Finite Group Databasebeta

← C127×#20934 #44584607

Subgroups — C127×#20934 #44584607

Order 32512.

2066 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D8×C127C211yesmaximal, characteristic
2C2×#518×C127C211yesmaximal, characteristic, complemented
3C2×#418×C127C211yesmaximal, characteristic, complemented
4C2×#418×C127C211yesmaximal, characteristic, complemented
5C127×#2309C211yesmaximal, characteristic, complemented
6C127×#1879C218yesmaximal, complemented
7C127×#1735C211yesmaximal, characteristic, complemented
8C127×#1729C211yesmaximal, characteristic, complemented
9C23×D4×C127C2211yescharacteristic
10C23×D4×C127C2211yescharacteristic
11C22×D8×C127—24no—
12C22×D8×C127—24no—
13C22×D8×C127C418yescomplemented
14C22×D8×C127C2214yes—
15C22×M16×C127C2211yescharacteristic
16C23×C8×C127C2211yescharacteristic
17#518×C127—24no—
18#518×C127—24no—
19C2×C4×D4×C127—22no—
20C2×C4×D4×C127C2214yescomplemented
21C2×#117×C127C2211yescharacteristic
22C2×#117×C127C2211yescharacteristic
23C2×#117×C127C2211yescharacteristic
24C22×C22⋊C4×C127—22no—
25#418×C127—24no—
26#418×C127—24no—
27C2×#102×C127C2214yescomplemented
28C2×#102×C127C2214yescomplemented
29#390×C127—22no—
30#390×C127C2214yescomplemented
31#379×C127—22no—
32#340×C127C2214yescomplemented
33#336×C127C2214yescomplemented
34C25×C127—21no—
35C25×C127—21no—
36C22×D4×C127—21no—
37C22×D4×C127—22no—
38C22×D4×C127—22no—
39C22×D4×C127—22no—
40C22×D4×C127—22no—
41C22×D4×C127—21no—
42C22×D4×C127—22no—
43C22×D4×C127—22no—
44C22×D4×C127—22no—
45C22×D4×C127—22no—
46C22×D4×C127C2×C414yes—
47C22×D4×C127C2×C414yescomplemented
48C22×D4×C127D414yes—
49C22×D4×C127D414yes—
50C22×D4×C127C2312yes—
51C22×D4×C127C2312yes—
52C23×C4×C127—24no—
53C23×C4×C127C2311yescharacteristic
54C2×D8×C127—232no—
55C2×D8×C127—28no—
56C2×D8×C127—28no—
57C2×D8×C127C2×C4116yescomplemented
58C2×M16×C127—22no—
59C2×M16×C127—22no—
60C2×M16×C127—22no—
61C22×C8×C127—22no—
62C22×C8×C127—22no—
63C22×C8×C127C2×C414yescomplemented
64C22×C8×C127C2312yes—
65C22×C8×C127C2312yes—
66C4×D4×C127—216no—
67C4×D4×C127—28no—
68C4×D4×C127—28no—
69#117×C127—22no—
70#117×C127—22no—
71#117×C127—22no—
72#117×C127—22no—
73#117×C127—22no—
74#117×C127D414yes—
75C2×C4⋊C4×C127D412yes—
76C2×C4⋊C4×C127C2312yes—
77C2×C4⋊C4×C127C2312yes—
78C2×C22⋊C4×C127—216no—
79C2×C22⋊C4×C127—21no—
80C2×C22⋊C4×C127—24no—
81C2×C22⋊C4×C127—21no—
82C2×C22⋊C4×C127—28no—
83C2×C22⋊C4×C127D412yes—
84C2×C42×C127—21no—
85C2×C42×C127—21no—
86C2×C42×C127C2312yes—
87#102×C127—28no—
88#102×C127—28no—
89C24×C127—22no—
90C24×C127—24no—
91C24×C127—24no—
92C24×C127—24no—
93C24×C127—22no—
94C24×C127—24no—
95C24×C127—42no—
96C24×C127—42no—
97C24×C127—84no—
98C24×C127—84no—
99C24×C127C2×D411yescharacteristic
100C2×D4×C127—28no—
101C2×D4×C127—28no—
102C2×D4×C127—24no—
103C2×D4×C127—28no—
104C2×D4×C127—24no—
105C2×D4×C127—24no—
106C2×D4×C127—28no—
107C2×D4×C127—24no—
108C2×D4×C127—28no—
109C2×D4×C127—22no—
110C2×D4×C127—22no—
111C2×D4×C127—22no—
112C2×D4×C127—22no—
113C2×D4×C127—22no—
114C2×D4×C127—22no—
115C2×D4×C127—22no—
116C2×D4×C127—22no—
117C2×D4×C127—42no—
118C2×D4×C127—44no—
119C2×D4×C127—42no—
120C2×D4×C127—44no—
121C2×D4×C127C22⋊C4116yescomplemented
122C2×D4×C127C22×C414yes—
123C2×D4×C127C22×C414yes—
124C2×D4×C127C2×D414yes—
125C2×D4×C127C2×D414yes—
126C22×C4×C127—22no—
127C22×C4×C127—216no—
128C22×C4×C127—22no—
129C22×C4×C127—88no—
130C22×C4×C127C22×C412yes—
131C22×C4×C127C2×D414yes—
132C22×C4×C127C2×D412yes—
133C22×C4×C127C2×D412yes—
134C22×C4×C127C2×D411yescharacteristic
135C22×C4×C127C2×D412yes—
136C22×C4×C127#4112yes—
137C22×C4×C127#4112yes—
138C22×C4×C127C2411yescharacteristic
139D8×C127—232no—
140M16×C127—44no—
141C2×C8×C127—28no—
142C2×C8×C127—22no—
143C2×C8×C127—22no—
144C2×C8×C127—22no—
145C2×C8×C127—22no—
146C2×C8×C127—22no—
147C2×C8×C127C22×C414yes—
148C4⋊C4×C127—24no—
149C4⋊C4×C127—22no—
150C4⋊C4×C127—22no—
151C4⋊C4×C127—22no—
152C4⋊C4×C127C2×D414yes—
153C22⋊C4×C127—216no—
154C22⋊C4×C127—24no—
155C22⋊C4×C127—24no—
156C22⋊C4×C127—42no—
157C22⋊C4×C127—88no—
158C42×C127—24no—
159C42×C127—22no—
160C42×C127—22no—
161C42×C127—42no—
162C23×C127—24no—
163C23×C127—24no—
164C23×C127—24no—
165C23×C127—24no—
166C23×C127—216no—
167C23×C127—24no—
168C23×C127—48no—
169C23×C127—42no—
170C23×C127—42no—
171C23×C127—48no—
172C23×C127—48no—
173C23×C127—88no—
174C23×C127—88no—
175C23×C127—88no—
176C23×C127—88no—
177C23×C127—88no—
178C23×C127—88no—
179C23×C127C4×D412yes—
180C23×C127#12012yes—
181C23×C127#12112yes—
182C23×C127C22×D411yescharacteristic
183D4×C127—24no—
184D4×C127—24no—
185D4×C127—24no—
186D4×C127—24no—
187D4×C127—24no—
188D4×C127—216no—
189D4×C127—42no—
190D4×C127—42no—
191D4×C127—48no—
192D4×C127C2×C22⋊C418yes—
193C2×C4×C127—24no—
194C2×C4×C127—24no—
195C2×C4×C127—28no—
196C2×C4×C127—44no—
197C2×C4×C127—42no—
198C2×C4×C127—44no—
199C2×C4×C127—816no—
200C2×C4×C127C2×C22⋊C414yes—
201C2×C4×C127C4×D414yes—
202C2×C4×C127C4×D412yes—
203C2×C4×C127#12012yes—
204C2×C4×C127#12114yes—
205C2×C4×C127#12112yes—
206C2×C4×C127#12314yes—
207C2×C4×C127C23×C411yescharacteristic
208C2×C4×C127C22×D411yescharacteristic
209C2×C4×C127C22×D411yescharacteristic
210C2×C4×C127C22×D411yescharacteristic
211C2×C4×C127C2×#4111yescharacteristic
212C2×C4×C127C2×#4111yescharacteristic
213C8×C127—24no—
214C8×C127—42no—
215C22×C127—24no—
216C22×C127—24no—
217C22×C127—24no—
218C22×C127—28no—
219C22×C127—48no—
220C22×C127—48no—
221C22×C127—48no—
222C22×C127—48no—
223C22×C127—44no—
224C22×C127—816no—
225C22×C127—816no—
226C22×C127—84no—
227C22×C127—84no—
228C22×C127#38614yes—
229C22×C127C2×C4×D411yescharacteristic
230C22×C127C2×#12011yescharacteristic
231C22×C127C2×#12111yescharacteristic
232C22×C127#57614yes—
233C4×C127—44no—
234C4×C127—44no—
235C4×C127—82no—
236C4×C127#38614yes—
237C4×C127C22×C22⋊C411yescharacteristic
238C4×C127C2×C4×D411yescharacteristic
239C4×C127C2×#12111yescharacteristic
240C4×C127C2×#12311yescharacteristic
241#20934C12711yesmaximal, characteristic, direct product factor, Sylow
242C2×C127—24no—
243C2×C127—48no—
244C2×C127—84no—
245C2×C127C2×#38611yescharacteristic
246C2×C127#294812yes—
247C2×C127#300812yes—
248C2×C127#304112yes—
249C23×D8C2×C12711yescharacteristic
250C2×#518C2×C12711yescharacteristic, complemented
251C2×#418C2×C12711yescharacteristic, complemented
252C2×#418C2×C12711yescharacteristic, complemented
253#2309C2×C12711yescharacteristic, complemented
254#1879C2×C12718yescomplemented
255#1735C2×C12711yescharacteristic, complemented
256#1729C2×C12711yescharacteristic, complemented
257C127#2093411yescharacteristic, direct product factor, Sylow
258C23×D4C22×C12711yescharacteristic
259C23×D4C22×C12711yescharacteristic
260C22×D8—24no—
261C22×D8—24no—
262C22×D8C4×C12718yescomplemented
263C22×D8C22×C12714yes—
264C22×M16C22×C12711yescharacteristic
265C23×C8C22×C12711yescharacteristic
266#518—24no—
267#518—24no—
268C2×C4×D4—22no—
269C2×C4×D4C22×C12714yescomplemented
270C2×#117C22×C12711yescharacteristic
271C2×#117C22×C12711yescharacteristic
272C2×#117C22×C12711yescharacteristic
273C22×C22⋊C4—22no—
274#418—24no—
275#418—24no—
276C2×#102C22×C12714yescomplemented
277C2×#102C22×C12714yescomplemented
278#390—22no—
279#390C22×C12714yescomplemented
280#379—22no—
281#340C22×C12714yescomplemented
282#336C22×C12714yescomplemented
283C25—21no—
284C25—21no—
285C22×D4—21no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—21no—
291C22×D4—22no—
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—22no—
295C22×D4C2×C4×C12714yes—
296C22×D4C2×C4×C12714yescomplemented
297C22×D4D4×C12714yes—
298C22×D4D4×C12714yes—
299C22×D4C23×C12712yes—
300C22×D4C23×C12712yes—
301C23×C4—24no—
302C23×C4C23×C12711yescharacteristic
303C2×D8—232no—
304C2×D8—28no—
305C2×D8—28no—
306C2×D8C2×C4×C127116yescomplemented
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8C2×C4×C12714yescomplemented
313C22×C8C23×C12712yes—
314C22×C8C23×C12712yes—
315C4×D4—216no—
316C4×D4—28no—
317C4×D4—28no—
318#117—22no—
319#117—22no—
320#117—22no—
321#117—22no—
322#117—22no—
323#117D4×C12714yes—
324C2×C4⋊C4D4×C12712yes—
325C2×C4⋊C4C23×C12712yes—
326C2×C4⋊C4C23×C12712yes—
327C2×C22⋊C4—216no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4D4×C12712yes—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42C23×C12712yes—
336#102—28no—
337#102—28no—
338C24—22no—
339C24—24no—
340C24—24no—
341C24—24no—
342C24—22no—
343C24—24no—
344C24—42no—
345C24—42no—
346C24—84no—
347C24—84no—
348C24C2×D4×C12711yescharacteristic
349C2×D4—28no—
350C2×D4—28no—
351C2×D4—24no—
352C2×D4—28no—
353C2×D4—24no—
354C2×D4—24no—
355C2×D4—28no—
356C2×D4—24no—
357C2×D4—28no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—42no—
367C2×D4—44no—
368C2×D4—42no—
369C2×D4—44no—
370C2×D4C22⋊C4×C127116yescomplemented
371C2×D4C22×C4×C12714yes—
372C2×D4C22×C4×C12714yes—
373C2×D4C2×D4×C12714yes—
374C2×D4C2×D4×C12714yes—
375C22×C4—22no—
376C22×C4—216no—
377C22×C4—22no—
378C22×C4—88no—
379C22×C4C22×C4×C12712yes—
380C22×C4C2×D4×C12714yes—
381C22×C4C2×D4×C12712yes—
382C22×C4C2×D4×C12712yes—
383C22×C4C2×D4×C12711yescharacteristic
384C22×C4C2×D4×C12712yes—
385C22×C4#41×C12712yes—
386C22×C4#41×C12712yes—
387C22×C4C24×C12711yescharacteristic
388D8—232no—
389M16—44no—
390C2×C8—28no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8C22×C4×C12714yes—
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4C2×D4×C12714yes—
402C22⋊C4—216no—
403C22⋊C4—24no—
404C22⋊C4—24no—
405C22⋊C4—42no—
406C22⋊C4—88no—
407C42—24no—
408C42—22no—
409C42—22no—
410C42—42no—
411C23—24no—
412C23—24no—
413C23—24no—
414C23—24no—
415C23—216no—
416C23—24no—
417C23—48no—
418C23—42no—
419C23—42no—
420C23—48no—
421C23—48no—
422C23—88no—
423C23—88no—
424C23—88no—
425C23—88no—
426C23—88no—
427C23—88no—
428C23C4×D4×C12712yes—
429C23#120×C12712yes—
430C23#121×C12712yes—
431C23C22×D4×C12711yescharacteristic
432D4—24no—
433D4—24no—
434D4—24no—
435D4—24no—
436D4—24no—
437D4—216no—
438D4—42no—
439D4—42no—
440D4—48no—
441D4C2×C22⋊C4×C12718yes—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—28no—
445C2×C4—44no—
446C2×C4—42no—
447C2×C4—44no—
448C2×C4—816no—
449C2×C4C2×C22⋊C4×C12714yes—
450C2×C4C4×D4×C12714yes—
451C2×C4C4×D4×C12712yes—
452C2×C4#120×C12712yes—
453C2×C4#121×C12714yes—
454C2×C4#121×C12712yes—
455C2×C4#123×C12714yes—
456C2×C4C23×C4×C12711yescharacteristic
457C2×C4C22×D4×C12711yescharacteristic
458C2×C4C22×D4×C12711yescharacteristic
459C2×C4C22×D4×C12711yescharacteristic
460C2×C4C2×#41×C12711yescharacteristic
461C2×C4C2×#41×C12711yescharacteristic
462C8—24no—
463C8—42no—
464C22—24no—
465C22—24no—
466C22—24no—
467C22—28no—
468C22—48no—
469C22—48no—
470C22—48no—
471C22—48no—
472C22—44no—
473C22—816no—
474C22—816no—
475C22—84no—
476C22—84no—
477C22#386×C12714yes—
478C22C2×C4×D4×C12711yescharacteristic
479C22C2×#120×C12711yescharacteristic
480C22C2×#121×C12711yescharacteristic
481C22#576×C12714yes—
482C4—44no—
483C4—44no—
484C4—82no—
485C4#386×C12714yes—
486C4C22×C22⋊C4×C12711yescharacteristic
487C4C2×C4×D4×C12711yescharacteristic
488C4C2×#121×C12711yescharacteristic
489C4C2×#123×C12711yescharacteristic
490C2—24no—
491C2—48no—
492C2—84no—
493C2C2×#386×C12711yescharacteristic
494C2C127×#294812yes—
495C2C127×#300812yes—
496C2C127×#304112yes—
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC23×D8×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×#117×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#518×C127C2semidirect
3. C2×#418×C127C2semidirect
4. C2×#418×C127C2semidirect
5. C127×#2309C2semidirect
6. C127×#1879C2semidirect
7. C127×#1735C2semidirect
8. C127×#1729C2semidirect
13. C22×D8×C127C4semidirect
20. C2×C4×D4×C127C22semidirect
27. C2×#102×C127C22semidirect
28. C2×#102×C127C22semidirect
30. #390×C127C22semidirect
32. #340×C127C22semidirect
33. #336×C127C22semidirect
47. C22×D4×C127C2×C4semidirect
57. C2×D8×C127C2×C4semidirect
63. C22×C8×C127C2×C4semidirect
121. C2×D4×C127C22⋊C4semidirect
241. #20934C127direct (N × H)
250. C2×#518C2×C127semidirect
251. C2×#418C2×C127semidirect
252. C2×#418C2×C127semidirect
253. #2309C2×C127semidirect
254. #1879C2×C127semidirect
255. #1735C2×C127semidirect
256. #1729C2×C127semidirect
257. C127#20934direct (N × H)
262. C22×D8C4×C127semidirect
269. C2×C4×D4C22×C127semidirect
276. C2×#102C22×C127semidirect
277. C2×#102C22×C127semidirect
279. #390C22×C127semidirect
281. #340C22×C127semidirect
282. #336C22×C127semidirect
296. C22×D4C2×C4×C127semidirect
306. C2×D8C2×C4×C127semidirect
312. C22×C8C2×C4×C127semidirect
370. C2×D4C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C23×D8×C1272
C2×#518×C1272
C2×#418×C1272
C127×#23092
C127×#18792
C127×#17352
C127×#17292
#20934127