Finite Group Databasebeta

← #20253627

Subgroups — #20253627

Order 6016.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689726C211yesmaximal, characteristic, complemented
2#15689597C211yesmaximal, characteristic, complemented
3#15689447C211yesmaximal, characteristic, complemented
4#15689426C211yesmaximal, characteristic, complemented
5#15689422C211yesmaximal, characteristic, complemented
6#15689317C211yesmaximal, characteristic, complemented
7#15689317C211yesmaximal, characteristic, complemented
8#15689259C211yesmaximal, characteristic, complemented
9#15689256C211yesmaximal, characteristic, complemented
10#15689234C211yesmaximal, characteristic, complemented
11#15689232C211yesmaximal, characteristic, complemented
12#15689205C211yesmaximal, characteristic, complemented
13#15689203C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#482C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C2×D376C2211yescharacteristic
18C2×D376C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21#13094020C2211yescharacteristic, complemented
22#13094015C2211yescharacteristic, complemented
23#13094008—21no—
24#13094006—21no—
25#13093998C2211yescharacteristic
26#13093996—21no—
27#13093995—21no—
28C4×D188—21no—
29C4×D188—21no—
30D4×Dic47C2211yescharacteristic, complemented
31#13093986C2211yescharacteristic
32#13093986C2211yescharacteristic
33#13093986C2211yescharacteristic
34#13093986C2211yescharacteristic
35#13093986C2211yescharacteristic, complemented
36#13093983C2211yescharacteristic
37C22⋊C4×D47—21no—
38C22⋊C4×D47—21no—
39#13093957C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093944C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic, complemented
48#13093944C2211yescharacteristic, complemented
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52#121×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56#102×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic
59C23×D47—21no—
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C22×Dic47—21no—
67C2×D188—21no—
68C2×D188—22no—
69C2×D188—22no—
70C2×D188C2311yescharacteristic
71C2×D188C2311yescharacteristic
72C2×D188C2311yescharacteristic
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C42×C47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47D411yescharacteristic
88C22⋊Dic47D411yescharacteristic
89#10625334—22no—
90#10625334—22no—
91(C2×D47)⋊C4—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—
97C4⋊Dic47—21no—
98C4⋊Dic47D411yescharacteristic
99C4⋊Dic47D411yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106D376—22no—
107D376—22no—
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110C22×D47—21no—
111C22×D47—21no—
112C22×D47—24no—
113C22×D47—21no—
114C22×D47—81no—
115C22×D47—81no—
116D4×C47—21no—
117D4×C47—21no—
118D4×C47—81no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C22⋊D47—81no—
127C22⋊D47—81no—
128C22⋊D47—81no—
129C2×Dic47—21no—
130C2×Dic47—81no—
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135D188—24no—
136D188—21no—
137D188—21no—
138D188—21no—
139D188—21no—
140D188#4112yes—
141D188#4112yes—
142C4×D47—81no—
143C4×D47—81no—
144C4×D47—81no—
145C4×D47—81no—
146C4×D47—81no—
147C8×C47—21no—
148C8×C47—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47C22×D411yescharacteristic
158C2×D47—22no—
159C2×D47—22no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—84no—
168C4×C47—21no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47C2×#4111yescharacteristic
173C4×C47C2×#4111yescharacteristic
174Dic47—21no—
175Dic47—21no—
176Dic47—21no—
177Dic47—21no—
178Dic47—41no—
179#3122—471nomaximal, Sylow
180C2×C47—41no—
181C2×C47—81no—
182C2×C47#52511yescharacteristic
183C2×C47#57611yescharacteristic
184C2×C47#57611yescharacteristic
185D47—42no—
186D47—42no—
187D47—81no—
188#540—471no—
189#518—471no—
190#482—471no—
191#482D4711yescharacteristic, complemented
192#478—471no—
193#478—471no—
194#459—471no—
195#459—471no—
196#447—471no—
197#447—471no—
198#442—471no—
199#442—471no—
200C4×D8—471no—
201C4×D8—471no—
202#433—471no—
203C47#312211yescharacteristic, complemented, Sylow
204C22×D4—471no—
205C2×D8—471no—
206C2×D8—471no—
207C2×D8—471no—
208C2×D8—471no—
209#127—471no—
210#125—471no—
211#123—941no—
212#123—941no—
213#121—471no—
214#121—941no—
215#121—941no—
216#121C2×D4711yescharacteristic
217C4×D4—471no—
218C4×D4—471no—
219C4×D4—471no—
220C4×D4—471no—
221C4×D4—471no—
222C4×D4—471no—
223C4×D4—941no—
224C4×D4—941no—
225#117—471no—
226#117C2×D4711yescharacteristic
227C2×C22⋊C4—941no—
228C2×C22⋊C4—941no—
229#107—471no—
230#107C2×D4711yescharacteristic, complemented
231#106—471no—
232#106C2×D4711yescharacteristic, complemented
233C4⋊C8—471no—
234C4⋊C8—471no—
235#102—471no—
236#102—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#102—471no—
241#102C2×D4711yescharacteristic, complemented
242#102C2×D4711yescharacteristic, complemented
243C22⋊C8—471no—
244C22⋊C8C2×D4711yescharacteristic
245#97—471no—
246C4×C8—471no—
247C24—941no—
248C2×D4—21no—
249C2×D4—471no—
250C2×D4—471no—
251C2×D4—471no—
252C2×D4—942no—
253C2×D4—942no—
254C2×D4—941no—
255C2×D4—941no—
256C2×D4—941no—
257C2×D4—941no—
258C2×D4C22×D4711yescharacteristic
259C22×C4—941no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4—941no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4C22×D4711yescharacteristic
266D8—942no—
267D8—942no—
268D8—942no—
269D8—942no—
270C2×C8—471no—
271C2×C8—471no—
272C2×C8C22×D4711yescharacteristic
273C2×C8C22×D4711yescharacteristic
274C4⋊C4—471no—
275C4⋊C4—471no—
276C4⋊C4—471no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4C22×D4711yescharacteristic
280C4⋊C4C22×D4711yescharacteristic
281C4⋊C4C22×D4711yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—471no—
285C22⋊C4—471no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C42—21no—
294C42—471no—
295C42—471no—
296C23—21no—
297C23—944no—
298C23—941no—
299C23—941no—
300C23—941no—
301C23—3761no—
302C23—3761no—
303C23D4×D4711yescharacteristic
304D4—21no—
305D4—21no—
306D4—81no—
307D4—472no—
308D4—472no—
309D4—944no—
310D4—941no—
311D4—941no—
312D4—941no—
313D4—941no—
314D4—3761no—
315D4—3761no—
316D4—3761no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—471no—
323C2×C4—471no—
324C2×C4—471no—
325C2×C4—471no—
326C2×C4—941no—
327C2×C4—3761no—
328C2×C4—3761no—
329C2×C4—3761no—
330C2×C4—3761no—
331C2×C4—3761no—
332C2×C4—3761no—
333C2×C4D4×D4711yescharacteristic
334C2×C4C23×D4711yescharacteristic
335C8—21no—
336C8—21no—
337C8—941no—
338C8—941no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—942no—
346C22—942no—
347C22—3764no—
348C22—1881no—
349C22—1881no—
350C22—1881no—
351C22—1881no—
352C22—1881no—
353C22—1881no—
354C22—1881no—
355C22C2×D4×D4711yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—941no—
361C4—941no—
362C4—941no—
363C4—941no—
364C4—1881no—
365C4#41×D4711yescharacteristic
366C4#41×D4711yescharacteristic
367C2—41no—
368C2—81no—
369C2—3761no—
370C2—1882no—
371C2—1882no—
372C2#1568963111yescharacteristic
373C2#1568992511yescharacteristic
374C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#482C2
socleC22×C47C22×D4
hypercenter#482D47
hypocenterC47#3122
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #15689726C2semidirect
2. #15689597C2semidirect
3. #15689447C2semidirect
4. #15689426C2semidirect
5. #15689422C2semidirect
6. #15689317C2semidirect
7. #15689317C2semidirect
8. #15689259C2semidirect
9. #15689256C2semidirect
10. #15689234C2semidirect
11. #15689232C2semidirect
12. #15689205C2semidirect
13. #15689203C2semidirect
14. #15689181C2semidirect
15. C47×#482C2semidirect
21. #13094020C22semidirect
22. #13094015C22semidirect
30. D4×Dic47C22semidirect
35. #13093986C22semidirect
39. #13093957C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
42. Dic47⋊C8C22semidirect
47. #13093944C22semidirect
48. #13093944C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
54. #107×C47C22semidirect
55. #106×C47C22semidirect
56. #102×C47C22semidirect
57. #102×C47C22semidirect
191. #482D47semidirect
203. C47#3122semidirect
230. #107C2×D47semidirect
232. #106C2×D47semidirect
241. #102C2×D47semidirect
242. #102C2×D47semidirect