Finite Group Databasebeta

← C4×#13094045 #20252157

Subgroups — C4×#13094045 #20252157

Order 6016.

500 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094045C211yesmaximal, characteristic
2C4×#10625354C211yesmaximal, characteristic, complemented
3C4×#10625352C211yesmaximal, characteristic, complemented
4C4×#10625337C211yesmaximal, characteristic, complemented
5#15689215C211yesmaximal, characteristic, complemented
6C4×#10625325C211yesmaximal, characteristic, complemented
7SD16×Dic47C211yesmaximal, characteristic, complemented
8#15689210C211yesmaximal, characteristic, complemented
9C4×#10625334C211yesmaximal, characteristic, complemented
10#15689203C211yesmaximal, characteristic, complemented
11#15689158C211yesmaximal, characteristic, complemented
12#15689118C211yesmaximal, characteristic, complemented
13#15689116C211yesmaximal, characteristic, complemented
14C4×C8×D47C211yesmaximal, characteristic, complemented
15C4×SD16×C47C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625352C2211yescharacteristic
18#13094045C418yesdirect product factor
19C2×#10625337C2211yescharacteristic
20C2×#10625325C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22C2×C8×D47C2211yescharacteristic
23C2×C8×D47C2211yescharacteristic
24Q8×Dic47C2211yescharacteristic
25C4×Dic94C2211yescharacteristic
26#13093989C2211yescharacteristic
27C4×D188—21no—
28C4×D188C2211yescharacteristic
29D4×Dic47C2211yescharacteristic
30#13093986—21no—
31#13093986C2211yescharacteristic
32C4×C22⋊D47—21no—
33(C22⋊D47)⋊C4—21no—
34#13093982—21no—
35#13093982C2211yescharacteristic
36#13093982C2211yescharacteristic
37#13093980—21no—
38C2×C4×Dic47—21no—
39C42×D47—21no—
40C42×D47C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093957C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093944C2211yescharacteristic
50C4×C47⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C8×Dic47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C4×C8×C47C2211yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C22×Dic47—21no—
65C22×Dic47—21no—
66#10625354—22no—
67#10625354C2×C414yescomplemented
68#10625352—22no—
69#10625352C2×C414yescomplemented
70C2×D188—21no—
71C2×D188C2311yescharacteristic
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47D411yescharacteristic
76C2×C4×D47D411yescharacteristic
77C2×C4×D47C2311yescharacteristic
78C2×Dic94C2311yescharacteristic
79SD16×C47C2×C414yescomplemented
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C4⋊C4×C47—21no—
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C42×C47—21no—
87C42×C47C2311yescharacteristic
88C22⋊Dic47—21no—
89#10625337C2×C414yescomplemented
90#10625334C2×C414yescomplemented
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47D411yescharacteristic
106C4×Dic47D411yescharacteristic
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625325C2×C414yescomplemented
111C8×D47—22no—
112C8×D47C2×C414yescomplemented
113C23×C47—21no—
114C22×D47—21no—
115C22×D47C2×D411yescharacteristic
116Q8×C47—21no—
117Q8×C47C22×C412yes—
118D4×C47—21no—
119D4×C47C22×C412yes—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—42no—
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2411yescharacteristic
127C22⋊D47—24no—
128C2×Dic47—21no—
129C2×Dic47—24no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—42no—
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136D188—24no—
137D188—21no—
138D188C22×C412yes—
139C4×D47—22no—
140C4×D47—24no—
141C4×D47—22no—
142C4×D47—42no—
143C4×D47—42no—
144C4×D47C22×C412yes—
145C4×D47#4112yes—
146Dic94—21no—
147Dic94C22×C412yes—
148C8×C47—21no—
149C8×C47C22×C412yes—
150C47⋊C8—21no—
151C47⋊C8C22×C412yes—
152C22×C47—22no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47C22×D411yescharacteristic
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—22no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47C4×D412yes—
162C4×C47—22no—
163C4×C47—21no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47#13512yescomplemented
167C4×C47C23×C411yescharacteristic
168C4×C47C2×#4111yescharacteristic
169Dic47—22no—
170Dic47—21no—
171Dic47—41no—
172Dic47—41no—
173Dic47C4×D412yes—
174Dic47#13512yescomplemented
175C4×#135—471nomaximal, Sylow
176C2×C47—42no—
177C2×C47C2×C4×D411yescharacteristic
178C2×C47C2×#13511yescharacteristic
179C2×C47C2×#13511yescharacteristic
180D47—22no—
181D47—42no—
182C2×#135—471no—
183C4×#41—471no—
184C4×#41—471no—
185C4×Q16—471no—
186C4×Q16—471no—
187C4×SD16—471no—
188C4×SD16—471no—
189C4×SD16—471no—
190C4×SD16D4711yescharacteristic, complemented
191C4×D8—471no—
192C4×D8—471no—
193#427—471no—
194#416—471no—
195#416—471no—
196C2×C4×C8—471no—
197C47C4×#13511yescharacteristic, complemented, Sylow
198C2×#41—471no—
199C2×#41—471no—
200#135—478no—
201C2×Q16—471no—
202C2×SD16—471no—
203C2×SD16C2×D4711yescharacteristic
204C2×D8—471no—
205C22×C8—471no—
206C22×C8—471no—
207C4×Q8—471no—
208C4×Q8—471no—
209C4×Q8—471no—
210C4×Q8C2×D4711yescharacteristic
211C4×D4—471no—
212C4×D4—471no—
213C4×D4—471no—
214C4×D4—941no—
215C4×D4—941no—
216C4×D4—941no—
217C4×D4—941no—
218C4×D4C2×D4711yescharacteristic
219#117—471no—
220#117—471no—
221#117—941no—
222#117—941no—
223C2×C42—471no—
224C2×C42—941no—
225C2×C42—941no—
226#107—471no—
227#107—471no—
228#106—471no—
229#106C2×D4711yescharacteristic
230#103—471no—
231#103—471no—
232#103—471no—
233#103C2×D4711yescharacteristic
234#102—471no—
235#102—471no—
236#102—471no—
237#102C2×D4711yescharacteristic
238C4×C8—471no—
239C4×C8—471no—
240C4×C8—471no—
241C4×C8C2×D4711yescharacteristic
242#41—474no—
243#41—474no—
244#41—942no—
245#41—942no—
246C2×Q8—471no—
247C2×Q8C22×D4711yescharacteristic
248C2×D4—471no—
249C2×D4—941no—
250C2×D4—941no—
251C2×D4C22×D4711yescharacteristic
252C22×C4—21no—
253C22×C4—471no—
254C22×C4—471no—
255C22×C4—471no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4—941no—
259C22×C4—941no—
260C22×C4—941no—
261Q16—474no—
262SD16—474no—
263SD16C4×D4714yescomplemented
264D8—474no—
265C2×C8—471no—
266C2×C8—474no—
267C2×C8—471no—
268C2×C8—942no—
269C2×C8C22×D4711yescharacteristic
270C2×C8C22×D4711yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—471no—
273C4⋊C4—471no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4C22×D4711yescharacteristic
278C4⋊C4C22×D4711yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C42—21no—
286C42—471no—
287C42—471no—
288C42—471no—
289C42—941no—
290C42—941no—
291C42—941no—
292C42—941no—
293C42—941no—
294C42C22×D4711yescharacteristic
295C23—21no—
296C23—471no—
297C23—941no—
298Q8—21no—
299Q8—472no—
300Q8—941no—
301Q8C2×C4×D4712yes—
302D4—21no—
303D4—472no—
304D4—944no—
305D4—944no—
306D4—941no—
307D4C2×C4×D4712yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—471no—
313C2×C4—471no—
314C2×C4—472no—
315C2×C4—472no—
316C2×C4—471no—
317C2×C4—942no—
318C2×C4—944no—
319C2×C4—944no—
320C2×C4—941no—
321C2×C4—942no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—1882no—
325C2×C4—1882no—
326C2×C4—1882no—
327C2×C4D4×D4711yescharacteristic
328C2×C4D4×D4711yescharacteristic
329C2×C4C23×D4711yescharacteristic
330C8—21no—
331C8—472no—
332C8—941no—
333C8C2×C4×D4712yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—472no—
338C22—941no—
339C22—941no—
340C22—942no—
341C22—1881no—
342C22—1881no—
343C22C2×D4×D4711yescharacteristic
344C4—22no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—472no—
349C4—472no—
350C4—942no—
351C4—941no—
352C4—1881no—
353C4—1881no—
354C4#1309404512yesdirect product factor
355C4C22×C4×D4711yescharacteristic
356C4#41×D4711yescharacteristic
357C2—42no—
358C2—942no—
359C2—1882no—
360C2C4×D4×D4711yescharacteristic
361C2#135×D4711yescharacteristic
362C2C2×#1309404511yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC4×SD16×C47C2
socleC22×C47C22×D4
hypercenterC4×SD16D47
hypocenterC47C4×#135
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×#10625352C2semidirect
4. C4×#10625337C2semidirect
5. #15689215C2semidirect
6. C4×#10625325C2semidirect
7. SD16×Dic47C2semidirect
8. #15689210C2semidirect
9. C4×#10625334C2semidirect
10. #15689203C2semidirect
11. #15689158C2semidirect
12. #15689118C2semidirect
13. #15689116C2semidirect
14. C4×C8×D47C2semidirect
15. C4×SD16×C47C2semidirect
18. #13094045C4direct (N × H)
67. #10625354C2×C4semidirect
69. #10625352C2×C4semidirect
79. SD16×C47C2×C4semidirect
89. #10625337C2×C4semidirect
90. #10625334C2×C4semidirect
110. #10625325C2×C4semidirect
112. C8×D47C2×C4semidirect
166. C4×C47#135semidirect
174. Dic47#135semidirect
190. C4×SD16D47semidirect
197. C47C4×#135semidirect
263. SD16C4×D47semidirect
354. C4#13094045direct (N × H)