Finite Group Databasebeta

← #20255614

Subgroups — #20255614

Order 6016.

448 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689844C211yesmaximal, characteristic, complemented
2#15689757C211yesmaximal, characteristic
3#15689468C211yesmaximal, characteristic, complemented
4#15689450C211yesmaximal, characteristic, complemented
5#15689444C211yesmaximal, characteristic, complemented
6#15689402C211yesmaximal, characteristic, complemented
7#15689372C211yesmaximal, characteristic, complemented
8#15689321C211yesmaximal, characteristic, complemented
9#15689273C211yesmaximal, characteristic, complemented
10#15689272C211yesmaximal, characteristic, complemented
11#15689208C211yesmaximal, characteristic, complemented
12#15689199C211yesmaximal, characteristic, complemented
13#15689129C211yesmaximal, characteristic, complemented
14#15689126C211yesmaximal, characteristic, complemented
15C47×#468C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C2×D4×D47—21no—
18C2×D4×D47C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×#10625336C2211yescharacteristic, complemented
21C2×#10625324C2211yescharacteristic, complemented
22#13094023C2211yescharacteristic, complemented
23#13094020C2211yescharacteristic
24#13094019—21no—
25#13094017—21no—
26#13094010—21no—
27#13094000C2211yescharacteristic, complemented
28#13093999C2211yescharacteristic
29#13093997—21no—
30#13093994—21no—
31#13093992—21no—
32Q8×Dic47C2211yescharacteristic, complemented
33#13093989—21no—
34#13093986C2211yescharacteristic
35C4×C22⋊D47C2211yescharacteristic
36#13093983C2211yescharacteristic, complemented
37#13093982C2211yescharacteristic, complemented
38#13093957C2211yescharacteristic, complemented
39#13093955C2211yescharacteristic, complemented
40Dic47⋊C8C2211yescharacteristic, complemented
41#13093946C2211yescharacteristic
42#13093946C2211yescharacteristic
43#13093946C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic, complemented
45#13093945C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic, complemented
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic, complemented
49C22⋊(C47⋊C8)C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C2×SD16×C47C2211yescharacteristic, complemented
53C2×M16×C47C2211yescharacteristic, complemented
54C22⋊Q8×C47C2211yescharacteristic, complemented
55#121×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C23×D47—21no—
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—
68C2×C22⋊D47D411yescharacteristic
69D4×D47—22no—
70D4×D47—41no—
71D4×D47—44no—
72C2×D188—22no—
73C2×D188—21no—
74C2×D188—21no—
75C2×D188—41no—
76C2×D188C2311yescharacteristic
77C2×D188C2311yescharacteristic
78C2×C4×D47—21no—
79C2×C4×D47C2311yescharacteristic
80C2×Dic94—21no—
81SD16×C47—41no—
82M16×C47—41no—
83C2×C8×C47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C4⋊C4×C47—21no—
86C4⋊C4×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C22⋊C4×C47—21no—
89C22⋊C4×C47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47D411yescharacteristic
92#10625336—22no—
93#10625336—41no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4D411yescharacteristic
99C4⋊Dic47—21no—
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4D411yescharacteristic
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47—21no—
108C4×Dic47C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111#10625324—41no—
112C23×C47—21no—
113C23×C47C2×D411yescharacteristic
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47—42no—
120C22×D47—81no—
121C22×D47—81no—
122C22×D47C2×D411yescharacteristic
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×C47C2×D411yescharacteristic
134C2×C4×C47C2411yescharacteristic
135C22⋊D47—22no—
136C22⋊D47—42no—
137C22⋊D47—42no—
138C22⋊D47—81no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47C2×D411yescharacteristic
142C2×Dic47C2×D411yescharacteristic
143C2×Dic47C2×D411yescharacteristic
144D188—21no—
145D188—21no—
146D188—21no—
147D188—42no—
148D188—42no—
149D188#4112yes—
150C4×D47—21no—
151C4×D47—21no—
152C4×D47—42no—
153Dic94—42no—
154C8×C47—21no—
155C8×C47—21no—
156C47⋊C8—21no—
157C47⋊C8—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47C22×D411yescharacteristic
165C2×D47—21no—
166C2×D47—22no—
167C2×D47—21no—
168C2×D47—21no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—84no—
175C2×D47—84no—
176C4×C47—21no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47—41no—
180C4×C47C2×#4111yescharacteristic
181C4×C47H(5,𝔽2)11yescharacteristic
182Dic47—21no—
183Dic47—21no—
184Dic47—41no—
185Dic47—41no—
186Dic47AGL(1,ℤ/8)12yes—
187#3324—471nomaximal, Sylow
188C2×C47—41no—
189C2×C47—81no—
190C2×C47#54611yescharacteristic
191C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C47#57711yescharacteristic
193D47—41no—
194D47—42no—
195D47—81no—
196#556—471no—
197D42—471no—
198#486—471no—
199#482—471no—
200#482—471no—
201#474—471no—
202#468—471no—
203#468D4711yescharacteristic, complemented
204#460—471no—
205#450—471no—
206#450—471no—
207C4×SD16—471no—
208#436—471no—
209#418—471no—
210#418—471no—
211C47#332411yescharacteristic, complemented, Sylow
212C22×D4—471no—
213C22×D4—471no—
214C22×D4—941no—
215C2×SD16—471no—
216C2×SD16—471no—
217C2×SD16C2×D4711yescharacteristic, complemented
218C2×M16—471no—
219C2×M16C2×D4711yescharacteristic, complemented
220C4⋊Q8—471no—
221#127—471no—
222#126—941no—
223#126—941no—
224#124—941no—
225C22⋊Q8—471no—
226C22⋊Q8C2×D4711yescharacteristic, complemented
227#121—471no—
228#121—941no—
229#121C2×D4711yescharacteristic
230#120—941no—
231#120—941no—
232C4×Q8—471no—
233C4×Q8—941no—
234C4×D4—471no—
235C4×D4—471no—
236#117—471no—
237#117—471no—
238#107—471no—
239#107C2×D4711yescharacteristic, complemented
240#106—471no—
241C4⋊C8—471no—
242#103C2×D4711yescharacteristic, complemented
243#102—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247#102—471no—
248#102—471no—
249#102—471no—
250#102—471no—
251#102C2×D4711yescharacteristic, complemented
252C22⋊C8—471no—
253C22⋊C8—471no—
254C4×C8—471no—
255C24—941no—
256C24—941no—
257C2×Q8—941no—
258C2×Q8C22×D4711yescharacteristic
259C2×D4—21no—
260C2×D4—471no—
261C2×D4—471no—
262C2×D4—471no—
263C2×D4—942no—
264C2×D4—941no—
265C2×D4—941no—
266C2×D4—941no—
267C2×D4—941no—
268C2×D4—942no—
269C2×D4—941no—
270C2×D4—1881no—
271C2×D4—1881no—
272C2×D4—1884no—
273C2×D4C22×D4711yescharacteristic
274C22×C4—471no—
275C22×C4—941no—
276C22×C4C22×D4711yescharacteristic
277SD16—41no—
278SD16—942no—
279SD16—1881no—
280M16—41no—
281M16—1881no—
282C2×C8—471no—
283C2×C8—471no—
284C2×C8C22×D4711yescharacteristic
285C2×C8C22×D4711yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—471no—
288C4⋊C4—471no—
289C4⋊C4—471no—
290C4⋊C4—941no—
291C4⋊C4—941no—
292C4⋊C4—941no—
293C4⋊C4C22×D4711yescharacteristic
294C4⋊C4C22×D4711yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—471no—
298C22⋊C4—471no—
299C22⋊C4—941no—
300C22⋊C4—941no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C42—471no—
305C42—941no—
306C42—941no—
307C42—941no—
308C23—21no—
309C23—471no—
310C23—941no—
311C23—941no—
312C23—3761no—
313C23—3761no—
314C23—1882no—
315C23—1882no—
316C23—1882no—
317C23—1882no—
318C23D4×D4711yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—1882no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—472no—
326D4—942no—
327D4—941no—
328D4—941no—
329D4—941no—
330D4—3761no—
331D4—1882no—
332D4—1882no—
333D4—1882no—
334D4—1882no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—471no—
341C2×C4—471no—
342C2×C4—471no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—1882no—
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—941no—
361C22—942no—
362C22—941no—
363C22—941no—
364C22—3764no—
365C22—3764no—
366C22—1881no—
367C22—1881no—
368C22—1881no—
369C22—1881no—
370C22—1881no—
371C22C2×D4×D4711yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—472no—
377C4—941no—
378C4—941no—
379C4—1881no—
380C4—1881no—
381C4#41×D4711yescharacteristic
382C4#1309406911yescharacteristic
383C2—41no—
384C2—81no—
385C2—3761no—
386C2—1881no—
387C2—1882no—
388C2#1568976211yescharacteristic
389C2AGL(1,ℤ/8)×D4711yescharacteristic
390C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#468C2
socleC22×C47C22×D4
hypercenter#468D47
hypocenterC47#3324
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #15689844C2semidirect
3. #15689468C2semidirect
4. #15689450C2semidirect
5. #15689444C2semidirect
6. #15689402C2semidirect
7. #15689372C2semidirect
8. #15689321C2semidirect
9. #15689273C2semidirect
10. #15689272C2semidirect
11. #15689208C2semidirect
12. #15689199C2semidirect
13. #15689129C2semidirect
14. #15689126C2semidirect
15. C47×#468C2semidirect
20. C2×#10625336C22semidirect
21. C2×#10625324C22semidirect
22. #13094023C22semidirect
27. #13094000C22semidirect
32. Q8×Dic47C22semidirect
36. #13093983C22semidirect
37. #13093982C22semidirect
38. #13093957C22semidirect
39. #13093955C22semidirect
40. Dic47⋊C8C22semidirect
43. #13093946C22semidirect
44. #13093946C22semidirect
45. #13093945C22semidirect
46. #13093945C22semidirect
48. #13093944C22semidirect
49. C22⋊(C47⋊C8)C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. C8×Dic47C22semidirect
52. C2×SD16×C47C22semidirect
53. C2×M16×C47C22semidirect
54. C22⋊Q8×C47C22semidirect
56. #107×C47C22semidirect
57. #103×C47C22semidirect
58. #102×C47C22semidirect
203. #468D47semidirect
211. C47#3324semidirect
217. C2×SD16C2×D47semidirect
219. C2×M16C2×D47semidirect
226. C22⋊Q8C2×D47semidirect
239. #107C2×D47semidirect
242. #103C2×D47semidirect
251. #102C2×D47semidirect