Finite Group Databasebeta

← #20255077

Subgroups — #20255077

Order 6016.

546 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10625336C211yesmaximal, characteristic, complemented
2C2×SD16×D47C211yesmaximal, characteristic, complemented
3Q8×C22⋊D47C211yesmaximal, characteristic, complemented
4#15689757C211yesmaximal, characteristic
5#15689494C211yesmaximal, characteristic, complemented
6#15689355C211yesmaximal, characteristic, complemented
7#15689350C211yesmaximal, characteristic, complemented
8#15689327C211yesmaximal, characteristic, complemented
9#15689321C211yesmaximal, characteristic, complemented
10#15689276C211yesmaximal, characteristic, complemented
11#15689272C211yesmaximal, characteristic, complemented
12#15689263C211yesmaximal, characteristic, complemented
13#15689208C211yesmaximal, characteristic, complemented
14(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
15C47×#448C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic, complemented
17C22×D188C2211yescharacteristic
18C2×D4×D47—21no—
19C2×D4×D47C2211yescharacteristic
20C2×#10625325C2211yescharacteristic
21C2×#10625325C2211yescharacteristic, complemented
22C2×#10625335C2211yescharacteristic, complemented
23C2×#10625336—24no—
24C2×#10625336C2211yescharacteristic
25C2×#10625336C2211yescharacteristic
26C2×#10625336C2211yescharacteristic, complemented
27C2×#10625336C2211yescharacteristic, complemented
28SD16×D47—24no—
29C22×C47⋊C8C2211yescharacteristic, complemented
30C2×C8×D47C2211yescharacteristic, complemented
31#13094022—21no—
32#13094022C2211yescharacteristic, complemented
33#13094020C2211yescharacteristic
34#13094003—21no—
35#13094003C2211yescharacteristic, complemented
36#13094000—21no—
37#13094000C2211yescharacteristic, complemented
38#13093999C2211yescharacteristic
39#13093997—21no—
40#13093994—21no—
41#13093992—21no—
42Q8×Dic47C2211yescharacteristic, complemented
43#13093986C2211yescharacteristic
44C4×C22⋊D47—21no—
45C4×C22⋊D47C2211yescharacteristic
46#13093955C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093947C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic, complemented
51#13093945C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53C8×Dic47C2211yescharacteristic, complemented
54C22×Q8×C47C2211yescharacteristic, complemented
55C2×SD16×C47C2211yescharacteristic, complemented
56C2×SD16×C47C2211yescharacteristic, complemented
57#121×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60C22⋊C8×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47—21no—
63C2×Q8×C47—21no—
64C2×Q8×C47—22no—
65C2×Q8×C47—41no—
66C2×Q8×C47C2311yescharacteristic
67C2×Q8×C47C2311yescharacteristic
68C2×D4×C47—21no—
69C2×D4×C47C2311yescharacteristic
70C22×C4×C47—21no—
71C22×C4×C47C2311yescharacteristic
72C2×C22⋊D47—21no—
73C2×C22⋊D47—21no—
74C2×C22⋊D47—21no—
75C2×C22⋊D47D411yescharacteristic
76Q8×D47—22no—
77Q8×D47—41no—
78D4×D47—22no—
79D4×D47—41no—
80D4×D47—44no—
81C2×D188—22no—
82C2×D188—21no—
83C2×D188—21no—
84C2×D188—41no—
85C2×D188C2311yescharacteristic
86C2×D188C2311yescharacteristic
87C2×C4×D47—21no—
88C2×C4×D47—21no—
89C2×C4×D47C2311yescharacteristic
90C2×Dic94—21no—
91C2×Dic94C2311yescharacteristic
92SD16×C47—22no—
93SD16×C47—41no—
94C2×C8×C47C2311yescharacteristic
95C2×C8×C47C2311yescharacteristic
96C4⋊C4×C47C2311yescharacteristic
97C22⋊C4×C47—21no—
98C22⋊Dic47—21no—
99C22⋊Dic47D411yescharacteristic
100#10625336—22no—
101#10625336—22no—
102#10625336—22no—
103#10625336D414yescomplemented
104#10625335—22no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4D411yescharacteristic
109C4⋊Dic47—21no—
110C4⋊Dic47C2311yescharacteristic
111Dic47⋊C4—21no—
112Dic47⋊C4—21no—
113Dic47⋊C4—21no—
114Dic47⋊C4—21no—
115Dic47⋊C4D411yescharacteristic
116C4×Dic47—21no—
117C4×Dic47C2311yescharacteristic
118C2×C47⋊C8—22no—
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121#10625325—22no—
122#10625325—41no—
123C8×D47—22no—
124C23×C47—21no—
125C23×C47C2×D411yescharacteristic
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—42no—
129C22×D47—42no—
130C22×D47—42no—
131C22×D47—42no—
132C22×D47—81no—
133C22×D47—81no—
134C22×D47C2×D411yescharacteristic
135Q8×C47—21no—
136Q8×C47—21no—
137Q8×C47—21no—
138Q8×C47—42no—
139Q8×C47C2×D412yescomplemented
140D4×C47—21no—
141D4×C47—21no—
142D4×C47—42no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—42no—
149C2×C4×C47C2×D411yescharacteristic
150C2×C4×C47C2411yescharacteristic
151C22⋊D47—42no—
152C22⋊D47—42no—
153C22⋊D47—81no—
154C22⋊D47SD1614yescomplemented
155C2×Dic47—21no—
156C2×Dic47—21no—
157C2×Dic47C2×D411yescharacteristic
158C2×Dic47C2×D411yescharacteristic
159C2×Dic47C2×D411yescharacteristic
160D188—21no—
161D188—21no—
162D188—21no—
163D188—42no—
164D188—42no—
165D188C2×D412yes—
166C4×D47—21no—
167C4×D47—21no—
168C4×D47—42no—
169C4×D47—42no—
170Dic94—21no—
171Dic94—21no—
172Dic94—42no—
173C8×C47—21no—
174C8×C47—21no—
175C47⋊C8—21no—
176C47⋊C8C2×D412yescomplemented
177C22×C47—21no—
178C22×C47—21no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47C2×SD1612yescomplemented
183C22×C47C22×D411yescharacteristic
184C2×D47—21no—
185C2×D47—21no—
186C2×D47—22no—
187C2×D47—41no—
188C2×D47—41no—
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—84no—
193C2×D47—84no—
194C2×D47C2×SD1612yescomplemented
195C4×C47—22no—
196C4×C47—21no—
197C4×C47—41no—
198C4×C47—41no—
199C4×C47C22×D411yescharacteristic
200C4×C47H(5,𝔽2)11yescharacteristic
201Dic47—21no—
202Dic47—21no—
203Dic47—41no—
204Dic47—41no—
205Dic47C2×SD1612yescomplemented
206D4×SD16—471nomaximal, Sylow
207C2×C47—22no—
208C2×C47—81no—
209C2×C47D4211yescharacteristic
210C2×C47C22×SD1611yescharacteristic
211C2×C47#57711yescharacteristic
212D47—22no—
213D47—42no—
214D47—81no—
215C22×SD16—471no—
216C22×SD16—471no—
217D4×Q8—471no—
218D42—471no—
219#492—471no—
220#465—471no—
221#465—471no—
222#461—471no—
223#460—471no—
224#450—471no—
225#450—471no—
226#448—471no—
227#448D4711yescharacteristic, complemented
228C4×SD16—471no—
229C8×D4—471no—
230C47D4×SD1611yescharacteristic, complemented, Sylow
231C22×Q8—471no—
232C22×Q8C2×D4711yescharacteristic, complemented
233C22×D4—471no—
234C22×D4—471no—
235C22×D4—941no—
236C2×SD16—471no—
237C2×SD16—471no—
238C2×SD16—471no—
239C2×SD16—471no—
240C2×SD16—471no—
241C2×SD16—471no—
242C2×SD16—471no—
243C2×SD16—944no—
244C2×SD16—944no—
245C2×SD16C2×D4711yescharacteristic, complemented
246C2×SD16C2×D4711yescharacteristic, complemented
247C22×C8—471no—
248C22×C8—471no—
249C4⋊Q8—471no—
250C4⋊Q8—941no—
251#127—471no—
252C22⋊Q8—471no—
253C22⋊Q8—471no—
254C22⋊Q8—941no—
255C22⋊Q8—941no—
256#121—471no—
257#121—941no—
258#121C2×D4711yescharacteristic
259#120—941no—
260#120—941no—
261C4×Q8—471no—
262C4×D4—471no—
263C4×D4—471no—
264C4×D4—941no—
265#106—471no—
266C4⋊C8—471no—
267#103—471no—
268#103C2×D4711yescharacteristic, complemented
269#103C2×D4711yescharacteristic, complemented
270#102—471no—
271#102—471no—
272#102—471no—
273C22⋊C8—471no—
274C22⋊C8C2×D4711yescharacteristic, complemented
275C4×C8—471no—
276C24—941no—
277C24—941no—
278C2×Q8—21no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—471no—
282C2×Q8—941no—
283C2×Q8—942no—
284C2×Q8—1881no—
285C2×Q8C22×D4711yescharacteristic
286C2×Q8C22×D4711yescharacteristic
287C2×D4—21no—
288C2×D4—471no—
289C2×D4—471no—
290C2×D4—471no—
291C2×D4—942no—
292C2×D4—941no—
293C2×D4—941no—
294C2×D4—941no—
295C2×D4—941no—
296C2×D4—942no—
297C2×D4—941no—
298C2×D4—1881no—
299C2×D4—1881no—
300C2×D4—1884no—
301C2×D4C22×D4711yescharacteristic
302C22×C4—21no—
303C22×C4—471no—
304C22×C4—941no—
305C22×C4—941no—
306C22×C4C22×D4711yescharacteristic
307SD16—22no—
308SD16—41no—
309SD16—474no—
310SD16—942no—
311SD16—942no—
312SD16—942no—
313SD16—942no—
314SD16—942no—
315SD16—1881no—
316C2×C8—471no—
317C2×C8—471no—
318C2×C8—942no—
319C2×C8—942no—
320C2×C8C22×D4711yescharacteristic
321C2×C8C22×D4711yescharacteristic
322C4⋊C4—471no—
323C4⋊C4—471no—
324C4⋊C4—941no—
325C4⋊C4—941no—
326C4⋊C4—941no—
327C4⋊C4—941no—
328C4⋊C4—941no—
329C4⋊C4C22×D4711yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—471no—
332C22⋊C4—471no—
333C22⋊C4—941no—
334C22⋊C4—941no—
335C22⋊C4—941no—
336C22⋊C4—941no—
337C42—471no—
338C42—941no—
339C23—21no—
340C23—471no—
341C23—941no—
342C23—941no—
343C23—3761no—
344C23—3761no—
345C23—1882no—
346C23—1882no—
347C23—1882no—
348C23—1882no—
349C23D4×D4711yescharacteristic
350Q8—21no—
351Q8—21no—
352Q8—21no—
353Q8—42no—
354Q8—941no—
355Q8—941no—
356Q8—1882no—
357Q8D4×D4712yescomplemented
358D4—21no—
359D4—21no—
360D4—42no—
361D4—474no—
362D4—472no—
363D4—941no—
364D4—941no—
365D4—941no—
366D4—3761no—
367D4—1882no—
368D4—1882no—
369D4—1882no—
370D4—1882no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—471no—
378C2×C4—471no—
379C2×C4—471no—
380C2×C4—941no—
381C2×C4—941no—
382C2×C4—941no—
383C2×C4—941no—
384C2×C4—1882no—
385C2×C4—1882no—
386C2×C4D4×D4711yescharacteristic
387C2×C4C23×D4711yescharacteristic
388C8—21no—
389C8—21no—
390C8—472no—
391C8—941no—
392C22—21no—
393C22—21no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—472no—
398C22—941no—
399C22—941no—
400C22—942no—
401C22—3764no—
402C22—3764no—
403C22—1881no—
404C22—1881no—
405C22—1881no—
406C22—1881no—
407C22—1881no—
408C22SD16×D4712yescomplemented
409C22C2×D4×D4711yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—41no—
414C4—472no—
415C4—941no—
416C4—941no—
417C4—1881no—
418C4—1881no—
419C4C2×D4×D4711yescharacteristic
420C4#1309406911yescharacteristic
421C2—22no—
422C2—81no—
423C2—942no—
424C2—3761no—
425C2—1882no—
426C2#1568975511yescharacteristic
427C2C2×SD16×D4711yescharacteristic
428C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#448C2
socleC22×C47C22×D4
hypercenter#448D47
hypocenterC47D4×SD16
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C22×#10625336C2semidirect
2. C2×SD16×D47C2semidirect
3. Q8×C22⋊D47C2semidirect
5. #15689494C2semidirect
6. #15689355C2semidirect
7. #15689350C2semidirect
8. #15689327C2semidirect
9. #15689321C2semidirect
10. #15689276C2semidirect
11. #15689272C2semidirect
12. #15689263C2semidirect
13. #15689208C2semidirect
14. (C22⋊D47)⋊C8C2semidirect
15. C47×#448C2semidirect
16. C2×Q8×D47C22semidirect
21. C2×#10625325C22semidirect
22. C2×#10625335C22semidirect
26. C2×#10625336C22semidirect
27. C2×#10625336C22semidirect
29. C22×C47⋊C8C22semidirect
30. C2×C8×D47C22semidirect
32. #13094022C22semidirect
35. #13094003C22semidirect
37. #13094000C22semidirect
42. Q8×Dic47C22semidirect
46. #13093955C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093947C22semidirect
50. #13093946C22semidirect
51. #13093945C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. C8×Dic47C22semidirect
54. C22×Q8×C47C22semidirect
55. C2×SD16×C47C22semidirect
56. C2×SD16×C47C22semidirect
58. #103×C47C22semidirect
59. #103×C47C22semidirect
60. C22⋊C8×C47C22semidirect
103. #10625336D4semidirect
139. Q8×C47C2×D4semidirect
154. C22⋊D47SD16semidirect
176. C47⋊C8C2×D4semidirect
182. C22×C47C2×SD16semidirect
194. C2×D47C2×SD16semidirect
205. Dic47C2×SD16semidirect
227. #448D47semidirect
230. C47D4×SD16semidirect
232. C22×Q8C2×D47semidirect
245. C2×SD16C2×D47semidirect
246. C2×SD16C2×D47semidirect
268. #103C2×D47semidirect
269. #103C2×D47semidirect
274. C22⋊C8C2×D47semidirect
357. Q8D4×D47semidirect
408. C22SD16×D47semidirect