Finite Group Databasebeta

← #20257156

Subgroups — #20257156

Order 6016.

1492 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094072C211yesmaximal, characteristic, complemented
2C2×#13094071C211yesmaximal, characteristic, complemented
3#15689792C211yesmaximal, characteristic, complemented
4#15689791C213yesmaximal, complemented
5Q8×C22⋊D47C211yesmaximal, characteristic, complemented
6#15689786C213yesmaximal, complemented
7#15689785C211yesmaximal, characteristic, complemented
8#15689782C213yesmaximal, complemented
9#15689781C213yesmaximal, complemented
10#15689703C213yesmaximal, complemented
11#15689702C213yesmaximal, complemented
12#15689672C213yesmaximal, complemented
13#15689670C213yesmaximal, complemented
14C4×Q8×D47C211yesmaximal, characteristic, complemented
15C47×#548C211yesmaximal, characteristic, complemented
16#13094072—28no—
17#13094071—28no—
18C2×#10625354C2211yescharacteristic
19C2×#10625354C2213yes—
20C2×#10625350C2213yes—
21C2×#10625350C2213yes—
22C2×#10625350C2213yes—
23C2×#10625352C2213yes—
24C2×#10625352C2213yes—
25C22×Dic94C2213yes—
26C2×Q8×D47C2213yes—
27C2×Q8×D47C2211yescharacteristic
28C2×Q8×D47C2211yescharacteristic
29#13094023C2213yes—
30#13094022C2213yes—
31#13094020C2213yes—
32#13094020C2213yes—
33#13094012C2213yes—
34#13094010C2213yes—
35#13094010C2213yes—
36#13094004C2213yes—
37#13094003C2213yes—
38#13094002C2216yes—
39#13094001C2216yes—
40#13094000C2213yes—
41#13093999C2213yes—
42#13093999C2213yes—
43#13093998C2213yes—
44#13093997C2216yes—
45#13093997C2211yescharacteristic
46#13093997C2213yes—
47#13093997C2216yes—
48#13093996C2216yes—
49#13093995C2213yes—
50#13093995C2213yes—
51Q8×Dic47C2211yescharacteristic
52C4×Dic94C2213yes—
53#13093989C2213yes—
54C4×D188C2213yes—
55C4×C22⋊D47C2213yes—
56C4×C22⋊D47C2213yes—
57(C22⋊D47)⋊C4C2216yes—
58(C22⋊D47)⋊C4C2216yes—
59C4⋊C4×D47C2213yes—
60C42×D47C2213yes—
61C2×#41×C47C2211yescharacteristic
62C22×Q8×C47C2211yescharacteristic
63#124×C47C2213yes—
64C22⋊Q8×C47C2213yes—
65#121×C47C2213yes—
66C4×Q8×C47C2211yescharacteristic
67C4×D4×C47C2213yes—
68#41×C47—24no—
69C2×Q8×C47—24no—
70C2×Q8×C47C2313yes—
71C2×Q8×C47C2311yescharacteristic
72C2×D4×C47C2313yes—
73C2×D4×C47C2313yes—
74C22×C4×C47C2313yes—
75C22×C4×C47C2313yes—
76C2×C22⋊D47C2313yes—
77C2×C22⋊D47C2311yescharacteristic
78C2×C22⋊D47C2311yescharacteristic
79C2×C22⋊D47C2313yes—
80C2×C22⋊D47C2313yes—
81C2×C22⋊D47C2313yes—
82C2×C22⋊D47C2316yes—
83C22×Dic47C2316yes—
84#10625354—24no—
85#10625354—212no—
86Q8×D47—24no—
87Q8×D47—212no—
88Q8×D47D418yescomplemented
89#10625352—212no—
90#10625352—212no—
91#10625350—212no—
92#10625350—212no—
93#10625350—212no—
94C2×D188C2313yes—
95C2×D188C2311yescharacteristic
96C2×D188C2313yes—
97C2×D188C2313yes—
98C2×C4×D47C2311yescharacteristic
99C2×C4×D47C2316yes—
100C2×C4×D47C2313yes—
101C2×C4×D47C2313yes—
102C2×C4×D47C2313yes—
103C2×C4×D47C2313yes—
104C2×Dic94—212no—
105C2×Dic94C2313yes—
106C2×Dic94C2313yes—
107C2×Dic94C2313yes—
108C2×Dic94C2313yes—
109C4⋊C4×C47C2313yes—
110C4⋊C4×C47C2313yes—
111C22⋊C4×C47C2311yescharacteristic
112C22⋊C4×C47C2313yes—
113C22⋊C4×C47C2316yes—
114C42×C47C2313yes—
115C22⋊Dic47C2313yes—
116C22⋊Dic47C2313yes—
117(C2×D47)⋊C4C2313yes—
118(C2×D47)⋊C4C2316yes—
119(C2×D47)⋊C4C2313yes—
120(C2×D47)⋊C4C2313yes—
121(C2×D47)⋊C4C2311yescharacteristic
122C4⋊Dic47C2313yes—
123C4⋊Dic47C2313yes—
124Dic47⋊C4C2316yes—
125Dic47⋊C4C2313yes—
126Dic47⋊C4C2316yes—
127Dic47⋊C4C2311yescharacteristic
128C4×Dic47C2313yes—
129C4×Dic47C2313yes—
130C4×Dic47C2313yes—
131C23×C47C2411yescharacteristic
132C23×C47C2413yes—
133C22×D47C2413yes—
134C22×D47C2411yescharacteristic
135C22×D47C2411yescharacteristic
136Q8×C47—26no—
137Q8×C47C2×D414yes—
138D4×C47—26no—
139D4×C47—43no—
140C2×C4×C47—26no—
141C2×C4×C47—26no—
142C2×C4×C47C2411yescharacteristic
143C2×C4×C47C2413yes—
144C2×C4×C47C2413yes—
145C2×C4×C47C2411yescharacteristic
146C2×C4×C47C2413yes—
147C22⋊D47—22no—
148C22⋊D47—26no—
149C22⋊D47—26no—
150C22⋊D47—26no—
151C22⋊D47—26no—
152C22⋊D47—22no—
153C22⋊D47—46no—
154C2×Dic47—212no—
155C2×Dic47C2413yes—
156C2×Dic47C2413yes—
157C2×Dic47C2411yescharacteristic
158C2×Dic47C2413yes—
159C2×Dic47C2411yescharacteristic
160D188—22no—
161D188—26no—
162D188—26no—
163D188—43no—
164C4×D47—26no—
165C4×D47—26no—
166C4×D47—212no—
167C4×D47—22no—
168C4×D47—43no—
169C4×D47C2×D4112yes—
170Dic94—26no—
171Dic94—26no—
172Dic94—26no—
173Dic94C2×D4112yes—
174C22×C47—23no—
175C22×C47—21no—
176C22×C47—21no—
177C22×C47—23no—
178C22×C47—23no—
179C22×C47—21no—
180C22×C47C2511yescharacteristic
181C2×D47—21no—
182C2×D47—21no—
183C2×D47—23no—
184C2×D47—21no—
185C2×D47—23no—
186C2×D47—21no—
187C2×D47—21no—
188C2×D47—23no—
189C2×D47C22×D412yes—
190C4×C47—21no—
191C4×C47—23no—
192C4×C47—21no—
193C4×C47—23no—
194C4×C47C22×D416yes—
195Dic47—21no—
196Dic47—23no—
197Dic47—23no—
198Dic47C22×D416yes—
199Dic472−1+412yescomplemented
200#3497—471nomaximal, Sylow
201C2×C47—43no—
202C2×C47—41no—
203C2×C47C23×D411yescharacteristic
204C2×C47C2×2−1+411yescharacteristic
205C2×C47#58511yescharacteristic
206D47—22no—
207D47—43no—
208D47—41no—
209C2×2−1+4—471no—
210C2×2−1+4—471no—
211#550—471no—
212#550—473no—
213D4×Q8—471no—
214D4×Q8—473no—
215#548—473no—
216#548—471no—
217#548—473no—
218#548D4711yescharacteristic, complemented
219#537—473no—
220#537—473no—
221#532—473no—
222#532—473no—
223C2×C4×Q8—471no—
224C47#349711yescharacteristic, complemented, Sylow
2252−1+4—948no—
2262−1+4—948no—
227C2×#41—473no—
228C2×#41—471no—
229C2×#41—473no—
230C2×#41—473no—
231C2×#41—473no—
232C2×#41—473no—
233C2×#41—473no—
234C2×#41C2×D4711yescharacteristic
235C22×Q8—471no—
236C22×Q8—473no—
237C22×Q8—471no—
238C22×Q8—473no—
239C22×Q8C2×D4711yescharacteristic
240C4⋊Q8—473no—
241C4⋊Q8—473no—
242#127—473no—
243#127—473no—
244#124—473no—
245#124—473no—
246#124—473no—
247#124C2×D4713yes—
248C22⋊Q8—473no—
249C22⋊Q8—473no—
250C22⋊Q8—476no—
251C22⋊Q8—473no—
252C22⋊Q8—476no—
253C22⋊Q8C2×D4713yes—
254#121—473no—
255#121—473no—
256#121—476no—
257#121—473no—
258#121—473no—
259#121—473no—
260#121—473no—
261#121—471no—
262#121—476no—
263#121—476no—
264#121C2×D4713yes—
265C4×Q8—471no—
266C4×Q8—473no—
267C4×Q8—473no—
268C4×Q8C2×D4711yescharacteristic
269C4×D4—473no—
270C4×D4—473no—
271C4×D4—476no—
272C4×D4—476no—
273C4×D4—473no—
274C4×D4C2×D4713yes—
275C2×C4⋊C4—473no—
276C2×C42—473no—
277#41—24no—
278#41—9412no—
279#41—9412no—
280#41—9412no—
281#41—9412no—
282#41—9412no—
283#41—9412no—
284#41—944no—
285C2×Q8—24no—
286C2×Q8—478no—
287C2×Q8—473no—
288C2×Q8—473no—
289C2×Q8—473no—
290C2×Q8—473no—
291C2×Q8—9412no—
292C2×Q8—9412no—
293C2×Q8—944no—
294C2×Q8C22×D4713yes—
295C2×Q8C22×D4711yescharacteristic
296C2×D4—471no—
297C2×D4—473no—
298C2×D4—471no—
299C2×D4—473no—
300C2×D4—473no—
301C2×D4—473no—
302C2×D4—476no—
303C2×D4—471no—
304C2×D4—473no—
305C2×D4—473no—
306C2×D4—473no—
307C2×D4C22×D4713yes—
308C2×D4C22×D4713yes—
309C22×C4—473no—
310C22×C4—476no—
311C22×C4—471no—
312C22×C4—476no—
313C22×C4—473no—
314C22×C4—473no—
315C22×C4—473no—
316C22×C4C22×D4713yes—
317C22×C4C22×D4713yes—
318C4⋊C4—476no—
319C4⋊C4—471no—
320C4⋊C4—473no—
321C4⋊C4—476no—
322C4⋊C4—473no—
323C4⋊C4—473no—
324C4⋊C4C22×D4713yes—
325C4⋊C4C22×D4713yes—
326C22⋊C4—473no—
327C22⋊C4—473no—
328C22⋊C4—473no—
329C22⋊C4—471no—
330C22⋊C4—473no—
331C22⋊C4—473no—
332C22⋊C4—476no—
333C22⋊C4C22×D4713yes—
334C22⋊C4C22×D4716yes—
335C22⋊C4C22×D4711yescharacteristic
336C42—473no—
337C42—473no—
338C42—473no—
339C42C22×D4713yes—
340C23—471no—
341C23—471no—
342C23—473no—
343C23C23×D4711yescharacteristic
344C23C23×D4713yes—
345Q8—26no—
346Q8—4712no—
347Q8—946no—
348Q8—946no—
349Q8—946no—
350Q8D4×D4714yes—
351D4—26no—
352D4—43no—
353D4—942no—
354D4—946no—
355D4—942no—
356D4—946no—
357D4—946no—
358D4—946no—
359D4—942no—
360D4—946no—
361D4—946no—
362D4—1883no—
363D4—1886no—
364C2×C4—26no—
365C2×C4—26no—
366C2×C4—471no—
367C2×C4—473no—
368C2×C4—4712no—
369C2×C4—473no—
370C2×C4—473no—
371C2×C4—471no—
372C2×C4—942no—
373C2×C4—9412no—
374C2×C4—9412no—
375C2×C4—946no—
376C2×C4—946no—
377C2×C4—1883no—
378C2×C4C23×D4711yescharacteristic
379C2×C4C23×D4713yes—
380C2×C4C23×D4711yescharacteristic
381C2×C4C23×D4713yes—
382C2×C4C23×D4713yes—
383C22—21no—
384C22—23no—
385C22—21no—
386C22—23no—
387C22—21no—
388C22—23no—
389C22—472no—
390C22—941no—
391C22—941no—
392C22—943no—
393C22—941no—
394C22—941no—
395C22—943no—
396C22—941no—
397C22—943no—
398C22C24×D4711yescharacteristic
399C4—21no—
400C4—23no—
401C4—21no—
402C4—23no—
403C4—476no—
404C4—472no—
405C4—943no—
406C4—941no—
407C4—943no—
408C4C2×D4×D4716yes—
409C2—41no—
410C2—43no—
411C2—942no—
412C2—1883no—
413C2—1881no—
414C2C22×D4×D4711yescharacteristic
415C22−1+4×D4711yescharacteristic
416C2#1568995911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#548C2
hypercenter#548D47
hypocenterC47#3497
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#13094072C2semidirect
2. C2×#13094071C2semidirect
3. #15689792C2semidirect
4. #15689791C2semidirect
5. Q8×C22⋊D47C2semidirect
6. #15689786C2semidirect
7. #15689785C2semidirect
8. #15689782C2semidirect
9. #15689781C2semidirect
10. #15689703C2semidirect
11. #15689702C2semidirect
12. #15689672C2semidirect
13. #15689670C2semidirect
14. C4×Q8×D47C2semidirect
15. C47×#548C2semidirect
88. Q8×D47D4semidirect
199. Dic472−1+4semidirect
218. #548D47semidirect
224. C47#3497semidirect