Finite Group Databasebeta

← #20254140

Subgroups — #20254140

Order 6016.

468 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D47C211yesmaximal, characteristic, complemented
2#121×D47C211yesmaximal, characteristic
3#15689455C211yesmaximal, characteristic, complemented
4#15689452C211yesmaximal, characteristic, complemented
5#15689443C211yesmaximal, characteristic, complemented
6#15689440C211yesmaximal, characteristic, complemented
7#15689354C211yesmaximal, characteristic, complemented
8#15689352C211yesmaximal, characteristic, complemented
9#15689350C211yesmaximal, characteristic, complemented
10#15689275C211yesmaximal, characteristic, complemented
11#15689272C211yesmaximal, characteristic, complemented
12#15689263C211yesmaximal, characteristic, complemented
13#15689260C211yesmaximal, characteristic, complemented
14C2×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
15C47×#465C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic, complemented
17C2×D4×D47—21no—
18C2×D4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C2×#10625325C2211yescharacteristic, complemented
21C2×#10625335C2211yescharacteristic, complemented
22C2×#10625336C2211yescharacteristic, complemented
23C22×C47⋊C8C2211yescharacteristic, complemented
24#13094004C2211yescharacteristic
25#13094003C2211yescharacteristic, complemented
26#13094002—21no—
27#13094001—21no—
28#13094000C2211yescharacteristic
29#13093999C2211yescharacteristic
30#13093998C2211yescharacteristic
31#13093997—21no—
32#13093996—21no—
33#13093995C2211yescharacteristic
34C4⋊C4×D47—21no—
35C4⋊C4×D47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic, complemented
37C22⋊C4×D47—21no—
38C22⋊C4×D47—21no—
39#13093956C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41#13093955C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093948C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic, complemented
47#13093944C2211yescharacteristic, complemented
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C47C2211yescharacteristic, complemented
53C22×C8×C47C2211yescharacteristic, complemented
54C22⋊Q8×C47C2211yescharacteristic, complemented
55#121×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C23×D47D411yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C22×Dic47D411yescharacteristic
69Q8×D47—41no—
70Q8×D47—41no—
71D4×D47—41no—
72D4×D47—41no—
73D4×D47—44no—
74C2×D188—21no—
75C2×D188C2311yescharacteristic
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47—41no—
80C2×C4×D47—41no—
81C2×C4×D47D411yescharacteristic
82C2×C4×D47D411yescharacteristic
83C2×C4×D47C2311yescharacteristic
84C2×C4×D47C2311yescharacteristic
85C2×Dic94—21no—
86C2×Dic94C2311yescharacteristic
87SD16×C47—41no—
88C2×C8×C47—41no—
89C2×C8×C47C2311yescharacteristic
90C2×C8×C47C2311yescharacteristic
91C4⋊C4×C47—21no—
92C4⋊C4×C47C2311yescharacteristic
93C4⋊C4×C47C2311yescharacteristic
94C22⋊C4×C47—21no—
95C22⋊C4×C47—21no—
96C22⋊Dic47—21no—
97C22⋊Dic47—21no—
98#10625336—41no—
99#10625335—41no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104C4⋊Dic47—21no—
105C4⋊Dic47C2311yescharacteristic
106C4⋊Dic47C2311yescharacteristic
107Dic47⋊C4—21no—
108Dic47⋊C4—21no—
109Dic47⋊C4—21no—
110Dic47⋊C4—21no—
111C2×C47⋊C8—41no—
112C2×C47⋊C8C2311yescharacteristic
113C2×C47⋊C8C2311yescharacteristic
114#10625325—41no—
115C23×C47—21no—
116C23×C47C2×D411yescharacteristic
117C22×D47—21no—
118C22×D47—41no—
119C22×D47—41no—
120C22×D47—42no—
121C22×D47—42no—
122C22×D47—42no—
123C22×D47SD1614yescomplemented
124C22×D47C2×D411yescharacteristic
125C22×D47C2×D411yescharacteristic
126Q8×C47—21no—
127Q8×C47—21no—
128D4×C47—21no—
129D4×C47—21no—
130D4×C47—42no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2411yescharacteristic
138C22⋊D47—42no—
139C22⋊D47—42no—
140C22⋊D47—42no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—41no—
145C2×Dic47C2×D411yescharacteristic
146C2×Dic47C2×D411yescharacteristic
147D188—21no—
148D188—21no—
149D188—42no—
150C4×D47—21no—
151C4×D47—21no—
152C4×D47—21no—
153C4×D47—21no—
154C4×D47—41no—
155C4×D47—41no—
156C4×D47—42no—
157C4×D47—42no—
158C4×D47—42no—
159Dic94—21no—
160Dic94—21no—
161Dic94—42no—
162C8×C47—21no—
163C8×C47—21no—
164C47⋊C8—21no—
165C47⋊C8—21no—
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47C2×SD1612yes—
172C22×C47C22×D411yescharacteristic
173C2×D47—21no—
174C2×D47—21no—
175C2×D47—21no—
176C2×D47—21no—
177C2×D47—44no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—84no—
182C2×D47C2×SD1612yes—
183C2×D47C2×SD1612yes—
184C4×C47—21no—
185C4×C47—41no—
186C4×C47—41no—
187C4×C47—41no—
188C4×C47H(5,𝔽2)11yescharacteristic
189C4×C47H(5,𝔽2)11yescharacteristic
190Dic47—21no—
191Dic47—21no—
192Dic47—41no—
193Dic47—41no—
194Dic47—41no—
195#3187—471nomaximal, Sylow
196C2×C47—22no—
197C2×C47—81no—
198C2×C47#53411yescharacteristic
199C2×C47C22×SD1611yescharacteristic
200C2×C47#57511yescharacteristic
201D47—22no—
202D47—22no—
203D47—81no—
204C2×C22⋊Q8—471no—
205C2×#121—471no—
206#483—471no—
207#483—471no—
208#481—471no—
209#481—471no—
210#465—471no—
211#465—471no—
212#465—471no—
213#465D4711yescharacteristic, complemented
214#450—471no—
215#450—471no—
216#448—471no—
217#448—471no—
218C2×C22⋊C8—471no—
219C47#318711yescharacteristic, complemented, Sylow
220C22×Q8—471no—
221C22×D4—471no—
222C22×D4—941no—
223C23×C4—471no—
224C2×SD16—471no—
225C2×SD16—471no—
226C2×SD16—471no—
227C2×SD16C2×D4711yescharacteristic, complemented
228C22×C8—471no—
229C22×C8C2×D4711yescharacteristic, complemented
230C22⋊Q8—471no—
231C22⋊Q8—471no—
232C22⋊Q8—471no—
233C22⋊Q8—941no—
234C22⋊Q8—941no—
235C22⋊Q8C2×D4711yescharacteristic, complemented
236#121—471no—
237#121—471no—
238#121—471no—
239#121—941no—
240#121—941no—
241#121C2×D4711yescharacteristic
242C2×C4⋊C4—471no—
243C2×C4⋊C4—471no—
244C2×C4⋊C4—941no—
245C2×C22⋊C4—941no—
246C2×C22⋊C4—941no—
247#106—471no—
248#106—471no—
249#106—471no—
250#106C2×D4711yescharacteristic, complemented
251#103—471no—
252#103—471no—
253#103—471no—
254#103C2×D4711yescharacteristic, complemented
255#102—471no—
256#102—471no—
257#102—471no—
258#102C2×D4711yescharacteristic, complemented
259C22⋊C8—471no—
260C22⋊C8—471no—
261C22⋊C8—471no—
262C22⋊C8—471no—
263C24—471no—
264C24—941no—
265C2×Q8—471no—
266C2×Q8—941no—
267C2×Q8—1881no—
268C2×Q8—1881no—
269C2×Q8C22×D4711yescharacteristic
270C2×D4—21no—
271C2×D4—471no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—1881no—
277C2×D4—1881no—
278C2×D4—1884no—
279C2×D4C22×D4711yescharacteristic
280C22×C4—471no—
281C22×C4—471no—
282C22×C4—471no—
283C22×C4—471no—
284C22×C4—471no—
285C22×C4—941no—
286C22×C4—941no—
287C22×C4—941no—
288C22×C4—1881no—
289C22×C4—1881no—
290C22×C4C22×D4711yescharacteristic
291SD16—41no—
292SD16—1881no—
293SD16—1881no—
294SD16—1881no—
295C2×C8—41no—
296C2×C8—471no—
297C2×C8—471no—
298C2×C8—1881no—
299C2×C8C22×D4711yescharacteristic
300C2×C8C22×D4711yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—471no—
303C4⋊C4—471no—
304C4⋊C4—941no—
305C4⋊C4—941no—
306C4⋊C4—941no—
307C4⋊C4—941no—
308C4⋊C4—941no—
309C4⋊C4C22×D4711yescharacteristic
310C4⋊C4C22×D4711yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—941no—
314C22⋊C4—941no—
315C22⋊C4—941no—
316C22⋊C4—941no—
317C22⋊C4—941no—
318C22⋊C4—941no—
319C23—21no—
320C23—471no—
321C23—471no—
322C23—474no—
323C23—941no—
324C23—1881no—
325C23—1881no—
326C23—1882no—
327C23—1882no—
328C23—1882no—
329C23D4×D4711yescharacteristic
330Q8—21no—
331Q8—21no—
332Q8—941no—
333Q8—941no—
334Q8—1882no—
335D4—21no—
336D4—21no—
337D4—42no—
338D4—941no—
339D4—941no—
340D4—1882no—
341D4—1882no—
342D4—1882no—
343D4—1882no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—471no—
350C2×C4—471no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—941no—
358C2×C4—1881no—
359C2×C4—1881no—
360C2×C4—1882no—
361C2×C4—1882no—
362C2×C4—1882no—
363C2×C4—1881no—
364C2×C4D4×D4711yescharacteristic
365C2×C4C23×D4711yescharacteristic
366C8—21no—
367C8—21no—
368C8—941no—
369C8—941no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—472no—
376C22—472no—
377C22—941no—
378C22—941no—
379C22—941no—
380C22—941no—
381C22—3764no—
382C22—1884no—
383C22—1881no—
384C22—1881no—
385C22—1881no—
386C22SD16×D4712yes—
387C22C2×D4×D4711yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—941no—
393C4—941no—
394C4—1881no—
395C4—1881no—
396C4—1881no—
397C4#1309406911yescharacteristic
398C4#1309407011yescharacteristic
399C2—22no—
400C2—81no—
401C2—942no—
402C2—942no—
403C2—3761no—
404C2#1568968111yescharacteristic
405C2C2×SD16×D4711yescharacteristic
406C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#465C2
socleC22×C47C22×D4
hypercenter#465D47
hypocenterC47#3187
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C22⋊Q8×D47C2semidirect
3. #15689455C2semidirect
4. #15689452C2semidirect
5. #15689443C2semidirect
6. #15689440C2semidirect
7. #15689354C2semidirect
8. #15689352C2semidirect
9. #15689350C2semidirect
10. #15689275C2semidirect
11. #15689272C2semidirect
12. #15689263C2semidirect
13. #15689260C2semidirect
14. C2×(C2×D47)⋊C8C2semidirect
15. C47×#465C2semidirect
16. C2×Q8×D47C22semidirect
20. C2×#10625325C22semidirect
21. C2×#10625335C22semidirect
22. C2×#10625336C22semidirect
23. C22×C47⋊C8C22semidirect
25. #13094003C22semidirect
36. C4⋊C4×D47C22semidirect
39. #13093956C22semidirect
40. #13093955C22semidirect
41. #13093955C22semidirect
42. #13093949C22semidirect
43. #13093948C22semidirect
44. #13093947C22semidirect
45. #13093946C22semidirect
46. #13093945C22semidirect
47. #13093944C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. (C2×D47)⋊C8C22semidirect
52. C2×SD16×C47C22semidirect
53. C22×C8×C47C22semidirect
54. C22⋊Q8×C47C22semidirect
56. #106×C47C22semidirect
57. #103×C47C22semidirect
58. #102×C47C22semidirect
123. C22×D47SD16semidirect
213. #465D47semidirect
219. C47#3187semidirect
227. C2×SD16C2×D47semidirect
229. C22×C8C2×D47semidirect
235. C22⋊Q8C2×D47semidirect
250. #106C2×D47semidirect
254. #103C2×D47semidirect
258. #102C2×D47semidirect