Finite Group Databasebeta

← C127×#18480 #44582153

Subgroups — C127×#18480 #44582153

Order 32512.

1082 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3481C211yesmaximal, characteristic, complemented
2C127×#3147C211yesmaximal, characteristic, complemented
3C127×#3106C212yesmaximal, complemented
4C127×#1632C212yesmaximal, complemented
5C127×#1630C211yesmaximal, characteristic, complemented
6C127×#1629C211yesmaximal, characteristic, complemented
7C127×#1622C212yesmaximal, complemented
8C127×#1620C211yesmaximal, characteristic, complemented
9C127×#1619C211yesmaximal, characteristic, complemented
10C127×#1543C211yesmaximal, characteristic, complemented
11C127×#1476C212yesmaximal, complemented
12C2×#135×C127—22no—
13#559×C127C2211yescharacteristic
14#554×C127C2212yes—
15#553×C127—22no—
16#551×C127—22no—
17#546×C127—22no—
18D42×C127C2211yescharacteristic
19#532×C127C2211yescharacteristic
20#532×C127C2211yescharacteristic, complemented
21#529×C127—22no—
22#525×C127—22no—
23C4×#41×C127C2212yes—
24C2×C4×D4×C127—22no—
25#495×C127—22no—
26#494×C127C2211yescharacteristic, complemented
27#493×C127C2211yescharacteristic
28#492×C127C2211yescharacteristic
29#492×C127C2211yescharacteristic, complemented
30#482×C127—22no—
31#477×C127C2212yescomplemented
32#476×C127C2212yes—
33#460×C127C2212yescomplemented
34#459×C127C2212yes—
35#449×C127—22no—
36C4×SD16×C127—22no—
37C4×D8×C127—22no—
38#431×C127C2212yescomplemented
39C2×C4×C8×C127C2211yescharacteristic, complemented
40#333×C127C2212yescomplemented
41#331×C127C2211yescharacteristic
42#331×C127C2211yescharacteristic
43Q8⋊C8×C127C2212yescomplemented
44Q8⋊C8×C127C2212yescomplemented
45D4⋊C8×C127C2212yes—
46D4⋊C8×C127C2212yes—
47C2×#41×C127—21no—
48C2×#41×C127D412yes—
49C2×#41×C127D412yes—
50C22×D4×C127—22no—
51C23×C4×C127—22no—
52#135×C127—48no—
53C2×Q16×C127—22no—
54C2×SD16×C127—22no—
55C2×SD16×C127—22no—
56C2×SD16×C127—22no—
57C2×D8×C127—22no—
58C2×D8×C127—22no—
59C22×C8×C127—21no—
60C4⋊Q8×C127C2311yescharacteristic
61C4⋊Q8×C127C2311yescharacteristic
62#127×C127C2311yescharacteristic
63#127×C127C2311yescharacteristic
64#126×C127—24no—
65#125×C127—22no—
66#124×C127—22no—
67#124×C127—21no—
68#124×C127D412yes—
69#123×C127—22no—
70#123×C127—24no—
71#123×C127—22no—
72C22⋊Q8×C127—24no—
73C22⋊Q8×C127—22no—
74#121×C127—24no—
75#121×C127—22no—
76#121×C127—22no—
77#121×C127—22no—
78#120×C127—22no—
79#120×C127—22no—
80C4×Q8×C127D412yes—
81C4×Q8×C127C2312yes—
82C4×D4×C127—24no—
83C4×D4×C127—24no—
84C4×D4×C127—22no—
85C4×D4×C127—22no—
86C4×D4×C127—22no—
87C4×D4×C127—22no—
88C4×D4×C127—22no—
89C4×D4×C127—22no—
90C4×D4×C127D412yes—
91C4×D4×C127C2312yes—
92#117×C127—22no—
93#117×C127—22no—
94#117×C127D412yes—
95C2×C4⋊C4×C127—22no—
96C2×C22⋊C4×C127—24no—
97C2×C42×C127—22no—
98C2×C42×C127C2311yescharacteristic
99#107×C127—22no—
100#106×C127—22no—
101C4⋊C8×C127C2312yes—
102C4⋊C8×C127C2312yes—
103#103×C127—22no—
104#102×C127—22no—
105#102×C127—22no—
106#102×C127—22no—
107C22⋊C8×C127—22no—
108C4×C8×C127—21no—
109C4×C8×C127—22no—
110C4×C8×C127C2311yescharacteristic
111C4×C8×C127C2311yescharacteristic
112C24×C127—22no—
113#41×C127—24no—
114#41×C127—42no—
115#41×C127—44no—
116#41×C127—44no—
117C2×Q8×C127—21no—
118C2×Q8×C127C2×D412yes—
119C2×Q8×C127C2×D412yes—
120C2×D4×C127—24no—
121C2×D4×C127—22no—
122C2×D4×C127—22no—
123C2×D4×C127—22no—
124C2×D4×C127—22no—
125C2×D4×C127—21no—
126C2×D4×C127—44no—
127C2×D4×C127—44no—
128C2×D4×C127—41no—
129C2×D4×C127C2×D412yes—
130C2×D4×C127C2×D412yes—
131C22×C4×C127—24no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127—22no—
136C22×C4×C127—22no—
137C22×C4×C127—41no—
138C22×C4×C127—84no—
139C22×C4×C127C2×D412yes—
140C22×C4×C127C2×D411yescharacteristic
141Q16×C127—44no—
142SD16×C127—44no—
143SD16×C127—44no—
144SD16×C127—44no—
145D8×C127—44no—
146D8×C127—44no—
147C2×C8×C127—24no—
148C2×C8×C127—21no—
149C2×C8×C127—21no—
150C2×C8×C127—22no—
151C2×C8×C127—22no—
152C4⋊C4×C127—24no—
153C4⋊C4×C127—24no—
154C4⋊C4×C127—22no—
155C4⋊C4×C127—22no—
156C4⋊C4×C127—22no—
157C4⋊C4×C127—22no—
158C4⋊C4×C127C2×D412yes—
159C4⋊C4×C127C2×D412yes—
160C22⋊C4×C127—24no—
161C22⋊C4×C127—24no—
162C22⋊C4×C127—22no—
163C22⋊C4×C127—22no—
164C22⋊C4×C127—22no—
165C22⋊C4×C127—22no—
166C22⋊C4×C127—24no—
167C22⋊C4×C127—22no—
168C22⋊C4×C127—42no—
169C42×C127—22no—
170C42×C127—22no—
171C42×C127—22no—
172C42×C127C2×D411yescharacteristic
173C42×C127C2×D412yes—
174C42×C127C2411yescharacteristic
175C23×C127—22no—
176C23×C127—22no—
177C23×C127—48no—
178C23×C127—41no—
179C23×C127—82no—
180C23×C127#12011yescharacteristic
181Q8×C127—22no—
182Q8×C127—22no—
183Q8×C127—42no—
184Q8×C127—42no—
185D4×C127—22no—
186D4×C127—42no—
187D4×C127—42no—
188D4×C127—44no—
189D4×C127—48no—
190D4×C127—42no—
191D4×C127—42no—
192D4×C127—42no—
193D4×C127—42no—
194D4×C127—82no—
195D4×C127—82no—
196D4×C127#13514yescomplemented
197C2×C4×C127—22no—
198C2×C4×C127—22no—
199C2×C4×C127—22no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—22no—
203C2×C4×C127—22no—
204C2×C4×C127—44no—
205C2×C4×C127—42no—
206C2×C4×C127—42no—
207C2×C4×C127—44no—
208C2×C4×C127—44no—
209C2×C4×C127—41no—
210C2×C4×C127—82no—
211C2×C4×C127—84no—
212C2×C4×C127—82no—
213C2×C4×C127#12012yes—
214C2×C4×C127#12011yescharacteristic
215C2×C4×C127C22×D411yescharacteristic
216C2×C4×C127C22×D412yes—
217C8×C127—22no—
218C8×C127—22no—
219C8×C127—42no—
220C8×C127—42no—
221C22×C127—22no—
222C22×C127—24no—
223C22×C127—21no—
224C22×C127—42no—
225C22×C127—42no—
226C22×C127—44no—
227C22×C127—42no—
228C22×C127—88no—
229C22×C127—82no—
230C22×C127—81no—
231C22×C127C2×#12011yescharacteristic
232C4×C127—22no—
233C4×C127—21no—
234C4×C127—42no—
235C4×C127—42no—
236C4×C127—42no—
237C4×C127—42no—
238C4×C127—81no—
239C4×C127#45312yes—
240C4×C127C2×#13512yes—
241C4×C127#57512yes—
242#18480C12711yesmaximal, characteristic, direct product factor, Sylow
243C2×C127—41no—
244C2×C127—44no—
245C2×C127—82no—
246C2×C127—161no—
247C2×C127#300212yes—
248C2×C127C2×#45311yescharacteristic
249#3481C2×C12711yescharacteristic, complemented
250#3147C2×C12711yescharacteristic, complemented
251#3106C2×C12712yescomplemented
252#1632C2×C12712yescomplemented
253#1630C2×C12711yescharacteristic, complemented
254#1629C2×C12711yescharacteristic, complemented
255#1622C2×C12712yescomplemented
256#1620C2×C12711yescharacteristic, complemented
257#1619C2×C12711yescharacteristic, complemented
258#1543C2×C12711yescharacteristic, complemented
259#1476C2×C12712yescomplemented
260C127#1848011yescharacteristic, direct product factor, Sylow
261C2×#135—22no—
262#559C22×C12711yescharacteristic
263#554C22×C12712yes—
264#553—22no—
265#551—22no—
266#546—22no—
267D42C22×C12711yescharacteristic
268#532C22×C12711yescharacteristic
269#532C22×C12711yescharacteristic, complemented
270#529—22no—
271#525—22no—
272C4×#41C22×C12712yes—
273C2×C4×D4—22no—
274#495—22no—
275#494C22×C12711yescharacteristic, complemented
276#493C22×C12711yescharacteristic
277#492C22×C12711yescharacteristic
278#492C22×C12711yescharacteristic, complemented
279#482—22no—
280#477C22×C12712yescomplemented
281#476C22×C12712yes—
282#460C22×C12712yescomplemented
283#459C22×C12712yes—
284#449—22no—
285C4×SD16—22no—
286C4×D8—22no—
287#431C22×C12712yescomplemented
288C2×C4×C8C22×C12711yescharacteristic, complemented
289#333C22×C12712yescomplemented
290#331C22×C12711yescharacteristic
291#331C22×C12711yescharacteristic
292Q8⋊C8C22×C12712yescomplemented
293Q8⋊C8C22×C12712yescomplemented
294D4⋊C8C22×C12712yes—
295D4⋊C8C22×C12712yes—
296C2×#41—21no—
297C2×#41D4×C12712yes—
298C2×#41D4×C12712yes—
299C22×D4—22no—
300C23×C4—22no—
301#135—48no—
302C2×Q16—22no—
303C2×SD16—22no—
304C2×SD16—22no—
305C2×SD16—22no—
306C2×D8—22no—
307C2×D8—22no—
308C22×C8—21no—
309C4⋊Q8C23×C12711yescharacteristic
310C4⋊Q8C23×C12711yescharacteristic
311#127C23×C12711yescharacteristic
312#127C23×C12711yescharacteristic
313#126—24no—
314#125—22no—
315#124—22no—
316#124—21no—
317#124D4×C12712yes—
318#123—22no—
319#123—24no—
320#123—22no—
321C22⋊Q8—24no—
322C22⋊Q8—22no—
323#121—24no—
324#121—22no—
325#121—22no—
326#121—22no—
327#120—22no—
328#120—22no—
329C4×Q8D4×C12712yes—
330C4×Q8C23×C12712yes—
331C4×D4—24no—
332C4×D4—24no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4D4×C12712yes—
340C4×D4C23×C12712yes—
341#117—22no—
342#117—22no—
343#117D4×C12712yes—
344C2×C4⋊C4—22no—
345C2×C22⋊C4—24no—
346C2×C42—22no—
347C2×C42C23×C12711yescharacteristic
348#107—22no—
349#106—22no—
350C4⋊C8C23×C12712yes—
351C4⋊C8C23×C12712yes—
352#103—22no—
353#102—22no—
354#102—22no—
355#102—22no—
356C22⋊C8—22no—
357C4×C8—21no—
358C4×C8—22no—
359C4×C8C23×C12711yescharacteristic
360C4×C8C23×C12711yescharacteristic
361C24—22no—
362#41—24no—
363#41—42no—
364#41—44no—
365#41—44no—
366C2×Q8—21no—
367C2×Q8C2×D4×C12712yes—
368C2×Q8C2×D4×C12712yes—
369C2×D4—24no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—44no—
376C2×D4—44no—
377C2×D4—41no—
378C2×D4C2×D4×C12712yes—
379C2×D4C2×D4×C12712yes—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—41no—
387C22×C4—84no—
388C22×C4C2×D4×C12712yes—
389C22×C4C2×D4×C12711yescharacteristic
390Q16—44no—
391SD16—44no—
392SD16—44no—
393SD16—44no—
394D8—44no—
395D8—44no—
396C2×C8—24no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—22no—
400C2×C8—22no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4C2×D4×C12712yes—
408C4⋊C4C2×D4×C12712yes—
409C22⋊C4—24no—
410C22⋊C4—24no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—24no—
416C22⋊C4—22no—
417C22⋊C4—42no—
418C42—22no—
419C42—22no—
420C42—22no—
421C42C2×D4×C12712yes—
422C42C2×D4×C12711yescharacteristic
423C42C24×C12711yescharacteristic
424C23—22no—
425C23—22no—
426C23—48no—
427C23—41no—
428C23—82no—
429C23#120×C12711yescharacteristic
430Q8—22no—
431Q8—22no—
432Q8—42no—
433Q8—42no—
434D4—22no—
435D4—42no—
436D4—42no—
437D4—44no—
438D4—48no—
439D4—42no—
440D4—42no—
441D4—42no—
442D4—42no—
443D4—82no—
444D4—82no—
445D4#135×C12714yescomplemented
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—44no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—44no—
457C2×C4—44no—
458C2×C4—41no—
459C2×C4—82no—
460C2×C4—84no—
461C2×C4—82no—
462C2×C4#120×C12712yes—
463C2×C4#120×C12711yescharacteristic
464C2×C4C22×D4×C12711yescharacteristic
465C2×C4C22×D4×C12712yes—
466C8—22no—
467C8—22no—
468C8—42no—
469C8—42no—
470C22—22no—
471C22—24no—
472C22—21no—
473C22—42no—
474C22—42no—
475C22—44no—
476C22—42no—
477C22—88no—
478C22—82no—
479C22—81no—
480C22C2×#120×C12711yescharacteristic
481C4—22no—
482C4—21no—
483C4—42no—
484C4—42no—
485C4—42no—
486C4—42no—
487C4—81no—
488C4#453×C12712yes—
489C4C2×#135×C12712yes—
490C4#575×C12712yes—
491C2—41no—
492C2—44no—
493C2—82no—
494C2—161no—
495C2C127×#300212yes—
496C2C2×#453×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutator, Frattini, cosocleC42C24×C127
socleC22×C127C2×#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3481C2semidirect
2. C127×#3147C2semidirect
3. C127×#3106C2semidirect
4. C127×#1632C2semidirect
5. C127×#1630C2semidirect
6. C127×#1629C2semidirect
7. C127×#1622C2semidirect
8. C127×#1620C2semidirect
9. C127×#1619C2semidirect
10. C127×#1543C2semidirect
11. C127×#1476C2semidirect
20. #532×C127C22semidirect
26. #494×C127C22semidirect
29. #492×C127C22semidirect
31. #477×C127C22semidirect
33. #460×C127C22semidirect
38. #431×C127C22semidirect
39. C2×C4×C8×C127C22semidirect
40. #333×C127C22semidirect
43. Q8⋊C8×C127C22semidirect
44. Q8⋊C8×C127C22semidirect
196. D4×C127#135semidirect
242. #18480C127direct (N × H)
249. #3481C2×C127semidirect
250. #3147C2×C127semidirect
251. #3106C2×C127semidirect
252. #1632C2×C127semidirect
253. #1630C2×C127semidirect
254. #1629C2×C127semidirect
255. #1622C2×C127semidirect
256. #1620C2×C127semidirect
257. #1619C2×C127semidirect
258. #1543C2×C127semidirect
259. #1476C2×C127semidirect
260. C127#18480direct (N × H)
269. #532C22×C127semidirect
275. #494C22×C127semidirect
278. #492C22×C127semidirect
280. #477C22×C127semidirect
282. #460C22×C127semidirect
287. #431C22×C127semidirect
288. C2×C4×C8C22×C127semidirect
289. #333C22×C127semidirect
292. Q8⋊C8C22×C127semidirect
293. Q8⋊C8C22×C127semidirect
445. D4#135×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34812
C127×#31472
C127×#31062
C127×#16322
C127×#16302
C127×#16292
C127×#16222
C127×#16202
C127×#16192
C127×#15432
C127×#14762
#18480127