Finite Group Databasebeta

← #20255231

Subgroups — #20255231

Order 6016.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689820C211yesmaximal, characteristic, complemented
2#15689761C211yesmaximal, characteristic, complemented
3#15689479C211yesmaximal, characteristic, complemented
4#15689457C211yesmaximal, characteristic, complemented
5#15689448C211yesmaximal, characteristic, complemented
6#15689425C211yesmaximal, characteristic, complemented
7#15689357C211yesmaximal, characteristic, complemented
8#15689349C211yesmaximal, characteristic, complemented
9#15689340C211yesmaximal, characteristic, complemented
10#15689255C211yesmaximal, characteristic, complemented
11D8×Dic47C211yesmaximal, characteristic, complemented
12(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
13#15689119C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#449C211yesmaximal, characteristic, complemented
16C2×D4×D47C2211yescharacteristic
17C2×#10625334C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic, complemented
19C2×C8×D47C2211yescharacteristic
20#13094017—21no—
21#13094015C2211yescharacteristic, complemented
22#13094013C2211yescharacteristic
23#13094007—21no—
24#13094005—21no—
25#13094000C2211yescharacteristic
26#13093998C2211yescharacteristic
27#13093996—21no—
28#13093995—21no—
29#13093995C2211yescharacteristic
30#13093992—21no—
31D4×Dic47C2211yescharacteristic
32D4×Dic47C2211yescharacteristic, complemented
33C4×C22⋊D47C2211yescharacteristic
34(C22⋊D47)⋊C4—21no—
35#13093983C2211yescharacteristic, complemented
36C4⋊C4×D47C2211yescharacteristic
37C2×(C2×D47)⋊C4—21no—
38#13093958C2211yescharacteristic, complemented
39#13093957C2211yescharacteristic, complemented
40#13093956C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093948C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic, complemented
49#13093944C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic, complemented
52C2×#41×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic, complemented
54C2×D8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic, complemented
56#103×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60#41×C47—22no—
61#41×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C22×C4×C47—21no—
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47D411yescharacteristic
73C22×Dic47—21no—
74C22×Dic47—21no—
75D4×D47—22no—
76D4×D47—41no—
77C2×D188C2311yescharacteristic
78C2×C4×D47—21no—
79C2×C4×D47C2311yescharacteristic
80SD16×C47—41no—
81D8×C47—22no—
82C2×C8×C47C2311yescharacteristic
83C2×C8×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47D411yescharacteristic
91#10625334—41no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4D411yescharacteristic
97C4⋊Dic47—21no—
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4D411yescharacteristic
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8—41no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C8×D47—41no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47C2×D411yescharacteristic
114C22×D47—21no—
115C22×D47—42no—
116C22×D47—42no—
117C22×D47—81no—
118C22×D47C2×D411yescharacteristic
119Q8×C47—21no—
120Q8×C47—21no—
121D4×C47—21no—
122D4×C47—21no—
123D4×C47—21no—
124D4×C47—42no—
125D4×C47—81no—
126D4×C47#4112yes—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—42no—
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2411yescharacteristic
134C22⋊D47—22no—
135C22⋊D47—42no—
136C22⋊D47—42no—
137C22⋊D47—81no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—81no—
142C2×Dic47—81no—
143C2×Dic47C2×D411yescharacteristic
144C2×Dic47C2×D411yescharacteristic
145C2×Dic47C2×D411yescharacteristic
146D188—21no—
147D188—21no—
148C4×D47—21no—
149C4×D47—21no—
150C4×D47—81no—
151C8×C47—21no—
152C8×C47—21no—
153C47⋊C8—21no—
154C47⋊C8—21no—
155C22×C47—22no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—21no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47C22×D411yescharacteristic
165C2×D47—21no—
166C2×D47—21no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—84no—
171C2×D47#13512yes—
172C4×C47—21no—
173C4×C47—41no—
174C4×C47—41no—
175C4×C47C2×#4111yescharacteristic
176C4×C47H(5,𝔽2)11yescharacteristic
177Dic47—21no—
178Dic47—21no—
179Dic47—21no—
180Dic47—41no—
181Dic47—41no—
182Dic47—41no—
183#3297—471nomaximal, Sylow
184C2×C47—42no—
185C2×C47—41no—
186C2×C47—81no—
187C2×C47#54611yescharacteristic
188C2×C47C2×#13511yescharacteristic
189C2×C47#57611yescharacteristic
190D47—22no—
191D47—81no—
192#553—471no—
193#546—471no—
194#488—471no—
195#484—471no—
196#482—471no—
197#478—471no—
198#466—471no—
199#465—471no—
200#463—471no—
201#449D4711yescharacteristic, complemented
202#447—471no—
203C4×D8—471no—
204C8×D4—471no—
205#416—471no—
206C2×#102—471no—
207C47#329711yescharacteristic, complemented, Sylow
208C2×#41C2×D4711yescharacteristic
209C22×D4—471no—
210C2×SD16C2×D4711yescharacteristic, complemented
211C2×D8—471no—
212C2×D8C2×D4711yescharacteristic
213C22×C8—471no—
214C22×C8—471no—
215#126—941no—
216#125—471no—
217#124—471no—
218#123—941no—
219#123—941no—
220C22⋊Q8—471no—
221#121—471no—
222#121—471no—
223#121—941no—
224#121—941no—
225#121C2×D4711yescharacteristic, complemented
226#120—941no—
227C4×D4—471no—
228C4×D4—471no—
229C4×D4—471no—
230C4×D4—941no—
231#117—471no—
232C2×C4⋊C4—471no—
233C2×C22⋊C4—941no—
234#107—471no—
235#107—471no—
236#106—471no—
237C4⋊C8—471no—
238#103—471no—
239#103—471no—
240#103C2×D4711yescharacteristic, complemented
241#102—471no—
242#102—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247#102C2×D4711yescharacteristic
248C22⋊C8—471no—
249C22⋊C8C2×D4711yescharacteristic, complemented
250C4×C8—471no—
251C24—941no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D4711yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—471no—
258C2×D4—471no—
259C2×D4—941no—
260C2×D4—942no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4—1881no—
264C2×D4C22×D4711yescharacteristic
265C2×D4C22×D4711yescharacteristic
266C22×C4—21no—
267C22×C4—471no—
268C22×C4—941no—
269C22×C4—941no—
270C22×C4—941no—
271C22×C4C22×D4711yescharacteristic
272SD16—41no—
273D8—22no—
274D8—1881no—
275C2×C8—471no—
276C2×C8—471no—
277C2×C8—1881no—
278C2×C8—1881no—
279C2×C8C22×D4711yescharacteristic
280C2×C8C22×D4711yescharacteristic
281C4⋊C4—471no—
282C4⋊C4—471no—
283C4⋊C4—471no—
284C4⋊C4—471no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C4⋊C4—941no—
288C4⋊C4—941no—
289C4⋊C4C22×D4711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—471no—
292C22⋊C4—471no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4—941no—
300C22⋊C4—941no—
301C42—471no—
302C42—941no—
303C23—21no—
304C23—21no—
305C23—471no—
306C23—941no—
307C23—3761no—
308C23—1882no—
309C23—1882no—
310C23D4×D4711yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—942no—
319D4—941no—
320D4—941no—
321D4—3761no—
322D4—1882no—
323D4—1882no—
324D4#1062535212yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—471no—
331C2×C4—471no—
332C2×C4—471no—
333C2×C4—941no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—3761no—
339C2×C4—3761no—
340C2×C4—3761no—
341C2×C4D4×D4711yescharacteristic
342C2×C4C23×D4711yescharacteristic
343C8—21no—
344C8—21no—
345C8—941no—
346C8—941no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—472no—
357C22—941no—
358C22—941no—
359C22—3764no—
360C22—1881no—
361C22—1881no—
362C22—1881no—
363C22C2×D4×D4711yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—941no—
368C4—941no—
369C4—941no—
370C4—1881no—
371C4—1881no—
372C4—1881no—
373C4C2×#1062535211yescharacteristic
374C4#1309406911yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—942no—
379C2—3761no—
380C2#1568976011yescharacteristic
381C2#135×D4711yescharacteristic
382C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#449C2
socleC22×C47C22×D4
hypercenter#449D47
hypocenterC47#3297
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #15689820C2semidirect
2. #15689761C2semidirect
3. #15689479C2semidirect
4. #15689457C2semidirect
5. #15689448C2semidirect
6. #15689425C2semidirect
7. #15689357C2semidirect
8. #15689349C2semidirect
9. #15689340C2semidirect
10. #15689255C2semidirect
11. D8×Dic47C2semidirect
12. (C22⋊D47)⋊C8C2semidirect
13. #15689119C2semidirect
14. #102×D47C2semidirect
15. C47×#449C2semidirect
18. C22×C47⋊C8C22semidirect
21. #13094015C22semidirect
32. D4×Dic47C22semidirect
35. #13093983C22semidirect
38. #13093958C22semidirect
39. #13093957C22semidirect
40. #13093956C22semidirect
41. Dic47⋊C8C22semidirect
42. #13093948C22semidirect
43. #13093948C22semidirect
48. #13093945C22semidirect
51. C8×Dic47C22semidirect
53. C2×SD16×C47C22semidirect
55. #121×C47C22semidirect
56. #103×C47C22semidirect
58. C22⋊C8×C47C22semidirect
201. #449D47semidirect
207. C47#3297semidirect
210. C2×SD16C2×D47semidirect
225. #121C2×D47semidirect
240. #103C2×D47semidirect
249. C22⋊C8C2×D47semidirect