Finite Group Databasebeta

← C127×#13096 #44576769

Subgroups — C127×#13096 #44576769

Order 32512.

624 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3011C211yesmaximal, characteristic
2C127×#2889C211yesmaximal, characteristic
3C127×#2135C211yesmaximal, characteristic, complemented
4C127×#2123C211yesmaximal, characteristic, complemented
5C127×#1796C211yesmaximal, characteristic
6C127×#1395C211yesmaximal, characteristic, complemented
7C127×#1392C211yesmaximal, characteristic, complemented
8C2×2−1+4×C127C2211yescharacteristic
9C2×#137×C127C411yescharacteristic, complemented
10C22×Q16×C127C411yescharacteristic, complemented
11#568×C127—21no—
12#536×C127C2211yescharacteristic
13#452×C127—21no—
14#452×C127—21no—
15#451×C127—21no—
16#451×C127—21no—
17#421×C127—21no—
18#419×C127—21no—
19#419×C127C411yescharacteristic, complemented
20#416×C127C411yescharacteristic, complemented
21#413×C127—22no—
22#413×C127C2211yescharacteristic
23#413×C127C2211yescharacteristic
24#413×C127C2211yescharacteristic
25C2×#101×C127—21no—
26C2×#101×C127—22no—
27#410×C127C2211yescharacteristic
28#408×C127C2211yescharacteristic
29#356×C127—22no—
30#352×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×C127C2×C411yescharacteristic
43C22×Q8×C127D411yescharacteristic
44C22×Q8×C127D411yescharacteristic
45#137×C127—42no—
46C2×Q16×C127—21no—
47C2×Q16×C127—21no—
48C2×Q16×C127—21no—
49C2×Q16×C127—42no—
50C2×SD16×C127—21no—
51#131×C127—42no—
52#131×C127—42no—
53C2×M16×C127—24no—
54C2×M16×C127—21no—
55C2×M16×C127—21no—
56C2×M16×C127—21no—
57C2×M16×C127C2×C411yescharacteristic
58C22×C8×C127C2×C411yescharacteristic
59C4⋊Q8×C127—21no—
60#124×C127—21no—
61#123×C127—21no—
62#123×C127—21no—
63C22⋊Q8×C127—21no—
64C22⋊Q8×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—24no—
74#101×C127—21no—
75#101×C127—21no—
76#101×C127D412yes—
77#100×C127—21no—
78#100×C127—21no—
79#100×C127D412yes—
80#99×C127—21no—
81#99×C127—21no—
82C22⋊C8×C127—21no—
83C22⋊C8×C127—21no—
84#41×C127—22no—
85#41×C127—22no—
86#41×C127—22no—
87#41×C127—22no—
88#41×C127—41no—
89#41×C127—41no—
90#41×C127—41no—
91#41×C127—41no—
92#41×C127—44no—
93#41×C127—44no—
94#41×C127—44no—
95C2×Q8×C127—21no—
96C2×Q8×C127—21no—
97C2×Q8×C127—21no—
98C2×Q8×C127—22no—
99C2×Q8×C127—22no—
100C2×Q8×C127—21no—
101C2×Q8×C127—21no—
102C2×Q8×C127—41no—
103C2×Q8×C127—41no—
104C2×Q8×C127—41no—
105C2×Q8×C127—41no—
106C2×Q8×C127—44no—
107C2×Q8×C127—41no—
108C2×Q8×C127—41no—
109C2×Q8×C127C22⋊C411yescharacteristic
110C2×Q8×C127C22⋊C411yescharacteristic
111C2×Q8×C127C22⋊C411yescharacteristic
112C2×Q8×C127C2×D411yescharacteristic
113C2×D4×C127—21no—
114C2×D4×C127—21no—
115C2×D4×C127—21no—
116C2×D4×C127C22⋊C411yescharacteristic
117C2×D4×C127C2×D411yescharacteristic
118C2×D4×C127#4111yescharacteristic
119C2×D4×C127#4111yescharacteristic
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—21no—
123C22×C4×C127—21no—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
127C22×C4×C127C22×C411yescharacteristic
128C22×C4×C127C2×D411yescharacteristic
129C22×C4×C127C2×D411yescharacteristic
130Q16×C127—42no—
131Q16×C127—42no—
132Q16×C127—42no—
133SD16×C127—42no—
134M16×C127—22no—
135M16×C127—22no—
136M16×C127—44no—
137M16×C127—41no—
138M16×C127—41no—
139M16×C127—41no—
140M16×C127—41no—
141M16×C127—41no—
142C2×C8×C127—21no—
143C2×C8×C127—21no—
144C2×C8×C127—44no—
145C2×C8×C127—41no—
146C2×C8×C127—41no—
147C2×C8×C127—41no—
148C2×C8×C127—41no—
149C4⋊C4×C127—21no—
150C4⋊C4×C127—41no—
151C4⋊C4×C127—41no—
152C4⋊C4×C127—41no—
153C22⋊C4×C127—21no—
154C22⋊C4×C127—41no—
155C22⋊C4×C127—41no—
156C22⋊C4×C127—41no—
157C42×C127—21no—
158C42×C127—41no—
159C23×C127—21no—
160C23×C127C4×D411yescharacteristic
161C23×C127#12111yescharacteristic
162C23×C127#12311yescharacteristic
163Q8×C127—21no—
164Q8×C127—21no—
165Q8×C127—21no—
166Q8×C127—21no—
167Q8×C127—21no—
168Q8×C127—41no—
169Q8×C127—42no—
170Q8×C127—42no—
171Q8×C127—42no—
172Q8×C127—41no—
173Q8×C127—41no—
174Q8×C127—81no—
175Q8×C127#9912yes—
176D4×C127—24no—
177D4×C127—21no—
178D4×C127—41no—
179D4×C127—41no—
180D4×C127—41no—
181D4×C127—42no—
182D4×C127—42no—
183D4×C127#9912yes—
184C2×C4×C127—24no—
185C2×C4×C127—21no—
186C2×C4×C127—21no—
187C2×C4×C127—21no—
188C2×C4×C127—21no—
189C2×C4×C127—21no—
190C2×C4×C127—21no—
191C2×C4×C127—21no—
192C2×C4×C127—21no—
193C2×C4×C127—21no—
194C2×C4×C127—42no—
195C2×C4×C127—42no—
196C2×C4×C127—42no—
197C2×C4×C127—42no—
198C2×C4×C127—42no—
199C2×C4×C127—41no—
200C2×C4×C127—41no—
201C2×C4×C127—81no—
202C2×C4×C127—81no—
203C2×C4×C127C2×C22⋊C411yescharacteristic
204C2×C4×C127C4×D411yescharacteristic
205C2×C4×C127#12011yescharacteristic
206C2×C4×C127#12111yescharacteristic
207C8×C127—42no—
208C8×C127—42no—
209C8×C127—41no—
210C8×C127—41no—
211C8×C127—81no—
212C22×C127—21no—
213C22×C127—21no—
214C22×C127—21no—
215C22×C127—22no—
216C22×C127—41no—
217C22×C127—41no—
218C22×C127—41no—
219C22×C127—81no—
220C22×C127#38611yescharacteristic
221C4×C127—21no—
222C4×C127—21no—
223C4×C127—22no—
224C4×C127—21no—
225C4×C127—41no—
226C4×C127—41no—
227C4×C127—81no—
228C4×C127—81no—
229C4×C127—161no—
230C4×C127C2×#9911yescharacteristic
231C4×C127C2×#9911yescharacteristic
232#13096C12711yesmaximal, characteristic, direct product factor, Sylow
233C2×C127—21no—
234C2×C127—41no—
235C2×C127—41no—
236C2×C127—41no—
237C2×C127—42no—
238C2×C127#189811yescharacteristic
239#3011C2×C12711yescharacteristic
240#2889C2×C12711yescharacteristic
241#2135C2×C12711yescharacteristic, complemented
242#2123C2×C12711yescharacteristic, complemented
243#1796C2×C12711yescharacteristic
244#1395C2×C12711yescharacteristic, complemented
245#1392C2×C12711yescharacteristic, complemented
246C127#1309611yescharacteristic, direct product factor, Sylow
247C2×2−1+4C22×C12711yescharacteristic
248C2×#137C4×C12711yescharacteristic, complemented
249C22×Q16C4×C12711yescharacteristic, complemented
250#568—21no—
251#536C22×C12711yescharacteristic
252#452—21no—
253#452—21no—
254#451—21no—
255#451—21no—
256#421—21no—
257#419—21no—
258#419C4×C12711yescharacteristic, complemented
259#416C4×C12711yescharacteristic, complemented
260#413—22no—
261#413C22×C12711yescharacteristic
262#413C22×C12711yescharacteristic
263#413C22×C12711yescharacteristic
264C2×#101—21no—
265C2×#101—22no—
266#410C22×C12711yescharacteristic
267#408C22×C12711yescharacteristic
268#356—22no—
269#352—22no—
2702−1+4—42no—
2712−1+4—42no—
272C2×#41—21no—
273C2×#41—21no—
274C2×#41—21no—
275C2×#41C2×C4×C12711yescharacteristic
276C2×#41D4×C12711yescharacteristic
277C2×#41D4×C12711yescharacteristic
278C2×#41C23×C12711yescharacteristic
279C22×Q8—21no—
280C22×Q8C2×C4×C12711yescharacteristic
281C22×Q8C2×C4×C12711yescharacteristic
282C22×Q8D4×C12711yescharacteristic
283C22×Q8D4×C12711yescharacteristic
284#137—42no—
285C2×Q16—21no—
286C2×Q16—21no—
287C2×Q16—21no—
288C2×Q16—42no—
289C2×SD16—21no—
290#131—42no—
291#131—42no—
292C2×M16—24no—
293C2×M16—21no—
294C2×M16—21no—
295C2×M16—21no—
296C2×M16C2×C4×C12711yescharacteristic
297C22×C8C2×C4×C12711yescharacteristic
298C4⋊Q8—21no—
299#124—21no—
300#123—21no—
301#123—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304#117—21no—
305#117C2×C4×C12711yescharacteristic
306#104—42no—
307#103—21no—
308#103—21no—
309#103—21no—
310#103—42no—
311#102—21no—
312#101—24no—
313#101—21no—
314#101—21no—
315#101D4×C12712yes—
316#100—21no—
317#100—21no—
318#100D4×C12712yes—
319#99—21no—
320#99—21no—
321C22⋊C8—21no—
322C22⋊C8—21no—
323#41—22no—
324#41—22no—
325#41—22no—
326#41—22no—
327#41—41no—
328#41—41no—
329#41—41no—
330#41—41no—
331#41—44no—
332#41—44no—
333#41—44no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—41no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—41no—
345C2×Q8—44no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8C22⋊C4×C12711yescharacteristic
349C2×Q8C22⋊C4×C12711yescharacteristic
350C2×Q8C22⋊C4×C12711yescharacteristic
351C2×Q8C2×D4×C12711yescharacteristic
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4C22⋊C4×C12711yescharacteristic
356C2×D4C2×D4×C12711yescharacteristic
357C2×D4#41×C12711yescharacteristic
358C2×D4#41×C12711yescharacteristic
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4C22×C4×C12711yescharacteristic
367C22×C4C2×D4×C12711yescharacteristic
368C22×C4C2×D4×C12711yescharacteristic
369Q16—42no—
370Q16—42no—
371Q16—42no—
372SD16—42no—
373M16—22no—
374M16—22no—
375M16—44no—
376M16—41no—
377M16—41no—
378M16—41no—
379M16—41no—
380M16—41no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—44no—
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—41no—
387C2×C8—41no—
388C4⋊C4—21no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C22⋊C4—21no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C42—21no—
397C42—41no—
398C23—21no—
399C23C4×D4×C12711yescharacteristic
400C23#121×C12711yescharacteristic
401C23#123×C12711yescharacteristic
402Q8—21no—
403Q8—21no—
404Q8—21no—
405Q8—21no—
406Q8—21no—
407Q8—41no—
408Q8—42no—
409Q8—42no—
410Q8—42no—
411Q8—41no—
412Q8—41no—
413Q8—81no—
414Q8#99×C12712yes—
415D4—24no—
416D4—21no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—42no—
421D4—42no—
422D4#99×C12712yes—
423C2×C4—24no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4C2×C22⋊C4×C12711yescharacteristic
443C2×C4C4×D4×C12711yescharacteristic
444C2×C4#120×C12711yescharacteristic
445C2×C4#121×C12711yescharacteristic
446C8—42no—
447C8—42no—
448C8—41no—
449C8—41no—
450C8—81no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—22no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—81no—
459C22#386×C12711yescharacteristic
460C4—21no—
461C4—21no—
462C4—22no—
463C4—21no—
464C4—41no—
465C4—41no—
466C4—81no—
467C4—81no—
468C4—161no—
469C4C2×#99×C12711yescharacteristic
470C4C2×#99×C12711yescharacteristic
471C2—21no—
472C2—41no—
473C2—41no—
474C2—41no—
475C2—42no—
476C2C127×#189811yescharacteristic
subgroupG/H
center, socleC2×C127#1898
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×#41C23×C127
prime radicalC2×2−1+4×C127C22
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
3. C127×#2135C2semidirect
4. C127×#2123C2semidirect
6. C127×#1395C2semidirect
7. C127×#1392C2semidirect
9. C2×#137×C127C4semidirect
10. C22×Q16×C127C4semidirect
19. #419×C127C4semidirect
20. #416×C127C4semidirect
232. #13096C127direct (N × H)
241. #2135C2×C127semidirect
242. #2123C2×C127semidirect
244. #1395C2×C127semidirect
245. #1392C2×C127semidirect
246. C127#13096direct (N × H)
248. C2×#137C4×C127semidirect
249. C22×Q16C4×C127semidirect
258. #419C4×C127semidirect
259. #416C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#30112
C127×#28892
C127×#21352
C127×#21232
C127×#17962
C127×#13952
C127×#13922
#13096127