Finite Group Databasebeta

← C127×#21396 #44585069

Subgroups — C127×#21396 #44585069

Order 32512.

1182 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#529×C127C211yesmaximal, characteristic
2C2×#432×C127C211yesmaximal, characteristic, complemented
3C4×#117×C127C211yesmaximal, characteristic, complemented
4C127×#1989C212yesmaximal, complemented
5C127×#1983C212yesmaximal, complemented
6C127×#1875C212yesmaximal
7C127×#1873C212yesmaximal, complemented
8C127×#1763C212yesmaximal, complemented
9C127×#1762C212yesmaximal, complemented
10#529×C127—24no—
11#529×C127C418yescomplemented
12C2×#126×C127—21no—
13C2×#125×C127C2211yescharacteristic
14C2×#124×C127C2211yescharacteristic
15C2×#123×C127—21no—
16C2×C22⋊Q8×C127C2211yescharacteristic
17C2×#121×C127C2211yescharacteristic
18C2×C4×Q8×C127C2211yescharacteristic
19C2×C4×D4×C127—21no—
20C2×C4×D4×C127C2211yescharacteristic
21C2×#117×C127—21no—
22C2×#117×C127C2212yes—
23C22×C42×C127C2211yescharacteristic
24#432×C127—24no—
25C2×C4⋊C8×C127C2212yes—
26C2×#103×C127C2214yes—
27C2×#102×C127C2214yes—
28C2×C22⋊C8×C127C2212yes—
29C2×#97×C127C2212yes—
30C4×C4⋊C4×C127C2212yes—
31C4×C4⋊C4×C127C2212yes—
32C4×C22⋊C4×C127—21no—
33C4×C22⋊C4×C127—21no—
34#376×C127—21no—
35C43×C127—21no—
36#340×C127C2214yes—
37#340×C127C2214yes—
38C22×Q8×C127C2311yescharacteristic
39C22×D4×C127—21no—
40C22×D4×C127C2311yescharacteristic
41C23×C4×C127—21no—
42C23×C4×C127D411yescharacteristic
43C23×C4×C127D411yescharacteristic
44C23×C4×C127C2311yescharacteristic
45C22×C8×C127C2314yes—
46#126×C127—28no—
47#125×C127—22no—
48#125×C127C2×C414yes—
49#124×C127—22no—
50#124×C127C2×C414yes—
51#123×C127—28no—
52C22⋊Q8×C127—22no—
53C22⋊Q8×C127C2×C414yes—
54#121×C127—22no—
55#121×C127C2×C414yes—
56C4×Q8×C127—22no—
57C4×Q8×C127C2×C414yes—
58C4×D4×C127—28no—
59C4×D4×C127—22no—
60C4×D4×C127C2×C414yes—
61#117×C127—28no—
62#117×C127—28no—
63C2×C4⋊C4×C127—21no—
64C2×C4⋊C4×C127—21no—
65C2×C4⋊C4×C127—21no—
66C2×C4⋊C4×C127—21no—
67C2×C4⋊C4×C127C2311yescharacteristic
68C2×C4⋊C4×C127C2311yescharacteristic
69C2×C4⋊C4×C127C2314yes—
70C2×C22⋊C4×C127—22no—
71C2×C22⋊C4×C127—21no—
72C2×C22⋊C4×C127—21no—
73C2×C22⋊C4×C127—21no—
74C2×C22⋊C4×C127—21no—
75C2×C22⋊C4×C127—21no—
76C2×C42×C127—21no—
77C2×C42×C127—22no—
78C2×C42×C127—22no—
79C2×C42×C127—22no—
80C2×C42×C127C2×C414yes—
81C2×C42×C127D411yescharacteristic
82C2×C42×C127D411yescharacteristic
83C2×C42×C127D414yes—
84C2×C42×C127C2311yescharacteristic
85C2×C42×C127C2311yescharacteristic
86C4⋊C8×C127—24no—
87#103×C127—28no—
88#102×C127—28no—
89C22⋊C8×C127—24no—
90#97×C127—24no—
91#95×C127—22no—
92#95×C127—22no—
93C24×C127—21no—
94C24×C127C2×D411yescharacteristic
95C2×Q8×C127—21no—
96C2×Q8×C127—24no—
97C2×Q8×C127C22×C412yes—
98C2×D4×C127—24no—
99C2×D4×C127—21no—
100C2×D4×C127—24no—
101C2×D4×C127—44no—
102C2×D4×C127C22×C412yes—
103C22×C4×C127—24no—
104C22×C4×C127—24no—
105C22×C4×C127—21no—
106C22×C4×C127—21no—
107C22×C4×C127—21no—
108C22×C4×C127—24no—
109C22×C4×C127—42no—
110C22×C4×C127—42no—
111C22×C4×C127—44no—
112C22×C4×C127C22⋊C414yes—
113C22×C4×C127C22⋊C414yes—
114C22×C4×C127C22×C412yes—
115C22×C4×C127C2×D411yescharacteristic
116C22×C4×C127C2×D411yescharacteristic
117C22×C4×C127C2×D411yescharacteristic
118C22×C4×C127C2×D411yescharacteristic
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127C2×D412yes—
121C22×C4×C127C2411yescharacteristic
122C2×C8×C127—24no—
123C2×C8×C127—24no—
124C2×C8×C127—24no—
125C4⋊C4×C127—24no—
126C4⋊C4×C127—24no—
127C4⋊C4×C127—24no—
128C4⋊C4×C127—24no—
129C4⋊C4×C127—21no—
130C4⋊C4×C127—21no—
131C4⋊C4×C127—24no—
132C4⋊C4×C127C22×C412yes—
133C4⋊C4×C127C22×C412yes—
134C4⋊C4×C127#4118yes—
135C22⋊C4×C127—28no—
136C22⋊C4×C127—24no—
137C22⋊C4×C127—24no—
138C22⋊C4×C127—24no—
139C22⋊C4×C127—24no—
140C22⋊C4×C127—24no—
141C42×C127—28no—
142C42×C127—24no—
143C42×C127—44no—
144C42×C127—44no—
145C42×C127C22⋊C414yes—
146C42×C127C22⋊C414yes—
147C42×C127C22×C412yes—
148C42×C127C22×C412yes—
149C42×C127C2×D412yes—
150C42×C127C2×D412yes—
151C23×C127—22no—
152C23×C127—22no—
153C23×C127—22no—
154C23×C127—22no—
155C23×C127—42no—
156C23×C127—42no—
157C23×C127—42no—
158C23×C127C2×C22⋊C412yes—
159C23×C127C22×D411yescharacteristic
160Q8×C127—24no—
161Q8×C127—42no—
162D4×C127—24no—
163D4×C127—48no—
164D4×C127—42no—
165C2×C4×C127—22no—
166C2×C4×C127—22no—
167C2×C4×C127—22no—
168C2×C4×C127—22no—
169C2×C4×C127—22no—
170C2×C4×C127—24no—
171C2×C4×C127—24no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—22no—
175C2×C4×C127—28no—
176C2×C4×C127—44no—
177C2×C4×C127—44no—
178C2×C4×C127—48no—
179C2×C4×C127—42no—
180C2×C4×C127—44no—
181C2×C4×C127—44no—
182C2×C4×C127—42no—
183C2×C4×C127—42no—
184C2×C4×C127C2×C22⋊C412yes—
185C2×C4×C127C2×C22⋊C412yes—
186C2×C4×C127C2×C22⋊C412yes—
187C2×C4×C127C2×C22⋊C412yes—
188C2×C4×C127C2×C22⋊C412yes—
189C2×C4×C127C23×C411yescharacteristic
190C2×C4×C127C22×D411yescharacteristic
191C2×C4×C127C2×#4114yes—
192C8×C127—44no—
193C22×C127—22no—
194C22×C127—22no—
195C22×C127—22no—
196C22×C127—44no—
197C22×C127—42no—
198C22×C127—42no—
199C22×C127—42no—
200C22×C127—84no—
201C22×C127C22×C22⋊C411yescharacteristic
202C22×C127#52512yes—
203C22×C127#57512yes—
204C22×C127#57512yes—
205C4×C127—22no—
206C4×C127—22no—
207C4×C127—22no—
208C4×C127—22no—
209C4×C127—22no—
210C4×C127—48no—
211C4×C127—42no—
212C4×C127—42no—
213C4×C127—42no—
214C4×C127C4×#4112yes—
215C4×C127#53212yes—
216#21396C12711yesmaximal, characteristic, direct product factor, Sylow
217C2×C127—42no—
218C2×C127—82no—
219C2×C127#229711yescharacteristic
220C2×C127#289611yescharacteristic
221C2×C127#289611yescharacteristic
222C2×C127#311114yes—
223C2×#529C2×C12711yescharacteristic
224C2×#432C2×C12711yescharacteristic, complemented
225C4×#117C2×C12711yescharacteristic, complemented
226#1989C2×C12712yescomplemented
227#1983C2×C12712yescomplemented
228#1875C2×C12712yes—
229#1873C2×C12712yescomplemented
230#1763C2×C12712yescomplemented
231#1762C2×C12712yescomplemented
232C127#2139611yescharacteristic, direct product factor, Sylow
233#529—24no—
234#529C4×C12718yescomplemented
235C2×#126—21no—
236C2×#125C22×C12711yescharacteristic
237C2×#124C22×C12711yescharacteristic
238C2×#123—21no—
239C2×C22⋊Q8C22×C12711yescharacteristic
240C2×#121C22×C12711yescharacteristic
241C2×C4×Q8C22×C12711yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4C22×C12711yescharacteristic
244C2×#117—21no—
245C2×#117C22×C12712yes—
246C22×C42C22×C12711yescharacteristic
247#432—24no—
248C2×C4⋊C8C22×C12712yes—
249C2×#103C22×C12714yes—
250C2×#102C22×C12714yes—
251C2×C22⋊C8C22×C12712yes—
252C2×#97C22×C12712yes—
253C4×C4⋊C4C22×C12712yes—
254C4×C4⋊C4C22×C12712yes—
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257#376—21no—
258C43—21no—
259#340C22×C12714yes—
260#340C22×C12714yes—
261C22×Q8C23×C12711yescharacteristic
262C22×D4—21no—
263C22×D4C23×C12711yescharacteristic
264C23×C4—21no—
265C23×C4D4×C12711yescharacteristic
266C23×C4D4×C12711yescharacteristic
267C23×C4C23×C12711yescharacteristic
268C22×C8C23×C12714yes—
269#126—28no—
270#125—22no—
271#125C2×C4×C12714yes—
272#124—22no—
273#124C2×C4×C12714yes—
274#123—28no—
275C22⋊Q8—22no—
276C22⋊Q8C2×C4×C12714yes—
277#121—22no—
278#121C2×C4×C12714yes—
279C4×Q8—22no—
280C4×Q8C2×C4×C12714yes—
281C4×D4—28no—
282C4×D4—22no—
283C4×D4C2×C4×C12714yes—
284#117—28no—
285#117—28no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4C23×C12711yescharacteristic
291C2×C4⋊C4C23×C12711yescharacteristic
292C2×C4⋊C4C23×C12714yes—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C42—21no—
300C2×C42—22no—
301C2×C42—22no—
302C2×C42—22no—
303C2×C42C2×C4×C12714yes—
304C2×C42D4×C12711yescharacteristic
305C2×C42D4×C12711yescharacteristic
306C2×C42D4×C12714yes—
307C2×C42C23×C12711yescharacteristic
308C2×C42C23×C12711yescharacteristic
309C4⋊C8—24no—
310#103—28no—
311#102—28no—
312C22⋊C8—24no—
313#97—24no—
314#95—22no—
315#95—22no—
316C24—21no—
317C24C2×D4×C12711yescharacteristic
318C2×Q8—21no—
319C2×Q8—24no—
320C2×Q8C22×C4×C12712yes—
321C2×D4—24no—
322C2×D4—21no—
323C2×D4—24no—
324C2×D4—44no—
325C2×D4C22×C4×C12712yes—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—24no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—44no—
335C22×C4C22⋊C4×C12714yes—
336C22×C4C22⋊C4×C12714yes—
337C22×C4C22×C4×C12712yes—
338C22×C4C2×D4×C12711yescharacteristic
339C22×C4C2×D4×C12711yescharacteristic
340C22×C4C2×D4×C12711yescharacteristic
341C22×C4C2×D4×C12711yescharacteristic
342C22×C4C2×D4×C12711yescharacteristic
343C22×C4C2×D4×C12712yes—
344C22×C4C24×C12711yescharacteristic
345C2×C8—24no—
346C2×C8—24no—
347C2×C8—24no—
348C4⋊C4—24no—
349C4⋊C4—24no—
350C4⋊C4—24no—
351C4⋊C4—24no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—24no—
355C4⋊C4C22×C4×C12712yes—
356C4⋊C4C22×C4×C12712yes—
357C4⋊C4#41×C12718yes—
358C22⋊C4—28no—
359C22⋊C4—24no—
360C22⋊C4—24no—
361C22⋊C4—24no—
362C22⋊C4—24no—
363C22⋊C4—24no—
364C42—28no—
365C42—24no—
366C42—44no—
367C42—44no—
368C42C22⋊C4×C12714yes—
369C42C22⋊C4×C12714yes—
370C42C22×C4×C12712yes—
371C42C22×C4×C12712yes—
372C42C2×D4×C12712yes—
373C42C2×D4×C12712yes—
374C23—22no—
375C23—22no—
376C23—22no—
377C23—22no—
378C23—42no—
379C23—42no—
380C23—42no—
381C23C2×C22⋊C4×C12712yes—
382C23C22×D4×C12711yescharacteristic
383Q8—24no—
384Q8—42no—
385D4—24no—
386D4—48no—
387D4—42no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—28no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—48no—
402C2×C4—42no—
403C2×C4—44no—
404C2×C4—44no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4C2×C22⋊C4×C12712yes—
408C2×C4C2×C22⋊C4×C12712yes—
409C2×C4C2×C22⋊C4×C12712yes—
410C2×C4C2×C22⋊C4×C12712yes—
411C2×C4C2×C22⋊C4×C12712yes—
412C2×C4C23×C4×C12711yescharacteristic
413C2×C4C22×D4×C12711yescharacteristic
414C2×C4C2×#41×C12714yes—
415C8—44no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—44no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—84no—
424C22C22×C22⋊C4×C12711yescharacteristic
425C22#525×C12712yes—
426C22#575×C12712yes—
427C22#575×C12712yes—
428C4—22no—
429C4—22no—
430C4—22no—
431C4—22no—
432C4—22no—
433C4—48no—
434C4—42no—
435C4—42no—
436C4—42no—
437C4C4×#41×C12712yes—
438C4#532×C12712yes—
439C2—42no—
440C2—82no—
441C2C127×#229711yescharacteristic
442C2C127×#289611yescharacteristic
443C2C127×#289611yescharacteristic
444C2C127×#311114yes—
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC2×#121×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#432×C127C2semidirect
3. C4×#117×C127C2semidirect
4. C127×#1989C2semidirect
5. C127×#1983C2semidirect
7. C127×#1873C2semidirect
8. C127×#1763C2semidirect
9. C127×#1762C2semidirect
11. #529×C127C4semidirect
216. #21396C127direct (N × H)
224. C2×#432C2×C127semidirect
225. C4×#117C2×C127semidirect
226. #1989C2×C127semidirect
227. #1983C2×C127semidirect
229. #1873C2×C127semidirect
230. #1763C2×C127semidirect
231. #1762C2×C127semidirect
232. C127#21396direct (N × H)
234. #529C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#529×C1272
C2×#432×C1272
C4×#117×C1272
C127×#19892
C127×#19832
C127×#18752
C127×#18732
C127×#17632
C127×#17622
#21396127