Finite Group Databasebeta

← C127×#13102 #44576775

Subgroups — C127×#13102 #44576775

Order 32512.

688 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3008C211yesmaximal, characteristic
2C127×#2883C211yesmaximal, characteristic, complemented
3C127×#2128C211yesmaximal, characteristic, complemented
4C127×#2122C211yesmaximal, characteristic, complemented
5C127×#1795C211yesmaximal, characteristic, complemented
6C127×#1395C211yesmaximal, characteristic, complemented
7C127×#1391C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C127C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C127C411yescharacteristic, complemented
10C22×D8×C127C411yescharacteristic, complemented
11#535×C127C2211yescharacteristic
12#518×C127—21no—
13#449×C127—21no—
14#449×C127—21no—
15#447×C127—21no—
16#447×C127—21no—
17#421×C127—21no—
18#418×C127—21no—
19#418×C127C411yescharacteristic, complemented
20#416×C127C411yescharacteristic, complemented
21#413×C127C2211yescharacteristic
22#410×C127—21no—
23#410×C127C2211yescharacteristic
24#410×C127C2211yescharacteristic
25#410×C127C2211yescharacteristic
26C2×#99×C127—22no—
27C2×#99×C127—22no—
28#408×C127C2211yescharacteristic
29#353×C127—22no—
30AΣL(1,𝔽16)×C127—22no—
31H(5,𝔽2)×C127—42no—
32H(5,𝔽2)×C127—42no—
33C2×#41×C127—21no—
34C2×#41×C127C2×C411yescharacteristic
35C2×#41×C127D411yescharacteristic
36C2×#41×C127D411yescharacteristic
37C2×#41×C127C2311yescharacteristic
38C22×D4×C127—21no—
39C22×D4×C127—21no—
40C22×D4×C127—21no—
41C22×D4×C127C2×C411yescharacteristic
42C22×D4×C127C2×C411yescharacteristic, complemented
43C22×D4×C127D411yescharacteristic
44C22×D4×C127D411yescharacteristic
45AGL(1,ℤ/8)×C127—42no—
46C2×SD16×C127—21no—
47C2×D8×C127—21no—
48C2×D8×C127—21no—
49C2×D8×C127—21no—
50C2×D8×C127—42no—
51C2×M16×C127—21no—
52C2×M16×C127C2×C411yescharacteristic, complemented
53C22×C8×C127C2×C411yescharacteristic, complemented
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×D4×C127—42no—
61C4×D4×C127—42no—
62#117×C127—21no—
63#117×C127—21no—
64#117×C127—21no—
65#117×C127C2×C411yescharacteristic, complemented
66C2×C22⋊C4×C127—24no—
67#104×C127—42no—
68#103×C127—21no—
69#102×C127—21no—
70#102×C127—21no—
71#102×C127—21no—
72#102×C127—42no—
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—
85C24×C127—21no—
86C24×C127—21no—
87C24×C127—21no—
88#41×C127—22no—
89#41×C127—22no—
90#41×C127—41no—
91#41×C127—41no—
92#41×C127—41no—
93#41×C127—41no—
94#41×C127—41no—
95#41×C127—41no—
96#41×C127—44no—
97C2×Q8×C127C22⋊C411yescharacteristic
98C2×Q8×C127#4111yescharacteristic
99C2×D4×C127—22no—
100C2×D4×C127—22no—
101C2×D4×C127—22no—
102C2×D4×C127—22no—
103C2×D4×C127—21no—
104C2×D4×C127—21no—
105C2×D4×C127—21no—
106C2×D4×C127—21no—
107C2×D4×C127—21no—
108C2×D4×C127—21no—
109C2×D4×C127—21no—
110C2×D4×C127—21no—
111C2×D4×C127—41no—
112C2×D4×C127—41no—
113C2×D4×C127—41no—
114C2×D4×C127—41no—
115C2×D4×C127—44no—
116C2×D4×C127—44no—
117C2×D4×C127—44no—
118C2×D4×C127—41no—
119C2×D4×C127—41no—
120C2×D4×C127C22⋊C411yescharacteristic
121C2×D4×C127C22⋊C411yescharacteristic
122C2×D4×C127C22⋊C411yescharacteristic
123C2×D4×C127C2×D411yescharacteristic
124C2×D4×C127C2×D411yescharacteristic
125C2×D4×C127#4111yescharacteristic
126C22×C4×C127—21no—
127C22×C4×C127—21no—
128C22×C4×C127—21no—
129C22×C4×C127—44no—
130C22×C4×C127C22×C411yescharacteristic
131C22×C4×C127C2×D411yescharacteristic
132C22×C4×C127C2×D411yescharacteristic
133SD16×C127—42no—
134D8×C127—42no—
135D8×C127—42no—
136D8×C127—42no—
137M16×C127—41no—
138M16×C127—41no—
139M16×C127—41no—
140C2×C8×C127—21no—
141C2×C8×C127—21no—
142C2×C8×C127—41no—
143C2×C8×C127—41no—
144C4⋊C4×C127—21no—
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—44no—
152C22⋊C4×C127—41no—
153C22⋊C4×C127—41no—
154C22⋊C4×C127—41no—
155C42×C127—21no—
156C42×C127—41no—
157C42×C127—41no—
158C42×C127—41no—
159C23×C127—24no—
160C23×C127—21no—
161C23×C127—21no—
162C23×C127—21no—
163C23×C127—42no—
164C23×C127—42no—
165C23×C127—41no—
166C23×C127—81no—
167C23×C127—161no—
168C23×C127—161no—
169C23×C127—161no—
170C23×C127—161no—
171C23×C127C4×D411yescharacteristic
172C23×C127#12011yescharacteristic
173C23×C127#12111yescharacteristic
174Q8×C127—21no—
175Q8×C127—21no—
176Q8×C127—41no—
177D4×C127—24no—
178D4×C127—21no—
179D4×C127—21no—
180D4×C127—21no—
181D4×C127—21no—
182D4×C127—41no—
183D4×C127—41no—
184D4×C127—41no—
185D4×C127—42no—
186D4×C127—42no—
187D4×C127—42no—
188D4×C127—42no—
189D4×C127—42no—
190D4×C127—41no—
191D4×C127—41no—
192D4×C127—81no—
193D4×C127—161no—
194D4×C127—161no—
195D4×C127#9912yes—
196D4×C127#9912yes—
197C2×C4×C127—21no—
198C2×C4×C127—21no—
199C2×C4×C127—21no—
200C2×C4×C127—21no—
201C2×C4×C127—21no—
202C2×C4×C127—21no—
203C2×C4×C127—21no—
204C2×C4×C127—42no—
205C2×C4×C127—42no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—42no—
209C2×C4×C127—41no—
210C2×C4×C127—81no—
211C2×C4×C127—164no—
212C2×C4×C127C2×C22⋊C411yescharacteristic
213C2×C4×C127C4×D411yescharacteristic
214C2×C4×C127#12111yescharacteristic
215C2×C4×C127#12311yescharacteristic
216C8×C127—41no—
217C8×C127—41no—
218C8×C127—81no—
219C22×C127—21no—
220C22×C127—21no—
221C22×C127—21no—
222C22×C127—22no—
223C22×C127—22no—
224C22×C127—41no—
225C22×C127—41no—
226C22×C127—41no—
227C22×C127—41no—
228C22×C127—81no—
229C22×C127—81no—
230C22×C127—81no—
231C22×C127—81no—
232C22×C127—81no—
233C22×C127—84no—
234C22×C127—81no—
235C22×C127—162no—
236C22×C127—162no—
237C22×C127—162no—
238C22×C127#38611yescharacteristic
239C4×C127—21no—
240C4×C127—21no—
241C4×C127—21no—
242C4×C127—41no—
243C4×C127—81no—
244C4×C127—82no—
245C4×C127—82no—
246C4×C127—161no—
247C4×C127C2×#9911yescharacteristic
248C4×C127C2×#9911yescharacteristic
249#13102C12711yesmaximal, characteristic, direct product factor, Sylow
250C2×C127—21no—
251C2×C127—41no—
252C2×C127—41no—
253C2×C127—41no—
254C2×C127—42no—
255C2×C127—42no—
256C2×C127—81no—
257C2×C127—161no—
258C2×C127#189811yescharacteristic
259#3008C2×C12711yescharacteristic
260#2883C2×C12711yescharacteristic, complemented
261#2128C2×C12711yescharacteristic, complemented
262#2122C2×C12711yescharacteristic, complemented
263#1795C2×C12711yescharacteristic, complemented
264#1395C2×C12711yescharacteristic, complemented
265#1391C2×C12711yescharacteristic, complemented
266C127#1310211yescharacteristic, direct product factor, Sylow
267C2×H(5,𝔽2)C22×C12711yescharacteristic
268C2×AGL(1,ℤ/8)C4×C12711yescharacteristic, complemented
269C22×D8C4×C12711yescharacteristic, complemented
270#535C22×C12711yescharacteristic
271#518—21no—
272#449—21no—
273#449—21no—
274#447—21no—
275#447—21no—
276#421—21no—
277#418—21no—
278#418C4×C12711yescharacteristic, complemented
279#416C4×C12711yescharacteristic, complemented
280#413C22×C12711yescharacteristic
281#410—21no—
282#410C22×C12711yescharacteristic
283#410C22×C12711yescharacteristic
284#410C22×C12711yescharacteristic
285C2×#99—22no—
286C2×#99—22no—
287#408C22×C12711yescharacteristic
288#353—22no—
289AΣL(1,𝔽16)—22no—
290H(5,𝔽2)—42no—
291H(5,𝔽2)—42no—
292C2×#41—21no—
293C2×#41C2×C4×C12711yescharacteristic
294C2×#41D4×C12711yescharacteristic
295C2×#41D4×C12711yescharacteristic
296C2×#41C23×C12711yescharacteristic
297C22×D4—21no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4C2×C4×C12711yescharacteristic
301C22×D4C2×C4×C12711yescharacteristic, complemented
302C22×D4D4×C12711yescharacteristic
303C22×D4D4×C12711yescharacteristic
304AGL(1,ℤ/8)—42no—
305C2×SD16—21no—
306C2×D8—21no—
307C2×D8—21no—
308C2×D8—21no—
309C2×D8—42no—
310C2×M16—21no—
311C2×M16C2×C4×C12711yescharacteristic, complemented
312C22×C8C2×C4×C12711yescharacteristic, complemented
313#127—21no—
314#124—21no—
315#121—21no—
316#121—21no—
317#120—21no—
318#120—21no—
319C4×D4—42no—
320C4×D4—42no—
321#117—21no—
322#117—21no—
323#117—21no—
324#117C2×C4×C12711yescharacteristic, complemented
325C2×C22⋊C4—24no—
326#104—42no—
327#103—21no—
328#102—21no—
329#102—21no—
330#102—21no—
331#102—42no—
332#101—21no—
333#100—21no—
334#99—24no—
335#99—21no—
336#99—21no—
337#99—21no—
338#99—21no—
339#99D4×C12712yes—
340#99D4×C12712yes—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C24—21no—
344C24—21no—
345C24—21no—
346C24—21no—
347#41—22no—
348#41—22no—
349#41—41no—
350#41—41no—
351#41—41no—
352#41—41no—
353#41—41no—
354#41—41no—
355#41—44no—
356C2×Q8C22⋊C4×C12711yescharacteristic
357C2×Q8#41×C12711yescharacteristic
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—44no—
375C2×D4—44no—
376C2×D4—44no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4C22⋊C4×C12711yescharacteristic
380C2×D4C22⋊C4×C12711yescharacteristic
381C2×D4C22⋊C4×C12711yescharacteristic
382C2×D4C2×D4×C12711yescharacteristic
383C2×D4C2×D4×C12711yescharacteristic
384C2×D4#41×C12711yescharacteristic
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—44no—
389C22×C4C22×C4×C12711yescharacteristic
390C22×C4C2×D4×C12711yescharacteristic
391C22×C4C2×D4×C12711yescharacteristic
392SD16—42no—
393D8—42no—
394D8—42no—
395D8—42no—
396M16—41no—
397M16—41no—
398M16—41no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—41no—
402C2×C8—41no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C22⋊C4—21no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—44no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C42—21no—
415C42—41no—
416C42—41no—
417C42—41no—
418C23—24no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—42no—
423C23—42no—
424C23—41no—
425C23—81no—
426C23—161no—
427C23—161no—
428C23—161no—
429C23—161no—
430C23C4×D4×C12711yescharacteristic
431C23#120×C12711yescharacteristic
432C23#121×C12711yescharacteristic
433Q8—21no—
434Q8—21no—
435Q8—41no—
436D4—24no—
437D4—21no—
438D4—21no—
439D4—21no—
440D4—21no—
441D4—41no—
442D4—41no—
443D4—41no—
444D4—42no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—41no—
450D4—41no—
451D4—81no—
452D4—161no—
453D4—161no—
454D4#99×C12712yes—
455D4#99×C12712yes—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—81no—
470C2×C4—164no—
471C2×C4C2×C22⋊C4×C12711yescharacteristic
472C2×C4C4×D4×C12711yescharacteristic
473C2×C4#121×C12711yescharacteristic
474C2×C4#123×C12711yescharacteristic
475C8—41no—
476C8—41no—
477C8—81no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—22no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—84no—
493C22—81no—
494C22—162no—
495C22—162no—
496C22—162no—
497C22#386×C12711yescharacteristic
498C4—21no—
499C4—21no—
500C4—21no—
501C4—41no—
502C4—81no—
503C4—82no—
504C4—82no—
505C4—161no—
506C4C2×#99×C12711yescharacteristic
507C4C2×#99×C12711yescharacteristic
508C2—21no—
509C2—41no—
510C2—41no—
511C2—41no—
512C2—42no—
513C2—42no—
514C2—81no—
515C2—161no—
516C2C127×#189811yescharacteristic
subgroupG/H
center, socleC2×C127#1898
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×#41C23×C127
prime radicalC127×#3008C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C2×H(5,𝔽2)×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2883C2semidirect
3. C127×#2128C2semidirect
4. C127×#2122C2semidirect
5. C127×#1795C2semidirect
6. C127×#1395C2semidirect
7. C127×#1391C2semidirect
9. C2×AGL(1,ℤ/8)×C127C4semidirect
10. C22×D8×C127C4semidirect
19. #418×C127C4semidirect
20. #416×C127C4semidirect
42. C22×D4×C127C2×C4semidirect
52. C2×M16×C127C2×C4semidirect
53. C22×C8×C127C2×C4semidirect
65. #117×C127C2×C4semidirect
249. #13102C127direct (N × H)
260. #2883C2×C127semidirect
261. #2128C2×C127semidirect
262. #2122C2×C127semidirect
263. #1795C2×C127semidirect
264. #1395C2×C127semidirect
265. #1391C2×C127semidirect
266. C127#13102direct (N × H)
268. C2×AGL(1,ℤ/8)C4×C127semidirect
269. C22×D8C4×C127semidirect
278. #418C4×C127semidirect
279. #416C4×C127semidirect
301. C22×D4C2×C4×C127semidirect
311. C2×M16C2×C4×C127semidirect
312. C22×C8C2×C4×C127semidirect
324. #117C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#30082
C127×#28832
C127×#21282
C127×#21222
C127×#17952
C127×#13952
C127×#13912
#13102127