Finite Group Databasebeta

← C127×#19564 #44583237

Subgroups — C127×#19564 #44583237

Order 32512.

626 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3255C211yesmaximal, characteristic, complemented
2C127×#3208C211yesmaximal, characteristic
3C127×#3208C211yesmaximal, characteristic
4C127×#2986C211yesmaximal, characteristic, complemented
5C127×#1702C212yesmaximal, complemented
6C127×#1686C212yesmaximal, complemented
7C127×#1682C212yesmaximal, complemented
8C127×#1666C212yesmaximal, complemented
9C127×#1574C211yesmaximal, characteristic, complemented
10C127×#1545C211yesmaximal, characteristic
11C127×#1544C211yesmaximal, characteristic, complemented
12#533×C127C2211yescharacteristic
13#533×C127C2211yescharacteristic
14C2×#127×C127C2211yescharacteristic
15#492×C127—21no—
16#492×C127C2212yes—
17#486×C127—21no—
18#486×C127C2212yes—
19#475×C127—21no—
20#475×C127C2212yescomplemented
21#470×C127—22no—
22#462×C127—21no—
23#462×C127C2212yescomplemented
24#460×C127—21no—
25#460×C127—21no—
26#460×C127C2212yes—
27#460×C127C2212yes—
28#450×C127—22no—
29#450×C127—22no—
30#446×C127—21no—
31#446×C127C2212yescomplemented
32C8×Q8×C127—21no—
33C8×Q8×C127C2212yescomplemented
34#433×C127—22no—
35#431×C127C2211yescharacteristic
36#431×C127C2211yescharacteristic
37#431×C127C2211yescharacteristic
38#423×C127C2211yescharacteristic
39#335×C127C2212yescomplemented
40#334×C127C2212yescomplemented
41#332×C127C2211yescharacteristic, complemented
42#332×C127C2211yescharacteristic, complemented
43#332×C127C2211yescharacteristic, complemented
44#332×C127C2211yescharacteristic, complemented
45#331×C127C2212yes—
46#331×C127C2212yes—
47C22×D4×C127—21no—
48C22×D4×C127—21no—
49C22×D4×C127—21no—
50C2×Q16×C127—22no—
51C2×SD16×C127—22no—
52C2×SD16×C127—22no—
53C2×SD16×C127—22no—
54C2×SD16×C127—22no—
55C2×M16×C127—21no—
56C4⋊Q8×C127D411yescharacteristic
57C4⋊Q8×C127D411yescharacteristic
58C4⋊Q8×C127C2311yescharacteristic
59C4⋊Q8×C127C2311yescharacteristic
60#127×C127—21no—
61#127×C127—21no—
62#127×C127—21no—
63#127×C127C2312yes—
64#125×C127—21no—
65#125×C127—21no—
66C22⋊Q8×C127—21no—
67C22⋊Q8×C127—21no—
68C22⋊Q8×C127—21no—
69C22⋊Q8×C127D412yes—
70C4×Q8×C127—21no—
71C4×Q8×C127—21no—
72C4×Q8×C127—21no—
73C4×Q8×C127C2312yes—
74#117×C127—21no—
75#117×C127—21no—
76C2×C42×C127C2311yescharacteristic
77#106×C127—22no—
78C4⋊C8×C127—22no—
79C4⋊C8×C127—22no—
80C4⋊C8×C127—21no—
81C4⋊C8×C127D411yescharacteristic
82C4⋊C8×C127D411yescharacteristic
83C4⋊C8×C127C2311yescharacteristic
84C4⋊C8×C127C2311yescharacteristic
85C4⋊C8×C127C2312yes—
86C4⋊C8×C127C2311yescharacteristic
87C4⋊C8×C127C2311yescharacteristic
88#103×C127—22no—
89#103×C127—22no—
90#102×C127—22no—
91#102×C127—22no—
92#102×C127—22no—
93#102×C127—22no—
94C22⋊C8×C127—21no—
95C22⋊C8×C127—21no—
96C22⋊C8×C127D412yes—
97#97×C127—22no—
98C4×C8×C127—22no—
99C4×C8×C127—21no—
100C4×C8×C127—21no—
101C4×C8×C127C2312yes—
102C24×C127—41no—
103C2×Q8×C127—21no—
104C2×Q8×C127—21no—
105C2×Q8×C127—21no—
106C2×Q8×C127C2×D412yes—
107C2×D4×C127—22no—
108C2×D4×C127—22no—
109C2×D4×C127—22no—
110C2×D4×C127—41no—
111C2×D4×C127—41no—
112C2×D4×C127—41no—
113C2×D4×C127—81no—
114C2×D4×C127—81no—
115C2×D4×C127—81no—
116C2×D4×C127—81no—
117C2×D4×C127—82no—
118C22×C4×C127C2×D411yescharacteristic
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127#4111yescharacteristic
121Q16×C127—82no—
122SD16×C127—82no—
123SD16×C127—82no—
124SD16×C127—82no—
125SD16×C127—82no—
126M16×C127—81no—
127C2×C8×C127—21no—
128C2×C8×C127—21no—
129C2×C8×C127—21no—
130C2×C8×C127—21no—
131C2×C8×C127—22no—
132C2×C8×C127C2×D412yes—
133C2×C8×C127C2×D412yes—
134C4⋊C4×C127—21no—
135C4⋊C4×C127—21no—
136C4⋊C4×C127—21no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—21no—
140C4⋊C4×C127—21no—
141C4⋊C4×C127—21no—
142C4⋊C4×C127—21no—
143C4⋊C4×C127—41no—
144C4⋊C4×C127—41no—
145C4⋊C4×C127C2×D412yes—
146C22⋊C4×C127—22no—
147C22⋊C4×C127—41no—
148C42×C127—22no—
149C42×C127—41no—
150C42×C127C2×D411yescharacteristic
151C42×C127C2×D411yescharacteristic
152C42×C127#4111yescharacteristic
153C42×C127C2411yescharacteristic
154C23×C127—42no—
155C23×C127—82no—
156C23×C127—82no—
157C23×C127—82no—
158C23×C127#12111yescharacteristic
159Q8×C127—22no—
160Q8×C127—22no—
161Q8×C127—42no—
162Q8×C127—41no—
163Q8×C127—41no—
164Q8×C127—41no—
165Q8×C127—41no—
166D4×C127—42no—
167D4×C127—42no—
168D4×C127—42no—
169D4×C127—42no—
170D4×C127—82no—
171D4×C127—82no—
172D4×C127—82no—
173D4×C127—82no—
174C2×C4×C127—21no—
175C2×C4×C127—21no—
176C2×C4×C127—21no—
177C2×C4×C127—21no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—41no—
182C2×C4×C127—41no—
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—41no—
193C8×C127—41no—
194C8×C127—41no—
195C8×C127—41no—
196C22×C127—21no—
197C22×C127—21no—
198C22×C127—21no—
199C22×C127—82no—
200C22×C127—82no—
201C22×C127—82no—
202C22×C127—164no—
203C22×C127C2×#12111yescharacteristic
204C4×C127—21no—
205C4×C127—21no—
206C4×C127—21no—
207C4×C127—42no—
208C4×C127—42no—
209C4×C127—81no—
210C4×C127—81no—
211C4×C127#47112yes—
212C4×C127#57611yescharacteristic
213C4×C127#57711yescharacteristic
214C4×C127#57711yescharacteristic
215C4×C127#57711yescharacteristic
216#19564C12711yesmaximal, characteristic, direct product factor, Sylow
217C2×C127—41no—
218C2×C127—162no—
219C2×C127#304311yescharacteristic
220C2×C127#306211yescharacteristic
221C2×C127C2×#47111yescharacteristic
222#3255C2×C12711yescharacteristic, complemented
223#3208C2×C12711yescharacteristic
224#3208C2×C12711yescharacteristic
225#2986C2×C12711yescharacteristic, complemented
226#1702C2×C12712yescomplemented
227#1686C2×C12712yescomplemented
228#1682C2×C12712yescomplemented
229#1666C2×C12712yescomplemented
230#1574C2×C12711yescharacteristic, complemented
231#1545C2×C12711yescharacteristic
232#1544C2×C12711yescharacteristic, complemented
233C127#1956411yescharacteristic, direct product factor, Sylow
234#533C22×C12711yescharacteristic
235#533C22×C12711yescharacteristic
236C2×#127C22×C12711yescharacteristic
237#492—21no—
238#492C22×C12712yes—
239#486—21no—
240#486C22×C12712yes—
241#475—21no—
242#475C22×C12712yescomplemented
243#470—22no—
244#462—21no—
245#462C22×C12712yescomplemented
246#460—21no—
247#460—21no—
248#460C22×C12712yes—
249#460C22×C12712yes—
250#450—22no—
251#450—22no—
252#446—21no—
253#446C22×C12712yescomplemented
254C8×Q8—21no—
255C8×Q8C22×C12712yescomplemented
256#433—22no—
257#431C22×C12711yescharacteristic
258#431C22×C12711yescharacteristic
259#431C22×C12711yescharacteristic
260#423C22×C12711yescharacteristic
261#335C22×C12712yescomplemented
262#334C22×C12712yescomplemented
263#332C22×C12711yescharacteristic, complemented
264#332C22×C12711yescharacteristic, complemented
265#332C22×C12711yescharacteristic, complemented
266#332C22×C12711yescharacteristic, complemented
267#331C22×C12712yes—
268#331C22×C12712yes—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272C2×Q16—22no—
273C2×SD16—22no—
274C2×SD16—22no—
275C2×SD16—22no—
276C2×SD16—22no—
277C2×M16—21no—
278C4⋊Q8D4×C12711yescharacteristic
279C4⋊Q8D4×C12711yescharacteristic
280C4⋊Q8C23×C12711yescharacteristic
281C4⋊Q8C23×C12711yescharacteristic
282#127—21no—
283#127—21no—
284#127—21no—
285#127C23×C12712yes—
286#125—21no—
287#125—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8D4×C12712yes—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8C23×C12712yes—
296#117—21no—
297#117—21no—
298C2×C42C23×C12711yescharacteristic
299#106—22no—
300C4⋊C8—22no—
301C4⋊C8—22no—
302C4⋊C8—21no—
303C4⋊C8D4×C12711yescharacteristic
304C4⋊C8D4×C12711yescharacteristic
305C4⋊C8C23×C12711yescharacteristic
306C4⋊C8C23×C12711yescharacteristic
307C4⋊C8C23×C12712yes—
308C4⋊C8C23×C12711yescharacteristic
309C4⋊C8C23×C12711yescharacteristic
310#103—22no—
311#103—22no—
312#102—22no—
313#102—22no—
314#102—22no—
315#102—22no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C22⋊C8D4×C12712yes—
319#97—22no—
320C4×C8—22no—
321C4×C8—21no—
322C4×C8—21no—
323C4×C8C23×C12712yes—
324C24—41no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8C2×D4×C12712yes—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—81no—
336C2×D4—81no—
337C2×D4—81no—
338C2×D4—81no—
339C2×D4—82no—
340C22×C4C2×D4×C12711yescharacteristic
341C22×C4C2×D4×C12711yescharacteristic
342C22×C4#41×C12711yescharacteristic
343Q16—82no—
344SD16—82no—
345SD16—82no—
346SD16—82no—
347SD16—82no—
348M16—81no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—22no—
354C2×C8C2×D4×C12712yes—
355C2×C8C2×D4×C12712yes—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4C2×D4×C12712yes—
368C22⋊C4—22no—
369C22⋊C4—41no—
370C42—22no—
371C42—41no—
372C42C2×D4×C12711yescharacteristic
373C42C2×D4×C12711yescharacteristic
374C42#41×C12711yescharacteristic
375C42C24×C12711yescharacteristic
376C23—42no—
377C23—82no—
378C23—82no—
379C23—82no—
380C23#121×C12711yescharacteristic
381Q8—22no—
382Q8—22no—
383Q8—42no—
384Q8—41no—
385Q8—41no—
386Q8—41no—
387Q8—41no—
388D4—42no—
389D4—42no—
390D4—42no—
391D4—42no—
392D4—82no—
393D4—82no—
394D4—82no—
395D4—82no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4#121×C12711yescharacteristic
406C2×C4#121×C12711yescharacteristic
407C2×C4#121×C12711yescharacteristic
408C2×C4C22×D4×C12711yescharacteristic
409C2×C4C22×D4×C12711yescharacteristic
410C2×C4C2×#41×C12711yescharacteristic
411C8—22no—
412C8—22no—
413C8—42no—
414C8—41no—
415C8—41no—
416C8—41no—
417C8—41no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—82no—
422C22—82no—
423C22—82no—
424C22—164no—
425C22C2×#121×C12711yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—42no—
430C4—42no—
431C4—81no—
432C4—81no—
433C4#471×C12712yes—
434C4#576×C12711yescharacteristic
435C4#577×C12711yescharacteristic
436C4#577×C12711yescharacteristic
437C4#577×C12711yescharacteristic
438C2—41no—
439C2—162no—
440C2C127×#304311yescharacteristic
441C2C127×#306211yescharacteristic
442C2C2×#471×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×#127×C127C22
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×#3255C2semidirect
4. C127×#2986C2semidirect
5. C127×#1702C2semidirect
6. C127×#1686C2semidirect
7. C127×#1682C2semidirect
8. C127×#1666C2semidirect
9. C127×#1574C2semidirect
11. C127×#1544C2semidirect
20. #475×C127C22semidirect
23. #462×C127C22semidirect
31. #446×C127C22semidirect
33. C8×Q8×C127C22semidirect
39. #335×C127C22semidirect
40. #334×C127C22semidirect
41. #332×C127C22semidirect
42. #332×C127C22semidirect
43. #332×C127C22semidirect
44. #332×C127C22semidirect
216. #19564C127direct (N × H)
222. #3255C2×C127semidirect
225. #2986C2×C127semidirect
226. #1702C2×C127semidirect
227. #1686C2×C127semidirect
228. #1682C2×C127semidirect
229. #1666C2×C127semidirect
230. #1574C2×C127semidirect
232. #1544C2×C127semidirect
233. C127#19564direct (N × H)
242. #475C22×C127semidirect
245. #462C22×C127semidirect
253. #446C22×C127semidirect
255. C8×Q8C22×C127semidirect
261. #335C22×C127semidirect
262. #334C22×C127semidirect
263. #332C22×C127semidirect
264. #332C22×C127semidirect
265. #332C22×C127semidirect
266. #332C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32552
C127×#32082
C127×#29862
C127×#17022
C127×#16862
C127×#16822
C127×#16662
C127×#15742
C127×#15452
C127×#15442
#19564127