Group #32973704 — subgroups

Subgroups — #32973704

Order 18688.

162 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 91 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×#17988421	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988417	C₂	1	1	yes	maximal, characteristic
3	C₂×#368×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#14556527	—	2	1	no	—
5	#17988421	—	2	1	no	—
6	#17988421	C₄	1	2	yes	—
7	C₂×#14556497	—	2	1	no	—
8	#17988417	—	2	1	no	—
9	#17988417	C₄	1	2	yes	—
10	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
11	C₂×#108×C₇₃	—	2	1	no	—
12	#368×C₇₃	—	2	1	no	—
13	#368×C₇₃	C₄	1	2	yes	—
14	C₂×#11924012	—	4	1	no	—
15	#14556527	—	2	2	no	—
16	#14556527	—	4	1	no	—
17	#14556497	—	2	2	no	—
18	C₂×M₁₆×C₇₃	—	4	1	no	—
19	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
20	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
24	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
25	C₂×C₁₆×C₇₃	Q₈	1	1	yes	characteristic
26	#108×C₇₃	—	2	2	no	—
27	#108×C₇₃	—	4	1	no	—
28	#11924012	—	4	2	no	—
29	#11924012	—	8	1	no	—
30	C₂×#10596831	—	8	1	no	—
31	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
32	M₁₆×C₇₃	—	4	2	no	—
33	M₁₆×C₇₃	—	8	1	no	—
34	C₂×C₈×C₇₃	—	8	1	no	—
35	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₇₃	SD₁₆	1	1	yes	characteristic
39	C₂×C₈×C₇₃	SD₁₆	1	1	yes	characteristic
40	C₂×C₈×C₇₃	Q₁₆	1	1	yes	characteristic
41	C₁₆×C₇₃	C₄²	1	1	yes	characteristic
42	C₁₆×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
43	C₁₆×C₇₃	C₄⋊C₄	1	1	yes	characteristic
44	C₁₆×C₇₃	C₄⋊C₄	1	1	yes	characteristic
45	C₂³×C₇₃	Q₃₂	1	1	yes	characteristic
46	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
47	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
48	C₂×C₄×C₇₃	#107	1	1	yes	characteristic
49	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
50	C₂×C₄×C₇₃	SD₃₂	1	1	yes	characteristic
51	C₂×C₄×C₇₃	SD₃₂	1	1	yes	characteristic
52	C₈×C₇₃	—	8	2	no	—
53	C₈×C₇₃	#95	1	1	yes	characteristic
54	C₈×C₇₃	#103	1	1	yes	characteristic
55	C₈×C₇₃	#103	1	1	yes	characteristic
56	C₈×C₇₃	#106	1	1	yes	characteristic
57	#10596831	—	8	2	no	—
58	C₂²×C₇₃	—	4	1	no	—
59	C₂²×C₇₃	#358	1	1	yes	characteristic
60	C₂²×C₇₃	#358	1	1	yes	characteristic
61	C₂²×C₇₃	#366	1	1	yes	characteristic
62	C₄×C₇₃	#340	1	1	yes	characteristic
63	C₄×C₇₃	#357	1	1	yes	characteristic
64	C₄×C₇₃	#357	1	1	yes	characteristic
65	C₄×C₇₃	#367	1	1	yes	characteristic
66	#7479	—	73	1	no	maximal, Sylow
67	C₂×C₇₃	—	2	1	no	—
68	C₂×C₇₃	—	2	1	no	—
69	C₂×C₇₃	—	2	1	no	—
70	C₂×C₇₃	#1380	1	1	yes	characteristic
71	C₂×M₆₄	—	73	1	no	—
72	C₂×#368	—	73	1	no	—
73	C₂×#368	D₇₃	1	1	yes	characteristic
74	C₇₃	#7479	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
76	C₂×#108	—	2	1	no	—
77	C₂×#108	—	146	1	no	—
78	M₆₄	—	73	2	no	—
79	M₆₄	—	146	1	no	—
80	C₂×C₃₂	—	146	1	no	—
81	#368	—	2	1	no	—
82	#368	—	73	2	no	—
83	#368	—	146	1	no	—
84	#368	Dic₇₃	1	2	yes	—
85	C₂×M₁₆	—	4	1	no	—
86	C₂×M₁₆	—	292	1	no	—
87	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
88	C₂×C₁₆	Dic₁₄₆	1	1	yes	characteristic
89	C₂×C₁₆	C₄×D₇₃	1	1	yes	characteristic
90	C₂×C₁₆	C₄×D₇₃	1	1	yes	characteristic
91	C₂×C₁₆	D₂₉₂	1	1	yes	characteristic
92	C₂×C₁₆	C₂×Dic₇₃	1	1	yes	characteristic
93	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
94	#108	—	2	2	no	—
95	#108	—	4	1	no	—
96	#108	—	292	1	no	—
97	#108	—	146	2	no	—
98	C₃₂	—	146	2	no	—
99	C₂²×C₄	#11924013	1	1	yes	characteristic
100	M₁₆	—	4	2	no	—
101	M₁₆	—	8	1	no	—
102	M₁₆	—	292	2	no	—
103	M₁₆	—	584	1	no	—
104	C₂×C₈	—	8	1	no	—
105	C₂×C₈	—	584	1	no	—
106	C₂×C₈	#11924005	1	1	yes	characteristic
107	C₂×C₈	C₂²⋊Dic₇₃	1	1	yes	characteristic
108	C₂×C₈	#11924007	1	1	yes	characteristic
109	C₂×C₈	#11924015	1	1	yes	characteristic
110	C₂×C₈	#11924016	1	1	yes	characteristic
111	C₂×C₈	#11924018	1	1	yes	characteristic
112	C₁₆	C₄×Dic₇₃	1	1	yes	characteristic
113	C₁₆	#11924005	1	1	yes	characteristic
114	C₁₆	#11924007	1	1	yes	characteristic
115	C₁₆	C₄⋊Dic₇₃	1	1	yes	characteristic
116	C₂³	#14556537	1	1	yes	characteristic
117	C₂×C₄	#14556511	1	1	yes	characteristic
118	C₂×C₄	#14556512	1	1	yes	characteristic
119	C₂×C₄	#14556524	1	1	yes	characteristic
120	C₂×C₄	#14556532	1	1	yes	characteristic
121	C₂×C₄	#14556534	1	1	yes	characteristic
122	C₂×C₄	#14556535	1	1	yes	characteristic
123	C₈	—	8	2	no	—
124	C₈	—	584	2	no	—
125	C₈	#14556498	1	1	yes	characteristic
126	C₈	#14556514	1	1	yes	characteristic
127	C₈	#14556515	1	1	yes	characteristic
128	C₈	#14556522	1	1	yes	characteristic
129	C₂²	—	4	1	no	—
130	C₂²	#17988390	1	1	yes	characteristic
131	C₂²	#17988391	1	1	yes	characteristic
132	C₂²	#17988412	1	1	yes	characteristic
133	C₄	#17988349	1	1	yes	characteristic
134	C₄	#17988387	1	1	yes	characteristic
135	C₄	#17988388	1	1	yes	characteristic
136	C₄	#17988414	1	1	yes	characteristic
137	C₂	—	2	1	no	—
138	C₂	—	2	1	no	—
139	C₂	—	2	1	no	—
140	C₂	#22608022	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988421

C₂

yes

maximal, characteristic

C₂×#17988417

C₂

yes

maximal, characteristic

C₂×#368×C₇₃

C₂

yes

maximal, characteristic

C₂×#14556527

—

#17988421

—

#17988421

C₄

yes

—

C₂×#14556497

—

#17988417

—

#17988417

C₄

yes

—

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×#108×C₇₃

—

#368×C₇₃

—

#368×C₇₃

C₄

yes

—

—

—

—

—

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

Q₈

yes

characteristic

#108×C₇₃

—

#108×C₇₃

—

#11924012

—

#11924012

—

C₂×#10596831

—

C₂²×C₄×C₇₃

D₈

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₈×C₇₃

SD₁₆

yes

characteristic

C₂×C₈×C₇₃

SD₁₆

yes

characteristic

C₂×C₈×C₇₃

Q₁₆

yes

characteristic

C₁₆×C₇₃

C₄²

yes

characteristic

C₁₆×C₇₃

C₂²⋊C₄

yes

characteristic

C₁₆×C₇₃

C₄⋊C₄

yes

characteristic

C₁₆×C₇₃

C₄⋊C₄

yes

characteristic

C₂³×C₇₃

Q₃₂

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

D₁₆

yes

characteristic

C₂×C₄×C₇₃

SD₃₂

yes

characteristic

C₂×C₄×C₇₃

SD₃₂

yes

characteristic

C₈×C₇₃

—

C₈×C₇₃

yes

C₈×C₇₃

yes

C₈×C₇₃

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#1380

yes

characteristic

C₂×M₆₄

—

C₂×#368

—

C₂×#368

D₇₃

yes

characteristic

C₇₃

#7479

yes

characteristic, complemented, Sylow

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

C₂×#108

—

C₂×#108

—

146

—

M₆₄

—

M₆₄

—

146

—

C₂×C₃₂

—

146

—

#368

—

#368

—

#368

—

146

—

#368

Dic₇₃

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

292

—

C₂²×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₁₆

Dic₁₄₆

yes

characteristic

C₂×C₁₆

C₄×D₇₃

yes

characteristic

C₂×C₁₆

C₄×D₇₃

yes

characteristic

C₂×C₁₆

D₂₉₂

yes

characteristic

C₂×C₁₆

C₂×Dic₇₃

yes

characteristic

C₂×C₁₆

C₂²⋊D₇₃

yes

—

—

—

292

—

#108

—

146

—

C₃₂

—

146

—

C₂²×C₄

#11924013

yes

characteristic

100

M₁₆

—

101

M₁₆

—

102

M₁₆

—

292

—

103

M₁₆

—

584

—

104

C₂×C₈

—

105

C₂×C₈

—

584

—

106

C₂×C₈

#11924005

yes

characteristic

107

C₂×C₈

C₂²⋊Dic₇₃

yes

characteristic

108

C₂×C₈

#11924007

yes

characteristic

109

C₂×C₈

#11924015

yes

characteristic

110

C₂×C₈

#11924016

yes

characteristic

111

C₂×C₈

#11924018

yes

characteristic

112

C₁₆

C₄×Dic₇₃

yes

characteristic

113

C₁₆

#11924005

yes

characteristic

114

C₁₆

#11924007

yes

characteristic

115

C₁₆

C₄⋊Dic₇₃

yes

characteristic

116

C₂³

#14556537

yes

characteristic

117

C₂×C₄

#14556511

yes

characteristic

118

C₂×C₄

#14556512

yes

characteristic

119

C₂×C₄

#14556524

yes

characteristic

120

C₂×C₄

#14556532

yes

characteristic

121

C₂×C₄

#14556534

yes

characteristic

122

C₂×C₄

#14556535

yes

characteristic

123

C₈

—

124

C₈

—

584

—

125

C₈

#14556498

yes

characteristic

126

C₈

#14556514

yes

characteristic

127

C₈

#14556515

yes

characteristic

128

C₈

#14556522

yes

characteristic

129

C₂²

—

130

C₂²

#17988390

yes

characteristic

131

C₂²

#17988391

yes

characteristic

132

C₂²

#17988412

yes

characteristic

133

C₄

#17988349

yes

characteristic

134

C₄

#17988387

yes

characteristic

135

C₄

#17988388

yes

characteristic

136

C₄

#17988414

yes

characteristic

137

C₂

—

138

C₂

—

139

C₂

—

140

C₂

#22608022

yes

characteristic

	subgroup	G/H
center	C₄	#17988388
commutator	C₁₆×C₇₃	C₄²
Frattini	C₂²×C₁₆	C₂×D₇₃
Fitting	C₂×#368×C₇₃	C₂
socle	C₂×C₇₃	#1380
prime radical	C₂³×C₇₃	Q₃₂
cosocle	C₂²×C₁₆×C₇₃	C₂²
hypercenter	C₂×#368	D₇₃
hypocenter	C₇₃	#7479
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×#368

subgroup

G/H

center

C₄

#17988388

commutator

C₁₆×C₇₃

C₄²

Frattini

C₂²×C₁₆

C₂×D₇₃

Fitting

C₂×#368×C₇₃

C₂

socle

C₂×C₇₃

#1380

prime radical

C₂³×C₇₃

Q₃₂

cosocle

C₂²×C₁₆×C₇₃

C₂²

D₇₃

C₇₃

G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×#368

N	H ≅ G/N	type
74. C₇₃	#7479	semidirect

H ≅ G/N

type

74. C₇₃

#7479

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#17988421	2
C₂×#17988417	2
C₂×#368×C₇₃	2
#7479	73

subgroup

index

C₂×#17988421

C₂×#17988417

C₂×#368×C₇₃

#7479

Subgroups — #32973704

Conjugacy classes of subgroups

Complements

Maximal subgroups