Finite Group Databasebeta

← C127×#19294 #44582967

Subgroups — C127×#19294 #44582967

Order 32512.

694 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3147C211yesmaximal, characteristic, complemented
2C127×#3115C212yesmaximal, complemented
3C127×#2965C211yesmaximal, characteristic, complemented
4C127×#1690C211yesmaximal, characteristic, complemented
5C127×#1689C211yesmaximal, characteristic, complemented
6C127×#1688C211yesmaximal, characteristic, complemented
7C127×#1687C211yesmaximal, characteristic, complemented
8C127×#1686C212yesmaximal, complemented
9C127×#1685C212yesmaximal, complemented
10C127×#1568C211yesmaximal, characteristic, complemented
11C127×#1553C212yesmaximal, complemented
12C2×#135×C127—21no—
13C2×#135×C127—21no—
14#532×C127C2212yes—
15C4×#41×C127C2211yescharacteristic
16#495×C127—21no—
17#495×C127—21no—
18#494×C127C2211yescharacteristic
19#493×C127C2211yescharacteristic
20#492×C127C2212yes—
21#482×C127—22no—
22#475×C127C2212yes—
23#474×C127C2212yes—
24#460×C127C2212yes—
25#459×C127C2212yes—
26#449×C127—22no—
27#446×C127C2211yescharacteristic
28#446×C127C2211yescharacteristic
29#442×C127—22no—
30#440×C127—22no—
31#436×C127C2211yescharacteristic
32#436×C127C2211yescharacteristic
33#435×C127—21no—
34#435×C127—21no—
35#432×C127C2212yes—
36#431×C127—21no—
37#431×C127C2211yescharacteristic
38C4×M16×C127—21no—
39C2×C4×C8×C127C2211yescharacteristic
40#335×C127C2212yes—
41#334×C127C2211yescharacteristic
42#334×C127C2211yescharacteristic
43#332×C127C2212yes—
44#332×C127C2212yes—
45#331×C127C2212yes—
46#331×C127C2212yes—
47C2×#41×C127—22no—
48C2×#41×C127D411yescharacteristic
49#135×C127—44no—
50#135×C127—44no—
51C2×Q16×C127—21no—
52C2×Q16×C127—21no—
53C2×SD16×C127—22no—
54C2×SD16×C127—22no—
55C2×SD16×C127—22no—
56C2×D8×C127—22no—
57C2×D8×C127—21no—
58C2×D8×C127—21no—
59C2×M16×C127—21no—
60C2×M16×C127—21no—
61C22×C8×C127D411yescharacteristic
62C22×C8×C127D411yescharacteristic
63C4⋊Q8×C127C2312yes—
64#127×C127C2312yes—
65#124×C127—22no—
66#121×C127—22no—
67#121×C127—22no—
68C4×Q8×C127D411yescharacteristic
69C4×Q8×C127C2311yescharacteristic
70C4×D4×C127—21no—
71C4×D4×C127—21no—
72C4×D4×C127—22no—
73C4×D4×C127—22no—
74C4×D4×C127D411yescharacteristic
75C4×D4×C127C2311yescharacteristic
76#117×C127—21no—
77#117×C127D411yescharacteristic
78C2×C42×C127—21no—
79C2×C42×C127C2311yescharacteristic
80#107×C127—22no—
81#106×C127—22no—
82C4⋊C8×C127—21no—
83C4⋊C8×C127—21no—
84C4⋊C8×C127C2311yescharacteristic
85C4⋊C8×C127C2311yescharacteristic
86C4⋊C8×C127C2312yes—
87C4⋊C8×C127C2312yes—
88#103×C127—22no—
89#102×C127—22no—
90#102×C127—22no—
91#102×C127—22no—
92C22⋊C8×C127—21no—
93C22⋊C8×C127—22no—
94C22⋊C8×C127—21no—
95C22⋊C8×C127—21no—
96#97×C127—21no—
97#97×C127—21no—
98#97×C127—22no—
99C4×C8×C127—21no—
100C4×C8×C127D411yescharacteristic
101C4×C8×C127D411yescharacteristic
102C4×C8×C127C2311yescharacteristic
103C4×C8×C127C2311yescharacteristic
104#41×C127—42no—
105#41×C127—44no—
106#41×C127—44no—
107C2×Q8×C127—22no—
108C2×Q8×C127C2×D411yescharacteristic
109C2×D4×C127—21no—
110C2×D4×C127—22no—
111C2×D4×C127—22no—
112C2×D4×C127—22no—
113C2×D4×C127—42no—
114C2×D4×C127C2×D411yescharacteristic
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—42no—
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127C2×D411yescharacteristic
121C22×C4×C127#4111yescharacteristic
122Q16×C127—42no—
123Q16×C127—42no—
124SD16×C127—44no—
125SD16×C127—44no—
126SD16×C127—44no—
127D8×C127—42no—
128D8×C127—44no—
129D8×C127—42no—
130M16×C127—42no—
131M16×C127—42no—
132C2×C8×C127—22no—
133C2×C8×C127—22no—
134C2×C8×C127—21no—
135C2×C8×C127—21no—
136C2×C8×C127—22no—
137C2×C8×C127—22no—
138C2×C8×C127C2×D411yescharacteristic
139C2×C8×C127C2×D411yescharacteristic
140C2×C8×C127C2×D411yescharacteristic
141C2×C8×C127C2×D411yescharacteristic
142C4⋊C4×C127—21no—
143C4⋊C4×C127—21no—
144C4⋊C4×C127—22no—
145C4⋊C4×C127—22no—
146C4⋊C4×C127C2×D411yescharacteristic
147C4⋊C4×C127C2×D411yescharacteristic
148C22⋊C4×C127—21no—
149C22⋊C4×C127—21no—
150C22⋊C4×C127—21no—
151C22⋊C4×C127—42no—
152C22⋊C4×C127—42no—
153C42×C127—21no—
154C42×C127—21no—
155C42×C127—21no—
156C42×C127C2×D411yescharacteristic
157C42×C127C2×D411yescharacteristic
158C42×C127#4111yescharacteristic
159C42×C127C2411yescharacteristic
160C23×C127—21no—
161C23×C127—42no—
162C23×C127#12111yescharacteristic
163Q8×C127—22no—
164Q8×C127—42no—
165Q8×C127—42no—
166D4×C127—22no—
167D4×C127—42no—
168D4×C127—42no—
169D4×C127—42no—
170D4×C127—42no—
171D4×C127—42no—
172D4×C127—82no—
173D4×C127—84no—
174C2×C4×C127—21no—
175C2×C4×C127—21no—
176C2×C4×C127—22no—
177C2×C4×C127—21no—
178C2×C4×C127—21no—
179C2×C4×C127—21no—
180C2×C4×C127—41no—
181C2×C4×C127—42no—
182C2×C4×C127—42no—
183C2×C4×C127—41no—
184C2×C4×C127—41no—
185C2×C4×C127—42no—
186C2×C4×C127—84no—
187C2×C4×C127#12111yescharacteristic
188C2×C4×C127#12111yescharacteristic
189C2×C4×C127#12111yescharacteristic
190C2×C4×C127C22×D411yescharacteristic
191C2×C4×C127C22×D411yescharacteristic
192C2×C4×C127C2×#4111yescharacteristic
193C8×C127—21no—
194C8×C127—21no—
195C8×C127—41no—
196C8×C127—41no—
197C8×C127—42no—
198C8×C127—42no—
199C8×C127AGL(1,ℤ/8)12yes—
200C8×C127AGL(1,ℤ/8)12yes—
201C22×C127—21no—
202C22×C127—21no—
203C22×C127—21no—
204C22×C127—41no—
205C22×C127—41no—
206C22×C127—41no—
207C22×C127—82no—
208C22×C127—82no—
209C22×C127—82no—
210C22×C127C2×#12111yescharacteristic
211C4×C127—21no—
212C4×C127—21no—
213C4×C127—21no—
214C4×C127—21no—
215C4×C127—41no—
216C4×C127—41no—
217C4×C127—41no—
218C4×C127—82no—
219C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
220C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
221C4×C127#57512yes—
222#19294C12711yesmaximal, characteristic, direct product factor, Sylow
223C2×C127—41no—
224C2×C127—81no—
225C2×C127—162no—
226C2×C127#303811yescharacteristic
227C2×C127#305411yescharacteristic
228C2×C127#306711yescharacteristic
229#3147C2×C12711yescharacteristic, complemented
230#3115C2×C12712yescomplemented
231#2965C2×C12711yescharacteristic, complemented
232#1690C2×C12711yescharacteristic, complemented
233#1689C2×C12711yescharacteristic, complemented
234#1688C2×C12711yescharacteristic, complemented
235#1687C2×C12711yescharacteristic, complemented
236#1686C2×C12712yescomplemented
237#1685C2×C12712yescomplemented
238#1568C2×C12711yescharacteristic, complemented
239#1553C2×C12712yescomplemented
240C127#1929411yescharacteristic, direct product factor, Sylow
241C2×#135—21no—
242C2×#135—21no—
243#532C22×C12712yes—
244C4×#41C22×C12711yescharacteristic
245#495—21no—
246#495—21no—
247#494C22×C12711yescharacteristic
248#493C22×C12711yescharacteristic
249#492C22×C12712yes—
250#482—22no—
251#475C22×C12712yes—
252#474C22×C12712yes—
253#460C22×C12712yes—
254#459C22×C12712yes—
255#449—22no—
256#446C22×C12711yescharacteristic
257#446C22×C12711yescharacteristic
258#442—22no—
259#440—22no—
260#436C22×C12711yescharacteristic
261#436C22×C12711yescharacteristic
262#435—21no—
263#435—21no—
264#432C22×C12712yes—
265#431—21no—
266#431C22×C12711yescharacteristic
267C4×M16—21no—
268C2×C4×C8C22×C12711yescharacteristic
269#335C22×C12712yes—
270#334C22×C12711yescharacteristic
271#334C22×C12711yescharacteristic
272#332C22×C12712yes—
273#332C22×C12712yes—
274#331C22×C12712yes—
275#331C22×C12712yes—
276C2×#41—22no—
277C2×#41D4×C12711yescharacteristic
278#135—44no—
279#135—44no—
280C2×Q16—21no—
281C2×Q16—21no—
282C2×SD16—22no—
283C2×SD16—22no—
284C2×SD16—22no—
285C2×D8—22no—
286C2×D8—21no—
287C2×D8—21no—
288C2×M16—21no—
289C2×M16—21no—
290C22×C8D4×C12711yescharacteristic
291C22×C8D4×C12711yescharacteristic
292C4⋊Q8C23×C12712yes—
293#127C23×C12712yes—
294#124—22no—
295#121—22no—
296#121—22no—
297C4×Q8D4×C12711yescharacteristic
298C4×Q8C23×C12711yescharacteristic
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—22no—
302C4×D4—22no—
303C4×D4D4×C12711yescharacteristic
304C4×D4C23×C12711yescharacteristic
305#117—21no—
306#117D4×C12711yescharacteristic
307C2×C42—21no—
308C2×C42C23×C12711yescharacteristic
309#107—22no—
310#106—22no—
311C4⋊C8—21no—
312C4⋊C8—21no—
313C4⋊C8C23×C12711yescharacteristic
314C4⋊C8C23×C12711yescharacteristic
315C4⋊C8C23×C12712yes—
316C4⋊C8C23×C12712yes—
317#103—22no—
318#102—22no—
319#102—22no—
320#102—22no—
321C22⋊C8—21no—
322C22⋊C8—22no—
323C22⋊C8—21no—
324C22⋊C8—21no—
325#97—21no—
326#97—21no—
327#97—22no—
328C4×C8—21no—
329C4×C8D4×C12711yescharacteristic
330C4×C8D4×C12711yescharacteristic
331C4×C8C23×C12711yescharacteristic
332C4×C8C23×C12711yescharacteristic
333#41—42no—
334#41—44no—
335#41—44no—
336C2×Q8—22no—
337C2×Q8C2×D4×C12711yescharacteristic
338C2×D4—21no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—42no—
343C2×D4C2×D4×C12711yescharacteristic
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—42no—
348C22×C4C2×D4×C12711yescharacteristic
349C22×C4C2×D4×C12711yescharacteristic
350C22×C4#41×C12711yescharacteristic
351Q16—42no—
352Q16—42no—
353SD16—44no—
354SD16—44no—
355SD16—44no—
356D8—42no—
357D8—44no—
358D8—42no—
359M16—42no—
360M16—42no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8C2×D4×C12711yescharacteristic
368C2×C8C2×D4×C12711yescharacteristic
369C2×C8C2×D4×C12711yescharacteristic
370C2×C8C2×D4×C12711yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4C2×D4×C12711yescharacteristic
376C4⋊C4C2×D4×C12711yescharacteristic
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—42no—
381C22⋊C4—42no—
382C42—21no—
383C42—21no—
384C42—21no—
385C42C2×D4×C12711yescharacteristic
386C42C2×D4×C12711yescharacteristic
387C42#41×C12711yescharacteristic
388C42C24×C12711yescharacteristic
389C23—21no—
390C23—42no—
391C23#121×C12711yescharacteristic
392Q8—22no—
393Q8—42no—
394Q8—42no—
395D4—22no—
396D4—42no—
397D4—42no—
398D4—42no—
399D4—42no—
400D4—42no—
401D4—82no—
402D4—84no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—84no—
416C2×C4#121×C12711yescharacteristic
417C2×C4#121×C12711yescharacteristic
418C2×C4#121×C12711yescharacteristic
419C2×C4C22×D4×C12711yescharacteristic
420C2×C4C22×D4×C12711yescharacteristic
421C2×C4C2×#41×C12711yescharacteristic
422C8—21no—
423C8—21no—
424C8—41no—
425C8—41no—
426C8—42no—
427C8—42no—
428C8AGL(1,ℤ/8)×C12712yes—
429C8AGL(1,ℤ/8)×C12712yes—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—82no—
437C22—82no—
438C22—82no—
439C22C2×#121×C12711yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—41no—
445C4—41no—
446C4—41no—
447C4—82no—
448C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
449C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
450C4#575×C12712yes—
451C2—41no—
452C2—81no—
453C2—162no—
454C2C127×#303811yescharacteristic
455C2C127×#305411yescharacteristic
456C2C127×#306711yescharacteristic
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×#3147C2semidirect
2. C127×#3115C2semidirect
3. C127×#2965C2semidirect
4. C127×#1690C2semidirect
5. C127×#1689C2semidirect
6. C127×#1688C2semidirect
7. C127×#1687C2semidirect
8. C127×#1686C2semidirect
9. C127×#1685C2semidirect
10. C127×#1568C2semidirect
11. C127×#1553C2semidirect
222. #19294C127direct (N × H)
229. #3147C2×C127semidirect
230. #3115C2×C127semidirect
231. #2965C2×C127semidirect
232. #1690C2×C127semidirect
233. #1689C2×C127semidirect
234. #1688C2×C127semidirect
235. #1687C2×C127semidirect
236. #1686C2×C127semidirect
237. #1685C2×C127semidirect
238. #1568C2×C127semidirect
239. #1553C2×C127semidirect
240. C127#19294direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31472
C127×#31152
C127×#29652
C127×#16902
C127×#16892
C127×#16882
C127×#16872
C127×#16862
C127×#16852
C127×#15682
C127×#15532
#19294127