Finite Group Databasebeta

← C127×#13103 #44576776

Subgroups — C127×#13103 #44576776

Order 32512.

646 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
1C127×#3010C211yesmaximal, characteristic
2C127×#2884C211yesmaximal, characteristic, complemented
3C127×#2128C211yesmaximal, characteristic, complemented
4C127×#2122C211yesmaximal, characteristic, complemented
5C127×#1796C211yesmaximal, characteristic, complemented
6C127×#1395C211yesmaximal, characteristic, complemented
7C127×#1391C211yesmaximal, characteristic, complemented
8C2×2−1+4×C127C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C127C411yescharacteristic, complemented
10C22×SD16×C127C411yescharacteristic, complemented
11#535×C127C2211yescharacteristic
12#519×C127—21no—
13#449×C127—21no—
14#449×C127—21no—
15#448×C127—21no—
16#448×C127—21no—
17#421×C127—21no—
18#419×C127—21no—
19#419×C127C411yescharacteristic, complemented
20#416×C127C411yescharacteristic, complemented
21#413×C127C2211yescharacteristic
22#410×C127—21no—
23#410×C127—22no—
24#410×C127—22no—
25#410×C127C2211yescharacteristic
26#410×C127C2211yescharacteristic
27#410×C127C2211yescharacteristic
28#408×C127C2211yescharacteristic
29#353×C127—22no—
30AΣL(1,𝔽16)×C127—22no—
312−1+4×C127—42no—
322−1+4×C127—42no—
33C2×#41×C127—21no—
34C2×#41×C127—21no—
35C2×#41×C127—21no—
36C2×#41×C127C2×C411yescharacteristic
37C2×#41×C127D411yescharacteristic
38C2×#41×C127D411yescharacteristic
39C2×#41×C127C2311yescharacteristic
40C22×Q8×C127—21no—
41C22×Q8×C127C2×C411yescharacteristic
42C22×Q8×C127D411yescharacteristic
43C22×Q8×C127D411yescharacteristic
44C22×D4×C127C2×C411yescharacteristic
45AGL(1,ℤ/8)×C127—42no—
46C2×SD16×C127—21no—
47C2×SD16×C127—21no—
48C2×SD16×C127—21no—
49C2×SD16×C127—42no—
50C2×D8×C127—21no—
51C2×M16×C127—21no—
52C2×M16×C127C2×C411yescharacteristic
53C22×C8×C127C2×C411yescharacteristic
54#127×C127—21no—
55#124×C127—21no—
56#121×C127—21no—
57#121×C127—21no—
58#120×C127—21no—
59#120×C127—21no—
60C4×Q8×C127—42no—
61C4×Q8×C127—42no—
62#117×C127—24no—
63#117×C127—21no—
64#117×C127—21no—
65#117×C127—21no—
66#117×C127C2×C411yescharacteristic
67#104×C127—42no—
68#103×C127—21no—
69#103×C127—21no—
70#103×C127—21no—
71#103×C127—42no—
72#102×C127—21no—
73#101×C127—21no—
74#100×C127—21no—
75#99×C127—24no—
76#99×C127—21no—
77#99×C127—21no—
78#99×C127—21no—
79#99×C127—21no—
80#99×C127D412yes—
81#99×C127D412yes—
82C22⋊C8×C127—21no—
83C22⋊C8×C127—21no—
84C24×C127—21no—
85#41×C127—22no—
86#41×C127—22no—
87#41×C127—41no—
88#41×C127—41no—
89#41×C127—41no—
90#41×C127—41no—
91#41×C127—41no—
92#41×C127—41no—
93#41×C127—44no—
94#41×C127—44no—
95#41×C127—44no—
96C2×Q8×C127—22no—
97C2×Q8×C127—22no—
98C2×Q8×C127—21no—
99C2×Q8×C127—21no—
100C2×Q8×C127—21no—
101C2×Q8×C127—22no—
102C2×Q8×C127—22no—
103C2×Q8×C127—41no—
104C2×Q8×C127—41no—
105C2×Q8×C127—44no—
106C2×Q8×C127C22⋊C411yescharacteristic
107C2×Q8×C127C22⋊C411yescharacteristic
108C2×Q8×C127C22⋊C411yescharacteristic
109C2×Q8×C127#4111yescharacteristic
110C2×D4×C127—21no—
111C2×D4×C127—21no—
112C2×D4×C127—21no—
113C2×D4×C127—21no—
114C2×D4×C127—21no—
115C2×D4×C127—41no—
116C2×D4×C127—41no—
117C2×D4×C127—41no—
118C2×D4×C127—41no—
119C2×D4×C127C22⋊C411yescharacteristic
120C2×D4×C127C2×D411yescharacteristic
121C2×D4×C127C2×D411yescharacteristic
122C2×D4×C127#4111yescharacteristic
123C22×C4×C127—21no—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
127C22×C4×C127—21no—
128C22×C4×C127—21no—
129C22×C4×C127C22×C411yescharacteristic
130C22×C4×C127C2×D411yescharacteristic
131C22×C4×C127C2×D411yescharacteristic
132SD16×C127—42no—
133SD16×C127—42no—
134SD16×C127—42no—
135D8×C127—42no—
136M16×C127—41no—
137M16×C127—41no—
138M16×C127—41no—
139C2×C8×C127—21no—
140C2×C8×C127—21no—
141C2×C8×C127—41no—
142C2×C8×C127—41no—
143C4⋊C4×C127—21no—
144C4⋊C4×C127—44no—
145C4⋊C4×C127—41no—
146C4⋊C4×C127—41no—
147C4⋊C4×C127—41no—
148C22⋊C4×C127—21no—
149C22⋊C4×C127—22no—
150C22⋊C4×C127—22no—
151C22⋊C4×C127—41no—
152C22⋊C4×C127—41no—
153C22⋊C4×C127—41no—
154C42×C127—21no—
155C42×C127—44no—
156C42×C127—41no—
157C42×C127—41no—
158C42×C127—41no—
159C23×C127—21no—
160C23×C127—41no—
161C23×C127—81no—
162C23×C127—161no—
163C23×C127C4×D411yescharacteristic
164C23×C127#12011yescharacteristic
165C23×C127#12111yescharacteristic
166Q8×C127—24no—
167Q8×C127—21no—
168Q8×C127—21no—
169Q8×C127—21no—
170Q8×C127—21no—
171Q8×C127—41no—
172Q8×C127—42no—
173Q8×C127—42no—
174Q8×C127#9912yes—
175Q8×C127#9912yes—
176D4×C127—21no—
177D4×C127—21no—
178D4×C127—41no—
179D4×C127—41no—
180D4×C127—41no—
181D4×C127—42no—
182D4×C127—42no—
183D4×C127—42no—
184D4×C127—41no—
185D4×C127—41no—
186D4×C127—81no—
187D4×C127—161no—
188D4×C127—161no—
189C2×C4×C127—24no—
190C2×C4×C127—21no—
191C2×C4×C127—21no—
192C2×C4×C127—21no—
193C2×C4×C127—21no—
194C2×C4×C127—21no—
195C2×C4×C127—21no—
196C2×C4×C127—21no—
197C2×C4×C127—21no—
198C2×C4×C127—21no—
199C2×C4×C127—42no—
200C2×C4×C127—42no—
201C2×C4×C127—42no—
202C2×C4×C127—42no—
203C2×C4×C127—42no—
204C2×C4×C127—42no—
205C2×C4×C127—42no—
206C2×C4×C127—41no—
207C2×C4×C127—81no—
208C2×C4×C127C2×C22⋊C411yescharacteristic
209C2×C4×C127C4×D411yescharacteristic
210C2×C4×C127#12111yescharacteristic
211C2×C4×C127#12311yescharacteristic
212C8×C127—41no—
213C8×C127—41no—
214C8×C127—81no—
215C22×C127—21no—
216C22×C127—21no—
217C22×C127—21no—
218C22×C127—41no—
219C22×C127—41no—
220C22×C127—41no—
221C22×C127—41no—
222C22×C127—81no—
223C22×C127—81no—
224C22×C127—81no—
225C22×C127—81no—
226C22×C127—162no—
227C22×C127#38611yescharacteristic
228C4×C127—21no—
229C4×C127—22no—
230C4×C127—22no—
231C4×C127—21no—
232C4×C127—21no—
233C4×C127—41no—
234C4×C127—81no—
235C4×C127—82no—
236C4×C127—82no—
237C4×C127—161no—
238C4×C127C2×#9911yescharacteristic
239C4×C127C2×#9911yescharacteristic
240#13103C12711yesmaximal, characteristic, direct product factor, Sylow
241C2×C127—21no—
242C2×C127—41no—
243C2×C127—41no—
244C2×C127—41no—
245C2×C127—81no—
246C2×C127—161no—
247C2×C127#189811yescharacteristic
248#3010C2×C12711yescharacteristic
249#2884C2×C12711yescharacteristic, complemented
250#2128C2×C12711yescharacteristic, complemented
251#2122C2×C12711yescharacteristic, complemented
252#1796C2×C12711yescharacteristic, complemented
253#1395C2×C12711yescharacteristic, complemented
254#1391C2×C12711yescharacteristic, complemented
255C127#1310311yescharacteristic, direct product factor, Sylow
256C2×2−1+4C22×C12711yescharacteristic
257C2×AGL(1,ℤ/8)C4×C12711yescharacteristic, complemented
258C22×SD16C4×C12711yescharacteristic, complemented
259#535C22×C12711yescharacteristic
260#519—21no—
261#449—21no—
262#449—21no—
263#448—21no—
264#448—21no—
265#421—21no—
266#419—21no—
267#419C4×C12711yescharacteristic, complemented
268#416C4×C12711yescharacteristic, complemented
269#413C22×C12711yescharacteristic
270#410—21no—
271#410—22no—
272#410—22no—
273#410C22×C12711yescharacteristic
274#410C22×C12711yescharacteristic
275#410C22×C12711yescharacteristic
276#408C22×C12711yescharacteristic
277#353—22no—
278AΣL(1,𝔽16)—22no—
2792−1+4—42no—
2802−1+4—42no—
281C2×#41—21no—
282C2×#41—21no—
283C2×#41—21no—
284C2×#41C2×C4×C12711yescharacteristic
285C2×#41D4×C12711yescharacteristic
286C2×#41D4×C12711yescharacteristic
287C2×#41C23×C12711yescharacteristic
288C22×Q8—21no—
289C22×Q8C2×C4×C12711yescharacteristic
290C22×Q8D4×C12711yescharacteristic
291C22×Q8D4×C12711yescharacteristic
292C22×D4C2×C4×C12711yescharacteristic
293AGL(1,ℤ/8)—42no—
294C2×SD16—21no—
295C2×SD16—21no—
296C2×SD16—21no—
297C2×SD16—42no—
298C2×D8—21no—
299C2×M16—21no—
300C2×M16C2×C4×C12711yescharacteristic
301C22×C8C2×C4×C12711yescharacteristic
302#127—21no—
303#124—21no—
304#121—21no—
305#121—21no—
306#120—21no—
307#120—21no—
308C4×Q8—42no—
309C4×Q8—42no—
310#117—24no—
311#117—21no—
312#117—21no—
313#117—21no—
314#117C2×C4×C12711yescharacteristic
315#104—42no—
316#103—21no—
317#103—21no—
318#103—21no—
319#103—42no—
320#102—21no—
321#101—21no—
322#100—21no—
323#99—24no—
324#99—21no—
325#99—21no—
326#99—21no—
327#99—21no—
328#99D4×C12712yes—
329#99D4×C12712yes—
330C22⋊C8—21no—
331C22⋊C8—21no—
332C24—21no—
333#41—22no—
334#41—22no—
335#41—41no—
336#41—41no—
337#41—41no—
338#41—41no—
339#41—41no—
340#41—41no—
341#41—44no—
342#41—44no—
343#41—44no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—41no—
352C2×Q8—41no—
353C2×Q8—44no—
354C2×Q8C22⋊C4×C12711yescharacteristic
355C2×Q8C22⋊C4×C12711yescharacteristic
356C2×Q8C22⋊C4×C12711yescharacteristic
357C2×Q8#41×C12711yescharacteristic
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4C22⋊C4×C12711yescharacteristic
368C2×D4C2×D4×C12711yescharacteristic
369C2×D4C2×D4×C12711yescharacteristic
370C2×D4#41×C12711yescharacteristic
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4C22×C4×C12711yescharacteristic
378C22×C4C2×D4×C12711yescharacteristic
379C22×C4C2×D4×C12711yescharacteristic
380SD16—42no—
381SD16—42no—
382SD16—42no—
383D8—42no—
384M16—41no—
385M16—41no—
386M16—41no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—41no—
390C2×C8—41no—
391C4⋊C4—21no—
392C4⋊C4—44no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C22⋊C4—21no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C42—21no—
403C42—44no—
404C42—41no—
405C42—41no—
406C42—41no—
407C23—21no—
408C23—41no—
409C23—81no—
410C23—161no—
411C23C4×D4×C12711yescharacteristic
412C23#120×C12711yescharacteristic
413C23#121×C12711yescharacteristic
414Q8—24no—
415Q8—21no—
416Q8—21no—
417Q8—21no—
418Q8—21no—
419Q8—41no—
420Q8—42no—
421Q8—42no—
422Q8#99×C12712yes—
423Q8#99×C12712yes—
424D4—21no—
425D4—21no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—42no—
430D4—42no—
431D4—42no—
432D4—41no—
433D4—41no—
434D4—81no—
435D4—161no—
436D4—161no—
437C2×C4—24no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—81no—
456C2×C4C2×C22⋊C4×C12711yescharacteristic
457C2×C4C4×D4×C12711yescharacteristic
458C2×C4#121×C12711yescharacteristic
459C2×C4#123×C12711yescharacteristic
460C8—41no—
461C8—41no—
462C8—81no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—162no—
475C22#386×C12711yescharacteristic
476C4—21no—
477C4—22no—
478C4—22no—
479C4—21no—
480C4—21no—
481C4—41no—
482C4—81no—
483C4—82no—
484C4—82no—
485C4—161no—
486C4C2×#99×C12711yescharacteristic
487C4C2×#99×C12711yescharacteristic
488C2—21no—
489C2—41no—
490C2—41no—
491C2—41no—
492C2—81no—
493C2—161no—
494C2C127×#189811yescharacteristic
subgroupG/H
center, socleC2×C127#1898
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×#41C23×C127
prime radicalC127×#3010C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C2×2−1+4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2884C2semidirect
3. C127×#2128C2semidirect
4. C127×#2122C2semidirect
5. C127×#1796C2semidirect
6. C127×#1395C2semidirect
7. C127×#1391C2semidirect
9. C2×AGL(1,ℤ/8)×C127C4semidirect
10. C22×SD16×C127C4semidirect
19. #419×C127C4semidirect
20. #416×C127C4semidirect
240. #13103C127direct (N × H)
249. #2884C2×C127semidirect
250. #2128C2×C127semidirect
251. #2122C2×C127semidirect
252. #1796C2×C127semidirect
253. #1395C2×C127semidirect
254. #1391C2×C127semidirect
255. C127#13103direct (N × H)
257. C2×AGL(1,ℤ/8)C4×C127semidirect
258. C22×SD16C4×C127semidirect
267. #419C4×C127semidirect
268. #416C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#30102
C127×#28842
C127×#21282
C127×#21222
C127×#17962
C127×#13952
C127×#13912
#13103127