Group #32979639 — subgroups

Subgroups — #32979639

Order 18688.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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	#22609684	C₂	1	1	yes	maximal, characteristic
2	#22608677	C₂	1	2	yes	maximal
3	#22607776	C₂	1	1	yes	maximal, characteristic
4	#22607759	C₂	1	2	yes	maximal
5	C₇₃×#1281	C₂	1	1	yes	maximal, characteristic
6	#17988640	C₂²	1	2	yes	—
7	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
8	#17988433	C₂²	1	1	yes	characteristic
9	#17988341	C₄	1	2	yes	—
10	#17988341	C₄	1	2	yes	—
11	#17988339	—	2	2	no	—
12	#17988337	—	2	2	no	—
13	#431×C₇₃	C₂²	1	2	yes	—
14	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
15	C₂²×#10596831	C₂×C₄	1	2	yes	—
16	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
18	C₄⋊#10596831	—	2	2	no	—
19	C₂²⋊#10596831	—	2	2	no	—
20	C₄×#10596831	—	2	2	no	—
21	C₄×#10596831	D₄	1	2	yes	—
22	C₄×#10596831	Q₈	1	2	yes	—
23	#14556498	—	2	2	no	—
24	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
26	C₄⋊C₈×C₇₃	—	2	2	no	—
27	C₂²⋊C₈×C₇₃	—	2	2	no	—
28	#97×C₇₃	—	2	2	no	—
29	C₄×C₈×C₇₃	—	2	2	no	—
30	C₂²×Dic₇₃	—	2	1	no	—
31	C₂²×Dic₇₃	—	2	1	no	—
32	C₂×#10596831	—	2	2	no	—
33	C₂×#10596831	—	2	2	no	—
34	C₂×#10596831	—	4	2	no	—
35	C₂×#10596831	C₄⋊C₄	1	4	yes	—
36	C₄×Dic₇₃	—	2	2	no	—
37	C₄×Dic₇₃	—	2	2	no	—
38	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₇₃	#41	1	2	yes	—
40	C₂×C₈×C₇₃	—	2	2	no	—
41	C₂×C₈×C₇₃	—	2	2	no	—
42	C₂×C₈×C₇₃	—	2	2	no	—
43	C₂×C₈×C₇₃	—	4	2	no	—
44	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
45	C₄²×C₇₃	C₂×Q₈	1	1	yes	characteristic
46	C₄²×C₇₃	#41	1	2	yes	—
47	C₂³×C₇₃	#117	1	1	yes	characteristic
48	C₂×C₄×C₇₃	—	4	2	no	—
49	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
51	C₂×C₄×C₇₃	#124	1	2	yes	—
52	C₂×C₄×C₇₃	#125	1	2	yes	—
53	C₂×C₄×C₇₃	#131	1	2	yes	—
54	C₂×C₄×C₇₃	#131	1	2	yes	—
55	C₂×Dic₇₃	—	4	2	no	—
56	C₂×Dic₇₃	—	4	2	no	—
57	C₂×Dic₇₃	—	4	1	no	—
58	C₂×Dic₇₃	—	4	1	no	—
59	C₈×C₇₃	—	4	2	no	—
60	C₈×C₇₃	—	8	2	no	—
61	#10596831	—	2	4	no	—
62	#10596831	—	8	2	no	—
63	C₂²×C₇₃	—	2	2	no	—
64	C₂²×C₇₃	#382	1	1	yes	characteristic
65	C₂²×C₇₃	#433	1	1	yes	characteristic
66	C₂²×C₇₃	#433	1	1	yes	characteristic
67	C₄×C₇₃	—	2	2	no	—
68	C₄×C₇₃	—	2	2	no	—
69	C₄×C₇₃	#424	1	2	yes	—
70	C₄×C₇₃	#433	1	2	yes	—
71	Dic₇₃	—	8	1	no	—
72	Dic₇₃	—	8	1	no	—
73	#8783	—	73	1	no	maximal, Sylow
74	C₂×C₇₃	—	2	1	no	—
75	C₂×C₇₃	—	2	1	no	—
76	C₂×C₇₃	#1832	1	1	yes	characteristic
77	C₂×C₇₃	#1833	1	2	yes	—
78	#1746	—	73	1	no	—
79	#1564	—	73	2	no	—
80	#1281	—	73	1	no	—
81	#1281	D₇₃	1	1	yes	characteristic
82	#1274	—	73	2	no	—
83	C₇₃	#8783	1	1	yes	characteristic, complemented, Sylow
84	#431	—	73	2	no	—
85	#431	C₂×D₇₃	1	2	yes	—
86	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
87	C₂×C₄×C₈	—	73	1	no	—
88	#376	—	73	1	no	—
89	#336	—	73	2	no	—
90	#336	—	73	2	no	—
91	#335	—	146	2	no	—
92	#334	—	146	2	no	—
93	C₂²×C₈	—	73	2	no	—
94	C₂²×C₈	C₄×D₇₃	1	2	yes	—
95	C₂×C₄²	—	73	1	no	—
96	C₂×C₄²	—	73	1	no	—
97	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
98	C₄⋊C₈	—	2	2	no	—
99	C₄⋊C₈	—	146	2	no	—
100	C₂²⋊C₈	—	2	2	no	—
101	C₂²⋊C₈	—	146	2	no	—
102	#97	—	2	2	no	—
103	C₄×C₈	—	2	2	no	—
104	C₄×C₈	—	73	2	no	—
105	C₄×C₈	—	73	2	no	—
106	C₄×C₈	—	146	2	no	—
107	#95	—	146	2	no	—
108	C₂²×C₄	—	146	1	no	—
109	C₂²×C₄	—	146	1	no	—
110	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
111	C₂²×C₄	#11924028	1	2	yes	—
112	C₂×C₈	—	2	2	no	—
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	—	2	2	no	—
115	C₂×C₈	—	4	2	no	—
116	C₂×C₈	—	292	2	no	—
117	C₂×C₈	—	73	4	no	—
118	C₂×C₈	—	146	2	no	—
119	C₂×C₈	—	146	2	no	—
120	C₄²	—	146	2	no	—
121	C₄²	—	146	2	no	—
122	C₄²	D₄×D₇₃	1	1	yes	characteristic
123	C₄²	Q₈×D₇₃	1	1	yes	characteristic
124	C₄²	#11924027	1	2	yes	—
125	C₂³	#14556548	1	1	yes	characteristic
126	C₂×C₄	—	4	2	no	—
127	C₂×C₄	—	292	2	no	—
128	C₂×C₄	—	292	2	no	—
129	C₂×C₄	—	292	1	no	—
130	C₂×C₄	—	292	1	no	—
131	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
132	C₂×C₄	#14556547	1	1	yes	characteristic
133	C₂×C₄	#14556577	1	2	yes	—
134	C₂×C₄	#14556581	1	2	yes	—
135	C₂×C₄	#14556597	1	2	yes	—
136	C₂×C₄	#14556599	1	2	yes	—
137	C₈	—	4	2	no	—
138	C₈	—	8	2	no	—
139	C₈	—	584	2	no	—
140	C₈	—	146	4	no	—
141	C₂²	—	2	2	no	—
142	C₂²	#17988451	1	1	yes	characteristic
143	C₂²	#17988646	1	1	yes	characteristic
144	C₂²	#17988649	1	1	yes	characteristic
145	C₄	—	2	2	no	—
146	C₄	—	2	2	no	—
147	C₄	—	584	1	no	—
148	C₄	—	584	1	no	—
149	C₄	#17988612	1	2	yes	—
150	C₄	#17988645	1	2	yes	—
151	C₂	—	2	1	no	—
152	C₂	—	2	1	no	—
153	C₂	#22610049	1	1	yes	characteristic
154	C₂	#22610052	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22609684

C₂

yes

maximal, characteristic

#22608677

C₂

yes

maximal

#22607776

C₂

yes

maximal, characteristic

#22607759

C₂

yes

maximal

C₇₃×#1281

C₂

yes

maximal, characteristic

#17988640

C₂²

yes

—

C₂×C₄×#10596831

C₂²

yes

characteristic

#17988433

C₂²

yes

characteristic

#17988341

C₄

yes

—

#17988341

C₄

yes

—

#17988339

—

#17988337

—

#431×C₇₃

C₂²

yes

—

C₂×#97×C₇₃

C₂²

yes

characteristic

C₂²×#10596831

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₇₃

C₂×C₄

yes

—

—

—

D₄

yes

—

C₄×#10596831

Q₈

yes

—

#14556498

—

C₂²×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

#97×C₇₃

—

C₄×C₈×C₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

—

—

—

C₄⋊C₄

yes

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₃

#41

yes

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

C₂×Q₈

yes

characteristic

C₄²×C₇₃

#41

yes

—

C₂³×C₇₃

#117

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

—

C₂×C₄×C₇₃

#125

yes

—

C₂×C₄×C₇₃

#131

yes

—

C₂×C₄×C₇₃

#131

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#424

yes

—

C₄×C₇₃

#433

yes

—

Dic₇₃

—

Dic₇₃

—

#8783

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#1832

yes

characteristic

C₂×C₇₃

#1833

yes

—

—

—

—

D₇₃

yes

characteristic

#1274

—

C₇₃

#8783

yes

characteristic, complemented, Sylow

#431

—

#431

C₂×D₇₃

yes

—

C₂×#97

C₂×D₇₃

yes

characteristic

C₂×C₄×C₈

—

—

—

—

—

146

—

#334

—

146

—

C₂²×C₈

—

C₂²×C₈

C₄×D₇₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₇₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

146

—

100

C₂²⋊C₈

—

101

C₂²⋊C₈

—

146

—

102

#97

—

103

C₄×C₈

—

104

C₄×C₈

—

105

C₄×C₈

—

106

C₄×C₈

—

146

—

107

#95

—

146

—

108

C₂²×C₄

—

146

—

109

C₂²×C₄

—

146

—

110

C₂²×C₄

C₂×C₄×D₇₃

yes

characteristic

111

C₂²×C₄

#11924028

yes

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

292

—

117

C₂×C₈

—

118

C₂×C₈

—

146

—

119

C₂×C₈

—

146

—

120

C₄²

—

146

—

121

C₄²

—

146

—

122

C₄²

D₄×D₇₃

yes

characteristic

123

C₄²

Q₈×D₇₃

yes

characteristic

124

C₄²

#11924027

yes

—

125

C₂³

#14556548

yes

characteristic

126

C₂×C₄

—

127

C₂×C₄

—

292

—

128

C₂×C₄

—

292

—

129

C₂×C₄

—

292

—

130

C₂×C₄

—

292

—

131

C₂×C₄

C₄⋊C₄×D₇₃

yes

characteristic

132

C₂×C₄

#14556547

yes

characteristic

133

C₂×C₄

#14556577

yes

—

134

C₂×C₄

#14556581

yes

—

135

C₂×C₄

#14556597

yes

—

136

C₂×C₄

#14556599

yes

—

137

C₈

—

138

C₈

—

139

C₈

—

584

—

140

C₈

—

146

—

141

C₂²

—

142

C₂²

#17988451

yes

characteristic

143

C₂²

#17988646

yes

characteristic

144

C₂²

#17988649

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

584

—

148

C₄

—

584

—

149

C₄

#17988612

yes

—

150

C₄

#17988645

yes

—

151

C₂

—

152

C₂

—

153

C₂

#22610049

yes

characteristic

154

C₂

#22610052

yes

—

	subgroup	G/H
center	C₂×C₄	#14556547
commutator	C₂²×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1281	C₂
socle	C₂²×C₇₃	#382
prime radical	C₂³×C₇₃	#117
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1281	D₇₃
hypocenter	C₇₃	#8783
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1281

subgroup

G/H

center

C₂×C₄

#14556547

commutator

C₂²×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1281

C₂

C₂²×C₇₃

C₂³×C₇₃

C₂×C₄²×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1281

N	H ≅ G/N	type
83. C₇₃	#8783	semidirect

H ≅ G/N

type

83. C₇₃

#8783

semidirect

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

subgroup	index
#22609684	2
#22608677	2
#22607776	2
#22607759	2
C₇₃×#1281	2
#8783	73

subgroup

index

C₇₃×#1281

Subgroups — #32979639

Conjugacy classes of subgroups

Complements

Maximal subgroups