Finite Group Databasebeta

← C2×C127×#1629 #44582148

Subgroups — C2×C127×#1629 #44582148

Order 32512.

1722 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C127C211yesmaximal, characteristic
2C2×#492×C127C211yesmaximal, characteristic, complemented
3C2×#476×C127C212yesmaximal, complemented
4C127×#1629C218yesmaximal, direct product factor
5C2×#331×C127C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C127C212yesmaximal, complemented
7C23×D4×C127—22no—
8C22×SD16×C127—22no—
9D42×C127—22no—
10D42×C127—24no—
11D42×C127C2214yes—
12C2×C4⋊Q8×C127C2211yescharacteristic, complemented
13C2×#127×C127C2211yescharacteristic
14C2×#121×C127—22no—
15C2×#120×C127—22no—
16C2×C4×D4×C127C2212yes—
17#492×C127—22no—
18#492×C127C2214yescomplemented
19#476×C127—24no—
20#476×C127C2218yescomplemented
21C2×#106×C127—22no—
22C2×C4⋊C8×C127C2212yescomplemented
23C2×#102×C127—22no—
24C2×C4×C8×C127C2211yescharacteristic, complemented
25#331×C127C2214yescomplemented
26D4⋊C8×C127C2218yescomplemented
27C25×C127—22no—
28C22×Q8×C127—21no—
29C22×D4×C127—24no—
30C22×D4×C127—28no—
31C22×D4×C127—28no—
32C22×D4×C127—22no—
33C22×D4×C127—48no—
34C22×D4×C127—48no—
35C22×D4×C127D412yes—
36C22×D4×C127D412yes—
37C23×C4×C127—22no—
38C2×SD16×C127—28no—
39C2×SD16×C127—48no—
40C22×C8×C127—21no—
41C22×C8×C127—22no—
42C4⋊Q8×C127—22no—
43C4⋊Q8×C127—21no—
44C4⋊Q8×C127C2312yescomplemented
45#127×C127—22no—
46#127×C127D412yes—
47#127×C127C2312yes—
48#121×C127—28no—
49#121×C127—28no—
50#120×C127—28no—
51#120×C127—28no—
52C4×D4×C127—22no—
53C4×D4×C127—22no—
54C4×D4×C127D414yes—
55C4×D4×C127C2314yes—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127D412yes—
58C2×C22⋊C4×C127—22no—
59C2×C22⋊C4×C127—22no—
60C2×C42×C127C2311yescharacteristic
61#106×C127—28no—
62C4⋊C8×C127—22no—
63C4⋊C8×C127C2314yescomplemented
64#102×C127—28no—
65C4×C8×C127—21no—
66C4×C8×C127C2312yescomplemented
67C24×C127—22no—
68C24×C127—28no—
69C24×C127—22no—
70C24×C127—416no—
71C24×C127—84no—
72C2×Q8×C127—22no—
73C2×Q8×C127—44no—
74C2×Q8×C127—41no—
75C2×D4×C127—216no—
76C2×D4×C127—22no—
77C2×D4×C127—24no—
78C2×D4×C127—22no—
79C2×D4×C127—24no—
80C2×D4×C127—24no—
81C2×D4×C127—44no—
82C2×D4×C127—416no—
83C2×D4×C127—432no—
84C2×D4×C127—416no—
85C2×D4×C127—416no—
86C2×D4×C127—44no—
87C2×D4×C127—44no—
88C2×D4×C127SD1618yescomplemented
89C2×D4×C127C2×D414yes—
90C2×D4×C127C2×D414yes—
91C22×C4×C127—22no—
92C22×C4×C127—24no—
93C22×C4×C127—24no—
94C22×C4×C127—44no—
95C22×C4×C127—44no—
96C22×C4×C127—41no—
97C22×C4×C127C2×D411yescharacteristic
98C22×C4×C127C2×D412yes—
99SD16×C127—416no—
100C2×C8×C127—24no—
101C2×C8×C127—22no—
102C2×C8×C127—24no—
103C2×C8×C127—44no—
104C4⋊C4×C127—22no—
105C4⋊C4×C127—24no—
106C4⋊C4×C127—42no—
107C4⋊C4×C127C2×D414yes—
108C22⋊C4×C127—28no—
109C22⋊C4×C127—24no—
110C22⋊C4×C127—24no—
111C42×C127C2×D411yescharacteristic
112C42×C127C2×D412yes—
113C42×C127C2411yescharacteristic
114C23×C127—24no—
115C23×C127—28no—
116C23×C127—24no—
117C23×C127—432no—
118C23×C127—44no—
119C23×C127—44no—
120C23×C127—48no—
121C23×C127—44no—
122C23×C127—88no—
123C23×C127—832no—
124C23×C127#12011yescharacteristic
125Q8×C127—44no—
126Q8×C127—82no—
127D4×C127—24no—
128D4×C127—28no—
129D4×C127—44no—
130D4×C127—432no—
131D4×C127—44no—
132D4×C127—44no—
133D4×C127—48no—
134D4×C127—82no—
135D4×C127C2×SD1618yescomplemented
136C2×C4×C127—22no—
137C2×C4×C127—24no—
138C2×C4×C127—44no—
139C2×C4×C127—44no—
140C2×C4×C127—44no—
141C2×C4×C127—48no—
142C2×C4×C127—42no—
143C2×C4×C127—82no—
144C2×C4×C127#12011yescharacteristic
145C2×C4×C127#12012yes—
146C2×C4×C127C2×SD1614yes—
147C2×C4×C127AGL(1,ℤ/8)14yes—
148C2×C4×C127C22×D411yescharacteristic
149C2×C4×C127C22×D412yes—
150C8×C127—24no—
151C8×C127—44no—
152C22×C127—28no—
153C22×C127—416no—
154C22×C127—44no—
155C22×C127—44no—
156C22×C127—48no—
157C22×C127—44no—
158C22×C127—832no—
159C22×C127—88no—
160C22×C127#45014yes—
161C22×C127#45312yes—
162C22×C127C2×#12011yescharacteristic
163C4×C127—21no—
164C4×C127—21no—
165C4×C127—44no—
166C4×C127—82no—
167C4×C127#45014yes—
168C4×C127C22×SD1612yes—
169C4×C127C2×AGL(1,ℤ/8)12yes—
170C2×#1629C12711yesmaximal, characteristic, direct product factor, Sylow
171C2×C127—48no—
172C2×C127—84no—
173C2×C127#162914yesdirect product factor
174C2×C127C2×#45012yes—
175C2×C127C2×#45311yescharacteristic
176C2×D42C2×C12711yescharacteristic
177C2×#492C2×C12711yescharacteristic, complemented
178C2×#476C2×C12712yescomplemented
179#1629C2×C12718yesdirect product factor
180C2×#331C2×C12711yescharacteristic, complemented
181C2×D4⋊C8C2×C12712yescomplemented
182C127C2×#162911yescharacteristic, direct product factor, Sylow
183C23×D4—22no—
184C22×SD16—22no—
185D42—22no—
186D42—24no—
187D42C22×C12714yes—
188C2×C4⋊Q8C22×C12711yescharacteristic, complemented
189C2×#127C22×C12711yescharacteristic
190C2×#121—22no—
191C2×#120—22no—
192C2×C4×D4C22×C12712yes—
193#492—22no—
194#492C22×C12714yescomplemented
195#476—24no—
196#476C22×C12718yescomplemented
197C2×#106—22no—
198C2×C4⋊C8C22×C12712yescomplemented
199C2×#102—22no—
200C2×C4×C8C22×C12711yescharacteristic, complemented
201#331C22×C12714yescomplemented
202D4⋊C8C22×C12718yescomplemented
203C25—22no—
204C22×Q8—21no—
205C22×D4—24no—
206C22×D4—28no—
207C22×D4—28no—
208C22×D4—22no—
209C22×D4—48no—
210C22×D4—48no—
211C22×D4D4×C12712yes—
212C22×D4D4×C12712yes—
213C23×C4—22no—
214C2×SD16—28no—
215C2×SD16—48no—
216C22×C8—21no—
217C22×C8—22no—
218C4⋊Q8—22no—
219C4⋊Q8—21no—
220C4⋊Q8C23×C12712yescomplemented
221#127—22no—
222#127D4×C12712yes—
223#127C23×C12712yes—
224#121—28no—
225#121—28no—
226#120—28no—
227#120—28no—
228C4×D4—22no—
229C4×D4—22no—
230C4×D4D4×C12714yes—
231C4×D4C23×C12714yes—
232C2×C4⋊C4—22no—
233C2×C4⋊C4D4×C12712yes—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C42C23×C12711yescharacteristic
237#106—28no—
238C4⋊C8—22no—
239C4⋊C8C23×C12714yescomplemented
240#102—28no—
241C4×C8—21no—
242C4×C8C23×C12712yescomplemented
243C24—22no—
244C24—28no—
245C24—22no—
246C24—416no—
247C24—84no—
248C2×Q8—22no—
249C2×Q8—44no—
250C2×Q8—41no—
251C2×D4—216no—
252C2×D4—22no—
253C2×D4—24no—
254C2×D4—22no—
255C2×D4—24no—
256C2×D4—24no—
257C2×D4—44no—
258C2×D4—416no—
259C2×D4—432no—
260C2×D4—416no—
261C2×D4—416no—
262C2×D4—44no—
263C2×D4—44no—
264C2×D4SD16×C12718yescomplemented
265C2×D4C2×D4×C12714yes—
266C2×D4C2×D4×C12714yes—
267C22×C4—22no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—44no—
271C22×C4—44no—
272C22×C4—41no—
273C22×C4C2×D4×C12711yescharacteristic
274C22×C4C2×D4×C12712yes—
275SD16—416no—
276C2×C8—24no—
277C2×C8—22no—
278C2×C8—24no—
279C2×C8—44no—
280C4⋊C4—22no—
281C4⋊C4—24no—
282C4⋊C4—42no—
283C4⋊C4C2×D4×C12714yes—
284C22⋊C4—28no—
285C22⋊C4—24no—
286C22⋊C4—24no—
287C42C2×D4×C12711yescharacteristic
288C42C2×D4×C12712yes—
289C42C24×C12711yescharacteristic
290C23—24no—
291C23—28no—
292C23—24no—
293C23—432no—
294C23—44no—
295C23—44no—
296C23—48no—
297C23—44no—
298C23—88no—
299C23—832no—
300C23#120×C12711yescharacteristic
301Q8—44no—
302Q8—82no—
303D4—24no—
304D4—28no—
305D4—44no—
306D4—432no—
307D4—44no—
308D4—44no—
309D4—48no—
310D4—82no—
311D4C2×SD16×C12718yescomplemented
312C2×C4—22no—
313C2×C4—24no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—48no—
318C2×C4—42no—
319C2×C4—82no—
320C2×C4#120×C12711yescharacteristic
321C2×C4#120×C12712yes—
322C2×C4C2×SD16×C12714yes—
323C2×C4AGL(1,ℤ/8)×C12714yes—
324C2×C4C22×D4×C12711yescharacteristic
325C2×C4C22×D4×C12712yes—
326C8—24no—
327C8—44no—
328C22—28no—
329C22—416no—
330C22—44no—
331C22—44no—
332C22—48no—
333C22—44no—
334C22—832no—
335C22—88no—
336C22#450×C12714yes—
337C22#453×C12712yes—
338C22C2×#120×C12711yescharacteristic
339C4—21no—
340C4—21no—
341C4—44no—
342C4—82no—
343C4#450×C12714yes—
344C4C22×SD16×C12712yes—
345C4C2×AGL(1,ℤ/8)×C12712yes—
346C2—48no—
347C2—84no—
348C2C127×#162914yesdirect product factor
349C2C2×#450×C12712yes—
350C2C2×#453×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×D42×C127C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#492×C127C2semidirect
3. C2×#476×C127C2semidirect
4. C127×#1629C2direct (N × H)
5. C2×#331×C127C2semidirect
6. C2×D4⋊C8×C127C2semidirect
12. C2×C4⋊Q8×C127C22semidirect
18. #492×C127C22semidirect
20. #476×C127C22semidirect
22. C2×C4⋊C8×C127C22semidirect
24. C2×C4×C8×C127C22semidirect
25. #331×C127C22semidirect
26. D4⋊C8×C127C22semidirect
44. C4⋊Q8×C127C23semidirect
63. C4⋊C8×C127C23semidirect
66. C4×C8×C127C23semidirect
88. C2×D4×C127SD16semidirect
135. D4×C127C2×SD16semidirect
170. C2×#1629C127direct (N × H)
173. C2×C127#1629direct (N × H)
177. C2×#492C2×C127semidirect
178. C2×#476C2×C127semidirect
179. #1629C2×C127direct (N × H)
180. C2×#331C2×C127semidirect
181. C2×D4⋊C8C2×C127semidirect
182. C127C2×#1629direct (N × H)
188. C2×C4⋊Q8C22×C127semidirect
194. #492C22×C127semidirect
196. #476C22×C127semidirect
198. C2×C4⋊C8C22×C127semidirect
200. C2×C4×C8C22×C127semidirect
201. #331C22×C127semidirect
202. D4⋊C8C22×C127semidirect
220. C4⋊Q8C23×C127semidirect
239. C4⋊C8C23×C127semidirect
242. C4×C8C23×C127semidirect
264. C2×D4SD16×C127semidirect
311. D4C2×SD16×C127semidirect
348. C2C127×#1629direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D42×C1272
C2×#492×C1272
C2×#476×C1272
C127×#16292
C2×#331×C1272
C2×D4⋊C8×C1272
C2×#1629127