Finite Group Databasebeta

← C127×#19301 #44582974

Subgroups — C127×#19301 #44582974

Order 32512.

732 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#486×C127C211yesmaximal, characteristic, complemented
2C127×#3039C211yesmaximal, characteristic, complemented
3C127×#3038C211yesmaximal, characteristic
4C127×#2965C211yesmaximal, characteristic, complemented
5C127×#1702C214yesmaximal, complemented
6C127×#1701C214yesmaximal, complemented
7C127×#1566C211yesmaximal, characteristic, complemented
8C127×#1546C211yesmaximal, characteristic, complemented
9C127×#1545C211yesmaximal, characteristic, complemented
10C2×#137×C127—21no—
11C2×AGL(1,ℤ/8)×C127—21no—
12C2×C4⋊Q8×C127C2211yescharacteristic
13C2×#127×C127C2211yescharacteristic
14C4×#41×C127C2211yescharacteristic
15#486×C127—21no—
16#486×C127—21no—
17#486×C127C2214yes—
18#462×C127—21no—
19#462×C127C2212yescomplemented
20#461×C127—21no—
21#461×C127C2212yescomplemented
22#460×C127—21no—
23#460×C127C2212yes—
24#459×C127—21no—
25#459×C127C2212yes—
26#446×C127C2212yescomplemented
27#436×C127C2212yescomplemented
28#435×C127—22no—
29#431×C127—21no—
30#431×C127C2211yescharacteristic
31#423×C127C2211yescharacteristic
32#423×C127C2211yescharacteristic
33#419×C127—21no—
34#418×C127—21no—
35C2×#102×C127—22no—
36C4×M16×C127—21no—
37C2×C4×C8×C127C2211yescharacteristic
38#334×C127C2214yescomplemented
39#332×C127C2214yescomplemented
40#331×C127C2214yes—
41C2×#41×C127D411yescharacteristic
42C22×Q8×C127—21no—
43C22×D4×C127—21no—
44C22×D4×C127—21no—
45C22×D4×C127—21no—
46#137×C127—44no—
47AGL(1,ℤ/8)×C127—44no—
48C2×Q16×C127—22no—
49C2×SD16×C127—22no—
50C2×SD16×C127—22no—
51C2×D8×C127—22no—
52C2×M16×C127—21no—
53C2×M16×C127—21no—
54C2×M16×C127—22no—
55C22×C8×C127D412yes—
56C4⋊Q8×C127—21no—
57C4⋊Q8×C127—21no—
58C4⋊Q8×C127—21no—
59C4⋊Q8×C127C2312yes—
60#127×C127—21no—
61#127×C127—21no—
62#127×C127—21no—
63#127×C127C2312yes—
64C4×Q8×C127D411yescharacteristic
65C4×Q8×C127C2311yescharacteristic
66C4×D4×C127—21no—
67C4×D4×C127—21no—
68C4×D4×C127D411yescharacteristic
69C4×D4×C127C2311yescharacteristic
70#117×C127—21no—
71#117×C127D411yescharacteristic
72C2×C4⋊C4×C127—21no—
73C2×C4⋊C4×C127—21no—
74C2×C42×C127—21no—
75C2×C42×C127C2311yescharacteristic
76C4⋊C8×C127—22no—
77C4⋊C8×C127—21no—
78C4⋊C8×C127—21no—
79C4⋊C8×C127C2312yes—
80C4⋊C8×C127C2312yes—
81C4⋊C8×C127C2312yes—
82#103×C127—22no—
83#103×C127—22no—
84#102×C127—24no—
85#102×C127—24no—
86#102×C127—22no—
87#102×C127—22no—
88C22⋊C8×C127—21no—
89C22⋊C8×C127—22no—
90#97×C127—22no—
91C4×C8×C127—21no—
92C4×C8×C127D411yescharacteristic
93C4×C8×C127D411yescharacteristic
94C4×C8×C127C2312yes—
95C24×C127—41no—
96#41×C127—22no—
97#41×C127—22no—
98C2×Q8×C127—22no—
99C2×Q8×C127—41no—
100C2×Q8×C127—42no—
101C2×Q8×C127—42no—
102C2×Q8×C127C2×D411yescharacteristic
103C2×D4×C127—21no—
104C2×D4×C127—22no—
105C2×D4×C127—22no—
106C2×D4×C127—22no—
107C2×D4×C127—44no—
108C2×D4×C127—41no—
109C2×D4×C127—41no—
110C2×D4×C127—41no—
111C2×D4×C127—42no—
112C2×D4×C127—42no—
113C2×D4×C127—82no—
114C2×D4×C127C2×D411yescharacteristic
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—41no—
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127C2×D411yescharacteristic
121C22×C4×C127#4111yescharacteristic
122Q16×C127—44no—
123SD16×C127—44no—
124SD16×C127—44no—
125D8×C127—44no—
126M16×C127—44no—
127M16×C127—42no—
128M16×C127—42no—
129C2×C8×C127—22no—
130C2×C8×C127—22no—
131C2×C8×C127—22no—
132C2×C8×C127—42no—
133C2×C8×C127C2×D412yes—
134C2×C8×C127C2×D412yes—
135C4⋊C4×C127—21no—
136C4⋊C4×C127—21no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—41no—
140C4⋊C4×C127—41no—
141C4⋊C4×C127C2×D411yescharacteristic
142C4⋊C4×C127C2×D411yescharacteristic
143C22⋊C4×C127—21no—
144C22⋊C4×C127—21no—
145C22⋊C4×C127—21no—
146C42×C127—21no—
147C42×C127—21no—
148C42×C127—21no—
149C42×C127C2×D411yescharacteristic
150C42×C127C2×D411yescharacteristic
151C42×C127#4111yescharacteristic
152C42×C127C2411yescharacteristic
153C23×C127—21no—
154C23×C127—42no—
155C23×C127—82no—
156C23×C127—82no—
157C23×C127—82no—
158C23×C127#12111yescharacteristic
159Q8×C127—21no—
160Q8×C127—21no—
161Q8×C127—42no—
162Q8×C127—42no—
163Q8×C127—82no—
164D4×C127—21no—
165D4×C127—21no—
166D4×C127—42no—
167D4×C127—42no—
168D4×C127—42no—
169D4×C127—44no—
170D4×C127—82no—
171D4×C127—82no—
172D4×C127—82no—
173D4×C127—82no—
174C2×C4×C127—22no—
175C2×C4×C127—22no—
176C2×C4×C127—21no—
177C2×C4×C127—21no—
178C2×C4×C127—21no—
179C2×C4×C127—42no—
180C2×C4×C127—42no—
181C2×C4×C127—42no—
182C2×C4×C127—42no—
183C2×C4×C127—82no—
184C2×C4×C127#12111yescharacteristic
185C2×C4×C127#12111yescharacteristic
186C2×C4×C127#12111yescharacteristic
187C2×C4×C127AGL(1,ℤ/8)12yes—
188C2×C4×C127AGL(1,ℤ/8)12yes—
189C2×C4×C127C22×D411yescharacteristic
190C2×C4×C127C22×D411yescharacteristic
191C2×C4×C127C2×#4111yescharacteristic
192C8×C127—22no—
193C8×C127—22no—
194C8×C127—42no—
195C8×C127—42no—
196C8×C127—42no—
197C22×C127—21no—
198C22×C127—21no—
199C22×C127—41no—
200C22×C127—41no—
201C22×C127—41no—
202C22×C127—82no—
203C22×C127—82no—
204C22×C127—82no—
205C22×C127—164no—
206C22×C127#46912yes—
207C22×C127C2×#12111yescharacteristic
208C4×C127—21no—
209C4×C127—21no—
210C4×C127—41no—
211C4×C127—41no—
212C4×C127—41no—
213C4×C127—82no—
214C4×C127#46912yes—
215C4×C127#47112yes—
216C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
217C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
218C4×C127#57512yes—
219#19301C12711yesmaximal, characteristic, direct product factor, Sylow
220C2×C127—22no—
221C2×C127—81no—
222C2×C127—162no—
223C2×C127#304011yescharacteristic
224C2×C127C2×#46911yescharacteristic
225C2×C127C2×#47111yescharacteristic
226C2×#486C2×C12711yescharacteristic, complemented
227#3039C2×C12711yescharacteristic, complemented
228#3038C2×C12711yescharacteristic
229#2965C2×C12711yescharacteristic, complemented
230#1702C2×C12714yescomplemented
231#1701C2×C12714yescomplemented
232#1566C2×C12711yescharacteristic, complemented
233#1546C2×C12711yescharacteristic, complemented
234#1545C2×C12711yescharacteristic, complemented
235C127#1930111yescharacteristic, direct product factor, Sylow
236C2×#137—21no—
237C2×AGL(1,ℤ/8)—21no—
238C2×C4⋊Q8C22×C12711yescharacteristic
239C2×#127C22×C12711yescharacteristic
240C4×#41C22×C12711yescharacteristic
241#486—21no—
242#486—21no—
243#486C22×C12714yes—
244#462—21no—
245#462C22×C12712yescomplemented
246#461—21no—
247#461C22×C12712yescomplemented
248#460—21no—
249#460C22×C12712yes—
250#459—21no—
251#459C22×C12712yes—
252#446C22×C12712yescomplemented
253#436C22×C12712yescomplemented
254#435—22no—
255#431—21no—
256#431C22×C12711yescharacteristic
257#423C22×C12711yescharacteristic
258#423C22×C12711yescharacteristic
259#419—21no—
260#418—21no—
261C2×#102—22no—
262C4×M16—21no—
263C2×C4×C8C22×C12711yescharacteristic
264#334C22×C12714yescomplemented
265#332C22×C12714yescomplemented
266#331C22×C12714yes—
267C2×#41D4×C12711yescharacteristic
268C22×Q8—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272#137—44no—
273AGL(1,ℤ/8)—44no—
274C2×Q16—22no—
275C2×SD16—22no—
276C2×SD16—22no—
277C2×D8—22no—
278C2×M16—21no—
279C2×M16—21no—
280C2×M16—22no—
281C22×C8D4×C12712yes—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8C23×C12712yes—
286#127—21no—
287#127—21no—
288#127—21no—
289#127C23×C12712yes—
290C4×Q8D4×C12711yescharacteristic
291C4×Q8C23×C12711yescharacteristic
292C4×D4—21no—
293C4×D4—21no—
294C4×D4D4×C12711yescharacteristic
295C4×D4C23×C12711yescharacteristic
296#117—21no—
297#117D4×C12711yescharacteristic
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C42—21no—
301C2×C42C23×C12711yescharacteristic
302C4⋊C8—22no—
303C4⋊C8—21no—
304C4⋊C8—21no—
305C4⋊C8C23×C12712yes—
306C4⋊C8C23×C12712yes—
307C4⋊C8C23×C12712yes—
308#103—22no—
309#103—22no—
310#102—24no—
311#102—24no—
312#102—22no—
313#102—22no—
314C22⋊C8—21no—
315C22⋊C8—22no—
316#97—22no—
317C4×C8—21no—
318C4×C8D4×C12711yescharacteristic
319C4×C8D4×C12711yescharacteristic
320C4×C8C23×C12712yes—
321C24—41no—
322#41—22no—
323#41—22no—
324C2×Q8—22no—
325C2×Q8—41no—
326C2×Q8—42no—
327C2×Q8—42no—
328C2×Q8C2×D4×C12711yescharacteristic
329C2×D4—21no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—44no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—42no—
338C2×D4—42no—
339C2×D4—82no—
340C2×D4C2×D4×C12711yescharacteristic
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—41no—
345C22×C4C2×D4×C12711yescharacteristic
346C22×C4C2×D4×C12711yescharacteristic
347C22×C4#41×C12711yescharacteristic
348Q16—44no—
349SD16—44no—
350SD16—44no—
351D8—44no—
352M16—44no—
353M16—42no—
354M16—42no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—42no—
359C2×C8C2×D4×C12712yes—
360C2×C8C2×D4×C12712yes—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4C2×D4×C12711yescharacteristic
368C4⋊C4C2×D4×C12711yescharacteristic
369C22⋊C4—21no—
370C22⋊C4—21no—
371C22⋊C4—21no—
372C42—21no—
373C42—21no—
374C42—21no—
375C42C2×D4×C12711yescharacteristic
376C42C2×D4×C12711yescharacteristic
377C42#41×C12711yescharacteristic
378C42C24×C12711yescharacteristic
379C23—21no—
380C23—42no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23#121×C12711yescharacteristic
385Q8—21no—
386Q8—21no—
387Q8—42no—
388Q8—42no—
389Q8—82no—
390D4—21no—
391D4—21no—
392D4—42no—
393D4—42no—
394D4—42no—
395D4—44no—
396D4—82no—
397D4—82no—
398D4—82no—
399D4—82no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—82no—
410C2×C4#121×C12711yescharacteristic
411C2×C4#121×C12711yescharacteristic
412C2×C4#121×C12711yescharacteristic
413C2×C4AGL(1,ℤ/8)×C12712yes—
414C2×C4AGL(1,ℤ/8)×C12712yes—
415C2×C4C22×D4×C12711yescharacteristic
416C2×C4C22×D4×C12711yescharacteristic
417C2×C4C2×#41×C12711yescharacteristic
418C8—22no—
419C8—22no—
420C8—42no—
421C8—42no—
422C8—42no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—82no—
429C22—82no—
430C22—82no—
431C22—164no—
432C22#469×C12712yes—
433C22C2×#121×C12711yescharacteristic
434C4—21no—
435C4—21no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—82no—
440C4#469×C12712yes—
441C4#471×C12712yes—
442C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
443C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
444C4#575×C12712yes—
445C2—22no—
446C2—81no—
447C2—162no—
448C2C127×#304011yescharacteristic
449C2C2×#469×C12711yescharacteristic
450C2C2×#471×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3038C2
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. C2×#486×C127C2semidirect
2. C127×#3039C2semidirect
4. C127×#2965C2semidirect
5. C127×#1702C2semidirect
6. C127×#1701C2semidirect
7. C127×#1566C2semidirect
8. C127×#1546C2semidirect
9. C127×#1545C2semidirect
19. #462×C127C22semidirect
21. #461×C127C22semidirect
26. #446×C127C22semidirect
27. #436×C127C22semidirect
38. #334×C127C22semidirect
39. #332×C127C22semidirect
219. #19301C127direct (N × H)
226. C2×#486C2×C127semidirect
227. #3039C2×C127semidirect
229. #2965C2×C127semidirect
230. #1702C2×C127semidirect
231. #1701C2×C127semidirect
232. #1566C2×C127semidirect
233. #1546C2×C127semidirect
234. #1545C2×C127semidirect
235. C127#19301direct (N × H)
245. #462C22×C127semidirect
247. #461C22×C127semidirect
252. #446C22×C127semidirect
253. #436C22×C127semidirect
264. #334C22×C127semidirect
265. #332C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#486×C1272
C127×#30392
C127×#30382
C127×#29652
C127×#17022
C127×#17012
C127×#15662
C127×#15462
C127×#15452
#19301127