Finite Group Databasebeta

← C127×#18485 #44582158

Subgroups — C127×#18485 #44582158

Order 32512.

996 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3481C211yesmaximal, characteristic
2C127×#3131C211yesmaximal, characteristic, complemented
3C127×#3107C212yesmaximal, complemented
4C127×#1644C212yesmaximal, complemented
5C127×#1643C212yesmaximal, complemented
6C127×#1640C212yesmaximal, complemented
7C127×#1639C212yesmaximal, complemented
8C127×#1543C211yesmaximal, characteristic, complemented
9C127×#1476C212yesmaximal, complemented
10#559×C127C2211yescharacteristic
11#554×C127C2212yes—
12#553×C127—22no—
13#551×C127—22no—
14#546×C127—22no—
15D42×C127C2211yescharacteristic
16#533×C127C2211yescharacteristic, complemented
17#532×C127C2211yescharacteristic
18#529×C127—22no—
19#525×C127—22no—
20C4×#41×C127C2212yes—
21C2×C4×D4×C127—22no—
22#488×C127—22no—
23#487×C127C2212yescomplemented
24#486×C127C2212yes—
25#485×C127—22no—
26#475×C127C2212yescomplemented
27#474×C127C2212yes—
28#462×C127C2212yescomplemented
29#461×C127C2212yes—
30#452×C127—22no—
31C4×Q16×C127—22no—
32C4×SD16×C127—22no—
33#431×C127C2212yescomplemented
34#416×C127—22no—
35C2×C4×C8×C127C2211yescharacteristic, complemented
36#333×C127C2211yescharacteristic, complemented
37#333×C127C2211yescharacteristic, complemented
38#331×C127C2212yes—
39Q8⋊C8×C127C2212yescomplemented
40Q8⋊C8×C127C2212yescomplemented
41D4⋊C8×C127C2212yes—
42D4⋊C8×C127C2212yes—
43C2×#41×C127D412yes—
44C2×#41×C127D412yes—
45C22×D4×C127—22no—
46C23×C4×C127—22no—
47C2×Q16×C127—22no—
48C2×SD16×C127—22no—
49C22×C8×C127—21no—
50C4⋊Q8×C127C2312yes—
51C4⋊Q8×C127C2311yescharacteristic
52#127×C127C2311yescharacteristic
53#126×C127—24no—
54#125×C127—22no—
55#125×C127—21no—
56#124×C127—22no—
57#124×C127D412yes—
58#123×C127—22no—
59#123×C127—24no—
60#123×C127—22no—
61C22⋊Q8×C127—24no—
62C22⋊Q8×C127—22no—
63C22⋊Q8×C127—22no—
64#121×C127—24no—
65#121×C127—22no—
66#121×C127—22no—
67#120×C127—22no—
68#120×C127—22no—
69C4×Q8×C127—22no—
70C4×Q8×C127D412yes—
71C4×Q8×C127C2312yes—
72C4×D4×C127—24no—
73C4×D4×C127—24no—
74C4×D4×C127—22no—
75C4×D4×C127—22no—
76C4×D4×C127—22no—
77C4×D4×C127—22no—
78C4×D4×C127—22no—
79C4×D4×C127D412yes—
80C4×D4×C127C2312yes—
81#117×C127—22no—
82#117×C127—22no—
83#117×C127—21no—
84#117×C127D412yes—
85C2×C4⋊C4×C127—22no—
86C2×C22⋊C4×C127—24no—
87C2×C42×C127—22no—
88C2×C42×C127C2311yescharacteristic
89#107×C127—22no—
90#106×C127—22no—
91C4⋊C8×C127C2312yes—
92C4⋊C8×C127C2312yes—
93#103×C127—24no—
94#103×C127—22no—
95#103×C127—22no—
96#103×C127—22no—
97#102×C127—24no—
98#102×C127—22no—
99C22⋊C8×C127—22no—
100C4×C8×C127—21no—
101C4×C8×C127—22no—
102C4×C8×C127C2312yes—
103C24×C127—22no—
104#41×C127—24no—
105#41×C127—42no—
106#41×C127—44no—
107C2×Q8×C127—22no—
108C2×Q8×C127C2×D412yes—
109C2×Q8×C127C2×D412yes—
110C2×D4×C127—24no—
111C2×D4×C127—22no—
112C2×D4×C127—22no—
113C2×D4×C127—22no—
114C2×D4×C127—44no—
115C2×D4×C127—44no—
116C2×D4×C127C2×D412yes—
117C2×D4×C127C2×D412yes—
118C22×C4×C127—24no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—84no—
125C22×C4×C127C2×D412yes—
126C22×C4×C127C2×D411yescharacteristic
127Q16×C127—44no—
128SD16×C127—44no—
129C2×C8×C127—22no—
130C2×C8×C127—22no—
131C2×C8×C127—22no—
132C2×C8×C127—42no—
133C4⋊C4×C127—24no—
134C4⋊C4×C127—24no—
135C4⋊C4×C127—22no—
136C4⋊C4×C127—22no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—22no—
140C4⋊C4×C127—42no—
141C4⋊C4×C127C2×D412yes—
142C4⋊C4×C127C2×D412yes—
143C22⋊C4×C127—24no—
144C22⋊C4×C127—24no—
145C22⋊C4×C127—22no—
146C22⋊C4×C127—22no—
147C22⋊C4×C127—22no—
148C22⋊C4×C127—22no—
149C22⋊C4×C127—24no—
150C22⋊C4×C127—22no—
151C22⋊C4×C127—41no—
152C42×C127—22no—
153C42×C127—22no—
154C42×C127—22no—
155C42×C127—41no—
156C42×C127C2×D411yescharacteristic
157C42×C127C2×D412yes—
158C42×C127C2411yescharacteristic
159C23×C127—22no—
160C23×C127—22no—
161C23×C127—48no—
162C23×C127—82no—
163C23×C127#12011yescharacteristic
164Q8×C127—22no—
165Q8×C127—22no—
166Q8×C127—42no—
167Q8×C127—42no—
168Q8×C127—42no—
169D4×C127—22no—
170D4×C127—42no—
171D4×C127—44no—
172D4×C127—48no—
173D4×C127—42no—
174D4×C127—42no—
175D4×C127—82no—
176D4×C127#13514yes—
177C2×C4×C127—22no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
182C2×C4×C127—22no—
183C2×C4×C127—22no—
184C2×C4×C127—44no—
185C2×C4×C127—42no—
186C2×C4×C127—42no—
187C2×C4×C127—44no—
188C2×C4×C127—44no—
189C2×C4×C127—42no—
190C2×C4×C127—82no—
191C2×C4×C127—84no—
192C2×C4×C127#12012yes—
193C2×C4×C127#12011yescharacteristic
194C2×C4×C127C22×D411yescharacteristic
195C2×C4×C127C22×D412yes—
196C8×C127—42no—
197C8×C127—42no—
198C8×C127—42no—
199C22×C127—22no—
200C22×C127—24no—
201C22×C127—21no—
202C22×C127—42no—
203C22×C127—42no—
204C22×C127—44no—
205C22×C127—42no—
206C22×C127—88no—
207C22×C127C2×#12011yescharacteristic
208C4×C127—22no—
209C4×C127—21no—
210C4×C127—42no—
211C4×C127—42no—
212C4×C127—42no—
213C4×C127—42no—
214C4×C127—82no—
215C4×C127#45512yes—
216C4×C127C2×#13512yes—
217C4×C127#57512yes—
218#18485C12711yesmaximal, characteristic, direct product factor, Sylow
219C2×C127—41no—
220C2×C127—44no—
221C2×C127—82no—
222C2×C127#300212yes—
223C2×C127C2×#45511yescharacteristic
224#3481C2×C12711yescharacteristic
225#3131C2×C12711yescharacteristic, complemented
226#3107C2×C12712yescomplemented
227#1644C2×C12712yescomplemented
228#1643C2×C12712yescomplemented
229#1640C2×C12712yescomplemented
230#1639C2×C12712yescomplemented
231#1543C2×C12711yescharacteristic, complemented
232#1476C2×C12712yescomplemented
233C127#1848511yescharacteristic, direct product factor, Sylow
234#559C22×C12711yescharacteristic
235#554C22×C12712yes—
236#553—22no—
237#551—22no—
238#546—22no—
239D42C22×C12711yescharacteristic
240#533C22×C12711yescharacteristic, complemented
241#532C22×C12711yescharacteristic
242#529—22no—
243#525—22no—
244C4×#41C22×C12712yes—
245C2×C4×D4—22no—
246#488—22no—
247#487C22×C12712yescomplemented
248#486C22×C12712yes—
249#485—22no—
250#475C22×C12712yescomplemented
251#474C22×C12712yes—
252#462C22×C12712yescomplemented
253#461C22×C12712yes—
254#452—22no—
255C4×Q16—22no—
256C4×SD16—22no—
257#431C22×C12712yescomplemented
258#416—22no—
259C2×C4×C8C22×C12711yescharacteristic, complemented
260#333C22×C12711yescharacteristic, complemented
261#333C22×C12711yescharacteristic, complemented
262#331C22×C12712yes—
263Q8⋊C8C22×C12712yescomplemented
264Q8⋊C8C22×C12712yescomplemented
265D4⋊C8C22×C12712yes—
266D4⋊C8C22×C12712yes—
267C2×#41D4×C12712yes—
268C2×#41D4×C12712yes—
269C22×D4—22no—
270C23×C4—22no—
271C2×Q16—22no—
272C2×SD16—22no—
273C22×C8—21no—
274C4⋊Q8C23×C12712yes—
275C4⋊Q8C23×C12711yescharacteristic
276#127C23×C12711yescharacteristic
277#126—24no—
278#125—22no—
279#125—21no—
280#124—22no—
281#124D4×C12712yes—
282#123—22no—
283#123—24no—
284#123—22no—
285C22⋊Q8—24no—
286C22⋊Q8—22no—
287C22⋊Q8—22no—
288#121—24no—
289#121—22no—
290#121—22no—
291#120—22no—
292#120—22no—
293C4×Q8—22no—
294C4×Q8D4×C12712yes—
295C4×Q8C23×C12712yes—
296C4×D4—24no—
297C4×D4—24no—
298C4×D4—22no—
299C4×D4—22no—
300C4×D4—22no—
301C4×D4—22no—
302C4×D4—22no—
303C4×D4D4×C12712yes—
304C4×D4C23×C12712yes—
305#117—22no—
306#117—22no—
307#117—21no—
308#117D4×C12712yes—
309C2×C4⋊C4—22no—
310C2×C22⋊C4—24no—
311C2×C42—22no—
312C2×C42C23×C12711yescharacteristic
313#107—22no—
314#106—22no—
315C4⋊C8C23×C12712yes—
316C4⋊C8C23×C12712yes—
317#103—24no—
318#103—22no—
319#103—22no—
320#103—22no—
321#102—24no—
322#102—22no—
323C22⋊C8—22no—
324C4×C8—21no—
325C4×C8—22no—
326C4×C8C23×C12712yes—
327C24—22no—
328#41—24no—
329#41—42no—
330#41—44no—
331C2×Q8—22no—
332C2×Q8C2×D4×C12712yes—
333C2×Q8C2×D4×C12712yes—
334C2×D4—24no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—44no—
339C2×D4—44no—
340C2×D4C2×D4×C12712yes—
341C2×D4C2×D4×C12712yes—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—84no—
349C22×C4C2×D4×C12712yes—
350C22×C4C2×D4×C12711yescharacteristic
351Q16—44no—
352SD16—44no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—42no—
357C4⋊C4—24no—
358C4⋊C4—24no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—42no—
365C4⋊C4C2×D4×C12712yes—
366C4⋊C4C2×D4×C12712yes—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C22⋊C4—22no—
372C22⋊C4—22no—
373C22⋊C4—24no—
374C22⋊C4—22no—
375C22⋊C4—41no—
376C42—22no—
377C42—22no—
378C42—22no—
379C42—41no—
380C42C2×D4×C12712yes—
381C42C2×D4×C12711yescharacteristic
382C42C24×C12711yescharacteristic
383C23—22no—
384C23—22no—
385C23—48no—
386C23—82no—
387C23#120×C12711yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—42no—
391Q8—42no—
392Q8—42no—
393D4—22no—
394D4—42no—
395D4—44no—
396D4—48no—
397D4—42no—
398D4—42no—
399D4—82no—
400D4#135×C12714yes—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—42no—
414C2×C4—82no—
415C2×C4—84no—
416C2×C4#120×C12712yes—
417C2×C4#120×C12711yescharacteristic
418C2×C4C22×D4×C12711yescharacteristic
419C2×C4C22×D4×C12712yes—
420C8—42no—
421C8—42no—
422C8—42no—
423C22—22no—
424C22—24no—
425C22—21no—
426C22—42no—
427C22—42no—
428C22—44no—
429C22—42no—
430C22—88no—
431C22C2×#120×C12711yescharacteristic
432C4—22no—
433C4—21no—
434C4—42no—
435C4—42no—
436C4—42no—
437C4—42no—
438C4—82no—
439C4#455×C12712yes—
440C4C2×#135×C12712yes—
441C4#575×C12712yes—
442C2—41no—
443C2—44no—
444C2—82no—
445C2C127×#300212yes—
446C2C2×#455×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutator, Frattini, cosocleC42C24×C127
socleC22×C127C2×#120
prime radicalC127×#3481C2
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
2. C127×#3131C2semidirect
3. C127×#3107C2semidirect
4. C127×#1644C2semidirect
5. C127×#1643C2semidirect
6. C127×#1640C2semidirect
7. C127×#1639C2semidirect
8. C127×#1543C2semidirect
9. C127×#1476C2semidirect
16. #533×C127C22semidirect
23. #487×C127C22semidirect
26. #475×C127C22semidirect
28. #462×C127C22semidirect
33. #431×C127C22semidirect
35. C2×C4×C8×C127C22semidirect
36. #333×C127C22semidirect
37. #333×C127C22semidirect
39. Q8⋊C8×C127C22semidirect
40. Q8⋊C8×C127C22semidirect
218. #18485C127direct (N × H)
225. #3131C2×C127semidirect
226. #3107C2×C127semidirect
227. #1644C2×C127semidirect
228. #1643C2×C127semidirect
229. #1640C2×C127semidirect
230. #1639C2×C127semidirect
231. #1543C2×C127semidirect
232. #1476C2×C127semidirect
233. C127#18485direct (N × H)
240. #533C22×C127semidirect
247. #487C22×C127semidirect
250. #475C22×C127semidirect
252. #462C22×C127semidirect
257. #431C22×C127semidirect
259. C2×C4×C8C22×C127semidirect
260. #333C22×C127semidirect
261. #333C22×C127semidirect
263. Q8⋊C8C22×C127semidirect
264. Q8⋊C8C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34812
C127×#31312
C127×#31072
C127×#16442
C127×#16432
C127×#16402
C127×#16392
C127×#15432
C127×#14762
#18485127