Finite Group Databasebeta

← C127×#19266 #44582939

Subgroups — C127×#19266 #44582939

Order 32512.

786 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
1C2×#492×C127C211yesmaximal, characteristic, complemented
2C127×#3079C211yesmaximal, characteristic, complemented
3C127×#3038C211yesmaximal, characteristic
4C8×#41×C127C211yesmaximal, characteristic, complemented
5C127×#1666C214yesmaximal, complemented
6C127×#1665C214yesmaximal, complemented
7C127×#1566C211yesmaximal, characteristic, complemented
8C127×#1549C211yesmaximal, characteristic, complemented
9C127×#1545C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C127—21no—
11C22×SD16×C127—22no—
12C2×C4⋊Q8×C127C2211yescharacteristic
13C2×#127×C127C2211yescharacteristic
14C4×#41×C127C2211yescharacteristic
15#492×C127—21no—
16#492×C127—21no—
17#492×C127C2214yes—
18#477×C127—21no—
19#476×C127—21no—
20#475×C127C2212yescomplemented
21#474×C127C2212yescomplemented
22#460×C127—21no—
23#460×C127C2212yes—
24#459×C127—21no—
25#459×C127C2212yes—
26C8×Q8×C127C2212yescomplemented
27C8×D4×C127—22no—
28C8×D4×C127C2212yescomplemented
29#431×C127—21no—
30#431×C127C2211yescharacteristic
31#428×C127—21no—
32#423×C127C2211yescharacteristic
33#423×C127C2211yescharacteristic
34#418×C127—21no—
35#417×C127—21no—
36C2×C4×C8×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—
46AGL(1,ℤ/8)×C127—44no—
47C2×SD16×C127—22no—
48C2×SD16×C127—24no—
49C2×SD16×C127—24no—
50C2×SD16×C127—48no—
51C2×D8×C127—22no—
52C2×M16×C127—21no—
53C2×M16×C127—21no—
54C22×C8×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
76#107×C127—22no—
77#106×C127—22no—
78C4⋊C8×C127—22no—
79C4⋊C8×C127—21no—
80C4⋊C8×C127—21no—
81C4⋊C8×C127C2312yes—
82C4⋊C8×C127C2312yes—
83C4⋊C8×C127C2312yes—
84#103×C127—22no—
85#102×C127—22no—
86#102×C127—22no—
87#102×C127—22no—
88C22⋊C8×C127—21no—
89C22⋊C8×C127—22no—
90C4×C8×C127—22no—
91C4×C8×C127—21no—
92C4×C8×C127D411yescharacteristic
93C4×C8×C127D411yescharacteristic
94C4×C8×C127C2312yes—
95C24×C127—41no—
96#41×C127—22no—
97#41×C127SD1614yescomplemented
98C2×Q8×C127—22no—
99C2×Q8×C127—44no—
100C2×Q8×C127—41no—
101C2×Q8×C127C2×D411yescharacteristic
102C2×D4×C127—21no—
103C2×D4×C127—22no—
104C2×D4×C127—22no—
105C2×D4×C127—22no—
106C2×D4×C127—44no—
107C2×D4×C127—41no—
108C2×D4×C127—41no—
109C2×D4×C127—41no—
110C2×D4×C127—42no—
111C2×D4×C127—42no—
112C2×D4×C127—82no—
113C2×D4×C127C2×D411yescharacteristic
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—41no—
118C22×C4×C127C2×D411yescharacteristic
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127#4111yescharacteristic
121SD16×C127—48no—
122SD16×C127—44no—
123SD16×C127—48no—
124D8×C127—44no—
125M16×C127—42no—
126M16×C127—42no—
127C2×C8×C127—24no—
128C2×C8×C127—22no—
129C2×C8×C127—22no—
130C2×C8×C127—22no—
131C2×C8×C127—44no—
132C2×C8×C127C2×D412yes—
133C2×C8×C127C2×D412yes—
134C4⋊C4×C127—21no—
135C4⋊C4×C127—21no—
136C4⋊C4×C127—22no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—41no—
139C4⋊C4×C127—41no—
140C4⋊C4×C127C2×D411yescharacteristic
141C4⋊C4×C127C2×D411yescharacteristic
142C22⋊C4×C127—21no—
143C22⋊C4×C127—21no—
144C22⋊C4×C127—21no—
145C42×C127—21no—
146C42×C127—21no—
147C42×C127—21no—
148C42×C127C2×D411yescharacteristic
149C42×C127C2×D411yescharacteristic
150C42×C127#4111yescharacteristic
151C42×C127C2411yescharacteristic
152C23×C127—21no—
153C23×C127—42no—
154C23×C127—82no—
155C23×C127—82no—
156C23×C127—82no—
157C23×C127#12111yescharacteristic
158Q8×C127—21no—
159Q8×C127—44no—
160Q8×C127—82no—
161Q8×C127C2×SD1612yescomplemented
162D4×C127—24no—
163D4×C127—21no—
164D4×C127—42no—
165D4×C127—42no—
166D4×C127—44no—
167D4×C127—82no—
168D4×C127—82no—
169D4×C127—82no—
170D4×C127—82no—
171D4×C127C2×SD1612yescomplemented
172C2×C4×C127—21no—
173C2×C4×C127—22no—
174C2×C4×C127—24no—
175C2×C4×C127—22no—
176C2×C4×C127—21no—
177C2×C4×C127—21no—
178C2×C4×C127—42no—
179C2×C4×C127—42no—
180C2×C4×C127—42no—
181C2×C4×C127—82no—
182C2×C4×C127#12111yescharacteristic
183C2×C4×C127#12111yescharacteristic
184C2×C4×C127#12111yescharacteristic
185C2×C4×C127C2×SD1612yes—
186C2×C4×C127#13512yes—
187C2×C4×C127C22×D411yescharacteristic
188C2×C4×C127C22×D411yescharacteristic
189C2×C4×C127C2×#4111yescharacteristic
190C8×C127—22no—
191C8×C127—42no—
192C8×C127—42no—
193C8×C127—42no—
194C8×C127AGL(1,ℤ/8)14yescomplemented
195C22×C127—21no—
196C22×C127—21no—
197C22×C127—22no—
198C22×C127—41no—
199C22×C127—41no—
200C22×C127—82no—
201C22×C127—82no—
202C22×C127—82no—
203C22×C127—164no—
204C22×C127#46512yes—
205C22×C127C2×#12111yescharacteristic
206C4×C127—21no—
207C4×C127—22no—
208C4×C127—21no—
209C4×C127—41no—
210C4×C127—41no—
211C4×C127—82no—
212C4×C127#46512yes—
213C4×C127#47112yes—
214C4×C127C22×SD1611yescharacteristic
215C4×C127C2×#13511yescharacteristic
216C4×C127C2×AGL(1,ℤ/8)12yes—
217#19266C12711yesmaximal, characteristic, direct product factor, Sylow
218C2×C127—22no—
219C2×C127—42no—
220C2×C127—162no—
221C2×C127#303811yescharacteristic
222C2×C127C2×#46511yescharacteristic
223C2×C127C2×#47111yescharacteristic
224C2×#492C2×C12711yescharacteristic, complemented
225#3079C2×C12711yescharacteristic, complemented
226#3038C2×C12711yescharacteristic
227C8×#41C2×C12711yescharacteristic, complemented
228#1666C2×C12714yescomplemented
229#1665C2×C12714yescomplemented
230#1566C2×C12711yescharacteristic, complemented
231#1549C2×C12711yescharacteristic, complemented
232#1545C2×C12711yescharacteristic, complemented
233C127#1926611yescharacteristic, direct product factor, Sylow
234C2×AGL(1,ℤ/8)—21no—
235C22×SD16—22no—
236C2×C4⋊Q8C22×C12711yescharacteristic
237C2×#127C22×C12711yescharacteristic
238C4×#41C22×C12711yescharacteristic
239#492—21no—
240#492—21no—
241#492C22×C12714yes—
242#477—21no—
243#476—21no—
244#475C22×C12712yescomplemented
245#474C22×C12712yescomplemented
246#460—21no—
247#460C22×C12712yes—
248#459—21no—
249#459C22×C12712yes—
250C8×Q8C22×C12712yescomplemented
251C8×D4—22no—
252C8×D4C22×C12712yescomplemented
253#431—21no—
254#431C22×C12711yescharacteristic
255#428—21no—
256#423C22×C12711yescharacteristic
257#423C22×C12711yescharacteristic
258#418—21no—
259#417—21no—
260C2×C4×C8—21no—
261C2×C4×C8C22×C12711yescharacteristic
262#334C22×C12714yescomplemented
263#332C22×C12714yescomplemented
264#331C22×C12714yes—
265C2×#41D4×C12711yescharacteristic
266C22×Q8—21no—
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270AGL(1,ℤ/8)—44no—
271C2×SD16—22no—
272C2×SD16—24no—
273C2×SD16—24no—
274C2×SD16—48no—
275C2×D8—22no—
276C2×M16—21no—
277C2×M16—21no—
278C22×C8—22no—
279C22×C8D4×C12712yes—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8C23×C12712yes—
284#127—21no—
285#127—21no—
286#127—21no—
287#127C23×C12712yes—
288C4×Q8D4×C12711yescharacteristic
289C4×Q8C23×C12711yescharacteristic
290C4×D4—21no—
291C4×D4—21no—
292C4×D4D4×C12711yescharacteristic
293C4×D4C23×C12711yescharacteristic
294#117—21no—
295#117D4×C12711yescharacteristic
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C42—21no—
299C2×C42C23×C12711yescharacteristic
300#107—22no—
301#106—22no—
302C4⋊C8—22no—
303C4⋊C8—21no—
304C4⋊C8—21no—
305C4⋊C8C23×C12712yes—
306C4⋊C8C23×C12712yes—
307C4⋊C8C23×C12712yes—
308#103—22no—
309#102—22no—
310#102—22no—
311#102—22no—
312C22⋊C8—21no—
313C22⋊C8—22no—
314C4×C8—22no—
315C4×C8—21no—
316C4×C8D4×C12711yescharacteristic
317C4×C8D4×C12711yescharacteristic
318C4×C8C23×C12712yes—
319C24—41no—
320#41—22no—
321#41SD16×C12714yescomplemented
322C2×Q8—22no—
323C2×Q8—44no—
324C2×Q8—41no—
325C2×Q8C2×D4×C12711yescharacteristic
326C2×D4—21no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—44no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—82no—
337C2×D4C2×D4×C12711yescharacteristic
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—41no—
342C22×C4C2×D4×C12711yescharacteristic
343C22×C4C2×D4×C12711yescharacteristic
344C22×C4#41×C12711yescharacteristic
345SD16—48no—
346SD16—44no—
347SD16—48no—
348D8—44no—
349M16—42no—
350M16—42no—
351C2×C8—24no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—44no—
356C2×C8C2×D4×C12712yes—
357C2×C8C2×D4×C12712yes—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4C2×D4×C12711yescharacteristic
365C4⋊C4C2×D4×C12711yescharacteristic
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—21no—
369C42—21no—
370C42—21no—
371C42—21no—
372C42C2×D4×C12711yescharacteristic
373C42C2×D4×C12711yescharacteristic
374C42#41×C12711yescharacteristic
375C42C24×C12711yescharacteristic
376C23—21no—
377C23—42no—
378C23—82no—
379C23—82no—
380C23—82no—
381C23#121×C12711yescharacteristic
382Q8—21no—
383Q8—44no—
384Q8—82no—
385Q8C2×SD16×C12712yescomplemented
386D4—24no—
387D4—21no—
388D4—42no—
389D4—42no—
390D4—44no—
391D4—82no—
392D4—82no—
393D4—82no—
394D4—82no—
395D4C2×SD16×C12712yescomplemented
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—82no—
406C2×C4#121×C12711yescharacteristic
407C2×C4#121×C12711yescharacteristic
408C2×C4#121×C12711yescharacteristic
409C2×C4C2×SD16×C12712yes—
410C2×C4#135×C12712yes—
411C2×C4C22×D4×C12711yescharacteristic
412C2×C4C22×D4×C12711yescharacteristic
413C2×C4C2×#41×C12711yescharacteristic
414C8—22no—
415C8—42no—
416C8—42no—
417C8—42no—
418C8AGL(1,ℤ/8)×C12714yescomplemented
419C22—21no—
420C22—21no—
421C22—22no—
422C22—41no—
423C22—41no—
424C22—82no—
425C22—82no—
426C22—82no—
427C22—164no—
428C22#465×C12712yes—
429C22C2×#121×C12711yescharacteristic
430C4—21no—
431C4—22no—
432C4—21no—
433C4—41no—
434C4—41no—
435C4—82no—
436C4#465×C12712yes—
437C4#471×C12712yes—
438C4C22×SD16×C12711yescharacteristic
439C4C2×#135×C12711yescharacteristic
440C4C2×AGL(1,ℤ/8)×C12712yes—
441C2—22no—
442C2—42no—
443C2—162no—
444C2C127×#303811yescharacteristic
445C2C2×#465×C12711yescharacteristic
446C2C2×#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×#492×C127C2semidirect
2. C127×#3079C2semidirect
4. C8×#41×C127C2semidirect
5. C127×#1666C2semidirect
6. C127×#1665C2semidirect
7. C127×#1566C2semidirect
8. C127×#1549C2semidirect
9. C127×#1545C2semidirect
20. #475×C127C22semidirect
21. #474×C127C22semidirect
26. C8×Q8×C127C22semidirect
28. C8×D4×C127C22semidirect
38. #334×C127C22semidirect
39. #332×C127C22semidirect
97. #41×C127SD16semidirect
161. Q8×C127C2×SD16semidirect
171. D4×C127C2×SD16semidirect
194. C8×C127AGL(1,ℤ/8)semidirect
217. #19266C127direct (N × H)
224. C2×#492C2×C127semidirect
225. #3079C2×C127semidirect
227. C8×#41C2×C127semidirect
228. #1666C2×C127semidirect
229. #1665C2×C127semidirect
230. #1566C2×C127semidirect
231. #1549C2×C127semidirect
232. #1545C2×C127semidirect
233. C127#19266direct (N × H)
244. #475C22×C127semidirect
245. #474C22×C127semidirect
250. C8×Q8C22×C127semidirect
252. C8×D4C22×C127semidirect
262. #334C22×C127semidirect
263. #332C22×C127semidirect
321. #41SD16×C127semidirect
385. Q8C2×SD16×C127semidirect
395. D4C2×SD16×C127semidirect
418. C8AGL(1,ℤ/8)×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#492×C1272
C127×#30792
C127×#30382
C8×#41×C1272
C127×#16662
C127×#16652
C127×#15662
C127×#15492
C127×#15452
#19266127