Finite Group Databasebeta

← C127×#18536 #44582209

Subgroups — C127×#18536 #44582209

Order 32512.

940 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C127C211yesmaximal, characteristic, complemented
2C127×#3141C211yesmaximal, characteristic, complemented
3C127×#3112C211yesmaximal, characteristic, complemented
4C127×#3109C211yesmaximal, characteristic
5C127×#1638C214yesmaximal, complemented
6C127×#1628C214yesmaximal, complemented
7C127×#1556C211yesmaximal, characteristic, complemented
8C127×#1491C211yesmaximal, characteristic, complemented
9C127×#1490C211yesmaximal, characteristic, complemented
10#556×C127—22no—
11#556×C127—22no—
12#556×C127—22no—
13#556×C127C2214yes—
14#532×C127C2211yescharacteristic
15C2×C4⋊Q8×C127C2211yescharacteristic
16C2×#126×C127—22no—
17C2×#124×C127—21no—
18C2×C22⋊Q8×C127—21no—
19C2×C4×Q8×C127—21no—
20C2×C4×Q8×C127C2211yescharacteristic
21C2×C4×D4×C127C2211yescharacteristic
22C2×#117×C127—21no—
23#489×C127—22no—
24#487×C127C2212yescomplemented
25#486×C127C2212yescomplemented
26#481×C127—21no—
27#480×C127—21no—
28#477×C127C2212yescomplemented
29#476×C127C2212yes—
30#460×C127C2212yescomplemented
31#459×C127C2212yes—
32#448×C127—21no—
33#447×C127—21no—
34#442×C127—22no—
35#440×C127—22no—
36#432×C127C2211yescharacteristic
37#432×C127C2211yescharacteristic
38#417×C127—22no—
39C4×M16×C127C2211yescharacteristic
40#332×C127C2214yescomplemented
41Q8⋊C8×C127C2214yescomplemented
42D4⋊C8×C127C2214yes—
43C2×#41×C127—21no—
44C22×Q8×C127—21no—
45C22×Q8×C127D411yescharacteristic
46C22×D4×C127D411yescharacteristic
47C23×C4×C127—21no—
48C2×SD16×C127—22no—
49C2×D8×C127—22no—
50C2×M16×C127—21no—
51C4⋊Q8×C127—21no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127D412yes—
54C4⋊Q8×C127C2311yescharacteristic
55C4⋊Q8×C127C2312yes—
56#127×C127C2311yescharacteristic
57#126×C127—28no—
58#126×C127—28no—
59#124×C127—24no—
60#124×C127—24no—
61#124×C127—21no—
62C22⋊Q8×C127—24no—
63C22⋊Q8×C127—24no—
64#121×C127—21no—
65#121×C127—21no—
66C4×Q8×C127—24no—
67C4×Q8×C127—24no—
68C4×Q8×C127—21no—
69C4×Q8×C127—21no—
70C4×Q8×C127D412yes—
71C4×Q8×C127C2312yes—
72C4×D4×C127—21no—
73C4×D4×C127—21no—
74C4×D4×C127—21no—
75C4×D4×C127—21no—
76C4×D4×C127D412yes—
77C4×D4×C127C2312yes—
78#117×C127—24no—
79#117×C127—24no—
80C2×C4⋊C4×C127—22no—
81C2×C4⋊C4×C127—21no—
82C2×C4⋊C4×C127—21no—
83C2×C4⋊C4×C127D411yescharacteristic
84C2×C4⋊C4×C127D411yescharacteristic
85C2×C4⋊C4×C127D412yes—
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—22no—
88C2×C22⋊C4×C127—21no—
89C2×C42×C127—22no—
90C2×C42×C127—21no—
91C2×C42×C127C2311yescharacteristic
92#107×C127—22no—
93#106×C127—22no—
94C4⋊C8×C127C2312yes—
95C4⋊C8×C127C2312yes—
96#103×C127—22no—
97#103×C127—24no—
98#102×C127—22no—
99#102×C127—24no—
100#102×C127—22no—
101#102×C127—22no—
102C22⋊C8×C127—21no—
103C22⋊C8×C127—21no—
104#97×C127—21no—
105#97×C127—21no—
106#97×C127—21no—
107C4×C8×C127C2312yes—
108C24×C127—21no—
109#41×C127—44no—
110C2×Q8×C127—21no—
111C2×Q8×C127—22no—
112C2×Q8×C127—22no—
113C2×Q8×C127—21no—
114C2×Q8×C127—42no—
115C2×Q8×C127—44no—
116C2×Q8×C127C2×D412yes—
117C2×D4×C127—21no—
118C2×D4×C127—21no—
119C2×D4×C127—21no—
120C2×D4×C127—21no—
121C2×D4×C127—42no—
122C2×D4×C127—41no—
123C2×D4×C127C2×D412yes—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
130C22×C4×C127—44no—
131C22×C4×C127—41no—
132C22×C4×C127C2×D411yescharacteristic
133C22×C4×C127C2×D411yescharacteristic
134C22×C4×C127C2×D411yescharacteristic
135SD16×C127—44no—
136D8×C127—44no—
137M16×C127—42no—
138C2×C8×C127—22no—
139C2×C8×C127—22no—
140C2×C8×C127—22no—
141C4⋊C4×C127—28no—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—21no—
145C4⋊C4×C127—21no—
146C4⋊C4×C127—22no—
147C4⋊C4×C127—22no—
148C4⋊C4×C127—22no—
149C4⋊C4×C127—21no—
150C4⋊C4×C127—21no—
151C4⋊C4×C127C2×D414yes—
152C4⋊C4×C127C2×D412yes—
153C4⋊C4×C127C2×D412yes—
154C22⋊C4×C127—28no—
155C22⋊C4×C127—28no—
156C22⋊C4×C127—22no—
157C22⋊C4×C127—22no—
158C22⋊C4×C127—41no—
159C22⋊C4×C127—41no—
160C42×C127—28no—
161C42×C127—22no—
162C42×C127—22no—
163C42×C127C2×D411yescharacteristic
164C42×C127C2×D411yescharacteristic
165C42×C127C2×D411yescharacteristic
166C42×C127C2411yescharacteristic
167C23×C127—22no—
168C23×C127—42no—
169C23×C127—42no—
170C23×C127—42no—
171C23×C127—41no—
172C23×C127#12011yescharacteristic
173Q8×C127—22no—
174Q8×C127—22no—
175Q8×C127—42no—
176Q8×C127—44no—
177Q8×C127—42no—
178Q8×C127—44no—
179D4×C127—22no—
180D4×C127—22no—
181D4×C127—42no—
182D4×C127—42no—
183D4×C127—42no—
184D4×C127—42no—
185D4×C127—82no—
186C2×C4×C127—22no—
187C2×C4×C127—22no—
188C2×C4×C127—22no—
189C2×C4×C127—22no—
190C2×C4×C127—22no—
191C2×C4×C127—22no—
192C2×C4×C127—24no—
193C2×C4×C127—44no—
194C2×C4×C127—42no—
195C2×C4×C127—42no—
196C2×C4×C127—44no—
197C2×C4×C127—42no—
198C2×C4×C127—44no—
199C2×C4×C127—41no—
200C2×C4×C127—82no—
201C2×C4×C127#12011yescharacteristic
202C2×C4×C127#12011yescharacteristic
203C2×C4×C127#12011yescharacteristic
204C2×C4×C127C22×D411yescharacteristic
205C2×C4×C127C22×D411yescharacteristic
206C2×C4×C127C22×D411yescharacteristic
207C8×C127—42no—
208C8×C127—42no—
209C8×C127—42no—
210C22×C127—21no—
211C22×C127—21no—
212C22×C127—42no—
213C22×C127—42no—
214C22×C127—42no—
215C22×C127—84no—
216C22×C127—81no—
217C22×C127—81no—
218C22×C127—81no—
219C22×C127#45412yes—
220C22×C127C2×#12011yescharacteristic
221C4×C127—21no—
222C4×C127—21no—
223C4×C127—21no—
224C4×C127—21no—
225C4×C127—42no—
226C4×C127—42no—
227C4×C127—44no—
228C4×C127—42no—
229C4×C127—81no—
230C4×C127#57512yes—
231C4×C127#57512yes—
232#18536C12711yesmaximal, characteristic, direct product factor, Sylow
233C2×C127—22no—
234C2×C127—82no—
235C2×C127—161no—
236C2×C127#300511yescharacteristic
237C2×C127#300511yescharacteristic
238C2×C127C2×#45411yescharacteristic
239C2×#556C2×C12711yescharacteristic, complemented
240#3141C2×C12711yescharacteristic, complemented
241#3112C2×C12711yescharacteristic, complemented
242#3109C2×C12711yescharacteristic
243#1638C2×C12714yescomplemented
244#1628C2×C12714yescomplemented
245#1556C2×C12711yescharacteristic, complemented
246#1491C2×C12711yescharacteristic, complemented
247#1490C2×C12711yescharacteristic, complemented
248C127#1853611yescharacteristic, direct product factor, Sylow
249#556—22no—
250#556—22no—
251#556—22no—
252#556C22×C12714yes—
253#532C22×C12711yescharacteristic
254C2×C4⋊Q8C22×C12711yescharacteristic
255C2×#126—22no—
256C2×#124—21no—
257C2×C22⋊Q8—21no—
258C2×C4×Q8—21no—
259C2×C4×Q8C22×C12711yescharacteristic
260C2×C4×D4C22×C12711yescharacteristic
261C2×#117—21no—
262#489—22no—
263#487C22×C12712yescomplemented
264#486C22×C12712yescomplemented
265#481—21no—
266#480—21no—
267#477C22×C12712yescomplemented
268#476C22×C12712yes—
269#460C22×C12712yescomplemented
270#459C22×C12712yes—
271#448—21no—
272#447—21no—
273#442—22no—
274#440—22no—
275#432C22×C12711yescharacteristic
276#432C22×C12711yescharacteristic
277#417—22no—
278C4×M16C22×C12711yescharacteristic
279#332C22×C12714yescomplemented
280Q8⋊C8C22×C12714yescomplemented
281D4⋊C8C22×C12714yes—
282C2×#41—21no—
283C22×Q8—21no—
284C22×Q8D4×C12711yescharacteristic
285C22×D4D4×C12711yescharacteristic
286C23×C4—21no—
287C2×SD16—22no—
288C2×D8—22no—
289C2×M16—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8D4×C12712yes—
293C4⋊Q8C23×C12711yescharacteristic
294C4⋊Q8C23×C12712yes—
295#127C23×C12711yescharacteristic
296#126—28no—
297#126—28no—
298#124—24no—
299#124—24no—
300#124—21no—
301C22⋊Q8—24no—
302C22⋊Q8—24no—
303#121—21no—
304#121—21no—
305C4×Q8—24no—
306C4×Q8—24no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8D4×C12712yes—
310C4×Q8C23×C12712yes—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4D4×C12712yes—
316C4×D4C23×C12712yes—
317#117—24no—
318#117—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4D4×C12711yescharacteristic
323C2×C4⋊C4D4×C12711yescharacteristic
324C2×C4⋊C4D4×C12712yes—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—21no—
328C2×C42—22no—
329C2×C42—21no—
330C2×C42C23×C12711yescharacteristic
331#107—22no—
332#106—22no—
333C4⋊C8C23×C12712yes—
334C4⋊C8C23×C12712yes—
335#103—22no—
336#103—24no—
337#102—22no—
338#102—24no—
339#102—22no—
340#102—22no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343#97—21no—
344#97—21no—
345#97—21no—
346C4×C8C23×C12712yes—
347C24—21no—
348#41—44no—
349C2×Q8—21no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—21no—
353C2×Q8—42no—
354C2×Q8—44no—
355C2×Q8C2×D4×C12712yes—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—42no—
361C2×D4—41no—
362C2×D4C2×D4×C12712yes—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—44no—
370C22×C4—41no—
371C22×C4C2×D4×C12711yescharacteristic
372C22×C4C2×D4×C12711yescharacteristic
373C22×C4C2×D4×C12711yescharacteristic
374SD16—44no—
375D8—44no—
376M16—42no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C4⋊C4—28no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4C2×D4×C12714yes—
391C4⋊C4C2×D4×C12712yes—
392C4⋊C4C2×D4×C12712yes—
393C22⋊C4—28no—
394C22⋊C4—28no—
395C22⋊C4—22no—
396C22⋊C4—22no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C42—28no—
400C42—22no—
401C42—22no—
402C42C2×D4×C12711yescharacteristic
403C42C2×D4×C12711yescharacteristic
404C42C2×D4×C12711yescharacteristic
405C42C24×C12711yescharacteristic
406C23—22no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—41no—
411C23#120×C12711yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—42no—
415Q8—44no—
416Q8—42no—
417Q8—44no—
418D4—22no—
419D4—22no—
420D4—42no—
421D4—42no—
422D4—42no—
423D4—42no—
424D4—82no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—41no—
439C2×C4—82no—
440C2×C4#120×C12711yescharacteristic
441C2×C4#120×C12711yescharacteristic
442C2×C4#120×C12711yescharacteristic
443C2×C4C22×D4×C12711yescharacteristic
444C2×C4C22×D4×C12711yescharacteristic
445C2×C4C22×D4×C12711yescharacteristic
446C8—42no—
447C8—42no—
448C8—42no—
449C22—21no—
450C22—21no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22#454×C12712yes—
459C22C2×#120×C12711yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—42no—
465C4—42no—
466C4—44no—
467C4—42no—
468C4—81no—
469C4#575×C12712yes—
470C4#575×C12712yes—
471C2—22no—
472C2—82no—
473C2—161no—
474C2C127×#300511yescharacteristic
475C2C127×#300511yescharacteristic
476C2C2×#454×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3109C2
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×#556×C127C2semidirect
2. C127×#3141C2semidirect
3. C127×#3112C2semidirect
5. C127×#1638C2semidirect
6. C127×#1628C2semidirect
7. C127×#1556C2semidirect
8. C127×#1491C2semidirect
9. C127×#1490C2semidirect
24. #487×C127C22semidirect
25. #486×C127C22semidirect
28. #477×C127C22semidirect
30. #460×C127C22semidirect
40. #332×C127C22semidirect
41. Q8⋊C8×C127C22semidirect
232. #18536C127direct (N × H)
239. C2×#556C2×C127semidirect
240. #3141C2×C127semidirect
241. #3112C2×C127semidirect
243. #1638C2×C127semidirect
244. #1628C2×C127semidirect
245. #1556C2×C127semidirect
246. #1491C2×C127semidirect
247. #1490C2×C127semidirect
248. C127#18536direct (N × H)
263. #487C22×C127semidirect
264. #486C22×C127semidirect
267. #477C22×C127semidirect
269. #460C22×C127semidirect
279. #332C22×C127semidirect
280. Q8⋊C8C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#556×C1272
C127×#31412
C127×#31122
C127×#31092
C127×#16382
C127×#16282
C127×#15562
C127×#14912
C127×#14902
#18536127