Finite Group Databasebeta

← #20252219

Subgroups — #20252219

Order 6016.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094051C211yesmaximal, characteristic
2#15689605C211yesmaximal, characteristic, complemented
3#15689595C211yesmaximal, characteristic, complemented
4#15689236C211yesmaximal, characteristic, complemented
5#15689232C211yesmaximal, characteristic, complemented
6#15689226C211yesmaximal, characteristic, complemented
7SD16×Dic47C211yesmaximal, characteristic, complemented
8C4×#10625336C211yesmaximal, characteristic, complemented
9#15689205C211yesmaximal, characteristic, complemented
10C4×#10625334C211yesmaximal, characteristic, complemented
11#15689164C211yesmaximal, characteristic, complemented
12#15689118C211yesmaximal, characteristic, complemented
13#102×D47C211yesmaximal, characteristic, complemented
14#15689080C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18#13094051C418yescomplemented
19C2×#10625336C2211yescharacteristic
20C2×D376C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22C2×#10625324C2211yescharacteristic
23C2×C8×D47C2211yescharacteristic
24Q8×Dic47C2211yescharacteristic, complemented
25C4×D188—21no—
26C4×D188C2211yescharacteristic
27C4×D188C2211yescharacteristic, complemented
28D4×Dic47C2211yescharacteristic
29#13093986—21no—
30#13093986C2211yescharacteristic
31#13093986C2211yescharacteristic, complemented
32C4×C22⋊D47—21no—
33(C22⋊D47)⋊C4—21no—
34#13093982C2211yescharacteristic
35#13093981—21no—
36#13093981C2211yescharacteristic
37C4⋊C4×D47—21no—
38C4⋊C4×D47C2211yescharacteristic
39C2×(C2×D47)⋊C4—21no—
40C22⋊C4×D47—21no—
41#13093957C2211yescharacteristic, complemented
42#13093956C2211yescharacteristic, complemented
43#13093955C2211yescharacteristic, complemented
44#13093948C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093944C2211yescharacteristic, complemented
50#13093934C2211yescharacteristic, complemented
51C4×C47⋊C8C2211yescharacteristic, complemented
52C8×Dic47C2211yescharacteristic, complemented
53C2×SD16×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic, complemented
55C4×D4×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic
59#97×C47C2211yescharacteristic, complemented
60C23×D47—21no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C2×C22⋊D47—21no—
65C22×Dic47—21no—
66#10625354—22no—
67#10625354C2×C414yescomplemented
68D4×D47—22no—
69D4×D47C2×C414yescomplemented
70C2×D188—21no—
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×C4×D47—21no—
79C2×C4×D47C2311yescharacteristic
80SD16×C47C2×C414yescomplemented
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C4⋊C4×C47—21no—
84C4⋊C4×C47C2311yescharacteristic
85C4⋊C4×C47C2311yescharacteristic
86C22⋊C4×C47—21no—
87C42×C47—21no—
88C42×C47C2311yescharacteristic
89C22⋊Dic47—21no—
90#10625336C2×C414yescomplemented
91#10625334C2×C414yescomplemented
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)⋊C4D411yescharacteristic
98(C2×D47)⋊C4D411yescharacteristic
99C4⋊Dic47—21no—
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4D411yescharacteristic
104Dic47⋊C4D411yescharacteristic
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110D376C2×C414yescomplemented
111#10625324C2×C414yescomplemented
112C8×D47—22no—
113C23×C47—21no—
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—24no—
117C22×D47—81no—
118C22×D47—81no—
119C22×D47C2×D411yescharacteristic
120Q8×C47—21no—
121Q8×C47C22×C412yes—
122D4×C47—21no—
123D4×C47C22×C412yes—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—81no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2411yescharacteristic
131C22⋊D47—24no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—81no—
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138D188—24no—
139D188—21no—
140D188—21no—
141D188C22×C412yes—
142D188C22×C412yes—
143C4×D47—24no—
144C4×D47—81no—
145C4×D47—81no—
146C4×D47—81no—
147C4×D47—81no—
148C4×D47—81no—
149C4×D47C22×C412yes—
150C4×D47#4112yes—
151C8×C47—21no—
152C8×C47C22×C412yes—
153C47⋊C8—21no—
154C47⋊C8C22×C412yes—
155C22×C47—22no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47C22×D411yescharacteristic
159C2×D47—21no—
160C2×D47—21no—
161C2×D47—22no—
162C2×D47—22no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—84no—
168C2×D47C4×D412yes—
169C4×C47—22no—
170C4×C47—21no—
171C4×C47—21no—
172C4×C47—41no—
173C4×C47—41no—
174C4×C47C23×C411yescharacteristic
175C4×C47C2×#4111yescharacteristic
176Dic47—21no—
177Dic47—21no—
178Dic47—41no—
179Dic47—41no—
180Dic47C4×D412yes—
181#2946—471nomaximal, Sylow
182C2×C47—42no—
183C2×C47C2×C4×D411yescharacteristic
184C2×C47#57611yescharacteristic
185C2×C47#57711yescharacteristic
186D47—22no—
187D47—42no—
188D47—42no—
189C2×AGL(1,ℤ/8)—471no—
190#520—471no—
191#518—471no—
192#442—471no—
193#442—471no—
194#440—471no—
195#440D4711yescharacteristic, complemented
196C4×SD16—471no—
197C4×SD16—471no—
198C4×D8—471no—
199C4×D8—471no—
200#428—471no—
201#416—471no—
202C2×#102—471no—
203#405—471no—
204C47#294611yescharacteristic, complemented, Sylow
205C2×#41—471no—
206C22×D4—471no—
207AGL(1,ℤ/8)—478no—
208C2×SD16—471no—
209C2×SD16C2×D4711yescharacteristic
210C2×D8—471no—
211C2×D8—471no—
212C2×M16—471no—
213C22×C8—471no—
214C4×Q8—471no—
215C4×Q8C2×D4711yescharacteristic, complemented
216C4×D4—471no—
217C4×D4—471no—
218C4×D4—471no—
219C4×D4—471no—
220C4×D4—471no—
221C4×D4—941no—
222C4×D4—941no—
223C4×D4—941no—
224C4×D4—941no—
225C4×D4C2×D4711yescharacteristic
226#117—471no—
227#117—471no—
228#117—941no—
229C2×C4⋊C4—471no—
230C2×C4⋊C4—941no—
231C2×C22⋊C4—941no—
232C2×C22⋊C4—941no—
233#107—471no—
234#107C2×D4711yescharacteristic, complemented
235#106—471no—
236#106—471no—
237#103—471no—
238#103C2×D4711yescharacteristic, complemented
239#102—471no—
240#102—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244#102C2×D4711yescharacteristic
245#97—471no—
246#97C2×D4711yescharacteristic, complemented
247C4×C8—471no—
248C4×C8—471no—
249C24—941no—
250#41—474no—
251#41—942no—
252C2×Q8C22×D4711yescharacteristic
253C2×D4—474no—
254C2×D4—471no—
255C2×D4—471no—
256C2×D4—941no—
257C2×D4—942no—
258C2×D4—941no—
259C2×D4C22×D4711yescharacteristic
260C22×C4—21no—
261C22×C4—471no—
262C22×C4—941no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4—941no—
267C22×C4—941no—
268C22×C4—941no—
269SD16—474no—
270SD16C4×D4714yescomplemented
271D8—474no—
272D8—474no—
273M16—474no—
274C2×C8—471no—
275C2×C8—471no—
276C2×C8—942no—
277C2×C8C22×D4711yescharacteristic
278C2×C8C22×D4711yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—471no—
281C4⋊C4—471no—
282C4⋊C4—471no—
283C4⋊C4—471no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4C22×D4711yescharacteristic
287C4⋊C4C22×D4711yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—471no—
290C22⋊C4—471no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C42—21no—
298C42—471no—
299C42—941no—
300C42—941no—
301C42C22×D4711yescharacteristic
302C23—21no—
303C23—471no—
304C23—944no—
305C23—941no—
306C23—941no—
307C23—3761no—
308C23—3761no—
309Q8—21no—
310Q8C2×C4×D4712yes—
311D4—21no—
312D4—472no—
313D4—472no—
314D4—944no—
315D4—944no—
316D4—941no—
317D4—941no—
318D4C2×C4×D4712yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—471no—
324C2×C4—472no—
325C2×C4—472no—
326C2×C4—471no—
327C2×C4—471no—
328C2×C4—944no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—3761no—
332C2×C4—3761no—
333C2×C4—3761no—
334C2×C4—3761no—
335C2×C4—3761no—
336C2×C4—3761no—
337C2×C4D4×D4711yescharacteristic
338C2×C4D4×D4711yescharacteristic
339C2×C4C23×D4711yescharacteristic
340C8—21no—
341C8—472no—
342C8—941no—
343C8C2×C4×D4712yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—472no—
348C22—941no—
349C22—941no—
350C22—942no—
351C22—942no—
352C22—3764no—
353C22—1881no—
354C22—1881no—
355C22—1881no—
356C22—1881no—
357C22C2×D4×D4711yescharacteristic
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—472no—
364C4—941no—
365C4—941no—
366C4—1881no—
367C4—1881no—
368C4C22×C4×D4711yescharacteristic
369C4#41×D4711yescharacteristic
370C2—42no—
371C2—942no—
372C2—1882no—
373C2—1882no—
374C2C4×D4×D4711yescharacteristic
375C2#1568992711yescharacteristic
376C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#2946
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #15689605C2semidirect
3. #15689595C2semidirect
4. #15689236C2semidirect
5. #15689232C2semidirect
6. #15689226C2semidirect
7. SD16×Dic47C2semidirect
8. C4×#10625336C2semidirect
9. #15689205C2semidirect
10. C4×#10625334C2semidirect
11. #15689164C2semidirect
12. #15689118C2semidirect
13. #102×D47C2semidirect
14. #15689080C2semidirect
15. C47×#440C2semidirect
18. #13094051C4semidirect
24. Q8×Dic47C22semidirect
27. C4×D188C22semidirect
31. #13093986C22semidirect
41. #13093957C22semidirect
42. #13093956C22semidirect
43. #13093955C22semidirect
44. #13093948C22semidirect
46. #13093946C22semidirect
49. #13093944C22semidirect
50. #13093934C22semidirect
51. C4×C47⋊C8C22semidirect
52. C8×Dic47C22semidirect
54. C4×Q8×C47C22semidirect
56. #107×C47C22semidirect
57. #103×C47C22semidirect
59. #97×C47C22semidirect
67. #10625354C2×C4semidirect
69. D4×D47C2×C4semidirect
80. SD16×C47C2×C4semidirect
90. #10625336C2×C4semidirect
91. #10625334C2×C4semidirect
110. D376C2×C4semidirect
111. #10625324C2×C4semidirect
195. #440D47semidirect
204. C47#2946semidirect
215. C4×Q8C2×D47semidirect
234. #107C2×D47semidirect
238. #103C2×D47semidirect
246. #97C2×D47semidirect
270. SD16C4×D47semidirect