Finite Group Databasebeta

← #19133543

Subgroups — #19133543

Order 5504.

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

normal subgroups only

This group has 320 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#14583487C211yesmaximal, characteristic, complemented
2#14583052C211yesmaximal, characteristic, complemented
3#14583035C211yesmaximal, characteristic, complemented
4#14582808C211yesmaximal, characteristic, complemented
5#14582637C211yesmaximal, characteristic, complemented
6#14582634C211yesmaximal, characteristic, complemented
7C43×#323C211yesmaximal, characteristic, complemented
8C22×D172C2211yescharacteristic
9C22×C22⋊D43—21no—
10C2×#10621873—21no—
11C2×D344—21no—
12#13063318—21no—
13#13063311—21no—
14#13063307—21no—
15#13063304C2211yescharacteristic
16#13063299C2211yescharacteristic
17#13063298—21no—
18#13063294—21no—
19C4×C22⋊D43—21no—
20C2×(C2×D43)⋊C4—21no—
21#13063247—21no—
22#13063247—21no—
23C43⋊#95C2211yescharacteristic
24C2×C22⋊C4×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26C22⋊C8×C43C2211yescharacteristic
27C24×C43D411yescharacteristic
28C23×D43—21no—
29C22×C4×C43D411yescharacteristic
30C22×C4×C43C2311yescharacteristic
31C2×C22⋊D43—21no—
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C2×C22⋊D43—42no—
35C2×C22⋊D43—42no—
36C2×C22⋊D43—42no—
37C22×Dic43—21no—
38C2×D172—21no—
39C2×D172—21no—
40C2×D172—42no—
41C2×D172D411yescharacteristic, complemented
42C2×C4×D43—21no—
43C2×Dic86D411yescharacteristic, complemented
44C2×C8×C43—21no—
45C2×C8×C43—21no—
46C22⋊C4×C43—21no—
47C22⋊C4×C43—21no—
48C22⋊Dic43—21no—
49C22⋊Dic43—21no—
50C22⋊Dic43—21no—
51(C2×D43)⋊C4—21no—
52(C2×D43)⋊C4—21no—
53(C2×D43)⋊C4—42no—
54C4⋊Dic43D411yescharacteristic, complemented
55C4⋊Dic43D411yescharacteristic, complemented
56Dic43⋊C4—21no—
57Dic43⋊C4—21no—
58C4×Dic43—21no—
59D344—42no—
60#10621873—42no—
61C23×C43—21no—
62C23×C43—21no—
63C23×C43—21no—
64C23×C43—41no—
65C23×C43—41no—
66C23×C43C2×D411yescharacteristic
67C22×D43—22no—
68C22×D43—21no—
69C22×D43—41no—
70C22×D43—41no—
71C22×D43—41no—
72C22×D43—41no—
73C22×D43—41no—
74C22×D43—41no—
75C2×C4×C43—21no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2×D411yescharacteristic
80C22⋊D43—48no—
81C22⋊D43—41no—
82C22⋊D43—41no—
83C22⋊D43—81no—
84C22⋊D43—81no—
85C2×Dic43—22no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43—41no—
90C2×Dic43—41no—
91D172—22no—
92D172—22no—
93D172—41no—
94D172—41no—
95D172—41no—
96C4×D43—81no—
97Dic86—41no—
98C8×C43—41no—
99C8×C43—41no—
100C22×C43—21no—
101C22×C43—21no—
102C22×C43—42no—
103C22×C43—41no—
104C22×C43—41no—
105C22×C43—41no—
106C22×C43—81no—
107C22×C43#12011yescharacteristic
108C22×C43#13511yescharacteristic
109C22×C43AGL(1,ℤ/8)11yescharacteristic
110C2×D43—42no—
111C2×D43—42no—
112C2×D43—41no—
113C2×D43—41no—
114C2×D43—42no—
115C2×D43—41no—
116C2×D43—81no—
117C2×D43—81no—
118C2×D43—81no—
119C2×D43—81no—
120C4×C43—21no—
121C4×C43—21no—
122C4×C43—41no—
123Dic43—42no—
124Dic43—41no—
125Dic43—41no—
126Dic43—41no—
127#1600—431nomaximal, Sylow
128C2×C43—21no—
129C2×C43—21no—
130C2×C43—81no—
131C2×C43#44911yescharacteristic
132C2×C43#45311yescharacteristic
133C2×C43B(4,𝔽2)11yescharacteristic
134D43—81no—
135D43—82no—
136#538—431no—
137#450—431no—
138#447—431no—
139#392—431no—
140#328—431no—
141#327—431no—
142#323D4311yescharacteristic, complemented
143C43#160011yescharacteristic, complemented, Sylow
144C22×D4—431no—
145C22×D4—861no—
146C2×SD16—861no—
147C2×D8—861no—
148#126—861no—
149#124—861no—
150#123—861no—
151C22⋊Q8—431no—
152#121—431no—
153#121—861no—
154#120—861no—
155C4×D4—861no—
156C2×C22⋊C4—861no—
157C2×C22⋊C4C2×D4311yescharacteristic
158#102—861no—
159#102—861no—
160C22⋊C8C2×D4311yescharacteristic
161C22⋊C8C2×D4311yescharacteristic
162#95—431no—
163C24—861no—
164C24D17211yescharacteristic
165C2×Q8—431no—
166C2×D4—431no—
167C2×D4—861no—
168C2×D4—861no—
169C2×D4—861no—
170C2×D4—861no—
171C2×D4—861no—
172C2×D4—1722no—
173C2×D4—1722no—
174C2×D4—1722no—
175C2×D4—1722no—
176C22×C4—861no—
177C22×C4—861no—
178C22×C4D17211yescharacteristic
179C22×C4C22×D4311yescharacteristic
180SD16—1722no—
181D8—1722no—
182C2×C8—21no—
183C2×C8—21no—
184C4⋊C4—431no—
185C4⋊C4—431no—
186C4⋊C4—861no—
187C4⋊C4—861no—
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—861no—
191C22⋊C4—861no—
192C22⋊C4—861no—
193C22⋊C4—861no—
194C22⋊C4—861no—
195C22⋊C4—1722no—
196C42—861no—
197C23—21no—
198C23—21no—
199C23—21no—
200C23—41no—
201C23—41no—
202C23—862no—
203C23—861no—
204C23—1721no—
205C23—1721no—
206C23—1721no—
207C23—1721no—
208C23—1721no—
209C23—1721no—
210C23C2×D17211yescharacteristic
211Q8—1721no—
212D4—862no—
213D4—862no—
214D4—3441no—
215D4—3441no—
216D4—1721no—
217D4—1721no—
218D4—1721no—
219D4—1728no—
220D4—1721no—
221D4—1721no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—862no—
226C2×C4—861no—
227C2×C4—861no—
228C2×C4—861no—
229C2×C4—3441no—
230C2×C4—1721no—
231C2×C4—1721no—
232C2×C4D4×D4311yescharacteristic
233C2×C4D4×D4311yescharacteristic
234C8—41no—
235C8—41no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—81no—
243C22—3441no—
244C22—3441no—
245C22—3441no—
246C22—3441no—
247C22—1722no—
248C22—1722no—
249C22—1721no—
250C22—1721no—
251C22—1722no—
252C22—1721no—
253C22#1306329511yescharacteristic
254C22#1306334711yescharacteristic
255C22#1306335311yescharacteristic
256C4—21no—
257C4—21no—
258C4—41no—
259C4—1722no—
260C4—1721no—
261C4—1721no—
262C4—1721no—
263C2—21no—
264C2—21no—
265C2—81no—
266C2—3442no—
267C2—3441no—
268C2#1458304611yescharacteristic
269C2#1458306911yescharacteristic
270C2#1458308711yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#323C2
socleC22×C43#120
hypercenter#323D43
hypocenterC43#1600
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
1. #14583487C2semidirect
2. #14583052C2semidirect
3. #14583035C2semidirect
4. #14582808C2semidirect
5. #14582637C2semidirect
6. #14582634C2semidirect
7. C43×#323C2semidirect
41. C2×D172D4semidirect
43. C2×Dic86D4semidirect
54. C4⋊Dic43D4semidirect
55. C4⋊Dic43D4semidirect
142. #323D43semidirect
143. C43#1600semidirect