Group #21425857 — subgroups

Subgroups — #364×D₅₉ #21425857

Order 7552.

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

normal subgroups only

This group has 168 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	M₃₂×D₅₉	C₂	1	2	yes	maximal
2	C₄×C₈×D₅₉	C₂	1	1	yes	maximal, characteristic
3	#16837223	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837222	C₂	1	2	yes	maximal, complemented
5	C₅₉×#364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₅₉	C₄	1	1	yes	characteristic
7	C₂×C₈×D₅₉	C₂²	1	1	yes	characteristic
8	C₄²×D₅₉	C₄	1	1	yes	characteristic
9	#14273667	C₂²	1	2	yes	—
10	#14273666	—	2	2	no	—
11	C₁₆×D₅₉	—	2	2	no	—
12	C₄×C₅₉⋊C₈	C₄	1	1	yes	characteristic
13	C₈×Dic₅₉	C₄	1	1	yes	characteristic
14	C₈×Dic₅₉	C₂²	1	1	yes	characteristic
15	M₃₂×C₅₉	C₂²	1	2	yes	—
16	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₅₉	—	2	1	no	—
18	C₂×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
21	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₅₉	—	2	1	no	—
23	C₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₂×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₈×D₅₉	C₈	1	2	yes	—
27	C₈×D₅₉	C₈	1	2	yes	—
28	C₈×D₅₉	D₄	1	1	yes	characteristic
29	C₈×D₅₉	D₄	1	1	yes	characteristic
30	C₈×D₅₉	Q₈	1	1	yes	characteristic
31	C₈×D₅₉	Q₈	1	1	yes	characteristic
32	C₁₆×C₅₉	—	2	2	no	—
33	C₅₉⋊C₁₆	—	2	2	no	—
34	C₂²×D₅₉	M₁₆	1	1	yes	characteristic
35	C₂×C₄×C₅₉	—	2	1	no	—
36	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₅₉	—	2	1	no	—
38	C₂×Dic₅₉	M₁₆	1	1	yes	characteristic
39	C₄×D₅₉	—	2	4	no	—
40	C₄×D₅₉	C₄⋊C₄	1	1	yes	characteristic
41	C₄×D₅₉	C₄⋊C₄	1	1	yes	characteristic
42	C₄×D₅₉	C₂×C₈	1	1	yes	characteristic
43	C₄×D₅₉	C₂×C₈	1	1	yes	characteristic
44	C₈×C₅₉	C₂×C₈	1	2	yes	—
45	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
46	C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
47	C₅₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
48	C₅₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
49	C₅₉⋊C₈	C₂×C₈	1	2	yes	—
50	C₂²×C₅₉	C₂×M₁₆	1	1	yes	characteristic
51	C₂×D₅₉	—	2	2	no	—
52	C₂×D₅₉	C₄⋊C₈	1	1	yes	characteristic
53	C₂×D₅₉	C₄⋊C₈	1	1	yes	characteristic
54	C₄×C₅₉	—	2	2	no	—
55	C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
57	Dic₅₉	—	2	2	no	—
58	Dic₅₉	C₄⋊C₈	1	1	yes	characteristic
59	Dic₅₉	C₄⋊C₈	1	1	yes	characteristic
60	C₂×#364	—	59	1	no	maximal, Sylow
61	C₂×C₅₉	—	2	1	no	—
62	C₂×C₅₉	C₂×C₄⋊C₈	1	1	yes	characteristic
63	D₅₉	—	2	1	no	—
64	D₅₉	#364	1	2	yes	direct product factor
65	C₂×M₃₂	—	59	2	no	—
66	C₂×C₄×C₈	—	59	1	no	—
67	#364	—	59	2	no	—
68	#364	—	59	1	no	—
69	#364	D₅₉	1	1	yes	characteristic, direct product factor
70	C₅₉	C₂×#364	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₈	—	59	1	no	—
72	C₂²×C₈	—	59	1	no	—
73	C₂×C₄²	—	59	1	no	—
74	M₃₂	—	59	2	no	—
75	M₃₂	—	118	2	no	—
76	M₃₂	C₂×D₅₉	1	2	yes	—
77	C₂×C₁₆	—	118	2	no	—
78	C₄×C₈	—	59	1	no	—
79	C₄×C₈	—	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	C₂²×C₄	—	118	1	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	—	59	1	no	—
89	C₂×C₈	—	59	1	no	—
90	C₂×C₈	—	59	1	no	—
91	C₂×C₈	—	59	1	no	—
92	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
93	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
94	C₄²	—	59	1	no	—
95	C₄²	—	118	1	no	—
96	C₄²	C₄×D₅₉	1	1	yes	characteristic
97	C₁₆	—	2	2	no	—
98	C₁₆	—	118	2	no	—
99	C₂³	—	59	1	no	—
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	59	1	no	—
102	C₂×C₄	—	59	1	no	—
103	C₂×C₄	—	59	1	no	—
104	C₂×C₄	—	59	1	no	—
105	C₂×C₄	—	59	1	no	—
106	C₂×C₄	—	118	4	no	—
107	C₂×C₄	—	118	1	no	—
108	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
109	C₈	—	59	1	no	—
110	C₈	—	59	1	no	—
111	C₈	—	59	2	no	—
112	C₈	C₈×D₅₉	1	2	yes	—
113	C₈	D₄×D₅₉	1	1	yes	characteristic
114	C₈	Q₈×D₅₉	1	1	yes	characteristic
115	C₂²	—	59	1	no	—
116	C₂²	—	59	1	no	—
117	C₂²	—	118	2	no	—
118	C₂²	M₁₆×D₅₉	1	1	yes	characteristic
119	C₄	—	2	2	no	—
120	C₄	—	59	1	no	—
121	C₄	—	59	1	no	—
122	C₄	—	118	2	no	—
123	C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
124	C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
125	C₂	—	2	1	no	—
126	C₂	—	59	2	no	—
127	C₂	—	118	1	no	—
128	C₂	C₄⋊C₈×D₅₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

M₃₂×D₅₉

C₂

yes

maximal

C₄×C₈×D₅₉

C₂

yes

maximal, characteristic

#16837223

C₂

yes

maximal, characteristic, complemented

#16837222

C₂

yes

maximal, complemented

C₅₉×#364

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₅₉

C₄

yes

characteristic

C₂×C₈×D₅₉

C₂²

yes

characteristic

C₄²×D₅₉

C₄

yes

characteristic

#14273667

C₂²

yes

—

#14273666

—

C₁₆×D₅₉

—

C₄×C₅₉⋊C₈

C₄

yes

characteristic

C₈×Dic₅₉

C₄

yes

characteristic

C₈×Dic₅₉

C₂²

yes

characteristic

M₃₂×C₅₉

C₂²

yes

—

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×C₄×D₅₉

—

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

C₄×Dic₅₉

—

C₄×Dic₅₉

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₈×D₅₉

C₈

yes

—

C₈×D₅₉

C₈

yes

—

C₈×D₅₉

D₄

yes

characteristic

C₈×D₅₉

D₄

yes

characteristic

C₈×D₅₉

Q₈

yes

characteristic

C₈×D₅₉

Q₈

yes

characteristic

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂²×D₅₉

M₁₆

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

M₁₆

yes

characteristic

C₄×D₅₉

—

C₄×D₅₉

C₄⋊C₄

yes

characteristic

C₄×D₅₉

C₄⋊C₄

yes

characteristic

C₄×D₅₉

C₂×C₈

yes

characteristic

C₄×D₅₉

C₂×C₈

yes

characteristic

C₈×C₅₉

C₂×C₈

yes

—

C₈×C₅₉

C₂×D₄

yes

characteristic

C₈×C₅₉

C₂×Q₈

yes

characteristic

C₅₉⋊C₈

C₄⋊C₄

yes

characteristic

C₅₉⋊C₈

C₄⋊C₄

yes

characteristic

C₅₉⋊C₈

C₂×C₈

yes

—

C₂²×C₅₉

C₂×M₁₆

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

C₄⋊C₈

yes

characteristic

C₂×D₅₉

C₄⋊C₈

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₅₉

C₂²×C₈

yes

characteristic

Dic₅₉

—

Dic₅₉

C₄⋊C₈

yes

characteristic

Dic₅₉

C₄⋊C₈

yes

characteristic

C₂×#364

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

C₂×C₄⋊C₈

yes

characteristic

D₅₉

—

D₅₉

#364

yes

direct product factor

C₂×M₃₂

—

C₂×C₄×C₈

—

#364

—

#364

—

#364

D₅₉

yes

characteristic, direct product factor

C₅₉

C₂×#364

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

M₃₂

—

118

—

M₃₂

C₂×D₅₉

yes

—

C₂×C₁₆

—

118

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₅₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

118

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₅₉

yes

characteristic

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄²

—

C₄²

—

118

—

C₄²

C₄×D₅₉

yes

characteristic

C₁₆

—

C₁₆

—

118

—

C₂³

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

118

—

107

C₂×C₄

—

118

—

108

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

109

C₈

—

110

C₈

—

111

C₈

—

112

C₈

C₈×D₅₉

yes

—

113

C₈

D₄×D₅₉

yes

characteristic

114

C₈

Q₈×D₅₉

yes

characteristic

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

—

118

C₂²

M₁₆×D₅₉

yes

characteristic

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

118

—

123

C₄

C₄⋊C₄×D₅₉

yes

characteristic

124

C₄

C₂×C₈×D₅₉

yes

characteristic

125

C₂

—

126

C₂

—

127

C₂

—

118

—

128

C₂

C₄⋊C₈×D₅₉

yes

characteristic

	subgroup	G/H
center	C₈	D₄×D₅₉
commutator	C₄×C₅₉	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#364	C₂
socle	C₂×C₅₉	C₂×C₄⋊C₈
hypercenter	#364	D₅₉
hypocenter	C₅₉	C₂×#364
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

subgroup

G/H

center

C₈

D₄×D₅₉

commutator

C₄×C₅₉

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#364

C₂

socle

C₂×C₅₉

C₂×C₄⋊C₈

D₅₉

C₅₉

G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

N	H ≅ G/N	type
3. #16837223	C₂	semidirect
4. #16837222	C₂	semidirect
5. C₅₉×#364	C₂	semidirect
64. D₅₉	#364	direct (N × H)
69. #364	D₅₉	direct (N × H)
70. C₅₉	C₂×#364	semidirect

H ≅ G/N

type

3. #16837223

C₂

semidirect

4. #16837222

C₂

semidirect

5. C₅₉×#364

C₂

semidirect

64. D₅₉

#364

direct (N × H)

69. #364

D₅₉

direct (N × H)

70. C₅₉

C₂×#364

semidirect

Subgroups — #364×D₅₉ #21425857

Conjugacy classes of subgroups

Complements

Subgroups — #364×D59 #21425857

Conjugacy classes of subgroups

Complements

Subgroups — #364×D₅₉ #21425857