Finite Group Databasebeta

← #20257004

Subgroups — #20257004

Order 6016.

1094 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689849C211yesmaximal, characteristic, complemented
2#15689842C213yesmaximal, complemented
3#15689813C213yesmaximal, complemented
4#15689807C213yesmaximal, complemented
5Q8×C22⋊D47C211yesmaximal, characteristic, complemented
6#15689780C211yesmaximal, characteristic, complemented
7#15689773C213yesmaximal, complemented
8#15689675C213yesmaximal, complemented
9#15689654C213yesmaximal, complemented
10#15689652C213yesmaximal, complemented
11#41×Dic47C211yesmaximal, characteristic, complemented
12C4×#10625352C213yesmaximal, complemented
13C2×Q8×Dic47C211yesmaximal, characteristic, complemented
14C4×Q8×D47C211yesmaximal, characteristic, complemented
15C47×#548C211yesmaximal, characteristic, complemented
16C2×#10625352C2213yes—
17C2×Q8×D47C2211yescharacteristic
18#13094023C2213yes—
19#13094022C2213yes—
20#13094017C2216yes—
21#13094017C2216yes—
22#13094016C2213yes—
23#13094015C2213yes—
24#13094014C2216yes—
25#13094011C2213yes—
26#13094006C2216yes—
27#13094005C2216yes—
28#13094003C2213yes—
29#13094003C2213yes—
30#13094001C2216yes—
31#13094000C2213yes—
32#13093995C2213yes—
33Q8×Dic47C2211yescharacteristic
34Q8×Dic47C2211yescharacteristic
35Q8×Dic47C2213yes—
36Q8×Dic47C2211yescharacteristic
37Q8×Dic47C2213yes—
38C4×Dic94C2213yes—
39C4×Dic94C2213yes—
40#13093989C2213yes—
41#13093989C2213yes—
42D4×Dic47C2213yes—
43D4×Dic47C2213yes—
44D4×Dic47C2213yes—
45C4×C22⋊D47C2213yes—
46C4×C22⋊D47C2213yes—
47(C22⋊D47)⋊C4C2211yescharacteristic
48(C22⋊D47)⋊C4C2213yes—
49#13093983C2213yes—
50#13093982C2213yes—
51#13093980C2213yes—
52#13093980C2213yes—
53#13093980C2216yes—
54C2×C4⋊Dic47C2213yes—
55C4⋊C4×D47C2213yes—
56C2×C4×Dic47C2213yes—
57C2×C4×Dic47C2213yes—
58C42×D47C2213yes—
59C2×#41×C47C2211yescharacteristic
60C22×Q8×C47C2211yescharacteristic
61#124×C47C2213yes—
62C22⋊Q8×C47C2213yes—
63#121×C47C2213yes—
64C4×Q8×C47C2211yescharacteristic
65C4×D4×C47C2213yes—
66#41×C47—24no—
67C2×Q8×C47—24no—
68C2×Q8×C47C2313yes—
69C2×Q8×C47C2311yescharacteristic
70C2×D4×C47C2313yes—
71C2×D4×C47C2313yes—
72C22×C4×C47C2313yes—
73C22×C4×C47C2313yes—
74C2×C22⋊D47C2313yes—
75C2×C22⋊D47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2313yes—
78C22×Dic47C2313yes—
79C22×Dic47C2313yes—
80Q8×D47—24no—
81#10625352—212no—
82C2×C4×D47C2311yescharacteristic
83C2×C4×D47C2313yes—
84C2×C4×D47C2313yes—
85C2×Dic94C2313yes—
86C2×Dic94C2313yes—
87C4⋊C4×C47C2313yes—
88C4⋊C4×C47C2313yes—
89C22⋊C4×C47C2311yescharacteristic
90C22⋊C4×C47C2313yes—
91C22⋊C4×C47C2316yes—
92C42×C47C2313yes—
93C22⋊Dic47C2313yes—
94C22⋊Dic47C2313yes—
95C22⋊Dic47C2316yes—
96C22⋊Dic47C2316yes—
97(C2×D47)⋊C4C2311yescharacteristic
98(C2×D47)⋊C4C2313yes—
99C4⋊Dic47C2313yes—
100C4⋊Dic47C2313yes—
101C4⋊Dic47C2316yes—
102C4⋊Dic47C2313yes—
103C4⋊Dic47C2313yes—
104Dic47⋊C4C2316yes—
105Dic47⋊C4C2311yescharacteristic
106Dic47⋊C4C2313yes—
107Dic47⋊C4C2313yes—
108Dic47⋊C4C2313yes—
109Dic47⋊C4C2316yes—
110Dic47⋊C4C2316yes—
111C4×Dic47C2313yes—
112C4×Dic47C2313yes—
113C4×Dic47C2313yes—
114C4×Dic47C2311yescharacteristic
115C4×Dic47C2313yes—
116C4×Dic47C2313yes—
117C4×Dic47C2313yes—
118C4×Dic47C2313yes—
119C4×Dic47C2313yes—
120C23×C47C2413yes—
121C23×C47C2411yescharacteristic
122C22×D47C2411yescharacteristic
123Q8×C47—26no—
124Q8×C47#4114yescomplemented
125D4×C47—26no—
126D4×C47—26no—
127C2×C4×C47—26no—
128C2×C4×C47—26no—
129C2×C4×C47C2411yescharacteristic
130C2×C4×C47C2411yescharacteristic
131C2×C4×C47C2413yes—
132C2×C4×C47C2413yes—
133C2×C4×C47C2413yes—
134C22⋊D47—26no—
135C22⋊D47#4114yescomplemented
136C2×Dic47—26no—
137C2×Dic47—26no—
138C2×Dic47—22no—
139C2×Dic47—26no—
140C2×Dic47C2411yescharacteristic
141C2×Dic47C2413yes—
142C2×Dic47C2413yes—
143C2×Dic47C2413yes—
144C2×Dic47C2413yes—
145C2×Dic47C2411yescharacteristic
146C2×Dic47C2411yescharacteristic
147C4×D47—26no—
148C4×D47—26no—
149C4×D47—22no—
150Dic94—26no—
151Dic94—26no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—23no—
155C22×C47—23no—
156C22×C47—23no—
157C22×C47C2×#4112yes—
158C22×C47C2511yescharacteristic
159C2×D47—21no—
160C2×D47—21no—
161C2×D47C2×#4112yes—
162C4×C47—23no—
163C4×C47—21no—
164C4×C47—23no—
165C4×C47—21no—
166C4×C47C2×#4116yes—
167Dic47—23no—
168Dic47—23no—
169Dic47—23no—
170Dic47—21no—
171Dic47—23no—
172Dic47C2×#4112yes—
173Dic472−1+412yes—
174#3482—471nomaximal, Sylow
175C2×C47—22no—
176C2×C47—43no—
177C2×C47C22×#4111yescharacteristic
178C2×C47C22×#4111yescharacteristic
179C2×C47C2×2−1+411yescharacteristic
180D47—22no—
181#557—471no—
182#556—473no—
183#552—473no—
184#552—473no—
185D4×Q8—471no—
186#548—471no—
187#548D4711yescharacteristic, complemented
188#547—473no—
189#533—473no—
190#529—473no—
191#529—473no—
192C4×#41—471no—
193C4×#41—473no—
194C2×C4×Q8—471no—
195C2×C4×Q8—471no—
196C47#348211yescharacteristic, complemented, Sylow
197C2×#41—473no—
198C2×#41C2×D4711yescharacteristic
199C22×Q8—471no—
200C22×Q8C2×D4711yescharacteristic
201C4⋊Q8—473no—
202C4⋊Q8—473no—
203#126—476no—
204#126—476no—
205#125—473no—
206#125—476no—
207#125—473no—
208#124—473no—
209#124C2×D4713yes—
210#123—476no—
211#123—476no—
212C22⋊Q8—473no—
213C22⋊Q8—473no—
214C22⋊Q8—473no—
215C22⋊Q8—476no—
216C22⋊Q8C2×D4713yes—
217#121—473no—
218#121C2×D4713yes—
219C4×Q8—471no—
220C4×Q8—473no—
221C4×Q8—471no—
222C4×Q8—473no—
223C4×Q8—471no—
224C4×Q8—473no—
225C4×Q8—473no—
226C4×Q8—473no—
227C4×Q8—473no—
228C4×Q8C2×D4711yescharacteristic
229C4×D4—473no—
230C4×D4—473no—
231C4×D4—473no—
232C4×D4—473no—
233C4×D4—473no—
234C4×D4—471no—
235C4×D4—473no—
236C4×D4C2×D4713yes—
237#117—473no—
238#117—473no—
239#117—473no—
240#117—473no—
241#117—476no—
242C2×C4⋊C4—473no—
243C2×C4⋊C4—473no—
244C2×C42—473no—
245C2×C42—473no—
246C2×C42—473no—
247#41—24no—
248#41—9412no—
249C2×Q8—24no—
250C2×Q8—473no—
251C2×Q8—473no—
252C2×Q8—944no—
253C2×Q8C22×D4713yes—
254C2×Q8C22×D4711yescharacteristic
255C2×D4—471no—
256C2×D4—473no—
257C2×D4C22×D4713yes—
258C2×D4C22×D4713yes—
259C22×C4—471no—
260C22×C4—473no—
261C22×C4—473no—
262C22×C4—473no—
263C22×C4—471no—
264C22×C4—473no—
265C22×C4—473no—
266C22×C4C22×D4713yes—
267C22×C4C22×D4713yes—
268C4⋊C4—476no—
269C4⋊C4—471no—
270C4⋊C4—473no—
271C4⋊C4—473no—
272C4⋊C4—473no—
273C4⋊C4—476no—
274C4⋊C4—476no—
275C4⋊C4—473no—
276C4⋊C4—473no—
277C4⋊C4—476no—
278C4⋊C4—473no—
279C4⋊C4—473no—
280C4⋊C4C22×D4713yes—
281C4⋊C4C22×D4713yes—
282C22⋊C4—473no—
283C22⋊C4—476no—
284C22⋊C4—473no—
285C22⋊C4—476no—
286C22⋊C4—471no—
287C22⋊C4—473no—
288C22⋊C4C22×D4711yescharacteristic
289C22⋊C4C22×D4713yes—
290C22⋊C4C22×D4716yes—
291C42—471no—
292C42—473no—
293C42—473no—
294C42—473no—
295C42—473no—
296C42—473no—
297C42—473no—
298C42—473no—
299C42—473no—
300C42C22×D4713yes—
301C23—471no—
302C23C23×D4713yes—
303C23C23×D4711yescharacteristic
304Q8—26no—
305Q8—946no—
306Q8—946no—
307Q8#1062535214yescomplemented
308D4—26no—
309D4—26no—
310D4—474no—
311D4—946no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—471no—
315C2×C4—471no—
316C2×C4—471no—
317C2×C4—473no—
318C2×C4—473no—
319C2×C4—473no—
320C2×C4—473no—
321C2×C4—942no—
322C2×C4—946no—
323C2×C4—942no—
324C2×C4—946no—
325C2×C4—946no—
326C2×C4—946no—
327C2×C4—946no—
328C2×C4C23×D4711yescharacteristic
329C2×C4C23×D4711yescharacteristic
330C2×C4C23×D4713yes—
331C2×C4C23×D4713yes—
332C2×C4C23×D4713yes—
333C22—21no—
334C22—21no—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—472no—
339C22—941no—
340C22—941no—
341C22#41×D4712yes—
342C22C24×D4711yescharacteristic
343C4—23no—
344C4—21no—
345C4—23no—
346C4—21no—
347C4—472no—
348C4—472no—
349C4—943no—
350C4—943no—
351C4—943no—
352C4—941no—
353C4—943no—
354C4C2×#1062535216yes—
355C2—22no—
356C2—43no—
357C2—942no—
358C2C2×#41×D4711yescharacteristic
359C2C22×#1062535211yescharacteristic
360C22−1+4×D4711yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#548C2
hypercenter#548D47
hypocenterC47#3482
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #15689849C2semidirect
2. #15689842C2semidirect
3. #15689813C2semidirect
4. #15689807C2semidirect
5. Q8×C22⋊D47C2semidirect
6. #15689780C2semidirect
7. #15689773C2semidirect
8. #15689675C2semidirect
9. #15689654C2semidirect
10. #15689652C2semidirect
11. #41×Dic47C2semidirect
12. C4×#10625352C2semidirect
13. C2×Q8×Dic47C2semidirect
14. C4×Q8×D47C2semidirect
15. C47×#548C2semidirect
124. Q8×C47#41semidirect
135. C22⋊D47#41semidirect
187. #548D47semidirect
196. C47#3482semidirect
307. Q8#10625352semidirect