Finite Group Databasebeta

← #19144948

Subgroups — #19144948

Order 5504.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583529C211yesmaximal, characteristic, complemented
2#14583467C211yesmaximal, characteristic
3#14583265C211yesmaximal, characteristic, complemented
4#14583262C211yesmaximal, characteristic, complemented
5#14583260C211yesmaximal, characteristic, complemented
6#14583258C211yesmaximal, characteristic, complemented
7#14583255C211yesmaximal, characteristic, complemented
8#14583246C211yesmaximal, characteristic, complemented
9#14583244C211yesmaximal, characteristic, complemented
10#14582902C211yesmaximal, characteristic, complemented
11#14582899C211yesmaximal, characteristic, complemented
12#14582894C211yesmaximal, characteristic, complemented
13#102×D43C211yesmaximal, characteristic, complemented
14#14582853C211yesmaximal, characteristic, complemented
15C43×#488C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621872C2211yescharacteristic
19C2×C8×D43C2211yescharacteristic
20#13063325C2211yescharacteristic, complemented
21#13063324—21no—
22#13063324C2211yescharacteristic, complemented
23#13063322C2211yescharacteristic
24#13063321C2211yescharacteristic
25#13063316C2211yescharacteristic, complemented
26#13063315—21no—
27#13063314C2211yescharacteristic
28#13063305—21no—
29#13063303—21no—
30#13063298—21no—
31#13063298—21no—
32#13063295—21no—
33#13063295—21no—
34#13063283C2211yescharacteristic
35#13063282C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic
37#13063249C2211yescharacteristic, complemented
38#13063249C2211yescharacteristic, complemented
39#13063247C2211yescharacteristic
40#13063247C2211yescharacteristic
41#13063247C2211yescharacteristic, complemented
42#13063247C2211yescharacteristic, complemented
43#13063246C2211yescharacteristic
44#13063246C2211yescharacteristic
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic, complemented
48#13063245C2211yescharacteristic, complemented
49#13063236C2211yescharacteristic, complemented
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52#125×C43C2211yescharacteristic, complemented
53#124×C43C2211yescharacteristic
54#103×C43C2211yescharacteristic, complemented
55#103×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C4×C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43C2311yescharacteristic
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65#10621902—22no—
66#10621902—22no—
67D4×D43—22no—
68D4×D43—22no—
69C2×D172—21no—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172C2311yescharacteristic
73C2×D172C2311yescharacteristic
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43C2311yescharacteristic
77C2×Dic86—21no—
78C2×Dic86—21no—
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C42×C43C2311yescharacteristic
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4D411yescharacteristic
92(C2×D43)⋊C4D411yescharacteristic
93C4⋊Dic43—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4D411yescharacteristic
101Dic43⋊C4D411yescharacteristic
102C4×Dic43—21no—
103C4×Dic43C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106#10621872—22no—
107C8×D43—22no—
108C23×C43—21no—
109C22×D43—21no—
110C22×D43—21no—
111C22×D43—42no—
112C22×D43—81no—
113C22×D43—81no—
114C22×D43C2×D411yescharacteristic
115Q8×C43—21no—
116Q8×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2411yescharacteristic
125C22⋊D43—42no—
126C22⋊D43—81no—
127C22⋊D43—81no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43C2×D411yescharacteristic
131C2×Dic43C2×D411yescharacteristic
132C2×Dic43C2×D411yescharacteristic
133D172—21no—
134D172—21no—
135D172—21no—
136D172—21no—
137D172—42no—
138D172—81no—
139D172—81no—
140C4×D43—42no—
141C4×D43—81no—
142C4×D43#4112yes—
143C4×D43#4112yes—
144Dic86—81no—
145Dic86—81no—
146C8×C43—21no—
147C8×C43—21no—
148C43⋊C8—21no—
149C43⋊C8—21no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43C22×D411yescharacteristic
154C2×D43—21no—
155C2×D43—21no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—84no—
163C2×D43#12412yes—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43C2×#4111yescharacteristic
170C4×C43C2×#4111yescharacteristic
171Dic43—21no—
172Dic43—21no—
173Dic43—41no—
174Dic43—41no—
175Dic43#12412yes—
176#3136—431nomaximal, Sylow
177C2×C43—81no—
178C2×C43C2×#12411yescharacteristic
179C2×C43#57611yescharacteristic
180C2×C43#57711yescharacteristic
181D43—22no—
182D43—81no—
183D43—81no—
184#544—431no—
185#535—431no—
186#490—431no—
187#490—431no—
188#489—431no—
189#489—431no—
190#488—431no—
191#488D4311yescharacteristic, complemented
192#486—431no—
193#486—431no—
194#418—431no—
195#417—431no—
196#416—431no—
197C2×#102—431no—
198#405—431no—
199C43#313611yescharacteristic, complemented, Sylow
200C2×#41—431no—
201C22×D4—431no—
202C2×M16—431no—
203C22×C8—431no—
204C4⋊Q8—431no—
205C4⋊Q8—431no—
206C4⋊Q8—861no—
207#127—431no—
208#127—431no—
209#125—431no—
210#125—861no—
211#125C2×D4311yescharacteristic, complemented
212#124—431no—
213#124C2×D4311yescharacteristic
214C22⋊Q8—861no—
215C22⋊Q8—861no—
216#121—861no—
217#121—861no—
218#120—861no—
219#120—861no—
220#117—431no—
221#117—431no—
222C2×C4⋊C4—431no—
223#103—431no—
224#103—431no—
225#103C2×D4311yescharacteristic, complemented
226#103C2×D4311yescharacteristic, complemented
227#102—431no—
228#102—431no—
229#102—431no—
230#102—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#102—431no—
235#102—431no—
236#102—431no—
237#102C2×D4311yescharacteristic
238#102C2×D4311yescharacteristic
239#97—431no—
240#97—431no—
241C4×C8—431no—
242C4×C8C2×D4311yescharacteristic, complemented
243C24—861no—
244#41—862no—
245#41—862no—
246C2×Q8—861no—
247C2×Q8—861no—
248C2×Q8C22×D4311yescharacteristic
249C2×D4—431no—
250C2×D4—431no—
251C2×D4—861no—
252C2×D4—862no—
253C2×D4—862no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4—861no—
259C2×D4C22×D4311yescharacteristic
260C22×C4—431no—
261C22×C4—861no—
262C22×C4—861no—
263M16—862no—
264C2×C8—431no—
265C2×C8—431no—
266C2×C8—862no—
267C2×C8C22×D4311yescharacteristic
268C2×C8C22×D4311yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—431no—
272C4⋊C4—431no—
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4C22×D4311yescharacteristic
281C4⋊C4C22×D4311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—431no—
285C22⋊C4—431no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C42—431no—
290C42—861no—
291C42C22×D4311yescharacteristic
292C23—21no—
293C23—431no—
294C23—861no—
295C23—861no—
296C23—3441no—
297C23—3441no—
298C23—1722no—
299Q8—21no—
300Q8—21no—
301Q8—3441no—
302Q8—3441no—
303D4—21no—
304D4—21no—
305D4—861no—
306D4—861no—
307D4—861no—
308D4—861no—
309D4—3441no—
310D4—3441no—
311D4—3441no—
312D4—3441no—
313D4—1722no—
314D4—1722no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—431no—
319C2×C4—432no—
320C2×C4—432no—
321C2×C4—431no—
322C2×C4—431no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—3441no—
326C2×C4—1722no—
327C2×C4D4×D4311yescharacteristic
328C2×C4D4×D4311yescharacteristic
329C2×C4C23×D4311yescharacteristic
330C8—21no—
331C8—21no—
332C8—861no—
333C8—861no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—432no—
338C22—861no—
339C22—861no—
340C22—3444no—
341C22—1721no—
342C22—1721no—
343C22—1721no—
344C22—1721no—
345C22—1721no—
346C22—1721no—
347C22C2×D4×D4311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—432no—
354C4—861no—
355C4—861no—
356C4—1721no—
357C4—1721no—
358C4#41×D4311yescharacteristic
359C4#41×D4311yescharacteristic
360C2—81no—
361C2—862no—
362C2—3441no—
363C2—3441no—
364C2#124×D4311yescharacteristic
365C2#1458370111yescharacteristic
366C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#488C2
socleC22×C43C22×D4
hypercenter#488D43
hypocenterC43#3136
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #14583529C2semidirect
3. #14583265C2semidirect
4. #14583262C2semidirect
5. #14583260C2semidirect
6. #14583258C2semidirect
7. #14583255C2semidirect
8. #14583246C2semidirect
9. #14583244C2semidirect
10. #14582902C2semidirect
11. #14582899C2semidirect
12. #14582894C2semidirect
13. #102×D43C2semidirect
14. #14582853C2semidirect
15. C43×#488C2semidirect
20. #13063325C22semidirect
22. #13063324C22semidirect
25. #13063316C22semidirect
37. #13063249C22semidirect
38. #13063249C22semidirect
41. #13063247C22semidirect
42. #13063247C22semidirect
47. #13063245C22semidirect
48. #13063245C22semidirect
49. #13063236C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
52. #125×C43C22semidirect
54. #103×C43C22semidirect
55. #103×C43C22semidirect
58. C4×C8×C43C22semidirect
191. #488D43semidirect
199. C43#3136semidirect
211. #125C2×D43semidirect
225. #103C2×D43semidirect
226. #103C2×D43semidirect
242. C4×C8C2×D43semidirect