Finite Group Databasebeta

← #19145840

Subgroups — #19145840

Order 5504.

328 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583455C211yesmaximal, characteristic, complemented
2#14583436C211yesmaximal, characteristic
3#14583307C211yesmaximal, characteristic, complemented
4#14583306C211yesmaximal, characteristic, complemented
5#14583260C211yesmaximal, characteristic, complemented
6#14583260C211yesmaximal, characteristic, complemented
7#14583239C211yesmaximal, characteristic, complemented
8#14583238C211yesmaximal, characteristic, complemented
9#14583226C211yesmaximal, characteristic
10#14583225C211yesmaximal, characteristic
11#14583206C211yesmaximal, characteristic, complemented
12#14583200C211yesmaximal, characteristic, complemented
13#14583196C211yesmaximal, characteristic, complemented
14#14582955C211yesmaximal, characteristic, complemented
15C43×#479C211yesmaximal, characteristic, complemented
16#13063324C2211yescharacteristic
17#13063324C2211yescharacteristic
18#13063320—21no—
19#13063317C2211yescharacteristic
20#13063316C2211yescharacteristic
21#13063314C2211yescharacteristic
22#13063310—21no—
23#13063303—21no—
24#13063303—21no—
25#13063301C2211yescharacteristic
26#13063300C2211yescharacteristic
27#13063290—21no—
28#13063290—21no—
29C4×D172—21no—
30C4×D172C2211yescharacteristic
31#13063283C2211yescharacteristic
32#13063283C2211yescharacteristic
33#13063282—21no—
34C42×D43C2211yescharacteristic
35#13063259C2211yescharacteristic
36#13063258C2211yescharacteristic
37#13063258C2211yescharacteristic
38#13063257C2211yescharacteristic
39#13063256C2211yescharacteristic
40#13063256C2211yescharacteristic
41C4⋊(C43⋊C8)C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50#13063235C2211yescharacteristic
51#13063235C2211yescharacteristic
52#125×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D172—21no—
61C2×D172C2311yescharacteristic
62C2×C4×D43—21no—
63C2×C4×D43D411yescharacteristic
64C2×C4×D43D411yescharacteristic
65C2×C4×D43C2311yescharacteristic
66C2×Dic86—21no—
67C2×Dic86—21no—
68C2×C8×C43C2311yescharacteristic
69C2×C8×C43C2311yescharacteristic
70C4⋊C4×C43—21no—
71C4⋊C4×C43—21no—
72C4⋊C4×C43—21no—
73C4⋊C4×C43C2311yescharacteristic
74C4⋊C4×C43C2311yescharacteristic
75C4⋊C4×C43C2311yescharacteristic
76C42×C43—21no—
77C42×C43C2311yescharacteristic
78(C2×D43)⋊C4—21no—
79(C2×D43)⋊C4—21no—
80(C2×D43)⋊C4—21no—
81(C2×D43)⋊C4—21no—
82(C2×D43)⋊C4—21no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43C2311yescharacteristic
87C4⋊Dic43C2311yescharacteristic
88C4⋊Dic43C2311yescharacteristic
89Dic43⋊C4—21no—
90Dic43⋊C4—21no—
91Dic43⋊C4—21no—
92Dic43⋊C4—21no—
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95C4×Dic43—21no—
96C4×Dic43—21no—
97C4×Dic43D411yescharacteristic
98C4×Dic43D411yescharacteristic
99C4×Dic43C2311yescharacteristic
100C2×C43⋊C8C2311yescharacteristic
101C2×C43⋊C8C2311yescharacteristic
102C22×D43—21no—
103C22×D43C2×D411yescharacteristic
104Q8×C43—21no—
105Q8×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43C2×D411yescharacteristic
111C2×C4×C43C2×D411yescharacteristic
112C2×C4×C43C2411yescharacteristic
113C2×Dic43—21no—
114C2×Dic43—21no—
115C2×Dic43—21no—
116C2×Dic43C2×D411yescharacteristic
117C2×Dic43C2×D411yescharacteristic
118C2×Dic43C2×D411yescharacteristic
119D172—21no—
120D172—21no—
121D172—42no—
122C4×D43—21no—
123C4×D43—21no—
124C4×D43—41no—
125C4×D43—41no—
126C4×D43—42no—
127Dic86—42no—
128Dic86—42no—
129C8×C43—21no—
130C8×C43—21no—
131C43⋊C8—21no—
132C43⋊C8—21no—
133C22×C43C22×D411yescharacteristic
134C2×D43—21no—
135C2×D43—21no—
136C2×D43—21no—
137C2×D43—41no—
138C2×D43—41no—
139C2×D43—41no—
140C4×C43—21no—
141C4×C43—21no—
142C4×C43—41no—
143C4×C43—41no—
144C4×C43—41no—
145C4×C43—41no—
146C4×C432−1+411yescharacteristic
147C4×C432−1+411yescharacteristic
148Dic43—21no—
149Dic43—21no—
150Dic43—21no—
151Dic43—41no—
152Dic43—41no—
153Dic43—41no—
154#3240—431nomaximal, Sylow
155C2×C43#53611yescharacteristic
156C2×C43#57511yescharacteristic
157C2×C43#57511yescharacteristic
158D43—41no—
159D43—81no—
160#533—431no—
161#529—431no—
162#501—431no—
163#501—431no—
164#489—431no—
165#489—431no—
166#485—431no—
167#485—431no—
168#482—431no—
169#482—431no—
170#479—431no—
171#479D4311yescharacteristic, complemented
172#478—431no—
173#478—431no—
174#432—431no—
175C43#324011yescharacteristic, complemented, Sylow
176C4⋊Q8—431no—
177C4⋊Q8—431no—
178#126—861no—
179#125—431no—
180#125—431no—
181#125C2×D4311yescharacteristic
182#124—431no—
183#123—861no—
184C22⋊Q8—431no—
185C22⋊Q8—861no—
186C22⋊Q8—861no—
187#121—431no—
188C4×Q8—861no—
189C4×Q8—861no—
190C4×Q8C2×D4311yescharacteristic
191C4×D4—431no—
192C4×D4—861no—
193#117—431no—
194#117—431no—
195#117—861no—
196C2×C42—431no—
197#107—431no—
198#107—431no—
199#107—431no—
200#107C2×D4311yescharacteristic
201#106—431no—
202#106—431no—
203#106—431no—
204#106C2×D4311yescharacteristic
205C4⋊C8—431no—
206C4⋊C8C2×D4311yescharacteristic
207#103—431no—
208#103—431no—
209#103C2×D4311yescharacteristic
210#103C2×D4311yescharacteristic
211#102—431no—
212#102—431no—
213#102—431no—
214#102—431no—
215C22⋊C8—431no—
216C22⋊C8—431no—
217#97—431no—
218#97—431no—
219C2×Q8—861no—
220C2×Q8—861no—
221C2×Q8C22×D4311yescharacteristic
222C2×D4—431no—
223C2×D4—861no—
224C22×C4—431no—
225C22×C4—431no—
226C22×C4—431no—
227C22×C4—861no—
228C2×C8—431no—
229C2×C8—431no—
230C2×C8C22×D4311yescharacteristic
231C2×C8C22×D4311yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—431no—
236C4⋊C4—431no—
237C4⋊C4—431no—
238C4⋊C4—861no—
239C4⋊C4—861no—
240C4⋊C4—861no—
241C4⋊C4—861no—
242C4⋊C4—861no—
243C4⋊C4—861no—
244C4⋊C4—861no—
245C4⋊C4C22×D4311yescharacteristic
246C4⋊C4C22×D4311yescharacteristic
247C4⋊C4C22×D4311yescharacteristic
248C22⋊C4—861no—
249C22⋊C4—861no—
250C22⋊C4—861no—
251C22⋊C4—861no—
252C22⋊C4—861no—
253C22⋊C4—861no—
254C22⋊C4—861no—
255C42—21no—
256C42—431no—
257C42—431no—
258C42—431no—
259C42—861no—
260C42—861no—
261C42C22×D4311yescharacteristic
262C23—431no—
263C23—861no—
264Q8—21no—
265Q8—21no—
266Q8—1722no—
267Q8—1722no—
268D4—861no—
269D4—861no—
270D4—1722no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—431no—
276C2×C4—431no—
277C2×C4—431no—
278C2×C4—861no—
279C2×C4—861no—
280C2×C4—861no—
281C2×C4—861no—
282C2×C4—861no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1722no—
286C2×C4D4×D4311yescharacteristic
287C2×C4D4×D4311yescharacteristic
288C2×C4C23×D4311yescharacteristic
289C8—21no—
290C8—21no—
291C8—861no—
292C8—861no—
293C22—861no—
294C22—861no—
295C22—861no—
296C22—1721no—
297C22—1721no—
298C22—1721no—
299C22C2×D4×D4311yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—861no—
307C4—861no—
308C4—861no—
309C4—1721no—
310C4—1721no—
311C4—1721no—
312C4#1306337211yescharacteristic
313C4#1306337311yescharacteristic
314C2—3441no—
315C2—1721no—
316C2#1458347211yescharacteristic
317C2#1458369611yescharacteristic
318C2#1458369811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#479C2
socleC22×C43C22×D4
hypercenter#479D43
hypocenterC43#3240
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #14583455C2semidirect
3. #14583307C2semidirect
4. #14583306C2semidirect
5. #14583260C2semidirect
6. #14583260C2semidirect
7. #14583239C2semidirect
8. #14583238C2semidirect
11. #14583206C2semidirect
12. #14583200C2semidirect
13. #14583196C2semidirect
14. #14582955C2semidirect
15. C43×#479C2semidirect
171. #479D43semidirect
175. C43#3240semidirect