Finite Group Databasebeta

← #20255240

Subgroups — #20255240

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#15689819C211yesmaximal, characteristic, complemented
2#15689769C211yesmaximal, characteristic, complemented
3#15689478C211yesmaximal, characteristic, complemented
4#15689459C211yesmaximal, characteristic, complemented
5#15689448C211yesmaximal, characteristic, complemented
6#15689424C211yesmaximal, characteristic, complemented
7#15689359C211yesmaximal, characteristic, complemented
8#15689352C211yesmaximal, characteristic, complemented
9#15689339C211yesmaximal, characteristic, complemented
10#15689270C211yesmaximal, characteristic, complemented
11#15689259C211yesmaximal, characteristic, complemented
12C4×D376C211yesmaximal, characteristic, complemented
13#15689120C211yesmaximal, characteristic, complemented
14C2×#13093946C211yesmaximal, characteristic, complemented
15C8×D4×C47C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×#10625325C2211yescharacteristic, complemented
19C2×D376C2211yescharacteristic
20C2×D376C2211yescharacteristic
21#13094019—21no—
22#13094016C2211yescharacteristic, complemented
23#13094012C2211yescharacteristic
24#13094009—21no—
25#13094006—21no—
26#13094003C2211yescharacteristic
27#13093998C2211yescharacteristic
28#13093998C2211yescharacteristic
29#13093998C2211yescharacteristic, complemented
30#13093997—21no—
31#13093996—21no—
32#13093992—21no—
33C4×D188C2211yescharacteristic
34C4×D188C2211yescharacteristic, complemented
35(C22⋊D47)⋊C4—21no—
36#13093983C2211yescharacteristic, complemented
37C2×C4⋊Dic47C2211yescharacteristic
38C22⋊C4×D47—21no—
39#13093958C2211yescharacteristic, complemented
40#13093958C2211yescharacteristic, complemented
41#13093956C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic, complemented
52C22×C8×C47C2211yescharacteristic
53C22×C8×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—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C22×Dic47—21no—
68#10625350—22no—
69#10625350—41no—
70C2×D188—22no—
71C2×D188—21no—
72C2×D188—41no—
73C2×D188C2311yescharacteristic
74C2×D188C2311yescharacteristic
75C2×D188C2311yescharacteristic
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×Dic94C2311yescharacteristic
80C2×C8×C47—41no—
81C2×C8×C47—41no—
82C2×C8×C47C2311yescharacteristic
83C2×C8×C47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C2×C8×C47C2311yescharacteristic
86C4⋊C4×C47D411yescharacteristic
87C22⋊C4×C47D411yescharacteristic
88C22⋊C4×C47D411yescharacteristic
89C42×C47C2311yescharacteristic
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99C4⋊Dic47—21no—
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103C4⋊Dic47C2311yescharacteristic
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107C4×Dic47—21no—
108D376—22no—
109D376—41no—
110#10625325—41no—
111C23×C47C2×D411yescharacteristic
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—81no—
119D4×C47—22no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—42no—
130C22⋊D47—42no—
131C22⋊D47—81no—
132C22⋊D47—81no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—81no—
139D188—21no—
140D188—21no—
141D188—21no—
142D188—21no—
143D188—21no—
144D188—42no—
145D188#4112yes—
146C4×D47—42no—
147C4×D47—81no—
148C4×D47—81no—
149Dic94—21no—
150Dic94—21no—
151C8×C47—21no—
152C8×C47—21no—
153C8×C47—21no—
154C8×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47#13512yes—
161C22×C47C22×D411yescharacteristic
162C2×D47—22no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—84no—
172C4×C47—21no—
173C4×C47—21no—
174C4×C47—21no—
175C4×C47—21no—
176C4×C47C2×#4111yescharacteristic
177C4×C47H(5,𝔽2)11yescharacteristic
178Dic47—41no—
179Dic47—41no—
180Dic47—41no—
181Dic47—41no—
182Dic47—41no—
183#3297—471nomaximal, Sylow
184C2×C47—22no—
185C2×C47—41no—
186C2×C47#54611yescharacteristic
187C2×C47C2×#13511yescharacteristic
188C2×C47#57611yescharacteristic
189D47—42no—
190D47—81no—
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#449—471no—
202#447—471no—
203C4×D8—471no—
204C8×D4D4711yescharacteristic, complemented
205#416—471no—
206C2×#102—471no—
207C47#329711yescharacteristic, complemented, Sylow
208C2×#41—471no—
209C22×D4—471no—
210C2×SD16—471no—
211C2×D8—471no—
212C2×D8—471no—
213C22×C8C2×D4711yescharacteristic
214C22×C8C2×D4711yescharacteristic, complemented
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—471no—
224#121—941no—
225#121—941no—
226#120—941no—
227C4×D4—471no—
228C4×D4—471no—
229C4×D4—941no—
230C4×D4C2×D4711yescharacteristic
231#117—471no—
232C2×C4⋊C4—471no—
233C2×C22⋊C4—941no—
234#107—471no—
235#107—471no—
236#106—471no—
237C4⋊C8C2×D4711yescharacteristic, complemented
238#103—471no—
239#103—471no—
240#103—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247#102—471no—
248C22⋊C8C2×D4711yescharacteristic
249C22⋊C8C2×D4711yescharacteristic, complemented
250C4×C8C2×D4711yescharacteristic, complemented
251C24—941no—
252#41—942no—
253#41—1881no—
254C2×Q8—471no—
255C2×D4—471no—
256C2×D4—471no—
257C2×D4—471no—
258C2×D4—942no—
259C2×D4—941no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4—941no—
264C2×D4—1881no—
265C2×D4D18811yescharacteristic
266C22×C4—941no—
267C22×C4—941no—
268C22×C4—941no—
269C22×C4—941no—
270C22×C4C22×D4711yescharacteristic
271C22×C4C22×D4711yescharacteristic
272SD16—1881no—
273D8—942no—
274D8—1881no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D4711yescharacteristic
278C2×C8C22×D4711yescharacteristic
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⋊C4D18811yescharacteristic
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4D18811yescharacteristic
300C22⋊C4D18811yescharacteristic
301C42—941no—
302C42C22×D4711yescharacteristic
303C23—941no—
304C23—941no—
305C23—941no—
306C23—3761no—
307C23—1882no—
308C23—1882no—
309C23C2×D18811yescharacteristic
310C23C2×D18811yescharacteristic
311Q8—941no—
312Q8—941no—
313D4—22no—
314D4—472no—
315D4—941no—
316D4—941no—
317D4—941no—
318D4—941no—
319D4—941no—
320D4—3761no—
321D4—3761no—
322D4—1882no—
323D4—1882no—
324D4—1882no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—941no—
333C2×C4—941no—
334C2×C4—3761no—
335C2×C4—3761no—
336C2×C4—3761no—
337C2×C4—1882no—
338C2×C4C2×D18811yescharacteristic
339C2×C4C2×D18811yescharacteristic
340C2×C4C2×D18811yescharacteristic
341C2×C4C2×D18811yescharacteristic
342C2×C4C23×D4711yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—942no—
353C22—3764no—
354C22—1881no—
355C22—1881no—
356C22—1881no—
357C22—1881no—
358C22—1881no—
359C22—1881no—
360C22—1881no—
361C22—1881no—
362C22#1309404612yes—
363C22C22×D18811yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—1881no—
369C4—1881no—
370C4—1881no—
371C4—1881no—
372C4—1881no—
373C4#41×D4711yescharacteristic
374C4#1309406911yescharacteristic
375C2—22no—
376C2—41no—
377C2—3761no—
378C2—3761no—
379C2—1882no—
380C2#1568976811yescharacteristic
381C2C2×#1309404611yescharacteristic
382C2#1568992811yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC8×D4×C47C2
socleC22×C47C22×D4
hypercenterC8×D4D47
hypocenterC47#3297
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #15689819C2semidirect
2. #15689769C2semidirect
3. #15689478C2semidirect
4. #15689459C2semidirect
5. #15689448C2semidirect
6. #15689424C2semidirect
7. #15689359C2semidirect
8. #15689352C2semidirect
9. #15689339C2semidirect
10. #15689270C2semidirect
11. #15689259C2semidirect
12. C4×D376C2semidirect
13. #15689120C2semidirect
14. C2×#13093946C2semidirect
15. C8×D4×C47C2semidirect
18. C2×#10625325C22semidirect
22. #13094016C22semidirect
29. #13093998C22semidirect
34. C4×D188C22semidirect
36. #13093983C22semidirect
39. #13093958C22semidirect
40. #13093958C22semidirect
41. #13093956C22semidirect
42. #13093949C22semidirect
43. #13093949C22semidirect
44. #13093949C22semidirect
51. #13093946C22semidirect
53. C22×C8×C47C22semidirect
55. C4⋊C8×C47C22semidirect
57. C22⋊C8×C47C22semidirect
58. C4×C8×C47C22semidirect
204. C8×D4D47semidirect
207. C47#3297semidirect
214. C22×C8C2×D47semidirect
237. C4⋊C8C2×D47semidirect
249. C22⋊C8C2×D47semidirect
250. C4×C8C2×D47semidirect