Finite Group Databasebeta

← #19133525

Subgroups — #19133525

Order 5504.

272 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583494C211yesmaximal, characteristic, complemented
2#14583052C211yesmaximal, characteristic, complemented
3#14583032C211yesmaximal, characteristic
4#14582817C211yesmaximal, characteristic, complemented
5#14582635C211yesmaximal, characteristic, complemented
6#14582624C211yesmaximal, characteristic, complemented
7C43×#327C211yesmaximal, characteristic, complemented
8C22×D172C2211yescharacteristic
9C2×#10621873—21no—
10C2×#10621882—21no—
11#13063318—21no—
12#13063315—21no—
13#13063306—21no—
14#13063306—21no—
15#13063304C2211yescharacteristic
16#13063302—21no—
17D4×Dic43—21no—
18C2×Dic43⋊C4C2211yescharacteristic
19C2×(C2×D43)⋊C4—21no—
20C2×(C2×D43)⋊C4—21no—
21#13063247—21no—
22#13063245—21no—
23C22⋊(C43⋊C8)C2211yescharacteristic
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C23×D43—21no—
28C2×D4×C43—21no—
29C2×D4×C43D411yescharacteristic
30C22×C4×C43—21no—
31C22×C4×C43C2311yescharacteristic
32C22×Dic43—21no—
33C22×Dic43D411yescharacteristic
34C22×Dic43D411yescharacteristic
35C2×D172—21no—
36C2×D172—21no—
37C2×D172—42no—
38C2×Dic86D411yescharacteristic
39C2×C8×C43—21no—
40C4⋊C4×C43D411yescharacteristic
41C22⋊C4×C43—21no—
42C22⋊Dic43—21no—
43C22⋊Dic43—21no—
44C22⋊Dic43—21no—
45C22⋊Dic43—21no—
46#10621882—42no—
47(C2×D43)⋊C4—42no—
48(C2×D43)⋊C4—42no—
49C4⋊Dic43—21no—
50C4⋊Dic43D411yescharacteristic
51Dic43⋊C4—21no—
52Dic43⋊C4—21no—
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55Dic43⋊C4—21no—
56C4×Dic43—21no—
57C2×C43⋊C8—21no—
58#10621873—42no—
59C23×C43—21no—
60C23×C43C2×D411yescharacteristic
61C22×D43—22no—
62C22×D43—41no—
63C22×D43—41no—
64C22×D43—41no—
65C22×D43—41no—
66C22×D43—41no—
67C22×D43—41no—
68D4×C43—41no—
69D4×C43—41no—
70D4×C43—41no—
71C2×C4×C43—21no—
72C2×C4×C43—41no—
73C2×C4×C43—41no—
74C2×C4×C43—41no—
75C2×C4×C43—41no—
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2×D411yescharacteristic
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—41no—
85C2×Dic43—81no—
86D172—22no—
87D172—22no—
88D172—41no—
89D172—41no—
90Dic86—41no—
91C8×C43—41no—
92C43⋊C8—41no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43—41no—
96C22×C43—41no—
97C22×C43—41no—
98C22×C43#12011yescharacteristic
99C22×C43#13511yescharacteristic
100C22×C43AGL(1,ℤ/8)11yescharacteristic
101C2×D43—42no—
102C2×D43—42no—
103C2×D43—42no—
104C2×D43—81no—
105C2×D43—81no—
106C2×D43—81no—
107C2×D43—81no—
108C4×C43—21no—
109C4×C43—21no—
110C4×C43—41no—
111C4×C43—81no—
112Dic43—41no—
113Dic43—41no—
114Dic43—41no—
115Dic43—41no—
116#1597—431nomaximal, Sylow
117C2×C43—21no—
118C2×C43—21no—
119C2×C43—81no—
120C2×C43#44911yescharacteristic
121C2×C43#45411yescharacteristic
122C2×C43B(4,𝔽2)11yescharacteristic
123D43—82no—
124#539—431no—
125#450—431no—
126#447—431no—
127#394—431no—
128#328—431no—
129#327D4311yescharacteristic, complemented
130#324—431no—
131C43#159711yescharacteristic, complemented, Sylow
132C22×D4—431no—
133C2×SD16—861no—
134C2×D8—861no—
135#126—861no—
136#125—861no—
137#123—861no—
138#123—861no—
139C22⋊Q8—431no—
140C22⋊Q8—861no—
141#121C2×D4311yescharacteristic
142C4×D4—861no—
143C2×C4⋊C4—431no—
144C2×C22⋊C4—861no—
145C2×C22⋊C4—861no—
146#102—861no—
147#102—861no—
148C22⋊C8—431no—
149C22⋊C8C2×D4311yescharacteristic
150#95C2×D4311yescharacteristic
151C24—861no—
152C2×Q8—431no—
153C2×D4—21no—
154C2×D4—861no—
155C2×D4—861no—
156C2×D4—1722no—
157C2×D4D17211yescharacteristic
158C22×C4—21no—
159C22×C4—431no—
160C22×C4—431no—
161C22×C4—861no—
162C22×C4C22×D4311yescharacteristic
163SD16—1722no—
164D8—1722no—
165C2×C8—21no—
166C2×C8—861no—
167C4⋊C4—431no—
168C4⋊C4—861no—
169C4⋊C4—861no—
170C4⋊C4—861no—
171C4⋊C4—861no—
172C4⋊C4—861no—
173C4⋊C4—861no—
174C4⋊C4D17211yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—861no—
177C22⋊C4—861no—
178C22⋊C4—861no—
179C22⋊C4—861no—
180C22⋊C4—1722no—
181C22⋊C4—1722no—
182C42—861no—
183C23—21no—
184C23—862no—
185C23—1721no—
186C23—1721no—
187C23—1721no—
188C23—1721no—
189C23—1721no—
190C23—1721no—
191C23D4×D4311yescharacteristic
192Q8—1721no—
193D4—41no—
194D4—41no—
195D4—41no—
196D4—862no—
197D4—862no—
198D4—1721no—
199D4—1721no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—861no—
206C2×C4—861no—
207C2×C4—861no—
208C2×C4—861no—
209C2×C4—861no—
210C2×C4—861no—
211C2×C4—3441no—
212C2×C4—1721no—
213C2×C4C2×D17211yescharacteristic
214C2×C4D4×D4311yescharacteristic
215C8—41no—
216C8—1721no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—3441no—
223C22—3441no—
224C22—3441no—
225C22—3441no—
226C22—1722no—
227C22—1722no—
228C22—1722no—
229C22#1306329511yescharacteristic
230C22#1306334611yescharacteristic
231C22#1306334911yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—81no—
236C4—1721no—
237C4—1721no—
238C4—1721no—
239C4—1721no—
240C2—21no—
241C2—21no—
242C2—81no—
243C2—3442no—
244C2#1458304511yescharacteristic
245C2#1458307311yescharacteristic
246C2#1458308711yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43#120
hypercenter#327D43
hypocenterC43#1597
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14583494C2semidirect
2. #14583052C2semidirect
4. #14582817C2semidirect
5. #14582635C2semidirect
6. #14582624C2semidirect
7. C43×#327C2semidirect
129. #327D43semidirect
131. C43#1597semidirect