Finite Group Databasebeta

← C127×#19425 #44583098

Subgroups — C127×#19425 #44583098

Order 32512.

660 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3207C211yesmaximal, characteristic, complemented
2C127×#3109C211yesmaximal, characteristic, complemented
3C127×#3100C211yesmaximal, characteristic, complemented
4C127×#2975C211yesmaximal, characteristic, complemented
5C127×#1703C212yesmaximal, complemented
6C127×#1697C212yesmaximal, complemented
7C127×#1687C212yesmaximal, complemented
8C127×#1685C212yesmaximal, complemented
9C127×#1572C211yesmaximal, characteristic, complemented
10C127×#1553C211yesmaximal, characteristic, complemented
11C127×#1543C211yesmaximal, characteristic, complemented
12#532×C127C2211yescharacteristic
13#532×C127C2211yescharacteristic
14C2×C4×D4×C127C2211yescharacteristic
15#493×C127C2211yescharacteristic, complemented
16#492×C127C2211yescharacteristic, complemented
17#487×C127C2211yescharacteristic, complemented
18#486×C127C2211yescharacteristic, complemented
19#481×C127—21no—
20#480×C127—21no—
21#476×C127C2212yes—
22#474×C127C2212yes—
23#463×C127—22no—
24#459×C127C2212yes—
25#459×C127C2212yes—
26#449×C127—22no—
27#447×C127—21no—
28#447×C127—21no—
29#442×C127—22no—
30C4×D8×C127—22no—
31#436×C127—22no—
32#436×C127C2212yes—
33#436×C127C2212yes—
34#432×C127C2211yescharacteristic
35#431×C127C2211yescharacteristic
36#431×C127C2211yescharacteristic
37#431×C127C2211yescharacteristic
38#407×C127—22no—
39#335×C127C2212yescomplemented
40#334×C127C2212yescomplemented
41#333×C127C2212yescomplemented
42#332×C127C2212yescomplemented
43#331×C127C2212yescomplemented
44#331×C127C2212yescomplemented
45C2×#41×C127—21no—
46C2×#41×C127—21no—
47C22×D4×C127D411yescharacteristic
48C23×C4×C127—21no—
49C2×SD16×C127—22no—
50C2×D8×C127—22no—
51C2×D8×C127—22no—
52C2×D8×C127—22no—
53C2×M16×C127—22no—
54C2×M16×C127—22no—
55C4⋊Q8×C127C2311yescharacteristic
56C4⋊Q8×C127C2311yescharacteristic
57#127×C127C2311yescharacteristic
58#127×C127C2311yescharacteristic
59#124×C127—21no—
60#124×C127—21no—
61#121×C127—21no—
62#121×C127—21no—
63#121×C127—21no—
64#121×C127—21no—
65C4×D4×C127—21no—
66C4×D4×C127—21no—
67C4×D4×C127—21no—
68C4×D4×C127—21no—
69C4×D4×C127—21no—
70C4×D4×C127—21no—
71C4×D4×C127D412yes—
72C4×D4×C127C2312yes—
73C2×C4⋊C4×C127D411yescharacteristic
74C2×C22⋊C4×C127—21no—
75C2×C42×C127C2311yescharacteristic
76#107×C127—22no—
77#106×C127—22no—
78C4⋊C8×C127D412yes—
79C4⋊C8×C127C2312yes—
80C4⋊C8×C127C2312yes—
81C4⋊C8×C127C2312yes—
82#103×C127—22no—
83#102×C127—22no—
84#102×C127—22no—
85#102×C127—22no—
86#102×C127—22no—
87#102×C127—22no—
88C22⋊C8×C127—21no—
89C22⋊C8×C127—21no—
90C22⋊C8×C127—21no—
91C22⋊C8×C127—22no—
92C22⋊C8×C127—22no—
93C22⋊C8×C127D412yes—
94#97×C127—21no—
95C4×C8×C127—21no—
96C4×C8×C127—21no—
97C4×C8×C127C2311yescharacteristic
98C4×C8×C127C2311yescharacteristic
99C24×C127—21no—
100#41×C127—82no—
101#41×C127—82no—
102C2×Q8×C127—21no—
103C2×Q8×C127—21no—
104C2×D4×C127—21no—
105C2×D4×C127—21no—
106C2×D4×C127—21no—
107C2×D4×C127—21no—
108C2×D4×C127—21no—
109C2×D4×C127—21no—
110C2×D4×C127—21no—
111C2×D4×C127—42no—
112C2×D4×C127—41no—
113C2×D4×C127—41no—
114C2×D4×C127C2×D412yes—
115C22×C4×C127—21no—
116C22×C4×C127—22no—
117C22×C4×C127—22no—
118C22×C4×C127—41no—
119C22×C4×C127—41no—
120C22×C4×C127—82no—
121C22×C4×C127C2×D411yescharacteristic
122C22×C4×C127C2×D411yescharacteristic
123C22×C4×C127#4111yescharacteristic
124SD16×C127—82no—
125D8×C127—44no—
126D8×C127—44no—
127D8×C127—82no—
128M16×C127—82no—
129M16×C127—82no—
130C2×C8×C127—22no—
131C2×C8×C127—22no—
132C2×C8×C127—22no—
133C2×C8×C127C2×D412yes—
134C2×C8×C127C2×D412yes—
135C4⋊C4×C127—21no—
136C4⋊C4×C127—21no—
137C4⋊C4×C127—21no—
138C4⋊C4×C127—21no—
139C4⋊C4×C127—21no—
140C4⋊C4×C127C2×D412yes—
141C22⋊C4×C127—22no—
142C22⋊C4×C127—22no—
143C22⋊C4×C127—41no—
144C22⋊C4×C127—41no—
145C22⋊C4×C127—41no—
146C22⋊C4×C127—41no—
147C42×C127C2×D411yescharacteristic
148C42×C127C2×D411yescharacteristic
149C42×C127#4111yescharacteristic
150C42×C127C2411yescharacteristic
151C23×C127—22no—
152C23×C127—42no—
153C23×C127—41no—
154C23×C127—41no—
155C23×C127—81no—
156C23×C127—81no—
157C23×C127#12111yescharacteristic
158Q8×C127—42no—
159Q8×C127—81no—
160D4×C127—22no—
161D4×C127—22no—
162D4×C127—42no—
163D4×C127—42no—
164D4×C127—42no—
165D4×C127—42no—
166D4×C127—42no—
167D4×C127—81no—
168D4×C127—81no—
169D4×C127—82no—
170D4×C127—82no—
171C2×C4×C127—22no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—41no—
175C2×C4×C127—42no—
176C2×C4×C127—42no—
177C2×C4×C127—41no—
178C2×C4×C127—41no—
179C2×C4×C127—82no—
180C2×C4×C127—82no—
181C2×C4×C127—82no—
182C2×C4×C127—81no—
183C2×C4×C127#12111yescharacteristic
184C2×C4×C127#12111yescharacteristic
185C2×C4×C127#12111yescharacteristic
186C2×C4×C127C22×D411yescharacteristic
187C2×C4×C127C22×D411yescharacteristic
188C2×C4×C127C2×#4111yescharacteristic
189C8×C127—22no—
190C8×C127—22no—
191C8×C127—42no—
192C8×C127—42no—
193C8×C127—42no—
194C22×C127—21no—
195C22×C127—21no—
196C22×C127—21no—
197C22×C127—42no—
198C22×C127—42no—
199C22×C127—42no—
200C22×C127—84no—
201C22×C127—81no—
202C22×C127—81no—
203C22×C127—81no—
204C22×C127—81no—
205C22×C127—81no—
206C22×C127—81no—
207C22×C127C2×#12111yescharacteristic
208C4×C127—21no—
209C4×C127—21no—
210C4×C127—21no—
211C4×C127—21no—
212C4×C127—42no—
213C4×C127—81no—
214C4×C127—81no—
215C4×C127#57512yes—
216C4×C127#57612yes—
217#19425C12711yesmaximal, characteristic, direct product factor, Sylow
218C2×C127—41no—
219C2×C127—82no—
220C2×C127—161no—
221C2×C127—161no—
222C2×C127#304111yescharacteristic
223C2×C127#305411yescharacteristic
224C2×C127#306811yescharacteristic
225#3207C2×C12711yescharacteristic, complemented
226#3109C2×C12711yescharacteristic, complemented
227#3100C2×C12711yescharacteristic, complemented
228#2975C2×C12711yescharacteristic, complemented
229#1703C2×C12712yescomplemented
230#1697C2×C12712yescomplemented
231#1687C2×C12712yescomplemented
232#1685C2×C12712yescomplemented
233#1572C2×C12711yescharacteristic, complemented
234#1553C2×C12711yescharacteristic, complemented
235#1543C2×C12711yescharacteristic, complemented
236C127#1942511yescharacteristic, direct product factor, Sylow
237#532C22×C12711yescharacteristic
238#532C22×C12711yescharacteristic
239C2×C4×D4C22×C12711yescharacteristic
240#493C22×C12711yescharacteristic, complemented
241#492C22×C12711yescharacteristic, complemented
242#487C22×C12711yescharacteristic, complemented
243#486C22×C12711yescharacteristic, complemented
244#481—21no—
245#480—21no—
246#476C22×C12712yes—
247#474C22×C12712yes—
248#463—22no—
249#459C22×C12712yes—
250#459C22×C12712yes—
251#449—22no—
252#447—21no—
253#447—21no—
254#442—22no—
255C4×D8—22no—
256#436—22no—
257#436C22×C12712yes—
258#436C22×C12712yes—
259#432C22×C12711yescharacteristic
260#431C22×C12711yescharacteristic
261#431C22×C12711yescharacteristic
262#431C22×C12711yescharacteristic
263#407—22no—
264#335C22×C12712yescomplemented
265#334C22×C12712yescomplemented
266#333C22×C12712yescomplemented
267#332C22×C12712yescomplemented
268#331C22×C12712yescomplemented
269#331C22×C12712yescomplemented
270C2×#41—21no—
271C2×#41—21no—
272C22×D4D4×C12711yescharacteristic
273C23×C4—21no—
274C2×SD16—22no—
275C2×D8—22no—
276C2×D8—22no—
277C2×D8—22no—
278C2×M16—22no—
279C2×M16—22no—
280C4⋊Q8C23×C12711yescharacteristic
281C4⋊Q8C23×C12711yescharacteristic
282#127C23×C12711yescharacteristic
283#127C23×C12711yescharacteristic
284#124—21no—
285#124—21no—
286#121—21no—
287#121—21no—
288#121—21no—
289#121—21no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—21no—
296C4×D4D4×C12712yes—
297C4×D4C23×C12712yes—
298C2×C4⋊C4D4×C12711yescharacteristic
299C2×C22⋊C4—21no—
300C2×C42C23×C12711yescharacteristic
301#107—22no—
302#106—22no—
303C4⋊C8D4×C12712yes—
304C4⋊C8C23×C12712yes—
305C4⋊C8C23×C12712yes—
306C4⋊C8C23×C12712yes—
307#103—22no—
308#102—22no—
309#102—22no—
310#102—22no—
311#102—22no—
312#102—22no—
313C22⋊C8—21no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316C22⋊C8—22no—
317C22⋊C8—22no—
318C22⋊C8D4×C12712yes—
319#97—21no—
320C4×C8—21no—
321C4×C8—21no—
322C4×C8C23×C12711yescharacteristic
323C4×C8C23×C12711yescharacteristic
324C24—21no—
325#41—82no—
326#41—82no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—42no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4C2×D4×C12712yes—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—82no—
346C22×C4C2×D4×C12711yescharacteristic
347C22×C4C2×D4×C12711yescharacteristic
348C22×C4#41×C12711yescharacteristic
349SD16—82no—
350D8—44no—
351D8—44no—
352D8—82no—
353M16—82no—
354M16—82no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8C2×D4×C12712yes—
359C2×C8C2×D4×C12712yes—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4C2×D4×C12712yes—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C42C2×D4×C12711yescharacteristic
373C42C2×D4×C12711yescharacteristic
374C42#41×C12711yescharacteristic
375C42C24×C12711yescharacteristic
376C23—22no—
377C23—42no—
378C23—41no—
379C23—41no—
380C23—81no—
381C23—81no—
382C23#121×C12711yescharacteristic
383Q8—42no—
384Q8—81no—
385D4—22no—
386D4—22no—
387D4—42no—
388D4—42no—
389D4—42no—
390D4—42no—
391D4—42no—
392D4—81no—
393D4—81no—
394D4—82no—
395D4—82no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—81no—
408C2×C4#121×C12711yescharacteristic
409C2×C4#121×C12711yescharacteristic
410C2×C4#121×C12711yescharacteristic
411C2×C4C22×D4×C12711yescharacteristic
412C2×C4C22×D4×C12711yescharacteristic
413C2×C4C2×#41×C12711yescharacteristic
414C8—22no—
415C8—22no—
416C8—42no—
417C8—42no—
418C8—42no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—84no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22C2×#121×C12711yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—42no—
438C4—81no—
439C4—81no—
440C4#575×C12712yes—
441C4#576×C12712yes—
442C2—41no—
443C2—82no—
444C2—161no—
445C2—161no—
446C2C127×#304111yescharacteristic
447C2C127×#305411yescharacteristic
448C2C127×#306811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
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×#3207C2semidirect
2. C127×#3109C2semidirect
3. C127×#3100C2semidirect
4. C127×#2975C2semidirect
5. C127×#1703C2semidirect
6. C127×#1697C2semidirect
7. C127×#1687C2semidirect
8. C127×#1685C2semidirect
9. C127×#1572C2semidirect
10. C127×#1553C2semidirect
11. C127×#1543C2semidirect
15. #493×C127C22semidirect
16. #492×C127C22semidirect
17. #487×C127C22semidirect
18. #486×C127C22semidirect
39. #335×C127C22semidirect
40. #334×C127C22semidirect
41. #333×C127C22semidirect
42. #332×C127C22semidirect
43. #331×C127C22semidirect
44. #331×C127C22semidirect
217. #19425C127direct (N × H)
225. #3207C2×C127semidirect
226. #3109C2×C127semidirect
227. #3100C2×C127semidirect
228. #2975C2×C127semidirect
229. #1703C2×C127semidirect
230. #1697C2×C127semidirect
231. #1687C2×C127semidirect
232. #1685C2×C127semidirect
233. #1572C2×C127semidirect
234. #1553C2×C127semidirect
235. #1543C2×C127semidirect
236. C127#19425direct (N × H)
240. #493C22×C127semidirect
241. #492C22×C127semidirect
242. #487C22×C127semidirect
243. #486C22×C127semidirect
264. #335C22×C127semidirect
265. #334C22×C127semidirect
266. #333C22×C127semidirect
267. #332C22×C127semidirect
268. #331C22×C127semidirect
269. #331C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32072
C127×#31092
C127×#31002
C127×#29752
C127×#17032
C127×#16972
C127×#16872
C127×#16852
C127×#15722
C127×#15532
C127×#15432
#19425127