Finite Group Databasebeta

← C127×#20679 #44584352

Subgroups — C127×#20679 #44584352

Order 32512.

1330 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#568×C127C211yesmaximal, characteristic
2C2×#430×C127C211yesmaximal, characteristic, complemented
3C2×#428×C127C211yesmaximal, characteristic, complemented
4C127×#2896C211yesmaximal, characteristic
5C2×#417×C127C211yesmaximal, characteristic
6C127×#1816C214yesmaximal, complemented
7C127×#1815C214yesmaximal, complemented
8C127×#1742C211yesmaximal, characteristic, complemented
9C2×#343×C127C211yesmaximal, characteristic, complemented
10C22×#41×C127C2211yescharacteristic
11#568×C127—24no—
12#568×C127C418yescomplemented
13C2×#131×C127—22no—
14C2×#131×C127C2214yes—
15C22×M16×C127—22no—
16C22×M16×C127C2211yescharacteristic
17C22×M16×C127C2211yescharacteristic
18C22×M16×C127C2211yescharacteristic
19C22×M16×C127C2211yescharacteristic
20C2×#117×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22#430×C127—24no—
23C2×#108×C127C2214yescomplemented
24#428×C127—22no—
25#428×C127—22no—
26C2×#107×C127C2212yescomplemented
27C2×#106×C127C2212yescomplemented
28#419×C127—21no—
29#418×C127—21no—
30#417×C127—22no—
31#417×C127C2212yes—
32#417×C127C2214yes—
33#417×C127C2212yes—
34#416×C127—22no—
35C2×#103×C127—21no—
36C2×#102×C127—21no—
37#343×C127C2212yescomplemented
38#343×C127C2214yescomplemented
39#343×C127C2212yescomplemented
40C2×#41×C127—21no—
41C2×#41×C127—22no—
42C2×#41×C127—21no—
43C2×#41×C127—22no—
44C2×#41×C127C2×C414yes—
45C2×#41×C127D412yes—
46C2×#41×C127Q814yes—
47C2×#41×C127C2312yes—
48C22×Q8×C127D411yescharacteristic
49C22×D4×C127—21no—
50C22×D4×C127D411yescharacteristic
51C23×C4×C127—21no—
52C23×C4×C127—21no—
53C23×C4×C127C2311yescharacteristic
54#131×C127—216no—
55#131×C127—28no—
56#131×C127C2×C4116yescomplemented
57C2×M16×C127—21no—
58C2×M16×C127—22no—
59C2×M16×C127—216no—
60C2×M16×C127—21no—
61C2×M16×C127—21no—
62C2×M16×C127—24no—
63C2×M16×C127—22no—
64C2×M16×C127—22no—
65C2×M16×C127—22no—
66C2×M16×C127—22no—
67C2×M16×C127C2×C414yes—
68C2×M16×C127C2×C414yes—
69C2×M16×C127D412yes—
70C2×M16×C127D412yes—
71C2×M16×C127D414yes—
72C2×M16×C127C2312yes—
73C2×M16×C127C2312yes—
74C2×M16×C127C2312yes—
75C22×C8×C127—21no—
76C22×C8×C127—24no—
77C22×C8×C127—21no—
78C22×C8×C127—21no—
79C22×C8×C127C2312yes—
80#117×C127—21no—
81#117×C127—21no—
82#117×C127—21no—
83#117×C127—21no—
84C2×C4⋊C4×C127—21no—
85C2×C4⋊C4×C127—21no—
86C2×C4⋊C4×C127—21no—
87C2×C4⋊C4×C127—21no—
88C2×C4⋊C4×C127—21no—
89C2×C4⋊C4×C127C2312yes—
90C2×C4⋊C4×C127C2311yescharacteristic
91C2×C4⋊C4×C127C2311yescharacteristic
92C2×C22⋊C4×C127—21no—
93C2×C42×C127—21no—
94#108×C127—28no—
95#107×C127—24no—
96#106×C127—24no—
97#103×C127—24no—
98#103×C127—22no—
99#103×C127—22no—
100#102×C127—24no—
101#102×C127—22no—
102#102×C127—22no—
103C24×C127—21no—
104C24×C127#4111yescharacteristic
105#41×C127—24no—
106#41×C127—24no—
107#41×C127—24no—
108#41×C127—24no—
109#41×C127—24no—
110#41×C127—22no—
111#41×C127—22no—
112#41×C127C4⋊C418yes—
113#41×C127C22×C414yes—
114#41×C127C2×Q814yes—
115C2×Q8×C127—21no—
116C2×Q8×C127—22no—
117C2×Q8×C127C4⋊C414yes—
118C2×Q8×C127C2×D412yes—
119C2×D4×C127—24no—
120C2×D4×C127—22no—
121C2×D4×C127—24no—
122C2×D4×C127—22no—
123C2×D4×C127—22no—
124C2×D4×C127—21no—
125C2×D4×C127C4⋊C414yes—
126C2×D4×C127C2×D412yes—
127C22×C4×C127—21no—
128C22×C4×C127—24no—
129C22×C4×C127—22no—
130C22×C4×C127—24no—
131C22×C4×C127—22no—
132C22×C4×C127—21no—
133C22×C4×C127—21no—
134C22×C4×C127—22no—
135C22×C4×C127—41no—
136C22×C4×C127—41no—
137C22×C4×C127—82no—
138C22×C4×C127C22×C412yes—
139C22×C4×C127C2×D412yes—
140C22×C4×C127C2×D411yescharacteristic
141C22×C4×C127C2×D411yescharacteristic
142C22×C4×C127C2×D411yescharacteristic
143C22×C4×C127C2×D411yescharacteristic
144C22×C4×C127C2×Q812yes—
145C22×C4×C127#4111yescharacteristic
146C22×C4×C127#4112yes—
147C22×C4×C127C2411yescharacteristic
148M16×C127—24no—
149M16×C127—22no—
150M16×C127—216no—
151M16×C127—22no—
152M16×C127—22no—
153M16×C127—22no—
154M16×C127—22no—
155M16×C127—42no—
156M16×C127—42no—
157M16×C127C22⋊C418yes—
158M16×C127C22⋊C418yes—
159M16×C127C22×C414yes—
160C2×C8×C127—24no—
161C2×C8×C127—22no—
162C2×C8×C127—216no—
163C2×C8×C127—22no—
164C2×C8×C127—22no—
165C2×C8×C127—42no—
166C2×C8×C127—42no—
167C2×C8×C127C22×C414yes—
168C2×C8×C127C2×D414yes—
169C2×C8×C127C2×D414yes—
170C4⋊C4×C127—22no—
171C4⋊C4×C127—21no—
172C4⋊C4×C127—21no—
173C4⋊C4×C127—21no—
174C4⋊C4×C127—22no—
175C4⋊C4×C127—21no—
176C4⋊C4×C127—41no—
177C4⋊C4×C127—41no—
178C22⋊C4×C127—41no—
179C22⋊C4×C127—41no—
180C42×C127—41no—
181C42×C127—41no—
182C23×C127—22no—
183C23×C127—24no—
184C23×C127—41no—
185C23×C127—41no—
186C23×C127—81no—
187C23×C127—81no—
188C23×C127#11712yes—
189C23×C127#12111yescharacteristic
190C23×C127#12111yescharacteristic
191C23×C127C22⋊Q812yes—
192C23×C127C2×#4111yescharacteristic
193Q8×C127—22no—
194Q8×C127—24no—
195Q8×C127C2×C4⋊C414yes—
196D4×C127—24no—
197D4×C127—24no—
198D4×C127—28no—
199D4×C127—22no—
200D4×C127—24no—
201D4×C127C2×C4⋊C414yes—
202C2×C4×C127—22no—
203C2×C4×C127—24no—
204C2×C4×C127—24no—
205C2×C4×C127—24no—
206C2×C4×C127—28no—
207C2×C4×C127—41no—
208C2×C4×C127—41no—
209C2×C4×C127—42no—
210C2×C4×C127—82no—
211C2×C4×C127—82no—
212C2×C4×C127—81no—
213C2×C4×C127—81no—
214C2×C4×C127—82no—
215C2×C4×C127C2×C22⋊C412yes—
216C2×C4×C127C2×C22⋊C412yes—
217C2×C4×C127C2×C4⋊C412yes—
218C2×C4×C127C2×C4⋊C412yes—
219C2×C4×C127#11712yes—
220C2×C4×C127#12112yes—
221C2×C4×C127#12112yes—
222C2×C4×C127#12111yescharacteristic
223C2×C4×C127#12111yescharacteristic
224C2×C4×C127C22⋊Q812yes—
225C2×C4×C127C22⋊Q812yes—
226C2×C4×C127C22⋊Q812yes—
227C2×C4×C127C23×C411yescharacteristic
228C2×C4×C127C22×D411yescharacteristic
229C2×C4×C127C22×D411yescharacteristic
230C2×C4×C127C22×D411yescharacteristic
231C2×C4×C127C22×Q811yescharacteristic
232C2×C4×C127C2×#4111yescharacteristic
233C8×C127—24no—
234C8×C127—42no—
235C8×C127—42no—
236C8×C127C2×C22⋊C418yes—
237C22×C127—21no—
238C22×C127—21no—
239C22×C127—21no—
240C22×C127—21no—
241C22×C127—21no—
242C22×C127—21no—
243C22×C127—24no—
244C22×C127—42no—
245C22×C127—42no—
246C22×C127—42no—
247C22×C127—42no—
248C22×C127—84no—
249C22×C127#38012yes—
250C22×C127#38012yes—
251C22×C127C2×#11711yescharacteristic
252C22×C127C2×#12111yescharacteristic
253C22×C127C2×C22⋊Q811yescharacteristic
254C4×C127—24no—
255C4×C127—81no—
256C4×C127—82no—
257C4×C127—81no—
258C4×C127#38012yes—
259C4×C127#38012yes—
260C4×C127C22×C22⋊C411yescharacteristic
261C4×C127C22×C4⋊C411yescharacteristic
262C4×C127C2×#12111yescharacteristic
263C4×C127C2×C22⋊Q811yescharacteristic
264#20679C12711yesmaximal, characteristic, direct product factor, Sylow
265C2×C127—22no—
266C2×C127—21no—
267C2×C127—21no—
268C2×C127—22no—
269C2×C127—44no—
270C2×C127C2×#38011yescharacteristic
271C2×C127#306811yescharacteristic
272C2×C127#306911yescharacteristic
273C2×#568C2×C12711yescharacteristic
274C2×#430C2×C12711yescharacteristic, complemented
275C2×#428C2×C12711yescharacteristic, complemented
276#2896C2×C12711yescharacteristic
277C2×#417C2×C12711yescharacteristic
278#1816C2×C12714yescomplemented
279#1815C2×C12714yescomplemented
280#1742C2×C12711yescharacteristic, complemented
281C2×#343C2×C12711yescharacteristic, complemented
282C127#2067911yescharacteristic, direct product factor, Sylow
283C22×#41C22×C12711yescharacteristic
284#568—24no—
285#568C4×C12718yescomplemented
286C2×#131—22no—
287C2×#131C22×C12714yes—
288C22×M16—22no—
289C22×M16C22×C12711yescharacteristic
290C22×M16C22×C12711yescharacteristic
291C22×M16C22×C12711yescharacteristic
292C22×M16C22×C12711yescharacteristic
293C2×#117C22×C12711yescharacteristic
294C22×C4⋊C4C22×C12711yescharacteristic
295#430—24no—
296C2×#108C22×C12714yescomplemented
297#428—22no—
298#428—22no—
299C2×#107C22×C12712yescomplemented
300C2×#106C22×C12712yescomplemented
301#419—21no—
302#418—21no—
303#417—22no—
304#417C22×C12712yes—
305#417C22×C12714yes—
306#417C22×C12712yes—
307#416—22no—
308C2×#103—21no—
309C2×#102—21no—
310#343C22×C12712yescomplemented
311#343C22×C12714yescomplemented
312#343C22×C12712yescomplemented
313C2×#41—21no—
314C2×#41—22no—
315C2×#41—21no—
316C2×#41—22no—
317C2×#41C2×C4×C12714yes—
318C2×#41D4×C12712yes—
319C2×#41Q8×C12714yes—
320C2×#41C23×C12712yes—
321C22×Q8D4×C12711yescharacteristic
322C22×D4—21no—
323C22×D4D4×C12711yescharacteristic
324C23×C4—21no—
325C23×C4—21no—
326C23×C4C23×C12711yescharacteristic
327#131—216no—
328#131—28no—
329#131C2×C4×C127116yescomplemented
330C2×M16—21no—
331C2×M16—22no—
332C2×M16—216no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—24no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16C2×C4×C12714yes—
341C2×M16C2×C4×C12714yes—
342C2×M16D4×C12712yes—
343C2×M16D4×C12712yes—
344C2×M16D4×C12714yes—
345C2×M16C23×C12712yes—
346C2×M16C23×C12712yes—
347C2×M16C23×C12712yes—
348C22×C8—21no—
349C22×C8—24no—
350C22×C8—21no—
351C22×C8—21no—
352C22×C8C23×C12712yes—
353#117—21no—
354#117—21no—
355#117—21no—
356#117—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4C23×C12712yes—
363C2×C4⋊C4C23×C12711yescharacteristic
364C2×C4⋊C4C23×C12711yescharacteristic
365C2×C22⋊C4—21no—
366C2×C42—21no—
367#108—28no—
368#107—24no—
369#106—24no—
370#103—24no—
371#103—22no—
372#103—22no—
373#102—24no—
374#102—22no—
375#102—22no—
376C24—21no—
377C24#41×C12711yescharacteristic
378#41—24no—
379#41—24no—
380#41—24no—
381#41—24no—
382#41—24no—
383#41—22no—
384#41—22no—
385#41C4⋊C4×C12718yes—
386#41C22×C4×C12714yes—
387#41C2×Q8×C12714yes—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8C4⋊C4×C12714yes—
391C2×Q8C2×D4×C12712yes—
392C2×D4—24no—
393C2×D4—22no—
394C2×D4—24no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—21no—
398C2×D4C4⋊C4×C12714yes—
399C2×D4C2×D4×C12712yes—
400C22×C4—21no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—82no—
411C22×C4C22×C4×C12712yes—
412C22×C4C2×D4×C12712yes—
413C22×C4C2×D4×C12711yescharacteristic
414C22×C4C2×D4×C12711yescharacteristic
415C22×C4C2×D4×C12711yescharacteristic
416C22×C4C2×D4×C12711yescharacteristic
417C22×C4C2×Q8×C12712yes—
418C22×C4#41×C12711yescharacteristic
419C22×C4#41×C12712yes—
420C22×C4C24×C12711yescharacteristic
421M16—24no—
422M16—22no—
423M16—216no—
424M16—22no—
425M16—22no—
426M16—22no—
427M16—22no—
428M16—42no—
429M16—42no—
430M16C22⋊C4×C12718yes—
431M16C22⋊C4×C12718yes—
432M16C22×C4×C12714yes—
433C2×C8—24no—
434C2×C8—22no—
435C2×C8—216no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—42no—
439C2×C8—42no—
440C2×C8C22×C4×C12714yes—
441C2×C8C2×D4×C12714yes—
442C2×C8C2×D4×C12714yes—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C42—41no—
454C42—41no—
455C23—22no—
456C23—24no—
457C23—41no—
458C23—41no—
459C23—81no—
460C23—81no—
461C23#117×C12712yes—
462C23#121×C12711yescharacteristic
463C23#121×C12711yescharacteristic
464C23C22⋊Q8×C12712yes—
465C23C2×#41×C12711yescharacteristic
466Q8—22no—
467Q8—24no—
468Q8C2×C4⋊C4×C12714yes—
469D4—24no—
470D4—24no—
471D4—28no—
472D4—22no—
473D4—24no—
474D4C2×C4⋊C4×C12714yes—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—28no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4—82no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4C2×C22⋊C4×C12712yes—
489C2×C4C2×C22⋊C4×C12712yes—
490C2×C4C2×C4⋊C4×C12712yes—
491C2×C4C2×C4⋊C4×C12712yes—
492C2×C4#117×C12712yes—
493C2×C4#121×C12712yes—
494C2×C4#121×C12712yes—
495C2×C4#121×C12711yescharacteristic
496C2×C4#121×C12711yescharacteristic
497C2×C4C22⋊Q8×C12712yes—
498C2×C4C22⋊Q8×C12712yes—
499C2×C4C22⋊Q8×C12712yes—
500C2×C4C23×C4×C12711yescharacteristic
501C2×C4C22×D4×C12711yescharacteristic
502C2×C4C22×D4×C12711yescharacteristic
503C2×C4C22×D4×C12711yescharacteristic
504C2×C4C22×Q8×C12711yescharacteristic
505C2×C4C2×#41×C12711yescharacteristic
506C8—24no—
507C8—42no—
508C8—42no—
509C8C2×C22⋊C4×C12718yes—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—24no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—84no—
522C22#380×C12712yes—
523C22#380×C12712yes—
524C22C2×#117×C12711yescharacteristic
525C22C2×#121×C12711yescharacteristic
526C22C2×C22⋊Q8×C12711yescharacteristic
527C4—24no—
528C4—82no—
529C4—81no—
530C4—81no—
531C4#380×C12712yes—
532C4#380×C12712yes—
533C4C22×C22⋊C4×C12711yescharacteristic
534C4C22×C4⋊C4×C12711yescharacteristic
535C4C2×#121×C12711yescharacteristic
536C4C2×C22⋊Q8×C12711yescharacteristic
537C2—22no—
538C2—21no—
539C2—21no—
540C2—22no—
541C2—44no—
542C2C2×#380×C12711yescharacteristic
543C2C127×#306811yescharacteristic
544C2C127×#306911yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×#41×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#430×C127C2semidirect
3. C2×#428×C127C2semidirect
6. C127×#1816C2semidirect
7. C127×#1815C2semidirect
8. C127×#1742C2semidirect
9. C2×#343×C127C2semidirect
12. #568×C127C4semidirect
23. C2×#108×C127C22semidirect
26. C2×#107×C127C22semidirect
27. C2×#106×C127C22semidirect
37. #343×C127C22semidirect
38. #343×C127C22semidirect
39. #343×C127C22semidirect
56. #131×C127C2×C4semidirect
264. #20679C127direct (N × H)
274. C2×#430C2×C127semidirect
275. C2×#428C2×C127semidirect
278. #1816C2×C127semidirect
279. #1815C2×C127semidirect
280. #1742C2×C127semidirect
281. C2×#343C2×C127semidirect
282. C127#20679direct (N × H)
285. #568C4×C127semidirect
296. C2×#108C22×C127semidirect
299. C2×#107C22×C127semidirect
300. C2×#106C22×C127semidirect
310. #343C22×C127semidirect
311. #343C22×C127semidirect
312. #343C22×C127semidirect
329. #131C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#568×C1272
C2×#430×C1272
C2×#428×C1272
C127×#28962
C2×#417×C1272
C127×#18162
C127×#18152
C127×#17422
C2×#343×C1272
#20679127