Finite Group Databasebeta

← #20252879

Subgroups — #20252879

Order 6016.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094056C211yesmaximal, characteristic, complemented
2C2×#13094051C211yesmaximal, characteristic
3#124×D47C211yesmaximal, characteristic, complemented
4C4×#10625354C211yesmaximal, characteristic, complemented
5#15689347C211yesmaximal, characteristic, complemented
6#15689345C211yesmaximal, characteristic, complemented
7#15689343C211yesmaximal, characteristic, complemented
8#15689341C211yesmaximal, characteristic, complemented
9#15689339C211yesmaximal, characteristic, complemented
10#15689337C211yesmaximal, characteristic, complemented
11#15689335C211yesmaximal, characteristic, complemented
12#15689145C211yesmaximal, characteristic, complemented
13#15689130C211yesmaximal, characteristic, complemented
14#15689126C211yesmaximal, characteristic, complemented
15C47×#464C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19#13094056—24no—
20#13094051—24no—
21C2×#10625337C2211yescharacteristic, complemented
22C2×#10625325C2211yescharacteristic, complemented
23C2×#10625336C2211yescharacteristic
24C2×#10625336C2211yescharacteristic, complemented
25C2×D376C2211yescharacteristic
26C2×#10625334C2211yescharacteristic
27C2×#10625324C2211yescharacteristic
28C2×#10625324C2211yescharacteristic
29#13094013C2211yescharacteristic
30#13094012C2211yescharacteristic
31#13094011C2211yescharacteristic
32#13094010—21no—
33#13094010—21no—
34Q8×Dic47C2211yescharacteristic, complemented
35C4×D188—21no—
36C4×D188C2211yescharacteristic, complemented
37#13093986—21no—
38#13093986C2211yescharacteristic, complemented
39#13093982—21no—
40#13093982C2211yescharacteristic
41C22⋊C4×D47—21no—
42C22⋊C4×D47—21no—
43C42×D47—21no—
44C42×D47C2211yescharacteristic
45C4⋊(C47⋊C8)C2211yescharacteristic, complemented
46Dic47⋊C8C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093948C2211yescharacteristic, complemented
50#13093947C2211yescharacteristic, complemented
51#13093946C2211yescharacteristic
52#13093945C2211yescharacteristic
53#13093944C2211yescharacteristic
54C2×Q16×C47C2211yescharacteristic, complemented
55C2×SD16×C47C2211yescharacteristic
56#124×C47C2211yescharacteristic
57C4×Q8×C47C2211yescharacteristic, complemented
58C4⋊C8×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66#10625354—22no—
67#10625354D414yes—
68Q8×D47—22no—
69Q8×D47—22no—
70D4×D47—22no—
71D4×D47—22no—
72C2×D188—21no—
73C2×D188C2311yescharacteristic
74C2×D188C2311yescharacteristic
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47D411yescharacteristic
80C2×C4×D47D411yescharacteristic
81C2×C4×D47C2311yescharacteristic
82C2×Dic94—21no—
83C2×Dic94C2311yescharacteristic
84Q16×C47—22no—
85SD16×C47—22no—
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C4⋊C4×C47—21no—
89C4⋊C4×C47C2311yescharacteristic
90C22⋊C4×C47—21no—
91C22⋊C4×C47—21no—
92C42×C47—21no—
93C42×C47C2311yescharacteristic
94C22⋊Dic47—21no—
95C22⋊Dic47—21no—
96#10625337—22no—
97#10625336—22no—
98#10625336—22no—
99#10625334—22no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107C4⋊Dic47—21no—
108C4⋊Dic47C2311yescharacteristic
109C4×Dic47—21no—
110C4×Dic47—21no—
111C4×Dic47D411yescharacteristic
112C4×Dic47D411yescharacteristic
113C4×Dic47C2311yescharacteristic
114C2×C47⋊C8C2311yescharacteristic
115C2×C47⋊C8C2311yescharacteristic
116D376—22no—
117#10625325—22no—
118#10625324—22no—
119#10625324—22no—
120C23×C47—21no—
121C22×D47—21no—
122C22×D47—21no—
123C22×D47—42no—
124C22×D47—42no—
125C22×D47—42no—
126C22×D47C2×D411yescharacteristic
127Q8×C47—21no—
128Q8×C47—21no—
129Q8×C47—21no—
130Q8×C47C2×D412yes—
131D4×C47—21no—
132D4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2411yescharacteristic
139C22⋊D47—42no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47C2×D411yescharacteristic
143C2×Dic47C2×D411yescharacteristic
144C2×Dic47C2×D411yescharacteristic
145D188—24no—
146D188—21no—
147D188—21no—
148D188—21no—
149D188C2×D412yes—
150C4×D47—24no—
151C4×D47—41no—
152C4×D47—41no—
153C4×D47—42no—
154C4×D47—42no—
155C4×D47—42no—
156C4×D47C2×D412yes—
157C4×D47#4112yes—
158Dic94—21no—
159Dic94—21no—
160Dic94—42no—
161C8×C47—21no—
162C8×C47—21no—
163C47⋊C8—21no—
164C47⋊C8—21no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47C22×D411yescharacteristic
169C2×D47—21no—
170C2×D47—21no—
171C2×D47—22no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—84no—
178C2×D47#12112yes—
179C4×C47—22no—
180C4×C47—21no—
181C4×C47—21no—
182C4×C47—41no—
183C4×C47—41no—
184C4×C47C22×D411yescharacteristic
185C4×C47C2×#4111yescharacteristic
186Dic47—21no—
187Dic47—21no—
188Dic47—41no—
189Dic47—41no—
190Dic47#12112yes—
191#3040—471nomaximal, Sylow
192C2×C47—81no—
193C2×C47C2×#12111yescharacteristic
194C2×C47#57511yescharacteristic
195C2×C47#57511yescharacteristic
196D47—22no—
197D47—42no—
198D47—81no—
199C2×#137—471no—
200C2×AGL(1,ℤ/8)—471no—
201C2×#124—471no—
202C4×#41—471no—
203#464—471no—
204#464—471no—
205#464—471no—
206#464D4711yescharacteristic, complemented
207#463—471no—
208#463—471no—
209#463—471no—
210#463—471no—
211#423—471no—
212#419—471no—
213#418—471no—
214C47#304011yescharacteristic, complemented, Sylow
215C2×#41—471no—
216C22×Q8—471no—
217C22×D4—471no—
218#137—944no—
219AGL(1,ℤ/8)—944no—
220C2×Q16—471no—
221C2×Q16C2×D4711yescharacteristic, complemented
222C2×SD16—471no—
223C2×SD16—471no—
224C2×SD16—471no—
225C2×SD16C2×D4711yescharacteristic
226C2×D8—471no—
227C2×D8—471no—
228C2×M16—471no—
229C2×M16—471no—
230#124—471no—
231#124—471no—
232#124—471no—
233#124—941no—
234#124—941no—
235#124C2×D4711yescharacteristic
236C4×Q8—471no—
237C4×Q8C2×D4711yescharacteristic, complemented
238C4×D4—471no—
239C4×D4—471no—
240C4×D4—941no—
241C4×D4—941no—
242#117—471no—
243#117—941no—
244C2×C22⋊C4—941no—
245C2×C22⋊C4—941no—
246C2×C42—471no—
247C2×C42—941no—
248C4⋊C8—471no—
249C4⋊C8—471no—
250C4⋊C8—471no—
251C4⋊C8C2×D4711yescharacteristic, complemented
252#103—471no—
253#103—471no—
254#103—471no—
255#103C2×D4711yescharacteristic, complemented
256#102—471no—
257#102—471no—
258#102—471no—
259#102C2×D4711yescharacteristic
260C24—941no—
261#41—474no—
262#41—942no—
263C2×Q8—471no—
264C2×Q8—941no—
265C2×Q8—942no—
266C2×Q8—942no—
267C2×Q8C22×D4711yescharacteristic
268C2×Q8C22×D4711yescharacteristic
269C2×D4—471no—
270C2×D4—471no—
271C2×D4—941no—
272C2×D4—942no—
273C2×D4—942no—
274C2×D4—941no—
275C2×D4C22×D4711yescharacteristic
276C22×C4—471no—
277C22×C4—471no—
278C22×C4—471no—
279C22×C4—941no—
280C22×C4—941no—
281C22×C4—941no—
282C22×C4—941no—
283Q16—22no—
284Q16—942no—
285SD16—22no—
286SD16—942no—
287SD16—942no—
288SD16—942no—
289D8—942no—
290D8—942no—
291M16—942no—
292M16—942no—
293C2×C8—471no—
294C2×C8—471no—
295C2×C8C22×D4711yescharacteristic
296C2×C8C22×D4711yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—471no—
299C4⋊C4—941no—
300C4⋊C4C22×D4711yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C22⋊C4—941no—
307C22⋊C4—941no—
308C22⋊C4—941no—
309C22⋊C4—941no—
310C22⋊C4—941no—
311C22⋊C4—941no—
312C42—21no—
313C42—471no—
314C42—471no—
315C42—471no—
316C42—941no—
317C42—941no—
318C42C22×D4711yescharacteristic
319C23—21no—
320C23—471no—
321C23—941no—
322C23—941no—
323C23—1882no—
324C23—1882no—
325C23—1882no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—941no—
330Q8—941no—
331Q8—1882no—
332Q8D4×D4712yes—
333D4—21no—
334D4—21no—
335D4—472no—
336D4—944no—
337D4—941no—
338D4—941no—
339D4—941no—
340D4—1882no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—471no—
345C2×C4—472no—
346C2×C4—472no—
347C2×C4—471no—
348C2×C4—471no—
349C2×C4—944no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—1881no—
353C2×C4—1881no—
354C2×C4—1882no—
355C2×C4—1882no—
356C2×C4—1882no—
357C2×C4D4×D4711yescharacteristic
358C2×C4D4×D4711yescharacteristic
359C2×C4C23×D4711yescharacteristic
360C8—21no—
361C8—21no—
362C8—941no—
363C8—941no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—472no—
368C22—941no—
369C22—941no—
370C22—942no—
371C22—3764no—
372C22—1881no—
373C22—1881no—
374C22—1881no—
375C22—1881no—
376C22—1881no—
377C22C2×D4×D4711yescharacteristic
378C4—22no—
379C4—21no—
380C4—21no—
381C4—41no—
382C4—41no—
383C4—472no—
384C4—941no—
385C4—941no—
386C4—1881no—
387C4—1881no—
388C4C2×D4×D4711yescharacteristic
389C4#41×D4711yescharacteristic
390C2—81no—
391C2—942no—
392C2—3761no—
393C2—1882no—
394C2#121×D4711yescharacteristic
395C2#1568992011yescharacteristic
396C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#464C2
socleC22×C47C22×D4
hypercenter#464D47
hypocenterC47#3040
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#13094056C2semidirect
3. #124×D47C2semidirect
4. C4×#10625354C2semidirect
5. #15689347C2semidirect
6. #15689345C2semidirect
7. #15689343C2semidirect
8. #15689341C2semidirect
9. #15689339C2semidirect
10. #15689337C2semidirect
11. #15689335C2semidirect
12. #15689145C2semidirect
13. #15689130C2semidirect
14. #15689126C2semidirect
15. C47×#464C2semidirect
21. C2×#10625337C22semidirect
22. C2×#10625325C22semidirect
24. C2×#10625336C22semidirect
34. Q8×Dic47C22semidirect
36. C4×D188C22semidirect
38. #13093986C22semidirect
45. C4⋊(C47⋊C8)C22semidirect
46. Dic47⋊C8C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093949C22semidirect
49. #13093948C22semidirect
50. #13093947C22semidirect
54. C2×Q16×C47C22semidirect
57. C4×Q8×C47C22semidirect
58. C4⋊C8×C47C22semidirect
59. #103×C47C22semidirect
206. #464D47semidirect
214. C47#3040semidirect
221. C2×Q16C2×D47semidirect
237. C4×Q8C2×D47semidirect
251. C4⋊C8C2×D47semidirect
255. #103C2×D47semidirect