Finite Group Databasebeta

← C4×#13094051 #20252197

Subgroups — C4×#13094051 #20252197

Order 6016.

548 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
1C2×#13094051C211yesmaximal, characteristic
2C4×#10625354C211yesmaximal, characteristic, complemented
3C4×D4×D47C211yesmaximal, characteristic, complemented
4#15689234C211yesmaximal, characteristic, complemented
5#15689232C211yesmaximal, characteristic, complemented
6#15689226C211yesmaximal, characteristic, complemented
7#15689224C211yesmaximal, characteristic, complemented
8C4×#10625336C211yesmaximal, characteristic, complemented
9C4×D376C211yesmaximal, characteristic, complemented
10C4×#10625334C211yesmaximal, characteristic, complemented
11#15689162C211yesmaximal, characteristic, complemented
12#15689126C211yesmaximal, characteristic, complemented
13#15689123C211yesmaximal, characteristic, complemented
14C4×#10625324C211yesmaximal, characteristic, complemented
15C4×SD16×C47C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C22×C4×D47—21no—
19#13094051C418yesdirect product factor
20C2×#10625336C2211yescharacteristic
21C2×D376C2211yescharacteristic
22C2×#10625334C2211yescharacteristic
23C2×#10625324C2211yescharacteristic
24C2×#10625324C2211yescharacteristic
25Q8×Dic47C2211yescharacteristic, complemented
26C4×D188—21no—
27C4×D188C2211yescharacteristic
28C4×D188C2211yescharacteristic, complemented
29D4×Dic47C2211yescharacteristic
30#13093986—21no—
31#13093986C2211yescharacteristic
32#13093986C2211yescharacteristic, complemented
33C4×C22⋊D47—21no—
34(C22⋊D47)⋊C4—21no—
35#13093982—21no—
36#13093982C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38C22⋊C4×D47—21no—
39C42×D47—21no—
40C42×D47C2211yescharacteristic
41#13093958C2211yescharacteristic, complemented
42#13093957C2211yescharacteristic, complemented
43#13093955C2211yescharacteristic, complemented
44#13093948C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093944C2211yescharacteristic, complemented
50#13093934C2211yescharacteristic, complemented
51#13093934C2211yescharacteristic, complemented
52C4×C47⋊C8C2211yescharacteristic, complemented
53C2×SD16×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic, complemented
55C4×D4×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic
59C4×C8×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×D47—44no—
80C2×C4×D47D411yescharacteristic
81C2×C4×D47D411yescharacteristic
82C2×C4×D47C2311yescharacteristic
83SD16×C47C2×C414yescomplemented
84C2×C8×C47C2311yescharacteristic
85C2×C8×C47C2311yescharacteristic
86C4⋊C4×C47—21no—
87C4⋊C4×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C42×C47—21no—
91C42×C47C2311yescharacteristic
92C22⋊Dic47—21no—
93#10625336C2×C414yescomplemented
94#10625334C2×C414yescomplemented
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100C4⋊Dic47—21no—
101C4⋊Dic47C2311yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103Dic47⋊C4—21no—
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47D411yescharacteristic
107C4×Dic47D411yescharacteristic
108C4×Dic47C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111D376C2×C414yescomplemented
112#10625324—22no—
113#10625324C2×C414yescomplemented
114C23×C47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—24no—
118C22×D47—42no—
119C22×D47—42no—
120C22×D47C2×D411yescharacteristic
121Q8×C47—21no—
122Q8×C47C22×C412yescomplemented
123D4×C47—21no—
124D4×C47C22×C412yes—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—42no—
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C22⋊D47—24no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—42no—
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138C2×Dic47C2×D411yescharacteristic
139D188—24no—
140D188—21no—
141D188—21no—
142D188C22×C412yes—
143D188C22×C412yescomplemented
144C4×D47—22no—
145C4×D47—24no—
146C4×D47—41no—
147C4×D47—42no—
148C4×D47—42no—
149C4×D47—42no—
150C4×D47—42no—
151C4×D47—42no—
152C4×D47C22×C412yes—
153C4×D47#4112yes—
154C8×C47—21no—
155C8×C47C22×C412yescomplemented
156C47⋊C8—21no—
157C47⋊C8C22×C412yescomplemented
158C22×C47—22no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47C22×D411yescharacteristic
162C2×D47—21no—
163C2×D47—21no—
164C2×D47—22no—
165C2×D47—22no—
166C2×D47—48no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47C4×D412yes—
172C4×C47—22no—
173C4×C47—21no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47AGL(1,ℤ/8)12yescomplemented
177C4×C47C23×C411yescharacteristic
178C4×C47C2×#4111yescharacteristic
179Dic47—21no—
180Dic47—21no—
181Dic47—41no—
182Dic47—41no—
183Dic47C4×D412yes—
184C4×AGL(1,ℤ/8)—471nomaximal, Sylow
185C2×C47—42no—
186C2×C47C2×C4×D411yescharacteristic
187C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C47#57511yescharacteristic
189D47—22no—
190D47—42no—
191D47—42no—
192C2×AGL(1,ℤ/8)—471no—
193C4×#41—471no—
194C2×C4×D4—471no—
195#442—471no—
196#442—471no—
197#440—471no—
198#440—471no—
199C4×SD16—471no—
200C4×SD16D4711yescharacteristic, complemented
201C4×D8—471no—
202C4×D8—471no—
203#428—471no—
204#418—471no—
205#417—471no—
206C4×M16—471no—
207C47C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
208C2×#41—471no—
209C22×D4—471no—
210C23×C4—941no—
211AGL(1,ℤ/8)—478no—
212C2×SD16—471no—
213C2×SD16C2×D4711yescharacteristic
214C2×D8—471no—
215C2×D8—471no—
216C2×M16—471no—
217C2×M16—471no—
218C4×Q8—471no—
219C4×Q8C2×D4711yescharacteristic, complemented
220C4×D4—471no—
221C4×D4—471no—
222C4×D4—471no—
223C4×D4—471no—
224C4×D4—471no—
225C4×D4—941no—
226C4×D4—941no—
227C4×D4—941no—
228C4×D4—941no—
229C4×D4C2×D4711yescharacteristic
230#117—471no—
231#117—941no—
232C2×C4⋊C4—471no—
233C2×C22⋊C4—941no—
234C2×C42—471no—
235C2×C42—941no—
236#107—471no—
237#107—471no—
238#106—471no—
239#106C2×D4711yescharacteristic, complemented
240#103—471no—
241#103C2×D4711yescharacteristic, complemented
242#102—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247#102C2×D4711yescharacteristic
248#97—471no—
249#97—471no—
250C4×C8—471no—
251C4×C8C2×D4711yescharacteristic, complemented
252C24—941no—
253#41—474no—
254#41—942no—
255C2×Q8C22×D4711yescharacteristic
256C2×D4—474no—
257C2×D4—471no—
258C2×D4—471no—
259C2×D4—941no—
260C2×D4—942no—
261C2×D4—941no—
262C2×D4C22×D4711yescharacteristic
263C22×C4—21no—
264C22×C4—471no—
265C22×C4—471no—
266C22×C4—471no—
267C22×C4—941no—
268C22×C4—941no—
269C22×C4—941no—
270C22×C4—941no—
271C22×C4—941no—
272C22×C4—941no—
273C22×C4—941no—
274C22×C4—1884no—
275SD16—474no—
276SD16C4×D4714yescomplemented
277D8—474no—
278D8—474no—
279M16—474no—
280M16—942no—
281C2×C8—471no—
282C2×C8—471no—
283C2×C8C22×D4711yescharacteristic
284C2×C8C22×D4711yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—471no—
287C4⋊C4—471no—
288C4⋊C4—941no—
289C4⋊C4—941no—
290C4⋊C4C22×D4711yescharacteristic
291C4⋊C4C22×D4711yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C42—21no—
300C42—471no—
301C42—471no—
302C42—471no—
303C42—941no—
304C42—941no—
305C42C22×D4711yescharacteristic
306C23—21no—
307C23—471no—
308C23—944no—
309C23—941no—
310C23—941no—
311C23—1882no—
312C23—1882no—
313Q8—21no—
314Q8C2×C4×D4712yescomplemented
315D4—21no—
316D4—472no—
317D4—472no—
318D4—944no—
319D4—944no—
320D4—941no—
321D4—941no—
322D4C2×C4×D4712yes—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—471no—
328C2×C4—472no—
329C2×C4—472no—
330C2×C4—471no—
331C2×C4—471no—
332C2×C4—944no—
333C2×C4—942no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—1881no—
337C2×C4—1882no—
338C2×C4—1882no—
339C2×C4—1882no—
340C2×C4—1882no—
341C2×C4—1882no—
342C2×C4—1882no—
343C2×C4D4×D4711yescharacteristic
344C2×C4D4×D4711yescharacteristic
345C2×C4C23×D4711yescharacteristic
346C8—21no—
347C8—472no—
348C8—941no—
349C8C2×C4×D4712yescomplemented
350C22—22no—
351C22—41no—
352C22—41no—
353C22—472no—
354C22—941no—
355C22—941no—
356C22—942no—
357C22—942no—
358C22—1888no—
359C22—1881no—
360C22—1881no—
361C22—1881no—
362C22—1881no—
363C22C2×D4×D4711yescharacteristic
364C4—22no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—472no—
369C4—941no—
370C4—941no—
371C4—1881no—
372C4—1881no—
373C4#1309405112yesdirect product factor
374C4C22×C4×D4711yescharacteristic
375C4#41×D4711yescharacteristic
376C2—42no—
377C2—942no—
378C2—1882no—
379C2—1882no—
380C2C4×D4×D4711yescharacteristic
381C2C2×#1309405111yescharacteristic
382C2#1568992011yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC4×SD16×C47C2
socleC22×C47C22×D4
hypercenterC4×SD16D47
hypocenterC47C4×AGL(1,ℤ/8)
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×#10625354C2semidirect
3. C4×D4×D47C2semidirect
4. #15689234C2semidirect
5. #15689232C2semidirect
6. #15689226C2semidirect
7. #15689224C2semidirect
8. C4×#10625336C2semidirect
9. C4×D376C2semidirect
10. C4×#10625334C2semidirect
11. #15689162C2semidirect
12. #15689126C2semidirect
13. #15689123C2semidirect
14. C4×#10625324C2semidirect
15. C4×SD16×C47C2semidirect
19. #13094051C4direct (N × H)
25. Q8×Dic47C22semidirect
28. C4×D188C22semidirect
32. #13093986C22semidirect
41. #13093958C22semidirect
42. #13093957C22semidirect
43. #13093955C22semidirect
44. #13093948C22semidirect
46. #13093946C22semidirect
49. #13093944C22semidirect
50. #13093934C22semidirect
51. #13093934C22semidirect
52. C4×C47⋊C8C22semidirect
54. C4×Q8×C47C22semidirect
56. #106×C47C22semidirect
57. #103×C47C22semidirect
59. C4×C8×C47C22semidirect
67. #10625354C2×C4semidirect
69. D4×D47C2×C4semidirect
83. SD16×C47C2×C4semidirect
93. #10625336C2×C4semidirect
94. #10625334C2×C4semidirect
111. D376C2×C4semidirect
113. #10625324C2×C4semidirect
122. Q8×C47C22×C4semidirect
143. D188C22×C4semidirect
155. C8×C47C22×C4semidirect
157. C47⋊C8C22×C4semidirect
176. C4×C47AGL(1,ℤ/8)semidirect
200. C4×SD16D47semidirect
207. C47C4×AGL(1,ℤ/8)semidirect
219. C4×Q8C2×D47semidirect
239. #106C2×D47semidirect
241. #103C2×D47semidirect
251. C4×C8C2×D47semidirect
276. SD16C4×D47semidirect
314. Q8C2×C4×D47semidirect
349. C8C2×C4×D47semidirect
373. C4#13094051direct (N × H)