Finite Group Databasebeta

← #19146428

Subgroups — #19146428

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#14583584C211yesmaximal, characteristic, complemented
2#14583540C211yesmaximal, characteristic
3#14583255C211yesmaximal, characteristic, complemented
4#14583225C211yesmaximal, characteristic, complemented
5#14583198C211yesmaximal, characteristic, complemented
6#14583138C211yesmaximal, characteristic, complemented
7#14583129C211yesmaximal, characteristic, complemented
8#14583124C211yesmaximal, characteristic, complemented
9#14583064C211yesmaximal, characteristic, complemented
10#14583052C211yesmaximal, characteristic, complemented
11#14582986C211yesmaximal, characteristic, complemented
12(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
13#14582894C211yesmaximal, characteristic, complemented
14C2×#13063245C211yesmaximal, characteristic, complemented
15C43×#483C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C2×#10621885C2211yescharacteristic, complemented
19C2×#10621873C2211yescharacteristic
20C2×#10621873C2211yescharacteristic
21C22×C43⋊C8C2211yescharacteristic
22C2×C8×D43C2211yescharacteristic, complemented
23#13063320—21no—
24#13063316C2211yescharacteristic, complemented
25#13063315—21no—
26#13063314C2211yescharacteristic
27#13063310—21no—
28#13063308—21no—
29#13063305C2211yescharacteristic, complemented
30#13063304C2211yescharacteristic
31#13063300—21no—
32#13063300C2211yescharacteristic
33#13063295—21no—
34#13063290C2211yescharacteristic, complemented
35#13063287C2211yescharacteristic
36C4×C22⋊D43C2211yescharacteristic
37#13063284—21no—
38#13063283C2211yescharacteristic, complemented
39C22⋊C4×D43—21no—
40#13063258C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C22⋊Q8×C43C2211yescharacteristic
53C2×C4⋊C4×C43C2211yescharacteristic
54#106×C43C2211yescharacteristic, complemented
55#106×C43C2211yescharacteristic, complemented
56#103×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58C22⋊C8×C43C2211yescharacteristic
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43D411yescharacteristic
64#10621902—22no—
65#10621902—41no—
66C2×D172—21no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172—22no—
70C2×D172—41no—
71C2×D172C2311yescharacteristic
72C2×D172C2311yescharacteristic
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43C2311yescharacteristic
76C2×Dic86C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C22⋊C4×C43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43D411yescharacteristic
87#10621885—41no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4D411yescharacteristic
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4D411yescharacteristic
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105C2×C43⋊C8—41no—
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108#10621873—22no—
109#10621873—41no—
110C8×D43—41no—
111C23×C43C2×D411yescharacteristic
112C22×D43—21no—
113C22×D43—21no—
114C22×D43—42no—
115C22×D43—42no—
116C22×D43—81no—
117C22×D43C2×D411yescharacteristic
118Q8×C43—21no—
119Q8×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—42no—
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—22no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43C2×D411yescharacteristic
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135D172—21no—
136D172—21no—
137D172—21no—
138D172—42no—
139D172—42no—
140D172—81no—
141D172#4112yes—
142C4×D43—21no—
143C4×D43—21no—
144C4×D43—42no—
145C4×D43—81no—
146Dic86—21no—
147Dic86—21no—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43#13512yes—
155C22×C43C22×D411yescharacteristic
156C2×D43—22no—
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—21no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—84no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43C2×#4111yescharacteristic
172C4×C43H(5,𝔽2)11yescharacteristic
173Dic43—21no—
174Dic43—21no—
175Dic43—21no—
176Dic43—41no—
177Dic43—41no—
178#3296—431nomaximal, Sylow
179C2×C43—22no—
180C2×C43#54611yescharacteristic
181C2×C43C2×#13511yescharacteristic
182C2×C43#57711yescharacteristic
183D43—41no—
184D43—42no—
185D43—81no—
186#552—431no—
187#546—431no—
188#488—431no—
189#483D4311yescharacteristic, complemented
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—861no—
210#125—431no—
211#125—861no—
212#124—431no—
213#123—861no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8—431no—
217C22⋊Q8C2×D4311yescharacteristic
218#121—431no—
219#121—861no—
220#120—861no—
221C4×Q8—431no—
222C4×D4—431no—
223C4×D4—431no—
224#117—431no—
225#117—861no—
226C2×C4⋊C4C2×D4311yescharacteristic
227C2×C22⋊C4—861no—
228#107—431no—
229#106C2×D4311yescharacteristic, complemented
230#106C2×D4311yescharacteristic, complemented
231C4⋊C8—431no—
232#103—431no—
233#103—431no—
234#103C2×D4311yescharacteristic, complemented
235#103C2×D4311yescharacteristic, complemented
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102—431no—
242C22⋊C8—431no—
243C22⋊C8C2×D4311yescharacteristic
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—431no—
253C2×D4—862no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4—1721no—
258C22×C4—21no—
259C22×C4—431no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4C22×D4311yescharacteristic
263Q16—1721no—
264SD16—862no—
265SD16—1721no—
266C2×C8—431no—
267C2×C8—431no—
268C2×C8—1721no—
269C2×C8—1721no—
270C2×C8C22×D4311yescharacteristic
271C2×C8C22×D4311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4C22×D4311yescharacteristic
282C4⋊C4C22×D4311yescharacteristic
283C4⋊C4C22×D4311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—431no—
286C22⋊C4—431no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C42—431no—
295C42—861no—
296C42—861no—
297C23—431no—
298C23—861no—
299C23—861no—
300C23—3441no—
301C23—1722no—
302C23—1722no—
303C23D4×D4311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—861no—
307Q8—861no—
308D4—432no—
309D4—862no—
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—42no—
323C2×C4—431no—
324C2×C4—431no—
325C2×C4—431no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—3441no—
331C2×C4—1722no—
332C2×C4D4×D4311yescharacteristic
333C2×C4C23×D4311yescharacteristic
334C8—21no—
335C8—21no—
336C8—861no—
337C8—861no—
338C22—21no—
339C22—21no—
340C22—861no—
341C22—861no—
342C22—861no—
343C22—862no—
344C22—3444no—
345C22—1721no—
346C22—1721no—
347C22—1721no—
348C22—1721no—
349C22—1721no—
350C22#1306334612yes—
351C22C2×D4×D4311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—861no—
358C4—861no—
359C4—861no—
360C4—1721no—
361C4—1721no—
362C4#41×D4311yescharacteristic
363C4#1306337111yescharacteristic
364C2—22no—
365C2—3441no—
366C2—1721no—
367C2—1722no—
368C2#1458354111yescharacteristic
369C2C2×#1306334611yescharacteristic
370C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#483C2
socleC22×C43C22×D4
hypercenter#483D43
hypocenterC43#3296
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #14583584C2semidirect
3. #14583255C2semidirect
4. #14583225C2semidirect
5. #14583198C2semidirect
6. #14583138C2semidirect
7. #14583129C2semidirect
8. #14583124C2semidirect
9. #14583064C2semidirect
10. #14583052C2semidirect
11. #14582986C2semidirect
12. (C22⋊D43)⋊C8C2semidirect
13. #14582894C2semidirect
14. C2×#13063245C2semidirect
15. C43×#483C2semidirect
18. C2×#10621885C22semidirect
22. C2×C8×D43C22semidirect
24. #13063316C22semidirect
29. #13063305C22semidirect
34. #13063290C22semidirect
38. #13063283C22semidirect
40. #13063258C22semidirect
41. Dic43⋊C8C22semidirect
42. #13063249C22semidirect
43. #13063248C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. C8×Dic43C22semidirect
54. #106×C43C22semidirect
55. #106×C43C22semidirect
56. #103×C43C22semidirect
57. #103×C43C22semidirect
189. #483D43semidirect
201. C43#3296semidirect
229. #106C2×D43semidirect
230. #106C2×D43semidirect
234. #103C2×D43semidirect
235. #103C2×D43semidirect