Group #21422175 — subgroups

Subgroups — #21422175

Order 7552.

140 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 77 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×#14273667	C₂	1	1	yes	maximal, characteristic
2	C₂×#14273637	C₂	1	1	yes	maximal, characteristic
3	C₂×M₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₅₉⋊C₈	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₅₉	C₄	1	1	yes	characteristic
6	#14273667	—	2	1	no	—
7	#14273667	—	2	1	no	—
8	C₂×C₅₉⋊C₁₆	C₄	1	2	yes	complemented
9	#14273637	—	2	1	no	—
10	#14273637	—	2	1	no	—
11	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
12	M₃₂×C₅₉	—	2	1	no	—
13	M₃₂×C₅₉	—	2	1	no	—
14	C₂×C₁₆×C₅₉	C₄	1	2	yes	complemented
15	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₅₉	—	2	1	no	—
17	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₅₉	Q₈	1	1	yes	characteristic
23	C₄×Dic₅₉	—	2	1	no	—
24	C₄×Dic₅₉	C₈	1	2	yes	—
25	C₂×C₅₉⋊C₈	—	2	1	no	—
26	C₂×C₅₉⋊C₈	—	2	1	no	—
27	C₂×C₅₉⋊C₈	C₈	1	2	yes	—
28	C₁₆×C₅₉	—	2	2	no	—
29	C₅₉⋊C₁₆	—	2	2	no	—
30	C₂³×C₅₉	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₅₉	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₅₉	M₁₆	1	1	yes	characteristic
37	C₂×Dic₅₉	—	2	2	no	—
38	C₂×Dic₅₉	—	4	2	no	—
39	C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₈×C₅₉	C₄⋊C₄	1	1	yes	characteristic
42	C₈×C₅₉	C₄⋊C₄	1	1	yes	characteristic
43	C₅₉⋊C₈	—	2	2	no	—
44	C₂²×C₅₉	—	2	2	no	—
45	C₂²×C₅₉	#97	1	1	yes	characteristic
46	C₂²×C₅₉	C₂²⋊C₈	1	1	yes	characteristic
47	C₂²×C₅₉	C₄⋊C₈	1	1	yes	characteristic
48	C₄×C₅₉	#95	1	1	yes	characteristic
49	C₄×C₅₉	C₄×C₈	1	1	yes	characteristic
50	C₄×C₅₉	C₂²⋊C₈	1	1	yes	characteristic
51	C₄×C₅₉	C₄⋊C₈	1	1	yes	characteristic
52	Dic₅₉	—	4	2	no	—
53	#1375	—	59	1	no	maximal, Sylow
54	C₂×C₅₉	—	2	1	no	—
55	C₂×C₅₉	—	2	1	no	—
56	C₂×C₅₉	#336	1	1	yes	characteristic
57	C₂×C₅₉	#347	1	2	yes	—
58	C₂×M₃₂	—	59	1	no	—
59	C₂×M₃₂	D₅₉	1	1	yes	characteristic
60	C₂×#97	—	59	1	no	—
61	C₅₉	#1375	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	—	59	1	no	—
63	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
64	C₂×C₄²	—	59	1	no	—
65	M₃₂	—	2	1	no	—
66	M₃₂	—	2	1	no	—
67	M₃₂	—	118	1	no	—
68	M₃₂	—	118	1	no	—
69	C₂×C₁₆	—	59	2	no	—
70	C₂×C₁₆	Dic₅₉	1	2	yes	complemented
71	#97	—	118	1	no	—
72	#97	—	118	1	no	—
73	C₂²×C₄	—	118	1	no	—
74	C₂²×C₄	C₄×D₅₉	1	1	yes	characteristic
75	C₂×C₈	—	59	2	no	—
76	C₂×C₈	—	118	1	no	—
77	C₂×C₈	—	118	1	no	—
78	C₂×C₈	Dic₁₁₈	1	1	yes	characteristic
79	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
80	C₂×C₈	D₂₃₆	1	1	yes	characteristic
81	C₂×C₈	C₂×Dic₅₉	1	1	yes	characteristic
82	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
83	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
84	C₄²	—	59	2	no	—
85	C₄²	—	118	1	no	—
86	C₁₆	—	2	2	no	—
87	C₁₆	—	118	2	no	—
88	C₂³	#11745659	1	1	yes	characteristic
89	C₂×C₄	—	118	2	no	—
90	C₂×C₄	—	236	2	no	—
91	C₂×C₄	C₈×D₅₉	1	1	yes	characteristic
92	C₂×C₄	C₈×D₅₉	1	1	yes	characteristic
93	C₂×C₄	#11745659	1	1	yes	characteristic
94	C₂×C₄	C₄×Dic₅₉	1	1	yes	characteristic
95	C₂×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
96	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
97	C₈	—	118	2	no	—
98	C₈	Dic₅₉⋊C₄	1	1	yes	characteristic
99	C₈	C₄⋊Dic₅₉	1	1	yes	characteristic
100	C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
101	C₈	C₂²⋊Dic₅₉	1	1	yes	characteristic
102	C₂²	—	2	2	no	—
103	C₂²	#14273637	1	1	yes	characteristic
104	C₂²	(C₂×D₅₉)⋊C₈	1	1	yes	characteristic
105	C₂²	Dic₅₉⋊C₈	1	1	yes	characteristic
106	C₄	—	236	2	no	—
107	C₄	C₅₉⋊#95	1	1	yes	characteristic
108	C₄	C₈×Dic₅₉	1	1	yes	characteristic
109	C₄	(C₂×D₅₉)⋊C₈	1	1	yes	characteristic
110	C₄	Dic₅₉⋊C₈	1	1	yes	characteristic
111	C₂	—	2	1	no	—
112	C₂	—	2	1	no	—
113	C₂	#16837156	1	1	yes	characteristic
114	C₂	#16837179	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273667

C₂

yes

maximal, characteristic

C₂×#14273637

C₂

yes

maximal, characteristic

C₂×M₃₂×C₅₉

C₂

yes

maximal, characteristic

C₂²×C₅₉⋊C₈

C₄

yes

characteristic

C₂×C₄×Dic₅₉

C₄

yes

characteristic

#14273667

—

#14273667

—

C₂×C₅₉⋊C₁₆

C₄

yes

complemented

#14273637

—

#14273637

—

C₂²×C₈×C₅₉

C₂²

yes

characteristic

M₃₂×C₅₉

—

M₃₂×C₅₉

—

C₂×C₁₆×C₅₉

C₄

yes

complemented

C₂²×C₄×C₅₉

C₂×C₄

yes

characteristic

C₂²×Dic₅₉

—

C₂×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

Q₈

yes

characteristic

C₄×Dic₅₉

—

C₄×Dic₅₉

C₈

yes

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₈

yes

—

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

M₁₆

yes

characteristic

C₂×C₄×C₅₉

C₄²

yes

characteristic

C₂×C₄×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₂×C₈

yes

characteristic

C₂×C₄×C₅₉

C₂×C₈

yes

characteristic

C₂×C₄×C₅₉

M₁₆

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₈×C₅₉

C₄⋊C₄

yes

characteristic

C₈×C₅₉

C₄⋊C₄

yes

characteristic

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

#97

yes

characteristic

C₂²×C₅₉

C₂²⋊C₈

yes

characteristic

C₂²×C₅₉

C₄⋊C₈

yes

characteristic

C₄×C₅₉

#95

yes

characteristic

C₄×C₅₉

C₄×C₈

yes

characteristic

C₄×C₅₉

C₂²⋊C₈

yes

characteristic

C₄×C₅₉

C₄⋊C₈

yes

characteristic

Dic₅₉

—

#1375

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

#336

yes

characteristic

C₂×C₅₉

#347

yes

—

C₂×M₃₂

—

C₂×M₃₂

D₅₉

yes

characteristic

C₂×#97

—

C₅₉

#1375

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₅₉

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

M₃₂

—

118

—

M₃₂

—

118

—

C₂×C₁₆

—

C₂×C₁₆

Dic₅₉

yes

complemented

#97

—

118

—

#97

—

118

—

C₂²×C₄

—

118

—

C₂²×C₄

C₄×D₅₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

—

118

—

C₂×C₈

Dic₁₁₈

yes

characteristic

C₂×C₈

C₄×D₅₉

yes

characteristic

C₂×C₈

D₂₃₆

yes

characteristic

C₂×C₈

C₂×Dic₅₉

yes

characteristic

C₂×C₈

C₂²⋊D₅₉

yes

characteristic

C₂×C₈

C₂²⋊D₅₉

yes

characteristic

C₄²

—

C₄²

—

118

—

C₁₆

—

C₁₆

—

118

—

C₂³

#11745659

yes

characteristic

C₂×C₄

—

118

—

C₂×C₄

—

236

—

C₂×C₄

C₈×D₅₉

yes

characteristic

C₂×C₄

C₈×D₅₉

yes

characteristic

C₂×C₄

#11745659

yes

characteristic

C₂×C₄

C₄×Dic₅₉

yes

characteristic

C₂×C₄

Dic₅₉⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₅₉)⋊C₄

yes

characteristic

C₈

—

118

—

C₈

Dic₅₉⋊C₄

yes

characteristic

C₈

C₄⋊Dic₅₉

yes

characteristic

100

C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

101

C₈

C₂²⋊Dic₅₉

yes

characteristic

102

C₂²

—

103

C₂²

#14273637

yes

characteristic

104

C₂²

(C₂×D₅₉)⋊C₈

yes

characteristic

105

C₂²

Dic₅₉⋊C₈

yes

characteristic

106

C₄

—

236

—

107

C₄

C₅₉⋊#95

yes

characteristic

108

C₄

C₈×Dic₅₉

yes

characteristic

109

C₄

(C₂×D₅₉)⋊C₈

yes

characteristic

110

C₄

Dic₅₉⋊C₈

yes

characteristic

111

C₂

—

112

C₂

—

113

C₂

#16837156

yes

characteristic

114

C₂

#16837179

yes

—

	subgroup	G/H
center	C₂×C₄	C₄×Dic₅₉
commutator	C₄×C₅₉	C₄×C₈
Frattini	C₂²×C₈	C₂×D₅₉
Fitting	C₂×M₃₂×C₅₉	C₂
socle	C₂²×C₅₉	#97
hypercenter	C₂×M₃₂	D₅₉
hypocenter	C₅₉	#1375
LCS	G ▷ C₄×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₃₂

subgroup

G/H

center

C₂×C₄

C₄×Dic₅₉

commutator

C₄×C₅₉

C₄×C₈

Frattini

C₂²×C₈

C₂×D₅₉

Fitting

C₂×M₃₂×C₅₉

C₂

socle

C₂²×C₅₉

#97

hypercenter

C₂×M₃₂

D₅₉

C₅₉

G ▷ C₄×C₅₉ ▷ C₅₉

C₁ ◁ C₂×C₄ ◁ C₂×M₃₂

N	H ≅ G/N	type
8. C₂×C₅₉⋊C₁₆	C₄	semidirect
14. C₂×C₁₆×C₅₉	C₄	semidirect
61. C₅₉	#1375	semidirect
70. C₂×C₁₆	Dic₅₉	semidirect

H ≅ G/N

type

8. C₂×C₅₉⋊C₁₆

C₄

semidirect

14. C₂×C₁₆×C₅₉

C₄

semidirect

61. C₅₉

#1375

semidirect

70. C₂×C₁₆

Dic₅₉

semidirect

Subgroups — #21422175

Conjugacy classes of subgroups

Complements