Finite Group Databasebeta

← #20253625

Subgroups — #20253625

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#15689598C211yesmaximal, characteristic, complemented
3#15689448C211yesmaximal, characteristic, complemented
4#15689444C211yesmaximal, characteristic, complemented
5#15689425C211yesmaximal, characteristic, complemented
6#15689421C211yesmaximal, characteristic, complemented
7#15689316C211yesmaximal, characteristic, complemented
8#15689316C211yesmaximal, characteristic, complemented
9#15689257C211yesmaximal, characteristic, complemented
10#15689235C211yesmaximal, characteristic, complemented
11#15689232C211yesmaximal, characteristic, complemented
12D8×Dic47C211yesmaximal, characteristic, complemented
13#15689203C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#447C211yesmaximal, characteristic, complemented
16C2×#10625334C2211yescharacteristic
17C2×#10625334C2211yescharacteristic
18#13094020C2211yescharacteristic, complemented
19#13094015C2211yescharacteristic, complemented
20#13094008—21no—
21#13094006—21no—
22#13093998C2211yescharacteristic
23#13093996—21no—
24#13093995—21no—
25D4×Dic47—21no—
26D4×Dic47—21no—
27D4×Dic47C2211yescharacteristic
28D4×Dic47C2211yescharacteristic
29D4×Dic47C2211yescharacteristic
30D4×Dic47C2211yescharacteristic
31D4×Dic47C2211yescharacteristic, complemented
32#13093986C2211yescharacteristic, complemented
33#13093983C2211yescharacteristic
34#13093983C2211yescharacteristic
35C2×C22⋊Dic47—21no—
36C2×C22⋊Dic47—21no—
37#13093958C2211yescharacteristic, complemented
38#13093957C2211yescharacteristic, complemented
39#13093956C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic, complemented
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic, complemented
48#13093945C2211yescharacteristic, complemented
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C22×D4×C47C2211yescharacteristic
53C2×D8×C47C2211yescharacteristic
54C2×D8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C24×C47—21no—
60C2×D4×C47—22no—
61C2×D4×C47—22no—
62C2×D4×C47—21no—
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C22×Dic47—21no—
72C22×Dic47—21no—
73C22×Dic47—21no—
74C22×Dic47—21no—
75C22×Dic47—21no—
76C2×D188C2311yescharacteristic
77C2×C4×D47—21no—
78D8×C47—22no—
79D8×C47—22no—
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47D411yescharacteristic
91C22⋊Dic47D411yescharacteristic
92#10625334—22no—
93#10625334—22no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47D411yescharacteristic
98C4⋊Dic47D411yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103C4×Dic47—21no—
104C4×Dic47C2311yescharacteristic
105C4×Dic47C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—24no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—81no—
113C23×C47—81no—
114C23×C47C2×D411yescharacteristic
115C22×D47—21no—
116D4×C47—24no—
117D4×C47—21no—
118D4×C47—21no—
119D4×C47—21no—
120D4×C47—21no—
121D4×C47—81no—
122D4×C47#4112yes—
123D4×C47#4112yes—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—81no—
130C22⋊D47—81no—
131C22⋊D47—81no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—81no—
136C2×Dic47—81no—
137C2×Dic47—81no—
138C2×Dic47—81no—
139C2×Dic47—81no—
140C2×Dic47C2×D411yescharacteristic
141C2×Dic47C2×D411yescharacteristic
142C2×Dic47C2×D411yescharacteristic
143C2×Dic47C2×D411yescharacteristic
144D188—21no—
145D188—21no—
146C4×D47—81no—
147C8×C47—21no—
148C8×C47—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—21no—
152C22×C47—22no—
153C22×C47—22no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—84no—
164C22×C47C22×D411yescharacteristic
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—41no—
168C4×C47—21no—
169C4×C47—41no—
170C4×C47C2×#4111yescharacteristic
171C4×C47C2×#4111yescharacteristic
172Dic47—21no—
173Dic47—21no—
174Dic47—21no—
175Dic47—21no—
176Dic47—41no—
177Dic47—41no—
178Dic47—41no—
179#3122—471nomaximal, Sylow
180C2×C47—41no—
181C2×C47—42no—
182C2×C47—42no—
183C2×C47—81no—
184C2×C47#52511yescharacteristic
185C2×C47#57611yescharacteristic
186C2×C47#57611yescharacteristic
187D47—81no—
188#540—471no—
189#518—471no—
190#482—471no—
191#482—471no—
192#478—471no—
193#478—471no—
194#459—471no—
195#459—471no—
196#447—471no—
197#447D4711yescharacteristic, complemented
198#442—471no—
199#442—471no—
200C4×D8—471no—
201C4×D8—471no—
202#433—471no—
203C47#312211yescharacteristic, complemented, Sylow
204C22×D4C2×D4711yescharacteristic
205C2×D8—471no—
206C2×D8—471no—
207C2×D8C2×D4711yescharacteristic
208C2×D8C2×D4711yescharacteristic
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#117—471no—
227C2×C22⋊C4—941no—
228C2×C22⋊C4—941no—
229#107—471no—
230#107—471no—
231#106—471no—
232#106—471no—
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
242#102C2×D4711yescharacteristic
243C22⋊C8—471no—
244C22⋊C8C2×D4711yescharacteristic
245#97—471no—
246C4×C8—471no—
247C24—21no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—471no—
253C2×D4—941no—
254C2×D4—941no—
255C2×D4—941no—
256C2×D4C22×D4711yescharacteristic
257C2×D4C22×D4711yescharacteristic
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—22no—
267D8—22no—
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—471no—
278C4⋊C4—471no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4C22×D4711yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—471no—
284C22⋊C4—471no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C42—471no—
294C42—471no—
295C42—941no—
296C23—24no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—81no—
301C23—81no—
302C23—941no—
303C23D4×D4711yescharacteristic
304D4—24no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—941no—
311D4—941no—
312D4—3761no—
313D4—3761no—
314D4—3761no—
315D4#1062535212yes—
316D4#1062535212yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—471no—
321C2×C4—471no—
322C2×C4—471no—
323C2×C4—471no—
324C2×C4—941no—
325C2×C4—941no—
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—22no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—84no—
352C22—1881no—
353C22—1881no—
354C22—1881no—
355C22C2×D4×D4711yescharacteristic
356C4—21no—
357C4—41no—
358C4—941no—
359C4—941no—
360C4—941no—
361C4—941no—
362C4—1881no—
363C4—1881no—
364C4—1881no—
365C4C2×#1062535211yescharacteristic
366C4C2×#1062535211yescharacteristic
367C2—41no—
368C2—42no—
369C2—42no—
370C2—81no—
371C2—3761no—
372C2#1568962911yescharacteristic
373C2#1568992411yescharacteristic
374C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#447C2
socleC22×C47C22×D4
hypercenter#447D47
hypocenterC47#3122
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #15689726C2semidirect
2. #15689598C2semidirect
3. #15689448C2semidirect
4. #15689444C2semidirect
5. #15689425C2semidirect
6. #15689421C2semidirect
7. #15689316C2semidirect
8. #15689316C2semidirect
9. #15689257C2semidirect
10. #15689235C2semidirect
11. #15689232C2semidirect
12. D8×Dic47C2semidirect
13. #15689203C2semidirect
14. #15689181C2semidirect
15. C47×#447C2semidirect
18. #13094020C22semidirect
19. #13094015C22semidirect
31. D4×Dic47C22semidirect
32. #13093986C22semidirect
37. #13093958C22semidirect
38. #13093957C22semidirect
39. #13093956C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093946C22semidirect
44. #13093946C22semidirect
47. #13093945C22semidirect
48. #13093945C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
197. #447D47semidirect
203. C47#3122semidirect