Finite Group Databasebeta

← C127×#21504 #44585177

Subgroups — C127×#21504 #44585177

Order 32512.

1092 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C127C211yesmaximal, characteristic
2C2×#440×C127C212yesmaximal
3C4×C4⋊Q8×C127C211yesmaximal, characteristic, complemented
4C42×D4×C127C211yesmaximal, characteristic
5C127×#1981C211yesmaximal, characteristic, complemented
6C127×#1947C211yesmaximal, characteristic, complemented
7C127×#1928C212yesmaximal, complemented
8C127×#1877C212yesmaximal
9C127×#1802C211yesmaximal, characteristic
10C127×#1767C211yesmaximal, characteristic, complemented
11C127×#1763C212yesmaximal, complemented
12C22×SD16×C127C2212yes—
13C2×C4⋊Q8×C127C2211yescharacteristic
14C2×C4×Q8×C127C2212yes—
15C2×C4×D4×C127C2211yescharacteristic
16C2×C4×D4×C127C2211yescharacteristic
17C2×C4×D4×C127C2211yescharacteristic
18C22×C42×C127—21no—
19#461×C127C418yescomplemented
20#440×C127—28no—
21C2×#107×C127C2212yes—
22C2×C4⋊C8×C127C2211yescharacteristic
23C2×C4⋊C8×C127C2211yescharacteristic
24C2×#103×C127C2212yes—
25C2×#103×C127C2212yes—
26C2×#103×C127C2212yes—
27C2×#102×C127C2212yes—
28C2×#97×C127C2212yes—
29#391×C127C2212yes—
30#389×C127—21no—
31#389×C127—21no—
32#384×C127C2211yescharacteristic
33C4×C4⋊C4×C127—21no—
34C4×C4⋊C4×C127—21no—
35C4×C4⋊C4×C127C2211yescharacteristic
36C4×C4⋊C4×C127C2211yescharacteristic
37C4×C4⋊C4×C127C2211yescharacteristic
38C4×C22⋊C4×C127—21no—
39C4×C22⋊C4×C127—21no—
40C4×C22⋊C4×C127—21no—
41C43×C127C2211yescharacteristic
42#340×C127C2212yes—
43#340×C127C2212yes—
44#336×C127C2212yes—
45C22×Q8×C127C2312yes—
46C22×D4×C127C2311yescharacteristic
47C23×C4×C127—21no—
48C23×C4×C127—21no—
49C23×C4×C127—21no—
50C2×SD16×C127—24no—
51C2×SD16×C127—24no—
52C2×SD16×C127C2×C418yes—
53C22×C8×C127C2312yes—
54C22×C8×C127C2312yes—
55C4⋊Q8×C127—22no—
56C4⋊Q8×C127C2×C414yescomplemented
57C4×Q8×C127—24no—
58C4×Q8×C127—24no—
59C4×D4×C127—22no—
60C4×D4×C127—22no—
61C4×D4×C127—22no—
62C4×D4×C127—22no—
63C4×D4×C127C2×C414yes—
64C4×D4×C127D414yes—
65C2×C4⋊C4×C127—21no—
66C2×C4⋊C4×C127—21no—
67C2×C4⋊C4×C127—22no—
68C2×C4⋊C4×C127—21no—
69C2×C4⋊C4×C127—21no—
70C2×C4⋊C4×C127C2312yes—
71C2×C4⋊C4×C127C2311yescharacteristic
72C2×C4⋊C4×C127C2311yescharacteristic
73C2×C4⋊C4×C127C2311yescharacteristic
74C2×C22⋊C4×C127—21no—
75C2×C22⋊C4×C127—21no—
76C2×C22⋊C4×C127—21no—
77C2×C42×C127—21no—
78C2×C42×C127—21no—
79C2×C42×C127—21no—
80C2×C42×C127—22no—
81C2×C42×C127—44no—
82C2×C42×C127D411yescharacteristic
83C2×C42×C127D411yescharacteristic
84C2×C42×C127D411yescharacteristic
85C2×C42×C127D411yescharacteristic
86C2×C42×C127C2311yescharacteristic
87C2×C42×C127C2311yescharacteristic
88C2×C42×C127C2311yescharacteristic
89#107×C127—24no—
90C4⋊C8×C127—22no—
91C4⋊C8×C127C2×C414yescomplemented
92#103×C127—24no—
93#103×C127—24no—
94#103×C127C2×C418yescomplemented
95#102×C127—24no—
96#97×C127—24no—
97#95×C127—21no—
98#95×C127—21no—
99#95×C127—21no—
100#95×C127—22no—
101#95×C127—22no—
102C24×C127—21no—
103C2×Q8×C127—22no—
104C2×Q8×C127—22no—
105C2×Q8×C127—22no—
106C2×Q8×C127—22no—
107C2×Q8×C127—22no—
108C2×Q8×C127C22×C414yes—
109C2×D4×C127—21no—
110C2×D4×C127—21no—
111C2×D4×C127—21no—
112C2×D4×C127C22×C412yes—
113C2×D4×C127C2×D412yes—
114C2×D4×C127#4112yes—
115C22×C4×C127—24no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—21no—
119C22×C4×C127—22no—
120C22×C4×C127—24no—
121C22×C4×C127—24no—
122C22×C4×C127—22no—
123C22×C4×C127—42no—
124C22×C4×C127—42no—
125C22×C4×C127—42no—
126C22×C4×C127—42no—
127C22×C4×C127—42no—
128C22×C4×C127—42no—
129C22×C4×C127C2×D411yescharacteristic
130C22×C4×C127C2×D411yescharacteristic
131C22×C4×C127C2×D411yescharacteristic
132C22×C4×C127C2×D411yescharacteristic
133C22×C4×C127C2×D411yescharacteristic
134C22×C4×C127C2×D411yescharacteristic
135C22×C4×C127C2411yescharacteristic
136SD16×C127—216no—
137C2×C8×C127—22no—
138C2×C8×C127—22no—
139C2×C8×C127—22no—
140C2×C8×C127—22no—
141C2×C8×C127—22no—
142C2×C8×C127C22×C414yes—
143C4⋊C4×C127—24no—
144C4⋊C4×C127—24no—
145C4⋊C4×C127—21no—
146C4⋊C4×C127—21no—
147C4⋊C4×C127—21no—
148C4⋊C4×C127—22no—
149C4⋊C4×C127—22no—
150C4⋊C4×C127—42no—
151C4⋊C4×C127—44no—
152C4⋊C4×C127—42no—
153C4⋊C4×C127C22×C412yes—
154C4⋊C4×C127C2×D412yes—
155C4⋊C4×C127#4112yes—
156C22⋊C4×C127—24no—
157C22⋊C4×C127—24no—
158C22⋊C4×C127—24no—
159C42×C127—22no—
160C42×C127—22no—
161C42×C127—22no—
162C42×C127—21no—
163C42×C127—21no—
164C42×C127—41no—
165C42×C127—42no—
166C42×C127—42no—
167C42×C127—44no—
168C42×C127—42no—
169C42×C127C22×C412yes—
170C42×C127C2×D412yes—
171C42×C127#4112yes—
172C42×C127#4112yes—
173C23×C127—22no—
174C23×C127—22no—
175C23×C127—22no—
176C23×C127—41no—
177C23×C127—41no—
178C23×C127—41no—
179C23×C127—41no—
180C23×C127C22×D411yescharacteristic
181Q8×C127—24no—
182Q8×C127—24no—
183Q8×C127—42no—
184Q8×C127—42no—
185D4×C127—22no—
186D4×C127—22no—
187D4×C127—22no—
188D4×C127C4×D414yes—
189C2×C4×C127—21no—
190C2×C4×C127—21no—
191C2×C4×C127—21no—
192C2×C4×C127—21no—
193C2×C4×C127—21no—
194C2×C4×C127—21no—
195C2×C4×C127—21no—
196C2×C4×C127—21no—
197C2×C4×C127—22no—
198C2×C4×C127—24no—
199C2×C4×C127—22no—
200C2×C4×C127—21no—
201C2×C4×C127—22no—
202C2×C4×C127—21no—
203C2×C4×C127—21no—
204C2×C4×C127—48no—
205C2×C4×C127—48no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—41no—
209C2×C4×C127—41no—
210C2×C4×C127—41no—
211C2×C4×C127—41no—
212C2×C4×C127—41no—
213C2×C4×C127—41no—
214C2×C4×C127—48no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—42no—
218C2×C4×C127C4×D412yes—
219C2×C4×C127C4×D412yes—
220C2×C4×C127#12112yes—
221C2×C4×C127#12112yes—
222C2×C4×C127AGL(1,ℤ/8)12yes—
223C2×C4×C127#13712yes—
224C2×C4×C127#13712yes—
225C2×C4×C127C23×C411yescharacteristic
226C2×C4×C127C22×D411yescharacteristic
227C2×C4×C127C2×#4111yescharacteristic
228C2×C4×C127C2×#4111yescharacteristic
229C2×C4×C127C2×#4111yescharacteristic
230C2×C4×C127C2×#4111yescharacteristic
231C8×C127—24no—
232C8×C127—42no—
233C22×C127—24no—
234C22×C127—42no—
235C22×C127—42no—
236C22×C127—42no—
237C22×C127—42no—
238C22×C127—42no—
239C22×C127—42no—
240C22×C127C2×C4×D411yescharacteristic
241C22×C127C2×#12111yescharacteristic
242C22×C127#52511yescharacteristic
243C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
244C22×C127C2×#13711yescharacteristic
245C22×C127C2×#13711yescharacteristic
246C22×C127#57511yescharacteristic
247C4×C127—22no—
248C4×C127—22no—
249C4×C127—22no—
250C4×C127—22no—
251C4×C127—42no—
252C4×C127—41no—
253C4×C127—42no—
254C4×C127—42no—
255C4×C127—44no—
256C4×C127—82no—
257C4×C127#44014yescomplemented
258C4×C127C2×C4×D411yescharacteristic
259C4×C127C4×#4111yescharacteristic
260C4×C127#52911yescharacteristic
261C4×C127#53211yescharacteristic
262#21504C12711yesmaximal, characteristic, direct product factor, Sylow
263C2×C127—44no—
264C2×C127C4×#12111yescharacteristic
265C2×C127C2×#44011yescharacteristic
266C2×C127C4×#13711yescharacteristic
267C2×C127#303611yescharacteristic
268C2×C127#303911yescharacteristic
269C2×C127#311011yescharacteristic
270C2×C127#311611yescharacteristic
271C2×#461C2×C12711yescharacteristic
272C2×#440C2×C12712yes—
273C4×C4⋊Q8C2×C12711yescharacteristic, complemented
274C42×D4C2×C12711yescharacteristic
275#1981C2×C12711yescharacteristic, complemented
276#1947C2×C12711yescharacteristic, complemented
277#1928C2×C12712yescomplemented
278#1877C2×C12712yes—
279#1802C2×C12711yescharacteristic
280#1767C2×C12711yescharacteristic, complemented
281#1763C2×C12712yescomplemented
282C127#2150411yescharacteristic, direct product factor, Sylow
283C22×SD16C22×C12712yes—
284C2×C4⋊Q8C22×C12711yescharacteristic
285C2×C4×Q8C22×C12712yes—
286C2×C4×D4C22×C12711yescharacteristic
287C2×C4×D4C22×C12711yescharacteristic
288C2×C4×D4C22×C12711yescharacteristic
289C22×C42—21no—
290#461C4×C12718yescomplemented
291#440—28no—
292C2×#107C22×C12712yes—
293C2×C4⋊C8C22×C12711yescharacteristic
294C2×C4⋊C8C22×C12711yescharacteristic
295C2×#103C22×C12712yes—
296C2×#103C22×C12712yes—
297C2×#103C22×C12712yes—
298C2×#102C22×C12712yes—
299C2×#97C22×C12712yes—
300#391C22×C12712yes—
301#389—21no—
302#389—21no—
303#384C22×C12711yescharacteristic
304C4×C4⋊C4—21no—
305C4×C4⋊C4—21no—
306C4×C4⋊C4C22×C12711yescharacteristic
307C4×C4⋊C4C22×C12711yescharacteristic
308C4×C4⋊C4C22×C12711yescharacteristic
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311C4×C22⋊C4—21no—
312C43C22×C12711yescharacteristic
313#340C22×C12712yes—
314#340C22×C12712yes—
315#336C22×C12712yes—
316C22×Q8C23×C12712yes—
317C22×D4C23×C12711yescharacteristic
318C23×C4—21no—
319C23×C4—21no—
320C23×C4—21no—
321C2×SD16—24no—
322C2×SD16—24no—
323C2×SD16C2×C4×C12718yes—
324C22×C8C23×C12712yes—
325C22×C8C23×C12712yes—
326C4⋊Q8—22no—
327C4⋊Q8C2×C4×C12714yescomplemented
328C4×Q8—24no—
329C4×Q8—24no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4C2×C4×C12714yes—
335C4×D4D4×C12714yes—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4C23×C12712yes—
342C2×C4⋊C4C23×C12711yescharacteristic
343C2×C4⋊C4C23×C12711yescharacteristic
344C2×C4⋊C4C23×C12711yescharacteristic
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C42—22no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—44no—
353C2×C42D4×C12711yescharacteristic
354C2×C42D4×C12711yescharacteristic
355C2×C42D4×C12711yescharacteristic
356C2×C42D4×C12711yescharacteristic
357C2×C42C23×C12711yescharacteristic
358C2×C42C23×C12711yescharacteristic
359C2×C42C23×C12711yescharacteristic
360#107—24no—
361C4⋊C8—22no—
362C4⋊C8C2×C4×C12714yescomplemented
363#103—24no—
364#103—24no—
365#103C2×C4×C12718yescomplemented
366#102—24no—
367#97—24no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—22no—
372#95—22no—
373C24—21no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8C22×C4×C12714yes—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4C22×C4×C12712yes—
384C2×D4C2×D4×C12712yes—
385C2×D4#41×C12712yes—
386C22×C4—24no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4C2×D4×C12711yescharacteristic
401C22×C4C2×D4×C12711yescharacteristic
402C22×C4C2×D4×C12711yescharacteristic
403C22×C4C2×D4×C12711yescharacteristic
404C22×C4C2×D4×C12711yescharacteristic
405C22×C4C2×D4×C12711yescharacteristic
406C22×C4C24×C12711yescharacteristic
407SD16—216no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8C22×C4×C12714yes—
414C4⋊C4—24no—
415C4⋊C4—24no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—42no—
422C4⋊C4—44no—
423C4⋊C4—42no—
424C4⋊C4C22×C4×C12712yes—
425C4⋊C4C2×D4×C12712yes—
426C4⋊C4#41×C12712yes—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C42—22no—
431C42—22no—
432C42—22no—
433C42—21no—
434C42—21no—
435C42—41no—
436C42—42no—
437C42—42no—
438C42—44no—
439C42—42no—
440C42C22×C4×C12712yes—
441C42C2×D4×C12712yes—
442C42#41×C12712yes—
443C42#41×C12712yes—
444C23—22no—
445C23—22no—
446C23—22no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23C22×D4×C12711yescharacteristic
452Q8—24no—
453Q8—24no—
454Q8—42no—
455Q8—42no—
456D4—22no—
457D4—22no—
458D4—22no—
459D4C4×D4×C12714yes—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—48no—
476C2×C4—48no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—48no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4C4×D4×C12712yes—
490C2×C4C4×D4×C12712yes—
491C2×C4#121×C12712yes—
492C2×C4#121×C12712yes—
493C2×C4AGL(1,ℤ/8)×C12712yes—
494C2×C4#137×C12712yes—
495C2×C4#137×C12712yes—
496C2×C4C23×C4×C12711yescharacteristic
497C2×C4C22×D4×C12711yescharacteristic
498C2×C4C2×#41×C12711yescharacteristic
499C2×C4C2×#41×C12711yescharacteristic
500C2×C4C2×#41×C12711yescharacteristic
501C2×C4C2×#41×C12711yescharacteristic
502C8—24no—
503C8—42no—
504C22—24no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22C2×C4×D4×C12711yescharacteristic
512C22C2×#121×C12711yescharacteristic
513C22#525×C12711yescharacteristic
514C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
515C22C2×#137×C12711yescharacteristic
516C22C2×#137×C12711yescharacteristic
517C22#575×C12711yescharacteristic
518C4—22no—
519C4—22no—
520C4—22no—
521C4—22no—
522C4—42no—
523C4—41no—
524C4—42no—
525C4—42no—
526C4—44no—
527C4—82no—
528C4#440×C12714yescomplemented
529C4C2×C4×D4×C12711yescharacteristic
530C4C4×#41×C12711yescharacteristic
531C4#529×C12711yescharacteristic
532C4#532×C12711yescharacteristic
533C2—44no—
534C2C4×#121×C12711yescharacteristic
535C2C2×#440×C12711yescharacteristic
536C2C4×#137×C12711yescharacteristic
537C2C127×#303611yescharacteristic
538C2C127×#303911yescharacteristic
539C2C127×#311011yescharacteristic
540C2C127×#311611yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×D4×C127C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C43×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C4×C4⋊Q8×C127C2semidirect
5. C127×#1981C2semidirect
6. C127×#1947C2semidirect
7. C127×#1928C2semidirect
10. C127×#1767C2semidirect
11. C127×#1763C2semidirect
19. #461×C127C4semidirect
56. C4⋊Q8×C127C2×C4semidirect
91. C4⋊C8×C127C2×C4semidirect
94. #103×C127C2×C4semidirect
257. C4×C127#440semidirect
262. #21504C127direct (N × H)
273. C4×C4⋊Q8C2×C127semidirect
275. #1981C2×C127semidirect
276. #1947C2×C127semidirect
277. #1928C2×C127semidirect
280. #1767C2×C127semidirect
281. #1763C2×C127semidirect
282. C127#21504direct (N × H)
290. #461C4×C127semidirect
327. C4⋊Q8C2×C4×C127semidirect
362. C4⋊C8C2×C4×C127semidirect
365. #103C2×C4×C127semidirect
528. C4#440×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1272
C2×#440×C1272
C4×C4⋊Q8×C1272
C42×D4×C1272
C127×#19812
C127×#19472
C127×#19282
C127×#18772
C127×#18022
C127×#17672
C127×#17632
#21504127