Finite Group Databasebeta

← #20256978

Subgroups — #20256978

Order 6016.

1112 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#15689855C213yesmaximal, complemented
2#15689849C211yesmaximal, characteristic, complemented
3#15689844C213yesmaximal, complemented
4#15689825C213yesmaximal, complemented
5#15689819C213yesmaximal, complemented
6#15689792C211yesmaximal, characteristic, complemented
7#15689784C211yesmaximal, characteristic, complemented
8#15689668C213yesmaximal, complemented
9#15689659C213yesmaximal, complemented
10#15689652C213yesmaximal, complemented
11#41×Dic47C211yesmaximal, characteristic, complemented
12C4×#10625354C211yesmaximal, characteristic, complemented
13C4×#10625352C213yesmaximal, complemented
14C2×Q8×Dic47C211yesmaximal, characteristic, complemented
15C47×#548C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625352C2213yes—
18#13094023C2213yes—
19#13094020C2213yes—
20#13094019C2216yes—
21#13094017C2216yes—
22#13094016C2213yes—
23#13094015C2213yes—
24#13094013C2213yes—
25#13094010C2216yes—
26#13094008C2216yes—
27#13094006C2216yes—
28#13094000C2213yes—
29#13093998C2213yes—
30#13093998C2213yes—
31#13093996C2216yes—
32#13093995C2213yes—
33Q8×Dic47C2211yescharacteristic
34Q8×Dic47C2211yescharacteristic
35Q8×Dic47C2213yes—
36Q8×Dic47C2211yescharacteristic
37Q8×Dic47C2213yes—
38C4×Dic94C2213yes—
39#13093989C2213yes—
40C4×D188C2213yes—
41D4×Dic47C2213yes—
42D4×Dic47C2213yes—
43D4×Dic47C2213yes—
44#13093986C2213yes—
45C4×C22⋊D47C2213yes—
46C4×C22⋊D47C2213yes—
47(C22⋊D47)⋊C4C2213yes—
48(C22⋊D47)⋊C4C2213yes—
49(C22⋊D47)⋊C4C2216yes—
50#13093983C2213yes—
51#13093982C2213yes—
52#13093982C2213yes—
53#13093980C2211yescharacteristic
54#13093980C2213yes—
55C2×C4⋊Dic47C2213yes—
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⋊D47C2313yes—
76C2×C22⋊D47C2316yes—
77C22×Dic47C2313yes—
78C22×Dic47C2313yes—
79C22×Dic47C2313yes—
80C22×Dic47C2311yescharacteristic
81#10625354—24no—
82#10625352—212no—
83C2×D188C2313yes—
84C2×C4×D47C2313yes—
85C2×C4×D47C2313yes—
86C2×C4×D47C2313yes—
87C2×Dic94C2313yes—
88C4⋊C4×C47C2313yes—
89C4⋊C4×C47C2313yes—
90C22⋊C4×C47C2311yescharacteristic
91C22⋊C4×C47C2313yes—
92C22⋊C4×C47C2316yes—
93C42×C47C2313yes—
94C22⋊Dic47C2311yescharacteristic
95C22⋊Dic47C2313yes—
96C22⋊Dic47C2316yes—
97(C2×D47)⋊C4C2313yes—
98(C2×D47)⋊C4C2313yes—
99(C2×D47)⋊C4C2316yes—
100(C2×D47)⋊C4C2316yes—
101C4⋊Dic47C2313yes—
102C4⋊Dic47C2313yes—
103C4⋊Dic47C2316yes—
104C4⋊Dic47C2313yes—
105C4⋊Dic47C2313yes—
106Dic47⋊C4C2311yescharacteristic
107Dic47⋊C4C2313yes—
108Dic47⋊C4C2311yescharacteristic
109Dic47⋊C4C2313yes—
110Dic47⋊C4C2316yes—
111C4×Dic47C2311yescharacteristic
112C4×Dic47C2313yes—
113C4×Dic47C2313yes—
114C4×Dic47C2311yescharacteristic
115C4×Dic47C2313yes—
116C4×Dic47C2313yes—
117C4×Dic47C2313yes—
118C4×Dic47C2313yes—
119C4×Dic47C2313yes—
120C23×C47C2413yes—
121C23×C47C2411yescharacteristic
122C22×D47C2413yes—
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×C47C2413yes—
131C2×C4×C47C2411yescharacteristic
132C2×C4×C47C2413yes—
133C2×C4×C47C2413yes—
134C22⋊D47—26no—
135C22⋊D47—26no—
136C22⋊D47—46no—
137C2×Dic47—26no—
138C2×Dic47—43no—
139C2×Dic47—43no—
140C2×Dic47#4114yescomplemented
141C2×Dic47C2411yescharacteristic
142C2×Dic47C2411yescharacteristic
143C2×Dic47C2413yes—
144C2×Dic47C2413yes—
145C2×Dic47C2413yes—
146C2×Dic47C2411yescharacteristic
147C2×Dic47C2411yescharacteristic
148D188—26no—
149C4×D47—26no—
150C4×D47—26no—
151C4×D47—43no—
152Dic94—26no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—23no—
156C22×C47—23no—
157C22×C47—23no—
158C22×C47C2×#4112yes—
159C22×C47C2511yescharacteristic
160C2×D47—23no—
161C2×D47—23no—
162C2×D47—23no—
163C4×C47—23no—
164C4×C47—21no—
165C4×C47—23no—
166C4×C47—21no—
167C4×C47C2×#4116yes—
168Dic47—23no—
169Dic47—21no—
170Dic47—23no—
171Dic47—21no—
172Dic47—23no—
173Dic47C2×#4112yes—
174Dic47C2×#4112yes—
175#3480—471nomaximal, Sylow
176C2×C47—22no—
177C2×C47—43no—
178C2×C47C22×#4111yescharacteristic
179C2×C47C22×#4111yescharacteristic
180C2×C47#58511yescharacteristic
181D47—43no—
182#559—473no—
183#557—471no—
184#556—473no—
185#553—473no—
186#553—473no—
187#550—471no—
188#548—471no—
189#548D4711yescharacteristic, complemented
190#532—473no—
191#529—473no—
192#529—473no—
193C4×#41—471no—
194C4×#41—471no—
195C4×#41—473no—
196C2×C4×Q8—471no—
197C47#348011yescharacteristic, complemented, Sylow
198C2×#41—471no—
199C2×#41—473no—
200C2×#41C2×D4711yescharacteristic
201C22×Q8C2×D4711yescharacteristic
202C4⋊Q8—473no—
203#127—473no—
204#126—476no—
205#126—476no—
206#125—473no—
207#125—473no—
208#124—473no—
209#124—476no—
210#124C2×D4713yes—
211#123—476no—
212#123—476no—
213C22⋊Q8—473no—
214C22⋊Q8C2×D4713yes—
215#121—473no—
216#121—476no—
217#121—473no—
218#121—473no—
219#121C2×D4713yes—
220C4×Q8—471no—
221C4×Q8—473no—
222C4×Q8—471no—
223C4×Q8—473no—
224C4×Q8—471no—
225C4×Q8—473no—
226C4×Q8—473no—
227C4×Q8C2×D4711yescharacteristic
228C4×D4—473no—
229C4×D4—473no—
230C4×D4—473no—
231C4×D4—473no—
232C4×D4—473no—
233C4×D4—473no—
234C4×D4—473no—
235C4×D4—473no—
236C4×D4—476no—
237C4×D4—473no—
238C4×D4C2×D4713yes—
239#117—473no—
240#117—473no—
241#117—473no—
242#117—471no—
243#117—473no—
244C2×C4⋊C4—473no—
245C2×C42—473no—
246C2×C42—473no—
247C2×C42—473no—
248#41—24no—
249#41—9412no—
250#41—944no—
251C2×Q8—24no—
252C2×Q8—473no—
253C2×Q8C22×D4713yes—
254C2×Q8C22×D4711yescharacteristic
255C2×D4—473no—
256C2×D4—473no—
257C2×D4—476no—
258C2×D4—473no—
259C2×D4C22×D4713yes—
260C2×D4C22×D4713yes—
261C22×C4—471no—
262C22×C4—473no—
263C22×C4—473no—
264C22×C4—473no—
265C22×C4—473no—
266C22×C4—473no—
267C22×C4—473no—
268C22×C4C22×D4713yes—
269C22×C4C22×D4713yes—
270C4⋊C4—471no—
271C4⋊C4—471no—
272C4⋊C4—473no—
273C4⋊C4—473no—
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—471no—
283C22⋊C4—473no—
284C22⋊C4—476no—
285C22⋊C4—473no—
286C22⋊C4—476no—
287C22⋊C4—473no—
288C22⋊C4—476no—
289C22⋊C4C22×D4711yescharacteristic
290C22⋊C4C22×D4713yes—
291C22⋊C4C22×D4716yes—
292C42—471no—
293C42—471no—
294C42—473no—
295C42—473no—
296C42—473no—
297C42—473no—
298C42—473no—
299C42—473no—
300C42—473no—
301C42C22×D4713yes—
302C23—473no—
303C23C23×D4713yes—
304C23C23×D4711yescharacteristic
305Q8—26no—
306Q8—946no—
307Q8#1062535214yescomplemented
308D4—26no—
309D4—26no—
310D4—946no—
311D4—946no—
312D4—946no—
313D4—1886no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—474no—
317C2×C4—471no—
318C2×C4—471no—
319C2×C4—471no—
320C2×C4—471no—
321C2×C4—473no—
322C2×C4—473no—
323C2×C4—473no—
324C2×C4—946no—
325C2×C4—946no—
326C2×C4—946no—
327C2×C4—1883no—
328C2×C4—1883no—
329C2×C4—1883no—
330C2×C4C23×D4711yescharacteristic
331C2×C4C23×D4713yes—
332C2×C4C23×D4711yescharacteristic
333C2×C4C23×D4713yes—
334C2×C4C23×D4713yes—
335C22—21no—
336C22—21no—
337C22—23no—
338C22—23no—
339C22—23no—
340C22—943no—
341C22—943no—
342C22—943no—
343C22#41×D4712yes—
344C22C24×D4711yescharacteristic
345C4—23no—
346C4—21no—
347C4—23no—
348C4—21no—
349C4—472no—
350C4—472no—
351C4—943no—
352C4—941no—
353C4—943no—
354C4—941no—
355C4—943no—
356C4C2×#1062535216yes—
357C2—22no—
358C2—43no—
359C2—1883no—
360C2C2×#41×D4711yescharacteristic
361C2C22×#1062535211yescharacteristic
362C2#1568996011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#548C2
hypercenter#548D47
hypocenterC47#3480
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #15689855C2semidirect
2. #15689849C2semidirect
3. #15689844C2semidirect
4. #15689825C2semidirect
5. #15689819C2semidirect
6. #15689792C2semidirect
7. #15689784C2semidirect
8. #15689668C2semidirect
9. #15689659C2semidirect
10. #15689652C2semidirect
11. #41×Dic47C2semidirect
12. C4×#10625354C2semidirect
13. C4×#10625352C2semidirect
14. C2×Q8×Dic47C2semidirect
15. C47×#548C2semidirect
124. Q8×C47#41semidirect
140. C2×Dic47#41semidirect
189. #548D47semidirect
197. C47#3480semidirect
307. Q8#10625352semidirect