Finite Group Databasebeta

← #19146424

Subgroups — #19146424

Order 5504.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583545C211yesmaximal, characteristic
2#14583256C211yesmaximal, characteristic, complemented
3#14583229C211yesmaximal, characteristic, complemented
4#14583223C211yesmaximal, characteristic, complemented
5#14583196C211yesmaximal, characteristic, complemented
6#14583138C211yesmaximal, characteristic, complemented
7#14583130C211yesmaximal, characteristic, complemented
8#14583121C211yesmaximal, characteristic, complemented
9#14583059C211yesmaximal, characteristic, complemented
10#14583049C211yesmaximal, characteristic, complemented
11C4×#10621884C211yesmaximal, characteristic, complemented
12D4×C43⋊C8C211yesmaximal, characteristic, complemented
13#14582893C211yesmaximal, characteristic, complemented
14C2×#13063245C211yesmaximal, characteristic, complemented
15C43×#552C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C2×#10621885C2211yescharacteristic, complemented
19C2×#10621884C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C22×C43⋊C8C2211yescharacteristic
22C22×C43⋊C8C2211yescharacteristic, complemented
23#13063313C2211yescharacteristic
24#13063310—21no—
25#13063304C2211yescharacteristic
26#13063299C2211yescharacteristic
27#13063298—21no—
28#13063293—21no—
29C4×D172C2211yescharacteristic
30C22⋊C4×D43—21no—
31#13063258C2211yescharacteristic, complemented
32#13063256C2211yescharacteristic, complemented
33#13063256C2211yescharacteristic, complemented
34C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35#13063249C2211yescharacteristic, complemented
36#13063248C2211yescharacteristic, complemented
37#13063248C2211yescharacteristic, complemented
38#13063248C2211yescharacteristic, complemented
39#13063245C2211yescharacteristic
40#13063245C2211yescharacteristic
41#13063245C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44#13063245C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic, complemented
47C4×C43⋊C8C2211yescharacteristic, complemented
48#126×C43—21no—
49#125×C43—21no—
50#125×C43C2211yescharacteristic, complemented
51#123×C43—21no—
52C22⋊Q8×C43C2211yescharacteristic
53C22⋊Q8×C43C2211yescharacteristic, complemented
54C4×Q8×C43C2211yescharacteristic, complemented
55C4×D4×C43C2211yescharacteristic
56#117×C43—21no—
57#117×C43C2211yescharacteristic, complemented
58C2×C4⋊C4×C43C2211yescharacteristic
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43D411yescharacteristic
62C22×C4×C43—21no—
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67#10621898—22no—
68#10621898—41no—
69C2×D172—21no—
70C2×D172—22no—
71C2×D172—41no—
72C2×D172C2311yescharacteristic
73C2×D172C2311yescharacteristic
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×Dic86C2311yescharacteristic
77C4⋊C4×C43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43D411yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C22⋊C4×C43—21no—
88C22⋊C4×C43—21no—
89C22⋊C4×C43—21no—
90C22⋊C4×C43D411yescharacteristic
91C22⋊C4×C43D411yescharacteristic
92C42×C43—21no—
93C42×C43—21no—
94C42×C43C2311yescharacteristic
95C22⋊Dic43—21no—
96#10621885—41no—
97#10621884—22no—
98#10621884—41no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103C4⋊Dic43C2311yescharacteristic
104Dic43⋊C4—21no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C23×C43C2×D411yescharacteristic
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—42no—
116C22×D43—42no—
117C22×D43—81no—
118Q8×C43—21no—
119Q8×C43—21no—
120D4×C43—22no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—42no—
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2411yescharacteristic
135C22⋊D43—42no—
136C22⋊D43—81no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139D172—21no—
140D172—21no—
141D172—21no—
142D172—42no—
143D172#4112yes—
144C4×D43—42no—
145C4×D43—81no—
146Dic86—21no—
147Dic86—21no—
148C43⋊C8—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43#13512yes—
158C22×C43C22×D411yescharacteristic
159C2×D43—22no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—84no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43C2×#4111yescharacteristic
175C4×C43H(5,𝔽2)11yescharacteristic
176Dic43—41no—
177Dic43—41no—
178#3296—431nomaximal, Sylow
179C2×C43—22no—
180C2×C43—41no—
181C2×C43#54611yescharacteristic
182C2×C43C2×#13511yescharacteristic
183C2×C43#57711yescharacteristic
184D43—42no—
185D43—81no—
186#552D4311yescharacteristic, complemented
187#546—431no—
188#488—431no—
189#483—431no—
190#482—431no—
191#478—431no—
192#467—431no—
193#465—431no—
194#464—431no—
195#452—431no—
196#450—431no—
197C4×SD16—431no—
198C8×D4—431no—
199#416—431no—
200C2×#102—431no—
201C43#329611yescharacteristic, complemented, Sylow
202C2×#41—431no—
203C22×D4—431no—
204C2×Q16—431no—
205C2×SD16—431no—
206C2×SD16—431no—
207C22×C8—431no—
208C22×C8—431no—
209#126—21no—
210#125—21no—
211#125C2×D4311yescharacteristic, complemented
212#124—431no—
213#123—21no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8C2×D4311yescharacteristic
217C22⋊Q8C2×D4311yescharacteristic, complemented
218#121—431no—
219#121—861no—
220#120—861no—
221C4×Q8C2×D4311yescharacteristic, complemented
222C4×D4—431no—
223C4×D4C2×D4311yescharacteristic
224#117—21no—
225#117C2×D4311yescharacteristic, complemented
226C2×C4⋊C4C2×D4311yescharacteristic
227C2×C22⋊C4—861no—
228#107—431no—
229#106—431no—
230#106—431no—
231C4⋊C8—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102—431no—
242C22⋊C8—431no—
243C22⋊C8—431no—
244C4×C8—431no—
245C24—861no—
246#41—862no—
247#41—1721no—
248C2×Q8—431no—
249C2×Q8C22×D4311yescharacteristic
250C2×D4—431no—
251C2×D4—431no—
252C2×D4—862no—
253C2×D4—861no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4—1721no—
257C2×D4C22⋊D4311yescharacteristic
258C22×C4—21no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4C22×D4311yescharacteristic
262C22×C4C22×D4311yescharacteristic
263Q16—1721no—
264SD16—862no—
265SD16—1721no—
266C2×C8—431no—
267C2×C8—431no—
268C2×C8—431no—
269C2×C8—431no—
270C2×C8—1721no—
271C2×C8—1721no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—431no—
279C4⋊C4—861no—
280C4⋊C4C22⋊D4311yescharacteristic
281C4⋊C4C22×D4311yescharacteristic
282C4⋊C4C22×D4311yescharacteristic
283C4⋊C4C22×D4311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4C22⋊D4311yescharacteristic
293C22⋊C4C22⋊D4311yescharacteristic
294C42—21no—
295C42—21no—
296C42C22×D4311yescharacteristic
297C23—861no—
298C23—861no—
299C23—3441no—
300C23—1722no—
301C23—1722no—
302C23C2×C22⋊D4311yescharacteristic
303C23C2×C22⋊D4311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—861no—
307Q8—861no—
308D4—22no—
309D4—432no—
310D4—861no—
311D4—861no—
312D4—861no—
313D4—3441no—
314D4—1722no—
315D4—1722no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—3441no—
328C2×C4—1722no—
329C2×C4C2×C22⋊D4311yescharacteristic
330C2×C4C2×C22⋊D4311yescharacteristic
331C2×C4C2×C22⋊D4311yescharacteristic
332C2×C4C2×C22⋊D4311yescharacteristic
333C2×C4C23×D4311yescharacteristic
334C8—861no—
335C8—861no—
336C8—861no—
337C8—861no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—862no—
344C22—3444no—
345C22—1721no—
346C22—1721no—
347C22—1721no—
348C22—1721no—
349C22—1721no—
350C22#1306334512yes—
351C22C22×C22⋊D4311yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—1721no—
361C4—1721no—
362C4#41×D4311yescharacteristic
363C4#1306337111yescharacteristic
364C2—22no—
365C2—41no—
366C2—3441no—
367C2—1722no—
368C2#1458353711yescharacteristic
369C2C2×#1306334511yescharacteristic
370C2#1458370711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#552C2
socleC22×C43C22×D4
hypercenter#552D43
hypocenterC43#3296
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #14583256C2semidirect
3. #14583229C2semidirect
4. #14583223C2semidirect
5. #14583196C2semidirect
6. #14583138C2semidirect
7. #14583130C2semidirect
8. #14583121C2semidirect
9. #14583059C2semidirect
10. #14583049C2semidirect
11. C4×#10621884C2semidirect
12. D4×C43⋊C8C2semidirect
13. #14582893C2semidirect
14. C2×#13063245C2semidirect
15. C43×#552C2semidirect
18. C2×#10621885C22semidirect
22. C22×C43⋊C8C22semidirect
31. #13063258C22semidirect
32. #13063256C22semidirect
33. #13063256C22semidirect
34. C4⋊(C43⋊C8)C22semidirect
35. #13063249C22semidirect
36. #13063248C22semidirect
37. #13063248C22semidirect
38. #13063248C22semidirect
46. C22⋊(C43⋊C8)C22semidirect
47. C4×C43⋊C8C22semidirect
50. #125×C43C22semidirect
53. C22⋊Q8×C43C22semidirect
54. C4×Q8×C43C22semidirect
57. #117×C43C22semidirect
186. #552D43semidirect
201. C43#3296semidirect
211. #125C2×D43semidirect
217. C22⋊Q8C2×D43semidirect
221. C4×Q8C2×D43semidirect
225. #117C2×D43semidirect