Group #21423950 — subgroups

Subgroups — #21423950

Order 7552.

292 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 141 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×Dic₅₉⋊C₈	C₂	1	2	yes	maximal
2	C₂×#14273638	C₂	1	1	yes	maximal, characteristic
3	C₄²×Dic₅₉	C₂	1	1	yes	maximal, characteristic
4	#16837156	C₂	1	2	yes	maximal
5	C₂×#97×C₅₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₅₉⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×Dic₅₉	C₄	1	2	yes	—
8	C₂×C₄×Dic₅₉	C₄	1	2	yes	—
9	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
11	Dic₅₉⋊C₈	C₄	1	8	yes	complemented
12	#14273638	—	2	2	no	—
13	C₂²×C₈×C₅₉	C₂²	1	2	yes	—
14	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
15	#97×C₅₉	—	2	2	no	—
16	C₂²×C₄×C₅₉	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
18	C₂²×Dic₅₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₅₉	C₂×C₄	1	2	yes	—
20	C₂²×Dic₅₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₅₉	—	2	2	no	—
22	C₂×C₈×C₅₉	—	2	2	no	—
23	C₂×C₈×C₅₉	C₂×C₄	1	4	yes	—
24	C₄²×C₅₉	D₄	1	2	yes	—
25	C₄²×C₅₉	Q₈	1	2	yes	—
26	C₄×Dic₅₉	—	2	2	no	—
27	C₄×Dic₅₉	—	2	4	no	—
28	C₄×Dic₅₉	—	2	4	no	—
29	C₄×Dic₅₉	C₂×C₄	1	4	yes	—
30	C₂×C₅₉⋊C₈	—	2	2	no	—
31	C₂×C₅₉⋊C₈	—	2	2	no	—
32	C₂×C₅₉⋊C₈	C₂×C₄	1	4	yes	—
33	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₅₉	—	2	2	no	—
35	C₂×C₄×C₅₉	—	2	2	no	—
36	C₂×C₄×C₅₉	C₄⋊C₄	1	4	yes	—
37	C₂×C₄×C₅₉	C₂²×C₄	1	2	yes	—
38	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₅₉	#41	1	2	yes	—
41	C₂×Dic₅₉	—	2	2	no	—
42	C₂×Dic₅₉	—	2	2	no	—
43	C₂×Dic₅₉	—	2	2	no	—
44	C₂×Dic₅₉	C₄²	1	2	yes	—
45	C₂×Dic₅₉	C₄²	1	2	yes	—
46	C₂×Dic₅₉	M₁₆	1	4	yes	—
47	C₂×Dic₅₉	M₁₆	1	4	yes	—
48	C₈×C₅₉	—	2	4	no	—
49	C₅₉⋊C₈	—	2	4	no	—
50	C₂²×C₅₉	C₂×C₄²	1	1	yes	characteristic
51	C₂²×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₅₉	#117	1	1	yes	characteristic
53	C₂²×C₅₉	C₂×M₁₆	1	2	yes	—
54	C₂²×C₅₉	C₂×M₁₆	1	2	yes	—
55	C₄×C₅₉	—	2	4	no	—
56	C₄×C₅₉	C₄×D₄	1	2	yes	—
57	C₄×C₅₉	C₄×Q₈	1	2	yes	—
58	Dic₅₉	—	2	2	no	—
59	Dic₅₉	—	2	4	no	—
60	Dic₅₉	#97	1	4	yes	complemented
61	#1767	—	59	1	no	maximal, Sylow
62	C₂×C₅₉	C₄×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₅₉	C₂×#97	1	1	yes	characteristic
64	C₂×C₅₉	C₄×M₁₆	1	1	yes	characteristic
65	C₂×C₅₉	#423	1	2	yes	—
66	C₂×C₅₉	#432	1	2	yes	—
67	C₂×C₄⋊C₈	—	59	2	no	—
68	C₂×#97	—	59	1	no	—
69	C₂×#97	D₅₉	1	1	yes	characteristic
70	C₄³	—	59	1	no	—
71	#336	—	59	2	no	—
72	C₅₉	#1767	1	1	yes	characteristic, complemented, Sylow
73	C₂²×C₈	—	59	2	no	—
74	C₂²×C₈	C₂×D₅₉	1	2	yes	—
75	C₂×C₄²	—	59	1	no	—
76	C₂×C₄²	—	59	2	no	—
77	C₂×C₄²	—	59	2	no	—
78	C₂×C₄²	—	59	1	no	—
79	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
80	C₄⋊C₈	—	59	8	no	—
81	#97	—	2	2	no	—
82	#97	—	118	2	no	—
83	C₂²×C₄	—	59	1	no	—
84	C₂²×C₄	—	59	1	no	—
85	C₂²×C₄	—	59	2	no	—
86	C₂²×C₄	C₄×D₅₉	1	2	yes	—
87	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	59	4	no	—
91	C₂×C₈	—	118	2	no	—
92	C₂×C₈	—	118	2	no	—
93	C₂×C₈	C₄×D₅₉	1	4	yes	—
94	C₄²	—	59	4	no	—
95	C₄²	—	118	4	no	—
96	C₄²	—	118	4	no	—
97	C₄²	—	118	2	no	—
98	C₄²	Dic₁₁₈	1	2	yes	—
99	C₄²	C₂²⋊D₅₉	1	2	yes	—
100	C₂³	C₂×C₄×D₅₉	1	1	yes	characteristic
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	59	2	no	—
104	C₂×C₄	—	59	4	no	—
105	C₂×C₄	—	59	2	no	—
106	C₂×C₄	—	59	4	no	—
107	C₂×C₄	—	118	2	no	—
108	C₂×C₄	—	118	2	no	—
109	C₂×C₄	—	118	2	no	—
110	C₂×C₄	Dic₅₉⋊C₄	1	4	yes	—
111	C₂×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
112	C₂×C₄	C₂×C₄×D₅₉	1	2	yes	—
113	C₂×C₄	#11745685	1	2	yes	—
114	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
115	C₈	—	2	4	no	—
116	C₈	—	118	4	no	—
117	C₂²	C₄²×D₅₉	1	1	yes	characteristic
118	C₂²	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
119	C₂²	#14273684	1	1	yes	characteristic
120	C₂²	M₁₆×D₅₉	1	2	yes	—
121	C₂²	M₁₆×D₅₉	1	2	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	59	4	no	—
124	C₄	—	118	4	no	—
125	C₄	—	118	2	no	—
126	C₄	C₄×C₂²⋊D₅₉	1	2	yes	—
127	C₄	C₄×Dic₁₁₈	1	2	yes	—
128	C₂	C₄×Dic₅₉⋊C₄	1	1	yes	characteristic
129	C₂	#97×D₅₉	1	1	yes	characteristic
130	C₂	#16837354	1	1	yes	characteristic
131	C₂	#16837425	1	2	yes	—
132	C₂	#16837457	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₅₉⋊C₈

C₂

yes

maximal

C₂×#14273638

C₂

yes

maximal, characteristic

C₄²×Dic₅₉

C₂

yes

maximal, characteristic

#16837156

C₂

yes

maximal

C₂×#97×C₅₉

C₂

yes

maximal, characteristic

C₂²×C₅₉⋊C₈

C₂²

yes

—

C₂×C₄×Dic₅₉

C₄

yes

—

C₂×C₄×Dic₅₉

C₄

yes

—

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

Dic₅₉⋊C₈

C₄

yes

complemented

#14273638

—

C₂²×C₈×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

#97×C₅₉

—

C₂²×C₄×C₅₉

C₂×C₄

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

C₂×C₄

yes

characteristic

C₂²×Dic₅₉

C₂×C₄

yes

—

C₂²×Dic₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂×C₄

yes

—

C₄²×C₅₉

D₄

yes

—

C₄²×C₅₉

Q₈

yes

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

C₂×C₄

yes

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂×C₄

yes

—

C₂³×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₄⋊C₄

yes

—

C₂×C₄×C₅₉

C₂²×C₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₅₉

#41

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

C₄²

yes

—

C₂×Dic₅₉

C₄²

yes

—

C₂×Dic₅₉

M₁₆

yes

—

C₂×Dic₅₉

M₁₆

yes

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₂²×C₅₉

C₂×C₄²

yes

characteristic

C₂²×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₅₉

#117

yes

characteristic

C₂²×C₅₉

C₂×M₁₆

yes

—

C₂²×C₅₉

C₂×M₁₆

yes

—

C₄×C₅₉

—

C₄×C₅₉

C₄×D₄

yes

—

C₄×C₅₉

C₄×Q₈

yes

—

Dic₅₉

—

Dic₅₉

—

Dic₅₉

yes

—

C₂×C₅₉

C₄×C₄⋊C₄

yes

characteristic

C₂×C₅₉

C₂×#97

yes

characteristic

C₂×C₅₉

C₄×M₁₆

yes

characteristic

C₂×C₅₉

#423

yes

—

C₂×C₅₉

#432

yes

—

C₂×C₄⋊C₈

—

C₂×#97

—

C₂×#97

D₅₉

yes

characteristic

C₄³

—

#336

—

C₅₉

#1767

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₅₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

C₄⋊C₈

—

#97

—

#97

—

118

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

—

118

—

C₂×C₈

C₄×D₅₉

yes

—

C₄²

—

C₄²

—

118

—

C₄²

—

118

—

C₄²

—

118

—

C₄²

Dic₁₁₈

yes

—

C₄²

C₂²⋊D₅₉

yes

—

100

C₂³

C₂×C₄×D₅₉

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

118

—

108

C₂×C₄

—

118

—

109

C₂×C₄

—

118

—

110

C₂×C₄

Dic₅₉⋊C₄

yes

—

111

C₂×C₄

C₂×Dic₁₁₈

yes

characteristic

112

C₂×C₄

C₂×C₄×D₅₉

yes

—

113

C₂×C₄

#11745685

yes

—

114

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

115

C₈

—

116

C₈

—

118

—

117

C₂²

C₄²×D₅₉

yes

characteristic

118

C₂²

C₂×Dic₅₉⋊C₄

yes

characteristic

119

C₂²

#14273684

yes

characteristic

120

C₂²

M₁₆×D₅₉

yes

—

121

C₂²

M₁₆×D₅₉

yes

—

122

C₄

—

123

C₄

—

124

C₄

—

118

—

125

C₄

—

118

—

126

C₄

C₄×C₂²⋊D₅₉

yes

—

127

C₄

C₄×Dic₁₁₈

yes

—

128

C₂

C₄×Dic₅₉⋊C₄

yes

characteristic

129

C₂

#97×D₅₉

yes

characteristic

130

C₂

#16837354

yes

characteristic

131

C₂

#16837425

yes

—

132

C₂

#16837457

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₅₉
commutator	C₂²×C₅₉	C₂×C₄²
Fitting	C₂×#97×C₅₉	C₂
socle	C₂³×C₅₉	C₂²×C₄
hypercenter	C₂×#97	D₅₉
hypocenter	C₅₉	#1767
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₅₉

commutator

C₂²×C₅₉

C₂×C₄²

Fitting

C₂×#97×C₅₉

C₂

socle

C₂³×C₅₉

C₂²×C₄

hypercenter

C₂×#97

D₅₉

C₅₉

G ▷ C₂²×C₅₉ ▷ C₅₉

C₁ ◁ C₂²×C₄ ◁ C₂×#97

N	H ≅ G/N	type
11. Dic₅₉⋊C₈	C₄	semidirect
60. Dic₅₉	#97	semidirect
72. C₅₉	#1767	semidirect

H ≅ G/N

type

11. Dic₅₉⋊C₈

C₄

semidirect

60. Dic₅₉

#97

semidirect

72. C₅₉

#1767

semidirect

Subgroups — #21423950

Conjugacy classes of subgroups

Complements