Finite Group Databasebeta

← #463×D127 #30648150

Subgroups — #463×D127 #30648150

Order 16256.

564 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×SD16×D127C211yesmaximal, characteristic, complemented
2C2×D8×D127C211yesmaximal, characteristic
3#124×D127C211yesmaximal, characteristic, complemented
4C4×D4×D127C211yesmaximal, characteristic, complemented
5#22550094C211yesmaximal, characteristic, complemented
6#22550093C211yesmaximal, characteristic, complemented
7#22550092C211yesmaximal, characteristic, complemented
8#22550091C211yesmaximal, characteristic, complemented
9#22550090C211yesmaximal, characteristic, complemented
10#22550089C211yesmaximal, characteristic, complemented
11#22550088C211yesmaximal, characteristic, complemented
12C4⋊C8×D127C211yesmaximal, characteristic, complemented
13#103×D127C211yesmaximal, characteristic, complemented
14#102×D127C211yesmaximal, characteristic, complemented
15#463×C127C211yesmaximal, characteristic, complemented
16C2×Q8×D127C2211yescharacteristic
17C2×D4×D127C2211yescharacteristic
18C2×D4×D127C2211yescharacteristic
19C22×C4×D127—21no—
20C2×#14523237C2211yescharacteristic, complemented
21C2×#14523236C2211yescharacteristic, complemented
22C2×#14523235C2211yescharacteristic, complemented
23SD16×D127—24no—
24C2×D1016C2211yescharacteristic
25C2×#14523233C2211yescharacteristic
26C2×#14523233C2211yescharacteristic
27D8×D127—24no—
28C2×C8×D127C2211yescharacteristic
29C2×C8×D127C2211yescharacteristic
30#16861198C2211yescharacteristic, complemented
31#16861197C2211yescharacteristic, complemented
32#16861196C2211yescharacteristic, complemented
33#16861195—21no—
34#16861195—21no—
35C4×D508C2211yescharacteristic, complemented
36D4×Dic127C2211yescharacteristic, complemented
37#16861171C2211yescharacteristic, complemented
38C4×C22⋊D127—21no—
39(C22⋊D127)⋊C4—21no—
40C4⋊C4×D127C2211yescharacteristic
41C22⋊C4×D127—21no—
42C22⋊C4×D127—21no—
43C22⋊C4×D127—21no—
44C42×D127C2211yescharacteristic
45C4⋊(C127⋊C8)C2211yescharacteristic, complemented
46Dic127⋊C8C2211yescharacteristic, complemented
47Dic127⋊C8C2211yescharacteristic, complemented
48#16861134C2211yescharacteristic, complemented
49#16861133C2211yescharacteristic, complemented
50#16861132C2211yescharacteristic, complemented
51#16861131C2211yescharacteristic, complemented
52#16861130C2211yescharacteristic, complemented
53#16861129C2211yescharacteristic, complemented
54C2×SD16×C127C2211yescharacteristic, complemented
55C2×D8×C127C2211yescharacteristic
56#124×C127C2211yescharacteristic, complemented
57C4×D4×C127C2211yescharacteristic, complemented
58C4⋊C8×C127C2211yescharacteristic, complemented
59#103×C127C2211yescharacteristic, complemented
60#102×C127C2211yescharacteristic, complemented
61C23×D127—21no—
62C23×D127—21no—
63C2×Dic254—21no—
64C2×Dic254C2311yescharacteristic
65Q8×D127—22no—
66Q8×D127—22no—
67C2×D508C2311yescharacteristic
68C2×D508C2311yescharacteristic
69C2×C22⋊D127—21no—
70C2×C22⋊D127—21no—
71D4×D127—22no—
72D4×D127—22no—
73D4×D127—22no—
74D4×D127D414yes—
75C22×Dic127—21no—
76C2×C4×D127—21no—
77C2×C4×D127—21no—
78C2×C4×D127—21no—
79C2×C4×D127—21no—
80C2×C4×D127—44no—
81C2×C4×D127D411yescharacteristic
82C2×C4×D127D411yescharacteristic
83C2×C4×D127C2311yescharacteristic
84#14523237—22no—
85#14523236—22no—
86#14523235—22no—
87D1016—22no—
88#14523233—22no—
89#14523233—22no—
90C2×C127⋊C8C2311yescharacteristic
91C2×C127⋊C8C2311yescharacteristic
92C8×D127—22no—
93C8×D127—22no—
94C4⋊Dic127C2311yescharacteristic
95Dic127⋊C4—21no—
96C22⋊Dic127—21no—
97C22⋊Dic127—21no—
98C22⋊Dic127—21no—
99(C2×D127)⋊C4—21no—
100(C2×D127)⋊C4—21no—
101(C2×D127)⋊C4—21no—
102(C2×D127)⋊C4—21no—
103(C2×D127)⋊C4—21no—
104(C2×D127)⋊C4—21no—
105C4×Dic127D411yescharacteristic
106C4×Dic127D411yescharacteristic
107C4×Dic127C2311yescharacteristic
108C2×Q8×C127C2311yescharacteristic
109C2×D4×C127C2311yescharacteristic
110C2×D4×C127C2311yescharacteristic
111C22×C4×C127—21no—
112SD16×C127—22no—
113D8×C127—22no—
114C2×C8×C127C2311yescharacteristic
115C2×C8×C127C2311yescharacteristic
116C4⋊C4×C127C2311yescharacteristic
117C22⋊C4×C127—21no—
118C22⋊C4×C127—21no—
119C22⋊C4×C127—21no—
120C42×C127C2311yescharacteristic
121C22×D127—21no—
122C22×D127—24no—
123C22×D127—21no—
124C22×D127—42no—
125C22×D127—42no—
126C22×D127—42no—
127C22×D127—42no—
128C22×D127—42no—
129C22×D127C2×D411yescharacteristic
130Dic254—21no—
131Dic254—21no—
132Dic254—42no—
133D508—21no—
134D508—21no—
135D508—21no—
136D508C2×D412yes—
137C22⋊D127—24no—
138C22⋊D127—42no—
139C2×Dic127—21no—
140C2×Dic127—21no—
141C2×Dic127—42no—
142C2×Dic127C2×D411yescharacteristic
143C2×Dic127C2×D411yescharacteristic
144C2×Dic127C2×D411yescharacteristic
145C4×D127—22no—
146C4×D127—22no—
147C4×D127—42no—
148C4×D127—42no—
149C4×D127—42no—
150C4×D127—42no—
151C4×D127C2×D412yes—
152C4×D127#4112yes—
153C127⋊C8—21no—
154C127⋊C8—21no—
155C23×C127—21no—
156C23×C127—21no—
157Q8×C127—21no—
158Q8×C127—21no—
159D4×C127—21no—
160D4×C127—21no—
161D4×C127—21no—
162D4×C127C2×D412yes—
163C2×C4×C127—21no—
164C2×C4×C127—21no—
165C2×C4×C127—42no—
166C2×C4×C127C2×D411yescharacteristic
167C2×C4×C127C2×D411yescharacteristic
168C2×C4×C127C2411yescharacteristic
169C8×C127—21no—
170C8×C127—21no—
171C22×C127—22no—
172C22×C127—41no—
173C22×C127—41no—
174C22×C127—41no—
175C22×C127—41no—
176C22×C127—41no—
177C22×C127C22×D411yescharacteristic
178C2×D127—22no—
179C2×D127—41no—
180C2×D127—41no—
181C2×D127—48no—
182C2×D127—41no—
183C2×D127—41no—
184C2×D127—41no—
185C2×D127—84no—
186C2×D127#12112yes—
187C2×D127#13512yes—
188C2×D127AGL(1,ℤ/8)12yes—
189C4×C127—21no—
190C4×C127—21no—
191C4×C127—41no—
192C4×C127—41no—
193C4×C127C22×D411yescharacteristic
194C4×C127C2×#4111yescharacteristic
195Dic127—21no—
196Dic127—21no—
197Dic127—41no—
198Dic127—41no—
199Dic127#12112yes—
200C2×C127—42no—
201C2×C127—81no—
202C2×C127C2×#12111yescharacteristic
203C2×C127C2×#13511yescharacteristic
204C2×C127C2×AGL(1,ℤ/8)11yescharacteristic
205D127—42no—
206D127—81no—
207D127#46314yesdirect product factor
208C2×#463—1271nomaximal, Sylow
209C127C2×#46311yescharacteristic, complemented, Sylow
210C22×SD16—1271no—
211C22×D8—1271no—
212C2×#124—1271no—
213C2×C4×D4—1271no—
214#463—1271no—
215#463—1271no—
216#463—1271no—
217#463—1271no—
218#463—1271no—
219#463—1271no—
220#463—1271no—
221#463D12711yescharacteristic, direct product factor
222C2×C4⋊C8—1271no—
223C2×#103—1271no—
224C2×#102—1271no—
225C22×Q8—1271no—
226C22×D4—1271no—
227C22×D4—1271no—
228C23×C4—2541no—
229C2×SD16—1271no—
230C2×SD16—1271no—
231C2×SD16—1271no—
232C2×SD16—2544no—
233C2×SD16C2×D12711yescharacteristic, complemented
234C2×D8—1271no—
235C2×D8—1271no—
236C2×D8—1271no—
237C2×D8—2544no—
238C2×D8C2×D12711yescharacteristic
239C22×C8—1271no—
240C22×C8—1271no—
241#124—1271no—
242#124—1271no—
243#124—1271no—
244#124—2541no—
245#124—2541no—
246#124C2×D12711yescharacteristic, complemented
247C4×D4—1271no—
248C4×D4—1271no—
249C4×D4—1271no—
250C4×D4—2541no—
251C4×D4—2541no—
252C4×D4C2×D12711yescharacteristic, complemented
253C2×C4⋊C4—1271no—
254C2×C22⋊C4—2541no—
255C2×C22⋊C4—2541no—
256C2×C22⋊C4—2541no—
257C2×C42—1271no—
258C4⋊C8—1271no—
259C4⋊C8—1271no—
260C4⋊C8—1271no—
261C4⋊C8C2×D12711yescharacteristic, complemented
262#103—1271no—
263#103—1271no—
264#103—1271no—
265#103C2×D12711yescharacteristic, complemented
266#102—1271no—
267#102—1271no—
268#102—1271no—
269#102C2×D12711yescharacteristic, complemented
270C24—2541no—
271C24—2541no—
272C2×Q8—1271no—
273C2×Q8—2541no—
274C2×Q8—2542no—
275C2×Q8—2542no—
276C2×Q8C22×D12711yescharacteristic
277C2×D4—1274no—
278C2×D4—1271no—
279C2×D4—1271no—
280C2×D4—2542no—
281C2×D4—2542no—
282C2×D4—2542no—
283C2×D4—2541no—
284C2×D4—2541no—
285C2×D4C22×D12711yescharacteristic
286C2×D4C22×D12711yescharacteristic
287C22×C4—21no—
288C22×C4—1271no—
289C22×C4—1271no—
290C22×C4—1271no—
291C22×C4—5084no—
292C22×C4—2541no—
293C22×C4—2541no—
294C22×C4—2541no—
295C22×C4—2541no—
296C22×C4—2541no—
297SD16—22no—
298SD16—2542no—
299SD16—2542no—
300SD16—2542no—
301D8—22no—
302D8—2542no—
303D8—2542no—
304D8—2542no—
305C2×C8—1271no—
306C2×C8—1271no—
307C2×C8—2542no—
308C2×C8—2542no—
309C2×C8C22×D12711yescharacteristic
310C2×C8C22×D12711yescharacteristic
311C4⋊C4—1271no—
312C4⋊C4—2541no—
313C4⋊C4C22×D12711yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—2541no—
318C22⋊C4—2541no—
319C22⋊C4—2541no—
320C22⋊C4—2541no—
321C22⋊C4—2541no—
322C22⋊C4—2541no—
323C22⋊C4—2541no—
324C22⋊C4—2541no—
325C22⋊C4—2541no—
326C42—1271no—
327C42—1271no—
328C42—1271no—
329C42C22×D12711yescharacteristic
330C23—21no—
331C23—21no—
332C23—1271no—
333C23—5082no—
334C23—5082no—
335C23—5082no—
336C23—5082no—
337C23—5082no—
338C23—2544no—
339C23—2541no—
340C23—2541no—
341Q8—21no—
342Q8—21no—
343Q8—5082no—
344Q8—2541no—
345Q8—2541no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—1272no—
350D4—5082no—
351D4—2544no—
352D4—2541no—
353D4—2541no—
354D4—2541no—
355D4D4×D12712yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—1271no—
360C2×C4—1272no—
361C2×C4—1272no—
362C2×C4—1271no—
363C2×C4—1271no—
364C2×C4—5082no—
365C2×C4—5082no—
366C2×C4—5082no—
367C2×C4—5082no—
368C2×C4—5082no—
369C2×C4—2542no—
370C2×C4—2542no—
371C2×C4—2541no—
372C2×C4—2541no—
373C2×C4D4×D12711yescharacteristic
374C2×C4D4×D12711yescharacteristic
375C2×C4C23×D12711yescharacteristic
376C8—21no—
377C8—21no—
378C8—2541no—
379C8—2541no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—1272no—
387C22—1272no—
388C22—1272no—
389C22—10164no—
390C22—5088no—
391C22—5081no—
392C22—5081no—
393C22—5081no—
394C22—5081no—
395C22—5081no—
396C22—2542no—
397C22C2×D4×D12711yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—1272no—
403C4—5081no—
404C4—5081no—
405C4—2541no—
406C4—2541no—
407C4C2×D4×D12711yescharacteristic
408C4#41×D12711yescharacteristic
409C2—42no—
410C2—81no—
411C2—1274no—
412C2—10161no—
413C2—5082no—
414C2#121×D12711yescharacteristic
415C2#135×D12711yescharacteristic
416C2AGL(1,ℤ/8)×D12711yescharacteristic
subgroupG/H
centerC22C2×D4×D127
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
Fitting#463×C127C2
socleC22×C127C22×D4
prime radicalC2×D8×D127C2
hypercenter#463D127
hypocenterC127C2×#463
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D127C2semidirect
3. #124×D127C2semidirect
4. C4×D4×D127C2semidirect
5. #22550094C2semidirect
6. #22550093C2semidirect
7. #22550092C2semidirect
8. #22550091C2semidirect
9. #22550090C2semidirect
10. #22550089C2semidirect
11. #22550088C2semidirect
12. C4⋊C8×D127C2semidirect
13. #103×D127C2semidirect
14. #102×D127C2semidirect
15. #463×C127C2semidirect
20. C2×#14523237C22semidirect
21. C2×#14523236C22semidirect
22. C2×#14523235C22semidirect
30. #16861198C22semidirect
31. #16861197C22semidirect
32. #16861196C22semidirect
35. C4×D508C22semidirect
36. D4×Dic127C22semidirect
37. #16861171C22semidirect
45. C4⋊(C127⋊C8)C22semidirect
46. Dic127⋊C8C22semidirect
47. Dic127⋊C8C22semidirect
48. #16861134C22semidirect
49. #16861133C22semidirect
50. #16861132C22semidirect
51. #16861131C22semidirect
52. #16861130C22semidirect
53. #16861129C22semidirect
54. C2×SD16×C127C22semidirect
56. #124×C127C22semidirect
57. C4×D4×C127C22semidirect
58. C4⋊C8×C127C22semidirect
59. #103×C127C22semidirect
60. #102×C127C22semidirect
207. D127#463direct (N × H)
209. C127C2×#463semidirect
221. #463D127direct (N × H)
233. C2×SD16C2×D127semidirect
246. #124C2×D127semidirect
252. C4×D4C2×D127semidirect
261. C4⋊C8C2×D127semidirect
265. #103C2×D127semidirect
269. #102C2×D127semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×SD16×D1272
C2×D8×D1272
#124×D1272
C4×D4×D1272
#225500942
#225500932
#225500922
#225500912
#225500902
#225500892
#225500882
C4⋊C8×D1272
#103×D1272
#102×D1272
#463×C1272
C2×#463127