Finite Group Databasebeta

← C127×#2410 #30635362

Subgroups — C127×#2410 #30635362

Order 16256.

1246 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D4×C127C211yesmaximal, characteristic, complemented
2C2×#121×C127C212yesmaximal, complemented
3C2×#120×C127C211yesmaximal, characteristic, complemented
4C2×#120×C127C211yesmaximal, characteristic, complemented
5C22×C22⋊C4×C127C211yesmaximal, characteristic, complemented
6#394×C127C212yesmaximal, complemented
7#392×C127C212yesmaximal, complemented
8#386×C127C211yesmaximal, characteristic, complemented
9#386×C127C212yesmaximal, complemented
10#385×C127C211yesmaximal, characteristic, complemented
11#379×C127C211yesmaximal, characteristic, complemented
12C25×C127C2211yescharacteristic
13C25×C127C2211yescharacteristic
14C22×D4×C127—24no—
15C22×D4×C127—28no—
16C22×D4×C127C2211yescharacteristic
17C22×D4×C127C2212yes—
18C22×D4×C127C2212yes—
19C22×D4×C127C2211yescharacteristic, complemented
20C22×D4×C127C2212yescomplemented
21C22×D4×C127C2211yescharacteristic, complemented
22C23×C4×C127C2211yescharacteristic
23C23×C4×C127C2212yescomplemented
24#121×C127—28no—
25#120×C127—24no—
26#120×C127—24no—
27C2×C4⋊C4×C127C2212yescomplemented
28C2×C22⋊C4×C127—24no—
29C2×C22⋊C4×C127C2211yescharacteristic
30C2×C22⋊C4×C127C2211yescharacteristic
31C2×C22⋊C4×C127C2211yescharacteristic
32C2×C22⋊C4×C127C2212yescomplemented
33C2×C22⋊C4×C127C2211yescharacteristic, complemented
34C2×C22⋊C4×C127C2212yescomplemented
35C2×C22⋊C4×C127C2211yescharacteristic, complemented
36C2×C22⋊C4×C127C2212yescomplemented
37C2×C22⋊C4×C127C2212yescomplemented
38C2×C22⋊C4×C127C2212yescomplemented
39#95×C127C2212yescomplemented
40#95×C127C2212yescomplemented
41C24×C127—22no—
42C24×C127—24no—
43C24×C127—24no—
44C24×C127—22no—
45C24×C127—22no—
46C24×C127—22no—
47C24×C127—22no—
48C24×C127—42no—
49C24×C127—42no—
50C24×C127D414yescomplemented
51C24×C127C2311yescharacteristic
52C24×C127C2311yescharacteristic
53C24×C127C2312yes—
54C24×C127C2311yescharacteristic
55C24×C127C2311yescharacteristic
56C2×D4×C127—232no—
57C2×D4×C127—24no—
58C2×D4×C127—24no—
59C2×D4×C127—24no—
60C2×D4×C127—24no—
61C2×D4×C127—22no—
62C2×D4×C127—22no—
63C2×D4×C127—22no—
64C2×D4×C127—22no—
65C2×D4×C127—24no—
66C2×D4×C127—24no—
67C2×D4×C127—22no—
68C2×D4×C127—24no—
69C2×D4×C127—24no—
70C2×D4×C127—42no—
71C2×D4×C127—42no—
72C2×D4×C127D418yescomplemented
73C22×C4×C127—22no—
74C22×C4×C127—24no—
75C22×C4×C127—24no—
76C22×C4×C127—24no—
77C22×C4×C127—42no—
78C22×C4×C127C2311yescharacteristic
79C22×C4×C127C2311yescharacteristic
80C22×C4×C127C2312yes—
81C22×C4×C127C2311yescharacteristic
82C22×C4×C127C2312yes—
83C22×C4×C127C2312yes—
84C4⋊C4×C127—24no—
85C22⋊C4×C127—22no—
86C22⋊C4×C127—22no—
87C22⋊C4×C127—22no—
88C22⋊C4×C127—22no—
89C22⋊C4×C127—24no—
90C22⋊C4×C127—24no—
91C22⋊C4×C127—24no—
92C22⋊C4×C127—24no—
93C22⋊C4×C127—42no—
94C22⋊C4×C127D414yescomplemented
95C23×C127—21no—
96C23×C127—22no—
97C23×C127—21no—
98C23×C127—22no—
99C23×C127—22no—
100C23×C127—28no—
101C23×C127—28no—
102C23×C127—28no—
103C23×C127—21no—
104C23×C127—22no—
105C23×C127—22no—
106C23×C127—22no—
107C23×C127—22no—
108C23×C127—21no—
109C23×C127—22no—
110C23×C127—22no—
111C23×C127—22no—
112C23×C127—22no—
113C23×C127—22no—
114C23×C127—21no—
115C23×C127—21no—
116C23×C127—21no—
117C23×C127—22no—
118C23×C127—44no—
119C23×C127—48no—
120C23×C127—48no—
121C23×C127—48no—
122C23×C127—48no—
123C23×C127—44no—
124C23×C127—44no—
125C23×C127C2×D412yes—
126C23×C127C2×D414yes—
127C23×C127C2×D412yes—
128C23×C127C2×D414yes—
129C23×C127C2×D412yes—
130C23×C127C2×D412yes—
131C23×C127#4112yes—
132C23×C127C2411yescharacteristic
133D4×C127—216no—
134D4×C127—216no—
135D4×C127—48no—
136D4×C127—44no—
137D4×C127—44no—
138D4×C127—44no—
139C2×C4×C127—28no—
140C2×C4×C127—22no—
141C2×C4×C127—22no—
142C2×C4×C127—22no—
143C2×C4×C127—22no—
144C2×C4×C127—22no—
145C2×C4×C127—22no—
146C2×C4×C127—21no—
147C2×C4×C127—21no—
148C2×C4×C127—21no—
149C2×C4×C127—21no—
150C2×C4×C127—22no—
151C2×C4×C127—21no—
152C2×C4×C127—22no—
153C2×C4×C127—22no—
154C2×C4×C127—48no—
155C2×C4×C127C2×D414yes—
156C2×C4×C127C2×D414yescomplemented
157C22×C127—22no—
158C22×C127—22no—
159C22×C127—22no—
160C22×C127—22no—
161C22×C127—24no—
162C22×C127—24no—
163C22×C127—24no—
164C22×C127—24no—
165C22×C127—22no—
166C22×C127—24no—
167C22×C127—22no—
168C22×C127—22no—
169C22×C127—24no—
170C22×C127—24no—
171C22×C127—416no—
172C22×C127—416no—
173C22×C127—42no—
174C22×C127—42no—
175C22×C127—42no—
176C22×C127—42no—
177C22×C127—42no—
178C22×C127—42no—
179C22×C127—41no—
180C22×C127—41no—
181C22×C127—41no—
182C22×C127—42no—
183C22×C127—42no—
184C22×C127#12014yescomplemented
185C22×C127#12114yescomplemented
186C22×C127C22×D411yescharacteristic
187C22×C127C22×D412yes—
188C22×C127C22×D411yescharacteristic
189C22×C127C2×#4111yescharacteristic
190C22×C127H(5,𝔽2)12yes—
191C4×C127—24no—
192C4×C127—24no—
193C4×C127—41no—
194C4×C127—41no—
195C4×C127—41no—
196C4×C127—42no—
197C2×C127—24no—
198C2×C127—24no—
199C2×C127—42no—
200C2×C127—44no—
201C2×C127—81no—
202C2×C127C2×#12011yescharacteristic
203C2×C127C2×#12111yescharacteristic
204C2×C127#53411yescharacteristic
205C2×C127D4212yes—
206C2×C127#54612yes—
207#2410C12711yesmaximal, characteristic, direct product factor, Sylow
208C127#241011yescharacteristic, direct product factor, Sylow
209C23×D4C2×C12711yescharacteristic, complemented
210C2×#121C2×C12712yescomplemented
211C2×#120C2×C12711yescharacteristic, complemented
212C2×#120C2×C12711yescharacteristic, complemented
213C22×C22⋊C4C2×C12711yescharacteristic, complemented
214#394C2×C12712yescomplemented
215#392C2×C12712yescomplemented
216#386C2×C12711yescharacteristic, complemented
217#386C2×C12712yescomplemented
218#385C2×C12711yescharacteristic, complemented
219#379C2×C12711yescharacteristic, complemented
220C25C22×C12711yescharacteristic
221C25C22×C12711yescharacteristic
222C22×D4—24no—
223C22×D4—28no—
224C22×D4C22×C12711yescharacteristic
225C22×D4C22×C12712yes—
226C22×D4C22×C12712yes—
227C22×D4C22×C12711yescharacteristic, complemented
228C22×D4C22×C12712yescomplemented
229C22×D4C22×C12711yescharacteristic, complemented
230C23×C4C22×C12711yescharacteristic
231C23×C4C22×C12712yescomplemented
232#121—28no—
233#120—24no—
234#120—24no—
235C2×C4⋊C4C22×C12712yescomplemented
236C2×C22⋊C4—24no—
237C2×C22⋊C4C22×C12711yescharacteristic
238C2×C22⋊C4C22×C12711yescharacteristic
239C2×C22⋊C4C22×C12711yescharacteristic
240C2×C22⋊C4C22×C12712yescomplemented
241C2×C22⋊C4C22×C12711yescharacteristic, complemented
242C2×C22⋊C4C22×C12712yescomplemented
243C2×C22⋊C4C22×C12711yescharacteristic, complemented
244C2×C22⋊C4C22×C12712yescomplemented
245C2×C22⋊C4C22×C12712yescomplemented
246C2×C22⋊C4C22×C12712yescomplemented
247#95C22×C12712yescomplemented
248#95C22×C12712yescomplemented
249C24—22no—
250C24—24no—
251C24—24no—
252C24—22no—
253C24—22no—
254C24—22no—
255C24—22no—
256C24—42no—
257C24—42no—
258C24D4×C12714yescomplemented
259C24C23×C12711yescharacteristic
260C24C23×C12711yescharacteristic
261C24C23×C12712yes—
262C24C23×C12711yescharacteristic
263C24C23×C12711yescharacteristic
264C2×D4—232no—
265C2×D4—24no—
266C2×D4—24no—
267C2×D4—24no—
268C2×D4—24no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—24no—
274C2×D4—24no—
275C2×D4—22no—
276C2×D4—24no—
277C2×D4—24no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4D4×C12718yescomplemented
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—42no—
286C22×C4C23×C12711yescharacteristic
287C22×C4C23×C12711yescharacteristic
288C22×C4C23×C12712yes—
289C22×C4C23×C12711yescharacteristic
290C22×C4C23×C12712yes—
291C22×C4C23×C12712yes—
292C4⋊C4—24no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—24no—
298C22⋊C4—24no—
299C22⋊C4—24no—
300C22⋊C4—24no—
301C22⋊C4—42no—
302C22⋊C4D4×C12714yescomplemented
303C23—21no—
304C23—22no—
305C23—21no—
306C23—22no—
307C23—22no—
308C23—28no—
309C23—28no—
310C23—28no—
311C23—21no—
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—21no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—22no—
326C23—44no—
327C23—48no—
328C23—48no—
329C23—48no—
330C23—48no—
331C23—44no—
332C23—44no—
333C23C2×D4×C12712yes—
334C23C2×D4×C12714yes—
335C23C2×D4×C12712yes—
336C23C2×D4×C12714yes—
337C23C2×D4×C12712yes—
338C23C2×D4×C12712yes—
339C23#41×C12712yes—
340C23C24×C12711yescharacteristic
341D4—216no—
342D4—216no—
343D4—48no—
344D4—44no—
345D4—44no—
346D4—44no—
347C2×C4—28no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—48no—
363C2×C4C2×D4×C12714yes—
364C2×C4C2×D4×C12714yescomplemented
365C22—22no—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—24no—
370C22—24no—
371C22—24no—
372C22—24no—
373C22—22no—
374C22—24no—
375C22—22no—
376C22—22no—
377C22—24no—
378C22—24no—
379C22—416no—
380C22—416no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—42no—
392C22#120×C12714yescomplemented
393C22#121×C12714yescomplemented
394C22C22×D4×C12711yescharacteristic
395C22C22×D4×C12712yes—
396C22C22×D4×C12711yescharacteristic
397C22C2×#41×C12711yescharacteristic
398C22H(5,𝔽2)×C12712yes—
399C4—24no—
400C4—24no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—42no—
405C2—24no—
406C2—24no—
407C2—42no—
408C2—44no—
409C2—81no—
410C2C2×#120×C12711yescharacteristic
411C2C2×#121×C12711yescharacteristic
412C2#534×C12711yescharacteristic
413C2D42×C12712yes—
414C2#546×C12712yes—
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×D4×C127C2semidirect
2. C2×#121×C127C2semidirect
3. C2×#120×C127C2semidirect
4. C2×#120×C127C2semidirect
5. C22×C22⋊C4×C127C2semidirect
6. #394×C127C2semidirect
7. #392×C127C2semidirect
8. #386×C127C2semidirect
9. #386×C127C2semidirect
10. #385×C127C2semidirect
11. #379×C127C2semidirect
19. C22×D4×C127C22semidirect
20. C22×D4×C127C22semidirect
21. C22×D4×C127C22semidirect
23. C23×C4×C127C22semidirect
27. C2×C4⋊C4×C127C22semidirect
32. C2×C22⋊C4×C127C22semidirect
33. C2×C22⋊C4×C127C22semidirect
34. C2×C22⋊C4×C127C22semidirect
35. C2×C22⋊C4×C127C22semidirect
36. C2×C22⋊C4×C127C22semidirect
37. C2×C22⋊C4×C127C22semidirect
38. C2×C22⋊C4×C127C22semidirect
39. #95×C127C22semidirect
40. #95×C127C22semidirect
50. C24×C127D4semidirect
72. C2×D4×C127D4semidirect
94. C22⋊C4×C127D4semidirect
156. C2×C4×C127C2×D4semidirect
184. C22×C127#120semidirect
185. C22×C127#121semidirect
207. #2410C127direct (N × H)
208. C127#2410direct (N × H)
209. C23×D4C2×C127semidirect
210. C2×#121C2×C127semidirect
211. C2×#120C2×C127semidirect
212. C2×#120C2×C127semidirect
213. C22×C22⋊C4C2×C127semidirect
214. #394C2×C127semidirect
215. #392C2×C127semidirect
216. #386C2×C127semidirect
217. #386C2×C127semidirect
218. #385C2×C127semidirect
219. #379C2×C127semidirect
227. C22×D4C22×C127semidirect
228. C22×D4C22×C127semidirect
229. C22×D4C22×C127semidirect
231. C23×C4C22×C127semidirect
235. C2×C4⋊C4C22×C127semidirect
240. C2×C22⋊C4C22×C127semidirect
241. C2×C22⋊C4C22×C127semidirect
242. C2×C22⋊C4C22×C127semidirect
243. C2×C22⋊C4C22×C127semidirect
244. C2×C22⋊C4C22×C127semidirect
245. C2×C22⋊C4C22×C127semidirect
246. C2×C22⋊C4C22×C127semidirect
247. #95C22×C127semidirect
248. #95C22×C127semidirect
258. C24D4×C127semidirect
280. C2×D4D4×C127semidirect
302. C22⋊C4D4×C127semidirect
364. C2×C4C2×D4×C127semidirect
392. C22#120×C127semidirect
393. C22#121×C127semidirect

Maximal subgroups

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

subgroupindex
C23×D4×C1272
C2×#121×C1272
C2×#120×C1272
C22×C22⋊C4×C1272
#394×C1272
#392×C1272
#386×C1272
#385×C1272
#379×C1272
#2410127