Finite Group Databasebeta

← C127×#20985 #44584658

Subgroups — C127×#20985 #44584658

Order 32512.

2030 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
1C2×#535×C127C211yesmaximal, characteristic
2C2×#518×C127C211yesmaximal, characteristic, complemented
3C2×#410×C127C212yesmaximal, complemented
4C127×#2309C211yesmaximal, characteristic, complemented
5C127×#1898C218yesmaximal, complemented
6C127×#1740C212yesmaximal, complemented
7C22×#41×C127C2211yescharacteristic
8C23×D4×C127C2211yescharacteristic
9#535×C127—24no—
10#535×C127—24no—
11C2×#127×C127C412yescomplemented
12C2×#124×C127C412yescomplemented
13C2×#121×C127C414yescomplemented
14C2×#120×C127C2214yes—
15#518×C127—28no—
16C2×C4×D4×C127—24no—
17C2×#117×C127C2212yes—
18C2×#117×C127C2212yes—
19C2×#117×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2214yes—
21#410×C127—28no—
22C2×#99×C127C2218yes—
23#390×C127—24no—
24#379×C127C2214yes—
25#342×C127C2218yes—
26C25×C127C2312yes—
27C2×#41×C127—22no—
28C2×#41×C127—22no—
29C2×#41×C127—24no—
30C2×#41×C127—24no—
31C22×Q8×C127C2×C411yescharacteristic, complemented
32C22×D4×C127—24no—
33C22×D4×C127—24no—
34C22×D4×C127C2×C412yes—
35C22×D4×C127C2×C412yes—
36C22×D4×C127C2×C411yescharacteristic, complemented
37C22×D4×C127C2×C418yescomplemented
38C22×D4×C127D414yes—
39C22×D4×C127D414yes—
40C22×D4×C127C2312yes—
41C23×C4×C127—24no—
42C23×C4×C127C2×C412yescomplemented
43C23×C4×C127C2311yescharacteristic
44#127×C127—28no—
45#124×C127—28no—
46#121×C127—216no—
47#120×C127—28no—
48#120×C127—28no—
49C4×D4×C127—232no—
50#117×C127—24no—
51#117×C127—22no—
52#117×C127—22no—
53#117×C127—24no—
54#117×C127—24no—
55#117×C127D418yescomplemented
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127C2×C412yescomplemented
59C2×C22⋊C4×C127—24no—
60C2×C22⋊C4×C127—216no—
61C2×C22⋊C4×C127—28no—
62C2×C22⋊C4×C127C2×C418yescomplemented
63C2×C22⋊C4×C127C2314yes—
64C2×C22⋊C4×C127C2312yes—
65C2×C22⋊C4×C127C2314yes—
66C2×C42×C127—22no—
67C2×C42×C127—22no—
68C2×C42×C127C2×C412yescomplemented
69#99×C127—216no—
70C24×C127—24no—
71C24×C127—24no—
72C24×C127—84no—
73C24×C127C22×C412yes—
74C24×C127C22×C414yes—
75C24×C127C2×D414yes—
76C24×C127C2×D414yes—
77C24×C127C2411yescharacteristic
78#41×C127—44no—
79#41×C127—44no—
80#41×C127—44no—
81#41×C127—44no—
82C2×Q8×C127—22no—
83C2×Q8×C127—24no—
84C2×D4×C127—24no—
85C2×D4×C127—22no—
86C2×D4×C127—22no—
87C2×D4×C127—24no—
88C2×D4×C127—216no—
89C2×D4×C127—22no—
90C2×D4×C127—28no—
91C2×D4×C127—28no—
92C2×D4×C127—24no—
93C2×D4×C127—28no—
94C2×D4×C127—28no—
95C2×D4×C127—28no—
96C2×D4×C127—28no—
97C2×D4×C127—88no—
98C2×D4×C127C22⋊C418yes—
99C2×D4×C127C22⋊C418yes—
100C22×C4×C127—24no—
101C22×C4×C127—216no—
102C22×C4×C127—24no—
103C22×C4×C127—28no—
104C22×C4×C127—24no—
105C22×C4×C127—88no—
106C22×C4×C127C22×C412yes—
107C22×C4×C127C22×C414yes—
108C22×C4×C127C22×C411yescharacteristic
109C22×C4×C127C22×C411yescharacteristic
110C22×C4×C127C2×D412yes—
111C22×C4×C127C2×D412yes—
112C22×C4×C127C2×D414yes—
113C22×C4×C127#4114yes—
114C4⋊C4×C127—24no—
115C4⋊C4×C127—28no—
116C4⋊C4×C127—44no—
117C22⋊C4×C127—216no—
118C22⋊C4×C127—216no—
119C22⋊C4×C127—24no—
120C22⋊C4×C127—22no—
121C22⋊C4×C127—22no—
122C22⋊C4×C127—24no—
123C22⋊C4×C127—24no—
124C22⋊C4×C127—88no—
125C22⋊C4×C127C2×D418yes—
126C42×C127—24no—
127C42×C127—28no—
128C42×C127—44no—
129C23×C127—24no—
130C23×C127—24no—
131C23×C127—28no—
132C23×C127—28no—
133C23×C127—22no—
134C23×C127—24no—
135C23×C127—48no—
136C23×C127—42no—
137C23×C127—48no—
138C23×C127—48no—
139C23×C127—44no—
140C23×C127—88no—
141C23×C127—88no—
142C23×C127C2×C22⋊C418yes—
143C23×C127C23×C411yescharacteristic
144C23×C127C22×D411yescharacteristic
145C23×C127C22×D411yescharacteristic
146C23×C127C22×D412yes—
147C23×C127C2×#4112yes—
148Q8×C127—44no—
149D4×C127—216no—
150D4×C127—216no—
151D4×C127—42no—
152D4×C127—44no—
153D4×C127—42no—
154D4×C127—44no—
155D4×C127—816no—
156C2×C4×C127—24no—
157C2×C4×C127—22no—
158C2×C4×C127—24no—
159C2×C4×C127—28no—
160C2×C4×C127—48no—
161C2×C4×C127—48no—
162C2×C4×C127—44no—
163C2×C4×C127—48no—
164C2×C4×C127—44no—
165C2×C4×C127—816no—
166C2×C4×C127C2×C22⋊C412yes—
167C2×C4×C127C2×C22⋊C412yes—
168C2×C4×C127C4×D414yes—
169C2×C4×C127C4×D414yes—
170C2×C4×C127#12014yes—
171C2×C4×C127#12114yes—
172C2×C4×C127#12114yes—
173C2×C4×C127#12314yes—
174C22×C127—22no—
175C22×C127—22no—
176C22×C127—22no—
177C22×C127—216no—
178C22×C127—28no—
179C22×C127—42no—
180C22×C127—42no—
181C22×C127—48no—
182C22×C127—48no—
183C22×C127—44no—
184C22×C127—42no—
185C22×C127—88no—
186C22×C127—88no—
187C22×C127—84no—
188C22×C127C22×C22⋊C411yescharacteristic
189C22×C127C2×C4×D412yes—
190C22×C127C2×#12011yescharacteristic
191C22×C127C2×#12112yes—
192C22×C127C2×#12311yescharacteristic
193C4×C127—48no—
194C4×C127—44no—
195C4×C127—42no—
196C4×C127—84no—
197C4×C127#38614yes—
198C4×C127#38614yes—
199#20985C12711yesmaximal, characteristic, direct product factor, Sylow
200C2×C127—21no—
201C2×C127—22no—
202C2×C127—21no—
203C2×C127—22no—
204C2×C127—48no—
205C2×C127—82no—
206C2×C127C2×#38611yescharacteristic
207C2×C127#288312yes—
208C2×#535C2×C12711yescharacteristic
209C2×#518C2×C12711yescharacteristic, complemented
210C2×#410C2×C12712yescomplemented
211#2309C2×C12711yescharacteristic, complemented
212#1898C2×C12718yescomplemented
213#1740C2×C12712yescomplemented
214C127#2098511yescharacteristic, direct product factor, Sylow
215C22×#41C22×C12711yescharacteristic
216C23×D4C22×C12711yescharacteristic
217#535—24no—
218#535—24no—
219C2×#127C4×C12712yescomplemented
220C2×#124C4×C12712yescomplemented
221C2×#121C4×C12714yescomplemented
222C2×#120C22×C12714yes—
223#518—28no—
224C2×C4×D4—24no—
225C2×#117C22×C12712yes—
226C2×#117C22×C12712yes—
227C2×#117C22×C12711yescharacteristic
228C22×C22⋊C4C22×C12714yes—
229#410—28no—
230C2×#99C22×C12718yes—
231#390—24no—
232#379C22×C12714yes—
233#342C22×C12718yes—
234C25C23×C12712yes—
235C2×#41—22no—
236C2×#41—22no—
237C2×#41—24no—
238C2×#41—24no—
239C22×Q8C2×C4×C12711yescharacteristic, complemented
240C22×D4—24no—
241C22×D4—24no—
242C22×D4C2×C4×C12712yes—
243C22×D4C2×C4×C12712yes—
244C22×D4C2×C4×C12711yescharacteristic, complemented
245C22×D4C2×C4×C12718yescomplemented
246C22×D4D4×C12714yes—
247C22×D4D4×C12714yes—
248C22×D4C23×C12712yes—
249C23×C4—24no—
250C23×C4C2×C4×C12712yescomplemented
251C23×C4C23×C12711yescharacteristic
252#127—28no—
253#124—28no—
254#121—216no—
255#120—28no—
256#120—28no—
257C4×D4—232no—
258#117—24no—
259#117—22no—
260#117—22no—
261#117—24no—
262#117—24no—
263#117D4×C12718yescomplemented
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4C2×C4×C12712yescomplemented
267C2×C22⋊C4—24no—
268C2×C22⋊C4—216no—
269C2×C22⋊C4—28no—
270C2×C22⋊C4C2×C4×C12718yescomplemented
271C2×C22⋊C4C23×C12714yes—
272C2×C22⋊C4C23×C12712yes—
273C2×C22⋊C4C23×C12714yes—
274C2×C42—22no—
275C2×C42—22no—
276C2×C42C2×C4×C12712yescomplemented
277#99—216no—
278C24—24no—
279C24—24no—
280C24—84no—
281C24C22×C4×C12712yes—
282C24C22×C4×C12714yes—
283C24C2×D4×C12714yes—
284C24C2×D4×C12714yes—
285C24C24×C12711yescharacteristic
286#41—44no—
287#41—44no—
288#41—44no—
289#41—44no—
290C2×Q8—22no—
291C2×Q8—24no—
292C2×D4—24no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—24no—
296C2×D4—216no—
297C2×D4—22no—
298C2×D4—28no—
299C2×D4—28no—
300C2×D4—24no—
301C2×D4—28no—
302C2×D4—28no—
303C2×D4—28no—
304C2×D4—28no—
305C2×D4—88no—
306C2×D4C22⋊C4×C12718yes—
307C2×D4C22⋊C4×C12718yes—
308C22×C4—24no—
309C22×C4—216no—
310C22×C4—24no—
311C22×C4—28no—
312C22×C4—24no—
313C22×C4—88no—
314C22×C4C22×C4×C12712yes—
315C22×C4C22×C4×C12714yes—
316C22×C4C22×C4×C12711yescharacteristic
317C22×C4C22×C4×C12711yescharacteristic
318C22×C4C2×D4×C12712yes—
319C22×C4C2×D4×C12712yes—
320C22×C4C2×D4×C12714yes—
321C22×C4#41×C12714yes—
322C4⋊C4—24no—
323C4⋊C4—28no—
324C4⋊C4—44no—
325C22⋊C4—216no—
326C22⋊C4—216no—
327C22⋊C4—24no—
328C22⋊C4—22no—
329C22⋊C4—22no—
330C22⋊C4—24no—
331C22⋊C4—24no—
332C22⋊C4—88no—
333C22⋊C4C2×D4×C12718yes—
334C42—24no—
335C42—28no—
336C42—44no—
337C23—24no—
338C23—24no—
339C23—28no—
340C23—28no—
341C23—22no—
342C23—24no—
343C23—48no—
344C23—42no—
345C23—48no—
346C23—48no—
347C23—44no—
348C23—88no—
349C23—88no—
350C23C2×C22⋊C4×C12718yes—
351C23C23×C4×C12711yescharacteristic
352C23C22×D4×C12711yescharacteristic
353C23C22×D4×C12711yescharacteristic
354C23C22×D4×C12712yes—
355C23C2×#41×C12712yes—
356Q8—44no—
357D4—216no—
358D4—216no—
359D4—42no—
360D4—44no—
361D4—42no—
362D4—44no—
363D4—816no—
364C2×C4—24no—
365C2×C4—22no—
366C2×C4—24no—
367C2×C4—28no—
368C2×C4—48no—
369C2×C4—48no—
370C2×C4—44no—
371C2×C4—48no—
372C2×C4—44no—
373C2×C4—816no—
374C2×C4C2×C22⋊C4×C12712yes—
375C2×C4C2×C22⋊C4×C12712yes—
376C2×C4C4×D4×C12714yes—
377C2×C4C4×D4×C12714yes—
378C2×C4#120×C12714yes—
379C2×C4#121×C12714yes—
380C2×C4#121×C12714yes—
381C2×C4#123×C12714yes—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—216no—
386C22—28no—
387C22—42no—
388C22—42no—
389C22—48no—
390C22—48no—
391C22—44no—
392C22—42no—
393C22—88no—
394C22—88no—
395C22—84no—
396C22C22×C22⋊C4×C12711yescharacteristic
397C22C2×C4×D4×C12712yes—
398C22C2×#120×C12711yescharacteristic
399C22C2×#121×C12712yes—
400C22C2×#123×C12711yescharacteristic
401C4—48no—
402C4—44no—
403C4—42no—
404C4—84no—
405C4#386×C12714yes—
406C4#386×C12714yes—
407C2—21no—
408C2—22no—
409C2—21no—
410C2—22no—
411C2—48no—
412C2—82no—
413C2C2×#386×C12711yescharacteristic
414C2C127×#288312yes—
subgroupG/H
center, socleC22×C127C22×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC2×#535×C127C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#518×C127C2semidirect
3. C2×#410×C127C2semidirect
4. C127×#2309C2semidirect
5. C127×#1898C2semidirect
6. C127×#1740C2semidirect
11. C2×#127×C127C4semidirect
12. C2×#124×C127C4semidirect
13. C2×#121×C127C4semidirect
31. C22×Q8×C127C2×C4semidirect
36. C22×D4×C127C2×C4semidirect
37. C22×D4×C127C2×C4semidirect
42. C23×C4×C127C2×C4semidirect
55. #117×C127D4semidirect
58. C2×C4⋊C4×C127C2×C4semidirect
62. C2×C22⋊C4×C127C2×C4semidirect
68. C2×C42×C127C2×C4semidirect
199. #20985C127direct (N × H)
209. C2×#518C2×C127semidirect
210. C2×#410C2×C127semidirect
211. #2309C2×C127semidirect
212. #1898C2×C127semidirect
213. #1740C2×C127semidirect
214. C127#20985direct (N × H)
219. C2×#127C4×C127semidirect
220. C2×#124C4×C127semidirect
221. C2×#121C4×C127semidirect
239. C22×Q8C2×C4×C127semidirect
244. C22×D4C2×C4×C127semidirect
245. C22×D4C2×C4×C127semidirect
250. C23×C4C2×C4×C127semidirect
263. #117D4×C127semidirect
266. C2×C4⋊C4C2×C4×C127semidirect
270. C2×C22⋊C4C2×C4×C127semidirect
276. C2×C42C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1272
C2×#518×C1272
C2×#410×C1272
C127×#23092
C127×#18982
C127×#17402
#20985127