Finite Group Databasebeta

← C2×C127×#1619 #44582147

Subgroups — C2×C127×#1619 #44582147

Order 32512.

1838 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C127C211yesmaximal, characteristic, complemented
2C2×#493×C127C211yesmaximal, characteristic, complemented
3C2×#459×C127C212yesmaximal, complemented
4C127×#1619C218yesmaximal, direct product factor
5C2×#331×C127C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C127C212yesmaximal, complemented
7C23×D4×C127—22no—
8C22×D8×C127—22no—
9C22×D8×C127—22no—
10D42×C127—22no—
11D42×C127—24no—
12D42×C127C2214yescomplemented
13C2×#127×C127C2211yescharacteristic
14C2×#127×C127C2211yescharacteristic, complemented
15C2×#121×C127—22no—
16C2×#120×C127—22no—
17C2×C4×D4×C127C2212yes—
18#493×C127—22no—
19#493×C127C2214yescomplemented
20#459×C127—24no—
21#459×C127C2218yescomplemented
22C2×C4⋊C8×C127C2212yescomplemented
23C2×#102×C127—22no—
24C2×C4×C8×C127C2211yescharacteristic, complemented
25#331×C127C2214yescomplemented
26D4⋊C8×C127C2218yescomplemented
27C25×C127—22no—
28C22×D4×C127—24no—
29C22×D4×C127—28no—
30C22×D4×C127—28no—
31C22×D4×C127—22no—
32C22×D4×C127—21no—
33C22×D4×C127—22no—
34C22×D4×C127—48no—
35C22×D4×C127—48no—
36C22×D4×C127D412yes—
37C22×D4×C127D412yes—
38C23×C4×C127—22no—
39C2×D8×C127—28no—
40C2×D8×C127—28no—
41C2×D8×C127—48no—
42C2×D8×C127—48no—
43C22×C8×C127—21no—
44C22×C8×C127—22no—
45#127×C127—22no—
46#127×C127—22no—
47#127×C127—21no—
48#127×C127D412yes—
49#127×C127C2312yes—
50#127×C127C2312yescomplemented
51#121×C127—28no—
52#121×C127—28no—
53#120×C127—28no—
54#120×C127—28no—
55C4×D4×C127—22no—
56C4×D4×C127—22no—
57C4×D4×C127D414yes—
58C4×D4×C127C2314yes—
59C2×C4⋊C4×C127D412yes—
60C2×C22⋊C4×C127—22no—
61C2×C22⋊C4×C127—22no—
62C2×C42×C127C2311yescharacteristic
63C4⋊C8×C127—22no—
64C4⋊C8×C127C2314yescomplemented
65#102×C127—28no—
66C4×C8×C127—21no—
67C4×C8×C127C2312yescomplemented
68C24×C127—22no—
69C24×C127—28no—
70C24×C127—22no—
71C24×C127—416no—
72C24×C127—41no—
73C24×C127—84no—
74C2×D4×C127—216no—
75C2×D4×C127—22no—
76C2×D4×C127—24no—
77C2×D4×C127—22no—
78C2×D4×C127—24no—
79C2×D4×C127—24no—
80C2×D4×C127—24no—
81C2×D4×C127—22no—
82C2×D4×C127—44no—
83C2×D4×C127—44no—
84C2×D4×C127—416no—
85C2×D4×C127—432no—
86C2×D4×C127—416no—
87C2×D4×C127—416no—
88C2×D4×C127—41no—
89C2×D4×C127—42no—
90C2×D4×C127—44no—
91C2×D4×C127—44no—
92C2×D4×C127—44no—
93C2×D4×C127—44no—
94C2×D4×C127D818yescomplemented
95C2×D4×C127C2×D414yes—
96C2×D4×C127C2×D414yes—
97C22×C4×C127—22no—
98C22×C4×C127—24no—
99C22×C4×C127—24no—
100C22×C4×C127—44no—
101C22×C4×C127—44no—
102C22×C4×C127C2×D411yescharacteristic
103C22×C4×C127C2×D412yes—
104D8×C127—416no—
105D8×C127—416no—
106C2×C8×C127—24no—
107C2×C8×C127—22no—
108C2×C8×C127—24no—
109C2×C8×C127—44no—
110C4⋊C4×C127—22no—
111C4⋊C4×C127C2×D414yes—
112C22⋊C4×C127—28no—
113C22⋊C4×C127—24no—
114C22⋊C4×C127—24no—
115C42×C127C2×D411yescharacteristic
116C42×C127C2×D412yes—
117C42×C127C2411yescharacteristic
118C23×C127—24no—
119C23×C127—28no—
120C23×C127—24no—
121C23×C127—432no—
122C23×C127—44no—
123C23×C127—44no—
124C23×C127—48no—
125C23×C127—44no—
126C23×C127—42no—
127C23×C127—88no—
128C23×C127—832no—
129C23×C127—84no—
130C23×C127—82no—
131C23×C127#12011yescharacteristic
132D4×C127—24no—
133D4×C127—28no—
134D4×C127—44no—
135D4×C127—44no—
136D4×C127—432no—
137D4×C127—44no—
138D4×C127—44no—
139D4×C127—44no—
140D4×C127—44no—
141D4×C127—48no—
142D4×C127—82no—
143D4×C127—82no—
144D4×C127—84no—
145D4×C127C2×D818yescomplemented
146C2×C4×C127—22no—
147C2×C4×C127—24no—
148C2×C4×C127—44no—
149C2×C4×C127—44no—
150C2×C4×C127—44no—
151C2×C4×C127—48no—
152C2×C4×C127#12011yescharacteristic
153C2×C4×C127#12012yes—
154C2×C4×C127C2×D814yes—
155C2×C4×C127AGL(1,ℤ/8)14yes—
156C2×C4×C127C22×D411yescharacteristic
157C2×C4×C127C22×D412yes—
158C8×C127—24no—
159C8×C127—44no—
160C22×C127—28no—
161C22×C127—416no—
162C22×C127—44no—
163C22×C127—44no—
164C22×C127—48no—
165C22×C127—44no—
166C22×C127—832no—
167C22×C127—88no—
168C22×C127—84no—
169C22×C127—82no—
170C22×C127—164no—
171C22×C127#44714yes—
172C22×C127#45312yes—
173C22×C127C2×#12011yescharacteristic
174C4×C127—21no—
175C4×C127—21no—
176C4×C127—44no—
177C4×C127#44714yes—
178C4×C127C22×D812yes—
179C4×C127C2×AGL(1,ℤ/8)12yes—
180C2×#1619C12711yesmaximal, characteristic, direct product factor, Sylow
181C2×C127—48no—
182C2×C127—84no—
183C2×C127—162no—
184C2×C127#161914yesdirect product factor
185C2×C127C2×#44712yes—
186C2×C127C2×#45311yescharacteristic
187C2×D42C2×C12711yescharacteristic, complemented
188C2×#493C2×C12711yescharacteristic, complemented
189C2×#459C2×C12712yescomplemented
190#1619C2×C12718yesdirect product factor
191C2×#331C2×C12711yescharacteristic, complemented
192C2×D4⋊C8C2×C12712yescomplemented
193C127C2×#161911yescharacteristic, direct product factor, Sylow
194C23×D4—22no—
195C22×D8—22no—
196C22×D8—22no—
197D42—22no—
198D42—24no—
199D42C22×C12714yescomplemented
200C2×#127C22×C12711yescharacteristic
201C2×#127C22×C12711yescharacteristic, complemented
202C2×#121—22no—
203C2×#120—22no—
204C2×C4×D4C22×C12712yes—
205#493—22no—
206#493C22×C12714yescomplemented
207#459—24no—
208#459C22×C12718yescomplemented
209C2×C4⋊C8C22×C12712yescomplemented
210C2×#102—22no—
211C2×C4×C8C22×C12711yescharacteristic, complemented
212#331C22×C12714yescomplemented
213D4⋊C8C22×C12718yescomplemented
214C25—22no—
215C22×D4—24no—
216C22×D4—28no—
217C22×D4—28no—
218C22×D4—22no—
219C22×D4—21no—
220C22×D4—22no—
221C22×D4—48no—
222C22×D4—48no—
223C22×D4D4×C12712yes—
224C22×D4D4×C12712yes—
225C23×C4—22no—
226C2×D8—28no—
227C2×D8—28no—
228C2×D8—48no—
229C2×D8—48no—
230C22×C8—21no—
231C22×C8—22no—
232#127—22no—
233#127—22no—
234#127—21no—
235#127D4×C12712yes—
236#127C23×C12712yes—
237#127C23×C12712yescomplemented
238#121—28no—
239#121—28no—
240#120—28no—
241#120—28no—
242C4×D4—22no—
243C4×D4—22no—
244C4×D4D4×C12714yes—
245C4×D4C23×C12714yes—
246C2×C4⋊C4D4×C12712yes—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—22no—
249C2×C42C23×C12711yescharacteristic
250C4⋊C8—22no—
251C4⋊C8C23×C12714yescomplemented
252#102—28no—
253C4×C8—21no—
254C4×C8C23×C12712yescomplemented
255C24—22no—
256C24—28no—
257C24—22no—
258C24—416no—
259C24—41no—
260C24—84no—
261C2×D4—216no—
262C2×D4—22no—
263C2×D4—24no—
264C2×D4—22no—
265C2×D4—24no—
266C2×D4—24no—
267C2×D4—24no—
268C2×D4—22no—
269C2×D4—44no—
270C2×D4—44no—
271C2×D4—416no—
272C2×D4—432no—
273C2×D4—416no—
274C2×D4—416no—
275C2×D4—41no—
276C2×D4—42no—
277C2×D4—44no—
278C2×D4—44no—
279C2×D4—44no—
280C2×D4—44no—
281C2×D4D8×C12718yescomplemented
282C2×D4C2×D4×C12714yes—
283C2×D4C2×D4×C12714yes—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—44no—
288C22×C4—44no—
289C22×C4C2×D4×C12711yescharacteristic
290C22×C4C2×D4×C12712yes—
291D8—416no—
292D8—416no—
293C2×C8—24no—
294C2×C8—22no—
295C2×C8—24no—
296C2×C8—44no—
297C4⋊C4—22no—
298C4⋊C4C2×D4×C12714yes—
299C22⋊C4—28no—
300C22⋊C4—24no—
301C22⋊C4—24no—
302C42C2×D4×C12711yescharacteristic
303C42C2×D4×C12712yes—
304C42C24×C12711yescharacteristic
305C23—24no—
306C23—28no—
307C23—24no—
308C23—432no—
309C23—44no—
310C23—44no—
311C23—48no—
312C23—44no—
313C23—42no—
314C23—88no—
315C23—832no—
316C23—84no—
317C23—82no—
318C23#120×C12711yescharacteristic
319D4—24no—
320D4—28no—
321D4—44no—
322D4—44no—
323D4—432no—
324D4—44no—
325D4—44no—
326D4—44no—
327D4—44no—
328D4—48no—
329D4—82no—
330D4—82no—
331D4—84no—
332D4C2×D8×C12718yescomplemented
333C2×C4—22no—
334C2×C4—24no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—48no—
339C2×C4#120×C12711yescharacteristic
340C2×C4#120×C12712yes—
341C2×C4C2×D8×C12714yes—
342C2×C4AGL(1,ℤ/8)×C12714yes—
343C2×C4C22×D4×C12711yescharacteristic
344C2×C4C22×D4×C12712yes—
345C8—24no—
346C8—44no—
347C22—28no—
348C22—416no—
349C22—44no—
350C22—44no—
351C22—48no—
352C22—44no—
353C22—832no—
354C22—88no—
355C22—84no—
356C22—82no—
357C22—164no—
358C22#447×C12714yes—
359C22#453×C12712yes—
360C22C2×#120×C12711yescharacteristic
361C4—21no—
362C4—21no—
363C4—44no—
364C4#447×C12714yes—
365C4C22×D8×C12712yes—
366C4C2×AGL(1,ℤ/8)×C12712yes—
367C2—48no—
368C2—84no—
369C2—162no—
370C2C127×#161914yesdirect product factor
371C2C2×#447×C12712yes—
372C2C2×#453×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC42C24×C127
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
1. C2×D42×C127C2semidirect
2. C2×#493×C127C2semidirect
3. C2×#459×C127C2semidirect
4. C127×#1619C2direct (N × H)
5. C2×#331×C127C2semidirect
6. C2×D4⋊C8×C127C2semidirect
12. D42×C127C22semidirect
14. C2×#127×C127C22semidirect
19. #493×C127C22semidirect
21. #459×C127C22semidirect
22. C2×C4⋊C8×C127C22semidirect
24. C2×C4×C8×C127C22semidirect
25. #331×C127C22semidirect
26. D4⋊C8×C127C22semidirect
50. #127×C127C23semidirect
64. C4⋊C8×C127C23semidirect
67. C4×C8×C127C23semidirect
94. C2×D4×C127D8semidirect
145. D4×C127C2×D8semidirect
180. C2×#1619C127direct (N × H)
184. C2×C127#1619direct (N × H)
187. C2×D42C2×C127semidirect
188. C2×#493C2×C127semidirect
189. C2×#459C2×C127semidirect
190. #1619C2×C127direct (N × H)
191. C2×#331C2×C127semidirect
192. C2×D4⋊C8C2×C127semidirect
193. C127C2×#1619direct (N × H)
199. D42C22×C127semidirect
201. C2×#127C22×C127semidirect
206. #493C22×C127semidirect
208. #459C22×C127semidirect
209. C2×C4⋊C8C22×C127semidirect
211. C2×C4×C8C22×C127semidirect
212. #331C22×C127semidirect
213. D4⋊C8C22×C127semidirect
237. #127C23×C127semidirect
251. C4⋊C8C23×C127semidirect
254. C4×C8C23×C127semidirect
281. C2×D4D8×C127semidirect
332. D4C2×D8×C127semidirect
370. C2C127×#1619direct (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×#493×C1272
C2×#459×C1272
C127×#16192
C2×#331×C1272
C2×D4⋊C8×C1272
C2×#1619127