Finite Group Databasebeta

← C127×#11025 #44574698

Subgroups — C127×#11025 #44574698

Order 32512.

1334 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C127C211yesmaximal, characteristic
2C22×#104×C127C212yesmaximal, complemented
3C2×#408×C127C212yesmaximal, complemented
4C2×#341×C127C211yesmaximal, characteristic, complemented
5C2×#336×C127C211yesmaximal, characteristic, complemented
6C22×#41×C127C2212yes—
7C2×#135×C127—24no—
8C2×#135×C127—24no—
9C2×#135×C127—22no—
10C2×#135×C127—22no—
11C22×Q16×C127C411yescharacteristic, complemented
12C22×SD16×C127C412yescomplemented
13C22×D8×C127C411yescharacteristic, complemented
14C22×M16×C127C2212yes—
15C23×C8×C127C2211yescharacteristic
16C23×C8×C127C2211yescharacteristic
17C22×C42×C127C2211yescharacteristic
18C2×#104×C127—24no—
19C2×#104×C127—24no—
20C2×#104×C127—24no—
21#408×C127—24no—
22#408×C127—24no—
23C2×C22⋊C8×C127—24no—
24#341×C127—22no—
25#336×C127—22no—
26C2×#41×C127—22no—
27C2×#41×C127—22no—
28C2×#41×C127—22no—
29C2×#41×C127—22no—
30C2×#41×C127—22no—
31C2×#41×C127—22no—
32C2×#41×C127—22no—
33C2×#41×C127—22no—
34C2×#41×C127—22no—
35C2×#41×C127—22no—
36C2×#41×C127D414yes—
37C2×#41×C127D414yes—
38C22×Q8×C127C2×C412yes—
39C22×D4×C127—22no—
40C22×D4×C127C2×C412yes—
41C23×C4×C127—21no—
42C23×C4×C127—22no—
43C23×C4×C127C2311yescharacteristic
44#135×C127—28no—
45#135×C127—216no—
46#135×C127—28no—
47C2×Q16×C127—24no—
48C2×Q16×C127—22no—
49C2×SD16×C127—24no—
50C2×SD16×C127—24no—
51C2×SD16×C127—24no—
52C2×D8×C127—24no—
53C2×D8×C127—22no—
54C2×M16×C127—22no—
55C2×M16×C127—22no—
56C2×M16×C127—22no—
57C2×M16×C127—22no—
58C2×M16×C127—22no—
59C2×M16×C127D414yes—
60C22×C8×C127—22no—
61C22×C8×C127—22no—
62C22×C8×C127—21no—
63C22×C8×C127—22no—
64C22×C8×C127—22no—
65C22×C8×C127—22no—
66C22×C8×C127—21no—
67C22×C8×C127C2×C411yescharacteristic
68C22×C8×C127C2×C411yescharacteristic
69C22×C8×C127D412yes—
70C22×C8×C127D412yes—
71C22×C8×C127D412yes—
72C2×C42×C127—22no—
73C2×C42×C127—22no—
74C2×C42×C127—21no—
75C2×C42×C127D412yes—
76#104×C127—216no—
77C22⋊C8×C127—216no—
78C24×C127—22no—
79C24×C127#4111yescharacteristic
80#41×C127—24no—
81#41×C127—24no—
82#41×C127—24no—
83#41×C127—24no—
84#41×C127—24no—
85#41×C127—24no—
86#41×C127—24no—
87#41×C127—24no—
88#41×C127—42no—
89#41×C127—42no—
90#41×C127—42no—
91#41×C127—42no—
92#41×C127—42no—
93#41×C127—42no—
94#41×C127—42no—
95#41×C127—42no—
96C2×Q8×C127—22no—
97C2×Q8×C127—22no—
98C2×Q8×C127—22no—
99C2×Q8×C127—22no—
100C2×Q8×C127—22no—
101C2×Q8×C127C22⋊C414yes—
102C2×D4×C127—24no—
103C2×D4×C127—24no—
104C2×D4×C127—22no—
105C2×D4×C127—22no—
106C2×D4×C127—22no—
107C2×D4×C127—22no—
108C2×D4×C127—22no—
109C2×D4×C127—42no—
110C2×D4×C127—42no—
111C2×D4×C127—42no—
112C2×D4×C127—42no—
113C2×D4×C127C22⋊C414yes—
114C22×C4×C127—24no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—24no—
118C22×C4×C127—24no—
119C22×C4×C127—42no—
120C22×C4×C127—42no—
121C22×C4×C127—42no—
122C22×C4×C127—42no—
123C22×C4×C127—42no—
124C22×C4×C127—42no—
125C22×C4×C127C22×C411yescharacteristic
126C22×C4×C127C2×D412yes—
127C22×C4×C127C2×D412yes—
128C22×C4×C127C2×D411yescharacteristic
129C22×C4×C127C2×D411yescharacteristic
130C22×C4×C127C2×D412yes—
131C22×C4×C127C2×D411yescharacteristic
132C22×C4×C127C2×D411yescharacteristic
133C22×C4×C127#4111yescharacteristic
134C22×C4×C127#4112yes—
135Q16×C127—28no—
136SD16×C127—216no—
137D8×C127—28no—
138M16×C127—24no—
139M16×C127—24no—
140M16×C127—42no—
141M16×C127—42no—
142C2×C8×C127—22no—
143C2×C8×C127—22no—
144C2×C8×C127—22no—
145C2×C8×C127—24no—
146C2×C8×C127—22no—
147C2×C8×C127—24no—
148C2×C8×C127—24no—
149C2×C8×C127—22no—
150C2×C8×C127—41no—
151C2×C8×C127—42no—
152C2×C8×C127—42no—
153C2×C8×C127—41no—
154C2×C8×C127—42no—
155C2×C8×C127C22⋊C412yes—
156C2×C8×C127C22⋊C412yes—
157C42×C127—24no—
158C42×C127—41no—
159C42×C127—41no—
160C23×C127—22no—
161C23×C127—22no—
162C23×C127—24no—
163C23×C127—42no—
164C23×C127—42no—
165C23×C127—44no—
166C23×C127—44no—
167C23×C127C4×D411yescharacteristic
168C23×C127#12112yes—
169C23×C127#12111yescharacteristic
170C23×C127#12312yes—
171C23×C127#12411yescharacteristic
172Q8×C127—24no—
173Q8×C127—24no—
174Q8×C127—42no—
175Q8×C127—42no—
176D4×C127—24no—
177D4×C127—24no—
178D4×C127—44no—
179D4×C127—44no—
180D4×C127—44no—
181D4×C127—44no—
182D4×C127—42no—
183D4×C127—42no—
184C2×C4×C127—24no—
185C2×C4×C127—24no—
186C2×C4×C127—48no—
187C2×C4×C127—42no—
188C2×C4×C127—42no—
189C2×C4×C127—42no—
190C2×C4×C127—42no—
191C2×C4×C127—44no—
192C2×C4×C127—44no—
193C2×C4×C127—44no—
194C2×C4×C127—44no—
195C2×C4×C127C2×C22⋊C412yes—
196C2×C4×C127C2×C22⋊C411yescharacteristic
197C2×C4×C127C4×D411yescharacteristic
198C2×C4×C127C4×D412yes—
199C2×C4×C127#12011yescharacteristic
200C2×C4×C127#12012yes—
201C2×C4×C127#12011yescharacteristic
202C2×C4×C127#12012yes—
203C2×C4×C127#12012yes—
204C2×C4×C127#12112yes—
205C2×C4×C127#12112yes—
206C2×C4×C127#12112yes—
207C2×C4×C127#12112yes—
208C2×C4×C127#12111yescharacteristic
209C2×C4×C127#12312yes—
210C2×C4×C127#12411yescharacteristic
211C2×C4×C127#12711yescharacteristic
212C2×C4×C127#12711yescharacteristic
213C8×C127—22no—
214C8×C127—22no—
215C8×C127—42no—
216C8×C127—44no—
217C22×C127—24no—
218C22×C127—24no—
219C22×C127—21no—
220C22×C127—21no—
221C22×C127—21no—
222C22×C127—21no—
223C22×C127—48no—
224C22×C127—44no—
225C22×C127—84no—
226C22×C127—82no—
227C22×C127—82no—
228C22×C127#38612yes—
229C22×C127#39011yescharacteristic
230C22×C127#39211yescharacteristic
231C22×C127#39412yes—
232C22×C127#39411yescharacteristic
233C22×C127#44312yes—
234C22×C127#44412yes—
235C4×C127—44no—
236C4×C127—44no—
237C4×C127#37911yescharacteristic
238C4×C127#38612yes—
239C4×C127#39011yescharacteristic
240C4×C127#39211yescharacteristic
241C4×C127#39212yes—
242C4×C127#39411yescharacteristic
243#11025C12711yesmaximal, characteristic, direct product factor, Sylow
244C2×C127—21no—
245C2×C127—22no—
246C2×C127—21no—
247C2×C127—84no—
248C2×C127#143811yescharacteristic
249C2×C127#187614yes—
250C2×C127#197411yescharacteristic
251C2×C127#197511yescharacteristic
252C22×#135C2×C12711yescharacteristic
253C22×#104C2×C12712yescomplemented
254C2×#408C2×C12712yescomplemented
255C2×#341C2×C12711yescharacteristic, complemented
256C2×#336C2×C12711yescharacteristic, complemented
257C127#1102511yescharacteristic, direct product factor, Sylow
258C22×#41C22×C12712yes—
259C2×#135—24no—
260C2×#135—24no—
261C2×#135—22no—
262C2×#135—22no—
263C22×Q16C4×C12711yescharacteristic, complemented
264C22×SD16C4×C12712yescomplemented
265C22×D8C4×C12711yescharacteristic, complemented
266C22×M16C22×C12712yes—
267C23×C8C22×C12711yescharacteristic
268C23×C8C22×C12711yescharacteristic
269C22×C42C22×C12711yescharacteristic
270C2×#104—24no—
271C2×#104—24no—
272C2×#104—24no—
273#408—24no—
274#408—24no—
275C2×C22⋊C8—24no—
276#341—22no—
277#336—22no—
278C2×#41—22no—
279C2×#41—22no—
280C2×#41—22no—
281C2×#41—22no—
282C2×#41—22no—
283C2×#41—22no—
284C2×#41—22no—
285C2×#41—22no—
286C2×#41—22no—
287C2×#41—22no—
288C2×#41D4×C12714yes—
289C2×#41D4×C12714yes—
290C22×Q8C2×C4×C12712yes—
291C22×D4—22no—
292C22×D4C2×C4×C12712yes—
293C23×C4—21no—
294C23×C4—22no—
295C23×C4C23×C12711yescharacteristic
296#135—28no—
297#135—216no—
298#135—28no—
299C2×Q16—24no—
300C2×Q16—22no—
301C2×SD16—24no—
302C2×SD16—24no—
303C2×SD16—24no—
304C2×D8—24no—
305C2×D8—22no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—22no—
311C2×M16D4×C12714yes—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—21no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—21no—
319C22×C8C2×C4×C12711yescharacteristic
320C22×C8C2×C4×C12711yescharacteristic
321C22×C8D4×C12712yes—
322C22×C8D4×C12712yes—
323C22×C8D4×C12712yes—
324C2×C42—22no—
325C2×C42—22no—
326C2×C42—21no—
327C2×C42D4×C12712yes—
328#104—216no—
329C22⋊C8—216no—
330C24—22no—
331C24#41×C12711yescharacteristic
332#41—24no—
333#41—24no—
334#41—24no—
335#41—24no—
336#41—24no—
337#41—24no—
338#41—24no—
339#41—24no—
340#41—42no—
341#41—42no—
342#41—42no—
343#41—42no—
344#41—42no—
345#41—42no—
346#41—42no—
347#41—42no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8C22⋊C4×C12714yes—
354C2×D4—24no—
355C2×D4—24no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4C22⋊C4×C12714yes—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4C22×C4×C12711yescharacteristic
378C22×C4C2×D4×C12712yes—
379C22×C4C2×D4×C12712yes—
380C22×C4C2×D4×C12711yescharacteristic
381C22×C4C2×D4×C12711yescharacteristic
382C22×C4C2×D4×C12712yes—
383C22×C4C2×D4×C12711yescharacteristic
384C22×C4C2×D4×C12711yescharacteristic
385C22×C4#41×C12711yescharacteristic
386C22×C4#41×C12712yes—
387Q16—28no—
388SD16—216no—
389D8—28no—
390M16—24no—
391M16—24no—
392M16—42no—
393M16—42no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—24no—
398C2×C8—22no—
399C2×C8—24no—
400C2×C8—24no—
401C2×C8—22no—
402C2×C8—41no—
403C2×C8—42no—
404C2×C8—42no—
405C2×C8—41no—
406C2×C8—42no—
407C2×C8C22⋊C4×C12712yes—
408C2×C8C22⋊C4×C12712yes—
409C42—24no—
410C42—41no—
411C42—41no—
412C23—22no—
413C23—22no—
414C23—24no—
415C23—42no—
416C23—42no—
417C23—44no—
418C23—44no—
419C23C4×D4×C12711yescharacteristic
420C23#121×C12712yes—
421C23#121×C12711yescharacteristic
422C23#123×C12712yes—
423C23#124×C12711yescharacteristic
424Q8—24no—
425Q8—24no—
426Q8—42no—
427Q8—42no—
428D4—24no—
429D4—24no—
430D4—44no—
431D4—44no—
432D4—44no—
433D4—44no—
434D4—42no—
435D4—42no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—48no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4C2×C22⋊C4×C12712yes—
448C2×C4C2×C22⋊C4×C12711yescharacteristic
449C2×C4C4×D4×C12711yescharacteristic
450C2×C4C4×D4×C12712yes—
451C2×C4#120×C12711yescharacteristic
452C2×C4#120×C12712yes—
453C2×C4#120×C12711yescharacteristic
454C2×C4#120×C12712yes—
455C2×C4#120×C12712yes—
456C2×C4#121×C12712yes—
457C2×C4#121×C12712yes—
458C2×C4#121×C12712yes—
459C2×C4#121×C12712yes—
460C2×C4#121×C12711yescharacteristic
461C2×C4#123×C12712yes—
462C2×C4#124×C12711yescharacteristic
463C2×C4#127×C12711yescharacteristic
464C2×C4#127×C12711yescharacteristic
465C8—22no—
466C8—22no—
467C8—42no—
468C8—44no—
469C22—24no—
470C22—24no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—48no—
476C22—44no—
477C22—84no—
478C22—82no—
479C22—82no—
480C22#386×C12712yes—
481C22#390×C12711yescharacteristic
482C22#392×C12711yescharacteristic
483C22#394×C12712yes—
484C22#394×C12711yescharacteristic
485C22#443×C12712yes—
486C22#444×C12712yes—
487C4—44no—
488C4—44no—
489C4#379×C12711yescharacteristic
490C4#386×C12712yes—
491C4#390×C12711yescharacteristic
492C4#392×C12711yescharacteristic
493C4#392×C12712yes—
494C4#394×C12711yescharacteristic
495C2—21no—
496C2—22no—
497C2—21no—
498C2—84no—
499C2C127×#143811yescharacteristic
500C2C127×#187614yes—
501C2C127×#197411yescharacteristic
502C2C127×#197511yescharacteristic
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
socleC23×C127C4×D4
prime radicalC22×#135×C127C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#104×C127C2semidirect
3. C2×#408×C127C2semidirect
4. C2×#341×C127C2semidirect
5. C2×#336×C127C2semidirect
11. C22×Q16×C127C4semidirect
12. C22×SD16×C127C4semidirect
13. C22×D8×C127C4semidirect
243. #11025C127direct (N × H)
253. C22×#104C2×C127semidirect
254. C2×#408C2×C127semidirect
255. C2×#341C2×C127semidirect
256. C2×#336C2×C127semidirect
257. C127#11025direct (N × H)
263. C22×Q16C4×C127semidirect
264. C22×SD16C4×C127semidirect
265. C22×D8C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1272
C22×#104×C1272
C2×#408×C1272
C2×#341×C1272
C2×#336×C1272
#11025127