Finite Group Databasebeta

← #20255411

Subgroups — #20255411

Order 6016.

450 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#15689813C211yesmaximal, characteristic, complemented
2D4×D188C211yesmaximal, characteristic
3#15689488C211yesmaximal, characteristic, complemented
4#15689448C211yesmaximal, characteristic, complemented
5#15689437C211yesmaximal, characteristic, complemented
6#15689424C211yesmaximal, characteristic, complemented
7#15689369C211yesmaximal, characteristic, complemented
8#15689352C211yesmaximal, characteristic, complemented
9#15689324C211yesmaximal, characteristic, complemented
10#15689276C211yesmaximal, characteristic, complemented
11#15689276C211yesmaximal, characteristic, complemented
12#15689225C211yesmaximal, characteristic, complemented
13#15689129C211yesmaximal, characteristic, complemented
14C2×#13093946C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×D4×D47—21no—
19C2×#10625325C2211yescharacteristic
20C2×#10625325C2211yescharacteristic, complemented
21C2×#10625325C2211yescharacteristic, complemented
22#13094021C2211yescharacteristic
23#13094017—21no—
24#13094016C2211yescharacteristic, complemented
25#13094014—21no—
26#13094005—21no—
27#13094003C2211yescharacteristic, complemented
28#13094003C2211yescharacteristic, complemented
29#13093999—21no—
30#13093998C2211yescharacteristic
31#13093998C2211yescharacteristic
32#13093994—21no—
33#13093994—21no—
34C4×Dic94C2211yescharacteristic, complemented
35C4×D188C2211yescharacteristic
36#13093983C2211yescharacteristic, complemented
37#13093980—21no—
38C2×C4⋊Dic47C2211yescharacteristic, complemented
39#13093958C2211yescharacteristic, complemented
40#13093958C2211yescharacteristic, complemented
41#13093956C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic, complemented
47#13093946C2211yescharacteristic, complemented
48#13093946C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic, complemented
50#13093946C2211yescharacteristic, complemented
51#13093946C2211yescharacteristic, complemented
52C2×M16×C47C2211yescharacteristic, complemented
53C22×C8×C47C2211yescharacteristic, complemented
54C4×D4×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic, complemented
56C22⋊C8×C47C2211yescharacteristic, complemented
57C22⋊C8×C47C2211yescharacteristic, complemented
58#97×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C23×D47—21no—
61C2×D4×C47D411yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C22×Dic47—21no—
67D4×D47—44no—
68C2×D188—22no—
69C2×D188—22no—
70C2×D188—21no—
71C2×D188—21no—
72C2×D188—21no—
73C2×D188—21no—
74C2×D188—41no—
75C2×D188—41no—
76C2×D188C2311yescharacteristic
77C2×D188C2311yescharacteristic
78C2×D188C2311yescharacteristic
79C2×C4×D47—21no—
80C2×Dic94C2311yescharacteristic
81M16×C47—41no—
82C2×C8×C47—41no—
83C2×C8×C47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C4⋊C4×C47D411yescharacteristic
88C22⋊C4×C47D411yescharacteristic
89C22⋊C4×C47D411yescharacteristic
90C42×C47C2311yescharacteristic
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93C22⋊Dic47—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107C4×Dic47—21no—
108C4×Dic47—21no—
109#10625325—22no—
110#10625325—41no—
111#10625325—41no—
112C23×C47C2×D411yescharacteristic
113C23×C47C2×D411yescharacteristic
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47—42no—
120C22×D47—42no—
121C22×D47—81no—
122C22×D47—81no—
123D4×C47—22no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2411yescharacteristic
133C22⋊D47—42no—
134C22⋊D47—42no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—42no—
141D188—21no—
142D188—21no—
143D188—21no—
144D188—21no—
145D188—21no—
146D188—42no—
147D188—42no—
148D188—42no—
149D188—81no—
150D188#4112yes—
151C4×D47—42no—
152Dic94—21no—
153Dic94—21no—
154C8×C47—21no—
155C8×C47—21no—
156C8×C47—21no—
157C8×C47—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47AGL(1,ℤ/8)12yes—
164C22×C47C22×D411yescharacteristic
165C2×D47—22no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
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—21no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47C2×#4111yescharacteristic
181C4×C47H(5,𝔽2)11yescharacteristic
182Dic47—41no—
183Dic47—41no—
184Dic47—41no—
185Dic47—41no—
186Dic47—41no—
187#3310—471nomaximal, Sylow
188C2×C47—22no—
189C2×C47—41no—
190C2×C47#54611yescharacteristic
191C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C47#57711yescharacteristic
193D47—42no—
194D47—81no—
195D47—81no—
196#552—471no—
197D42—471no—
198#490—471no—
199#482—471no—
200#480—471no—
201#478—471no—
202#468—471no—
203#465—471no—
204#460—471no—
205#450—471no—
206#450—471no—
207#440—471no—
208#435D4711yescharacteristic, complemented
209#418—471no—
210C2×#102—471no—
211C47#331011yescharacteristic, complemented, Sylow
212C22×D4—471no—
213C22×D4—471no—
214C22×D4—941no—
215C2×SD16—471no—
216C2×SD16—471no—
217C2×SD16—471no—
218C2×M16C2×D4711yescharacteristic, complemented
219C22×C8C2×D4711yescharacteristic, complemented
220#127—471no—
221#126—941no—
222#125—471no—
223#125—941no—
224#123—941no—
225C22⋊Q8—471no—
226C22⋊Q8—471no—
227#121—471no—
228#121—471no—
229#121—941no—
230#120—941no—
231#120—941no—
232C4×Q8—471no—
233C4×D4—471no—
234C4×D4C2×D4711yescharacteristic
235#117—471no—
236#117—941no—
237C2×C4⋊C4—471no—
238#107—471no—
239#107—471no—
240#106—471no—
241C4⋊C8C2×D4711yescharacteristic, complemented
242#103—471no—
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#102—471no—
252C22⋊C8C2×D4711yescharacteristic, complemented
253C22⋊C8C2×D4711yescharacteristic, complemented
254#97C2×D4711yescharacteristic, complemented
255C24—941no—
256C24—941no—
257C2×Q8—471no—
258C2×D4—471no—
259C2×D4—471no—
260C2×D4—471no—
261C2×D4—942no—
262C2×D4—942no—
263C2×D4—941no—
264C2×D4—941no—
265C2×D4—941no—
266C2×D4—941no—
267C2×D4—941no—
268C2×D4—941no—
269C2×D4—1881no—
270C2×D4—1881no—
271C2×D4—1884no—
272C2×D4D18811yescharacteristic
273C22×C4—941no—
274C22×C4—941no—
275C22×C4C22×D4711yescharacteristic
276C22×C4C22×D4711yescharacteristic
277SD16—942no—
278SD16—1881no—
279SD16—1881no—
280M16—41no—
281C2×C8—41no—
282C2×C8C22×D4711yescharacteristic
283C2×C8C22×D4711yescharacteristic
284C2×C8C22×D4711yescharacteristic
285C2×C8C22×D4711yescharacteristic
286C4⋊C4—471no—
287C4⋊C4—471no—
288C4⋊C4—471no—
289C4⋊C4—471no—
290C4⋊C4—941no—
291C4⋊C4—941no—
292C4⋊C4—941no—
293C4⋊C4—941no—
294C4⋊C4—941no—
295C4⋊C4—941no—
296C4⋊C4D18811yescharacteristic
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4—941no—
300C22⋊C4—941no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4D18811yescharacteristic
304C22⋊C4D18811yescharacteristic
305C42—941no—
306C42—941no—
307C42C22×D4711yescharacteristic
308C23—941no—
309C23—941no—
310C23—941no—
311C23—3761no—
312C23—3761no—
313C23—1882no—
314C23—1882no—
315C23—1882no—
316C23—1882no—
317C23C2×D18811yescharacteristic
318C23C2×D18811yescharacteristic
319Q8—941no—
320Q8—941no—
321D4—22no—
322D4—472no—
323D4—941no—
324D4—941no—
325D4—941no—
326D4—941no—
327D4—941no—
328D4—3761no—
329D4—1882no—
330D4—1882no—
331D4—1882no—
332D4—1882no—
333D4—1882no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—1882no—
344C2×C4—1882no—
345C2×C4C2×D18811yescharacteristic
346C2×C4C2×D18811yescharacteristic
347C2×C4C2×D18811yescharacteristic
348C2×C4C2×D18811yescharacteristic
349C2×C4C23×D4711yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—942no—
360C22—3764no—
361C22—3764no—
362C22—1881no—
363C22—1881no—
364C22—1881no—
365C22—1881no—
366C22—1881no—
367C22—1881no—
368C22—1881no—
369C22—1881no—
370C22#1309405212yes—
371C22C22×D18811yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—1881no—
377C4—1881no—
378C4—1881no—
379C4—1881no—
380C4—1881no—
381C4#41×D4711yescharacteristic
382C4#1309406911yescharacteristic
383C2—22no—
384C2—41no—
385C2—3761no—
386C2—3761no—
387C2—1882no—
388C2#1568976811yescharacteristic
389C2C2×#1309405211yescharacteristic
390C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3310
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #15689813C2semidirect
3. #15689488C2semidirect
4. #15689448C2semidirect
5. #15689437C2semidirect
6. #15689424C2semidirect
7. #15689369C2semidirect
8. #15689352C2semidirect
9. #15689324C2semidirect
10. #15689276C2semidirect
11. #15689276C2semidirect
12. #15689225C2semidirect
13. #15689129C2semidirect
14. C2×#13093946C2semidirect
15. C47×#435C2semidirect
20. C2×#10625325C22semidirect
21. C2×#10625325C22semidirect
24. #13094016C22semidirect
27. #13094003C22semidirect
28. #13094003C22semidirect
34. C4×Dic94C22semidirect
36. #13093983C22semidirect
38. C2×C4⋊Dic47C22semidirect
39. #13093958C22semidirect
40. #13093958C22semidirect
41. #13093956C22semidirect
42. #13093949C22semidirect
46. #13093946C22semidirect
47. #13093946C22semidirect
48. #13093946C22semidirect
49. #13093946C22semidirect
50. #13093946C22semidirect
51. #13093946C22semidirect
52. C2×M16×C47C22semidirect
53. C22×C8×C47C22semidirect
55. C4⋊C8×C47C22semidirect
56. C22⋊C8×C47C22semidirect
57. C22⋊C8×C47C22semidirect
58. #97×C47C22semidirect
208. #435D47semidirect
211. C47#3310semidirect
218. C2×M16C2×D47semidirect
219. C22×C8C2×D47semidirect
241. C4⋊C8C2×D47semidirect
252. C22⋊C8C2×D47semidirect
253. C22⋊C8C2×D47semidirect
254. #97C2×D47semidirect