Finite Group Databasebeta

← C127×#14291 #44577964

Subgroups — C127×#14291 #44577964

Order 32512.

1610 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#126×C127C211yesmaximal, characteristic
2C2×#382×C127C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
4C127×#1441C212yesmaximal, complemented
5C127×#1441C212yesmaximal, complemented
6C127×#1439C212yesmaximal
7C127×#1439C212yesmaximal
8C127×#1437C212yesmaximal
9C127×#1436C212yesmaximal, complemented
10C2×#126×C127—24no—
11C2×#126×C127—24no—
12C2×#126×C127C418yescomplemented
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2214yes—
22C22×C42×C127C2212yes—
23C22×C42×C127C2211yescharacteristic
24#382×C127—24no—
25C4×C4⋊C4×C127—24no—
26C2×#95×C127C2212yes—
27C2×#95×C127C2214yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2214yes—
31C2×#95×C127C2214yes—
32C25×C127C2311yescharacteristic
33C23×C4×C127C2314yes—
34C23×C4×C127C2311yescharacteristic
35C23×C4×C127C2311yescharacteristic
36C23×C4×C127C2311yescharacteristic
37C23×C4×C127C2314yes—
38C23×C4×C127C2311yescharacteristic
39C23×C4×C127C2311yescharacteristic
40C23×C4×C127C2311yescharacteristic
41#126×C127—232no—
42C2×C4⋊C4×C127—22no—
43C2×C4⋊C4×C127—22no—
44C2×C4⋊C4×C127—22no—
45C2×C4⋊C4×C127—22no—
46C2×C4⋊C4×C127—22no—
47C2×C4⋊C4×C127—22no—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—28no—
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127—44no—
52C2×C4⋊C4×C127C2×C414yes—
53C2×C4⋊C4×C127C2×C414yes—
54C2×C4⋊C4×C127C2×C414yes—
55C2×C22⋊C4×C127—22no—
56C2×C22⋊C4×C127—22no—
57C2×C22⋊C4×C127—22no—
58C2×C22⋊C4×C127—22no—
59C2×C22⋊C4×C127—22no—
60C2×C22⋊C4×C127—22no—
61C2×C22⋊C4×C127—28no—
62C2×C22⋊C4×C127—44no—
63C2×C22⋊C4×C127—44no—
64C2×C22⋊C4×C127C2×C414yes—
65C2×C22⋊C4×C127C2×C414yes—
66C2×C22⋊C4×C127C2×C414yes—
67C2×C42×C127—24no—
68C2×C42×C127—44no—
69C2×C42×C127C2×C414yes—
70C2×C42×C127D414yes—
71C2×C42×C127D414yes—
72#95×C127—24no—
73#95×C127—24no—
74#95×C127—24no—
75#95×C127—28no—
76#95×C127—44no—
77#95×C127—44no—
78C24×C127—21no—
79C24×C127—21no—
80C24×C127—24no—
81C24×C127—22no—
82C24×C127—22no—
83C24×C127—22no—
84C24×C127—22no—
85C24×C127C22×C412yes—
86C24×C127C2411yescharacteristic
87C22×C4×C127—24no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—24no—
93C22×C4×C127—21no—
94C22×C4×C127—21no—
95C22×C4×C127—21no—
96C22×C4×C127—21no—
97C22×C4×C127—21no—
98C22×C4×C127—21no—
99C22×C4×C127—24no—
100C22×C4×C127—24no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—24no—
104C22×C4×C127—24no—
105C22×C4×C127—24no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—24no—
109C22×C4×C127—24no—
110C22×C4×C127—24no—
111C22×C4×C127—24no—
112C22×C4×C127—24no—
113C22×C4×C127—24no—
114C22×C4×C127—24no—
115C22×C4×C127—24no—
116C22×C4×C127C22×C412yes—
117C22×C4×C127C22×C412yes—
118C22×C4×C127C22×C412yes—
119C22×C4×C127C22×C412yes—
120C22×C4×C127C22×C412yes—
121C22×C4×C127C22×C412yes—
122C22×C4×C127C2×D412yes—
123C22×C4×C127C2×D412yes—
124C22×C4×C127C2×D412yes—
125C22×C4×C127C2×D412yes—
126C22×C4×C127C2×D412yes—
127C22×C4×C127C2×D412yes—
128C22×C4×C127#4118yes—
129C4⋊C4×C127—216no—
130C4⋊C4×C127—28no—
131C4⋊C4×C127—28no—
132C4⋊C4×C127—28no—
133C4⋊C4×C127—48no—
134C22⋊C4×C127—28no—
135C22⋊C4×C127—28no—
136C22⋊C4×C127—28no—
137C22⋊C4×C127—416no—
138C42×C127—48no—
139C42×C127C22⋊C4116yescomplemented
140C23×C127—22no—
141C23×C127—24no—
142C23×C127—24no—
143C23×C127—24no—
144C23×C127—42no—
145C23×C127—42no—
146C23×C127—41no—
147C23×C127—41no—
148C23×C127—41no—
149C23×C127—41no—
150C23×C127—42no—
151C23×C127—42no—
152C23×C127—44no—
153C23×C127—44no—
154C23×C127—44no—
155C23×C127—44no—
156C23×C127C23×C411yescharacteristic
157C23×C127C22×D411yescharacteristic
158C23×C127C22×D411yescharacteristic
159C23×C127C2×#4114yes—
160C23×C127H(5,𝔽2)12yes—
161C23×C127H(5,𝔽2)12yes—
162C23×C1272−1+412yes—
163C23×C1272−1+412yes—
164C2×C4×C127—24no—
165C2×C4×C127—24no—
166C2×C4×C127—24no—
167C2×C4×C127—24no—
168C2×C4×C127—24no—
169C2×C4×C127—22no—
170C2×C4×C127—22no—
171C2×C4×C127—22no—
172C2×C4×C127—22no—
173C2×C4×C127—24no—
174C2×C4×C127—24no—
175C2×C4×C127—22no—
176C2×C4×C127—22no—
177C2×C4×C127—22no—
178C2×C4×C127—24no—
179C2×C4×C127—24no—
180C2×C4×C127—24no—
181C2×C4×C127—28no—
182C2×C4×C127—28no—
183C2×C4×C127—28no—
184C2×C4×C127—42no—
185C2×C4×C127—42no—
186C2×C4×C127—44no—
187C2×C4×C127—41no—
188C2×C4×C127—41no—
189C2×C4×C127—41no—
190C2×C4×C127—41no—
191C2×C4×C127—42no—
192C2×C4×C127—42no—
193C2×C4×C127—44no—
194C2×C4×C127—44no—
195C2×C4×C127—44no—
196C2×C4×C127—44no—
197C2×C4×C127—44no—
198C2×C4×C127—44no—
199C2×C4×C127—44no—
200C2×C4×C127—44no—
201C2×C4×C127—44no—
202C2×C4×C127—44no—
203C2×C4×C127C2×C22⋊C414yes—
204C2×C4×C127C2×C22⋊C414yes—
205C2×C4×C127C2×C22⋊C414yes—
206C22×C127—42no—
207C22×C127—42no—
208C22×C127—48no—
209C22×C127—42no—
210C22×C127—82no—
211C22×C127—82no—
212C22×C127—82no—
213C22×C127—82no—
214C22×C127C22×C22⋊C411yescharacteristic
215C22×C127C4×#4112yes—
216C22×C127#52012yes—
217C22×C127#52012yes—
218C22×C127#52512yes—
219C22×C127#53212yes—
220C22×C127#53511yescharacteristic
221C22×C127#53511yescharacteristic
222C22×C127#53611yescharacteristic
223C22×C127#53611yescharacteristic
224C22×C127#53712yes—
225C22×C127#53712yes—
226C22×C127#53814yes—
227C22×C127#53914yes—
228C22×C127#54114yes—
229C22×C127#54214yes—
230C4×C127—24no—
231C4×C127—24no—
232C4×C127—24no—
233C4×C127—42no—
234C4×C127—42no—
235C4×C127—48no—
236C4×C127—42no—
237C4×C127—84no—
238#14291C12711yesmaximal, characteristic, direct product factor, Sylow
239C2×C127—82no—
240C2×C127#229711yescharacteristic
241C2×C127#231111yescharacteristic
242C2×C127#231111yescharacteristic
243C2×C127#233414yes—
244C2×C127#263612yes—
245C2×C127#263712yes—
246C2×C127#266212yes—
247C2×C127#266412yes—
248C22×#126C2×C12711yescharacteristic
249C2×#382C2×C12711yescharacteristic, complemented
250C2×C4×C4⋊C4C2×C12711yescharacteristic, complemented
251#1441C2×C12712yescomplemented
252#1441C2×C12712yescomplemented
253#1439C2×C12712yes—
254#1439C2×C12712yes—
255#1437C2×C12712yes—
256#1436C2×C12712yescomplemented
257C127#1429111yescharacteristic, direct product factor, Sylow
258C2×#126—24no—
259C2×#126—24no—
260C2×#126C4×C12718yescomplemented
261C22×C4⋊C4C22×C12712yes—
262C22×C4⋊C4C22×C12711yescharacteristic
263C22×C4⋊C4C22×C12711yescharacteristic
264C22×C4⋊C4C22×C12711yescharacteristic
265C22×C4⋊C4C22×C12712yes—
266C22×C22⋊C4C22×C12711yescharacteristic
267C22×C22⋊C4C22×C12711yescharacteristic
268C22×C22⋊C4C22×C12711yescharacteristic
269C22×C22⋊C4C22×C12714yes—
270C22×C42C22×C12712yes—
271C22×C42C22×C12711yescharacteristic
272#382—24no—
273C4×C4⋊C4—24no—
274C2×#95C22×C12712yes—
275C2×#95C22×C12714yes—
276C2×#95C22×C12712yes—
277C2×#95C22×C12712yes—
278C2×#95C22×C12714yes—
279C2×#95C22×C12714yes—
280C25C23×C12711yescharacteristic
281C23×C4C23×C12714yes—
282C23×C4C23×C12711yescharacteristic
283C23×C4C23×C12711yescharacteristic
284C23×C4C23×C12711yescharacteristic
285C23×C4C23×C12714yes—
286C23×C4C23×C12711yescharacteristic
287C23×C4C23×C12711yescharacteristic
288C23×C4C23×C12711yescharacteristic
289#126—232no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4C2×C4×C12714yes—
301C2×C4⋊C4C2×C4×C12714yes—
302C2×C4⋊C4C2×C4×C12714yes—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—44no—
311C2×C22⋊C4—44no—
312C2×C22⋊C4C2×C4×C12714yes—
313C2×C22⋊C4C2×C4×C12714yes—
314C2×C22⋊C4C2×C4×C12714yes—
315C2×C42—24no—
316C2×C42—44no—
317C2×C42C2×C4×C12714yes—
318C2×C42D4×C12714yes—
319C2×C42D4×C12714yes—
320#95—24no—
321#95—24no—
322#95—24no—
323#95—28no—
324#95—44no—
325#95—44no—
326C24—21no—
327C24—21no—
328C24—24no—
329C24—22no—
330C24—22no—
331C24—22no—
332C24—22no—
333C24C22×C4×C12712yes—
334C24C24×C12711yescharacteristic
335C22×C4—24no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4C22×C4×C12712yes—
365C22×C4C22×C4×C12712yes—
366C22×C4C22×C4×C12712yes—
367C22×C4C22×C4×C12712yes—
368C22×C4C22×C4×C12712yes—
369C22×C4C22×C4×C12712yes—
370C22×C4C2×D4×C12712yes—
371C22×C4C2×D4×C12712yes—
372C22×C4C2×D4×C12712yes—
373C22×C4C2×D4×C12712yes—
374C22×C4C2×D4×C12712yes—
375C22×C4C2×D4×C12712yes—
376C22×C4#41×C12718yes—
377C4⋊C4—216no—
378C4⋊C4—28no—
379C4⋊C4—28no—
380C4⋊C4—28no—
381C4⋊C4—48no—
382C22⋊C4—28no—
383C22⋊C4—28no—
384C22⋊C4—28no—
385C22⋊C4—416no—
386C42—48no—
387C42C22⋊C4×C127116yescomplemented
388C23—22no—
389C23—24no—
390C23—24no—
391C23—24no—
392C23—42no—
393C23—42no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—42no—
399C23—42no—
400C23—44no—
401C23—44no—
402C23—44no—
403C23—44no—
404C23C23×C4×C12711yescharacteristic
405C23C22×D4×C12711yescharacteristic
406C23C22×D4×C12711yescharacteristic
407C23C2×#41×C12714yes—
408C23H(5,𝔽2)×C12712yes—
409C23H(5,𝔽2)×C12712yes—
410C232−1+4×C12712yes—
411C232−1+4×C12712yes—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—28no—
430C2×C4—28no—
431C2×C4—28no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4C2×C22⋊C4×C12714yes—
452C2×C4C2×C22⋊C4×C12714yes—
453C2×C4C2×C22⋊C4×C12714yes—
454C22—48no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—82no—
459C22—82no—
460C22—82no—
461C22—82no—
462C22C22×C22⋊C4×C12711yescharacteristic
463C22C4×#41×C12712yes—
464C22#520×C12712yes—
465C22#520×C12712yes—
466C22#525×C12712yes—
467C22#532×C12712yes—
468C22#535×C12711yescharacteristic
469C22#535×C12711yescharacteristic
470C22#536×C12711yescharacteristic
471C22#536×C12711yescharacteristic
472C22#537×C12712yes—
473C22#537×C12712yes—
474C22#538×C12714yes—
475C22#539×C12714yes—
476C22#541×C12714yes—
477C22#542×C12714yes—
478C4—24no—
479C4—24no—
480C4—24no—
481C4—48no—
482C4—42no—
483C4—42no—
484C4—42no—
485C4—84no—
486C2—82no—
487C2C127×#229711yescharacteristic
488C2C127×#231111yescharacteristic
489C2C127×#231111yescharacteristic
490C2C127×#233414yes—
491C2C127×#263612yes—
492C2C127×#263712yes—
493C2C127×#266212yes—
494C2C127×#266412yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#382×C127C2semidirect
3. C2×C4×C4⋊C4×C127C2semidirect
4. C127×#1441C2semidirect
5. C127×#1441C2semidirect
9. C127×#1436C2semidirect
12. C2×#126×C127C4semidirect
139. C42×C127C22⋊C4semidirect
238. #14291C127direct (N × H)
249. C2×#382C2×C127semidirect
250. C2×C4×C4⋊C4C2×C127semidirect
251. #1441C2×C127semidirect
252. #1441C2×C127semidirect
256. #1436C2×C127semidirect
257. C127#14291direct (N × H)
260. C2×#126C4×C127semidirect
387. C42C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#126×C1272
C2×#382×C1272
C2×C4×C4⋊C4×C1272
C127×#14412
C127×#14392
C127×#14372
C127×#14362
#14291127