Finite Group Databasebeta

← #19146122

Subgroups — #19146122

Order 5504.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063349C211yesmaximal, characteristic, complemented
2C2×#13063344C211yesmaximal, characteristic, complemented
3#14583553C211yesmaximal, characteristic, complemented
4#14583544C211yesmaximal, characteristic, complemented
5#14583293C211yesmaximal, characteristic, complemented
6#14583158C211yesmaximal, characteristic, complemented
7#14583129C211yesmaximal, characteristic, complemented
8#14583114C211yesmaximal, characteristic, complemented
9#14583104C211yesmaximal, characteristic, complemented
10#14583062C211yesmaximal, characteristic, complemented
11#14583062C211yesmaximal, characteristic, complemented
12#14583051C211yesmaximal, characteristic, complemented
13#14583045C211yesmaximal, characteristic, complemented
14#14582972C211yesmaximal, characteristic, complemented
15C43×#442C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×#10621900C2211yescharacteristic, complemented
19C2×D4×D43C2211yescharacteristic
20#13063349—24no—
21#13063344—24no—
22C2×Dic172C2211yescharacteristic, complemented
23C2×Dic172C2211yescharacteristic, complemented
24C2×#10621873C2211yescharacteristic
25C2×#10621873C2211yescharacteristic
26C2×#10621883C2211yescharacteristic
27C2×#10621883C2211yescharacteristic
28C2×#10621883C2211yescharacteristic, complemented
29C2×#10621882C2211yescharacteristic
30C2×#10621872C2211yescharacteristic
31C2×C8×D43C2211yescharacteristic, complemented
32#13063325C2211yescharacteristic, complemented
33#13063313C2211yescharacteristic
34#13063309—21no—
35#13063309—21no—
36#13063309—21no—
37#13063305C2211yescharacteristic
38#13063305C2211yescharacteristic
39#13063305C2211yescharacteristic, complemented
40#13063300C2211yescharacteristic
41#13063299—21no—
42#13063299—21no—
43#13063295—21no—
44C4×D172C2211yescharacteristic
45C2×C4⋊Dic43—21no—
46C2×(C2×D43)⋊C4—21no—
47C4⋊(C43⋊C8)C2211yescharacteristic, complemented
48#13063248C2211yescharacteristic, complemented
49#13063248C2211yescharacteristic, complemented
50#13063248C2211yescharacteristic, complemented
51#13063245C2211yescharacteristic
52(C2×D43)⋊C8C2211yescharacteristic
53(C2×D43)⋊C8C2211yescharacteristic, complemented
54C2×D8×C43C2211yescharacteristic
55C4×D4×C43C2211yescharacteristic
56C4×D4×C43C2211yescharacteristic, complemented
57#106×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic
59#102×C43C2211yescharacteristic, complemented
60#97×C43C2211yescharacteristic, complemented
61C23×D43—21no—
62C2×D4×C43C2311yescharacteristic
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73#10621900—22no—
74#10621900—22no—
75#10621900—22no—
76#10621900—41no—
77#10621900—41no—
78#10621900—41no—
79D4×D43—22no—
80D4×D43—41no—
81C2×D172—21no—
82C2×D172D411yescharacteristic
83C2×D172C2311yescharacteristic
84C2×C4×D43C2311yescharacteristic
85C2×C4×D43C2311yescharacteristic
86C2×Dic86C2311yescharacteristic
87C2×Dic86C2311yescharacteristic
88C2×Dic86C2311yescharacteristic
89D8×C43D414yescomplemented
90C2×C8×C43C2311yescharacteristic
91C2×C8×C43C2311yescharacteristic
92C4⋊C4×C43C2311yescharacteristic
93C4⋊C4×C43C2311yescharacteristic
94C22⋊C4×C43—21no—
95C22⋊C4×C43—21no—
96C42×C43C2311yescharacteristic
97#10621883—22no—
98#10621883—22no—
99#10621883—22no—
100#10621882—22no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4D411yescharacteristic
108(C2×D43)⋊C4D411yescharacteristic
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43D411yescharacteristic
115C2×C43⋊C8C2311yescharacteristic
116C2×C43⋊C8C2311yescharacteristic
117Dic172—22no—
118Dic172—41no—
119#10621873—22no—
120#10621873—41no—
121#10621872—22no—
122C8×D43—22no—
123C23×C43—21no—
124C23×C43—21no—
125C22×D43—21no—
126C22×D43—42no—
127C22×D43—42no—
128C22×D43—81no—
129C22×D43C2×D411yescharacteristic
130C22×D43C2×D411yescharacteristic
131D4×C43—21no—
132D4×C43—21no—
133D4×C43C2×D412yes—
134D4×C43C2×D412yes—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—42no—
138C2×C4×C43—81no—
139C2×C4×C43C2×D411yescharacteristic
140C2×C4×C43C2×D411yescharacteristic
141C2×C4×C43C2411yescharacteristic
142C22⋊D43—42no—
143C22⋊D43—42no—
144C22⋊D43—42no—
145C22⋊D43—42no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—42no—
150C2×Dic43—42no—
151C2×Dic43—42no—
152C2×Dic43C2×D411yescharacteristic
153C2×Dic43C2×D411yescharacteristic
154D172—21no—
155D172—21no—
156D172—41no—
157D172—81no—
158C4×D43—21no—
159C4×D43—21no—
160C4×D43—21no—
161C4×D43—21no—
162Dic86—21no—
163Dic86—21no—
164Dic86—21no—
165Dic86—21no—
166Dic86—21no—
167Dic86—21no—
168C8×C43—21no—
169C8×C43C2×D412yes—
170C43⋊C8—21no—
171C43⋊C8—21no—
172C22×C43—22no—
173C22×C43—22no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43C22×D411yescharacteristic
179C2×D43—21no—
180C2×D43—21no—
181C2×D43—21no—
182C2×D43—21no—
183C2×D43—21no—
184C2×D43—21no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C2×D43—84no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—41no—
192C4×C43—41no—
193C4×C43C22×D411yescharacteristic
194C4×C43H(5,𝔽2)11yescharacteristic
195Dic43—21no—
196Dic43—21no—
197Dic43—41no—
198Dic43—41no—
199Dic43—41no—
200#3267—431nomaximal, Sylow
201C2×C43—42no—
202C2×C43—42no—
203C2×C43D4211yescharacteristic
204C2×C43#57511yescharacteristic
205C2×C43#57711yescharacteristic
206D43—41no—
207D43—41no—
208D43—81no—
209C2×AGL(1,ℤ/8)—431no—
210C2×#135—431no—
211#547—431no—
212#546—431no—
213#497—431no—
214#470—431no—
215#465—431no—
216#463—431no—
217#461—431no—
218#452—431no—
219#452—431no—
220#450—431no—
221#449—431no—
222#442D4311yescharacteristic, complemented
223#435—431no—
224C43#326711yescharacteristic, complemented, Sylow
225C2×#41—431no—
226C2×#41—431no—
227C2×#41—431no—
228C22×D4—431no—
229AGL(1,ℤ/8)—864no—
230#135—864no—
231C2×Q16—431no—
232C2×Q16—431no—
233C2×SD16—431no—
234C2×SD16—431no—
235C2×SD16—431no—
236C2×SD16—431no—
237C2×SD16—431no—
238C2×D8—431no—
239C2×D8C2×D4311yescharacteristic
240C2×M16—431no—
241C22×C8—431no—
242C4⋊Q8—431no—
243#124—431no—
244#123—861no—
245#123—861no—
246#123—861no—
247C22⋊Q8—431no—
248C22⋊Q8—431no—
249C22⋊Q8—431no—
250#121—431no—
251#121—861no—
252#121—861no—
253#120—861no—
254C4×D4—431no—
255C4×D4C2×D4311yescharacteristic
256C4×D4C2×D4311yescharacteristic, complemented
257C2×C4⋊C4—861no—
258C2×C22⋊C4—861no—
259#106C2×D4311yescharacteristic, complemented
260C4⋊C8—431no—
261#103—431no—
262#103—431no—
263#103—431no—
264#102—431no—
265#102C2×D4311yescharacteristic
266#102C2×D4311yescharacteristic, complemented
267C22⋊C8—431no—
268C22⋊C8—431no—
269#97C2×D4311yescharacteristic, complemented
270C24—861no—
271#41—862no—
272#41—862no—
273#41—862no—
274#41—1721no—
275#41—1721no—
276#41—1721no—
277C2×Q8—431no—
278C2×Q8—431no—
279C2×Q8—431no—
280C2×D4—431no—
281C2×D4—431no—
282C2×D4—861no—
283C2×D4—861no—
284C2×D4—862no—
285C2×D4—861no—
286C2×D4—861no—
287C2×D4—861no—
288C2×D4—1721no—
289C2×D4C22×D4311yescharacteristic
290C2×D4C22×D4311yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—431no—
294C22×C4—431no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—861no—
298Q16—862no—
299Q16—1721no—
300SD16—862no—
301SD16—862no—
302SD16—862no—
303SD16—862no—
304SD16—1721no—
305D8—862no—
306D8D17214yescomplemented
307M16—862no—
308C2×C8—431no—
309C2×C8—431no—
310C2×C8—862no—
311C2×C8C22×D4311yescharacteristic
312C2×C8C22×D4311yescharacteristic
313C4⋊C4—431no—
314C4⋊C4—861no—
315C4⋊C4—861no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4—861no—
319C4⋊C4C22×D4311yescharacteristic
320C4⋊C4C22×D4311yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—431no—
324C22⋊C4—431no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C22⋊C4—861no—
328C22⋊C4—861no—
329C22⋊C4—861no—
330C22⋊C4—861no—
331C42C22×D4311yescharacteristic
332C23—21no—
333C23—21no—
334C23—431no—
335C23—431no—
336C23—861no—
337C23—3441no—
338C23—1722no—
339C23—1722no—
340Q8—861no—
341Q8—861no—
342Q8—861no—
343Q8—861no—
344Q8—861no—
345Q8—861no—
346D4—21no—
347D4—21no—
348D4—861no—
349D4—861no—
350D4—3441no—
351D4—1721no—
352D4—1722no—
353D4—1722no—
354D4—1722no—
355D4—1722no—
356D4C2×D17212yes—
357D4C2×D17212yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—431no—
363C2×C4—431no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—861no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—861no—
370C2×C4—861no—
371C2×C4—1722no—
372C2×C4—1722no—
373C2×C4—1722no—
374C2×C4D4×D4311yescharacteristic
375C2×C4D4×D4311yescharacteristic
376C2×C4C23×D4311yescharacteristic
377C8—21no—
378C8—861no—
379C8—861no—
380C8C2×D17212yes—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—861no—
388C22—861no—
389C22—861no—
390C22—861no—
391C22—861no—
392C22—861no—
393C22—3444no—
394C22—1721no—
395C22—1721no—
396C22—1721no—
397C22C2×D4×D4311yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—861no—
403C4—861no—
404C4—1721no—
405C4—1721no—
406C4—1721no—
407C4C22×D17211yescharacteristic
408C4#1306337111yescharacteristic
409C2—42no—
410C2—42no—
411C2—3441no—
412C2—1721no—
413C2—1721no—
414C2D4×D17211yescharacteristic
415C2#1458369511yescharacteristic
416C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#442C2
socleC22×C43C22×D4
hypercenter#442D43
hypocenterC43#3267
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. C2×#13063349C2semidirect
2. C2×#13063344C2semidirect
3. #14583553C2semidirect
4. #14583544C2semidirect
5. #14583293C2semidirect
6. #14583158C2semidirect
7. #14583129C2semidirect
8. #14583114C2semidirect
9. #14583104C2semidirect
10. #14583062C2semidirect
11. #14583062C2semidirect
12. #14583051C2semidirect
13. #14583045C2semidirect
14. #14582972C2semidirect
15. C43×#442C2semidirect
18. C2×#10621900C22semidirect
22. C2×Dic172C22semidirect
23. C2×Dic172C22semidirect
28. C2×#10621883C22semidirect
31. C2×C8×D43C22semidirect
32. #13063325C22semidirect
39. #13063305C22semidirect
47. C4⋊(C43⋊C8)C22semidirect
48. #13063248C22semidirect
49. #13063248C22semidirect
50. #13063248C22semidirect
53. (C2×D43)⋊C8C22semidirect
56. C4×D4×C43C22semidirect
57. #106×C43C22semidirect
59. #102×C43C22semidirect
60. #97×C43C22semidirect
89. D8×C43D4semidirect
222. #442D43semidirect
224. C43#3267semidirect
256. C4×D4C2×D43semidirect
259. #106C2×D43semidirect
266. #102C2×D43semidirect
269. #97C2×D43semidirect
306. D8D172semidirect