Finite Group Databasebeta

← #20255606

Subgroups — #20255606

Order 6016.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689813C211yesmaximal, characteristic, complemented
2#15689769C211yesmaximal, characteristic
3#15689478C211yesmaximal, characteristic, complemented
4#15689465C211yesmaximal, characteristic, complemented
5#15689442C211yesmaximal, characteristic, complemented
6#15689424C211yesmaximal, characteristic, complemented
7#15689381C211yesmaximal, characteristic, complemented
8#15689369C211yesmaximal, characteristic, complemented
9#15689346C211yesmaximal, characteristic, complemented
10#15689287C211yesmaximal, characteristic, complemented
11#15689276C211yesmaximal, characteristic, complemented
12C4×#10625325C211yesmaximal, characteristic, complemented
13#15689129C211yesmaximal, characteristic, complemented
14#15689125C211yesmaximal, characteristic, complemented
15C47×#436C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×Dic188C2211yescharacteristic, complemented
19C2×#10625325C2211yescharacteristic
20C2×#10625325C2211yescharacteristic
21#13094017—21no—
22#13094016C2211yescharacteristic, complemented
23#13094014—21no—
24#13094012C2211yescharacteristic
25#13094009—21no—
26#13094005—21no—
27#13094003C2211yescharacteristic
28#13094003C2211yescharacteristic
29#13094003C2211yescharacteristic, complemented
30#13093998C2211yescharacteristic
31#13093997—21no—
32#13093992—21no—
33C4×Dic94C2211yescharacteristic, complemented
34C4×D188C2211yescharacteristic
35#13093983C2211yescharacteristic
36#13093980—21no—
37C2×C4⋊Dic47C2211yescharacteristic, complemented
38C22⋊C4×D47—21no—
39#13093958C2211yescharacteristic, complemented
40#13093956C2211yescharacteristic, complemented
41#13093956C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093949C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C2×M16×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic, complemented
54C4×D4×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic, complemented
56C22⋊C8×C47C2211yescharacteristic
57C22⋊C8×C47C2211yescharacteristic, complemented
58C4×C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×D4×C47D411yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C22×Dic47—21no—
66#10625350—22no—
67#10625350—41no—
68C2×D188—22no—
69C2×D188—21no—
70C2×D188—41no—
71C2×D188C2311yescharacteristic
72C2×D188C2311yescharacteristic
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×Dic94C2311yescharacteristic
76C2×Dic94C2311yescharacteristic
77M16×C47—41no—
78M16×C47—41no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C4⋊C4×C47D411yescharacteristic
84C22⋊C4×C47D411yescharacteristic
85C22⋊C4×C47D411yescharacteristic
86C42×C47C2311yescharacteristic
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106C4×Dic47—21no—
107C4×Dic47—21no—
108Dic188—41no—
109#10625325—22no—
110#10625325—41no—
111C23×C47C2×D411yescharacteristic
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—42no—
116C22×D47—42no—
117C22×D47—81no—
118D4×C47—41no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2411yescharacteristic
128C22⋊D47—42no—
129C22⋊D47—81no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—42no—
137D188—21no—
138D188—21no—
139D188—21no—
140D188—42no—
141D188#4112yes—
142C4×D47—42no—
143C4×D47—81no—
144Dic94—21no—
145Dic94—21no—
146Dic94—21no—
147Dic94—21no—
148C8×C47—21no—
149C8×C47—21no—
150C8×C47—21no—
151C8×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47C22×D411yescharacteristic
159C2×D47—22no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—84no—
166C4×C47—21no—
167C4×C47—21no—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47C2×#4111yescharacteristic
171C4×C47H(5,𝔽2)11yescharacteristic
172Dic47—41no—
173Dic47—41no—
174Dic47—41no—
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178#3323—471nomaximal, Sylow
179C2×C47—41no—
180C2×C47—41no—
181C2×C47#54611yescharacteristic
182C2×C47#57511yescharacteristic
183C2×C47#57711yescharacteristic
184D47—42no—
185D47—81no—
186#552—471no—
187#546—471no—
188#488—471no—
189#485—471no—
190#481—471no—
191#478—471no—
192#470—471no—
193#468—471no—
194#464—471no—
195#452—471no—
196#450—471no—
197C4×SD16—471no—
198#436D4711yescharacteristic, complemented
199#418—471no—
200#417—471no—
201C47#332311yescharacteristic, complemented, Sylow
202C2×#41—471no—
203C22×D4—471no—
204C2×Q16—471no—
205C2×SD16—471no—
206C2×SD16—471no—
207C2×M16C2×D4711yescharacteristic
208C2×M16C2×D4711yescharacteristic, complemented
209#126—941no—
210#125—471no—
211#125—941no—
212#124—471no—
213#123—941no—
214#123—941no—
215C22⋊Q8—471no—
216C22⋊Q8—471no—
217C22⋊Q8—471no—
218#121—471no—
219#121—941no—
220#120—941no—
221C4×Q8—471no—
222C4×D4—471no—
223C4×D4C2×D4711yescharacteristic
224#117—471no—
225#117—941no—
226C2×C4⋊C4—471no—
227C2×C22⋊C4—941no—
228#107—471no—
229#106—471no—
230#106—471no—
231C4⋊C8C2×D4711yescharacteristic, complemented
232#103—471no—
233#103—471no—
234#103—471no—
235#103—471no—
236#102—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#102—471no—
241#102—471no—
242C22⋊C8C2×D4711yescharacteristic
243C22⋊C8C2×D4711yescharacteristic, complemented
244C4×C8C2×D4711yescharacteristic, complemented
245C24—941no—
246#41—942no—
247#41—1881no—
248C2×Q8—471no—
249C2×Q8—471no—
250C2×D4—471no—
251C2×D4—471no—
252C2×D4—942no—
253C2×D4—941no—
254C2×D4—941no—
255C2×D4—941no—
256C2×D4—1881no—
257C2×D4D18811yescharacteristic
258C22×C4—941no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4C22×D4711yescharacteristic
262C22×C4C22×D4711yescharacteristic
263Q16—1881no—
264SD16—942no—
265SD16—1881no—
266M16—41no—
267M16—41no—
268C2×C8C22×D4711yescharacteristic
269C2×C8C22×D4711yescharacteristic
270C2×C8C22×D4711yescharacteristic
271C2×C8C22×D4711yescharacteristic
272C4⋊C4—471no—
273C4⋊C4—471no—
274C4⋊C4—471no—
275C4⋊C4—471no—
276C4⋊C4—941no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4—941no—
283C4⋊C4D18811yescharacteristic
284C22⋊C4—941no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4D18811yescharacteristic
293C22⋊C4D18811yescharacteristic
294C42—941no—
295C42—941no—
296C42C22×D4711yescharacteristic
297C23—941no—
298C23—941no—
299C23—3761no—
300C23—1882no—
301C23—1882no—
302C23C2×D18811yescharacteristic
303C23C2×D18811yescharacteristic
304Q8—941no—
305Q8—941no—
306Q8—941no—
307Q8—941no—
308D4—41no—
309D4—472no—
310D4—941no—
311D4—941no—
312D4—941no—
313D4—3761no—
314D4—1882no—
315D4—1882no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—3761no—
327C2×C4—1882no—
328C2×C4—1882no—
329C2×C4C2×D18811yescharacteristic
330C2×C4C2×D18811yescharacteristic
331C2×C4C2×D18811yescharacteristic
332C2×C4C2×D18811yescharacteristic
333C2×C4C23×D4711yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—942no—
345C22—3764no—
346C22—1881no—
347C22—1881no—
348C22—1881no—
349C22—1881no—
350C22—1881no—
351C22C22×D18811yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—1881no—
357C4—1881no—
358C4—1881no—
359C4—1881no—
360C4—1881no—
361C4—1881no—
362C4#41×D4711yescharacteristic
363C4#1309406911yescharacteristic
364C2—41no—
365C2—41no—
366C2—3761no—
367C2—1882no—
368C2#1568976811yescharacteristic
369C2#1568992311yescharacteristic
370C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#436C2
socleC22×C47C22×D4
hypercenter#436D47
hypocenterC47#3323
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #15689813C2semidirect
3. #15689478C2semidirect
4. #15689465C2semidirect
5. #15689442C2semidirect
6. #15689424C2semidirect
7. #15689381C2semidirect
8. #15689369C2semidirect
9. #15689346C2semidirect
10. #15689287C2semidirect
11. #15689276C2semidirect
12. C4×#10625325C2semidirect
13. #15689129C2semidirect
14. #15689125C2semidirect
15. C47×#436C2semidirect
18. C2×Dic188C22semidirect
22. #13094016C22semidirect
29. #13094003C22semidirect
33. C4×Dic94C22semidirect
37. C2×C4⋊Dic47C22semidirect
39. #13093958C22semidirect
40. #13093956C22semidirect
41. #13093956C22semidirect
42. #13093949C22semidirect
43. #13093949C22semidirect
44. #13093949C22semidirect
45. #13093949C22semidirect
53. C2×M16×C47C22semidirect
55. C4⋊C8×C47C22semidirect
57. C22⋊C8×C47C22semidirect
58. C4×C8×C47C22semidirect
198. #436D47semidirect
201. C47#3323semidirect
208. C2×M16C2×D47semidirect
231. C4⋊C8C2×D47semidirect
243. C22⋊C8C2×D47semidirect
244. C4×C8C2×D47semidirect