Finite Group Databasebeta

← #20254888

Subgroups — #20254888

Order 6016.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094052C211yesmaximal, characteristic, complemented
2C22×#10625325C211yesmaximal, characteristic, complemented
3#15689782C211yesmaximal, characteristic, complemented
4D4×D188C211yesmaximal, characteristic, complemented
5#15689512C211yesmaximal, characteristic, complemented
6#15689369C211yesmaximal, characteristic, complemented
7#15689359C211yesmaximal, characteristic, complemented
8#15689339C211yesmaximal, characteristic, complemented
9#15689324C211yesmaximal, characteristic, complemented
10#15689276C211yesmaximal, characteristic, complemented
11#15689270C211yesmaximal, characteristic, complemented
12#15689264C211yesmaximal, characteristic, complemented
13#15689259C211yesmaximal, characteristic, complemented
14#15689225C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic, complemented
17C22×Dic94C2211yescharacteristic, complemented
18C22×D188C2211yescharacteristic
19C22×D188C2211yescharacteristic
20C2×D4×D47—21no—
21#13094052—24no—
22C2×#10625325—24no—
23C2×#10625325C2211yescharacteristic
24C2×#10625325C2211yescharacteristic
25C2×#10625325C2211yescharacteristic, complemented
26C2×#10625325C2211yescharacteristic, complemented
27C2×#10625325C2211yescharacteristic, complemented
28C2×#10625325C2211yescharacteristic, complemented
29C2×D376C2211yescharacteristic
30C2×D376C2211yescharacteristic, complemented
31C2×D376C2211yescharacteristic, complemented
32#13094021C2211yescharacteristic
33#13094012C2211yescharacteristic, complemented
34#13094010—21no—
35#13094003C2211yescharacteristic, complemented
36#13094002—21no—
37#13093999—21no—
38#13093998C2211yescharacteristic
39#13093998C2211yescharacteristic
40#13093998C2211yescharacteristic, complemented
41#13093996—21no—
42#13093994—21no—
43#13093994—21no—
44C4×Dic94C2211yescharacteristic, complemented
45C4×D188C2211yescharacteristic
46(C22⋊D47)⋊C4—21no—
47#13093958C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093949C2211yescharacteristic, complemented
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic, complemented
52#13093946C2211yescharacteristic, complemented
53#13093946C2211yescharacteristic, complemented
54C2×M16×C47C2211yescharacteristic, complemented
55C22×C8×C47C2211yescharacteristic, complemented
56C4×D4×C47C2211yescharacteristic
57C4⋊C8×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic, complemented
59C22⋊C8×C47C2211yescharacteristic, complemented
60#97×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47—21no—
63C2×D4×C47D411yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C22×Dic47—21no—
71D4×D47—44no—
72#10625350—22no—
73#10625350—41no—
74C2×D188—22no—
75C2×D188—22no—
76C2×D188—21no—
77C2×D188—21no—
78C2×D188—21no—
79C2×D188—21no—
80C2×D188—41no—
81C2×D188—41no—
82C2×D188C2311yescharacteristic
83C2×D188C2311yescharacteristic
84C2×D188C2311yescharacteristic
85C2×D188C2311yescharacteristic
86C2×C4×D47—21no—
87C2×C4×D47—21no—
88C2×Dic94—22no—
89C2×Dic94—21no—
90C2×Dic94—41no—
91C2×Dic94C2311yescharacteristic
92C2×Dic94C2311yescharacteristic
93M16×C47—22no—
94C2×C8×C47—22no—
95C2×C8×C47C2311yescharacteristic
96C2×C8×C47C2311yescharacteristic
97C2×C8×C47C2311yescharacteristic
98C2×C8×C47C2311yescharacteristic
99C4⋊C4×C47D411yescharacteristic
100C22⋊C4×C47D411yescharacteristic
101C22⋊C4×C47D411yescharacteristic
102C42×C47C2311yescharacteristic
103C22⋊Dic47—21no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110C4⋊Dic47C2311yescharacteristic
111C4⋊Dic47C2311yescharacteristic
112Dic47⋊C4—21no—
113Dic47⋊C4—21no—
114C4×Dic47—21no—
115D376—22no—
116D376—22no—
117D376—41no—
118#10625325—22no—
119#10625325—22no—
120#10625325—22no—
121#10625325—22no—
122#10625325—41no—
123#10625325D414yescomplemented
124C23×C47C2×D411yescharacteristic
125C23×C47C2×D411yescharacteristic
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—21no—
130C22×D47—42no—
131C22×D47—42no—
132C22×D47—42no—
133C22×D47—42no—
134C22×D47—81no—
135C22×D47—81no—
136D4×C47—22no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47C2×D411yescharacteristic
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2×D411yescharacteristic
144C2×C4×C47C2×D411yescharacteristic
145C2×C4×C47C2411yescharacteristic
146C22⋊D47—42no—
147C22⋊D47—42no—
148C22⋊D47—42no—
149C22⋊D47—42no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—42no—
155D188—21no—
156D188—21no—
157D188—21no—
158D188—21no—
159D188—21no—
160D188—21no—
161D188—21no—
162D188—42no—
163D188—42no—
164D188—42no—
165D188—81no—
166D188C2×D412yes—
167C4×D47—42no—
168C4×D47—42no—
169Dic94—21no—
170Dic94—21no—
171Dic94—21no—
172Dic94—42no—
173Dic94C2×D412yescomplemented
174C8×C47—21no—
175C8×C47—21no—
176C8×C47—21no—
177C8×C47C2×D412yescomplemented
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—21no—
181C22×C47—21no—
182C22×C47—21no—
183C22×C47AGL(1,ℤ/8)12yescomplemented
184C22×C47C22×D411yescharacteristic
185C2×D47—22no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—41no—
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—41no—
195C2×D47—41no—
196C2×D47—41no—
197C2×D47—84no—
198C2×D47—84no—
199C4×C47—21no—
200C4×C47—21no—
201C4×C47—21no—
202C4×C47—21no—
203C4×C47C22×D411yescharacteristic
204C4×C47H(5,𝔽2)11yescharacteristic
205Dic47—22no—
206Dic47—41no—
207Dic47—41no—
208Dic47—41no—
209#3265—471nomaximal, Sylow
210C2×C47—22no—
211C2×C47—41no—
212C2×C47D4211yescharacteristic
213C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
214C2×C47#57711yescharacteristic
215D47—42no—
216D47—81no—
217D47—81no—
218D47—81no—
219C2×AGL(1,ℤ/8)—471no—
220C22×SD16—471no—
221#548—471no—
222D42—471no—
223#496—471no—
224#468—471no—
225#466—471no—
226#463—471no—
227#460—471no—
228#450—471no—
229#449—471no—
230#448—471no—
231#447—471no—
232#440—471no—
233#435D4711yescharacteristic, complemented
234C47#326511yescharacteristic, complemented, Sylow
235C2×#41—471no—
236C22×Q8—471no—
237C22×D4—471no—
238C22×D4—471no—
239C22×D4—941no—
240AGL(1,ℤ/8)—944no—
241C2×SD16—471no—
242C2×SD16—471no—
243C2×SD16—471no—
244C2×SD16—471no—
245C2×SD16—471no—
246C2×SD16—471no—
247C2×SD16—944no—
248C2×D8—471no—
249C2×D8—471no—
250C2×D8—471no—
251C2×M16C2×D4711yescharacteristic, complemented
252C22×C8C2×D4711yescharacteristic, complemented
253#127—471no—
254#124—471no—
255#124—941no—
256C22⋊Q8—471no—
257C22⋊Q8—941no—
258#121—471no—
259#121—471no—
260#121—471no—
261#121—941no—
262#121—941no—
263#120—941no—
264#120—941no—
265C4×Q8—471no—
266C4×D4—471no—
267C4×D4—941no—
268C4×D4C2×D4711yescharacteristic
269#107—471no—
270C4⋊C8C2×D4711yescharacteristic, complemented
271#103—471no—
272#103—471no—
273#102—471no—
274#102—471no—
275#102—471no—
276#102—471no—
277C22⋊C8C2×D4711yescharacteristic, complemented
278C22⋊C8C2×D4711yescharacteristic, complemented
279#97C2×D4711yescharacteristic, complemented
280C24—941no—
281C24—941no—
282#41—942no—
283#41—1881no—
284C2×Q8—471no—
285C2×Q8—471no—
286C2×Q8—942no—
287C2×Q8—941no—
288C2×Q8—1881no—
289C2×D4—471no—
290C2×D4—471no—
291C2×D4—471no—
292C2×D4—471no—
293C2×D4—942no—
294C2×D4—942no—
295C2×D4—941no—
296C2×D4—941no—
297C2×D4—941no—
298C2×D4—941no—
299C2×D4—941no—
300C2×D4—941no—
301C2×D4—941no—
302C2×D4—941no—
303C2×D4—1881no—
304C2×D4—1881no—
305C2×D4—1884no—
306C2×D4D18811yescharacteristic
307C22×C4—941no—
308C22×C4—941no—
309C22×C4—941no—
310C22×C4C22×D4711yescharacteristic
311C22×C4C22×D4711yescharacteristic
312SD16—474no—
313SD16—942no—
314SD16—942no—
315SD16—942no—
316SD16—942no—
317SD16—1881no—
318D8—942no—
319D8—942no—
320D8—1881no—
321M16—22no—
322C2×C8—22no—
323C2×C8C22×D4711yescharacteristic
324C2×C8C22×D4711yescharacteristic
325C2×C8C22×D4711yescharacteristic
326C2×C8C22×D4711yescharacteristic
327C4⋊C4—471no—
328C4⋊C4—471no—
329C4⋊C4—941no—
330C4⋊C4—941no—
331C4⋊C4D18811yescharacteristic
332C22⋊C4—941no—
333C22⋊C4—941no—
334C22⋊C4—941no—
335C22⋊C4—941no—
336C22⋊C4—941no—
337C22⋊C4—941no—
338C22⋊C4—941no—
339C22⋊C4D18811yescharacteristic
340C22⋊C4D18811yescharacteristic
341C42—941no—
342C42C22×D4711yescharacteristic
343C23—941no—
344C23—941no—
345C23—941no—
346C23—941no—
347C23—3761no—
348C23—3761no—
349C23—1882no—
350C23—1882no—
351C23—1882no—
352C23—1882no—
353C23C2×D18811yescharacteristic
354C23C2×D18811yescharacteristic
355Q8—472no—
356Q8—941no—
357Q8—941no—
358Q8—941no—
359Q8—1882no—
360D4—22no—
361D4—472no—
362D4—941no—
363D4—941no—
364D4—941no—
365D4—941no—
366D4—941no—
367D4—941no—
368D4—941no—
369D4—3761no—
370D4—1882no—
371D4—1882no—
372D4—1882no—
373D4—1882no—
374D4—1882no—
375D4—1882no—
376D4—1882no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—941no—
382C2×C4—941no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—1882no—
386C2×C4—1882no—
387C2×C4—1882no—
388C2×C4C2×D18811yescharacteristic
389C2×C4C2×D18811yescharacteristic
390C2×C4C2×D18811yescharacteristic
391C2×C4C2×D18811yescharacteristic
392C2×C4C23×D4711yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8D4×D4712yescomplemented
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—942no—
403C22—3764no—
404C22—3764no—
405C22—1881no—
406C22—1881no—
407C22—1881no—
408C22—1881no—
409C22—1881no—
410C22—1881no—
411C22—1881no—
412C22—1881no—
413C22—1881no—
414C22—1881no—
415C22—1881no—
416C22#1309405212yescomplemented
417C22C22×D18811yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—942no—
423C4—1881no—
424C4—1881no—
425C4—1881no—
426C4C2×D4×D4711yescharacteristic
427C4#1309407011yescharacteristic
428C2—22no—
429C2—41no—
430C2—3761no—
431C2—3761no—
432C2—3761no—
433C2—1882no—
434C2D4×D18811yescharacteristic
435C2C2×#1309405211yescharacteristic
436C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3265
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#13094052C2semidirect
2. C22×#10625325C2semidirect
3. #15689782C2semidirect
4. D4×D188C2semidirect
5. #15689512C2semidirect
6. #15689369C2semidirect
7. #15689359C2semidirect
8. #15689339C2semidirect
9. #15689324C2semidirect
10. #15689276C2semidirect
11. #15689270C2semidirect
12. #15689264C2semidirect
13. #15689259C2semidirect
14. #15689225C2semidirect
15. C47×#435C2semidirect
16. C2×#10625350C22semidirect
17. C22×Dic94C22semidirect
25. C2×#10625325C22semidirect
26. C2×#10625325C22semidirect
27. C2×#10625325C22semidirect
28. C2×#10625325C22semidirect
30. C2×D376C22semidirect
31. C2×D376C22semidirect
33. #13094012C22semidirect
35. #13094003C22semidirect
40. #13093998C22semidirect
44. C4×Dic94C22semidirect
47. #13093958C22semidirect
48. #13093949C22semidirect
49. #13093949C22semidirect
51. #13093946C22semidirect
52. #13093946C22semidirect
53. #13093946C22semidirect
54. C2×M16×C47C22semidirect
55. C22×C8×C47C22semidirect
57. C4⋊C8×C47C22semidirect
58. C22⋊C8×C47C22semidirect
59. C22⋊C8×C47C22semidirect
60. #97×C47C22semidirect
123. #10625325D4semidirect
173. Dic94C2×D4semidirect
177. C8×C47C2×D4semidirect
183. C22×C47AGL(1,ℤ/8)semidirect
233. #435D47semidirect
234. C47#3265semidirect
251. C2×M16C2×D47semidirect
252. C22×C8C2×D47semidirect
270. C4⋊C8C2×D47semidirect
277. C22⋊C8C2×D47semidirect
278. C22⋊C8C2×D47semidirect
279. #97C2×D47semidirect
396. C8D4×D47semidirect
416. C22#13094052semidirect