Group #21434839 — subgroups

Subgroups — #21434839

Order 7552.

358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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	#16837957	C₂	1	2	yes	maximal
2	#16837800	C₂	1	1	yes	maximal, characteristic, complemented
3	#16837752	C₂	1	2	yes	maximal, complemented
4	#16837657	C₂	1	4	yes	maximal
5	#16837509	C₂	1	4	yes	maximal, complemented
6	C₄×#11745659	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#494	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11745659	C₂²	1	2	yes	—
9	#14273727	C₂²	1	2	yes	—
10	#14273718	—	2	2	no	—
11	#14273707	—	2	2	no	—
12	#14273703	C₂²	1	4	yes	—
13	Q₈×Dic₅₉	C₂²	1	4	yes	—
14	#14273692	—	2	2	no	—
15	#14273685	—	2	2	no	—
16	C₄²×D₅₉	C₂²	1	1	yes	characteristic
17	#14273659	C₂²	1	4	yes	—
18	#14273651	C₂²	1	8	yes	—
19	#14273637	C₂²	1	2	yes	—
20	C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Q₁₆×C₅₉	C₂²	1	4	yes	—
22	C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
23	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×Q₈×C₅₉	C₂³	1	4	yes	—
25	C₂×C₄×D₅₉	D₄	1	2	yes	—
26	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
27	C₂×Dic₁₁₈	—	2	2	no	—
28	Q₁₆×C₅₉	—	2	8	no	—
29	C₂×C₈×C₅₉	C₂³	1	2	yes	—
30	C₄⋊C₄×C₅₉	—	2	2	no	—
31	C₄⋊C₄×C₅₉	—	2	2	no	—
32	C₄²×C₅₉	C₂³	1	1	yes	characteristic
33	(C₂×D₅₉)⋊C₄	—	2	4	no	—
34	C₄⋊Dic₅₉	—	2	2	no	—
35	C₄⋊Dic₅₉	—	2	4	no	—
36	C₄⋊Dic₅₉	C₂³	1	4	yes	—
37	Dic₅₉⋊C₄	—	2	4	no	—
38	C₄×Dic₅₉	—	2	4	no	—
39	C₄×Dic₅₉	D₄	1	2	yes	—
40	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
41	C₂×C₅₉⋊C₈	C₂³	1	2	yes	—
42	#11745659	—	2	4	no	—
43	C₂²×D₅₉	C₂×D₄	1	1	yes	characteristic
44	Q₈×C₅₉	—	2	8	no	—
45	C₂×C₄×C₅₉	—	2	4	no	—
46	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
48	C₂×Dic₅₉	—	2	4	no	—
49	C₂×Dic₅₉	C₂×D₄	1	2	yes	—
50	C₂×Dic₅₉	C₂×D₄	1	1	yes	characteristic
51	C₄×D₅₉	—	2	4	no	—
52	C₄×D₅₉	—	2	2	no	—
53	Dic₁₁₈	—	4	4	no	—
54	C₈×C₅₉	#41	1	4	yes	—
55	C₅₉⋊C₈	—	2	2	no	—
56	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
57	C₂×D₅₉	—	2	1	no	—
58	C₂×D₅₉	—	2	2	no	—
59	C₄×C₅₉	—	4	4	no	—
60	C₄×C₅₉	#137	1	4	yes	—
61	C₄×C₅₉	C₂×#41	1	2	yes	—
62	Dic₅₉	—	2	1	no	—
63	Dic₅₉	—	2	2	no	—
64	Dic₅₉	—	4	4	no	—
65	#3185	—	59	1	no	maximal, Sylow
66	C₂×C₅₉	#532	1	1	yes	characteristic
67	C₂×C₅₉	C₂×#137	1	2	yes	—
68	D₅₉	—	4	1	no	—
69	#533	—	59	2	no	—
70	#498	—	59	1	no	—
71	#494	D₅₉	1	1	yes	characteristic, complemented
72	#487	—	59	2	no	—
73	#470	—	59	4	no	—
74	#441	—	59	4	no	—
75	C₄×M₁₆	—	59	1	no	—
76	C₅₉	#3185	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₁₆	C₂×D₅₉	1	4	yes	—
78	C₂×M₁₆	—	59	2	no	—
79	C₄⋊Q₈	—	59	2	no	—
80	C₄⋊Q₈	C₂×D₅₉	1	2	yes	—
81	#125	—	118	2	no	—
82	C₂²⋊Q₈	—	59	4	no	—
83	C₂²⋊Q₈	—	118	2	no	—
84	C₄×Q₈	—	59	4	no	—
85	C₄×Q₈	—	118	2	no	—
86	#117	—	118	2	no	—
87	C₂×C₄²	—	59	1	no	—
88	#106	—	59	4	no	—
89	#103	—	59	8	no	—
90	#97	—	59	2	no	—
91	C₄×C₈	—	59	1	no	—
92	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
93	C₂×Q₈	—	118	2	no	—
94	C₂×Q₈	C₂²×D₅₉	1	4	yes	—
95	C₂²×C₄	—	59	2	no	—
96	C₂²×C₄	—	59	1	no	—
97	Q₁₆	—	2	8	no	—
98	M₁₆	—	118	4	no	—
99	C₂×C₈	—	59	2	no	—
100	C₂×C₈	C₂²×D₅₉	1	2	yes	—
101	C₄⋊C₄	—	2	2	no	—
102	C₄⋊C₄	—	2	2	no	—
103	C₄⋊C₄	—	59	4	no	—
104	C₄⋊C₄	—	118	4	no	—
105	C₄⋊C₄	—	118	4	no	—
106	C₄⋊C₄	—	118	2	no	—
107	C₂²⋊C₄	—	118	4	no	—
108	C₄²	—	59	2	no	—
109	C₄²	—	59	1	no	—
110	C₄²	—	118	4	no	—
111	C₄²	C₂²×D₅₉	1	1	yes	characteristic
112	C₂³	—	59	1	no	—
113	Q₈	—	2	8	no	—
114	Q₈	—	236	4	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	59	2	no	—
117	C₂×C₄	—	59	1	no	—
118	C₂×C₄	—	118	4	no	—
119	C₂×C₄	—	118	2	no	—
120	C₂×C₄	—	118	4	no	—
121	C₂×C₄	D₄×D₅₉	1	2	yes	—
122	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
123	C₈	—	118	2	no	—
124	C₈	#11745687	1	4	yes	—
125	C₂²	—	118	2	no	—
126	C₂²	—	118	1	no	—
127	C₂²	C₂×D₄×D₅₉	1	1	yes	characteristic
128	C₄	—	4	4	no	—
129	C₄	—	118	2	no	—
130	C₄	—	118	1	no	—
131	C₄	—	236	4	no	—
132	C₄	#14273759	1	4	yes	—
133	C₄	C₂×#11745687	1	2	yes	—
134	C₂	—	236	1	no	—
135	C₂	#16837950	1	1	yes	characteristic
136	C₂	C₂×#14273759	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16837957

C₂

yes

maximal

#16837800

C₂

yes

maximal, characteristic, complemented

#16837752

C₂

yes

maximal, complemented

#16837657

C₂

yes

maximal

#16837509

C₂

yes

maximal, complemented

C₄×#11745659

C₂

yes

maximal, characteristic

C₅₉×#494

C₂

yes

maximal, characteristic, complemented

C₂×#11745659

C₂²

yes

—

#14273727

C₂²

yes

—

#14273718

—

#14273707

—

#14273703

C₂²

yes

—

Q₈×Dic₅₉

C₂²

yes

—

#14273692

—

#14273685

—

C₄²×D₅₉

C₂²

yes

characteristic

#14273659

C₂²

yes

—

#14273651

C₂²

yes

—

#14273637

C₂²

yes

—

C₄×C₅₉⋊C₈

C₂²

yes

characteristic

C₂×Q₁₆×C₅₉

C₂²

yes

—

C₄⋊Q₈×C₅₉

C₂²

yes

—

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×Q₈×C₅₉

C₂³

yes

—

C₂×C₄×D₅₉

D₄

yes

—

C₂×C₄×D₅₉

C₂³

yes

characteristic

C₂×Dic₁₁₈

—

Q₁₆×C₅₉

—

C₂×C₈×C₅₉

C₂³

yes

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

C₂³

yes

characteristic

(C₂×D₅₉)⋊C₄

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₂³

yes

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

D₄

yes

—

C₄×Dic₅₉

C₂³

yes

characteristic

C₂×C₅₉⋊C₈

C₂³

yes

—

#11745659

—

C₂²×D₅₉

C₂×D₄

yes

characteristic

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂⁴

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

C₂×D₄

yes

—

C₂×Dic₅₉

C₂×D₄

yes

characteristic

C₄×D₅₉

—

C₄×D₅₉

—

Dic₁₁₈

—

C₈×C₅₉

#41

yes

—

C₅₉⋊C₈

—

C₂²×C₅₉

C₂²×D₄

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#137

yes

—

C₄×C₅₉

C₂×#41

yes

—

Dic₅₉

—

Dic₅₉

—

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

yes

—

D₅₉

—

#533

—

#498

—

#494

D₅₉

yes

characteristic, complemented

#487

—

#470

—

#441

—

C₄×M₁₆

—

C₅₉

#3185

yes

characteristic, complemented, Sylow

C₂×Q₁₆

C₂×D₅₉

yes

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₅₉

yes

—

#125

—

118

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

118

—

C₄×Q₈

—

C₄×Q₈

—

118

—

#117

—

118

—

C₂×C₄²

—

#106

—

#103

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₅₉

yes

characteristic

C₂×Q₈

—

118

—

C₂×Q₈

C₂²×D₅₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

Q₁₆

—

M₁₆

—

118

—

C₂×C₈

—

100

C₂×C₈

C₂²×D₅₉

yes

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

118

—

105

C₄⋊C₄

—

118

—

106

C₄⋊C₄

—

118

—

107

C₂²⋊C₄

—

118

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

118

—

111

C₄²

C₂²×D₅₉

yes

characteristic

112

C₂³

—

113

Q₈

—

114

Q₈

—

236

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

118

—

119

C₂×C₄

—

118

—

120

C₂×C₄

—

118

—

121

C₂×C₄

D₄×D₅₉

yes

—

122

C₂×C₄

C₂³×D₅₉

yes

characteristic

123

C₈

—

118

—

124

C₈

#11745687

yes

—

125

C₂²

—

118

—

126

C₂²

—

118

—

127

C₂²

C₂×D₄×D₅₉

yes

characteristic

128

C₄

—

129

C₄

—

118

—

130

C₄

—

118

—

131

C₄

—

236

—

132

C₄

#14273759

yes

—

133

C₄

C₂×#11745687

yes

—

134

C₂

—

236

—

135

C₂

#16837950

yes

characteristic

136

C₂

C₂×#14273759

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₅₉×#494	C₂
socle	C₂²×C₅₉	C₂²×D₄
hypercenter	#494	D₅₉
hypocenter	C₅₉	#3185
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

C₂×D₄×D₅₉

commutator

C₂×C₄×C₅₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₉

Fitting

C₅₉×#494

C₂

socle

C₂²×C₅₉

C₂²×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
2. #16837800	C₂	semidirect
3. #16837752	C₂	semidirect
5. #16837509	C₂	semidirect
7. C₅₉×#494	C₂	semidirect
71. #494	D₅₉	semidirect
76. C₅₉	#3185	semidirect

H ≅ G/N

type

2. #16837800

C₂

semidirect

3. #16837752

C₂

semidirect

5. #16837509

C₂

semidirect

7. C₅₉×#494

C₂

semidirect

71. #494

D₅₉

semidirect

76. C₅₉

#3185

semidirect

Subgroups — #21434839

Conjugacy classes of subgroups

Complements