Finite Group Databasebeta

← #20254167

Subgroups — #20254167

Order 6016.

420 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689630C211yesmaximal, characteristic
2C22⋊Q8×D47C211yesmaximal, characteristic, complemented
3#15689465C211yesmaximal, characteristic, complemented
4#15689461C211yesmaximal, characteristic, complemented
5#15689452C211yesmaximal, characteristic, complemented
6#15689435C211yesmaximal, characteristic, complemented
7#15689363C211yesmaximal, characteristic, complemented
8#15689361C211yesmaximal, characteristic, complemented
9#15689351C211yesmaximal, characteristic, complemented
10#15689349C211yesmaximal, characteristic, complemented
11#15689285C211yesmaximal, characteristic, complemented
12#15689277C211yesmaximal, characteristic, complemented
13#15689260C211yesmaximal, characteristic, complemented
14C22⋊C8×D47C211yesmaximal, characteristic, complemented
15C47×#452C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C2×#10625337C2211yescharacteristic, complemented
19C2×#10625335C2211yescharacteristic, complemented
20C2×C8×D47C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic
22#13094005—21no—
23#13094004C2211yescharacteristic
24#13094003C2211yescharacteristic
25#13094002—21no—
26#13094001—21no—
27#13094000C2211yescharacteristic
28#13094000C2211yescharacteristic
29#13094000C2211yescharacteristic
30#13093995C2211yescharacteristic
31#13093995C2211yescharacteristic
32#13093992—21no—
33C4×C22⋊D47—21no—
34C4×C22⋊D47—21no—
35#13093983C2211yescharacteristic
36C4⋊C4×D47—21no—
37C4⋊C4×D47C2211yescharacteristic
38C22⋊C4×D47—21no—
39#13093958C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41#13093956C2211yescharacteristic, complemented
42#13093955C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093948C2211yescharacteristic, complemented
46#13093948C2211yescharacteristic, complemented
47#13093948C2211yescharacteristic, complemented
48#13093945C2211yescharacteristic, complemented
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52C2×#41×C47C2211yescharacteristic
53C2×Q16×C47C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic, complemented
55C22⋊Q8×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic
59C23×D47D411yescharacteristic
60#41×C47—41no—
61#41×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47—21no—
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47—21no—
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C22×Dic47D411yescharacteristic
71Q8×D47—41no—
72Q8×D47—41no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47—41no—
76C2×C4×D47—41no—
77C2×C4×D47D411yescharacteristic
78C2×C4×D47D411yescharacteristic
79C2×C4×D47C2311yescharacteristic
80C2×C4×D47C2311yescharacteristic
81C2×Dic94—21no—
82C2×Dic94C2311yescharacteristic
83Q16×C47—41no—
84SD16×C47—41no—
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C4⋊C4×C47—21no—
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93C22⋊Dic47—21no—
94#10625337—41no—
95#10625335—41no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100C4⋊Dic47—21no—
101C4⋊Dic47C2311yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103C4⋊Dic47C2311yescharacteristic
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107Dic47⋊C4—21no—
108Dic47⋊C4—21no—
109C4×Dic47—21no—
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112C8×D47—41no—
113C8×D47—41no—
114C23×C47—21no—
115C23×C47C2×D411yescharacteristic
116C22×D47—22no—
117C22×D47—22no—
118C22×D47—41no—
119C22×D47C2×D411yescharacteristic
120C22×D47C2×D411yescharacteristic
121Q8×C47—21no—
122Q8×C47—21no—
123Q8×C47—21no—
124Q8×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—42no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—42no—
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2411yescharacteristic
136C22⋊D47—42no—
137C22⋊D47—42no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—41no—
143C2×Dic47C2×D411yescharacteristic
144C2×Dic47C2×D411yescharacteristic
145C4×D47—21no—
146C4×D47—21no—
147C4×D47—21no—
148C4×D47—21no—
149C4×D47—41no—
150C4×D47—41no—
151C4×D47—42no—
152C4×D47—42no—
153Dic94—21no—
154Dic94—21no—
155Dic94—42no—
156C8×C47—21no—
157C8×C47—21no—
158C47⋊C8—21no—
159C47⋊C8—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47C22×D411yescharacteristic
167C2×D47—21no—
168C2×D47—21no—
169C2×D47—21no—
170C2×D47—21no—
171C2×D47—44no—
172C2×D47#13512yes—
173C2×D47#13712yes—
174C4×C47—21no—
175C4×C47—41no—
176C4×C47—41no—
177C4×C47—41no—
178C4×C47H(5,𝔽2)11yescharacteristic
179C4×C47H(5,𝔽2)11yescharacteristic
180Dic47—21no—
181Dic47—21no—
182Dic47—41no—
183Dic47—41no—
184Dic47—41no—
185Dic47—41no—
186#3190—471nomaximal, Sylow
187C2×C47—41no—
188C2×C47—81no—
189C2×C47#53411yescharacteristic
190C2×C47C2×#13511yescharacteristic
191C2×C47C2×#13711yescharacteristic
192D47—22no—
193D47—22no—
194#525—471no—
195C2×C22⋊Q8—471no—
196#485—471no—
197#485—471no—
198#483—471no—
199#480—471no—
200#467—471no—
201#467—471no—
202#465—471no—
203#465—471no—
204#452—471no—
205#452D4711yescharacteristic, complemented
206#451—471no—
207#448—471no—
208C2×C22⋊C8—471no—
209C47#319011yescharacteristic, complemented, Sylow
210C2×#41C2×D4711yescharacteristic
211C22×Q8—471no—
212C23×C4—471no—
213C2×Q16—471no—
214C2×Q16C2×D4711yescharacteristic, complemented
215C2×SD16—471no—
216C2×SD16C2×D4711yescharacteristic, complemented
217C22×C8—471no—
218C22×C8—471no—
219#123—941no—
220C22⋊Q8—471no—
221C22⋊Q8—471no—
222C22⋊Q8—471no—
223C22⋊Q8—471no—
224C22⋊Q8—471no—
225C22⋊Q8—941no—
226C22⋊Q8—941no—
227C22⋊Q8C2×D4711yescharacteristic
228#121—471no—
229#121—471no—
230#120—941no—
231C4×D4—941no—
232C4×D4—941no—
233#117—471no—
234C2×C4⋊C4—471no—
235C2×C4⋊C4—941no—
236C2×C22⋊C4—941no—
237#107—471no—
238#107—471no—
239#106—471no—
240#106—471no—
241#103—471no—
242#103—471no—
243#103—471no—
244#103—471no—
245#103—471no—
246#103C2×D4711yescharacteristic, complemented
247#102—471no—
248#102C2×D4711yescharacteristic, complemented
249C22⋊C8—471no—
250C22⋊C8—471no—
251C22⋊C8—471no—
252C22⋊C8C2×D4711yescharacteristic
253C24—471no—
254#41—41no—
255#41—41no—
256C2×Q8—471no—
257C2×Q8—941no—
258C2×Q8—1881no—
259C2×Q8—1881no—
260C2×Q8C22×D4711yescharacteristic
261C2×Q8C22×D4711yescharacteristic
262C2×D4—21no—
263C2×D4—941no—
264C2×D4—941no—
265C2×D4C22×D4711yescharacteristic
266C22×C4—21no—
267C22×C4—471no—
268C22×C4—471no—
269C22×C4—471no—
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—941no—
273C22×C4—941no—
274C22×C4—1881no—
275C22×C4—1881no—
276C22×C4C22×D4711yescharacteristic
277Q16—41no—
278Q16—1881no—
279SD16—41no—
280SD16—1881no—
281C2×C8—471no—
282C2×C8—471no—
283C2×C8—1881no—
284C2×C8—1881no—
285C2×C8C22×D4711yescharacteristic
286C2×C8C22×D4711yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—471no—
289C4⋊C4—471no—
290C4⋊C4—471no—
291C4⋊C4—941no—
292C4⋊C4—941no—
293C4⋊C4—941no—
294C4⋊C4—941no—
295C4⋊C4—941no—
296C4⋊C4—941no—
297C4⋊C4C22×D4711yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—941no—
300C22⋊C4—941no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C22⋊C4—941no—
307C42—941no—
308C23—21no—
309C23—471no—
310C23—471no—
311C23—942no—
312C23—942no—
313C23—1881no—
314C23D4×D4711yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—941no—
320Q8—941no—
321Q8—1882no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—1882no—
326D4—1882no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—471no—
334C2×C4—471no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—1881no—
344C2×C4—1881no—
345C2×C4—1882no—
346C2×C4—1882no—
347C2×C4—1881no—
348C2×C4D4×D4711yescharacteristic
349C2×C4C23×D4711yescharacteristic
350C8—21no—
351C8—21no—
352C8—941no—
353C8—941no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—472no—
361C22—472no—
362C22—941no—
363C22—941no—
364C22—941no—
365C22—941no—
366C22—1884no—
367C22C2×D4×D4711yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—941no—
373C4—941no—
374C4—1881no—
375C4—1881no—
376C4—1881no—
377C4—1881no—
378C4#1309406911yescharacteristic
379C4#1309406911yescharacteristic
380C2—41no—
381C2—81no—
382C2—942no—
383C2—942no—
384C2#1568968311yescharacteristic
385C2#135×D4711yescharacteristic
386C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#452C2
socleC22×C47C22×D4
hypercenter#452D47
hypocenterC47#3190
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D47C2semidirect
3. #15689465C2semidirect
4. #15689461C2semidirect
5. #15689452C2semidirect
6. #15689435C2semidirect
7. #15689363C2semidirect
8. #15689361C2semidirect
9. #15689351C2semidirect
10. #15689349C2semidirect
11. #15689285C2semidirect
12. #15689277C2semidirect
13. #15689260C2semidirect
14. C22⋊C8×D47C2semidirect
15. C47×#452C2semidirect
18. C2×#10625337C22semidirect
19. C2×#10625335C22semidirect
39. #13093958C22semidirect
40. #13093957C22semidirect
41. #13093956C22semidirect
42. #13093955C22semidirect
43. #13093949C22semidirect
44. #13093949C22semidirect
45. #13093948C22semidirect
46. #13093948C22semidirect
47. #13093948C22semidirect
48. #13093945C22semidirect
53. C2×Q16×C47C22semidirect
54. C2×SD16×C47C22semidirect
56. #103×C47C22semidirect
57. #102×C47C22semidirect
205. #452D47semidirect
209. C47#3190semidirect
214. C2×Q16C2×D47semidirect
216. C2×SD16C2×D47semidirect
246. #103C2×D47semidirect
248. #102C2×D47semidirect