Finite Group Databasebeta

← C2×C127×#1391 #44576249

Subgroups — C2×C127×#1391 #44576249

Order 32512.

782 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#410×C127C212yesmaximal
2C2×#408×C127C211yesmaximal, characteristic
3C127×#1391C214yesmaximal, direct product factor
4C22×#41×C127C2211yescharacteristic
5C22×M16×C127C411yescharacteristic, complemented
6C23×C8×C127C411yescharacteristic, complemented
7C2×#117×C127—22no—
8#410×C127—22no—
9#410×C127—22no—
10#410×C127C414yescomplemented
11#410×C127C2214yes—
12C2×#99×C127—22no—
13C2×#99×C127C414yescomplemented
14#408×C127—22no—
15#408×C127C412yescomplemented
16#408×C127C2212yes—
17C2×C22⋊C8×C127—22no—
18C2×#41×C127—41no—
19C2×#41×C127—41no—
20C2×#41×C127—41no—
21C2×#41×C127—41no—
22C2×#41×C127C2×C412yes—
23C2×#41×C127C2×C411yescharacteristic
24C2×#41×C127D411yescharacteristic
25C2×#41×C127D412yes—
26C2×#41×C127Q811yescharacteristic
27C2×#41×C127C2311yescharacteristic
28C22×Q8×C127Q811yescharacteristic
29C22×D4×C127C2×C412yes—
30C22×D4×C127D411yescharacteristic
31C23×C4×C127C2×C411yescharacteristic
32C23×C4×C127D412yes—
33C2×M16×C127—21no—
34C2×M16×C127—41no—
35C2×M16×C127—41no—
36C2×M16×C127C2×C412yescomplemented
37C22×C8×C127—21no—
38C22×C8×C127—21no—
39C22×C8×C127—21no—
40C22×C8×C127—41no—
41C22×C8×C127—41no—
42C22×C8×C127C2×C412yescomplemented
43#117×C127—24no—
44#117×C127—24no—
45#117×C127—42no—
46#117×C127—42no—
47C2×C4⋊C4×C127—42no—
48C2×C22⋊C4×C127—24no—
49C2×C42×C127—42no—
50#99×C127—24no—
51#99×C127—24no—
52#99×C127—24no—
53#99×C127C2×C418yescomplemented
54C22⋊C8×C127—24no—
55C22⋊C8×C127—24no—
56C24×C127C4211yescharacteristic
57C24×C127C22⋊C412yes—
58#41×C127—42no—
59#41×C127—42no—
60#41×C127—41no—
61#41×C127—41no—
62#41×C127—41no—
63#41×C127—41no—
64#41×C127—42no—
65#41×C127—42no—
66#41×C127—41no—
67#41×C127—41no—
68#41×C127—41no—
69#41×C127—41no—
70C2×Q8×C127—41no—
71C2×Q8×C127—41no—
72C2×Q8×C127C4⋊C412yes—
73C2×Q8×C127C4⋊C411yescharacteristic
74C2×Q8×C127C2×Q811yescharacteristic
75C2×D4×C127—42no—
76C2×D4×C127—42no—
77C2×D4×C127—41no—
78C2×D4×C127—41no—
79C2×D4×C127C4212yes—
80C2×D4×C127C22⋊C412yes—
81C2×D4×C127C22⋊C412yes—
82C2×D4×C127C4⋊C412yes—
83C2×D4×C127C4⋊C411yescharacteristic
84C2×D4×C127C22×C412yes—
85C2×D4×C127C2×D411yescharacteristic
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—21no—
90C22×C4×C127—21no—
91C22×C4×C127—21no—
92C22×C4×C127—22no—
93C22×C4×C127—21no—
94C22×C4×C127—44no—
95C22×C4×C127C4211yescharacteristic
96C22×C4×C127C22⋊C412yes—
97C22×C4×C127C22⋊C412yes—
98C22×C4×C127C22⋊C411yescharacteristic
99C22×C4×C127C22⋊C411yescharacteristic
100C22×C4×C127C4⋊C411yescharacteristic
101C22×C4×C127C4⋊C411yescharacteristic
102C22×C4×C127C4⋊C412yes—
103C22×C4×C127C4⋊C412yes—
104C22×C4×C127C22×C411yescharacteristic
105C22×C4×C127C2×D412yes—
106M16×C127—42no—
107M16×C127—42no—
108C2×C8×C127—22no—
109C2×C8×C127—22no—
110C2×C8×C127—42no—
111C2×C8×C127—41no—
112C2×C8×C127—41no—
113C2×C8×C127—41no—
114C2×C8×C127—41no—
115C2×C8×C127—42no—
116C4⋊C4×C127—44no—
117C4⋊C4×C127—44no—
118C22⋊C4×C127—28no—
119C22⋊C4×C127—44no—
120C42×C127—44no—
121C42×C127—44no—
122C23×C127—22no—
123C23×C127—21no—
124C23×C127—21no—
125C23×C127—22no—
126C23×C127—42no—
127C23×C127—44no—
128C23×C127#9511yescharacteristic
129C23×C127#9512yes—
130C23×C127#9511yescharacteristic
131C23×C127C2×C4211yescharacteristic
132C23×C127C2×C22⋊C412yes—
133Q8×C127—41no—
134Q8×C127—42no—
135Q8×C127—41no—
136D4×C127—42no—
137D4×C127—42no—
138D4×C127—42no—
139D4×C127—42no—
140D4×C127—41no—
141D4×C127—42no—
142D4×C127—41no—
143C2×C4×C127—22no—
144C2×C4×C127—21no—
145C2×C4×C127—22no—
146C2×C4×C127—21no—
147C2×C4×C127—22no—
148C2×C4×C127—22no—
149C2×C4×C127—21no—
150C2×C4×C127—21no—
151C2×C4×C127—22no—
152C2×C4×C127—21no—
153C2×C4×C127—22no—
154C2×C4×C127—21no—
155C2×C4×C127—22no—
156C2×C4×C127—22no—
157C2×C4×C127—21no—
158C2×C4×C127—21no—
159C2×C4×C127—21no—
160C2×C4×C127—21no—
161C2×C4×C127—22no—
162C2×C4×C127—22no—
163C2×C4×C127—48no—
164C2×C4×C127—88no—
165C2×C4×C127#9511yescharacteristic
166C2×C4×C127#9512yes—
167C2×C4×C127#9511yescharacteristic
168C2×C4×C127#9911yescharacteristic
169C2×C4×C127#9911yescharacteristic
170C2×C4×C127#9911yescharacteristic
171C2×C4×C127#9911yescharacteristic
172C2×C4×C127C2×C22⋊C411yescharacteristic
173C2×C4×C127C2×C4⋊C411yescharacteristic
174C2×C4×C127C2×C4⋊C412yes—
175C8×C127—42no—
176C8×C127—42no—
177C22×C127—22no—
178C22×C127—22no—
179C22×C127—21no—
180C22×C127—22no—
181C22×C127—21no—
182C22×C127—41no—
183C22×C127—42no—
184C22×C127—41no—
185C22×C127—42no—
186C22×C127—42no—
187C22×C127—44no—
188C22×C127—42no—
189C22×C127—82no—
190C22×C127#34211yescharacteristic
191C22×C127#34211yescharacteristic
192C22×C127C2×#9511yescharacteristic
193C4×C127—22no—
194C4×C127—21no—
195C4×C127—22no—
196C4×C127—21no—
197C4×C127—88no—
198C4×C127#34211yescharacteristic
199C4×C127#34211yescharacteristic
200C4×C127C2×#9911yescharacteristic
201C4×C127C2×#9911yescharacteristic
202C2×#1391C12711yesmaximal, characteristic, direct product factor, Sylow
203C2×C127—21no—
204C2×C127—21no—
205C2×C127—42no—
206C2×C127—41no—
207C2×C127—41no—
208C2×C127—42no—
209C2×C127#139112yesdirect product factor
210C2×C127C2×#34211yescharacteristic
211C2×#410C2×C12712yes—
212C2×#408C2×C12711yescharacteristic
213#1391C2×C12714yesdirect product factor
214C127C2×#139111yescharacteristic, direct product factor, Sylow
215C22×#41C22×C12711yescharacteristic
216C22×M16C4×C12711yescharacteristic, complemented
217C23×C8C4×C12711yescharacteristic, complemented
218C2×#117—22no—
219#410—22no—
220#410—22no—
221#410C4×C12714yescomplemented
222#410C22×C12714yes—
223C2×#99—22no—
224C2×#99C4×C12714yescomplemented
225#408—22no—
226#408C4×C12712yescomplemented
227#408C22×C12712yes—
228C2×C22⋊C8—22no—
229C2×#41—41no—
230C2×#41—41no—
231C2×#41—41no—
232C2×#41—41no—
233C2×#41C2×C4×C12712yes—
234C2×#41C2×C4×C12711yescharacteristic
235C2×#41D4×C12711yescharacteristic
236C2×#41D4×C12712yes—
237C2×#41Q8×C12711yescharacteristic
238C2×#41C23×C12711yescharacteristic
239C22×Q8Q8×C12711yescharacteristic
240C22×D4C2×C4×C12712yes—
241C22×D4D4×C12711yescharacteristic
242C23×C4C2×C4×C12711yescharacteristic
243C23×C4D4×C12712yes—
244C2×M16—21no—
245C2×M16—41no—
246C2×M16—41no—
247C2×M16C2×C4×C12712yescomplemented
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—41no—
252C22×C8—41no—
253C22×C8C2×C4×C12712yescomplemented
254#117—24no—
255#117—24no—
256#117—42no—
257#117—42no—
258C2×C4⋊C4—42no—
259C2×C22⋊C4—24no—
260C2×C42—42no—
261#99—24no—
262#99—24no—
263#99—24no—
264#99C2×C4×C12718yescomplemented
265C22⋊C8—24no—
266C22⋊C8—24no—
267C24C42×C12711yescharacteristic
268C24C22⋊C4×C12712yes—
269#41—42no—
270#41—42no—
271#41—41no—
272#41—41no—
273#41—41no—
274#41—41no—
275#41—42no—
276#41—42no—
277#41—41no—
278#41—41no—
279#41—41no—
280#41—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8C4⋊C4×C12712yes—
284C2×Q8C4⋊C4×C12711yescharacteristic
285C2×Q8C2×Q8×C12711yescharacteristic
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4C42×C12712yes—
291C2×D4C22⋊C4×C12712yes—
292C2×D4C22⋊C4×C12712yes—
293C2×D4C4⋊C4×C12712yes—
294C2×D4C4⋊C4×C12711yescharacteristic
295C2×D4C22×C4×C12712yes—
296C2×D4C2×D4×C12711yescharacteristic
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—44no—
306C22×C4C42×C12711yescharacteristic
307C22×C4C22⋊C4×C12712yes—
308C22×C4C22⋊C4×C12712yes—
309C22×C4C22⋊C4×C12711yescharacteristic
310C22×C4C22⋊C4×C12711yescharacteristic
311C22×C4C4⋊C4×C12711yescharacteristic
312C22×C4C4⋊C4×C12711yescharacteristic
313C22×C4C4⋊C4×C12712yes—
314C22×C4C4⋊C4×C12712yes—
315C22×C4C22×C4×C12711yescharacteristic
316C22×C4C2×D4×C12712yes—
317M16—42no—
318M16—42no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—42no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—42no—
327C4⋊C4—44no—
328C4⋊C4—44no—
329C22⋊C4—28no—
330C22⋊C4—44no—
331C42—44no—
332C42—44no—
333C23—22no—
334C23—21no—
335C23—21no—
336C23—22no—
337C23—42no—
338C23—44no—
339C23#95×C12711yescharacteristic
340C23#95×C12712yes—
341C23#95×C12711yescharacteristic
342C23C2×C42×C12711yescharacteristic
343C23C2×C22⋊C4×C12712yes—
344Q8—41no—
345Q8—42no—
346Q8—41no—
347D4—42no—
348D4—42no—
349D4—42no—
350D4—42no—
351D4—41no—
352D4—42no—
353D4—41no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—22no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—48no—
375C2×C4—88no—
376C2×C4#95×C12711yescharacteristic
377C2×C4#95×C12712yes—
378C2×C4#95×C12711yescharacteristic
379C2×C4#99×C12711yescharacteristic
380C2×C4#99×C12711yescharacteristic
381C2×C4#99×C12711yescharacteristic
382C2×C4#99×C12711yescharacteristic
383C2×C4C2×C22⋊C4×C12711yescharacteristic
384C2×C4C2×C4⋊C4×C12711yescharacteristic
385C2×C4C2×C4⋊C4×C12712yes—
386C8—42no—
387C8—42no—
388C22—22no—
389C22—22no—
390C22—21no—
391C22—22no—
392C22—21no—
393C22—41no—
394C22—42no—
395C22—41no—
396C22—42no—
397C22—42no—
398C22—44no—
399C22—42no—
400C22—82no—
401C22#342×C12711yescharacteristic
402C22#342×C12711yescharacteristic
403C22C2×#95×C12711yescharacteristic
404C4—22no—
405C4—21no—
406C4—22no—
407C4—21no—
408C4—88no—
409C4#342×C12711yescharacteristic
410C4#342×C12711yescharacteristic
411C4C2×#99×C12711yescharacteristic
412C4C2×#99×C12711yescharacteristic
413C2—21no—
414C2—21no—
415C2—42no—
416C2—41no—
417C2—41no—
418C2—42no—
419C2C127×#139112yesdirect product factor
420C2C2×#342×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127#99
commutatorC23C2×C42×C127
Frattini, cosocleC2×#41C23×C127
socleC22×C127#342
prime radicalC22×#41×C127C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C22×#41×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1391C2direct (N × H)
5. C22×M16×C127C4semidirect
6. C23×C8×C127C4semidirect
10. #410×C127C4semidirect
13. C2×#99×C127C4semidirect
15. #408×C127C4semidirect
36. C2×M16×C127C2×C4semidirect
42. C22×C8×C127C2×C4semidirect
53. #99×C127C2×C4semidirect
202. C2×#1391C127direct (N × H)
209. C2×C127#1391direct (N × H)
213. #1391C2×C127direct (N × H)
214. C127C2×#1391direct (N × H)
216. C22×M16C4×C127semidirect
217. C23×C8C4×C127semidirect
221. #410C4×C127semidirect
224. C2×#99C4×C127semidirect
226. #408C4×C127semidirect
247. C2×M16C2×C4×C127semidirect
253. C22×C8C2×C4×C127semidirect
264. #99C2×C4×C127semidirect
419. C2C127×#1391direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#410×C1272
C2×#408×C1272
C127×#13912
C2×#1391127