Finite Group Databasebeta

← #20257385

Subgroups — #20257385

Order 6016.

1122 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
1#15689849C211yesmaximal, characteristic, complemented
2#15689820C213yesmaximal, complemented
3#15689819C213yesmaximal, complemented
4#15689793C213yesmaximal, complemented
5#15689792C211yesmaximal, characteristic, complemented
6#15689792C211yesmaximal, characteristic, complemented
7#15689773C213yesmaximal, complemented
8#15689727C213yesmaximal, complemented
9#15689726C213yesmaximal, complemented
10#15689668C213yesmaximal, complemented
11#15689653C213yesmaximal, complemented
12#15689606C211yesmaximal, characteristic, complemented
13#15689605C211yesmaximal, characteristic, complemented
14#41×Dic47C211yesmaximal, characteristic, complemented
15C47×#550C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625352C2216yes—
18#13094023C2213yes—
19#13094020C2213yes—
20#13094020C2213yes—
21#13094019C2213yes—
22#13094017C2213yes—
23#13094016C2213yes—
24#13094015C2213yes—
25#13094014C2211yescharacteristic
26#13094010C2213yes—
27#13094008C2213yes—
28#13094006C2216yes—
29#13094005C2216yes—
30#13094005C2213yes—
31#13094001C2213yes—
32#13093998C2213yes—
33#13093998C2213yes—
34#13093996C2213yes—
35#13093996C2216yes—
36#13093996C2216yes—
37#13093995C2213yes—
38#13093995C2213yes—
39#13093995C2216yes—
40Q8×Dic47C2211yescharacteristic
41Q8×Dic47C2211yescharacteristic
42Q8×Dic47C2211yescharacteristic
43C4×Dic94C2213yes—
44C4×D188C2213yes—
45D4×Dic47C2213yes—
46D4×Dic47C2213yes—
47D4×Dic47C2213yes—
48D4×Dic47C2213yes—
49#13093986C2213yes—
50C4×C22⋊D47C2213yes—
51C4×C22⋊D47C2213yes—
52(C22⋊D47)⋊C4C2216yes—
53#13093983C2213yes—
54#13093983C2213yes—
55#13093981C2213yes—
56C2×C4⋊Dic47C2213yes—
57C4⋊C4×D47C2213yes—
58C2×C4×Dic47C2213yes—
59C2×#41×C47C2211yescharacteristic
60C2×#41×C47C2211yescharacteristic
61#127×C47C2213yes—
62#121×C47C2213yes—
63#121×C47C2213yes—
64C4×Q8×C47C2211yescharacteristic
65C4×D4×C47C2213yes—
66#41×C47—24no—
67#41×C47—24no—
68C2×Q8×C47C2311yescharacteristic
69C2×D4×C47C2313yes—
70C2×D4×C47C2313yes—
71C2×D4×C47C2313yes—
72C2×D4×C47C2316yes—
73C22×C4×C47C2313yes—
74C22×C4×C47C2313yes—
75C2×C22⋊D47C2313yes—
76C2×C22⋊D47C2316yes—
77C2×C22⋊D47C2313yes—
78C2×C22⋊D47C2316yes—
79C22×Dic47C2313yes—
80C22×Dic47C2313yes—
81C22×Dic47C2316yes—
82#10625354—24no—
83#10625352—412no—
84C2×D188C2313yes—
85C2×C4×D47C2313yes—
86C2×C4×D47C2316yes—
87C2×Dic94C2313yes—
88C4⋊C4×C47C2311yescharacteristic
89C4⋊C4×C47C2313yes—
90C22⋊C4×C47C2313yes—
91C22⋊C4×C47C2313yes—
92C42×C47C2313yes—
93C22⋊Dic47C2313yes—
94C22⋊Dic47C2316yes—
95C22⋊Dic47C2313yes—
96C22⋊Dic47C2313yes—
97C22⋊Dic47C2313yes—
98(C2×D47)⋊C4C2313yes—
99(C2×D47)⋊C4C2313yes—
100(C2×D47)⋊C4C2313yes—
101(C2×D47)⋊C4C2313yes—
102C4⋊Dic47C2313yes—
103C4⋊Dic47C2313yes—
104C4⋊Dic47C2313yes—
105C4⋊Dic47C2311yescharacteristic
106C4⋊Dic47C2313yes—
107C4⋊Dic47C2313yes—
108Dic47⋊C4C2313yes—
109Dic47⋊C4C2311yescharacteristic
110Dic47⋊C4C2316yes—
111Dic47⋊C4C2311yescharacteristic
112Dic47⋊C4C2311yescharacteristic
113Dic47⋊C4C2311yescharacteristic
114Dic47⋊C4C2313yes—
115C4×Dic47C2311yescharacteristic
116C4×Dic47C2313yes—
117C4×Dic47C2313yes—
118C4×Dic47C2313yes—
119C4×Dic47C2313yes—
120C23×C47C2413yes—
121C23×C47C2413yes—
122C22×D47C2413yes—
123Q8×C47#4114yescomplemented
124D4×C47—26no—
125D4×C47—26no—
126D4×C47—46no—
127D4×C47—43no—
128C2×C4×C47—26no—
129C2×C4×C47—26no—
130C2×C4×C47C2411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C2×C4×C47C2413yes—
133C2×C4×C47C2411yescharacteristic
134C2×C4×C47C2413yes—
135C22⋊D47—26no—
136C22⋊D47—46no—
137C22⋊D47—46no—
138C22⋊D47—43no—
139C2×Dic47—26no—
140C2×Dic47—46no—
141C2×Dic47—43no—
142C2×Dic47C2411yescharacteristic
143C2×Dic47C2411yescharacteristic
144C2×Dic47C2413yes—
145C2×Dic47C2413yes—
146C2×Dic47C2413yes—
147C2×Dic47C2411yescharacteristic
148C2×Dic47C2411yescharacteristic
149D188—26no—
150C4×D47—26no—
151C4×D47—46no—
152Dic94—26no—
153C22×C47—23no—
154C22×C47—23no—
155C22×C47—23no—
156C22×C47—23no—
157C22×C47—23no—
158C22×C47—23no—
159C22×C47C2511yescharacteristic
160C2×D47—23no—
161C2×D47—23no—
162C2×D47—23no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—23no—
166C4×C47—21no—
167C4×C47C2×#4116yes—
168Dic47—21no—
169Dic47—23no—
170Dic47—23no—
171Dic47—21no—
172Dic47—23no—
173Dic47—21no—
174Dic47H(5,𝔽2)12yes—
175#3517—471nomaximal, Sylow
176C2×C47—43no—
177C2×C47—43no—
178C2×C47C22×#4111yescharacteristic
179C2×C47C2×H(5,𝔽2)11yescharacteristic
180C2×C47#58511yescharacteristic
181D47—43no—
182#557—471no—
183#553—473no—
184#553—473no—
185#550—471no—
186#550—471no—
187#550—473no—
188#550D4711yescharacteristic, complemented
189#547—473no—
190#540—473no—
191#540—473no—
192#532—473no—
193#529—473no—
194#520—471no—
195#520—471no—
196C4×#41—471no—
197C47#351711yescharacteristic, complemented, Sylow
198C2×#41—471no—
199C2×#41—476no—
200C2×#41C2×D4711yescharacteristic
201C2×#41C2×D4711yescharacteristic
202C4⋊Q8—473no—
203#127—473no—
204#127—473no—
205#127C2×D4713yes—
206#126—473no—
207#126—473no—
208#125—471no—
209#125—473no—
210#125—473no—
211#124—473no—
212#123—473no—
213#123—476no—
214#123—473no—
215#123—476no—
216C22⋊Q8—473no—
217#121—473no—
218#121—476no—
219#121—473no—
220#121—476no—
221#121—473no—
222#121—476no—
223#121—473no—
224#121—473no—
225#121C2×D4713yes—
226#121C2×D4713yes—
227C4×Q8—471no—
228C4×Q8—471no—
229C4×Q8—471no—
230C4×Q8—473no—
231C4×Q8C2×D4711yescharacteristic
232C4×D4—473no—
233C4×D4—473no—
234C4×D4—473no—
235C4×D4—473no—
236C4×D4—473no—
237C4×D4—473no—
238C4×D4—473no—
239C4×D4—476no—
240C4×D4—473no—
241C4×D4C2×D4713yes—
242#117—473no—
243#117—473no—
244#117—473no—
245C2×C4⋊C4—473no—
246C2×C4⋊C4—473no—
247C2×C42—473no—
248#41—24no—
249#41—24no—
250#41—944no—
251#41—18812no—
252C2×Q8—473no—
253C2×Q8C22×D4711yescharacteristic
254C2×D4—473no—
255C2×D4—476no—
256C2×D4—473no—
257C2×D4—476no—
258C2×D4—473no—
259C2×D4C22×D4713yes—
260C2×D4C22×D4713yes—
261C2×D4C22×D4713yes—
262C2×D4C22×D4716yes—
263C22×C4—473no—
264C22×C4—473no—
265C22×C4—476no—
266C22×C4—473no—
267C22×C4—476no—
268C22×C4C22×D4713yes—
269C22×C4C22×D4713yes—
270C4⋊C4—473no—
271C4⋊C4—471no—
272C4⋊C4—471no—
273C4⋊C4—471no—
274C4⋊C4—476no—
275C4⋊C4—471no—
276C4⋊C4—473no—
277C4⋊C4—473no—
278C4⋊C4—473no—
279C4⋊C4—473no—
280C4⋊C4—471no—
281C4⋊C4—473no—
282C4⋊C4—473no—
283C4⋊C4C22×D4713yes—
284C4⋊C4C22×D4711yescharacteristic
285C22⋊C4—473no—
286C22⋊C4—476no—
287C22⋊C4—473no—
288C22⋊C4—473no—
289C22⋊C4—473no—
290C22⋊C4—473no—
291C22⋊C4—473no—
292C22⋊C4—473no—
293C22⋊C4—473no—
294C22⋊C4C22×D4713yes—
295C22⋊C4C22×D4713yes—
296C42—471no—
297C42—473no—
298C42—473no—
299C42—473no—
300C42—473no—
301C42C22×D4713yes—
302C23—473no—
303C23C23×D4713yes—
304C23C23×D4713yes—
305Q8—946no—
306Q8#1062535214yescomplemented
307D4—26no—
308D4—26no—
309D4—43no—
310D4—46no—
311D4—946no—
312D4—946no—
313D4—1886no—
314D4—1883no—
315D4—1886no—
316C2×C4—26no—
317C2×C4—26no—
318C2×C4—471no—
319C2×C4—471no—
320C2×C4—471no—
321C2×C4—473no—
322C2×C4—473no—
323C2×C4—473no—
324C2×C4—471no—
325C2×C4—946no—
326C2×C4—946no—
327C2×C4—1886no—
328C2×C4—1883no—
329C2×C4—1886no—
330C2×C4C23×D4711yescharacteristic
331C2×C4C23×D4711yescharacteristic
332C2×C4C23×D4713yes—
333C2×C4C23×D4711yescharacteristic
334C2×C4C23×D4713yes—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—23no—
339C22—23no—
340C22—23no—
341C22—943no—
342C22—943no—
343C22—943no—
344C22C24×D4711yescharacteristic
345C4—21no—
346C4—21no—
347C4—23no—
348C4—21no—
349C4—472no—
350C4—941no—
351C4—943no—
352C4—943no—
353C4—941no—
354C4—943no—
355C4—941no—
356C4C2×#1062535216yes—
357C2—43no—
358C2—43no—
359C2—1883no—
360C2C22×#1062535211yescharacteristic
361C2H(5,𝔽2)×D4711yescharacteristic
362C2#1568995911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#550C2
hypercenter#550D47
hypocenterC47#3517
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #15689849C2semidirect
2. #15689820C2semidirect
3. #15689819C2semidirect
4. #15689793C2semidirect
5. #15689792C2semidirect
6. #15689792C2semidirect
7. #15689773C2semidirect
8. #15689727C2semidirect
9. #15689726C2semidirect
10. #15689668C2semidirect
11. #15689653C2semidirect
12. #15689606C2semidirect
13. #15689605C2semidirect
14. #41×Dic47C2semidirect
15. C47×#550C2semidirect
123. Q8×C47#41semidirect
188. #550D47semidirect
197. C47#3517semidirect
306. Q8#10625352semidirect