Finite Group Databasebeta

← #19133548

Subgroups — #19133548

Order 5504.

308 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 51 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#14583457C211yesmaximal, characteristic
2#14583040C211yesmaximal, characteristic, complemented
3#14583037C211yesmaximal, characteristic, complemented
4#14582812C211yesmaximal, characteristic, complemented
5#14582632C211yesmaximal, characteristic, complemented
6#14582622C211yesmaximal, characteristic, complemented
7C43×#327C211yesmaximal, characteristic, complemented
8C22×Dic86C2211yescharacteristic, complemented
9C2×D4×D43—21no—
10C2×#10621873—21no—
11C2×#10621883—21no—
12#13063310—21no—
13#13063307—21no—
14#13063299C2211yescharacteristic
15#13063297—21no—
16#13063295—21no—
17#13063293—21no—
18C2×(C2×D43)⋊C4—21no—
19C2×(C2×D43)⋊C4C2211yescharacteristic
20#13063250—21no—
21#13063248—21no—
22C22⋊(C43⋊C8)C2211yescharacteristic, complemented
23C43⋊#95—21no—
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic, complemented
26#95×C43C2211yescharacteristic, complemented
27C23×D43—21no—
28C23×D43D411yescharacteristic
29C2×D4×C43—21no—
30C2×D4×C43D411yescharacteristic
31C22×C4×C43—21no—
32C22×C4×C43C2311yescharacteristic
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35C2×C22⋊D43—21no—
36C22×Dic43—21no—
37C22×Dic43D411yescharacteristic
38D4×D43—42no—
39D4×D43—42no—
40C2×D172—21no—
41C2×D172D411yescharacteristic
42C2×C4×D43—21no—
43C2×Dic86—21no—
44C2×Dic86—21no—
45C2×Dic86—42no—
46C2×C8×C43—21no—
47C4⋊C4×C43D411yescharacteristic
48C22⋊C4×C43—21no—
49C22⋊Dic43—21no—
50#10621883—42no—
51(C2×D43)⋊C4—21no—
52(C2×D43)⋊C4—21no—
53(C2×D43)⋊C4—21no—
54(C2×D43)⋊C4—21no—
55(C2×D43)⋊C4—42no—
56C4⋊Dic43D411yescharacteristic
57Dic43⋊C4—21no—
58C2×C43⋊C8—21no—
59#10621873—42no—
60C23×C43—21no—
61C23×C43C2×D411yescharacteristic
62C22×D43—21no—
63C22×D43—21no—
64C22×D43—21no—
65C22×D43—42no—
66C22×D43—41no—
67C22×D43—41no—
68C22×D43—81no—
69C22×D43—81no—
70C22×D43SD1612yescomplemented
71D4×C43—41no—
72D4×C43—41no—
73D4×C43—41no—
74C2×C4×C43—21no—
75C2×C4×C43—41no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43—41no—
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C22⋊D43—42no—
82C22⋊D43—41no—
83C22⋊D43—41no—
84C22⋊D43—81no—
85C2×Dic43—22no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—41no—
89C2×Dic43—41no—
90C2×Dic43—41no—
91D172—41no—
92D172—42no—
93C4×D43—42no—
94Dic86—22no—
95Dic86—22no—
96Dic86—41no—
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×C43C2×SD1611yescharacteristic
107C22×C43AGL(1,ℤ/8)11yescharacteristic
108C2×D43—22no—
109C2×D43—41no—
110C2×D43—41no—
111C2×D43—42no—
112C2×D43—41no—
113C2×D43—41no—
114C2×D43—41no—
115C2×D43—81no—
116C2×D43—84no—
117C4×C43—21no—
118C4×C43—21no—
119C4×C43—41no—
120C4×C43—81no—
121Dic43—41no—
122Dic43—41no—
123Dic43—42no—
124#1601—431nomaximal, Sylow
125C2×C43—21no—
126C2×C43—21no—
127C2×C43—81no—
128C2×C43#45011yescharacteristic
129C2×C43#45511yescharacteristic
130C2×C43B(4,𝔽2)11yescharacteristic
131D43—42no—
132D43—81no—
133#534—431no—
134#448—431no—
135#448—431no—
136#393—431no—
137#327—431no—
138#327D4311yescharacteristic, complemented
139#323—431no—
140C43#160111yescharacteristic, complemented, Sylow
141C22×Q8—431no—
142C22×D4—861no—
143C2×SD16—861no—
144C2×SD16—861no—
145#123—861no—
146#123—861no—
147#121—431no—
148#121—861no—
149#121C2×D4311yescharacteristic
150#120—861no—
151#120—861no—
152C2×C22⋊C4—431no—
153C2×C22⋊C4—861no—
154#103—861no—
155#103—861no—
156C22⋊C8—431no—
157C22⋊C8C2×D4311yescharacteristic, complemented
158#95—861no—
159#95C2×D4311yescharacteristic, complemented
160C24—431no—
161C24—861no—
162C2×Q8—861no—
163C2×Q8—861no—
164C2×Q8—1722no—
165C2×D4—21no—
166C2×D4—431no—
167C2×D4—861no—
168C2×D4—861no—
169C2×D4—861no—
170C2×D4—861no—
171C2×D4—1722no—
172C2×D4—1722no—
173C2×D4D17211yescharacteristic
174C22×C4—21no—
175C22×C4—431no—
176C22×C4—861no—
177C22×C4—861no—
178C22×C4C22×D4311yescharacteristic
179SD16—1722no—
180SD16—1722no—
181C2×C8—21no—
182C2×C8—861no—
183C4⋊C4—431no—
184C4⋊C4—861no—
185C4⋊C4D17211yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—861no—
188C22⋊C4—861no—
189C22⋊C4—861no—
190C22⋊C4—861no—
191C22⋊C4—861no—
192C22⋊C4—1722no—
193C23—21no—
194C23—432no—
195C23—861no—
196C23—861no—
197C23—861no—
198C23—3441no—
199C23—3441no—
200C23—1721no—
201C23—1721no—
202C23—1722no—
203C23D4×D4311yescharacteristic
204Q8—862no—
205Q8—862no—
206Q8—1721no—
207Q8—1721no—
208D4—41no—
209D4—41no—
210D4—41no—
211D4—3441no—
212D4—1721no—
213D4—1722no—
214D4—1722no—
215D4—1721no—
216D4—1721no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—862no—
223C2×C4—861no—
224C2×C4—861no—
225C2×C4—1722no—
226C2×C4—1721no—
227C2×C4—1721no—
228C2×C4—1721no—
229C2×C4C2×D17211yescharacteristic
230C2×C4D4×D4311yescharacteristic
231C8—41no—
232C8—1721no—
233C22—21no—
234C22—21no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—862no—
239C22—3441no—
240C22—3444no—
241C22—1722no—
242C22—1721no—
243C22—1721no—
244C22—1721no—
245C22—1721no—
246C22—1721no—
247C22#1306329511yescharacteristic
248C22SD16×D4311yescharacteristic
249C22#1306334911yescharacteristic
250C4—21no—
251C4—21no—
252C4—41no—
253C4—81no—
254C4—1721no—
255C4—1721no—
256C4—1722no—
257C2—21no—
258C2—21no—
259C2—81no—
260C2—3441no—
261C2—1722no—
262C2#1458305111yescharacteristic
263C2#1458307811yescharacteristic
264C2#1458308711yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43#120
hypercenter#327D43
hypocenterC43#1601
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
2. #14583040C2semidirect
3. #14583037C2semidirect
4. #14582812C2semidirect
5. #14582632C2semidirect
6. #14582622C2semidirect
7. C43×#327C2semidirect
8. C22×Dic86C22semidirect
22. C22⋊(C43⋊C8)C22semidirect
25. C22⋊C8×C43C22semidirect
26. #95×C43C22semidirect
70. C22×D43SD16semidirect
138. #327D43semidirect
140. C43#1601semidirect
157. C22⋊C8C2×D43semidirect
159. #95C2×D43semidirect