Finite Group Databasebeta

← #20253849

Subgroups — #20253849

Order 6016.

572 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094056C211yesmaximal, characteristic, complemented
2C2×#13094053C211yesmaximal, characteristic, complemented
3C2×#13094051C211yesmaximal, characteristic, complemented
4C2×#13094048C211yesmaximal, characteristic, complemented
5#15689672C211yesmaximal, characteristic, complemented
6#124×D47C211yesmaximal, characteristic, complemented
7#15689516C211yesmaximal, characteristic, complemented
8#15689514C211yesmaximal, characteristic, complemented
9#15689511C211yesmaximal, characteristic, complemented
10#15689509C211yesmaximal, characteristic, complemented
11#15689507C211yesmaximal, characteristic, complemented
12#15689505C211yesmaximal, characteristic, complemented
13#15689505C211yesmaximal, characteristic, complemented
14C4×#10625324C211yesmaximal, characteristic, complemented
15C47×#495C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625352C2211yescharacteristic
18C2×Q8×D47C2211yescharacteristic
19C2×D4×D47C2211yescharacteristic
20#13094056—24no—
21#13094053—24no—
22#13094051—24no—
23#13094048—24no—
24C2×Dic188C2211yescharacteristic, complemented
25C2×#10625337C2211yescharacteristic, complemented
26C2×#10625337C2211yescharacteristic, complemented
27C2×#10625325C2211yescharacteristic
28C2×#10625325C2211yescharacteristic, complemented
29C2×#10625335C2211yescharacteristic
30C2×#10625335C2211yescharacteristic, complemented
31C2×#10625336C2211yescharacteristic
32C2×#10625336C2211yescharacteristic, complemented
33C2×D376C2211yescharacteristic
34C2×#10625334C2211yescharacteristic
35C2×#10625334C2211yescharacteristic
36C2×#10625324C2211yescharacteristic
37C2×#10625324C2211yescharacteristic
38#13094022C2211yescharacteristic, complemented
39#13094020C2211yescharacteristic, complemented
40#13094013C2211yescharacteristic
41#13094012C2211yescharacteristic
42#13094012C2211yescharacteristic, complemented
43#13094011C2211yescharacteristic
44#13094010—22no—
45#13093997—22no—
46(C22⋊D47)⋊C4—22no—
47C22⋊C4×D47—22no—
48C42×D47C2211yescharacteristic
49#13093934C2211yescharacteristic, complemented
50#13093934C2211yescharacteristic, complemented
51C4×C47⋊C8C2211yescharacteristic, complemented
52C2×Q16×C47C2211yescharacteristic, complemented
53C2×SD16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic, complemented
55C2×D8×C47C2211yescharacteristic
56#124×C47C2211yescharacteristic
57#124×C47C2211yescharacteristic, complemented
58C4×C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—22no—
66C2×C22⋊D47—21no—
67C22×Dic47—21no—
68#10625354—22no—
69#10625354—22no—
70Q8×D47—22no—
71Q8×D47—22no—
72#10625352—22no—
73#10625352—22no—
74D4×D47—22no—
75D4×D47—22no—
76C2×D188—21no—
77C2×D188C2311yescharacteristic
78C2×D188C2311yescharacteristic
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×C4×D47D412yes—
82C2×C4×D47C2311yescharacteristic
83C2×Dic94—21no—
84C2×Dic94C2311yescharacteristic
85C2×Dic94C2311yescharacteristic
86Q16×C47—22no—
87SD16×C47—22no—
88SD16×C47—22no—
89D8×C47—22no—
90C2×C8×C47C2311yescharacteristic
91C2×C8×C47C2311yescharacteristic
92C22⋊C4×C47—22no—
93C22⋊C4×C47—22no—
94C42×C47C2311yescharacteristic
95C22⋊Dic47—22no—
96#10625337—22no—
97#10625337—22no—
98#10625336—22no—
99#10625336—22no—
100#10625335—22no—
101#10625335—22no—
102#10625334—22no—
103#10625334—22no—
104(C2×D47)⋊C4—22no—
105(C2×D47)⋊C4—22no—
106(C2×D47)⋊C4—22no—
107Dic47⋊C4—22no—
108C4×Dic47D412yes—
109C4×Dic47C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112Dic188—22no—
113D376—22no—
114#10625325—22no—
115#10625325—22no—
116#10625324D414yescomplemented
117#10625324D414yescomplemented
118C23×C47—21no—
119C23×C47—21no—
120C22×D47—21no—
121C22×D47—21no—
122C22×D47—44no—
123C22×D47—42no—
124C22×D47C2×D411yescharacteristic
125Q8×C47—21no—
126Q8×C47—21no—
127Q8×C47—21no—
128Q8×C47—21no—
129D4×C47—21no—
130D4×C47—21no—
131D4×C47—21no—
132D4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47C2×D412yes—
136C2×C4×C47C2411yescharacteristic
137C22⋊D47—44no—
138C22⋊D47—42no—
139C22⋊D47—42no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—42no—
143C2×Dic47C2×D412yes—
144C2×Dic47C2×D411yescharacteristic
145D188—21no—
146D188—21no—
147D188—21no—
148D188—21no—
149D188—42no—
150C4×D47—42no—
151C4×D47—42no—
152C4×D47—42no—
153C4×D47C2×D412yes—
154C4×D47C2×D412yes—
155Dic94—21no—
156Dic94—21no—
157Dic94—21no—
158Dic94—21no—
159Dic94—42no—
160C8×C47C2×D412yes—
161C8×C47C2×D412yes—
162C47⋊C8C2×D412yes—
163C47⋊C8C2×D412yes—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—42no—
167C22×C47—42no—
168C22×C47C22×D411yescharacteristic
169C2×D47—22no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—42no—
173C2×D47—42no—
174C2×D47—84no—
175C2×D47#12712yes—
176C4×C47—22no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47C22×D411yescharacteristic
180C4×C47C22×D411yescharacteristic
181Dic47—22no—
182Dic47—41no—
183Dic47—41no—
184Dic47#12712yes—
185#3153—471nomaximal, Sylow
186C2×C47—81no—
187C2×C47—81no—
188C2×C47C2×#12711yescharacteristic
189C2×C47#57512yes—
190D47—22no—
191D47—81no—
192D47—81no—
193C2×#137—471no—
194C2×#137—471no—
195C2×AGL(1,ℤ/8)—471no—
196C2×AGL(1,ℤ/8)—471no—
197#532—471no—
198C2×#124—471no—
199#497—471no—
200#497—471no—
201#496—471no—
202#496—471no—
203#495—471no—
204#495—471no—
205#495—471no—
206#495D4711yescharacteristic, complemented
207C4×M16—471no—
208C47#315311yescharacteristic, complemented, Sylow
209C2×#41—471no—
210C2×#41—471no—
211C22×Q8—471no—
212C22×D4—471no—
213#137—944no—
214#137—944no—
215AGL(1,ℤ/8)—944no—
216AGL(1,ℤ/8)—944no—
217C2×Q16—471no—
218C2×Q16—471no—
219C2×Q16—471no—
220C2×Q16C2×D4711yescharacteristic, complemented
221C2×SD16—471no—
222C2×SD16—471no—
223C2×SD16—471no—
224C2×SD16—471no—
225C2×SD16—471no—
226C2×SD16—471no—
227C2×SD16C2×D4711yescharacteristic
228C2×SD16C2×D4711yescharacteristic, complemented
229C2×D8—471no—
230C2×D8—471no—
231C2×D8—471no—
232C2×D8C2×D4711yescharacteristic
233C2×M16—471no—
234C2×M16—471no—
235C4⋊Q8—471no—
236#127—471no—
237#124—471no—
238#124—471no—
239#124—471no—
240#124—471no—
241#124—942no—
242#124C2×D4711yescharacteristic
243#124C2×D4711yescharacteristic, complemented
244#121—942no—
245C4×D4—942no—
246C2×C22⋊C4—942no—
247C2×C42—471no—
248#97—471no—
249#97—471no—
250C4×C8—471no—
251C4×C8C2×D4711yescharacteristic, complemented
252C24—941no—
253#41—942no—
254#41—942no—
255#41—942no—
256#41—942no—
257C2×Q8—471no—
258C2×Q8—471no—
259C2×Q8—941no—
260C2×Q8—942no—
261C2×Q8—942no—
262C2×Q8C22×D4711yescharacteristic
263C2×Q8C22×D4711yescharacteristic
264C2×D4—471no—
265C2×D4—471no—
266C2×D4—941no—
267C2×D4—942no—
268C2×D4—942no—
269C2×D4—942no—
270C2×D4—941no—
271C2×D4—941no—
272C2×D4C22×D4711yescharacteristic
273C2×D4C22×D4711yescharacteristic
274C22×C4—471no—
275C22×C4—472no—
276C22×C4—941no—
277C22×C4—941no—
278C22×C4—941no—
279Q16—22no—
280Q16—942no—
281Q16—942no—
282Q16—942no—
283SD16—22no—
284SD16—22no—
285SD16—942no—
286SD16—942no—
287SD16—942no—
288SD16—942no—
289SD16—942no—
290SD16—942no—
291D8—22no—
292D8—942no—
293D8—942no—
294D8—942no—
295M16—474no—
296M16—474no—
297C2×C8—471no—
298C2×C8—471no—
299C2×C8C22×D4711yescharacteristic
300C2×C8C22×D4711yescharacteristic
301C4⋊C4—942no—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—942no—
305C22⋊C4—942no—
306C22⋊C4—942no—
307C22⋊C4—942no—
308C42—472no—
309C42—471no—
310C42C22×D4711yescharacteristic
311C23—21no—
312C23—21no—
313C23—471no—
314C23—941no—
315C23—941no—
316C23—1882no—
317C23—1884no—
318Q8—21no—
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—941no—
323Q8—941no—
324Q8—941no—
325Q8—941no—
326Q8—1882no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—941no—
332D4—941no—
333D4—941no—
334D4—941no—
335D4—1882no—
336D4—1882no—
337D4—1884no—
338D4—1882no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—471no—
342C2×C4—472no—
343C2×C4—472no—
344C2×C4—472no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—1882no—
348C2×C4—1882no—
349C2×C4—1882no—
350C2×C4—1882no—
351C2×C4D4×D4712yes—
352C2×C4C23×D4711yescharacteristic
353C8—472no—
354C8—472no—
355C8D4×D4712yes—
356C8D4×D4712yes—
357C22—41no—
358C22—41no—
359C22—42no—
360C22—42no—
361C22—472no—
362C22—942no—
363C22—3764no—
364C22—1881no—
365C22—1881no—
366C22—1882no—
367C22—1882no—
368C22C2×D4×D4711yescharacteristic
369C4—22no—
370C4—41no—
371C4—41no—
372C4—472no—
373C4—942no—
374C4—1881no—
375C4—1881no—
376C4C2×D4×D4711yescharacteristic
377C4C2×D4×D4711yescharacteristic
378C2—81no—
379C2—81no—
380C2—942no—
381C2—3761no—
382C2—3761no—
383C2#127×D4711yescharacteristic
384C2#1568992012yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#495C2
socleC22×C47C22×D4
hypercenter#495D47
hypocenterC47#3153
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#13094056C2semidirect
2. C2×#13094053C2semidirect
3. C2×#13094051C2semidirect
4. C2×#13094048C2semidirect
5. #15689672C2semidirect
6. #124×D47C2semidirect
7. #15689516C2semidirect
8. #15689514C2semidirect
9. #15689511C2semidirect
10. #15689509C2semidirect
11. #15689507C2semidirect
12. #15689505C2semidirect
13. #15689505C2semidirect
14. C4×#10625324C2semidirect
15. C47×#495C2semidirect
24. C2×Dic188C22semidirect
25. C2×#10625337C22semidirect
26. C2×#10625337C22semidirect
28. C2×#10625325C22semidirect
30. C2×#10625335C22semidirect
32. C2×#10625336C22semidirect
38. #13094022C22semidirect
39. #13094020C22semidirect
42. #13094012C22semidirect
49. #13093934C22semidirect
50. #13093934C22semidirect
51. C4×C47⋊C8C22semidirect
52. C2×Q16×C47C22semidirect
54. C2×SD16×C47C22semidirect
57. #124×C47C22semidirect
58. C4×C8×C47C22semidirect
116. #10625324D4semidirect
117. #10625324D4semidirect
206. #495D47semidirect
208. C47#3153semidirect
220. C2×Q16C2×D47semidirect
228. C2×SD16C2×D47semidirect
243. #124C2×D47semidirect
251. C4×C8C2×D47semidirect