Group #21425584 — subgroups

Subgroups — #21425584

Order 7552.

224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14273661	C₂	1	1	yes	maximal, characteristic
2	#16837300	C₂	1	2	yes	maximal
3	#16837165	C₂	1	2	yes	maximal
4	#16837165	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊C₈×C₅₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
8	C₂×Dic₅₉⋊C₄	—	2	2	no	—
9	#14273661	—	2	2	no	—
10	C₅₉⋊#95	—	2	2	no	—
11	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₅₉	—	2	2	no	—
15	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
18	C₂²×Dic₅₉	—	2	2	no	—
19	C₂²×Dic₅₉	—	2	2	no	—
20	C₂×C₈×C₅₉	—	2	2	no	—
21	C₂×C₈×C₅₉	—	2	1	no	—
22	C₂×C₈×C₅₉	—	2	2	no	—
23	C₂×C₈×C₅₉	D₄	1	2	yes	—
24	C₄²×C₅₉	—	2	1	no	—
25	C₄²×C₅₉	—	2	1	no	—
26	C₄⋊Dic₅₉	—	2	2	no	—
27	C₄⋊Dic₅₉	—	2	2	no	—
28	C₄⋊Dic₅₉	—	2	2	no	—
29	C₄⋊Dic₅₉	Q₈	1	4	yes	—
30	Dic₅₉⋊C₄	—	4	4	no	—
31	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₅₉	—	2	1	no	—
33	C₂×C₄×C₅₉	—	2	1	no	—
34	C₂×C₄×C₅₉	—	2	1	no	—
35	C₂×C₄×C₅₉	—	2	2	no	—
36	C₂×C₄×C₅₉	D₈	1	2	yes	—
37	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
39	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
40	C₂×C₄×C₅₉	#41	1	2	yes	—
41	C₂×Dic₅₉	—	2	4	no	—
42	C₂×Dic₅₉	—	4	2	no	—
43	C₂×Dic₅₉	—	4	2	no	—
44	C₂×Dic₅₉	—	4	2	no	—
45	C₂×Dic₅₉	—	4	2	no	—
46	C₂×Dic₅₉	—	4	2	no	—
47	C₈×C₅₉	—	2	2	no	—
48	C₈×C₅₉	—	4	1	no	—
49	C₂²×C₅₉	#121	1	1	yes	characteristic
50	C₂²×C₅₉	C₂²⋊Q₈	1	2	yes	—
51	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
52	C₂²×C₅₉	#135	1	1	yes	characteristic
53	C₂²×C₅₉	#137	1	2	yes	—
54	C₄×C₅₉	—	2	2	no	—
55	C₄×C₅₉	—	4	1	no	—
56	C₄×C₅₉	#123	1	1	yes	characteristic
57	C₄×C₅₉	#125	1	2	yes	—
58	C₄×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
59	Dic₅₉	—	4	4	no	—
60	Dic₅₉	—	8	2	no	—
61	#2086	—	59	1	no	maximal, Sylow
62	C₂×C₅₉	#398	1	1	yes	characteristic
63	C₂×C₅₉	#466	1	1	yes	characteristic
64	C₂×C₅₉	#470	1	1	yes	characteristic
65	C₂×C₅₉	#474	1	2	yes	—
66	C₂×C₅₉	#479	1	2	yes	—
67	C₂×#107	—	59	1	no	—
68	C₂×C₄⋊C₈	D₅₉	1	1	yes	characteristic
69	#389	—	59	2	no	—
70	#340	—	59	1	no	—
71	#340	—	59	2	no	—
72	C₅₉	#2086	1	1	yes	characteristic, complemented, Sylow
73	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
74	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
75	C₂×C₄⋊C₄	—	59	2	no	—
76	C₂×C₄⋊C₄	—	59	2	no	—
77	C₂×C₄⋊C₄	—	118	2	no	—
78	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
79	#107	—	118	2	no	—
80	C₄⋊C₈	—	2	2	no	—
81	#95	—	118	2	no	—
82	C₂²×C₄	—	118	2	no	—
83	C₂²×C₄	—	118	2	no	—
84	C₂²×C₄	D₂₃₆	1	1	yes	characteristic
85	C₂²×C₄	D₂₃₆	1	1	yes	characteristic
86	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	2	1	no	—
90	C₂×C₈	C₂²⋊D₅₉	1	2	yes	—
91	C₄⋊C₄	—	59	4	no	—
92	C₄⋊C₄	—	118	2	no	—
93	C₄⋊C₄	—	118	2	no	—
94	C₄⋊C₄	—	118	2	no	—
95	C₄⋊C₄	—	236	4	no	—
96	C₄²	—	2	1	no	—
97	C₄²	—	2	1	no	—
98	C₂³	C₂×D₂₃₆	1	1	yes	characteristic
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	118	4	no	—
104	C₂×C₄	—	236	2	no	—
105	C₂×C₄	—	236	2	no	—
106	C₂×C₄	—	236	2	no	—
107	C₂×C₄	—	236	2	no	—
108	C₂×C₄	—	236	2	no	—
109	C₂×C₄	D₄₇₂	1	2	yes	—
110	C₂×C₄	#11745685	1	1	yes	characteristic
111	C₂×C₄	#11745687	1	2	yes	—
112	C₂×C₄	Q₈×D₅₉	1	2	yes	—
113	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	4	1	no	—
116	C₂²	#14273701	1	1	yes	characteristic
117	C₂²	#14273707	1	2	yes	—
118	C₂²	C₂×D₄₇₂	1	1	yes	characteristic
119	C₂²	#14273749	1	1	yes	characteristic
120	C₂²	#14273760	1	2	yes	—
121	C₄	—	2	2	no	—
122	C₄	—	4	1	no	—
123	C₄	—	472	2	no	—
124	C₄	—	236	4	no	—
125	C₄	#14273708	1	1	yes	characteristic
126	C₄	#14273717	1	2	yes	—
127	C₄	#14273725	1	1	yes	characteristic
128	C₂	#16837332	1	1	yes	characteristic
129	C₂	#16837638	1	1	yes	characteristic
130	C₂	#16837660	1	1	yes	characteristic
131	C₂	#16837683	1	2	yes	—
132	C₂	#16837710	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273661

C₂

yes

maximal, characteristic

#16837300

C₂

yes

maximal

#16837165

C₂

yes

maximal

#16837165

C₂

yes

maximal, characteristic

C₂×C₄⋊C₈×C₅₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×Dic₅₉⋊C₄

—

#14273661

—

C₅₉⋊#95

—

C₂²×C₈×C₅₉

C₂²

yes

characteristic

C₂²×C₈×C₅₉

C₂²

yes

characteristic

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₄⋊C₈×C₅₉

—

C₂²×C₄×C₅₉

D₄

yes

characteristic

C₂²×C₄×C₅₉

D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

D₄

yes

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

Q₈

yes

—

Dic₅₉⋊C₄

—

C₂³×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

D₈

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₈

yes

—

C₂×C₄×C₅₉

#41

yes

characteristic

C₂×C₄×C₅₉

#41

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₂²×C₅₉

#121

yes

characteristic

C₂²×C₅₉

C₂²⋊Q₈

yes

—

C₂²×C₅₉

C₂×D₈

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#123

yes

characteristic

C₄×C₅₉

#125

yes

—

C₄×C₅₉

C₄⋊Q₈

yes

characteristic

Dic₅₉

—

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×C₅₉

#479

yes

—

C₂×#107

—

C₂×C₄⋊C₈

D₅₉

yes

—

—

—

C₅₉

#2086

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₅₉

yes

characteristic

C₂²×C₈

C₂×D₅₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

118

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

#107

—

118

—

C₄⋊C₈

—

#95

—

118

—

C₂²×C₄

—

118

—

C₂²×C₄

—

118

—

C₂²×C₄

D₂₃₆

yes

characteristic

C₂²×C₄

D₂₃₆

yes

characteristic

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₅₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

236

—

C₄²

—

C₄²

—

C₂³

C₂×D₂₃₆

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

118

—

104

C₂×C₄

—

236

—

105

C₂×C₄

—

236

—

106

C₂×C₄

—

236

—

107

C₂×C₄

—

236

—

108

C₂×C₄

—

236

—

109

C₂×C₄

D₄₇₂

yes

—

110

C₂×C₄

#11745685

yes

characteristic

111

C₂×C₄

#11745687

yes

—

112

C₂×C₄

Q₈×D₅₉

yes

—

113

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

114

C₈

—

115

C₈

—

116

C₂²

#14273701

yes

characteristic

117

C₂²

#14273707

yes

—

118

C₂²

C₂×D₄₇₂

yes

characteristic

119

C₂²

#14273749

yes

characteristic

120

C₂²

#14273760

yes

—

121

C₄

—

122

C₄

—

123

C₄

—

472

—

124

C₄

—

236

—

125

C₄

#14273708

yes

characteristic

126

C₄

#14273717

yes

—

127

C₄

#14273725

yes

characteristic

128

C₂

#16837332

yes

characteristic

129

C₂

#16837638

yes

characteristic

130

C₂

#16837660

yes

characteristic

131

C₂

#16837683

yes

—

132

C₂

#16837710

yes

—

	subgroup	G/H
center	C₂³	C₂×D₂₃₆
commutator	C₂²×C₄×C₅₉	C₂³
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₂×C₄⋊C₈×C₅₉	C₂
socle	C₂³×C₅₉	C₂×D₄
hypercenter	C₂×C₄⋊C₈	D₅₉
hypocenter	C₅₉	#2086
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂³

C₂×D₂₃₆

commutator

C₂²×C₄×C₅₉

C₂³

Frattini

C₂²×C₄

C₂²×D₅₉

Fitting

C₂×C₄⋊C₈×C₅₉

C₂

socle

C₂³×C₅₉

C₂×D₄

hypercenter

C₂×C₄⋊C₈

D₅₉

hypocenter

C₅₉

#2086

LCS

G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
72. C₅₉	#2086	semidirect

H ≅ G/N

type

72. C₅₉

#2086

semidirect

Subgroups — #21425584

Conjugacy classes of subgroups

Complements