅ G/N

type

1. #16837344

C₂

semidirect

3. #16837321

C₂

semidirect

61. C₅₉

#2835

semidirect

Subgroups — #21432287

Conjugacy classes of subgroups

Complements