Finite Group Databasebeta

← #19133542

Subgroups — #19133542

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#14583486C211yesmaximal, characteristic, complemented
2#14583052C211yesmaximal, characteristic, complemented
3#14583032C211yesmaximal, characteristic, complemented
4#14582809C211yesmaximal, characteristic, complemented
5#14582635C211yesmaximal, characteristic, complemented
6#14582622C211yesmaximal, characteristic, complemented
7C43×#327C211yesmaximal, characteristic, complemented
8C22×D172—21no—
9C22×D172C2211yescharacteristic
10C2×#10621873—21no—
11C2×#10621882—21no—
12#13063320—21no—
13#13063311—21no—
14#13063309—21no—
15#13063304C2211yescharacteristic
16#13063297—21no—
17#13063293—21no—
18D4×Dic43—21no—
19C2×(C2×D43)⋊C4—21no—
20C2×(C2×D43)⋊C4C2211yescharacteristic
21#13063247—21no—
22#13063245—21no—
23C22⋊(C43⋊C8)C2211yescharacteristic
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C23×D43—21no—
28C23×D43D411yescharacteristic
29C2×D4×C43—21no—
30C2×D4×C43D411yescharacteristic, complemented
31C22×C4×C43—21no—
32C22×C4×C43C2311yescharacteristic
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35C22×Dic43—21no—
36C22×Dic43D411yescharacteristic
37C2×D172—21no—
38C2×D172—21no—
39C2×D172—42no—
40C2×D172—42no—
41C2×D172—42no—
42C2×D172—42no—
43C2×Dic86D411yescharacteristic, complemented
44C2×C8×C43—21no—
45C4⋊C4×C43D411yescharacteristic, complemented
46C22⋊C4×C43—21no—
47C22⋊Dic43—21no—
48C22⋊Dic43—21no—
49#10621882—42no—
50(C2×D43)⋊C4—21no—
51(C2×D43)⋊C4—21no—
52(C2×D43)⋊C4—21no—
53(C2×D43)⋊C4—21no—
54(C2×D43)⋊C4—42no—
55C4⋊Dic43—21no—
56C4⋊Dic43D411yescharacteristic, complemented
57Dic43⋊C4—21no—
58C4×Dic43—21no—
59C2×C43⋊C8—21no—
60#10621873—42no—
61C23×C43—21no—
62C23×C43C2×D411yescharacteristic
63C22×D43—22no—
64C22×D43—21no—
65C22×D43—21no—
66C22×D43—21no—
67C22×D43—41no—
68C22×D43—41no—
69C22×D43—41no—
70C22×D43—41no—
71C22×D43—41no—
72C22×D43—41no—
73C22×D43—41no—
74C22×D43—41no—
75D4×C43—41no—
76D4×C43—41no—
77D4×C43—41no—
78C2×C4×C43—22no—
79C2×C4×C43—21no—
80C2×C4×C43—41no—
81C2×C4×C43—41no—
82C2×C4×C43—41no—
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43C2×D411yescharacteristic
85C22⋊D43—81no—
86C22⋊D43—81no—
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43—21no—
90C2×Dic43—41no—
91C2×Dic43—81no—
92D172—22no—
93D172—22no—
94D172—41no—
95D172—41no—
96D172—48no—
97Dic86—41no—
98C8×C43—41no—
99C43⋊C8—41no—
100C22×C43—21no—
101C22×C43—21no—
102C22×C43—41no—
103C22×C43—41no—
104C22×C43—41no—
105C22×C43#12011yescharacteristic
106C22×C43#13511yescharacteristic
107C22×C43AGL(1,ℤ/8)11yescharacteristic
108C2×D43—42no—
109C2×D43—42no—
110C2×D43—42no—
111C2×D43—41no—
112C2×D43—41no—
113C2×D43—42no—
114C2×D43—41no—
115C2×D43—81no—
116C2×D43—81no—
117C2×D43—81no—
118C2×D43—81no—
119C2×D43—81no—
120C4×C43—21no—
121C4×C43—21no—
122C4×C43—42no—
123C4×C43—41no—
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#327D4311yescharacteristic, complemented
142#323—431no—
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—861no—
153#121C2×D4311yescharacteristic
154#120—861no—
155C4×D4—861no—
156C2×C22⋊C4—431no—
157C2×C22⋊C4—861no—
158#102—861no—
159#102—861no—
160C22⋊C8—431no—
161C22⋊C8C2×D4311yescharacteristic
162#95C2×D4311yescharacteristic
163C24—431no—
164C24—861no—
165C2×Q8—431no—
166C2×D4—21no—
167C2×D4—861no—
168C2×D4—861no—
169C2×D4—861no—
170C2×D4—861no—
171C2×D4—1722no—
172C2×D4—1722no—
173C2×D4—1722no—
174C2×D4—1722no—
175C2×D4D17211yescharacteristic, complemented
176C22×C4—21no—
177C22×C4—431no—
178C22×C4—861no—
179C22×C4C22×D4311yescharacteristic
180SD16—1722no—
181D8—1722no—
182C2×C8—21no—
183C2×C8—861no—
184C4⋊C4—431no—
185C4⋊C4—861no—
186C4⋊C4—861no—
187C4⋊C4D17211yescharacteristic, complemented
188C22⋊C4—21no—
189C22⋊C4—861no—
190C22⋊C4—861no—
191C22⋊C4—861no—
192C22⋊C4—861no—
193C22⋊C4—861no—
194C22⋊C4—861no—
195C22⋊C4—1722no—
196C42—861no—
197C23—21no—
198C23—862no—
199C23—861no—
200C23—861no—
201C23—861no—
202C23—1721no—
203C23—1721no—
204C23—1721no—
205C23—1721no—
206C23—1721no—
207C23—1721no—
208C23—1721no—
209C23—1721no—
210C23D4×D4311yescharacteristic
211Q8—1721no—
212D4—41no—
213D4—41no—
214D4—41no—
215D4—862no—
216D4—862no—
217D4—3441no—
218D4—3441no—
219D4—1721no—
220D4—1721no—
221D4—1728no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—861no—
228C2×C4—861no—
229C2×C4—861no—
230C2×C4—3441no—
231C2×C4—1721no—
232C2×C4C2×D17211yescharacteristic
233C2×C4D4×D4311yescharacteristic
234C8—41no—
235C8—1721no—
236C22—21no—
237C22—21no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—3441no—
242C22—3441no—
243C22—3441no—
244C22—3441no—
245C22—3441no—
246C22—1722no—
247C22—1722no—
248C22—1722no—
249C22—1721no—
250C22—1721no—
251C22—1722no—
252C22—1721no—
253C22#1306329511yescharacteristic
254C22#1306334611yescharacteristic
255C22#1306334911yescharacteristic
256C4—21no—
257C4—21no—
258C4—42no—
259C4—41no—
260C4—1721no—
261C4—1721no—
262C4—1721no—
263C2—21no—
264C2—21no—
265C2—81no—
266C2—3442no—
267C2—3441no—
268C2#1458304511yescharacteristic
269C2#1458306811yescharacteristic
270C2#1458308711yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43#120
hypercenter#327D43
hypocenterC43#1600
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. #14583486C2semidirect
2. #14583052C2semidirect
3. #14583032C2semidirect
4. #14582809C2semidirect
5. #14582635C2semidirect
6. #14582622C2semidirect
7. C43×#327C2semidirect
30. C2×D4×C43D4semidirect
43. C2×Dic86D4semidirect
45. C4⋊C4×C43D4semidirect
56. C4⋊Dic43D4semidirect
141. #327D43semidirect
143. C43#1600semidirect
175. C2×D4D172semidirect
187. C4⋊C4D172semidirect