Finite Group Databasebeta

← C127×#19445 #44583118

Subgroups — C127×#19445 #44583118

Order 32512.

682 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3208C211yesmaximal, characteristic, complemented
2C127×#3076C211yesmaximal, characteristic, complemented
3C127×#3038C211yesmaximal, characteristic
4C127×#2989C211yesmaximal, characteristic, complemented
5C127×#1698C212yesmaximal, complemented
6C127×#1697C212yesmaximal, complemented
7C127×#1686C212yesmaximal, complemented
8C127×#1685C212yesmaximal, complemented
9C127×#1571C211yesmaximal, characteristic, complemented
10C127×#1550C211yesmaximal, characteristic, complemented
11C2×#331×C127C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C127—21no—
13#533×C127C2211yescharacteristic
14C2×#127×C127C2211yescharacteristic
15C4×#41×C127C2211yescharacteristic
16#492×C127C2212yes—
17#486×C127C2212yes—
18#479×C127—21no—
19#478×C127—21no—
20#477×C127C2211yescharacteristic, complemented
21#476×C127C2211yescharacteristic, complemented
22#475×C127C2211yescharacteristic, complemented
23#474×C127C2211yescharacteristic, complemented
24#460×C127—21no—
25#460×C127—21no—
26#460×C127—21no—
27#460×C127C2212yes—
28#459×C127—21no—
29#459×C127C2212yes—
30#450×C127—22no—
31#446×C127C2212yescomplemented
32#436×C127C2212yescomplemented
33#435×C127—22no—
34#432×C127—21no—
35#431×C127C2211yescharacteristic
36#427×C127—21no—
37#423×C127—21no—
38#423×C127C2211yescharacteristic
39C2×C4⋊C8×C127C2211yescharacteristic
40C2×C4⋊C8×C127C2211yescharacteristic
41#418×C127—21no—
42#416×C127—21no—
43#335×C127C2212yescomplemented
44#335×C127C2212yescomplemented
45#333×C127C2212yescomplemented
46#332×C127C2212yescomplemented
47#331×C127C2212yes—
48#331×C127C2212yes—
49C2×#41×C127D411yescharacteristic
50C22×D4×C127—21no—
51C22×D4×C127—21no—
52C22×D4×C127—21no—
53AGL(1,ℤ/8)×C127—44no—
54C2×SD16×C127—22no—
55C2×SD16×C127—22no—
56C2×SD16×C127—22no—
57C2×D8×C127—22no—
58C2×M16×C127—21no—
59C2×M16×C127—22no—
60C22×C8×C127—21no—
61C22×C8×C127—21no—
62C4⋊Q8×C127C2311yescharacteristic
63C4⋊Q8×C127C2311yescharacteristic
64#127×C127—21no—
65#127×C127—21no—
66#127×C127—21no—
67#127×C127C2312yes—
68#125×C127—21no—
69C22⋊Q8×C127—21no—
70C22⋊Q8×C127—21no—
71C4×Q8×C127—21no—
72C4×Q8×C127—21no—
73C4×Q8×C127D411yescharacteristic
74C4×Q8×C127C2311yescharacteristic
75C4×D4×C127—21no—
76C4×D4×C127—21no—
77C4×D4×C127D411yescharacteristic
78C4×D4×C127C2311yescharacteristic
79#117×C127—21no—
80#117×C127—21no—
81#117×C127D411yescharacteristic
82C2×C42×C127—21no—
83C2×C42×C127C2311yescharacteristic
84#107×C127—21no—
85#107×C127—21no—
86#106×C127—21no—
87#106×C127—21no—
88C4⋊C8×C127—22no—
89C4⋊C8×C127—21no—
90C4⋊C8×C127—21no—
91C4⋊C8×C127—21no—
92C4⋊C8×C127D411yescharacteristic
93C4⋊C8×C127D411yescharacteristic
94C4⋊C8×C127C2312yes—
95C4⋊C8×C127C2311yescharacteristic
96C4⋊C8×C127C2311yescharacteristic
97C4⋊C8×C127C2312yes—
98#103×C127—21no—
99#103×C127—21no—
100#102×C127—21no—
101#102×C127—21no—
102#102×C127—22no—
103#102×C127—22no—
104#102×C127—22no—
105#102×C127—22no—
106C22⋊C8×C127—22no—
107C22⋊C8×C127D412yes—
108#97×C127—22no—
109C4×C8×C127C2312yes—
110C24×C127—41no—
111#41×C127—22no—
112#41×C127—22no—
113C2×Q8×C127—21no—
114C2×Q8×C127—21no—
115C2×Q8×C127C2×D411yescharacteristic
116C2×D4×C127—21no—
117C2×D4×C127—22no—
118C2×D4×C127—22no—
119C2×D4×C127—22no—
120C2×D4×C127—41no—
121C2×D4×C127—41no—
122C2×D4×C127—41no—
123C2×D4×C127—42no—
124C2×D4×C127—42no—
125C2×D4×C127—81no—
126C2×D4×C127—81no—
127C2×D4×C127—82no—
128C2×D4×C127C2×D411yescharacteristic
129C22×C4×C127—21no—
130C22×C4×C127—21no—
131C22×C4×C127—21no—
132C22×C4×C127C2×D411yescharacteristic
133C22×C4×C127C2×D411yescharacteristic
134C22×C4×C127#4111yescharacteristic
135SD16×C127—44no—
136SD16×C127—82no—
137SD16×C127—82no—
138D8×C127—44no—
139M16×C127—42no—
140M16×C127—82no—
141C2×C8×C127—22no—
142C2×C8×C127—22no—
143C2×C8×C127—21no—
144C2×C8×C127—21no—
145C2×C8×C127—42no—
146C2×C8×C127—81no—
147C2×C8×C127C2×D412yes—
148C2×C8×C127C2×D412yes—
149C4⋊C4×C127—21no—
150C4⋊C4×C127—21no—
151C4⋊C4×C127—21no—
152C4⋊C4×C127—21no—
153C4⋊C4×C127—21no—
154C4⋊C4×C127—21no—
155C4⋊C4×C127—41no—
156C4⋊C4×C127—41no—
157C4⋊C4×C127C2×D411yescharacteristic
158C4⋊C4×C127C2×D411yescharacteristic
159C22⋊C4×C127—21no—
160C22⋊C4×C127—21no—
161C22⋊C4×C127—21no—
162C22⋊C4×C127—41no—
163C42×C127—21no—
164C42×C127—21no—
165C42×C127—21no—
166C42×C127—41no—
167C42×C127C2×D411yescharacteristic
168C42×C127C2×D411yescharacteristic
169C42×C127#4111yescharacteristic
170C42×C127C2411yescharacteristic
171C23×C127—21no—
172C23×C127—42no—
173C23×C127—82no—
174C23×C127—82no—
175C23×C127—82no—
176C23×C127#12111yescharacteristic
177Q8×C127—21no—
178Q8×C127—21no—
179Q8×C127—41no—
180Q8×C127—41no—
181Q8×C127—81no—
182D4×C127—21no—
183D4×C127—21no—
184D4×C127—42no—
185D4×C127—42no—
186D4×C127—42no—
187D4×C127—42no—
188D4×C127—42no—
189D4×C127—82no—
190D4×C127—82no—
191D4×C127—82no—
192D4×C127—82no—
193C2×C4×C127—21no—
194C2×C4×C127—21no—
195C2×C4×C127—21no—
196C2×C4×C127—21no—
197C2×C4×C127—21no—
198C2×C4×C127—41no—
199C2×C4×C127—41no—
200C2×C4×C127—41no—
201C2×C4×C127—42no—
202C2×C4×C127—41no—
203C2×C4×C127—41no—
204C2×C4×C127—81no—
205C2×C4×C127#12111yescharacteristic
206C2×C4×C127#12111yescharacteristic
207C2×C4×C127#12111yescharacteristic
208C2×C4×C127AGL(1,ℤ/8)12yes—
209C2×C4×C127#13712yes—
210C2×C4×C127C22×D411yescharacteristic
211C2×C4×C127C22×D411yescharacteristic
212C2×C4×C127C2×#4111yescharacteristic
213C8×C127—22no—
214C8×C127—22no—
215C8×C127—41no—
216C8×C127—41no—
217C8×C127—42no—
218C8×C127—42no—
219C22×C127—21no—
220C22×C127—21no—
221C22×C127—41no—
222C22×C127—41no—
223C22×C127—41no—
224C22×C127—82no—
225C22×C127—82no—
226C22×C127—82no—
227C22×C127—164no—
228C22×C127#46812yes—
229C22×C127C2×#12111yescharacteristic
230C4×C127—21no—
231C4×C127—21no—
232C4×C127—21no—
233C4×C127—41no—
234C4×C127—41no—
235C4×C127—41no—
236C4×C127—81no—
237C4×C127—81no—
238C4×C127#46812yes—
239C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
240C4×C127C2×#13711yescharacteristic
241C4×C127#57611yescharacteristic
242C4×C127#57711yescharacteristic
243#19445C12711yesmaximal, characteristic, direct product factor, Sylow
244C2×C127—22no—
245C2×C127—81no—
246C2×C127—162no—
247C2×C127#304511yescharacteristic
248C2×C127C2×#46811yescharacteristic
249C2×C127#306811yescharacteristic
250#3208C2×C12711yescharacteristic, complemented
251#3076C2×C12711yescharacteristic, complemented
252#3038C2×C12711yescharacteristic
253#2989C2×C12711yescharacteristic, complemented
254#1698C2×C12712yescomplemented
255#1697C2×C12712yescomplemented
256#1686C2×C12712yescomplemented
257#1685C2×C12712yescomplemented
258#1571C2×C12711yescharacteristic, complemented
259#1550C2×C12711yescharacteristic, complemented
260C2×#331C2×C12711yescharacteristic, complemented
261C127#1944511yescharacteristic, direct product factor, Sylow
262C2×AGL(1,ℤ/8)—21no—
263#533C22×C12711yescharacteristic
264C2×#127C22×C12711yescharacteristic
265C4×#41C22×C12711yescharacteristic
266#492C22×C12712yes—
267#486C22×C12712yes—
268#479—21no—
269#478—21no—
270#477C22×C12711yescharacteristic, complemented
271#476C22×C12711yescharacteristic, complemented
272#475C22×C12711yescharacteristic, complemented
273#474C22×C12711yescharacteristic, complemented
274#460—21no—
275#460—21no—
276#460—21no—
277#460C22×C12712yes—
278#459—21no—
279#459C22×C12712yes—
280#450—22no—
281#446C22×C12712yescomplemented
282#436C22×C12712yescomplemented
283#435—22no—
284#432—21no—
285#431C22×C12711yescharacteristic
286#427—21no—
287#423—21no—
288#423C22×C12711yescharacteristic
289C2×C4⋊C8C22×C12711yescharacteristic
290C2×C4⋊C8C22×C12711yescharacteristic
291#418—21no—
292#416—21no—
293#335C22×C12712yescomplemented
294#335C22×C12712yescomplemented
295#333C22×C12712yescomplemented
296#332C22×C12712yescomplemented
297#331C22×C12712yes—
298#331C22×C12712yes—
299C2×#41D4×C12711yescharacteristic
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—21no—
303AGL(1,ℤ/8)—44no—
304C2×SD16—22no—
305C2×SD16—22no—
306C2×SD16—22no—
307C2×D8—22no—
308C2×M16—21no—
309C2×M16—22no—
310C22×C8—21no—
311C22×C8—21no—
312C4⋊Q8C23×C12711yescharacteristic
313C4⋊Q8C23×C12711yescharacteristic
314#127—21no—
315#127—21no—
316#127—21no—
317#127C23×C12712yes—
318#125—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8D4×C12711yescharacteristic
324C4×Q8C23×C12711yescharacteristic
325C4×D4—21no—
326C4×D4—21no—
327C4×D4D4×C12711yescharacteristic
328C4×D4C23×C12711yescharacteristic
329#117—21no—
330#117—21no—
331#117D4×C12711yescharacteristic
332C2×C42—21no—
333C2×C42C23×C12711yescharacteristic
334#107—21no—
335#107—21no—
336#106—21no—
337#106—21no—
338C4⋊C8—22no—
339C4⋊C8—21no—
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8D4×C12711yescharacteristic
343C4⋊C8D4×C12711yescharacteristic
344C4⋊C8C23×C12712yes—
345C4⋊C8C23×C12711yescharacteristic
346C4⋊C8C23×C12711yescharacteristic
347C4⋊C8C23×C12712yes—
348#103—21no—
349#103—21no—
350#102—21no—
351#102—21no—
352#102—22no—
353#102—22no—
354#102—22no—
355#102—22no—
356C22⋊C8—22no—
357C22⋊C8D4×C12712yes—
358#97—22no—
359C4×C8C23×C12712yes—
360C24—41no—
361#41—22no—
362#41—22no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8C2×D4×C12711yescharacteristic
366C2×D4—21no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—42no—
374C2×D4—42no—
375C2×D4—81no—
376C2×D4—81no—
377C2×D4—82no—
378C2×D4C2×D4×C12711yescharacteristic
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4C2×D4×C12711yescharacteristic
383C22×C4C2×D4×C12711yescharacteristic
384C22×C4#41×C12711yescharacteristic
385SD16—44no—
386SD16—82no—
387SD16—82no—
388D8—44no—
389M16—42no—
390M16—82no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—42no—
396C2×C8—81no—
397C2×C8C2×D4×C12712yes—
398C2×C8C2×D4×C12712yes—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4C2×D4×C12711yescharacteristic
408C4⋊C4C2×D4×C12711yescharacteristic
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—41no—
413C42—21no—
414C42—21no—
415C42—21no—
416C42—41no—
417C42C2×D4×C12711yescharacteristic
418C42C2×D4×C12711yescharacteristic
419C42#41×C12711yescharacteristic
420C42C24×C12711yescharacteristic
421C23—21no—
422C23—42no—
423C23—82no—
424C23—82no—
425C23—82no—
426C23#121×C12711yescharacteristic
427Q8—21no—
428Q8—21no—
429Q8—41no—
430Q8—41no—
431Q8—81no—
432D4—21no—
433D4—21no—
434D4—42no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—42no—
439D4—82no—
440D4—82no—
441D4—82no—
442D4—82no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—81no—
455C2×C4#121×C12711yescharacteristic
456C2×C4#121×C12711yescharacteristic
457C2×C4#121×C12711yescharacteristic
458C2×C4AGL(1,ℤ/8)×C12712yes—
459C2×C4#137×C12712yes—
460C2×C4C22×D4×C12711yescharacteristic
461C2×C4C22×D4×C12711yescharacteristic
462C2×C4C2×#41×C12711yescharacteristic
463C8—22no—
464C8—22no—
465C8—41no—
466C8—41no—
467C8—42no—
468C8—42no—
469C22—21no—
470C22—21no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—164no—
478C22#468×C12712yes—
479C22C2×#121×C12711yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—81no—
487C4—81no—
488C4#468×C12712yes—
489C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
490C4C2×#137×C12711yescharacteristic
491C4#576×C12711yescharacteristic
492C4#577×C12711yescharacteristic
493C2—22no—
494C2—81no—
495C2—162no—
496C2C127×#304511yescharacteristic
497C2C2×#468×C12711yescharacteristic
498C2C127×#306811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3038C2
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
1. C127×#3208C2semidirect
2. C127×#3076C2semidirect
4. C127×#2989C2semidirect
5. C127×#1698C2semidirect
6. C127×#1697C2semidirect
7. C127×#1686C2semidirect
8. C127×#1685C2semidirect
9. C127×#1571C2semidirect
10. C127×#1550C2semidirect
11. C2×#331×C127C2semidirect
20. #477×C127C22semidirect
21. #476×C127C22semidirect
22. #475×C127C22semidirect
23. #474×C127C22semidirect
31. #446×C127C22semidirect
32. #436×C127C22semidirect
43. #335×C127C22semidirect
44. #335×C127C22semidirect
45. #333×C127C22semidirect
46. #332×C127C22semidirect
243. #19445C127direct (N × H)
250. #3208C2×C127semidirect
251. #3076C2×C127semidirect
253. #2989C2×C127semidirect
254. #1698C2×C127semidirect
255. #1697C2×C127semidirect
256. #1686C2×C127semidirect
257. #1685C2×C127semidirect
258. #1571C2×C127semidirect
259. #1550C2×C127semidirect
260. C2×#331C2×C127semidirect
261. C127#19445direct (N × H)
270. #477C22×C127semidirect
271. #476C22×C127semidirect
272. #475C22×C127semidirect
273. #474C22×C127semidirect
281. #446C22×C127semidirect
282. #436C22×C127semidirect
293. #335C22×C127semidirect
294. #335C22×C127semidirect
295. #333C22×C127semidirect
296. #332C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32082
C127×#30762
C127×#30382
C127×#29892
C127×#16982
C127×#16972
C127×#16862
C127×#16852
C127×#15712
C127×#15502
C2×#331×C1272
#19445127