Group #21425694 — subgroups

Subgroups — #21425694

Order 7552.

184 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 109 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×#14273666	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×D₅₉	C₂	1	1	yes	maximal, characteristic
3	#16837356	C₂	1	1	yes	maximal, characteristic
4	#16837177	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#346	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11745659	C₄	1	1	yes	characteristic
9	C₂×C₈×D₅₉	C₂²	1	1	yes	characteristic
10	#14273684	C₄	1	1	yes	characteristic
11	#14273666	C₄	1	4	yes	complemented
12	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₁₆×D₅₉	C₄	1	4	yes	complemented
15	#14273638	C₄	1	1	yes	characteristic
16	#14273637	C₄	1	1	yes	characteristic
17	C₈×Dic₅₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
20	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
24	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
25	(C₂×D₅₉)⋊C₄	C₈	1	2	yes	—
26	Dic₅₉⋊C₄	C₈	1	2	yes	—
27	C₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
29	C₂×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
30	#11745659	C₈	1	4	yes	—
31	C₈×D₅₉	C₂×C₄	1	2	yes	—
32	C₈×D₅₉	C₂×C₄	1	2	yes	—
33	C₁₆×C₅₉	C₂×C₄	1	2	yes	—
34	C₁₆×C₅₉	C₂×C₄	1	2	yes	—
35	C₅₉⋊C₁₆	C₂×C₄	1	2	yes	—
36	C₅₉⋊C₁₆	C₂×C₄	1	2	yes	—
37	C₂²×D₅₉	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₅₉	C₂×C₈	1	2	yes	—
39	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₅₉	C₂×C₈	1	2	yes	—
41	C₂×Dic₅₉	C₂×C₈	1	1	yes	characteristic
42	C₄×D₅₉	C₄²	1	2	yes	—
43	C₄×D₅₉	C₂×C₈	1	2	yes	—
44	C₈×C₅₉	C₂×C₈	1	2	yes	—
45	C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
46	C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
47	C₅₉⋊C₈	C₄²	1	2	yes	—
48	C₅₉⋊C₈	C₂×C₈	1	2	yes	—
49	C₂²×C₅₉	C₂²×C₈	1	1	yes	characteristic
50	C₂×D₅₉	—	2	2	no	—
51	C₂×D₅₉	C₄×C₈	1	2	yes	—
52	C₄×C₅₉	—	2	2	no	—
53	C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
54	C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
55	Dic₅₉	—	2	2	no	—
56	Dic₅₉	C₄×C₈	1	2	yes	—
57	#2108	—	59	1	no	maximal, Sylow
58	C₂×C₅₉	C₂×C₄×C₈	1	1	yes	characteristic
59	C₂×C₅₉	#504	1	2	yes	—
60	D₅₉	—	2	2	no	—
61	C₂×M₃₂	—	59	1	no	—
62	C₂²×C₁₆	—	59	1	no	—
63	#405	—	59	1	no	—
64	#346	—	59	1	no	—
65	#346	D₅₉	1	1	yes	characteristic, complemented
66	C₄×C₁₆	—	59	1	no	—
67	C₄×C₁₆	—	59	1	no	—
68	C₅₉	#2108	1	1	yes	characteristic, complemented, Sylow
69	C₂×M₁₆	—	59	1	no	—
70	C₂²×C₈	—	59	1	no	—
71	#117	—	59	1	no	—
72	M₃₂	—	59	4	no	—
73	C₂×C₁₆	—	59	1	no	—
74	C₂×C₁₆	—	59	1	no	—
75	C₂×C₁₆	—	59	4	no	—
76	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
77	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
78	#97	—	59	1	no	—
79	#97	—	59	1	no	—
80	C₄×C₈	—	59	1	no	—
81	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
82	C₂²×C₄	—	59	1	no	—
83	M₁₆	—	59	4	no	—
84	C₂×C₈	—	59	1	no	—
85	C₂×C₈	—	59	1	no	—
86	C₂×C₈	—	59	2	no	—
87	C₂×C₈	—	59	2	no	—
88	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
89	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
90	C₄⋊C₄	—	59	2	no	—
91	C₂²⋊C₄	—	59	2	no	—
92	C₄²	—	59	1	no	—
93	C₄²	C₄×D₅₉	1	1	yes	characteristic
94	C₁₆	—	59	2	no	—
95	C₁₆	—	59	2	no	—
96	C₁₆	C₄×D₅₉	1	2	yes	—
97	C₁₆	C₄×D₅₉	1	2	yes	—
98	C₂³	—	59	1	no	—
99	C₂×C₄	—	59	1	no	—
100	C₂×C₄	—	59	2	no	—
101	C₂×C₄	—	59	2	no	—
102	C₂×C₄	—	59	2	no	—
103	C₂×C₄	C₈×D₅₉	1	2	yes	—
104	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
105	C₈	—	59	2	no	—
106	C₈	—	59	2	no	—
107	C₈	C₈×D₅₉	1	2	yes	—
108	C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
109	C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
110	C₂²	—	59	2	no	—
111	C₂²	—	118	2	no	—
112	C₂²	C₂×C₈×D₅₉	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	59	2	no	—
115	C₄	—	118	2	no	—
116	C₄	C₄²×D₅₉	1	1	yes	characteristic
117	C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
118	C₂	—	118	2	no	—
119	C₂	C₄×C₈×D₅₉	1	1	yes	characteristic
120	C₂	#16837820	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273666

C₂

yes

maximal, characteristic

C₂×C₁₆×D₅₉

C₂

yes

maximal, characteristic

#16837356

C₂

yes

maximal, characteristic

#16837177

C₂

yes

maximal, characteristic, complemented

C₄×C₅₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₁₆×Dic₅₉

C₂

yes

maximal, characteristic, complemented

C₅₉×#346

C₂

yes

maximal, characteristic, complemented

C₂×#11745659

C₄

yes

characteristic

C₂×C₈×D₅₉

C₂²

yes

characteristic

#14273684

C₄

yes

characteristic

#14273666

C₄

yes

complemented

C₂×C₅₉⋊C₁₆

C₂²

yes

characteristic

C₂×C₅₉⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₅₉

C₄

yes

complemented

#14273638

C₄

yes

characteristic

#14273637

C₄

yes

characteristic

C₈×Dic₅₉

C₂²

yes

characteristic

C₂×C₁₆×C₅₉

C₂²

yes

characteristic

C₂×C₁₆×C₅₉

C₂²

yes

characteristic

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×C₄×D₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄²×C₅₉

C₂×C₄

yes

characteristic

(C₂×D₅₉)⋊C₄

C₈

yes

—

Dic₅₉⋊C₄

C₈

yes

—

C₄×Dic₅₉

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₄

yes

characteristic

#11745659

C₈

yes

—

C₈×D₅₉

C₂×C₄

yes

—

C₈×D₅₉

C₂×C₄

yes

—

C₁₆×C₅₉

C₂×C₄

yes

—

C₁₆×C₅₉

C₂×C₄

yes

—

C₅₉⋊C₁₆

C₂×C₄

yes

—

C₅₉⋊C₁₆

C₂×C₄

yes

—

C₂²×D₅₉

C₂×C₈

yes

characteristic

C₂×C₄×C₅₉

C₂×C₈

yes

—

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×Dic₅₉

C₂×C₈

yes

—

C₂×Dic₅₉

C₂×C₈

yes

characteristic

C₄×D₅₉

C₄²

yes

—

C₄×D₅₉

C₂×C₈

yes

—

C₈×C₅₉

C₂×C₈

yes

—

C₈×C₅₉

C₂²×C₄

yes

characteristic

C₈×C₅₉

C₂²×C₄

yes

characteristic

C₅₉⋊C₈

C₄²

yes

—

C₅₉⋊C₈

C₂×C₈

yes

—

C₂²×C₅₉

C₂²×C₈

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

C₄×C₈

yes

—

C₄×C₅₉

—

C₄×C₅₉

C₂×C₄²

yes

characteristic

C₄×C₅₉

C₂²×C₈

yes

characteristic

Dic₅₉

—

Dic₅₉

C₄×C₈

yes

—

#2108

—

maximal, Sylow

C₂×C₅₉

C₂×C₄×C₈

yes

characteristic

C₂×C₅₉

#504

yes

—

D₅₉

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

#346

—

#346

D₅₉

yes

characteristic, complemented

C₄×C₁₆

—

C₄×C₁₆

—

C₅₉

#2108

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₅₉

yes

characteristic

C₂×C₁₆

C₂×D₅₉

yes

characteristic

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₅₉

yes

characteristic

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₅₉

yes

characteristic

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₅₉

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

C₄×D₅₉

yes

—

C₁₆

C₄×D₅₉

yes

—

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

C₈×D₅₉

yes

—

104

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

C₈×D₅₉

yes

—

108

C₈

C₂×C₄×D₅₉

yes

characteristic

109

C₈

C₂×C₄×D₅₉

yes

characteristic

110

C₂²

—

111

C₂²

—

118

—

112

C₂²

C₂×C₈×D₅₉

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

118

—

116

C₄

C₄²×D₅₉

yes

characteristic

117

C₄

C₂×C₈×D₅₉

yes

characteristic

118

C₂

—

118

—

119

C₂

C₄×C₈×D₅₉

yes

characteristic

120

C₂

#16837820

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₅₉
commutator	C₂×C₅₉	C₂×C₄×C₈
Fitting	C₅₉×#346	C₂
socle	C₂²×C₅₉	C₂²×C₈
hypercenter	#346	D₅₉
hypocenter	C₅₉	#2108
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₅₉

commutator

C₂×C₅₉

C₂×C₄×C₈

Fitting

C₅₉×#346

C₂

socle

C₂²×C₅₉

C₂²×C₈

D₅₉

C₅₉

G ▷ C₂×C₅₉ ▷ C₅₉

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
4. #16837177	C₂	semidirect
5. C₄×C₅₉⋊C₁₆	C₂	semidirect
6. C₁₆×Dic₅₉	C₂	semidirect
7. C₅₉×#346	C₂	semidirect
11. #14273666	C₄	semidirect
14. C₁₆×D₅₉	C₄	semidirect
65. #346	D₅₉	semidirect
68. C₅₉	#2108	semidirect

H ≅ G/N

type

4. #16837177

C₂

semidirect

5. C₄×C₅₉⋊C₁₆

C₂

semidirect

6. C₁₆×Dic₅₉

C₂

semidirect

7. C₅₉×#346

C₂

semidirect

11. #14273666

C₄

semidirect

14. C₁₆×D₅₉

C₄

semidirect

65. #346

D₅₉

semidirect

68. C₅₉

#2108

semidirect

Subgroups — #21425694

Conjugacy classes of subgroups

Complements