Group #21421946 — subgroups

Subgroups — #21421946

Order 7552.

160 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 81 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	#16837455	C₂	1	1	yes	maximal, characteristic
2	C₄×#11745664	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₈×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11745664	C₄	1	2	yes	—
5	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
6	C₂²⋊(C₅₉⋊C₈)	C₄	1	2	yes	—
7	#14273638	—	2	1	no	—
8	C₄×C₅₉⋊C₈	—	2	1	no	—
9	C₄×C₅₉⋊C₈	—	2	1	no	—
10	C₂²×C₈×C₅₉	C₄	1	2	yes	—
11	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₅₉	—	2	1	no	—
13	C₄⋊C₈×C₅₉	—	2	1	no	—
14	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₅₉	—	2	2	no	—
18	C₂×C₈×C₅₉	—	4	2	no	—
19	C₄²×C₅₉	D₄	1	1	yes	characteristic
20	C₄²×C₅₉	D₄	1	1	yes	characteristic
21	C₄²×C₅₉	D₄	1	1	yes	characteristic
22	C₄²×C₅₉	Q₈	1	1	yes	characteristic
23	#11745664	—	2	2	no	—
24	#11745664	C₈	1	4	yes	complemented
25	C₂×C₅₉⋊C₈	—	2	2	no	—
26	C₂×C₅₉⋊C₈	—	2	2	no	—
27	C₂³×C₅₉	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₅₉	—	2	1	no	—
29	C₂×C₄×C₅₉	—	2	1	no	—
30	C₂×C₄×C₅₉	—	4	1	no	—
31	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₅₉	C₂×C₈	1	2	yes	—
38	C₂×C₄×C₅₉	M₁₆	1	2	yes	—
39	C₈×C₅₉	—	4	2	no	—
40	C₅₉⋊C₈	—	2	4	no	—
41	C₅₉⋊C₈	—	4	2	no	—
42	C₂²×C₅₉	—	2	1	no	—
43	C₂²×C₅₉	—	2	1	no	—
44	C₂²×C₅₉	#95	1	1	yes	characteristic
45	C₂²×C₅₉	C₄×C₈	1	1	yes	characteristic
46	C₂²×C₅₉	#97	1	1	yes	characteristic
47	C₄×C₅₉	—	2	1	no	—
48	C₄×C₅₉	—	2	1	no	—
49	C₄×C₅₉	—	2	1	no	—
50	C₄×C₅₉	C₂²⋊C₈	1	2	yes	—
51	C₄×C₅₉	#100	1	1	yes	characteristic
52	C₄×C₅₉	#101	1	1	yes	characteristic
53	C₄×C₅₉	C₄⋊C₈	1	2	yes	—
54	#1283	—	59	1	no	maximal, Sylow
55	C₂×C₅₉	—	2	1	no	—
56	C₂×C₅₉	—	2	1	no	—
57	C₂×C₅₉	#336	1	1	yes	characteristic
58	C₂×C₅₉	#343	1	1	yes	characteristic
59	C₂×C₅₉	#344	1	1	yes	characteristic
60	#431	—	59	1	no	—
61	C₂×C₄⋊C₈	D₅₉	1	1	yes	characteristic
62	C₄×M₁₆	—	59	1	no	—
63	C₅₉	#1283	1	1	yes	characteristic, complemented, Sylow
64	C₂×M₁₆	—	59	2	no	—
65	C₂²×C₈	Dic₅₉	1	2	yes	—
66	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
67	C₄⋊C₈	—	2	1	no	—
68	C₄⋊C₈	—	2	1	no	—
69	C₄⋊C₈	—	118	1	no	—
70	C₂²⋊C₈	—	59	2	no	—
71	#97	—	118	1	no	—
72	C₄×C₈	—	118	1	no	—
73	C₄×C₈	—	118	1	no	—
74	C₂²×C₄	C₄×D₅₉	1	1	yes	characteristic
75	C₂²×C₄	C₄×D₅₉	1	1	yes	characteristic
76	C₂²×C₄	C₂×Dic₅₉	1	1	yes	characteristic
77	M₁₆	—	59	4	no	—
78	M₁₆	—	118	2	no	—
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	4	2	no	—
81	C₂×C₈	—	118	2	no	—
82	C₂×C₈	—	118	2	no	—
83	C₄²	Dic₁₁₈	1	1	yes	characteristic
84	C₄²	D₂₃₆	1	1	yes	characteristic
85	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
86	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
87	C₂³	C₄×Dic₅₉	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	4	1	no	—
91	C₂×C₄	C₈×D₅₉	1	2	yes	—
92	C₂×C₄	#11745659	1	2	yes	—
93	C₂×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
94	C₂×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
95	C₂×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
96	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
97	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
98	C₂×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
99	C₈	—	4	2	no	—
100	C₈	—	118	4	no	—
101	C₈	—	236	2	no	—
102	C₂²	—	2	1	no	—
103	C₂²	—	2	1	no	—
104	C₂²	C₅₉⋊#95	1	1	yes	characteristic
105	C₂²	C₈×Dic₅₉	1	1	yes	characteristic
106	C₂²	#14273637	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	(C₂×D₅₉)⋊C₈	1	2	yes	—
111	C₄	#14273644	1	1	yes	characteristic
112	C₄	#14273646	1	1	yes	characteristic
113	C₄	Dic₅₉⋊C₈	1	2	yes	—
114	C₂	—	2	1	no	—
115	C₂	—	2	1	no	—
116	C₂	#16837156	1	1	yes	characteristic
117	C₂	#16837171	1	1	yes	characteristic
118	C₂	#16837173	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837455

C₂

yes

maximal, characteristic

C₄×#11745664

C₂

yes

maximal, characteristic

C₂×C₄⋊C₈×C₅₉

C₂

yes

maximal, characteristic

C₂×#11745664

C₄

yes

—

C₄⋊(C₅₉⋊C₈)

—

C₂²⋊(C₅₉⋊C₈)

C₄

yes

—

#14273638

—

C₄×C₅₉⋊C₈

—

C₄×C₅₉⋊C₈

—

C₂²×C₈×C₅₉

C₄

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₄⋊C₈×C₅₉

—

C₄⋊C₈×C₅₉

—

C₂²×C₄×C₅₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄²×C₅₉

D₄

yes

characteristic

C₄²×C₅₉

D₄

yes

characteristic

C₄²×C₅₉

D₄

yes

characteristic

C₄²×C₅₉

Q₈

yes

characteristic

#11745664

—

#11745664

C₈

yes

complemented

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

C₄²

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₂×C₈

yes

—

C₂×C₄×C₅₉

M₁₆

yes

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

#95

yes

characteristic

C₂²×C₅₉

C₄×C₈

yes

characteristic

C₂²×C₅₉

#97

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

C₂²⋊C₈

yes

—

C₄×C₅₉

yes

C₄×C₅₉

yes

C₄×C₅₉

C₄⋊C₈

yes

—

#1283

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×C₄⋊C₈

D₅₉

yes

characteristic

C₄×M₁₆

—

C₅₉

#1283

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

Dic₅₉

yes

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

118

—

C₂²⋊C₈

—

#97

—

118

—

C₄×C₈

—

118

—

C₄×C₈

—

118

—

C₂²×C₄

C₄×D₅₉

yes

characteristic

C₂²×C₄

C₄×D₅₉

yes

characteristic

C₂²×C₄

C₂×Dic₅₉

yes

characteristic

M₁₆

—

M₁₆

—

118

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

—

118

—

C₄²

Dic₁₁₈

yes

characteristic

C₄²

D₂₃₆

yes

characteristic

C₄²

C₂²⋊D₅₉

yes

characteristic

C₄²

C₂²⋊D₅₉

yes

characteristic

C₂³

C₄×Dic₅₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₅₉

yes

—

C₂×C₄

#11745659

yes

—

C₂×C₄

Dic₅₉⋊C₄

yes

characteristic

C₂×C₄

Dic₅₉⋊C₄

yes

characteristic

C₂×C₄

C₄⋊Dic₅₉

yes

characteristic

C₂×C₄

(C₂×D₅₉)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₅₉)⋊C₄

yes

characteristic

C₂×C₄

C₂²⋊Dic₅₉

yes

characteristic

C₈

—

100

C₈

—

118

—

101

C₈

—

236

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₅₉⋊#95

yes

characteristic

105

C₂²

C₈×Dic₅₉

yes

characteristic

106

C₂²

#14273637

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

(C₂×D₅₉)⋊C₈

yes

—

111

C₄

#14273644

yes

characteristic

112

C₄

#14273646

yes

characteristic

113

C₄

Dic₅₉⋊C₈

yes

—

114

C₂

—

115

C₂

—

116

C₂

#16837156

yes

characteristic

117

C₂

#16837171

yes

characteristic

118

C₂

#16837173

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₅₉
commutator	C₂²×C₅₉	C₄×C₈
Frattini	C₂×C₄²	C₂×D₅₉
Fitting	C₂×C₄⋊C₈×C₅₉	C₂
socle	C₂²×C₅₉	#95
hypercenter	C₂×C₄⋊C₈	D₅₉
hypocenter	C₅₉	#1283
LCS	G ▷ C₂²×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂×C₄

C₂²⋊Dic₅₉

commutator

C₂²×C₅₉

C₄×C₈

Frattini

C₂×C₄²

C₂×D₅₉

Fitting

C₂×C₄⋊C₈×C₅₉

C₂

socle

C₂²×C₅₉

#95

hypercenter

C₂×C₄⋊C₈

D₅₉

hypocenter

C₅₉

#1283

LCS

G ▷ C₂²×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
24. #11745664	C₈	semidirect
63. C₅₉	#1283	semidirect

H ≅ G/N

type

24. #11745664

C₈

semidirect

63. C₅₉

#1283

semidirect

Subgroups — #21421946

Conjugacy classes of subgroups

Complements