Finite Group Databasebeta

← #20257065

Subgroups — #20257065

Order 6016.

1522 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094072C211yesmaximal, characteristic, complemented
2C22×#10625354C211yesmaximal, characteristic, complemented
3Q8×C22⋊D47C211yesmaximal, characteristic, complemented
4#15689785C211yesmaximal, characteristic, complemented
5#15689784C211yesmaximal, characteristic, complemented
6#15689776C213yesmaximal, complemented
7#15689775C213yesmaximal, complemented
8#15689769C213yesmaximal, complemented
9#15689764C213yesmaximal, complemented
10#15689703C213yesmaximal, complemented
11#15689698C213yesmaximal, complemented
12#15689632C213yesmaximal, complemented
13C22⋊Q8×D47C213yesmaximal, complemented
14#15689605C211yesmaximal, characteristic, complemented
15D4×Q8×C47C211yesmaximal, characteristic, complemented
16#13094072—28no—
17C2×#10625354—28no—
18C2×#10625354C2213yes—
19C2×#10625354C2211yescharacteristic
20C2×#10625354C2213yes—
21C2×#10625354C2211yescharacteristic
22C2×#10625354C2213yescomplemented
23C2×#10625350C2213yescomplemented
24C2×#10625350C2213yescomplemented
25C2×Q8×D47C2211yescharacteristic, complemented
26C2×Q8×D47C2213yescomplemented
27C22×D188C2213yes—
28C22×C4×D47C2213yes—
29#13094022C2213yescomplemented
30#13094013C2213yescomplemented
31#13094012C2213yescomplemented
32#13094009C2216yescomplemented
33#13094009C2216yescomplemented
34#13094009C2213yescomplemented
35#13094006C2213yescomplemented
36#13094004C2213yescomplemented
37#13094003C2213yes—
38#13094002C2216yescomplemented
39#13094002C2213yescomplemented
40#13094001C2213yes—
41#13094000C2213yescomplemented
42#13094000C2213yescomplemented
43#13093999C2216yescomplemented
44#13093999C2213yescomplemented
45#13093998C2213yescomplemented
46#13093997C2216yescomplemented
47#13093997C2213yescomplemented
48#13093996C2211yescharacteristic
49#13093994C2213yes—
50#13093992C2213yes—
51Q8×Dic47C2211yescharacteristic, complemented
52C4×D188C2213yescomplemented
53C4×D188C2213yescomplemented
54#13093986C2213yescomplemented
55C4×C22⋊D47C2213yes—
56C4×C22⋊D47C2213yescomplemented
57#13093981C2213yescomplemented
58C4⋊C4×D47C2216yescomplemented
59C4⋊C4×D47C2213yescomplemented
60C22⋊C4×D47C2216yes—
61C22×Q8×C47C2211yescharacteristic
62C22×Q8×C47C2211yescharacteristic, complemented
63C4⋊Q8×C47C2213yescomplemented
64C22⋊Q8×C47C2213yes—
65C22⋊Q8×C47C2213yescomplemented
66C4×Q8×C47C2211yescharacteristic, complemented
67C4×D4×C47C2213yes—
68C23×D47C2313yes—
69C2×Q8×C47—24no—
70C2×Q8×C47—24no—
71C2×Q8×C47C2313yes—
72C2×Q8×C47C2313yes—
73C2×Q8×C47C2311yescharacteristic
74C2×D4×C47C2311yescharacteristic
75C22×C4×C47C2313yes—
76C22×C4×C47C2313yes—
77C2×C22⋊D47C2311yescharacteristic
78C2×C22⋊D47C2313yes—
79C2×C22⋊D47C2311yescharacteristic
80C2×C22⋊D47C2313yes—
81C22×Dic47C2311yescharacteristic
82#10625354—24no—
83#10625354—212no—
84#10625354—212no—
85#10625354—212no—
86#10625354D418yescomplemented
87Q8×D47—24no—
88Q8×D47—212no—
89#10625350—212no—
90#10625350—212no—
91C2×D188—212no—
92C2×D188C2313yes—
93C2×D188C2316yes—
94C2×D188C2313yes—
95C2×D188C2313yes—
96C2×D188C2313yes—
97C2×C4×D47—212no—
98C2×C4×D47C2316yes—
99C2×C4×D47C2313yes—
100C2×C4×D47C2313yes—
101C2×C4×D47C2313yes—
102C2×C4×D47C2313yes—
103C2×C4×D47C2316yes—
104C2×C4×D47C2313yes—
105C2×Dic94C2313yes—
106C2×Dic94C2313yes—
107C4⋊C4×C47C2313yes—
108C4⋊C4×C47C2313yes—
109C4⋊C4×C47C2316yes—
110C22⋊C4×C47C2313yes—
111C22⋊C4×C47C2313yes—
112C42×C47C2313yes—
113C22⋊Dic47C2313yes—
114C22⋊Dic47C2311yescharacteristic
115(C2×D47)⋊C4C2316yes—
116(C2×D47)⋊C4C2316yes—
117(C2×D47)⋊C4C2313yes—
118(C2×D47)⋊C4C2313yes—
119(C2×D47)⋊C4C2313yes—
120(C2×D47)⋊C4C2313yes—
121(C2×D47)⋊C4C2311yescharacteristic
122(C2×D47)⋊C4C2313yes—
123C4⋊Dic47C2313yes—
124C4⋊Dic47C2313yes—
125Dic47⋊C4C2313yes—
126Dic47⋊C4C2313yes—
127Dic47⋊C4C2316yes—
128Dic47⋊C4C2311yescharacteristic
129Dic47⋊C4C2313yes—
130C4×Dic47C2313yes—
131C23×C47C2411yescharacteristic
132C23×C47C2411yescharacteristic
133C22×D47—26no—
134C22×D47—26no—
135C22×D47—43no—
136C22×D47C2413yes—
137C22×D47C2411yescharacteristic
138C22×D47C2413yes—
139Q8×C47—26no—
140Q8×C47—26no—
141Q8×C47C2×D414yes—
142D4×C47—22no—
143C2×C4×C47—26no—
144C2×C4×C47—26no—
145C2×C4×C47C2413yes—
146C2×C4×C47C2413yes—
147C2×C4×C47C2411yescharacteristic
148C2×C4×C47C2413yes—
149C2×C4×C47C2413yes—
150C22⋊D47—22no—
151C22⋊D47—26no—
152C22⋊D47—22no—
153C22⋊D47—43no—
154C2×Dic47—22no—
155C2×Dic47C2411yescharacteristic
156C2×Dic47C2413yes—
157C2×Dic47C2411yescharacteristic
158C2×Dic47C2413yes—
159C2×Dic47C2411yescharacteristic
160D188—212no—
161D188—26no—
162D188—26no—
163D188—43no—
164D188C2×D4112yes—
165C4×D47—26no—
166C4×D47—212no—
167C4×D47—26no—
168C4×D47—26no—
169C4×D47—26no—
170C4×D47—46no—
171C4×D47C2×D4112yes—
172Dic94—26no—
173Dic94—26no—
174C22×C47—21no—
175C22×C47—21no—
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—21no—
179C22×C472−1+412yescomplemented
180C22×C47C2511yescharacteristic
181C2×D47—23no—
182C2×D47—23no—
183C2×D47—21no—
184C2×D47—23no—
185C2×D47—21no—
186C2×D47—23no—
187C2×D47—21no—
188C2×D47—23no—
189C2×D47—412no—
190C2×D47C22×D416yes—
191C4×C47—23no—
192C4×C47—23no—
193C4×C47—21no—
194C4×C47—23no—
195C4×C47C22×D416yes—
196Dic47—23no—
197Dic47—21no—
198Dic47—21no—
199Dic47—23no—
200Dic47C22×D412yes—
201#3489—471nomaximal, Sylow
202C2×C47—22no—
203C2×C47—41no—
204C2×C47C23×D411yescharacteristic
205C2×C47C2×2−1+411yescharacteristic
206C2×C47#58511yescharacteristic
207D47—26no—
208D47—41no—
209D47—43no—
210C2×2−1+4—471no—
211C22×#41—471no—
212D4×Q8—471no—
213D4×Q8D4711yescharacteristic, complemented
214#548—471no—
215#548—471no—
216#547—473no—
217#547—473no—
218#546—473no—
219#546—473no—
220#537—473no—
221#536—473no—
222#525—473no—
223C2×C22⋊Q8—473no—
224#520—471no—
225C47#348911yescharacteristic, complemented, Sylow
2262−1+4—948no—
227C2×#41—471no—
228C2×#41—473no—
229C2×#41—473no—
230C2×#41—473no—
231C2×#41—471no—
232C2×#41—473no—
233C2×#41—473no—
234C2×#41—948no—
235C22×Q8—473no—
236C22×Q8—471no—
237C22×Q8C2×D4711yescharacteristic
238C22×Q8C2×D4711yescharacteristic, complemented
239C22×D4—473no—
240C23×C4—473no—
241C4⋊Q8—473no—
242C4⋊Q8C2×D4713yescomplemented
243#124—473no—
244#124—473no—
245#123—473no—
246#123—476no—
247#123—476no—
248#123—473no—
249C22⋊Q8—473no—
250C22⋊Q8—473no—
251C22⋊Q8—473no—
252C22⋊Q8—476no—
253C22⋊Q8—473no—
254C22⋊Q8—473no—
255C22⋊Q8—473no—
256C22⋊Q8C2×D4713yes—
257C22⋊Q8C2×D4713yescomplemented
258#121—471no—
259#121—473no—
260#121—476no—
261#121—473no—
262#121—473no—
263#121—476no—
264#120—473no—
265#120—473no—
266C4×Q8—471no—
267C4×Q8C2×D4711yescharacteristic, complemented
268C4×D4—473no—
269C4×D4—473no—
270C4×D4—473no—
271C4×D4—473no—
272C4×D4—473no—
273C4×D4C2×D4713yes—
274#117—473no—
275C2×C4⋊C4—473no—
276C2×C4⋊C4—476no—
277C2×C22⋊C4—476no—
278C24—473no—
279#41—478no—
280#41—9412no—
281#41—9412no—
282#41—9412no—
283#41—9412no—
284#41—9412no—
285#41—944no—
286C2×Q8—24no—
287C2×Q8—24no—
288C2×Q8—473no—
289C2×Q8—473no—
290C2×Q8—9412no—
291C2×Q8—944no—
292C2×Q8C22×D4713yes—
293C2×Q8C22×D4713yes—
294C2×Q8C22×D4711yescharacteristic
295C2×D4—471no—
296C2×D4—473no—
297C2×D4—471no—
298C2×D4—473no—
299C2×D4—473no—
300C2×D4—473no—
301C2×D4—476no—
302C2×D4—473no—
303C2×D4—473no—
304C2×D4—9412no—
305C2×D4C22×D4711yescharacteristic
306C22×C4—473no—
307C22×C4—471no—
308C22×C4—476no—
309C22×C4—473no—
310C22×C4—473no—
311C22×C4—473no—
312C22×C4—473no—
313C22×C4—476no—
314C22×C4—9412no—
315C22×C4C22×D4713yes—
316C22×C4C22×D4713yes—
317C4⋊C4—473no—
318C4⋊C4—473no—
319C4⋊C4—476no—
320C4⋊C4—471no—
321C4⋊C4—473no—
322C4⋊C4—473no—
323C4⋊C4—473no—
324C4⋊C4C22×D4713yes—
325C4⋊C4C22×D4716yes—
326C4⋊C4C22×D4713yes—
327C22⋊C4—473no—
328C22⋊C4—471no—
329C22⋊C4—476no—
330C22⋊C4—476no—
331C22⋊C4—473no—
332C22⋊C4—473no—
333C22⋊C4—471no—
334C22⋊C4—473no—
335C22⋊C4—473no—
336C22⋊C4—473no—
337C22⋊C4C22×D4713yes—
338C22⋊C4C22×D4713yes—
339C42—473no—
340C42C22×D4713yes—
341C23—473no—
342C23—473no—
343C23—471no—
344C23—946no—
345C23—946no—
346C23—1883no—
347C23C23×D4711yescharacteristic
348C23C23×D4711yescharacteristic
349Q8—26no—
350Q8—26no—
351Q8—946no—
352Q8—946no—
353Q8D4×D4714yes—
354D4—22no—
355D4—4712no—
356D4—9412no—
357D4—946no—
358D4—942no—
359D4—946no—
360D4—942no—
361D4—946no—
362D4—1883no—
363D4—1883no—
364C2×C4—26no—
365C2×C4—26no—
366C2×C4—471no—
367C2×C4—4712no—
368C2×C4—471no—
369C2×C4—473no—
370C2×C4—473no—
371C2×C4—471no—
372C2×C4—946no—
373C2×C4—946no—
374C2×C4—9412no—
375C2×C4—942no—
376C2×C4—946no—
377C2×C4—946no—
378C2×C4—1886no—
379C2×C4C23×D4711yescharacteristic
380C2×C4C23×D4713yes—
381C2×C4C23×D4713yes—
382C2×C4C23×D4713yes—
383C2×C4C23×D4713yes—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—476no—
390C22—943no—
391C22—943no—
392C22—941no—
393C22—943no—
394C22—941no—
395C22—943no—
396C22—941no—
397C22—943no—
398C22—18812no—
399C22#1309407212yescomplemented
400C22C24×D4711yescharacteristic
401C4—23no—
402C4—23no—
403C4—21no—
404C4—23no—
405C4—472no—
406C4—941no—
407C4—943no—
408C4—941no—
409C4—943no—
410C4C2×D4×D4716yes—
411C2—22no—
412C2—41no—
413C2—946no—
414C2—1883no—
415C2—1881no—
416C2C22×D4×D4711yescharacteristic
417C2C2×#1309407211yescharacteristic
418C2#1568996011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingD4×Q8×C47C2
hypercenterD4×Q8D47
hypocenterC47#3489
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#13094072C2semidirect
2. C22×#10625354C2semidirect
3. Q8×C22⋊D47C2semidirect
4. #15689785C2semidirect
5. #15689784C2semidirect
6. #15689776C2semidirect
7. #15689775C2semidirect
8. #15689769C2semidirect
9. #15689764C2semidirect
10. #15689703C2semidirect
11. #15689698C2semidirect
12. #15689632C2semidirect
13. C22⋊Q8×D47C2semidirect
14. #15689605C2semidirect
15. D4×Q8×C47C2semidirect
22. C2×#10625354C22semidirect
23. C2×#10625350C22semidirect
24. C2×#10625350C22semidirect
25. C2×Q8×D47C22semidirect
26. C2×Q8×D47C22semidirect
29. #13094022C22semidirect
30. #13094013C22semidirect
31. #13094012C22semidirect
32. #13094009C22semidirect
33. #13094009C22semidirect
34. #13094009C22semidirect
35. #13094006C22semidirect
36. #13094004C22semidirect
38. #13094002C22semidirect
39. #13094002C22semidirect
41. #13094000C22semidirect
42. #13094000C22semidirect
43. #13093999C22semidirect
44. #13093999C22semidirect
45. #13093998C22semidirect
46. #13093997C22semidirect
47. #13093997C22semidirect
51. Q8×Dic47C22semidirect
52. C4×D188C22semidirect
53. C4×D188C22semidirect
54. #13093986C22semidirect
56. C4×C22⋊D47C22semidirect
57. #13093981C22semidirect
58. C4⋊C4×D47C22semidirect
59. C4⋊C4×D47C22semidirect
62. C22×Q8×C47C22semidirect
63. C4⋊Q8×C47C22semidirect
65. C22⋊Q8×C47C22semidirect
66. C4×Q8×C47C22semidirect
86. #10625354D4semidirect
179. C22×C472−1+4semidirect
213. D4×Q8D47semidirect
225. C47#3489semidirect
238. C22×Q8C2×D47semidirect
242. C4⋊Q8C2×D47semidirect
257. C22⋊Q8C2×D47semidirect
267. C4×Q8C2×D47semidirect
399. C22#13094072semidirect