Finite Group Databasebeta

← #440×D127 #30647505

Subgroups — #440×D127 #30647505

Order 16256.

544 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D127C211yesmaximal, characteristic
2C4×Q8×D127C211yesmaximal, characteristic, complemented
3C4×D4×D127C211yesmaximal, characteristic
4#22549979C211yesmaximal, characteristic, complemented
5#22549978C211yesmaximal, characteristic, complemented
6#22549977C211yesmaximal, characteristic, complemented
7#22549976C211yesmaximal, characteristic, complemented
8#22549975C211yesmaximal, characteristic, complemented
9#22549974C211yesmaximal, characteristic, complemented
10#22549973C211yesmaximal, characteristic, complemented
11#107×D127C211yesmaximal, characteristic, complemented
12#103×D127C211yesmaximal, characteristic, complemented
13#102×D127C211yesmaximal, characteristic
14#97×D127C211yesmaximal, characteristic, complemented
15#440×C127C211yesmaximal, characteristic, complemented
16C2×Q8×D127C2211yescharacteristic
17C2×D4×D127C2211yescharacteristic
18C22×C4×D127—21no—
19C2×#14523237C2211yescharacteristic
20C2×#14523236C2211yescharacteristic
21C2×#14523235C2211yescharacteristic
22SD16×D127C418yescomplemented
23C2×C8×D127C2211yescharacteristic
24C2×C8×D127C2211yescharacteristic
25Q8×Dic127C2211yescharacteristic, complemented
26C4×Dic254—21no—
27C4×Dic254C2211yescharacteristic, complemented
28#16861174—21no—
29#16861174C2211yescharacteristic, complemented
30C4×D508C2211yescharacteristic
31D4×Dic127C2211yescharacteristic
32#16861171C2211yescharacteristic
33C4×C22⋊D127—21no—
34(C22⋊D127)⋊C4—21no—
35C4⋊C4×D127—21no—
36C4⋊C4×D127C2211yescharacteristic
37C4⋊C4×D127C2211yescharacteristic
38C22⋊C4×D127—21no—
39C42×D127—21no—
40C42×D127C2211yescharacteristic
41#16861143C2211yescharacteristic, complemented
42#16861142C2211yescharacteristic, complemented
43#16861142C2211yescharacteristic, complemented
44#16861134C2211yescharacteristic, complemented
45#16861133C2211yescharacteristic, complemented
46#16861132C2211yescharacteristic, complemented
47#16861131C2211yescharacteristic
48#16861130C2211yescharacteristic
49#16861129C2211yescharacteristic
50#16861120C2211yescharacteristic, complemented
51#16861119C2211yescharacteristic, complemented
52#16861119C2211yescharacteristic, complemented
53C2×SD16×C127C2211yescharacteristic
54C4×Q8×C127C2211yescharacteristic, complemented
55C4×D4×C127C2211yescharacteristic
56#107×C127C2211yescharacteristic, complemented
57#103×C127C2211yescharacteristic, complemented
58#102×C127C2211yescharacteristic
59#97×C127C2211yescharacteristic, complemented
60C23×D127—21no—
61C2×Dic254—21no—
62C2×Dic254C2311yescharacteristic
63Q8×D127—22no—
64Q8×D127C2×C414yescomplemented
65C2×D508C2311yescharacteristic
66C2×C22⋊D127—21no—
67D4×D127—22no—
68D4×D127C2×C414yes—
69C22×Dic127—21no—
70C2×C4×D127—21no—
71C2×C4×D127—21no—
72C2×C4×D127—21no—
73C2×C4×D127—21no—
74C2×C4×D127—21no—
75C2×C4×D127—44no—
76C2×C4×D127D411yescharacteristic
77C2×C4×D127D411yescharacteristic
78C2×C4×D127C2311yescharacteristic
79#14523237C2×C414yescomplemented
80#14523236C2×C414yescomplemented
81#14523235C2×C414yescomplemented
82C2×C127⋊C8C2311yescharacteristic
83C2×C127⋊C8C2311yescharacteristic
84C8×D127—22no—
85C8×D127C2×C414yescomplemented
86C4⋊Dic127—21no—
87C4⋊Dic127C2311yescharacteristic
88C4⋊Dic127C2311yescharacteristic
89Dic127⋊C4—21no—
90Dic127⋊C4—21no—
91Dic127⋊C4—21no—
92Dic127⋊C4—21no—
93C22⋊Dic127—21no—
94(C2×D127)⋊C4—21no—
95(C2×D127)⋊C4—21no—
96C4×Dic127—21no—
97C4×Dic127—21no—
98C4×Dic127—21no—
99C4×Dic127D411yescharacteristic
100C4×Dic127D411yescharacteristic
101C4×Dic127C2311yescharacteristic
102C2×Q8×C127C2311yescharacteristic
103C2×D4×C127C2311yescharacteristic
104C22×C4×C127—21no—
105SD16×C127C2×C414yescomplemented
106C2×C8×C127C2311yescharacteristic
107C2×C8×C127C2311yescharacteristic
108C4⋊C4×C127—21no—
109C4⋊C4×C127C2311yescharacteristic
110C4⋊C4×C127C2311yescharacteristic
111C22⋊C4×C127—21no—
112C42×C127—21no—
113C42×C127C2311yescharacteristic
114C22×D127—21no—
115C22×D127—24no—
116C22×D127—42no—
117C22×D127—42no—
118C22×D127C2×D411yescharacteristic
119Dic254—21no—
120Dic254—24no—
121Dic254C22×C412yescomplemented
122D508—21no—
123D508C22×C412yes—
124C22⋊D127—24no—
125C2×Dic127—21no—
126C2×Dic127—21no—
127C2×Dic127—21no—
128C2×Dic127—42no—
129C2×Dic127C2×D411yescharacteristic
130C2×Dic127C2×D411yescharacteristic
131C2×Dic127C2×D411yescharacteristic
132C4×D127—24no—
133C4×D127—22no—
134C4×D127—22no—
135C4×D127—42no—
136C4×D127—42no—
137C4×D127—42no—
138C4×D127—42no—
139C4×D127C22×C412yes—
140C4×D127#4112yes—
141C127⋊C8—21no—
142C127⋊C8C22×C412yescomplemented
143C23×C127—21no—
144Q8×C127—21no—
145Q8×C127C22×C412yescomplemented
146D4×C127—21no—
147D4×C127C22×C412yes—
148C2×C4×C127—21no—
149C2×C4×C127—21no—
150C2×C4×C127—21no—
151C2×C4×C127—42no—
152C2×C4×C127C2×D411yescharacteristic
153C2×C4×C127C2×D411yescharacteristic
154C2×C4×C127C2411yescharacteristic
155C8×C127—21no—
156C8×C127C22×C412yescomplemented
157C22×C127—22no—
158C22×C127—41no—
159C22×C127—41no—
160C22×C127C22×D411yescharacteristic
161C2×D127—22no—
162C2×D127—41no—
163C2×D127—41no—
164C2×D127—48no—
165C2×D127C4×D412yes—
166C2×D127AGL(1,ℤ/8)12yes—
167C2×D127#13712yes—
168C4×C127—22no—
169C4×C127—21no—
170C4×C127—21no—
171C4×C127—41no—
172C4×C127—41no—
173C4×C127C23×C411yescharacteristic
174C4×C127C2×#4111yescharacteristic
175Dic127—22no—
176Dic127—21no—
177Dic127—21no—
178Dic127—41no—
179Dic127—41no—
180Dic127C4×D412yes—
181C2×C127—42no—
182C2×C127C2×C4×D411yescharacteristic
183C2×C127C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C127C2×#13711yescharacteristic
185D127—42no—
186D127#44014yesdirect product factor
187C2×#440—1271nomaximal, Sylow
188C127C2×#44011yescharacteristic, complemented, Sylow
189C22×SD16—1271no—
190C2×C4×Q8—1271no—
191C2×C4×D4—1271no—
192#440—1271no—
193#440—1271no—
194#440—1271no—
195#440—1271no—
196#440—1271no—
197#440—1271no—
198#440—1271no—
199#440D12711yescharacteristic, direct product factor
200C2×#107—1271no—
201C2×#103—1271no—
202C2×#102—1271no—
203C2×#97—1271no—
204C22×Q8—1271no—
205C22×D4—1271no—
206C23×C4—2541no—
207C2×SD16—1271no—
208C2×SD16—1271no—
209C2×SD16—1278no—
210C2×SD16—1271no—
211C2×SD16C2×D12711yescharacteristic
212C22×C8—1271no—
213C22×C8—1271no—
214C4×Q8—1271no—
215C4×Q8—1271no—
216C4×Q8—1271no—
217C4×Q8—2541no—
218C4×Q8—2541no—
219C4×Q8C2×D12711yescharacteristic, complemented
220C4×D4—1271no—
221C4×D4—1271no—
222C4×D4—1271no—
223C4×D4—2541no—
224C4×D4—2541no—
225C4×D4C2×D12711yescharacteristic
226C2×C4⋊C4—1271no—
227C2×C4⋊C4—1271no—
228C2×C4⋊C4—2541no—
229C2×C22⋊C4—2541no—
230C2×C42—1271no—
231C2×C42—2541no—
232#107—1271no—
233#107—1271no—
234#107—1271no—
235#107C2×D12711yescharacteristic, complemented
236#103—1271no—
237#103—1271no—
238#103—1271no—
239#103C2×D12711yescharacteristic, complemented
240#102—1271no—
241#102—1271no—
242#102—1271no—
243#102C2×D12711yescharacteristic
244#97—1271no—
245#97—1271no—
246#97—1271no—
247#97C2×D12711yescharacteristic, complemented
248C24—2541no—
249C2×Q8—1274no—
250C2×Q8—1271no—
251C2×Q8—2541no—
252C2×Q8—2542no—
253C2×Q8C22×D12711yescharacteristic
254C2×D4—1274no—
255C2×D4—1271no—
256C2×D4—2542no—
257C2×D4—2541no—
258C2×D4C22×D12711yescharacteristic
259C22×C4—21no—
260C22×C4—1271no—
261C22×C4—1271no—
262C22×C4—1271no—
263C22×C4—5084no—
264C22×C4—2541no—
265C22×C4—2541no—
266C22×C4—2541no—
267C22×C4—2541no—
268C22×C4—2541no—
269C22×C4—2541no—
270SD16—1274no—
271SD16—1274no—
272SD16—1274no—
273SD16C4×D12714yescomplemented
274C2×C8—1271no—
275C2×C8—1274no—
276C2×C8—1271no—
277C2×C8—2542no—
278C2×C8C22×D12711yescharacteristic
279C2×C8C22×D12711yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—1271no—
282C4⋊C4—1271no—
283C4⋊C4—2541no—
284C4⋊C4—2541no—
285C4⋊C4—2541no—
286C4⋊C4—2541no—
287C4⋊C4—2541no—
288C4⋊C4C22×D12711yescharacteristic
289C4⋊C4C22×D12711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—2541no—
292C22⋊C4—2541no—
293C22⋊C4—2541no—
294C42—21no—
295C42—1271no—
296C42—1271no—
297C42—1271no—
298C42—2541no—
299C42—2541no—
300C42—2541no—
301C42C22×D12711yescharacteristic
302C23—21no—
303C23—1271no—
304C23—5082no—
305C23—5082no—
306C23—2544no—
307C23—2541no—
308Q8—21no—
309Q8—1272no—
310Q8—2544no—
311Q8—2541no—
312Q8C2×C4×D12712yescomplemented
313D4—21no—
314D4—1272no—
315D4—2544no—
316D4—2541no—
317D4C2×C4×D12712yes—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—1271no—
323C2×C4—1272no—
324C2×C4—1272no—
325C2×C4—1271no—
326C2×C4—1271no—
327C2×C4—5082no—
328C2×C4—5082no—
329C2×C4—5082no—
330C2×C4—5082no—
331C2×C4—5082no—
332C2×C4—2542no—
333C2×C4—2542no—
334C2×C4—2544no—
335C2×C4—2541no—
336C2×C4—2541no—
337C2×C4—2541no—
338C2×C4D4×D12711yescharacteristic
339C2×C4D4×D12711yescharacteristic
340C2×C4C23×D12711yescharacteristic
341C8—21no—
342C8—1272no—
343C8—2541no—
344C8C2×C4×D12712yescomplemented
345C22—22no—
346C22—41no—
347C22—41no—
348C22—1272no—
349C22—1272no—
350C22—1272no—
351C22—5088no—
352C22—5081no—
353C22—5081no—
354C22—2542no—
355C22C2×D4×D12711yescharacteristic
356C4—22no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—1272no—
362C4—5081no—
363C4—5081no—
364C4—2542no—
365C4—2541no—
366C4—2541no—
367C4C22×C4×D12711yescharacteristic
368C4#41×D12711yescharacteristic
369C2—42no—
370C2—1274no—
371C2—5082no—
372C2C4×D4×D12711yescharacteristic
373C2AGL(1,ℤ/8)×D12711yescharacteristic
374C2#137×D12711yescharacteristic
subgroupG/H
centerC22C2×D4×D127
commutatorC4×C127C23×C4
FrattiniC2×C4C23×D127
Fitting#440×C127C2
socleC22×C127C22×D4
prime radicalC2×D4×D127C22
cosocleC2×C4×C127C24
hypercenter#440D127
hypocenterC127C2×#440
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D127C2semidirect
4. #22549979C2semidirect
5. #22549978C2semidirect
6. #22549977C2semidirect
7. #22549976C2semidirect
8. #22549975C2semidirect
9. #22549974C2semidirect
10. #22549973C2semidirect
11. #107×D127C2semidirect
12. #103×D127C2semidirect
14. #97×D127C2semidirect
15. #440×C127C2semidirect
22. SD16×D127C4semidirect
25. Q8×Dic127C22semidirect
27. C4×Dic254C22semidirect
29. #16861174C22semidirect
41. #16861143C22semidirect
42. #16861142C22semidirect
43. #16861142C22semidirect
44. #16861134C22semidirect
45. #16861133C22semidirect
46. #16861132C22semidirect
50. #16861120C22semidirect
51. #16861119C22semidirect
52. #16861119C22semidirect
54. C4×Q8×C127C22semidirect
56. #107×C127C22semidirect
57. #103×C127C22semidirect
59. #97×C127C22semidirect
64. Q8×D127C2×C4semidirect
79. #14523237C2×C4semidirect
80. #14523236C2×C4semidirect
81. #14523235C2×C4semidirect
85. C8×D127C2×C4semidirect
105. SD16×C127C2×C4semidirect
121. Dic254C22×C4semidirect
142. C127⋊C8C22×C4semidirect
145. Q8×C127C22×C4semidirect
156. C8×C127C22×C4semidirect
186. D127#440direct (N × H)
188. C127C2×#440semidirect
199. #440D127direct (N × H)
219. C4×Q8C2×D127semidirect
235. #107C2×D127semidirect
239. #103C2×D127semidirect
247. #97C2×D127semidirect
273. SD16C4×D127semidirect
312. Q8C2×C4×D127semidirect
344. C8C2×C4×D127semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1272
C4×Q8×D1272
C4×D4×D1272
#225499792
#225499782
#225499772
#225499762
#225499752
#225499742
#225499732
#107×D1272
#103×D1272
#102×D1272
#97×D1272
#440×C1272
C2×#440127