Finite Group Databasebeta

← #20257034

Subgroups — #20257034

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×#13094071C211yesmaximal, characteristic, complemented
2C22×Q8×D47C211yesmaximal, characteristic, complemented
3Q8×D188C211yesmaximal, characteristic, complemented
4D4×Dic94C213yesmaximal, complemented
5Q8×C22⋊D47C211yesmaximal, characteristic, complemented
6#15689786C213yesmaximal, complemented
7#15689781C213yesmaximal, complemented
8#15689780C211yesmaximal, characteristic, complemented
9#15689779C213yesmaximal, complemented
10#15689696C213yesmaximal, complemented
11#15689693C213yesmaximal, complemented
12#15689633C213yesmaximal, complemented
13#15689632C213yesmaximal, complemented
14#15689599C211yesmaximal, characteristic, complemented
15C47×#548C211yesmaximal, characteristic, complemented
16#13094071—28no—
17C2×#10625350C2213yes—
18C2×#10625352C2213yes—
19C2×#10625352C2213yescomplemented
20C22×Dic94C2213yes—
21C22×Dic94C2213yescomplemented
22C2×Q8×D47—28no—
23C2×Q8×D47C2211yescharacteristic
24C2×Q8×D47C2213yes—
25C2×Q8×D47C2213yes—
26C2×Q8×D47C2211yescharacteristic
27C2×Q8×D47C2211yescharacteristic, complemented
28C22×C4×D47C2213yes—
29#13094024C2213yescomplemented
30#13094023C2216yescomplemented
31#13094022C2213yescomplemented
32#13094011C2213yescomplemented
33#13094010C2216yescomplemented
34#13094009C2213yes—
35#13094006C2213yes—
36#13094006C2216yes—
37#13094004C2213yes—
38#13094004C2213yescomplemented
39#13094003C2213yes—
40#13094003C2213yescomplemented
41#13094002C2213yes—
42#13094001C2213yes—
43#13094001C2216yescomplemented
44#13094001C2216yescomplemented
45#13094000C2213yescomplemented
46#13093997C2213yes—
47#13093996C2213yes—
48#13093995C2213yes—
49#13093994C2211yescharacteristic
50#13093992C2213yes—
51Q8×Dic47C2211yescharacteristic, complemented
52C4×Dic94C2213yescomplemented
53#13093989C2213yescomplemented
54C4×D188C2213yes—
55D4×Dic47C2216yes—
56C4×C22⋊D47C2213yes—
57C4×C22⋊D47C2213yes—
58(C22⋊D47)⋊C4C2216yes—
59#13093982C2213yes—
60#13093981C2213yes—
61C2×#41×C47C2211yescharacteristic, complemented
62C22×Q8×C47C2211yescharacteristic
63#124×C47C2213yescomplemented
64C22⋊Q8×C47C2213yescomplemented
65#121×C47C2213yes—
66C4×Q8×C47C2211yescharacteristic, complemented
67C4×D4×C47C2213yes—
68C23×D47C2311yescharacteristic
69#41×C47—24no—
70C2×Q8×C47—24no—
71C2×Q8×C47C2313yes—
72C2×Q8×C47C2311yescharacteristic
73C2×D4×C47C2313yes—
74C2×D4×C47C2313yes—
75C22×C4×C47C2313yes—
76C22×C4×C47C2313yes—
77C2×C22⋊D47C2313yes—
78C2×C22⋊D47C2311yescharacteristic
79C2×C22⋊D47C2313yes—
80C2×C22⋊D47C2313yes—
81C22×Dic47C2316yes—
82C22×Dic47C2313yes—
83Q8×D47—24no—
84Q8×D47—24no—
85Q8×D47—212no—
86Q8×D47—212no—
87Q8×D47D418yescomplemented
88#10625352—212no—
89#10625352—212no—
90#10625350—212no—
91C2×D188C2311yescharacteristic
92C2×D188C2311yescharacteristic
93C2×C4×D47—212no—
94C2×C4×D47C2313yes—
95C2×C4×D47C2313yes—
96C2×C4×D47C2313yes—
97C2×C4×D47C2313yes—
98C2×C4×D47C2313yes—
99C2×Dic94—212no—
100C2×Dic94—212no—
101C2×Dic94C2313yes—
102C2×Dic94C2316yes—
103C2×Dic94C2313yes—
104C2×Dic94C2313yes—
105C2×Dic94C2313yes—
106C4⋊C4×C47C2313yes—
107C4⋊C4×C47C2313yes—
108C22⋊C4×C47C2311yescharacteristic
109C22⋊C4×C47C2313yes—
110C22⋊C4×C47C2316yes—
111C42×C47C2313yes—
112C22⋊Dic47C2313yes—
113C22⋊Dic47C2313yes—
114C22⋊Dic47C2316yes—
115(C2×D47)⋊C4C2311yescharacteristic
116(C2×D47)⋊C4C2313yes—
117(C2×D47)⋊C4C2313yes—
118(C2×D47)⋊C4C2311yescharacteristic
119(C2×D47)⋊C4C2313yes—
120(C2×D47)⋊C4C2313yes—
121C4⋊Dic47C2313yes—
122C4⋊Dic47C2316yes—
123C4⋊Dic47C2313yes—
124Dic47⋊C4C2313yes—
125Dic47⋊C4C2313yes—
126Dic47⋊C4C2316yes—
127Dic47⋊C4C2313yes—
128Dic47⋊C4C2313yes—
129C4×Dic47C2313yes—
130C4×Dic47C2316yes—
131C23×C47C2413yes—
132C23×C47C2411yescharacteristic
133C22×D47—22no—
134C22×D47—22no—
135C22×D47—22no—
136C22×D47C2411yescharacteristic
137C22×D47C2411yescharacteristic
138C22×D47C2411yescharacteristic
139Q8×C47—26no—
140Q8×C47C2×D414yes—
141D4×C47—26no—
142D4×C47—26no—
143C2×C4×C47—26no—
144C2×C4×C47—26no—
145C2×C4×C47C2413yes—
146C2×C4×C47C2411yescharacteristic
147C2×C4×C47C2413yes—
148C2×C4×C47C2411yescharacteristic
149C2×C4×C47C2413yes—
150C22⋊D47—22no—
151C22⋊D47—26no—
152C22⋊D47—26no—
153C22⋊D47—26no—
154C2×Dic47—26no—
155C2×Dic47—212no—
156C2×Dic47C2411yescharacteristic
157C2×Dic47C2413yes—
158C2×Dic47C2413yes—
159C2×Dic47C2413yes—
160C2×Dic47C2413yes—
161D188—22no—
162D188—22no—
163C4×D47—26no—
164C4×D47—26no—
165C4×D47—26no—
166C4×D47—26no—
167C4×D47C2×D4112yes—
168Dic94—26no—
169Dic94—26no—
170Dic94—26no—
171Dic94—212no—
172Dic94C2×D4112yes—
173C22×C47—21no—
174C22×C47—21no—
175C22×C47—23no—
176C22×C47—23no—
177C22×C47—23no—
178C22×C472−1+412yescomplemented
179C22×C47C2511yescharacteristic
180C2×D47—28no—
181C2×D47—21no—
182C2×D47—21no—
183C2×D47—21no—
184C2×D47—21no—
185C2×D47—21no—
186C2×D47—21no—
187C2×D47—21no—
188C2×D47C22×D412yes—
189C2×D472−1+412yescomplemented
190C4×C47—21no—
191C4×C47—23no—
192C4×C47—21no—
193C4×C47—23no—
194C4×C47C22×D416yes—
195Dic47—23no—
196Dic47—23no—
197Dic47—23no—
198Dic47—21no—
199Dic47C22×D416yes—
200#3486—471nomaximal, Sylow
201C2×C47—22no—
202C2×C47—43no—
203C2×C47C23×D411yescharacteristic
204C2×C47C2×2−1+411yescharacteristic
205C2×C47C2×2−1+411yescharacteristic
206D47—22no—
207D47—22no—
208D47—41no—
209C2×2−1+4—471no—
210C23×Q8—471no—
211D4×Q8—471no—
212D4×Q8—473no—
213D4×Q8—471no—
214D4×Q8—473no—
215#548—471no—
216#548—473no—
217#548—473no—
218#548D4711yescharacteristic, complemented
219#536—473no—
220#536—473no—
221#525—473no—
222#525—473no—
223#519—471no—
224C47#348611yescharacteristic, complemented, Sylow
2252−1+4—948no—
226C2×#41—473no—
227C2×#41—473no—
228C2×#41—473no—
229C2×#41C2×D4711yescharacteristic, complemented
230C22×Q8—471no—
231C22×Q8—473no—
232C22×Q8—473no—
233C22×Q8—471no—
234C22×Q8—471no—
235C22×Q8—473no—
236C22×Q8—473no—
237C22×Q8—948no—
238C22×Q8C2×D4711yescharacteristic
239C23×C4—473no—
240C4⋊Q8—473no—
241C4⋊Q8—476no—
242C4⋊Q8—473no—
243#124—473no—
244#124—476no—
245#124C2×D4713yescomplemented
246#123—473no—
247#123—476no—
248#123—473no—
249C22⋊Q8—473no—
250C22⋊Q8—473no—
251C22⋊Q8—473no—
252C22⋊Q8—473no—
253C22⋊Q8—473no—
254C22⋊Q8—473no—
255C22⋊Q8—473no—
256C22⋊Q8—476no—
257C22⋊Q8—476no—
258C22⋊Q8C2×D4713yescomplemented
259#121—473no—
260#121—473no—
261#121—473no—
262#121C2×D4713yes—
263#120—473no—
264#120—471no—
265C4×Q8—471no—
266C4×Q8—473no—
267C4×Q8—473no—
268C4×Q8C2×D4711yescharacteristic, complemented
269C4×D4—476no—
270C4×D4—473no—
271C4×D4—473no—
272C4×D4—476no—
273C4×D4—473no—
274C4×D4C2×D4713yes—
275#117—473no—
276#117—473no—
277C24—471no—
278#41—24no—
279#41—9412no—
280#41—9412no—
281#41—9412no—
282C2×Q8—24no—
283C2×Q8—478no—
284C2×Q8—473no—
285C2×Q8—476no—
286C2×Q8—473no—
287C2×Q8—473no—
288C2×Q8—473no—
289C2×Q8—9412no—
290C2×Q8—9412no—
291C2×Q8—9412no—
292C2×Q8—9412no—
293C2×Q8—944no—
294C2×Q8—944no—
295C2×Q8C22×D4713yes—
296C2×Q8C22×D4711yescharacteristic
297C2×D4—473no—
298C2×D4—471no—
299C2×D4—473no—
300C2×D4—473no—
301C2×D4—471no—
302C2×D4—471no—
303C2×D4C22×D4713yes—
304C2×D4C22×D4713yes—
305C22×C4—473no—
306C22×C4—473no—
307C22×C4—476no—
308C22×C4—473no—
309C22×C4—473no—
310C22×C4—473no—
311C22×C4—473no—
312C22×C4—9412no—
313C22×C4C22×D4713yes—
314C22×C4C22×D4713yes—
315C4⋊C4—473no—
316C4⋊C4—473no—
317C4⋊C4—473no—
318C4⋊C4—476no—
319C4⋊C4—473no—
320C4⋊C4—473no—
321C4⋊C4—476no—
322C4⋊C4—473no—
323C4⋊C4C22×D4713yes—
324C4⋊C4C22×D4713yes—
325C22⋊C4—473no—
326C22⋊C4—473no—
327C22⋊C4—476no—
328C22⋊C4—473no—
329C22⋊C4—471no—
330C22⋊C4—471no—
331C22⋊C4—473no—
332C22⋊C4—473no—
333C22⋊C4—473no—
334C22⋊C4C22×D4716yes—
335C22⋊C4C22×D4711yescharacteristic
336C22⋊C4C22×D4713yes—
337C42—476no—
338C42—473no—
339C42C22×D4713yes—
340C23—471no—
341C23—471no—
342C23—471no—
343C23—942no—
344C23—942no—
345C23—942no—
346C23C23×D4713yes—
347C23C23×D4711yescharacteristic
348Q8—26no—
349Q8—4712no—
350Q8—9412no—
351Q8—946no—
352Q8—946no—
353Q8—946no—
354Q8D4×D4714yes—
355D4—26no—
356D4—26no—
357D4—942no—
358D4—942no—
359D4—946no—
360D4—946no—
361D4—946no—
362D4—942no—
363C2×C4—26no—
364C2×C4—26no—
365C2×C4—473no—
366C2×C4—4712no—
367C2×C4—473no—
368C2×C4—471no—
369C2×C4—473no—
370C2×C4—473no—
371C2×C4—946no—
372C2×C4—946no—
373C2×C4—946no—
374C2×C4—9412no—
375C2×C4—946no—
376C2×C4—946no—
377C2×C4C23×D4713yes—
378C2×C4C23×D4711yescharacteristic
379C2×C4C23×D4713yes—
380C2×C4C23×D4711yescharacteristic
381C2×C4C23×D4713yes—
382C22—21no—
383C22—21no—
384C22—23no—
385C22—23no—
386C22—23no—
387C22—472no—
388C22—472no—
389C22—948no—
390C22—941no—
391C22—941no—
392C22—941no—
393C22—941no—
394C22—941no—
395C22—941no—
396C22—941no—
397C22#1309407112yescomplemented
398C22C24×D4711yescharacteristic
399C4—21no—
400C4—23no—
401C4—21no—
402C4—23no—
403C4—476no—
404C4—943no—
405C4—943no—
406C4—943no—
407C4—941no—
408C4C2×D4×D4716yes—
409C2—22no—
410C2—43no—
411C2—942no—
412C2—942no—
413C2—1881no—
414C2C22×D4×D4711yescharacteristic
415C22−1+4×D4711yescharacteristic
416C2C2×#1309407111yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#548C2
hypercenter#548D47
hypocenterC47#3486
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#13094071C2semidirect
2. C22×Q8×D47C2semidirect
3. Q8×D188C2semidirect
4. D4×Dic94C2semidirect
5. Q8×C22⋊D47C2semidirect
6. #15689786C2semidirect
7. #15689781C2semidirect
8. #15689780C2semidirect
9. #15689779C2semidirect
10. #15689696C2semidirect
11. #15689693C2semidirect
12. #15689633C2semidirect
13. #15689632C2semidirect
14. #15689599C2semidirect
15. C47×#548C2semidirect
19. C2×#10625352C22semidirect
21. C22×Dic94C22semidirect
27. C2×Q8×D47C22semidirect
29. #13094024C22semidirect
30. #13094023C22semidirect
31. #13094022C22semidirect
32. #13094011C22semidirect
33. #13094010C22semidirect
38. #13094004C22semidirect
40. #13094003C22semidirect
43. #13094001C22semidirect
44. #13094001C22semidirect
45. #13094000C22semidirect
51. Q8×Dic47C22semidirect
52. C4×Dic94C22semidirect
53. #13093989C22semidirect
61. C2×#41×C47C22semidirect
63. #124×C47C22semidirect
64. C22⋊Q8×C47C22semidirect
66. C4×Q8×C47C22semidirect
87. Q8×D47D4semidirect
178. C22×C472−1+4semidirect
189. C2×D472−1+4semidirect
218. #548D47semidirect
224. C47#3486semidirect
229. C2×#41C2×D47semidirect
245. #124C2×D47semidirect
258. C22⋊Q8C2×D47semidirect
268. C4×Q8C2×D47semidirect
397. C22#13094071semidirect