Finite Group Databasebeta

← #20257388

Subgroups — #20257388

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#15689823C213yesmaximal, complemented
3#15689821C213yesmaximal, complemented
4#15689795C211yesmaximal, characteristic, complemented
5#15689794C213yesmaximal, complemented
6#15689792C211yesmaximal, characteristic, complemented
7#15689792C211yesmaximal, characteristic, complemented
8#15689774C213yesmaximal, complemented
9#15689728C213yesmaximal, complemented
10#15689724C213yesmaximal, complemented
11#15689670C213yesmaximal, complemented
12#15689651C213yesmaximal, complemented
13#15689605C211yesmaximal, characteristic, complemented
14C4×#10625354C211yesmaximal, characteristic, complemented
15C47×#520C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625354C2211yescharacteristic
18C2×#10625350C2216yes—
19#13094023C2213yes—
20#13094021C2213yes—
21#13094020C2213yes—
22#13094020C2213yes—
23#13094019C2213yes—
24#13094017C2213yes—
25#13094016C2213yes—
26#13094015C2213yes—
27#13094014C2211yescharacteristic
28#13094010C2213yes—
29#13094009C2213yes—
30#13094009C2216yes—
31#13094007C2216yes—
32#13094006C2213yes—
33#13094002C2213yes—
34#13093999C2213yes—
35#13093999C2213yes—
36#13093998C2213yes—
37#13093998C2213yes—
38#13093998C2216yes—
39#13093997C2216yes—
40#13093997C2216yes—
41#13093997C2213yes—
42#13093995C2213yes—
43#13093995C2213yes—
44Q8×Dic47C2211yescharacteristic
45Q8×Dic47C2211yescharacteristic
46C4×Dic94C2213yes—
47C4×D188C2213yes—
48C4×D188C2213yes—
49C4×D188C2213yes—
50#13093986C2213yes—
51#13093986C2213yes—
52C4×C22⋊D47C2213yes—
53C4×C22⋊D47C2213yes—
54C4×C22⋊D47C2216yes—
55#13093982C2213yes—
56#13093981C2213yes—
57C4⋊C4×D47C2213yes—
58C42×D47C2213yes—
59C2×#41×C47C2211yescharacteristic
60C4×Q8×C47C2211yescharacteristic
61C4×Q8×C47C2211yescharacteristic
62C4×D4×C47C2213yes—
63C4×D4×C47C2213yes—
64#117×C47C2213yes—
65C2×C4⋊C4×C47C2213yes—
66#41×C47—24no—
67C2×Q8×C47C2311yescharacteristic
68C2×D4×C47C2313yes—
69C22×C4×C47C2313yes—
70C22×C4×C47C2316yes—
71C2×C22⋊D47C2313yes—
72C2×C22⋊D47C2316yes—
73C2×C22⋊D47C2313yes—
74C2×C22⋊D47C2316yes—
75#10625354—24no—
76#10625354—24no—
77#10625350—412no—
78C2×D188C2313yes—
79C2×D188C2313yes—
80C2×D188C2313yes—
81C2×D188C2316yes—
82C2×C4×D47C2313yes—
83C2×C4×D47C2313yes—
84C2×C4×D47C2313yes—
85C2×C4×D47C2313yes—
86C2×C4×D47C2316yes—
87C2×Dic94C2313yes—
88C4⋊C4×C47C2313yes—
89C4⋊C4×C47C2313yes—
90C4⋊C4×C47C2313yes—
91C4⋊C4×C47C2311yescharacteristic
92C22⋊C4×C47C2313yes—
93C22⋊C4×C47C2313yes—
94C42×C47C2313yes—
95C42×C47C2313yes—
96C22⋊Dic47C2313yes—
97C22⋊Dic47C2313yes—
98(C2×D47)⋊C4C2313yes—
99(C2×D47)⋊C4C2313yes—
100(C2×D47)⋊C4C2316yes—
101(C2×D47)⋊C4C2313yes—
102(C2×D47)⋊C4C2313yes—
103(C2×D47)⋊C4C2313yes—
104(C2×D47)⋊C4C2313yes—
105C4⋊Dic47C2313yes—
106C4⋊Dic47C2313yes—
107C4⋊Dic47C2311yescharacteristic
108C4⋊Dic47C2313yes—
109Dic47⋊C4C2313yes—
110Dic47⋊C4C2311yescharacteristic
111Dic47⋊C4C2311yescharacteristic
112Dic47⋊C4C2311yescharacteristic
113Dic47⋊C4C2316yes—
114Dic47⋊C4C2311yescharacteristic
115Dic47⋊C4C2313yes—
116C4×Dic47C2311yescharacteristic
117C4×Dic47C2313yes—
118C4×Dic47C2313yes—
119C4×Dic47C2313yes—
120C23×C47C2413yes—
121C22×D47C2413yes—
122C22×D47C2413yes—
123Q8×C47#4114yescomplemented
124D4×C47—26no—
125C2×C4×C47—26no—
126C2×C4×C47—46no—
127C2×C4×C47C2411yescharacteristic
128C2×C4×C47C2413yes—
129C2×C4×C47C2411yescharacteristic
130C2×C4×C47C2413yes—
131C2×C4×C47C2411yescharacteristic
132C2×C4×C47C2413yes—
133C22⋊D47—26no—
134C22⋊D47—46no—
135C22⋊D47—46no—
136C22⋊D47—43no—
137C2×Dic47C2411yescharacteristic
138C2×Dic47C2411yescharacteristic
139C2×Dic47C2413yes—
140C2×Dic47C2413yes—
141C2×Dic47C2411yescharacteristic
142C2×Dic47C2411yescharacteristic
143D188—26no—
144D188—26no—
145D188—43no—
146D188—46no—
147C4×D47—26no—
148C4×D47—26no—
149C4×D47—26no—
150C4×D47—43no—
151C4×D47—46no—
152Dic94—26no—
153C22×C47—23no—
154C22×C47—23no—
155C22×C47—23no—
156C22×C47C2511yescharacteristic
157C2×D47—23no—
158C2×D47—23no—
159C2×D47—23no—
160C2×D47—23no—
161C2×D47—23no—
162C2×D47—23no—
163C4×C47—21no—
164C4×C47—23no—
165C4×C47—23no—
166C4×C47—21no—
167C4×C47—21no—
168C4×C47C2×#4116yes—
169Dic47—21no—
170Dic47—21no—
171Dic47—23no—
172Dic47—23no—
173Dic47—21no—
174Dic47H(5,𝔽2)12yes—
175#3517—471nomaximal, Sylow
176C2×C47—43no—
177C2×C47C22×#4111yescharacteristic
178C2×C47C2×H(5,𝔽2)11yescharacteristic
179C2×C47#58511yescharacteristic
180D47—43no—
181D47—43no—
182#557—471no—
183#553—473no—
184#553—473no—
185#550—471no—
186#550—471no—
187#550—471no—
188#550—473no—
189#547—473no—
190#540—473no—
191#540—473no—
192#532—473no—
193#529—473no—
194#520—471no—
195#520D4711yescharacteristic, complemented
196C4×#41—471no—
197C47#351711yescharacteristic, complemented, Sylow
198C2×#41—471no—
199C2×#41—471no—
200C2×#41—476no—
201C2×#41C2×D4711yescharacteristic
202C4⋊Q8—473no—
203#127—473no—
204#127—473no—
205#127—473no—
206#126—473no—
207#126—473no—
208#125—471no—
209#125—473no—
210#125—473no—
211#124—473no—
212#123—476no—
213#123—473no—
214#123—476no—
215#123—473no—
216C22⋊Q8—473no—
217#121—473no—
218#121—473no—
219#121—473no—
220#121—476no—
221#121—473no—
222#121—473no—
223#121—473no—
224#121—473no—
225#121—476no—
226#121—476no—
227C4×Q8—471no—
228C4×Q8—471no—
229C4×Q8—473no—
230C4×Q8C2×D4711yescharacteristic
231C4×Q8C2×D4711yescharacteristic
232C4×D4—473no—
233C4×D4—473no—
234C4×D4—476no—
235C4×D4—473no—
236C4×D4—473no—
237C4×D4—473no—
238C4×D4—473no—
239C4×D4—473no—
240C4×D4C2×D4713yes—
241C4×D4C2×D4713yes—
242#117—473no—
243#117—473no—
244#117C2×D4713yes—
245C2×C4⋊C4—473no—
246C2×C4⋊C4C2×D4713yes—
247C2×C42—473no—
248#41—24no—
249#41—944no—
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×D4—473no—
260C2×D4—473no—
261C2×D4—476no—
262C2×D4C22×D4713yes—
263C22×C4—473no—
264C22×C4—473no—
265C22×C4—473no—
266C22×C4—473no—
267C22×C4—476no—
268C22×C4C22×D4713yes—
269C22×C4C22×D4716yes—
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—471no—
280C4⋊C4—473no—
281C4⋊C4C22×D4713yes—
282C4⋊C4C22×D4713yes—
283C4⋊C4C22×D4713yes—
284C4⋊C4C22×D4711yescharacteristic
285C22⋊C4—473no—
286C22⋊C4—473no—
287C22⋊C4—473no—
288C22⋊C4—476no—
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—
300C42C22×D4713yes—
301C42C22×D4713yes—
302C23—473no—
303C23—473no—
304C23C23×D4713yes—
305Q8—946no—
306Q8#1062535014yescomplemented
307D4—26no—
308D4—946no—
309D4—946no—
310D4—946no—
311D4—1883no—
312D4—1886no—
313D4—1886no—
314D4—1883no—
315D4—1886no—
316C2×C4—26no—
317C2×C4—46no—
318C2×C4—471no—
319C2×C4—471no—
320C2×C4—471no—
321C2×C4—473no—
322C2×C4—473no—
323C2×C4—471no—
324C2×C4—946no—
325C2×C4—946no—
326C2×C4—946no—
327C2×C4—1883no—
328C2×C4—1886no—
329C2×C4C23×D4711yescharacteristic
330C2×C4C23×D4713yes—
331C2×C4C23×D4711yescharacteristic
332C2×C4C23×D4713yes—
333C2×C4C23×D4711yescharacteristic
334C2×C4C23×D4713yes—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—943no—
339C22—943no—
340C22—943no—
341C22—943no—
342C22—943no—
343C22—943no—
344C22C24×D4711yescharacteristic
345C4—21no—
346C4—23no—
347C4—23no—
348C4—21no—
349C4—21no—
350C4—472no—
351C4—941no—
352C4—941no—
353C4—943no—
354C4—943no—
355C4—941no—
356C4C2×#1062535016yes—
357C2—43no—
358C2—1883no—
359C2—1883no—
360C2C22×#1062535011yescharacteristic
361C2H(5,𝔽2)×D4711yescharacteristic
362C2#1568996011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#520C2
hypercenter#520D47
hypocenterC47#3517
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #15689849C2semidirect
2. #15689823C2semidirect
3. #15689821C2semidirect
4. #15689795C2semidirect
5. #15689794C2semidirect
6. #15689792C2semidirect
7. #15689792C2semidirect
8. #15689774C2semidirect
9. #15689728C2semidirect
10. #15689724C2semidirect
11. #15689670C2semidirect
12. #15689651C2semidirect
13. #15689605C2semidirect
14. C4×#10625354C2semidirect
15. C47×#520C2semidirect
123. Q8×C47#41semidirect
195. #520D47semidirect
197. C47#3517semidirect
306. Q8#10625350semidirect