Finite Group Databasebeta

← C127×#18515 #44582188

Subgroups — C127×#18515 #44582188

Order 32512.

976 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3483C211yesmaximal, characteristic
2C127×#3131C211yesmaximal, characteristic, complemented
3C127×#3107C212yesmaximal, complemented
4C127×#1646C212yesmaximal, complemented
5C127×#1645C212yesmaximal, complemented
6C127×#1642C212yesmaximal, complemented
7C127×#1641C212yesmaximal, complemented
8C127×#1543C211yesmaximal, characteristic, complemented
9C127×#1476C212yesmaximal, complemented
10Q82×C127C2211yescharacteristic
11#555×C127—22no—
12#555×C127—22no—
13#555×C127C2211yescharacteristic
14#550×C127—22no—
15#550×C127C2212yes—
16#533×C127C2211yescharacteristic
17#532×C127—22no—
18#532×C127—22no—
19#532×C127C2211yescharacteristic
20C4×#41×C127—22no—
21C4×#41×C127C2212yes—
22#488×C127—22no—
23#487×C127C2212yes—
24#486×C127C2212yes—
25#485×C127—22no—
26#475×C127C2212yes—
27#474×C127C2212yes—
28#462×C127C2212yes—
29#461×C127C2212yes—
30#452×C127—22no—
31C4×Q16×C127—22no—
32C4×SD16×C127—22no—
33#431×C127C2212yes—
34#416×C127—22no—
35C2×C4×C8×C127C2211yescharacteristic
36#333×C127C2212yes—
37#331×C127C2211yescharacteristic
38#331×C127C2211yescharacteristic
39Q8⋊C8×C127C2212yes—
40Q8⋊C8×C127C2212yes—
41D4⋊C8×C127C2212yes—
42D4⋊C8×C127C2212yes—
43C2×#41×C127—22no—
44C2×#41×C127—22no—
45C2×#41×C127D412yes—
46C2×#41×C127D412yes—
47C2×Q16×C127—22no—
48C2×SD16×C127—22no—
49C22×C8×C127—21no—
50C4⋊Q8×C127—22no—
51C4⋊Q8×C127—22no—
52C4⋊Q8×C127C2312yes—
53C4⋊Q8×C127C2311yescharacteristic
54#127×C127—22no—
55#127×C127—22no—
56#127×C127C2311yescharacteristic
57#125×C127—21no—
58#124×C127—22no—
59#124×C127—24no—
60#124×C127—22no—
61#124×C127D412yes—
62C22⋊Q8×C127—22no—
63#121×C127—24no—
64#121×C127—24no—
65#121×C127—22no—
66#121×C127—24no—
67#121×C127—22no—
68#121×C127—22no—
69C4×Q8×C127—22no—
70C4×Q8×C127—22no—
71C4×Q8×C127D412yes—
72C4×Q8×C127C2312yes—
73C4×D4×C127—24no—
74C4×D4×C127—24no—
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—24no—
82#117×C127—22no—
83#117×C127—22no—
84#117×C127—21no—
85#117×C127D412yes—
86C2×C42×C127—22no—
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—
103#41×C127—24no—
104#41×C127—42no—
105#41×C127—44no—
106#41×C127—44no—
107#41×C127—44no—
108#41×C127—84no—
109C2×Q8×C127—22no—
110C2×Q8×C127—22no—
111C2×Q8×C127C2×D412yes—
112C2×Q8×C127C2×D412yes—
113C2×D4×C127—24no—
114C2×D4×C127—22no—
115C2×D4×C127—22no—
116C2×D4×C127—24no—
117C2×D4×C127—22no—
118C2×D4×C127—22no—
119C2×D4×C127C2×D412yes—
120C2×D4×C127C2×D412yes—
121C22×C4×C127—24no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—22no—
126C22×C4×C127C2×D412yes—
127C22×C4×C127C2×D411yescharacteristic
128Q16×C127—44no—
129SD16×C127—44no—
130C2×C8×C127—22no—
131C2×C8×C127—22no—
132C2×C8×C127—22no—
133C2×C8×C127—42no—
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—24no—
147C22⋊C4×C127—22no—
148C22⋊C4×C127—22no—
149C22⋊C4×C127—41no—
150C42×C127—22no—
151C42×C127—22no—
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#12011yescharacteristic
162Q8×C127—22no—
163Q8×C127—42no—
164Q8×C127—42no—
165Q8×C127—42no—
166Q8×C127—82no—
167Q8×C127#13514yes—
168D4×C127—22no—
169D4×C127—22no—
170D4×C127—44no—
171D4×C127—42no—
172D4×C127—48no—
173D4×C127—42no—
174D4×C127—42no—
175D4×C127—82no—
176D4×C127—82no—
177D4×C127—84no—
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—22no—
185C2×C4×C127—44no—
186C2×C4×C127—48no—
187C2×C4×C127—42no—
188C2×C4×C127—42no—
189C2×C4×C127—44no—
190C2×C4×C127—44no—
191C2×C4×C127—42no—
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—21no—
201C22×C127—42no—
202C22×C127—44no—
203C22×C127—42no—
204C22×C127—42no—
205C22×C127—42no—
206C22×C127C2×#12011yescharacteristic
207C4×C127—22no—
208C4×C127—24no—
209C4×C127—21no—
210C4×C127—42no—
211C4×C127—42no—
212C4×C127—42no—
213C4×C127—82no—
214C4×C127#45512yes—
215C4×C127C2×#13512yes—
216C4×C127#57512yes—
217#18515C12711yesmaximal, characteristic, direct product factor, Sylow
218C2×C127—41no—
219C2×C127—82no—
220C2×C127—82no—
221C2×C127#300212yes—
222C2×C127C2×#45511yescharacteristic
223#3483C2×C12711yescharacteristic
224#3131C2×C12711yescharacteristic, complemented
225#3107C2×C12712yescomplemented
226#1646C2×C12712yescomplemented
227#1645C2×C12712yescomplemented
228#1642C2×C12712yescomplemented
229#1641C2×C12712yescomplemented
230#1543C2×C12711yescharacteristic, complemented
231#1476C2×C12712yescomplemented
232C127#1851511yescharacteristic, direct product factor, Sylow
233Q82C22×C12711yescharacteristic
234#555—22no—
235#555—22no—
236#555C22×C12711yescharacteristic
237#550—22no—
238#550C22×C12712yes—
239#533C22×C12711yescharacteristic
240#532—22no—
241#532—22no—
242#532C22×C12711yescharacteristic
243C4×#41—22no—
244C4×#41C22×C12712yes—
245#488—22no—
246#487C22×C12712yes—
247#486C22×C12712yes—
248#485—22no—
249#475C22×C12712yes—
250#474C22×C12712yes—
251#462C22×C12712yes—
252#461C22×C12712yes—
253#452—22no—
254C4×Q16—22no—
255C4×SD16—22no—
256#431C22×C12712yes—
257#416—22no—
258C2×C4×C8C22×C12711yescharacteristic
259#333C22×C12712yes—
260#331C22×C12711yescharacteristic
261#331C22×C12711yescharacteristic
262Q8⋊C8C22×C12712yes—
263Q8⋊C8C22×C12712yes—
264D4⋊C8C22×C12712yes—
265D4⋊C8C22×C12712yes—
266C2×#41—22no—
267C2×#41—22no—
268C2×#41D4×C12712yes—
269C2×#41D4×C12712yes—
270C2×Q16—22no—
271C2×SD16—22no—
272C22×C8—21no—
273C4⋊Q8—22no—
274C4⋊Q8—22no—
275C4⋊Q8C23×C12712yes—
276C4⋊Q8C23×C12711yescharacteristic
277#127—22no—
278#127—22no—
279#127C23×C12711yescharacteristic
280#125—21no—
281#124—22no—
282#124—24no—
283#124—22no—
284#124D4×C12712yes—
285C22⋊Q8—22no—
286#121—24no—
287#121—24no—
288#121—22no—
289#121—24no—
290#121—22no—
291#121—22no—
292C4×Q8—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×D4D4×C12712yes—
303C4×D4C23×C12712yes—
304#117—24no—
305#117—22no—
306#117—22no—
307#117—21no—
308#117D4×C12712yes—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42C23×C12711yescharacteristic
312#107—22no—
313#106—22no—
314C4⋊C8C23×C12712yes—
315C4⋊C8C23×C12712yes—
316#103—24no—
317#103—22no—
318#103—22no—
319#103—22no—
320#102—24no—
321#102—22no—
322C22⋊C8—22no—
323C4×C8—21no—
324C4×C8—22no—
325C4×C8C23×C12712yes—
326#41—24no—
327#41—42no—
328#41—44no—
329#41—44no—
330#41—44no—
331#41—84no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8C2×D4×C12712yes—
335C2×Q8C2×D4×C12712yes—
336C2×D4—24no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—24no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4C2×D4×C12712yes—
343C2×D4C2×D4×C12712yes—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
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—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—42no—
364C4⋊C4C2×D4×C12712yes—
365C4⋊C4C2×D4×C12712yes—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—22no—
369C22⋊C4—24no—
370C22⋊C4—22no—
371C22⋊C4—22no—
372C22⋊C4—41no—
373C42—22no—
374C42—22no—
375C42—22no—
376C42—22no—
377C42—22no—
378C42—41no—
379C42C2×D4×C12712yes—
380C42C2×D4×C12711yescharacteristic
381C42C24×C12711yescharacteristic
382C23—22no—
383C23—22no—
384C23#120×C12711yescharacteristic
385Q8—22no—
386Q8—42no—
387Q8—42no—
388Q8—42no—
389Q8—82no—
390Q8#135×C12714yes—
391D4—22no—
392D4—22no—
393D4—44no—
394D4—42no—
395D4—48no—
396D4—42no—
397D4—42no—
398D4—82no—
399D4—82no—
400D4—84no—
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—48no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4#120×C12712yes—
416C2×C4#120×C12711yescharacteristic
417C2×C4C22×D4×C12711yescharacteristic
418C2×C4C22×D4×C12712yes—
419C8—42no—
420C8—42no—
421C8—42no—
422C22—22no—
423C22—21no—
424C22—42no—
425C22—44no—
426C22—42no—
427C22—42no—
428C22—42no—
429C22C2×#120×C12711yescharacteristic
430C4—22no—
431C4—24no—
432C4—21no—
433C4—42no—
434C4—42no—
435C4—42no—
436C4—82no—
437C4#455×C12712yes—
438C4C2×#135×C12712yes—
439C4#575×C12712yes—
440C2—41no—
441C2—82no—
442C2—82no—
443C2C127×#300212yes—
444C2C2×#455×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutator, Frattini, cosocleC42C24×C127
socleC22×C127C2×#120
prime radicalC127×#3483C2
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×#1646C2semidirect
5. C127×#1645C2semidirect
6. C127×#1642C2semidirect
7. C127×#1641C2semidirect
8. C127×#1543C2semidirect
9. C127×#1476C2semidirect
217. #18515C127direct (N × H)
224. #3131C2×C127semidirect
225. #3107C2×C127semidirect
226. #1646C2×C127semidirect
227. #1645C2×C127semidirect
228. #1642C2×C127semidirect
229. #1641C2×C127semidirect
230. #1543C2×C127semidirect
231. #1476C2×C127semidirect
232. C127#18515direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34832
C127×#31312
C127×#31072
C127×#16462
C127×#16452
C127×#16422
C127×#16412
C127×#15432
C127×#14762
#18515127