Finite Group Databasebeta

← #20253857

Subgroups — #20253857

Order 6016.

564 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×#13094053C211yesmaximal, characteristic, complemented
2C2×#13094051C211yesmaximal, characteristic, complemented
3C2×#13094045C211yesmaximal, characteristic, complemented
4C2×SD16×D47C211yesmaximal, characteristic, complemented
5#15689698C211yesmaximal, characteristic, complemented
6#15689686C211yesmaximal, characteristic, complemented
7#15689515C211yesmaximal, characteristic, complemented
8#15689514C211yesmaximal, characteristic, complemented
9#15689510C211yesmaximal, characteristic, complemented
10#15689509C211yesmaximal, characteristic, complemented
11#15689507C211yesmaximal, characteristic, complemented
12#15689504C211yesmaximal, characteristic, complemented
13#15689494C211yesmaximal, characteristic, complemented
14#15689077C211yesmaximal, characteristic, complemented
15C47×#492C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625352C2211yescharacteristic
18C2×Q8×D47C2211yescharacteristic
19C2×D4×D47C2211yescharacteristic
20#13094053—24no—
21#13094051—24no—
22#13094045—24no—
23C2×Dic188C2211yescharacteristic, complemented
24C2×#10625337C2211yescharacteristic, complemented
25C2×#10625337C2211yescharacteristic, complemented
26C2×#10625325C2211yescharacteristic
27C2×#10625325C2211yescharacteristic, complemented
28C2×#10625335C2211yescharacteristic
29C2×#10625335C2211yescharacteristic, complemented
30C2×#10625336C2211yescharacteristic
31C2×#10625336C2211yescharacteristic
32SD16×D47—24no—
33C2×D376C2211yescharacteristic
34C2×#10625334C2211yescharacteristic
35C2×#10625334C2211yescharacteristic, complemented
36C2×#10625324C2211yescharacteristic
37C2×C8×D47C2211yescharacteristic
38#13094022C2211yescharacteristic, complemented
39#13094020C2211yescharacteristic
40#13094013C2211yescharacteristic, complemented
41#13094012C2211yescharacteristic
42#13094012C2211yescharacteristic, complemented
43#13094011C2211yescharacteristic
44#13094009—22no—
45#13094002—22no—
46#13093996—22no—
47#13093992—22no—
48#13093981C2211yescharacteristic
49#13093935C2211yescharacteristic, complemented
50#13093934C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C2×SD16×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic, complemented
55C2×SD16×C47C2211yescharacteristic, complemented
56C4⋊Q8×C47C2211yescharacteristic, complemented
57#127×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—22no—
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—22no—
68C22×Dic47—21no—
69#10625354—22no—
70#10625354—22no—
71Q8×D47—22no—
72Q8×D47—22no—
73#10625352—22no—
74#10625352—22no—
75D4×D47—22no—
76D4×D47—22no—
77C2×D188—21no—
78C2×D188C2311yescharacteristic
79C2×D188C2311yescharacteristic
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47C2311yescharacteristic
83C2×Dic94—21no—
84C2×Dic94C2311yescharacteristic
85C2×Dic94C2311yescharacteristic
86SD16×C47—22no—
87SD16×C47—22no—
88SD16×C47—22no—
89SD16×C47—22no—
90C2×C8×C47C2311yescharacteristic
91C2×C8×C47C2311yescharacteristic
92C4⋊C4×C47—22no—
93C42×C47C2311yescharacteristic
94C22⋊Dic47—22no—
95#10625337—22no—
96#10625337—22no—
97#10625336—22no—
98#10625336—22no—
99#10625335—22no—
100#10625335—22no—
101#10625334—22no—
102#10625334—22no—
103(C2×D47)⋊C4—22no—
104(C2×D47)⋊C4—22no—
105(C2×D47)⋊C4—22no—
106(C2×D47)⋊C4D412yes—
107Dic47⋊C4—22no—
108Dic47⋊C4D412yes—
109C4×Dic47C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112Dic188—22no—
113D376—22no—
114#10625325—22no—
115#10625325—22no—
116#10625324D414yescomplemented
117C8×D47D414yescomplemented
118C23×C47—21no—
119C23×C47—21no—
120C22×D47—21no—
121C22×D47—21no—
122C22×D47—42no—
123C22×D47—82no—
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—
133D4×C47—82no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47C2×D412yes—
137C2×C4×C47C2411yescharacteristic
138C22⋊D47—42no—
139C22⋊D47—42no—
140C22⋊D47—82no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—42no—
144C2×Dic47C2×D412yes—
145C2×Dic47C2×D411yescharacteristic
146D188—21no—
147D188—21no—
148D188—21no—
149D188—21no—
150D188—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#3154—471nomaximal, Sylow
186C2×C47—81no—
187C2×C47—81no—
188C2×C47C2×#12711yescharacteristic
189C2×C47#57712yes—
190D47—22no—
191D47—81no—
192D47—81no—
193C2×#137—471no—
194C2×AGL(1,ℤ/8)—471no—
195C2×#135—471no—
196C22×SD16—471no—
197#536—471no—
198#535—471no—
199#497—471no—
200#497—471no—
201#496—471no—
202#496—471no—
203#495—471no—
204#495—471no—
205#492—471no—
206#492D4711yescharacteristic, complemented
207#405—471no—
208C47#315411yescharacteristic, complemented, Sylow
209C2×#41—471no—
210C2×#41—471no—
211C22×Q8—471no—
212C22×D4—471no—
213#137—944no—
214AGL(1,ℤ/8)—944no—
215#135—944no—
216C2×Q16—471no—
217C2×Q16—471no—
218C2×Q16—471no—
219C2×SD16—471no—
220C2×SD16—471no—
221C2×SD16—471no—
222C2×SD16—471no—
223C2×SD16—471no—
224C2×SD16—471no—
225C2×SD16—944no—
226C2×SD16C2×D4711yescharacteristic
227C2×SD16C2×D4711yescharacteristic
228C2×SD16C2×D4711yescharacteristic, complemented
229C2×SD16C2×D4711yescharacteristic, complemented
230C2×D8—471no—
231C2×D8—471no—
232C2×D8—471no—
233C2×M16—471no—
234C22×C8—471no—
235C4⋊Q8—471no—
236C4⋊Q8C2×D4711yescharacteristic, complemented
237#127—471no—
238#127C2×D4711yescharacteristic
239#124—471no—
240#124—471no—
241#124—471no—
242#124—471no—
243#123—942no—
244C22⋊Q8—942no—
245#121—942no—
246#120—942no—
247#117—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—22no—
265C2×D4—471no—
266C2×D4—471no—
267C2×D4—941no—
268C2×D4—942no—
269C2×D4—942no—
270C2×D4—942no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4C22×D4711yescharacteristic
274C2×D4C22×D4711yescharacteristic
275C22×C4—471no—
276C22×C4—941no—
277C22×C4—941no—
278C22×C4—941no—
279Q16—942no—
280Q16—942no—
281Q16—942no—
282SD16—22no—
283SD16—22no—
284SD16—22no—
285SD16—22no—
286SD16—942no—
287SD16—942no—
288SD16—942no—
289SD16—942no—
290SD16—942no—
291SD16—942no—
292D8—942no—
293D8—942no—
294D8—942no—
295M16—474no—
296C2×C8—471no—
297C2×C8—471no—
298C2×C8—474no—
299C2×C8C22×D4711yescharacteristic
300C2×C8C22×D4711yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—472no—
303C4⋊C4—942no—
304C22⋊C4—472no—
305C22⋊C4—942no—
306C22⋊C4—942no—
307C22⋊C4—942no—
308C22⋊C4—942no—
309C42—471no—
310C42C22×D4711yescharacteristic
311C23—21no—
312C23—21no—
313C23—471no—
314C23—941no—
315C23—941no—
316C23—3762no—
317C23—1882no—
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—82no—
332D4—941no—
333D4—941no—
334D4—941no—
335D4—941no—
336D4—3762no—
337D4—1882no—
338D4—1882no—
339D4—1882no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—471no—
343C2×C4—472no—
344C2×C4—472no—
345C2×C4—472no—
346C2×C4—941no—
347C2×C4—941no—
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#1568992912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#492C2
socleC22×C47C22×D4
hypercenter#492D47
hypocenterC47#3154
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×#13094053C2semidirect
2. C2×#13094051C2semidirect
3. C2×#13094045C2semidirect
4. C2×SD16×D47C2semidirect
5. #15689698C2semidirect
6. #15689686C2semidirect
7. #15689515C2semidirect
8. #15689514C2semidirect
9. #15689510C2semidirect
10. #15689509C2semidirect
11. #15689507C2semidirect
12. #15689504C2semidirect
13. #15689494C2semidirect
14. #15689077C2semidirect
15. C47×#492C2semidirect
23. C2×Dic188C22semidirect
24. C2×#10625337C22semidirect
25. C2×#10625337C22semidirect
27. C2×#10625325C22semidirect
29. C2×#10625335C22semidirect
35. C2×#10625334C22semidirect
38. #13094022C22semidirect
40. #13094013C22semidirect
42. #13094012C22semidirect
49. #13093935C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
54. C2×SD16×C47C22semidirect
55. C2×SD16×C47C22semidirect
56. C4⋊Q8×C47C22semidirect
58. C4×C8×C47C22semidirect
116. #10625324D4semidirect
117. C8×D47D4semidirect
206. #492D47semidirect
208. C47#3154semidirect
228. C2×SD16C2×D47semidirect
229. C2×SD16C2×D47semidirect
236. C4⋊Q8C2×D47semidirect
251. C4×C8C2×D47semidirect