Finite Group Databasebeta

← C127×#8423 #44572096

Subgroups — C127×#8423 #44572096

Order 32512.

772 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3511C211yesmaximal, characteristic
2C127×#1981C211yesmaximal, characteristic, complemented
3C127×#1806C211yesmaximal, characteristic, complemented
4C127×#1548C211yesmaximal, characteristic, complemented
5C127×#1547C211yesmaximal, characteristic, complemented
6C127×#1502C211yesmaximal, characteristic, complemented
7C127×#1477C211yesmaximal, characteristic, complemented
8#556×C127—21no—
9#555×C127C412yescomplemented
10#554×C127C412yescomplemented
11#553×C127—22no—
12#548×C127—22no—
13#547×C127—21no—
14#542×C127—22no—
15#537×C127—21no—
16#533×C127—21no—
17#532×C127—21no—
18#532×C127C2211yescharacteristic
19C2×C4⋊Q8×C127C2211yescharacteristic
20#520×C127—21no—
21C4×#41×C127C2211yescharacteristic
22#431×C127C2211yescharacteristic
23#423×C127C2211yescharacteristic
24C2×C4⋊C8×C127C2211yescharacteristic
25C2×#104×C127—21no—
26C2×#103×C127—22no—
27C4×C4⋊C4×C127C2211yescharacteristic
28#339×C127—21no—
29#333×C127—22no—
30#332×C127—21no—
31#331×C127—21no—
32#327×C127—22no—
33Q8⋊C8×C127—21no—
34D4⋊C8×C127—21no—
35C2×#41×C127—22no—
36C2×#41×C127—21no—
37C2×#41×C127D411yescharacteristic
38C22×Q8×C127D412yes—
39C2×M16×C127—21no—
40C22×C8×C127—21no—
41C4⋊Q8×C127—21no—
42C4⋊Q8×C127—21no—
43C4⋊Q8×C127C2×C412yes—
44C4⋊Q8×C127D412yes—
45C4⋊Q8×C127D411yescharacteristic
46#127×C127D411yescharacteristic
47#126×C127—24no—
48#125×C127—22no—
49#124×C127—22no—
50#124×C127—24no—
51#124×C127—21no—
52#123×C127—24no—
53C22⋊Q8×C127—22no—
54C22⋊Q8×C127—22no—
55C22⋊Q8×C127—22no—
56C22⋊Q8×C127—24no—
57#121×C127—22no—
58#121×C127—24no—
59#121×C127—22no—
60#121×C127—22no—
61#121×C127—21no—
62#121×C127D412yes—
63C4×Q8×C127—22no—
64C4×Q8×C127—22no—
65C4×Q8×C127C2×C411yescharacteristic
66C4×Q8×C127D411yescharacteristic
67C4×D4×C127—22no—
68C4×D4×C127—24no—
69C4×D4×C127—22no—
70C4×D4×C127—21no—
71C4×D4×C127—21no—
72C4×D4×C127—21no—
73C4×D4×C127C2×C411yescharacteristic
74C4×D4×C127C2×C412yes—
75C4×D4×C127D411yescharacteristic
76#117×C127—22no—
77#117×C127—22no—
78#117×C127—21no—
79#117×C127D411yescharacteristic
80C2×C4⋊C4×C127—21no—
81C2×C4⋊C4×C127—21no—
82C2×C4⋊C4×C127—22no—
83C2×C4⋊C4×C127—21no—
84C2×C42×C127—21no—
85C2×C42×C127—21no—
86C2×C42×C127C2311yescharacteristic
87C4⋊C8×C127—21no—
88C4⋊C8×C127—21no—
89C4⋊C8×C127—21no—
90C4⋊C8×C127—21no—
91C4⋊C8×C127—21no—
92#104×C127—42no—
93#103×C127—44no—
94C22⋊C8×C127—21no—
95C4×C8×C127—21no—
96#95×C127—21no—
97#41×C127—21no—
98#41×C127—21no—
99#41×C127—21no—
100#41×C127—21no—
101#41×C127—41no—
102#41×C127—41no—
103#41×C127—41no—
104#41×C127—41no—
105#41×C127—82no—
106#41×C127—82no—
107C2×Q8×C127—21no—
108C2×Q8×C127—22no—
109C2×Q8×C127—42no—
110C2×Q8×C127—42no—
111C2×Q8×C127C22⋊C411yescharacteristic
112C2×Q8×C127C22⋊C414yes—
113C2×D4×C127—21no—
114C2×D4×C127—22no—
115C2×D4×C127—24no—
116C2×D4×C127—21no—
117C2×D4×C127—21no—
118C2×D4×C127C22⋊C411yescharacteristic
119C2×D4×C127C22⋊C412yes—
120C22×C4×C127—24no—
121C22×C4×C127—22no—
122C22×C4×C127—21no—
123C22×C4×C127—22no—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—41no—
127C22×C4×C127C2×D411yescharacteristic
128C22×C4×C127C2×D411yescharacteristic
129C22×C4×C127C2×D411yescharacteristic
130M16×C127—41no—
131M16×C127—41no—
132C2×C8×C127—42no—
133C2×C8×C127—41no—
134C2×C8×C127—41no—
135C2×C8×C127—41no—
136C4⋊C4×C127—24no—
137C4⋊C4×C127—24no—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—22no—
140C4⋊C4×C127—21no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—21no—
144C4⋊C4×C127—21no—
145C4⋊C4×C127—22no—
146C4⋊C4×C127—41no—
147C4⋊C4×C127C22⋊C411yescharacteristic
148C4⋊C4×C127C22⋊C411yescharacteristic
149C4⋊C4×C127C22⋊C412yes—
150C22⋊C4×C127—24no—
151C22⋊C4×C127—24no—
152C22⋊C4×C127—24no—
153C22⋊C4×C127—21no—
154C22⋊C4×C127—21no—
155C22⋊C4×C127—22no—
156C22⋊C4×C127—21no—
157C22⋊C4×C127—22no—
158C42×C127—24no—
159C42×C127—21no—
160C42×C127—21no—
161C42×C127—21no—
162C42×C127—41no—
163C42×C127—41no—
164C42×C127C22×C411yescharacteristic
165C42×C127C2×D411yescharacteristic
166C42×C127C2×D411yescharacteristic
167C42×C127C2×D411yescharacteristic
168C23×C127—21no—
169C23×C127—22no—
170C23×C127#12011yescharacteristic
171Q8×C127—21no—
172Q8×C127—21no—
173Q8×C127—44no—
174Q8×C127—41no—
175Q8×C127—41no—
176Q8×C127—42no—
177Q8×C127—42no—
178D4×C127—21no—
179D4×C127—21no—
180D4×C127—42no—
181D4×C127—41no—
182D4×C127—42no—
183D4×C127—41no—
184D4×C127—42no—
185D4×C127—41no—
186D4×C127—41no—
187D4×C127—41no—
188D4×C127—41no—
189D4×C127—84no—
190C2×C4×C127—21no—
191C2×C4×C127—21no—
192C2×C4×C127—21no—
193C2×C4×C127—21no—
194C2×C4×C127—22no—
195C2×C4×C127—21no—
196C2×C4×C127—24no—
197C2×C4×C127—41no—
198C2×C4×C127—42no—
199C2×C4×C127—42no—
200C2×C4×C127—42no—
201C2×C4×C127—41no—
202C2×C4×C127—41no—
203C2×C4×C127—41no—
204C2×C4×C127—41no—
205C2×C4×C127—42no—
206C2×C4×C127—82no—
207C2×C4×C127—84no—
208C2×C4×C127—81no—
209C2×C4×C127—81no—
210C2×C4×C127C2×C22⋊C411yescharacteristic
211C2×C4×C127C2×C22⋊C411yescharacteristic
212C2×C4×C127C2×C22⋊C411yescharacteristic
213C2×C4×C127#12011yescharacteristic
214C2×C4×C127#12011yescharacteristic
215C2×C4×C127#12011yescharacteristic
216C2×C4×C127#13511yescharacteristic
217C2×C4×C127#13511yescharacteristic
218C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
219C2×C4×C127#13711yescharacteristic
220C8×C127—81no—
221C8×C127—81no—
222C8×C127—81no—
223C22×C127—21no—
224C22×C127—21no—
225C22×C127—41no—
226C22×C127—42no—
227C22×C127—41no—
228C22×C127—42no—
229C22×C127—41no—
230C22×C127—42no—
231C22×C127#37911yescharacteristic
232C22×C127#44911yescharacteristic
233C22×C127#45211yescharacteristic
234C4×C127—21no—
235C4×C127—21no—
236C4×C127—21no—
237C4×C127—41no—
238C4×C127—44no—
239C4×C127—41no—
240C4×C127—41no—
241C4×C127—42no—
242C4×C127—82no—
243C4×C127#41611yescharacteristic
244C4×C127#41711yescharacteristic
245C4×C127#44911yescharacteristic
246C4×C127#45211yescharacteristic
247C4×C127#45311yescharacteristic
248C4×C127#45511yescharacteristic
249#8423C12711yesmaximal, characteristic, direct product factor, Sylow
250C2×C127—21no—
251C2×C127—21no—
252C2×C127—81no—
253C2×C127—82no—
254C2×C127#178811yescharacteristic
255C2×C127#179211yescharacteristic
256C2×C127#179611yescharacteristic
257#3511C2×C12711yescharacteristic
258#1981C2×C12711yescharacteristic, complemented
259#1806C2×C12711yescharacteristic, complemented
260#1548C2×C12711yescharacteristic, complemented
261#1547C2×C12711yescharacteristic, complemented
262#1502C2×C12711yescharacteristic, complemented
263#1477C2×C12711yescharacteristic, complemented
264C127#842311yescharacteristic, direct product factor, Sylow
265#556—21no—
266#555C4×C12712yescomplemented
267#554C4×C12712yescomplemented
268#553—22no—
269#548—22no—
270#547—21no—
271#542—22no—
272#537—21no—
273#533—21no—
274#532—21no—
275#532C22×C12711yescharacteristic
276C2×C4⋊Q8C22×C12711yescharacteristic
277#520—21no—
278C4×#41C22×C12711yescharacteristic
279#431C22×C12711yescharacteristic
280#423C22×C12711yescharacteristic
281C2×C4⋊C8C22×C12711yescharacteristic
282C2×#104—21no—
283C2×#103—22no—
284C4×C4⋊C4C22×C12711yescharacteristic
285#339—21no—
286#333—22no—
287#332—21no—
288#331—21no—
289#327—22no—
290Q8⋊C8—21no—
291D4⋊C8—21no—
292C2×#41—22no—
293C2×#41—21no—
294C2×#41D4×C12711yescharacteristic
295C22×Q8D4×C12712yes—
296C2×M16—21no—
297C22×C8—21no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8C2×C4×C12712yes—
301C4⋊Q8D4×C12712yes—
302C4⋊Q8D4×C12711yescharacteristic
303#127D4×C12711yescharacteristic
304#126—24no—
305#125—22no—
306#124—22no—
307#124—24no—
308#124—21no—
309#123—24no—
310C22⋊Q8—22no—
311C22⋊Q8—22no—
312C22⋊Q8—22no—
313C22⋊Q8—24no—
314#121—22no—
315#121—24no—
316#121—22no—
317#121—22no—
318#121—21no—
319#121D4×C12712yes—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×Q8C2×C4×C12711yescharacteristic
323C4×Q8D4×C12711yescharacteristic
324C4×D4—22no—
325C4×D4—24no—
326C4×D4—22no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4C2×C4×C12711yescharacteristic
331C4×D4C2×C4×C12712yes—
332C4×D4D4×C12711yescharacteristic
333#117—22no—
334#117—22no—
335#117—21no—
336#117D4×C12711yescharacteristic
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42C23×C12711yescharacteristic
344C4⋊C8—21no—
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—21no—
349#104—42no—
350#103—44no—
351C22⋊C8—21no—
352C4×C8—21no—
353#95—21no—
354#41—21no—
355#41—21no—
356#41—21no—
357#41—21no—
358#41—41no—
359#41—41no—
360#41—41no—
361#41—41no—
362#41—82no—
363#41—82no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—42no—
367C2×Q8—42no—
368C2×Q8C22⋊C4×C12711yescharacteristic
369C2×Q8C22⋊C4×C12714yes—
370C2×D4—21no—
371C2×D4—22no—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4C22⋊C4×C12711yescharacteristic
376C2×D4C22⋊C4×C12712yes—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—41no—
384C22×C4C2×D4×C12711yescharacteristic
385C22×C4C2×D4×C12711yescharacteristic
386C22×C4C2×D4×C12711yescharacteristic
387M16—41no—
388M16—41no—
389C2×C8—42no—
390C2×C8—41no—
391C2×C8—41no—
392C2×C8—41no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—41no—
404C4⋊C4C22⋊C4×C12711yescharacteristic
405C4⋊C4C22⋊C4×C12711yescharacteristic
406C4⋊C4C22⋊C4×C12712yes—
407C22⋊C4—24no—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—22no—
413C22⋊C4—21no—
414C22⋊C4—22no—
415C42—24no—
416C42—21no—
417C42—21no—
418C42—21no—
419C42—41no—
420C42—41no—
421C42C22×C4×C12711yescharacteristic
422C42C2×D4×C12711yescharacteristic
423C42C2×D4×C12711yescharacteristic
424C42C2×D4×C12711yescharacteristic
425C23—21no—
426C23—22no—
427C23#120×C12711yescharacteristic
428Q8—21no—
429Q8—21no—
430Q8—44no—
431Q8—41no—
432Q8—41no—
433Q8—42no—
434Q8—42no—
435D4—21no—
436D4—21no—
437D4—42no—
438D4—41no—
439D4—42no—
440D4—41no—
441D4—42no—
442D4—41no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—84no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—24no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—82no—
464C2×C4—84no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4C2×C22⋊C4×C12711yescharacteristic
468C2×C4C2×C22⋊C4×C12711yescharacteristic
469C2×C4C2×C22⋊C4×C12711yescharacteristic
470C2×C4#120×C12711yescharacteristic
471C2×C4#120×C12711yescharacteristic
472C2×C4#120×C12711yescharacteristic
473C2×C4#135×C12711yescharacteristic
474C2×C4#135×C12711yescharacteristic
475C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
476C2×C4#137×C12711yescharacteristic
477C8—81no—
478C8—81no—
479C8—81no—
480C22—21no—
481C22—21no—
482C22—41no—
483C22—42no—
484C22—41no—
485C22—42no—
486C22—41no—
487C22—42no—
488C22#379×C12711yescharacteristic
489C22#449×C12711yescharacteristic
490C22#452×C12711yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—41no—
495C4—42no—
496C4—41no—
497C4—44no—
498C4—41no—
499C4—82no—
500C4#416×C12711yescharacteristic
501C4#417×C12711yescharacteristic
502C4#449×C12711yescharacteristic
503C4#452×C12711yescharacteristic
504C4#453×C12711yescharacteristic
505C4#455×C12711yescharacteristic
506C2—21no—
507C2—21no—
508C2—81no—
509C2—82no—
510C2C127×#178811yescharacteristic
511C2C127×#179211yescharacteristic
512C2C127×#179611yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3511C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1981C2semidirect
3. C127×#1806C2semidirect
4. C127×#1548C2semidirect
5. C127×#1547C2semidirect
6. C127×#1502C2semidirect
7. C127×#1477C2semidirect
9. #555×C127C4semidirect
10. #554×C127C4semidirect
249. #8423C127direct (N × H)
258. #1981C2×C127semidirect
259. #1806C2×C127semidirect
260. #1548C2×C127semidirect
261. #1547C2×C127semidirect
262. #1502C2×C127semidirect
263. #1477C2×C127semidirect
264. C127#8423direct (N × H)
266. #555C4×C127semidirect
267. #554C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35112
C127×#19812
C127×#18062
C127×#15482
C127×#15472
C127×#15022
C127×#14772
#8423127