Finite Group Databasebeta

← C127×#20633 #44584306

Subgroups — C127×#20633 #44584306

Order 32512.

1690 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#518×C127C211yesmaximal, characteristic
2C22×#99×C127C212yesmaximal
3C127×#2315C212yesmaximal, complemented
4C127×#1799C218yesmaximal, complemented
5C2×#342×C127C212yesmaximal, complemented
6C23×D4×C127C2211yescharacteristic
7#518×C127—28no—
8C2×C4×D4×C127C414yescomplemented
9C2×C4×D4×C127C2214yes—
10C2×#117×C127C412yescomplemented
11C22×C22⋊C4×C127C412yescomplemented
12C22×C22⋊C4×C127C2214yes—
13C22×C22⋊C4×C127C2211yescharacteristic
14C22×C22⋊C4×C127C2211yescharacteristic
15C2×#99×C127—28no—
16C2×#99×C127C2218yes—
17#385×C127—28no—
18#380×C127C2218yescomplemented
19#342×C127C2218yescomplemented
20C25×C127C2×C411yescharacteristic
21C25×C127C2311yescharacteristic
22C22×D4×C127—24no—
23C22×D4×C127—24no—
24C22×D4×C127C2×C412yes—
25C22×D4×C127D414yes—
26C22×D4×C127Q814yes—
27C22×D4×C127C2312yes—
28C23×C4×C127—24no—
29C23×C4×C127C2×C411yescharacteristic
30C23×C4×C127C2×C412yes—
31C23×C4×C127C2×C414yescomplemented
32C23×C4×C127C2312yes—
33C4×D4×C127—216no—
34C4×D4×C127—216no—
35#117×C127—28no—
36C2×C4⋊C4×C127—28no—
37C2×C4⋊C4×C127C2×C414yescomplemented
38C2×C22⋊C4×C127—24no—
39C2×C22⋊C4×C127—28no—
40C2×C22⋊C4×C127—28no—
41C2×C22⋊C4×C127—28no—
42C2×C22⋊C4×C127—24no—
43C2×C22⋊C4×C127C2×C412yes—
44C2×C22⋊C4×C127C2×C412yes—
45C2×C22⋊C4×C127C2×C412yes—
46C2×C22⋊C4×C127C2×C414yescomplemented
47C2×C22⋊C4×C127D418yes—
48C2×C22⋊C4×C127C2318yes—
49C2×C22⋊C4×C127C2312yes—
50C2×C42×C127C2×C414yescomplemented
51#99×C127—216no—
52#95×C127—28no—
53C24×C127—22no—
54C24×C127—22no—
55C24×C127—82no—
56C24×C127—82no—
57C24×C127C4⋊C414yescomplemented
58C24×C127C22×C412yes—
59C24×C127C22×C411yescharacteristic
60C24×C127C22×C411yescharacteristic
61C24×C127C2×D414yes—
62C24×C127C2×D412yes—
63C24×C127C2×Q812yes—
64C24×C127#4114yes—
65C24×C127C2411yescharacteristic
66C2×D4×C127—24no—
67C2×D4×C127—24no—
68C2×D4×C127—216no—
69C2×D4×C127—216no—
70C2×D4×C127—24no—
71C2×D4×C127—24no—
72C2×D4×C127C4⋊C418yescomplemented
73C2×D4×C127C2×D414yes—
74C2×D4×C127C2×Q814yes—
75C22×C4×C127—22no—
76C22×C4×C127—22no—
77C22×C4×C127—24no—
78C22×C4×C127—28no—
79C22×C4×C127—28no—
80C22×C4×C127—48no—
81C22×C4×C127—82no—
82C22×C4×C127—88no—
83C22×C4×C127—82no—
84C22×C4×C127—84no—
85C22×C4×C127C4⋊C414yescomplemented
86C22×C4×C127C22×C412yes—
87C22×C4×C127C22×C414yes—
88C22×C4×C127C22×C414yes—
89C22×C4×C127C2×D418yes—
90C4⋊C4×C127—28no—
91C4⋊C4×C127—88no—
92C22⋊C4×C127—24no—
93C22⋊C4×C127—24no—
94C22⋊C4×C127—28no—
95C22⋊C4×C127—28no—
96C22⋊C4×C127—28no—
97C22⋊C4×C127—48no—
98C22⋊C4×C127C22⋊C418yes—
99C22⋊C4×C127C22⋊C418yes—
100C42×C127—28no—
101C23×C127—22no—
102C23×C127—22no—
103C23×C127—28no—
104C23×C127—42no—
105C23×C127—48no—
106C23×C127—42no—
107C23×C127—42no—
108C23×C127—44no—
109C23×C127—84no—
110C23×C127—82no—
111C23×C127—82no—
112C23×C127—84no—
113C23×C127—84no—
114C23×C127—84no—
115C23×C127C2×C22⋊C412yes—
116C23×C127C2×C22⋊C412yes—
117C23×C127C2×C4⋊C414yes—
118C23×C127C2×C4⋊C412yes—
119C23×C127C2×C4⋊C412yes—
120C23×C127#11712yes—
121C23×C127#11712yes—
122C23×C127#12118yes—
123C23×C127C22⋊Q818yes—
124C23×C127C23×C411yescharacteristic
125C23×C127C22×D412yes—
126C23×C127C22×D411yescharacteristic
127C23×C127C22×Q811yescharacteristic
128C23×C127C2×#4112yes—
129D4×C127—28no—
130D4×C127—28no—
131D4×C127—216no—
132C2×C4×C127—22no—
133C2×C4×C127—22no—
134C2×C4×C127—28no—
135C2×C4×C127—24no—
136C2×C4×C127—48no—
137C2×C4×C127—44no—
138C2×C4×C127—44no—
139C2×C4×C127—416no—
140C2×C4×C127—48no—
141C2×C4×C127—88no—
142C2×C4×C127—84no—
143C2×C4×C127—816no—
144C2×C4×C127C2×C22⋊C418yes—
145C2×C4×C127C2×C4⋊C414yes—
146C22×C127—24no—
147C22×C127—22no—
148C22×C127—24no—
149C22×C127—24no—
150C22×C127—24no—
151C22×C127—48no—
152C22×C127—42no—
153C22×C127—42no—
154C22×C127—42no—
155C22×C127—42no—
156C22×C127—48no—
157C22×C127—41no—
158C22×C127—41no—
159C22×C127—42no—
160C22×C127—44no—
161C22×C127—44no—
162C22×C127—44no—
163C22×C127—88no—
164C22×C127#38014yes—
165C22×C127#38014yes—
166C22×C127C22×C22⋊C411yescharacteristic
167C22×C127C22×C4⋊C411yescharacteristic
168C22×C127C2×#11711yescharacteristic
169C22×C127C2×#12112yes—
170C22×C127C2×C22⋊Q812yes—
171C4×C127—28no—
172C4×C127—24no—
173C4×C127—44no—
174C4×C127—88no—
175#20633C12711yesmaximal, characteristic, direct product factor, Sylow
176C2×C127—22no—
177C2×C127—21no—
178C2×C127—21no—
179C2×C127—24no—
180C2×C127—22no—
181C2×C127—24no—
182C2×C127—44no—
183C2×C127C2×#38011yescharacteristic
184C2×C127#288312yes—
185C2×#518C2×C12711yescharacteristic
186C22×#99C2×C12712yes—
187#2315C2×C12712yescomplemented
188#1799C2×C12718yescomplemented
189C2×#342C2×C12712yescomplemented
190C127#2063311yescharacteristic, direct product factor, Sylow
191C23×D4C22×C12711yescharacteristic
192#518—28no—
193C2×C4×D4C4×C12714yescomplemented
194C2×C4×D4C22×C12714yes—
195C2×#117C4×C12712yescomplemented
196C22×C22⋊C4C4×C12712yescomplemented
197C22×C22⋊C4C22×C12714yes—
198C22×C22⋊C4C22×C12711yescharacteristic
199C22×C22⋊C4C22×C12711yescharacteristic
200C2×#99—28no—
201C2×#99C22×C12718yes—
202#385—28no—
203#380C22×C12718yescomplemented
204#342C22×C12718yescomplemented
205C25C2×C4×C12711yescharacteristic
206C25C23×C12711yescharacteristic
207C22×D4—24no—
208C22×D4—24no—
209C22×D4C2×C4×C12712yes—
210C22×D4D4×C12714yes—
211C22×D4Q8×C12714yes—
212C22×D4C23×C12712yes—
213C23×C4—24no—
214C23×C4C2×C4×C12711yescharacteristic
215C23×C4C2×C4×C12712yes—
216C23×C4C2×C4×C12714yescomplemented
217C23×C4C23×C12712yes—
218C4×D4—216no—
219C4×D4—216no—
220#117—28no—
221C2×C4⋊C4—28no—
222C2×C4⋊C4C2×C4×C12714yescomplemented
223C2×C22⋊C4—24no—
224C2×C22⋊C4—28no—
225C2×C22⋊C4—28no—
226C2×C22⋊C4—28no—
227C2×C22⋊C4—24no—
228C2×C22⋊C4C2×C4×C12712yes—
229C2×C22⋊C4C2×C4×C12712yes—
230C2×C22⋊C4C2×C4×C12712yes—
231C2×C22⋊C4C2×C4×C12714yescomplemented
232C2×C22⋊C4D4×C12718yes—
233C2×C22⋊C4C23×C12718yes—
234C2×C22⋊C4C23×C12712yes—
235C2×C42C2×C4×C12714yescomplemented
236#99—216no—
237#95—28no—
238C24—22no—
239C24—22no—
240C24—82no—
241C24—82no—
242C24C4⋊C4×C12714yescomplemented
243C24C22×C4×C12712yes—
244C24C22×C4×C12711yescharacteristic
245C24C22×C4×C12711yescharacteristic
246C24C2×D4×C12714yes—
247C24C2×D4×C12712yes—
248C24C2×Q8×C12712yes—
249C24#41×C12714yes—
250C24C24×C12711yescharacteristic
251C2×D4—24no—
252C2×D4—24no—
253C2×D4—216no—
254C2×D4—216no—
255C2×D4—24no—
256C2×D4—24no—
257C2×D4C4⋊C4×C12718yescomplemented
258C2×D4C2×D4×C12714yes—
259C2×D4C2×Q8×C12714yes—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—24no—
263C22×C4—28no—
264C22×C4—28no—
265C22×C4—48no—
266C22×C4—82no—
267C22×C4—88no—
268C22×C4—82no—
269C22×C4—84no—
270C22×C4C4⋊C4×C12714yescomplemented
271C22×C4C22×C4×C12712yes—
272C22×C4C22×C4×C12714yes—
273C22×C4C22×C4×C12714yes—
274C22×C4C2×D4×C12718yes—
275C4⋊C4—28no—
276C4⋊C4—88no—
277C22⋊C4—24no—
278C22⋊C4—24no—
279C22⋊C4—28no—
280C22⋊C4—28no—
281C22⋊C4—28no—
282C22⋊C4—48no—
283C22⋊C4C22⋊C4×C12718yes—
284C22⋊C4C22⋊C4×C12718yes—
285C42—28no—
286C23—22no—
287C23—22no—
288C23—28no—
289C23—42no—
290C23—48no—
291C23—42no—
292C23—42no—
293C23—44no—
294C23—84no—
295C23—82no—
296C23—82no—
297C23—84no—
298C23—84no—
299C23—84no—
300C23C2×C22⋊C4×C12712yes—
301C23C2×C22⋊C4×C12712yes—
302C23C2×C4⋊C4×C12714yes—
303C23C2×C4⋊C4×C12712yes—
304C23C2×C4⋊C4×C12712yes—
305C23#117×C12712yes—
306C23#117×C12712yes—
307C23#121×C12718yes—
308C23C22⋊Q8×C12718yes—
309C23C23×C4×C12711yescharacteristic
310C23C22×D4×C12712yes—
311C23C22×D4×C12711yescharacteristic
312C23C22×Q8×C12711yescharacteristic
313C23C2×#41×C12712yes—
314D4—28no—
315D4—28no—
316D4—216no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—28no—
320C2×C4—24no—
321C2×C4—48no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—416no—
325C2×C4—48no—
326C2×C4—88no—
327C2×C4—84no—
328C2×C4—816no—
329C2×C4C2×C22⋊C4×C12718yes—
330C2×C4C2×C4⋊C4×C12714yes—
331C22—24no—
332C22—22no—
333C22—24no—
334C22—24no—
335C22—24no—
336C22—48no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22—48no—
342C22—41no—
343C22—41no—
344C22—42no—
345C22—44no—
346C22—44no—
347C22—44no—
348C22—88no—
349C22#380×C12714yes—
350C22#380×C12714yes—
351C22C22×C22⋊C4×C12711yescharacteristic
352C22C22×C4⋊C4×C12711yescharacteristic
353C22C2×#117×C12711yescharacteristic
354C22C2×#121×C12712yes—
355C22C2×C22⋊Q8×C12712yes—
356C4—28no—
357C4—24no—
358C4—44no—
359C4—88no—
360C2—22no—
361C2—21no—
362C2—21no—
363C2—24no—
364C2—22no—
365C2—24no—
366C2—44no—
367C2C2×#380×C12711yescharacteristic
368C2C127×#288312yes—
subgroupG/H
center, socleC22×C127C22×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C22⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#2315C2semidirect
4. C127×#1799C2semidirect
5. C2×#342×C127C2semidirect
8. C2×C4×D4×C127C4semidirect
10. C2×#117×C127C4semidirect
11. C22×C22⋊C4×C127C4semidirect
18. #380×C127C22semidirect
19. #342×C127C22semidirect
31. C23×C4×C127C2×C4semidirect
37. C2×C4⋊C4×C127C2×C4semidirect
46. C2×C22⋊C4×C127C2×C4semidirect
50. C2×C42×C127C2×C4semidirect
57. C24×C127C4⋊C4semidirect
72. C2×D4×C127C4⋊C4semidirect
85. C22×C4×C127C4⋊C4semidirect
175. #20633C127direct (N × H)
187. #2315C2×C127semidirect
188. #1799C2×C127semidirect
189. C2×#342C2×C127semidirect
190. C127#20633direct (N × H)
193. C2×C4×D4C4×C127semidirect
195. C2×#117C4×C127semidirect
196. C22×C22⋊C4C4×C127semidirect
203. #380C22×C127semidirect
204. #342C22×C127semidirect
216. C23×C4C2×C4×C127semidirect
222. C2×C4⋊C4C2×C4×C127semidirect
231. C2×C22⋊C4C2×C4×C127semidirect
235. C2×C42C2×C4×C127semidirect
242. C24C4⋊C4×C127semidirect
257. C2×D4C4⋊C4×C127semidirect
270. C22×C4C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#518×C1272
C22×#99×C1272
C127×#23152
C127×#17992
C2×#342×C1272
#20633127