Finite Group Databasebeta

← #20254902

Subgroups — #20254902

Order 6016.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094053C211yesmaximal, characteristic, complemented
2C22×#10625335C211yesmaximal, characteristic, complemented
3#15689786C211yesmaximal, characteristic, complemented
4#15689767C211yesmaximal, characteristic
5#15689514C211yesmaximal, characteristic, complemented
6#15689368C211yesmaximal, characteristic, complemented
7#15689362C211yesmaximal, characteristic, complemented
8#15689344C211yesmaximal, characteristic, complemented
9#15689326C211yesmaximal, characteristic, complemented
10#15689286C211yesmaximal, characteristic, complemented
11#15689281C211yesmaximal, characteristic, complemented
12#15689260C211yesmaximal, characteristic, complemented
13#15689220C211yesmaximal, characteristic, complemented
14#15689191C211yesmaximal, characteristic, complemented
15C47×#450C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C2×Q8×D47C2211yescharacteristic, complemented
19#13094053—24no—
20C2×Dic188C2211yescharacteristic, complemented
21C2×Dic188C2211yescharacteristic, complemented
22C2×#10625337C2211yescharacteristic, complemented
23C2×#10625335—24no—
24C2×#10625335C2211yescharacteristic
25C2×#10625335C2211yescharacteristic
26C2×#10625335C2211yescharacteristic
27C2×#10625335C2211yescharacteristic
28C2×#10625324C2211yescharacteristic, complemented
29C22×C47⋊C8C2211yescharacteristic
30#13094023—21no—
31#13094022C2211yescharacteristic, complemented
32#13094011C2211yescharacteristic
33#13094005—21no—
34#13094004C2211yescharacteristic, complemented
35#13094003C2211yescharacteristic
36#13094002—21no—
37#13094001—21no—
38#13093996—21no—
39#13093995C2211yescharacteristic
40#13093993—21no—
41#13093989C2211yescharacteristic, complemented
42D4×Dic47C2211yescharacteristic
43C4×C22⋊D47C2211yescharacteristic
44(C22⋊D47)⋊C4—21no—
45C2×C22⋊Dic47—21no—
46#13093957C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093949C2211yescharacteristic, complemented
50#13093948C2211yescharacteristic, complemented
51#13093947C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53#13093934C2211yescharacteristic, complemented
54C22×D4×C47C2211yescharacteristic
55C2×SD16×C47C2211yescharacteristic
56C2×SD16×C47C2211yescharacteristic
57C22⋊Q8×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59#102×C47C2211yescharacteristic
60C22⋊C8×C47C2211yescharacteristic
61C24×C47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—22no—
64C2×D4×C47—21no—
65C2×D4×C47—41no—
66C2×D4×C47C2311yescharacteristic
67C2×D4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47D411yescharacteristic
72C22×Dic47—21no—
73C22×Dic47—21no—
74C22×Dic47—21no—
75Q8×D47—22no—
76Q8×D47—41no—
77#10625352—22no—
78#10625352—41no—
79C2×C4×D47—21no—
80C2×C4×D47C2311yescharacteristic
81C2×Dic94—22no—
82C2×Dic94—21no—
83C2×Dic94—21no—
84C2×Dic94—41no—
85C2×Dic94C2311yescharacteristic
86C2×Dic94C2311yescharacteristic
87C2×Dic94C2311yescharacteristic
88SD16×C47—22no—
89SD16×C47—41no—
90C2×C8×C47C2311yescharacteristic
91C2×C8×C47C2311yescharacteristic
92C4⋊C4×C47—21no—
93C4⋊C4×C47C2311yescharacteristic
94C22⋊C4×C47—21no—
95C22⋊Dic47—21no—
96C22⋊Dic47—21no—
97C22⋊Dic47—21no—
98C22⋊Dic47—21no—
99C22⋊Dic47—21no—
100C22⋊Dic47D411yescharacteristic
101#10625337—22no—
102#10625335—22no—
103#10625335—22no—
104#10625335—22no—
105#10625335D414yescomplemented
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4D411yescharacteristic
108C4⋊Dic47—21no—
109C4⋊Dic47C2311yescharacteristic
110Dic47⋊C4—21no—
111Dic47⋊C4—21no—
112Dic47⋊C4—21no—
113Dic47⋊C4—21no—
114Dic47⋊C4D411yescharacteristic
115C4×Dic47—21no—
116C4×Dic47C2311yescharacteristic
117C2×C47⋊C8—22no—
118C2×C47⋊C8C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120Dic188—22no—
121Dic188—41no—
122#10625324—22no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—42no—
126C23×C47—42no—
127C23×C47—81no—
128C23×C47C2×D411yescharacteristic
129C22×D47C2×D411yescharacteristic
130Q8×C47—21no—
131Q8×C47—21no—
132D4×C47—21no—
133D4×C47—21no—
134D4×C47—21no—
135D4×C47—42no—
136D4×C47C2×D412yes—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47C2×D411yescharacteristic
142C2×C4×C47C2411yescharacteristic
143C22⋊D47—22no—
144C22⋊D47—42no—
145C22⋊D47—81no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—42no—
151C2×Dic47—42no—
152C2×Dic47—81no—
153C2×Dic47C2×D411yescharacteristic
154C2×Dic47C2×D411yescharacteristic
155C2×Dic47C2×D411yescharacteristic
156C4×D47—21no—
157C4×D47—21no—
158C4×D47—42no—
159Dic94—21no—
160Dic94—21no—
161Dic94—21no—
162Dic94—21no—
163Dic94—21no—
164Dic94—42no—
165Dic94—42no—
166Dic94C2×D412yes—
167C8×C47—21no—
168C8×C47—21no—
169C47⋊C8—21no—
170C47⋊C8C2×D412yes—
171C22×C47—21no—
172C22×C47—21no—
173C22×C47—22no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47—84no—
180C22×C47#13712yescomplemented
181C22×C47C22×D411yescharacteristic
182C2×D47—21no—
183C2×D47—21no—
184C2×D47—21no—
185C4×C47—21no—
186C4×C47—41no—
187C4×C47—41no—
188C4×C47C22×D411yescharacteristic
189C4×C47H(5,𝔽2)11yescharacteristic
190Dic47—22no—
191Dic47—21no—
192Dic47—21no—
193Dic47—21no—
194Dic47—41no—
195Dic47—41no—
196Dic47—41no—
197#3266—471nomaximal, Sylow
198C2×C47—22no—
199C2×C47—42no—
200C2×C47—81no—
201C2×C47D4211yescharacteristic
202C2×C47C2×#13711yescharacteristic
203C2×C47#57711yescharacteristic
204D47—41no—
205C2×#137—471no—
206C22×SD16—471no—
207D4×Q8—471no—
208#546—471no—
209#497—471no—
210#468—471no—
211#467—471no—
212#464—471no—
213#461—471no—
214#452—471no—
215#451—471no—
216#450D4711yescharacteristic, complemented
217#448—471no—
218#440—471no—
219#435—471no—
220C47#326611yescharacteristic, complemented, Sylow
221C2×#41—471no—
222C22×Q8—471no—
223C22×Q8—471no—
224C22×D4C2×D4711yescharacteristic
225#137—944no—
226C2×Q16—471no—
227C2×Q16—471no—
228C2×Q16—471no—
229C2×SD16—471no—
230C2×SD16—471no—
231C2×SD16—471no—
232C2×SD16—471no—
233C2×SD16—944no—
234C2×SD16C2×D4711yescharacteristic
235C2×SD16C2×D4711yescharacteristic
236C2×M16—471no—
237C22×C8—471no—
238C4⋊Q8—471no—
239C4⋊Q8—941no—
240#124—471no—
241#123—941no—
242C22⋊Q8—471no—
243C22⋊Q8—471no—
244C22⋊Q8—941no—
245C22⋊Q8—941no—
246C22⋊Q8C2×D4711yescharacteristic
247#121—471no—
248#121—941no—
249#120—941no—
250C4×Q8—471no—
251C4×D4—471no—
252C4×D4—471no—
253C4×D4—941no—
254C2×C22⋊C4—941no—
255#107—471no—
256C4⋊C8—471no—
257#103—471no—
258#103—471no—
259#103—471no—
260#103—471no—
261#102C2×D4711yescharacteristic
262#102C2×D4711yescharacteristic
263C22⋊C8—471no—
264C22⋊C8C2×D4711yescharacteristic
265#97—471no—
266C24—21no—
267#41—942no—
268#41—1881no—
269C2×Q8—471no—
270C2×Q8—471no—
271C2×Q8—471no—
272C2×Q8—941no—
273C2×Q8—942no—
274C2×Q8—941no—
275C2×Q8—942no—
276C2×Q8—1881no—
277C2×Q8—1881no—
278C2×Q8C22×D4711yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—471no—
283C2×D4—941no—
284C2×D4—941no—
285C2×D4C22×D4711yescharacteristic
286C2×D4C22×D4711yescharacteristic
287C22×C4—471no—
288C22×C4—941no—
289C22×C4—941no—
290C22×C4—941no—
291C22×C4—941no—
292C22×C4C22×D4711yescharacteristic
293Q16—942no—
294Q16—942no—
295Q16—1881no—
296SD16—22no—
297SD16—41no—
298SD16—474no—
299SD16—942no—
300SD16—942no—
301SD16—942no—
302M16—942no—
303C2×C8—471no—
304C2×C8—471no—
305C2×C8—942no—
306C2×C8C22×D4711yescharacteristic
307C2×C8C22×D4711yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—471no—
310C4⋊C4—471no—
311C4⋊C4—941no—
312C4⋊C4—941no—
313C4⋊C4—941no—
314C4⋊C4—941no—
315C4⋊C4—941no—
316C4⋊C4C22×D4711yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—471no—
319C22⋊C4—471no—
320C22⋊C4—941no—
321C22⋊C4—941no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C42—471no—
327C42—941no—
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23—471no—
334C23D4×D4711yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—472no—
338Q8—941no—
339Q8—941no—
340Q8—941no—
341Q8—941no—
342Q8—941no—
343Q8—1882no—
344Q8—1882no—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—942no—
350D4—3761no—
351D4—1882no—
352D4D4×D4712yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—471no—
358C2×C4—471no—
359C2×C4—471no—
360C2×C4—941no—
361C2×C4—941no—
362C2×C4—941no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—941no—
366C2×C4—3761no—
367C2×C4—1882no—
368C2×C4—1882no—
369C2×C4—1882no—
370C2×C4D4×D4711yescharacteristic
371C2×C4C23×D4711yescharacteristic
372C8—21no—
373C8—21no—
374C8—472no—
375C8—941no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—84no—
385C22—941no—
386C22—941no—
387C22—941no—
388C22#1309405312yescomplemented
389C22C2×D4×D4711yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—941no—
394C4—942no—
395C4—941no—
396C4—941no—
397C4—1881no—
398C4—1881no—
399C4—1881no—
400C4C2×D4×D4711yescharacteristic
401C4#1309406911yescharacteristic
402C2—22no—
403C2—42no—
404C2—81no—
405C2—1881no—
406C2#1568975511yescharacteristic
407C2C2×#1309405311yescharacteristic
408C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3266
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#13094053C2semidirect
2. C22×#10625335C2semidirect
3. #15689786C2semidirect
5. #15689514C2semidirect
6. #15689368C2semidirect
7. #15689362C2semidirect
8. #15689344C2semidirect
9. #15689326C2semidirect
10. #15689286C2semidirect
11. #15689281C2semidirect
12. #15689260C2semidirect
13. #15689220C2semidirect
14. #15689191C2semidirect
15. C47×#450C2semidirect
18. C2×Q8×D47C22semidirect
20. C2×Dic188C22semidirect
21. C2×Dic188C22semidirect
22. C2×#10625337C22semidirect
28. C2×#10625324C22semidirect
31. #13094022C22semidirect
34. #13094004C22semidirect
41. #13093989C22semidirect
46. #13093957C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093949C22semidirect
49. #13093949C22semidirect
50. #13093948C22semidirect
51. #13093947C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. #13093934C22semidirect
105. #10625335D4semidirect
180. C22×C47#137semidirect
216. #450D47semidirect
220. C47#3266semidirect
388. C22#13094053semidirect