Finite Group Databasebeta

← C127×#18534 #44582207

Subgroups — C127×#18534 #44582207

Order 32512.

1168 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C127C211yesmaximal, characteristic, complemented
2C127×#3141C211yesmaximal, characteristic, complemented
3C127×#3112C211yesmaximal, characteristic, complemented
4C127×#3109C211yesmaximal, characteristic
5C127×#1637C214yesmaximal, complemented
6C127×#1627C214yesmaximal, complemented
7C127×#1556C211yesmaximal, characteristic, complemented
8C127×#1491C211yesmaximal, characteristic, complemented
9C127×#1490C211yesmaximal, characteristic, complemented
10C23×Q8×C127—21no—
11D4×Q8×C127—22no—
12D4×Q8×C127—22no—
13D4×Q8×C127—22no—
14D4×Q8×C127C2214yes—
15#532×C127C2211yescharacteristic
16C2×C4⋊Q8×C127—21no—
17C2×C4⋊Q8×C127C2211yescharacteristic
18C2×C22⋊Q8×C127—21no—
19C2×C22⋊Q8×C127—22no—
20C2×C4×Q8×C127C2211yescharacteristic
21C2×C4×D4×C127—21no—
22C2×C4×D4×C127C2211yescharacteristic
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—22no—
45C22×Q8×C127—24no—
46C22×Q8×C127—24no—
47C22×Q8×C127—21no—
48C22×Q8×C127—48no—
49C22×Q8×C127D411yescharacteristic
50C22×D4×C127D411yescharacteristic
51C23×C4×C127—22no—
52C23×C4×C127—21no—
53C2×SD16×C127—22no—
54C2×D8×C127—22no—
55C2×M16×C127—21no—
56C4⋊Q8×C127—24no—
57C4⋊Q8×C127—24no—
58C4⋊Q8×C127—21no—
59C4⋊Q8×C127—21no—
60C4⋊Q8×C127D412yes—
61C4⋊Q8×C127C2311yescharacteristic
62C4⋊Q8×C127C2312yes—
63#127×C127C2311yescharacteristic
64#124×C127—21no—
65C22⋊Q8×C127—24no—
66C22⋊Q8×C127—28no—
67C22⋊Q8×C127—24no—
68C22⋊Q8×C127—28no—
69#121×C127—21no—
70#121×C127—21no—
71C4×Q8×C127—21no—
72C4×Q8×C127—21no—
73C4×Q8×C127D412yes—
74C4×Q8×C127C2312yes—
75C4×D4×C127—24no—
76C4×D4×C127—24no—
77C4×D4×C127—21no—
78C4×D4×C127—21no—
79C4×D4×C127—21no—
80C4×D4×C127—21no—
81C4×D4×C127D412yes—
82C4×D4×C127C2312yes—
83C2×C4⋊C4×C127—22no—
84C2×C4⋊C4×C127—21no—
85C2×C4⋊C4×C127—21no—
86C2×C4⋊C4×C127D411yescharacteristic
87C2×C4⋊C4×C127D411yescharacteristic
88C2×C4⋊C4×C127D412yes—
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—21no—
91C2×C42×C127—21no—
92C2×C42×C127C2311yescharacteristic
93#107×C127—22no—
94#106×C127—22no—
95C4⋊C8×C127C2312yes—
96C4⋊C8×C127C2312yes—
97#103×C127—22no—
98#103×C127—24no—
99#102×C127—22no—
100#102×C127—24no—
101#102×C127—22no—
102#102×C127—22no—
103C22⋊C8×C127—21no—
104C22⋊C8×C127—21no—
105#97×C127—21no—
106#97×C127—21no—
107#97×C127—21no—
108C4×C8×C127C2312yes—
109C24×C127—21no—
110#41×C127—44no—
111C2×Q8×C127—24no—
112C2×Q8×C127—28no—
113C2×Q8×C127—21no—
114C2×Q8×C127—22no—
115C2×Q8×C127—22no—
116C2×Q8×C127—21no—
117C2×Q8×C127—48no—
118C2×Q8×C127—44no—
119C2×Q8×C127—416no—
120C2×Q8×C127—48no—
121C2×Q8×C127—48no—
122C2×Q8×C127C2×D412yes—
123C2×D4×C127—24no—
124C2×D4×C127—21no—
125C2×D4×C127—21no—
126C2×D4×C127—21no—
127C2×D4×C127—21no—
128C2×D4×C127—41no—
129C2×D4×C127C2×D412yes—
130C22×C4×C127—21no—
131C22×C4×C127—28no—
132C22×C4×C127—21no—
133C22×C4×C127—22no—
134C22×C4×C127—21no—
135C22×C4×C127—22no—
136C22×C4×C127—22no—
137C22×C4×C127—48no—
138C22×C4×C127—44no—
139C22×C4×C127—41no—
140C22×C4×C127C2×D411yescharacteristic
141C22×C4×C127C2×D411yescharacteristic
142C22×C4×C127C2×D411yescharacteristic
143SD16×C127—44no—
144D8×C127—44no—
145M16×C127—42no—
146C2×C8×C127—22no—
147C2×C8×C127—22no—
148C2×C8×C127—22no—
149C4⋊C4×C127—28no—
150C4⋊C4×C127—22no—
151C4⋊C4×C127—22no—
152C4⋊C4×C127—21no—
153C4⋊C4×C127—21no—
154C4⋊C4×C127—22no—
155C4⋊C4×C127—22no—
156C4⋊C4×C127—22no—
157C4⋊C4×C127—21no—
158C4⋊C4×C127—21no—
159C4⋊C4×C127C2×D414yes—
160C4⋊C4×C127C2×D412yes—
161C4⋊C4×C127C2×D412yes—
162C22⋊C4×C127—28no—
163C22⋊C4×C127—22no—
164C22⋊C4×C127—22no—
165C22⋊C4×C127—41no—
166C22⋊C4×C127—41no—
167C42×C127—22no—
168C42×C127—22no—
169C42×C127C2×D411yescharacteristic
170C42×C127C2×D411yescharacteristic
171C42×C127C2×D411yescharacteristic
172C42×C127C2411yescharacteristic
173C23×C127—24no—
174C23×C127—22no—
175C23×C127—42no—
176C23×C127—42no—
177C23×C127—41no—
178C23×C127#12011yescharacteristic
179Q8×C127—24no—
180Q8×C127—22no—
181Q8×C127—416no—
182Q8×C127—44no—
183Q8×C127—42no—
184Q8×C127—44no—
185Q8×C127AGL(1,ℤ/8)14yes—
186D4×C127—24no—
187D4×C127—22no—
188D4×C127—42no—
189D4×C127—42no—
190D4×C127—42no—
191D4×C127—82no—
192D4×C127#13714yes—
193C2×C4×C127—24no—
194C2×C4×C127—22no—
195C2×C4×C127—22no—
196C2×C4×C127—22no—
197C2×C4×C127—22no—
198C2×C4×C127—22no—
199C2×C4×C127—24no—
200C2×C4×C127—22no—
201C2×C4×C127—416no—
202C2×C4×C127—44no—
203C2×C4×C127—44no—
204C2×C4×C127—42no—
205C2×C4×C127—42no—
206C2×C4×C127—44no—
207C2×C4×C127—41no—
208C2×C4×C127—82no—
209C2×C4×C127#12011yescharacteristic
210C2×C4×C127#12011yescharacteristic
211C2×C4×C127#12011yescharacteristic
212C2×C4×C127C22×D411yescharacteristic
213C2×C4×C127C22×D411yescharacteristic
214C2×C4×C127C22×D411yescharacteristic
215C8×C127—42no—
216C8×C127—42no—
217C8×C127—42no—
218C22×C127—21no—
219C22×C127—21no—
220C22×C127—24no—
221C22×C127—48no—
222C22×C127—42no—
223C22×C127—42no—
224C22×C127—81no—
225C22×C127—81no—
226C22×C127—81no—
227C22×C127#45412yes—
228C22×C127C2×#12011yescharacteristic
229C4×C127—24no—
230C4×C127—21no—
231C4×C127—21no—
232C4×C127—21no—
233C4×C127—21no—
234C4×C127—44no—
235C4×C127—42no—
236C4×C127—42no—
237C4×C127—81no—
238C4×C127C2×AGL(1,ℤ/8)12yes—
239C4×C127C2×#13712yes—
240#18534C12711yesmaximal, characteristic, direct product factor, Sylow
241C2×C127—22no—
242C2×C127—44no—
243C2×C127—161no—
244C2×C127#300311yescharacteristic
245C2×C127#300411yescharacteristic
246C2×C127C2×#45411yescharacteristic
247C2×D4×Q8C2×C12711yescharacteristic, complemented
248#3141C2×C12711yescharacteristic, complemented
249#3112C2×C12711yescharacteristic, complemented
250#3109C2×C12711yescharacteristic
251#1637C2×C12714yescomplemented
252#1627C2×C12714yescomplemented
253#1556C2×C12711yescharacteristic, complemented
254#1491C2×C12711yescharacteristic, complemented
255#1490C2×C12711yescharacteristic, complemented
256C127#1853411yescharacteristic, direct product factor, Sylow
257C23×Q8—21no—
258D4×Q8—22no—
259D4×Q8—22no—
260D4×Q8—22no—
261D4×Q8C22×C12714yes—
262#532C22×C12711yescharacteristic
263C2×C4⋊Q8—21no—
264C2×C4⋊Q8C22×C12711yescharacteristic
265C2×C22⋊Q8—21no—
266C2×C22⋊Q8—22no—
267C2×C4×Q8C22×C12711yescharacteristic
268C2×C4×D4—21no—
269C2×C4×D4C22×C12711yescharacteristic
270#489—22no—
271#487C22×C12712yescomplemented
272#486C22×C12712yescomplemented
273#481—21no—
274#480—21no—
275#477C22×C12712yescomplemented
276#476C22×C12712yes—
277#460C22×C12712yescomplemented
278#459C22×C12712yes—
279#448—21no—
280#447—21no—
281#442—22no—
282#440—22no—
283#432C22×C12711yescharacteristic
284#432C22×C12711yescharacteristic
285#417—22no—
286C4×M16C22×C12711yescharacteristic
287#332C22×C12714yescomplemented
288Q8⋊C8C22×C12714yescomplemented
289D4⋊C8C22×C12714yes—
290C2×#41—21no—
291C22×Q8—22no—
292C22×Q8—24no—
293C22×Q8—24no—
294C22×Q8—21no—
295C22×Q8—48no—
296C22×Q8D4×C12711yescharacteristic
297C22×D4D4×C12711yescharacteristic
298C23×C4—22no—
299C23×C4—21no—
300C2×SD16—22no—
301C2×D8—22no—
302C2×M16—21no—
303C4⋊Q8—24no—
304C4⋊Q8—24no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8D4×C12712yes—
308C4⋊Q8C23×C12711yescharacteristic
309C4⋊Q8C23×C12712yes—
310#127C23×C12711yescharacteristic
311#124—21no—
312C22⋊Q8—24no—
313C22⋊Q8—28no—
314C22⋊Q8—24no—
315C22⋊Q8—28no—
316#121—21no—
317#121—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8D4×C12712yes—
321C4×Q8C23×C12712yes—
322C4×D4—24no—
323C4×D4—24no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4D4×C12712yes—
329C4×D4C23×C12712yes—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4D4×C12711yescharacteristic
334C2×C4⋊C4D4×C12711yescharacteristic
335C2×C4⋊C4D4×C12712yes—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C42—21no—
339C2×C42C23×C12711yescharacteristic
340#107—22no—
341#106—22no—
342C4⋊C8C23×C12712yes—
343C4⋊C8C23×C12712yes—
344#103—22no—
345#103—24no—
346#102—22no—
347#102—24no—
348#102—22no—
349#102—22no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352#97—21no—
353#97—21no—
354#97—21no—
355C4×C8C23×C12712yes—
356C24—21no—
357#41—44no—
358C2×Q8—24no—
359C2×Q8—28no—
360C2×Q8—21no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—21no—
364C2×Q8—48no—
365C2×Q8—44no—
366C2×Q8—416no—
367C2×Q8—48no—
368C2×Q8—48no—
369C2×Q8C2×D4×C12712yes—
370C2×D4—24no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—41no—
376C2×D4C2×D4×C12712yes—
377C22×C4—21no—
378C22×C4—28no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—48no—
385C22×C4—44no—
386C22×C4—41no—
387C22×C4C2×D4×C12711yescharacteristic
388C22×C4C2×D4×C12711yescharacteristic
389C22×C4C2×D4×C12711yescharacteristic
390SD16—44no—
391D8—44no—
392M16—42no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C4⋊C4—28no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4C2×D4×C12714yes—
407C4⋊C4C2×D4×C12712yes—
408C4⋊C4C2×D4×C12712yes—
409C22⋊C4—28no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C42—22no—
415C42—22no—
416C42C2×D4×C12711yescharacteristic
417C42C2×D4×C12711yescharacteristic
418C42C2×D4×C12711yescharacteristic
419C42C24×C12711yescharacteristic
420C23—24no—
421C23—22no—
422C23—42no—
423C23—42no—
424C23—41no—
425C23#120×C12711yescharacteristic
426Q8—24no—
427Q8—22no—
428Q8—416no—
429Q8—44no—
430Q8—42no—
431Q8—44no—
432Q8AGL(1,ℤ/8)×C12714yes—
433D4—24no—
434D4—22no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—82no—
439D4#137×C12714yes—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—416no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—44no—
454C2×C4—41no—
455C2×C4—82no—
456C2×C4#120×C12711yescharacteristic
457C2×C4#120×C12711yescharacteristic
458C2×C4#120×C12711yescharacteristic
459C2×C4C22×D4×C12711yescharacteristic
460C2×C4C22×D4×C12711yescharacteristic
461C2×C4C22×D4×C12711yescharacteristic
462C8—42no—
463C8—42no—
464C8—42no—
465C22—21no—
466C22—21no—
467C22—24no—
468C22—48no—
469C22—42no—
470C22—42no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22#454×C12712yes—
475C22C2×#120×C12711yescharacteristic
476C4—24no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—44no—
482C4—42no—
483C4—42no—
484C4—81no—
485C4C2×AGL(1,ℤ/8)×C12712yes—
486C4C2×#137×C12712yes—
487C2—22no—
488C2—44no—
489C2—161no—
490C2C127×#300311yescharacteristic
491C2C127×#300411yescharacteristic
492C2C2×#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×D4×Q8×C127C2semidirect
2. C127×#3141C2semidirect
3. C127×#3112C2semidirect
5. C127×#1637C2semidirect
6. C127×#1627C2semidirect
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
240. #18534C127direct (N × H)
247. C2×D4×Q8C2×C127semidirect
248. #3141C2×C127semidirect
249. #3112C2×C127semidirect
251. #1637C2×C127semidirect
252. #1627C2×C127semidirect
253. #1556C2×C127semidirect
254. #1491C2×C127semidirect
255. #1490C2×C127semidirect
256. C127#18534direct (N × H)
271. #487C22×C127semidirect
272. #486C22×C127semidirect
275. #477C22×C127semidirect
277. #460C22×C127semidirect
287. #332C22×C127semidirect
288. Q8⋊C8C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1272
C127×#31412
C127×#31122
C127×#31092
C127×#16372
C127×#16272
C127×#15562
C127×#14912
C127×#14902
#18534127