Group #21430056 — subgroups

Subgroups — #21430056

Order 7552.

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

normal subgroups only

This group has 420 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	#16837331	C₂	1	6	yes	maximal, complemented
2	#16837326	C₂	1	2	yes	maximal, complemented
3	#16837304	C₂	1	3	yes	maximal
4	#16837300	C₂	1	3	yes	maximal, complemented
5	C₅₉×#376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₂₃₆	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₅₉	C₂²	1	3	yes	—
8	C₂×Dic₅₉⋊C₄	C₂²	1	6	yes	—
9	C₂×(C₂×D₅₉)⋊C₄	C₂²	1	6	yes	—
10	C₂×(C₂×D₅₉)⋊C₄	C₂²	1	6	yes	—
11	C₅₉⋊#95	C₂²	1	6	yes	—
12	C₂×C₄²×C₅₉	C₂²	1	3	yes	—
13	#95×C₅₉	C₂²	1	1	yes	characteristic
14	#95×C₅₉	C₂²	1	3	yes	—
15	C₂³×D₅₉	C₂³	1	2	yes	—
16	C₂²×C₄×C₅₉	C₂³	1	3	yes	—
17	C₂²×C₄×C₅₉	C₂³	1	3	yes	—
18	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₅₉	C₂³	1	6	yes	—
20	C₂×D₂₃₆	—	2	6	no	—
21	C₄²×C₅₉	—	2	6	no	—
22	(C₂×D₅₉)⋊C₄	—	4	6	no	—
23	(C₂×D₅₉)⋊C₄	—	4	6	no	—
24	C₄⋊Dic₅₉	—	2	6	no	—
25	Dic₅₉⋊C₄	—	4	6	no	—
26	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
27	C₂²×D₅₉	—	2	6	no	—
28	C₂²×D₅₉	—	2	6	no	—
29	C₂²×D₅₉	—	2	2	no	—
30	C₂×C₄×C₅₉	—	2	3	no	—
31	C₂×C₄×C₅₉	—	2	3	no	—
32	C₂×C₄×C₅₉	—	2	3	no	—
33	C₂×C₄×C₅₉	—	2	3	no	—
34	C₂×C₄×C₅₉	—	2	3	no	—
35	C₂×C₄×C₅₉	—	2	3	no	—
36	C₂×C₄×C₅₉	#41	1	6	yes	—
37	C₂×Dic₅₉	—	2	6	no	—
38	C₂×Dic₅₉	—	2	6	no	—
39	C₂×Dic₅₉	—	2	6	no	—
40	D₂₃₆	—	4	4	no	—
41	C₂²×C₅₉	C₂×#41	1	3	yes	—
42	C₂²×C₅₉	H(5,𝔽₂)	1	3	yes	—
43	C₂²×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
44	C₂×D₅₉	—	4	2	no	—
45	C₂×D₅₉	—	4	6	no	—
46	C₂×D₅₉	—	4	6	no	—
47	C₄×C₅₉	—	4	3	no	—
48	C₄×C₅₉	—	4	3	no	—
49	C₄×C₅₉	#126	1	4	yes	—
50	Dic₅₉	—	4	6	no	—
51	#2644	—	59	1	no	maximal, Sylow
52	C₂×C₅₉	C₂×#126	1	1	yes	characteristic
53	C₂×C₅₉	#540	1	3	yes	—
54	C₂×C₅₉	#542	1	3	yes	—
55	D₅₉	—	8	2	no	—
56	#397	—	59	6	no	—
57	#396	—	59	2	no	—
58	#390	—	59	3	no	—
59	#389	—	59	3	no	—
60	#376	D₅₉	1	1	yes	characteristic, complemented
61	C₅₉	#2644	1	1	yes	characteristic, complemented, Sylow
62	C₂²×D₄	—	59	1	no	—
63	C₂×C₄⋊C₄	—	59	3	no	—
64	C₂×C₄⋊C₄	—	59	6	no	—
65	C₂×C₂²⋊C₄	—	59	6	no	—
66	C₂×C₂²⋊C₄	—	59	6	no	—
67	C₂×C₄²	C₂×D₅₉	1	3	yes	—
68	#95	—	59	6	no	—
69	#95	C₂×D₅₉	1	1	yes	characteristic
70	#95	C₂×D₅₉	1	3	yes	—
71	C₂⁴	—	59	2	no	—
72	C₂×D₄	—	118	6	no	—
73	C₂²×C₄	—	59	6	no	—
74	C₂²×C₄	C₂²×D₅₉	1	3	yes	—
75	C₂²×C₄	C₂²×D₅₉	1	3	yes	—
76	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
77	C₄⋊C₄	—	118	6	no	—
78	C₄⋊C₄	—	236	6	no	—
79	C₂²⋊C₄	—	236	6	no	—
80	C₂²⋊C₄	—	236	6	no	—
81	C₄²	—	2	6	no	—
82	C₂³	—	118	6	no	—
83	C₂³	—	118	6	no	—
84	C₂³	—	118	2	no	—
85	C₂³	C₂³×D₅₉	1	1	yes	characteristic
86	D₄	—	236	4	no	—
87	C₂×C₄	—	2	3	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	3	no	—
90	C₂×C₄	—	2	3	no	—
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	2	3	no	—
93	C₂×C₄	—	118	6	no	—
94	C₂×C₄	—	118	6	no	—
95	C₂×C₄	—	118	6	no	—
96	C₂×C₄	#11745685	1	6	yes	—
97	C₂²	—	236	2	no	—
98	C₂²	—	236	6	no	—
99	C₂²	—	236	6	no	—
100	C₂²	C₂×#11745685	1	3	yes	—
101	C₂²	#14273773	1	3	yes	—
102	C₂²	#14273774	1	1	yes	characteristic
103	C₄	—	4	3	no	—
104	C₄	—	4	3	no	—
105	C₄	—	236	6	no	—
106	C₄	#14273721	1	4	yes	—
107	C₂	—	472	2	no	—
108	C₂	C₂×#14273721	1	1	yes	characteristic
109	C₂	#16838007	1	3	yes	—
110	C₂	#16838023	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16837331

C₂

yes

maximal, complemented

#16837326

C₂

yes

maximal, complemented

#16837304

C₂

yes

maximal

#16837300

C₂

yes

maximal, complemented

C₅₉×#376

C₂

yes

maximal, characteristic, complemented

C₂²×D₂₃₆

C₂²

yes

characteristic

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×Dic₅₉⋊C₄

C₂²

yes

—

C₂×(C₂×D₅₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₅₉)⋊C₄

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

—

#95×C₅₉

C₂²

yes

characteristic

#95×C₅₉

C₂²

yes

—

C₂³×D₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

C₂³

yes

—

C₂×D₂₃₆

—

C₄²×C₅₉

—

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

C₂³×C₅₉

C₂⁴

yes

characteristic

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#41

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

D₂₃₆

—

C₂²×C₅₉

C₂×#41

yes

—

C₂²×C₅₉

H(5,𝔽₂)

yes

—

C₂²×C₅₉

2₋¹⁺⁴

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#126

yes

—

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×C₅₉

#542

yes

—

D₅₉

—

—

—

—

—

D₅₉

yes

characteristic, complemented

C₅₉

#2644

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₅₉

yes

—

#95

—

#95

C₂×D₅₉

yes

characteristic

#95

C₂×D₅₉

yes

—

C₂⁴

—

C₂×D₄

—

118

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

118

—

C₄⋊C₄

—

236

—

C₂²⋊C₄

—

236

—

C₂²⋊C₄

—

236

—

C₄²

—

C₂³

—

118

—

C₂³

—

118

—

C₂³

—

118

—

C₂³

C₂³×D₅₉

yes

characteristic

D₄

—

236

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

#11745685

yes

—

C₂²

—

236

—

C₂²

—

236

—

C₂²

—

236

—

100

C₂²

C₂×#11745685

yes

—

101

C₂²

#14273773

yes

—

102

C₂²

#14273774

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

236

—

106

C₄

#14273721

yes

—

107

C₂

—

472

—

108

C₂

C₂×#14273721

yes

characteristic

109

C₂

#16838007

yes

—

110

C₂

#16838023

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂⁴
Fitting	C₅₉×#376	C₂
hypercenter	#376	D₅₉
hypocenter	C₅₉	#2644
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₅₉

commutator, socle

C₂³×C₅₉

C₂⁴

Fitting

C₅₉×#376

C₂

D₅₉

C₅₉

G ▷ C₂³×C₅₉ ▷ C₅₉

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
1. #16837331	C₂	semidirect
2. #16837326	C₂	semidirect
4. #16837300	C₂	semidirect
5. C₅₉×#376	C₂	semidirect
60. #376	D₅₉	semidirect
61. C₅₉	#2644	semidirect

H ≅ G/N

type

1. #16837331

C₂

semidirect

2. #16837326

C₂

semidirect

4. #16837300

C₂

semidirect

5. C₅₉×#376

C₂

semidirect

60. #376

D₅₉

semidirect

61. C₅₉

#2644

semidirect

Subgroups — #21430056

Conjugacy classes of subgroups

Complements