Finite Group Databasebeta

← C127×#21593 #44585266

Subgroups — C127×#21593 #44585266

Order 32512.

782 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3091C211yesmaximal, characteristic
2C127×#2929C211yesmaximal, characteristic
3C2×#405×C127C211yesmaximal, characteristic, complemented
4C127×#1929C212yesmaximal, complemented
5C127×#1922C212yesmaximal, complemented
6C127×#1871C211yesmaximal, characteristic
7C127×#1855C211yesmaximal, characteristic, complemented
8C127×#1826C211yesmaximal, characteristic, complemented
9C127×#1773C212yesmaximal, complemented
10C127×#1765C212yesmaximal, complemented
11C127×#1752C211yesmaximal, characteristic, complemented
12C2×#131×C127C2211yescharacteristic
13C22×M16×C127C2211yescharacteristic
14C23×C8×C127C2211yescharacteristic
15#525×C127C2211yescharacteristic
16C2×#117×C127C2211yescharacteristic
17#485×C127C412yescomplemented
18#484×C127C411yescharacteristic, complemented
19#483×C127C411yescharacteristic, complemented
20#482×C127C412yescomplemented
21#481×C127C411yescharacteristic, complemented
22#480×C127C411yescharacteristic, complemented
23#435×C127—21no—
24#435×C127—21no—
25C8×D4×C127—21no—
26C8×D4×C127—21no—
27C2×#108×C127C2212yes—
28#427×C127C2212yes—
29#424×C127C2211yescharacteristic
30C2×#104×C127C2212yes—
31#416×C127C2212yes—
32#408×C127C2211yescharacteristic
33#407×C127C2211yescharacteristic
34C2×C22⋊C8×C127C2211yescharacteristic
35#405×C127—21no—
36#405×C127—21no—
37#405×C127C2212yes—
38#405×C127C2212yes—
39#405×C127C2211yescharacteristic
40C2×#97×C127—21no—
41C2×#97×C127C2212yes—
42C2×C4×C8×C127—21no—
43C4×C22⋊C4×C127C2211yescharacteristic
44#341×C127C2212yes—
45#339×C127C2212yes—
46#339×C127C2212yes—
47#339×C127C2212yes—
48#336×C127C2212yes—
49C2×#41×C127C2311yescharacteristic
50C23×C4×C127C2311yescharacteristic
51#131×C127—24no—
52C2×M16×C127—21no—
53C2×M16×C127—24no—
54C2×M16×C127—21no—
55C2×M16×C127C2311yescharacteristic
56C2×M16×C127C2311yescharacteristic
57C2×M16×C127C2312yes—
58C22×C8×C127—21no—
59C22×C8×C127—24no—
60C22×C8×C127—21no—
61C22×C8×C127D411yescharacteristic
62C22×C8×C127D411yescharacteristic
63C22×C8×C127D411yescharacteristic
64C22×C8×C127D411yescharacteristic
65C22×C8×C127C2312yes—
66C22×C8×C127C2311yescharacteristic
67C22×C8×C127C2311yescharacteristic
68#123×C127—21no—
69C22⋊Q8×C127C2×C411yescharacteristic
70C22⋊Q8×C127C2×C411yescharacteristic
71#121×C127C2×C411yescharacteristic
72#121×C127C2×C411yescharacteristic
73#120×C127—21no—
74C4×D4×C127—21no—
75C4×D4×C127—21no—
76#117×C127—21no—
77#117×C127—21no—
78#117×C127C2×C412yes—
79#117×C127C2312yes—
80#117×C127C2311yescharacteristic
81C2×C4⋊C4×C127C2×C411yescharacteristic
82C2×C4⋊C4×C127C2×C411yescharacteristic
83C2×C22⋊C4×C127—21no—
84C2×C22⋊C4×C127—21no—
85C2×C42×C127—21no—
86C2×C42×C127C2312yes—
87#108×C127—24no—
88#107×C127C2×C412yes—
89#107×C127C2×C412yes—
90#106×C127C2×C412yes—
91#106×C127C2×C412yes—
92C4⋊C8×C127—21no—
93C4⋊C8×C127—21no—
94#104×C127—24no—
95#103×C127C2×C412yes—
96#103×C127C2×C412yes—
97#102×C127C2×C412yes—
98#102×C127C2×C412yes—
99C22⋊C8×C127—21no—
100C22⋊C8×C127—21no—
101C22⋊C8×C127—21no—
102C22⋊C8×C127—21no—
103C22⋊C8×C127C2×C411yescharacteristic
104C22⋊C8×C127C2×C411yescharacteristic
105C22⋊C8×C127C2×C412yes—
106#97×C127—22no—
107#97×C127—22no—
108#97×C127—21no—
109#97×C127—24no—
110C4×C8×C127—22no—
111C4×C8×C127—22no—
112C4×C8×C127—21no—
113#95×C127—21no—
114C24×C127#4111yescharacteristic
115#41×C127—22no—
116#41×C127—22no—
117C2×Q8×C127C22×C411yescharacteristic
118C2×D4×C127—21no—
119C2×D4×C127—21no—
120C2×D4×C127—21no—
121C2×D4×C127C22×C411yescharacteristic
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
127C22×C4×C127—22no—
128C22×C4×C127C22×C411yescharacteristic
129C22×C4×C127C22×C411yescharacteristic
130C22×C4×C127C2×D411yescharacteristic
131C22×C4×C127C2×D411yescharacteristic
132C22×C4×C127#4111yescharacteristic
133C22×C4×C127C2411yescharacteristic
134M16×C127—24no—
135M16×C127—22no—
136M16×C127—22no—
137M16×C127—22no—
138M16×C127—42no—
139M16×C127#4114yes—
140C2×C8×C127—24no—
141C2×C8×C127—22no—
142C2×C8×C127—22no—
143C2×C8×C127—22no—
144C2×C8×C127—22no—
145C2×C8×C127—22no—
146C2×C8×C127—22no—
147C2×C8×C127—22no—
148C2×C8×C127—22no—
149C2×C8×C127—21no—
150C2×C8×C127—21no—
151C2×C8×C127—42no—
152C2×C8×C127C22×C412yes—
153C2×C8×C127C22×C412yes—
154C2×C8×C127C2×D411yescharacteristic
155C2×C8×C127C2×D411yescharacteristic
156C2×C8×C127C2×D411yescharacteristic
157C2×C8×C127C2×D411yescharacteristic
158C2×C8×C127#4114yes—
159C4⋊C4×C127—21no—
160C4⋊C4×C127—21no—
161C4⋊C4×C127—21no—
162C4⋊C4×C127—21no—
163C4⋊C4×C127C22×C412yes—
164C4⋊C4×C127C22×C412yes—
165C4⋊C4×C127C22×C411yescharacteristic
166C4⋊C4×C127C22×C411yescharacteristic
167C22⋊C4×C127—22no—
168C22⋊C4×C127—21no—
169C22⋊C4×C127—21no—
170C22⋊C4×C127—22no—
171C22⋊C4×C127—21no—
172C22⋊C4×C127—21no—
173C22⋊C4×C127—21no—
174C22⋊C4×C127—42no—
175C42×C127—22no—
176C42×C127—22no—
177C42×C127—21no—
178C42×C127—22no—
179C42×C127—22no—
180C23×C127—22no—
181C23×C127—22no—
182C23×C127—21no—
183C23×C127—41no—
184C23×C127C4×D411yescharacteristic
185C23×C127C4×D411yescharacteristic
186C23×C127C2×#4111yescharacteristic
187Q8×C127—22no—
188D4×C127—22no—
189D4×C127—42no—
190D4×C127—42no—
191D4×C127—42no—
192C2×C4×C127—22no—
193C2×C4×C127—22no—
194C2×C4×C127—22no—
195C2×C4×C127—21no—
196C2×C4×C127—21no—
197C2×C4×C127—21no—
198C2×C4×C127—21no—
199C2×C4×C127—22no—
200C2×C4×C127—22no—
201C2×C4×C127—21no—
202C2×C4×C127—21no—
203C2×C4×C127—21no—
204C2×C4×C127—42no—
205C2×C4×C127—42no—
206C2×C4×C127—41no—
207C2×C4×C127—41no—
208C2×C4×C127—42no—
209C2×C4×C127—42no—
210C2×C4×C127—42no—
211C2×C4×C127C4×D411yescharacteristic
212C2×C4×C127C4×D411yescharacteristic
213C2×C4×C127C23×C411yescharacteristic
214C2×C4×C127C22×D411yescharacteristic
215C2×C4×C127C2×#4112yes—
216C2×C4×C127C2×#4112yes—
217C8×C127—22no—
218C8×C127—22no—
219C8×C127—21no—
220C8×C127—21no—
221C8×C127—24no—
222C8×C127—41no—
223C8×C127—41no—
224C8×C127#12312yes—
225C8×C127#12312yes—
226C22×C127—21no—
227C22×C127—21no—
228C22×C127—21no—
229C22×C127—21no—
230C22×C127—21no—
231C22×C127—21no—
232C22×C127—21no—
233C22×C127—44no—
234C22×C127—41no—
235C22×C127—41no—
236C22×C127—41no—
237C22×C127#44412yes—
238C22×C127C2×C4×D411yescharacteristic
239C22×C127#52912yes—
240C4×C127—21no—
241C4×C127—21no—
242C4×C127—42no—
243C4×C127—41no—
244C4×C127—42no—
245C4×C127—41no—
246C4×C127—41no—
247C4×C127—82no—
248C4×C127C4×#4112yes—
249C4×C127C2×#12311yescharacteristic
250C4×C127#52511yescharacteristic
251#21593C12711yesmaximal, characteristic, direct product factor, Sylow
252C2×C127—22no—
253C2×C127—22no—
254C2×C127—41no—
255C2×C127—81no—
256C2×C127C4×#12311yescharacteristic
257C2×C127C2×#44411yescharacteristic
258C2×C127#295511yescharacteristic
259#3091C2×C12711yescharacteristic
260#2929C2×C12711yescharacteristic
261C2×#405C2×C12711yescharacteristic, complemented
262#1929C2×C12712yescomplemented
263#1922C2×C12712yescomplemented
264#1871C2×C12711yescharacteristic
265#1855C2×C12711yescharacteristic, complemented
266#1826C2×C12711yescharacteristic, complemented
267#1773C2×C12712yescomplemented
268#1765C2×C12712yescomplemented
269#1752C2×C12711yescharacteristic, complemented
270C127#2159311yescharacteristic, direct product factor, Sylow
271C2×#131C22×C12711yescharacteristic
272C22×M16C22×C12711yescharacteristic
273C23×C8C22×C12711yescharacteristic
274#525C22×C12711yescharacteristic
275C2×#117C22×C12711yescharacteristic
276#485C4×C12712yescomplemented
277#484C4×C12711yescharacteristic, complemented
278#483C4×C12711yescharacteristic, complemented
279#482C4×C12712yescomplemented
280#481C4×C12711yescharacteristic, complemented
281#480C4×C12711yescharacteristic, complemented
282#435—21no—
283#435—21no—
284C8×D4—21no—
285C8×D4—21no—
286C2×#108C22×C12712yes—
287#427C22×C12712yes—
288#424C22×C12711yescharacteristic
289C2×#104C22×C12712yes—
290#416C22×C12712yes—
291#408C22×C12711yescharacteristic
292#407C22×C12711yescharacteristic
293C2×C22⋊C8C22×C12711yescharacteristic
294#405—21no—
295#405—21no—
296#405C22×C12712yes—
297#405C22×C12712yes—
298#405C22×C12711yescharacteristic
299C2×#97—21no—
300C2×#97C22×C12712yes—
301C2×C4×C8—21no—
302C4×C22⋊C4C22×C12711yescharacteristic
303#341C22×C12712yes—
304#339C22×C12712yes—
305#339C22×C12712yes—
306#339C22×C12712yes—
307#336C22×C12712yes—
308C2×#41C23×C12711yescharacteristic
309C23×C4C23×C12711yescharacteristic
310#131—24no—
311C2×M16—21no—
312C2×M16—24no—
313C2×M16—21no—
314C2×M16C23×C12711yescharacteristic
315C2×M16C23×C12711yescharacteristic
316C2×M16C23×C12712yes—
317C22×C8—21no—
318C22×C8—24no—
319C22×C8—21no—
320C22×C8D4×C12711yescharacteristic
321C22×C8D4×C12711yescharacteristic
322C22×C8D4×C12711yescharacteristic
323C22×C8D4×C12711yescharacteristic
324C22×C8C23×C12712yes—
325C22×C8C23×C12711yescharacteristic
326C22×C8C23×C12711yescharacteristic
327#123—21no—
328C22⋊Q8C2×C4×C12711yescharacteristic
329C22⋊Q8C2×C4×C12711yescharacteristic
330#121C2×C4×C12711yescharacteristic
331#121C2×C4×C12711yescharacteristic
332#120—21no—
333C4×D4—21no—
334C4×D4—21no—
335#117—21no—
336#117—21no—
337#117C2×C4×C12712yes—
338#117C23×C12712yes—
339#117C23×C12711yescharacteristic
340C2×C4⋊C4C2×C4×C12711yescharacteristic
341C2×C4⋊C4C2×C4×C12711yescharacteristic
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C42—21no—
345C2×C42C23×C12712yes—
346#108—24no—
347#107C2×C4×C12712yes—
348#107C2×C4×C12712yes—
349#106C2×C4×C12712yes—
350#106C2×C4×C12712yes—
351C4⋊C8—21no—
352C4⋊C8—21no—
353#104—24no—
354#103C2×C4×C12712yes—
355#103C2×C4×C12712yes—
356#102C2×C4×C12712yes—
357#102C2×C4×C12712yes—
358C22⋊C8—21no—
359C22⋊C8—21no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8C2×C4×C12711yescharacteristic
363C22⋊C8C2×C4×C12711yescharacteristic
364C22⋊C8C2×C4×C12712yes—
365#97—22no—
366#97—22no—
367#97—21no—
368#97—24no—
369C4×C8—22no—
370C4×C8—22no—
371C4×C8—21no—
372#95—21no—
373C24#41×C12711yescharacteristic
374#41—22no—
375#41—22no—
376C2×Q8C22×C4×C12711yescharacteristic
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4C22×C4×C12711yescharacteristic
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4C22×C4×C12711yescharacteristic
388C22×C4C22×C4×C12711yescharacteristic
389C22×C4C2×D4×C12711yescharacteristic
390C22×C4C2×D4×C12711yescharacteristic
391C22×C4#41×C12711yescharacteristic
392C22×C4C24×C12711yescharacteristic
393M16—24no—
394M16—22no—
395M16—22no—
396M16—22no—
397M16—42no—
398M16#41×C12714yes—
399C2×C8—24no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—42no—
411C2×C8C22×C4×C12712yes—
412C2×C8C22×C4×C12712yes—
413C2×C8C2×D4×C12711yescharacteristic
414C2×C8C2×D4×C12711yescharacteristic
415C2×C8C2×D4×C12711yescharacteristic
416C2×C8C2×D4×C12711yescharacteristic
417C2×C8#41×C12714yes—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4C22×C4×C12712yes—
423C4⋊C4C22×C4×C12712yes—
424C4⋊C4C22×C4×C12711yescharacteristic
425C4⋊C4C22×C4×C12711yescharacteristic
426C22⋊C4—22no—
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—22no—
430C22⋊C4—21no—
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—42no—
434C42—22no—
435C42—22no—
436C42—21no—
437C42—22no—
438C42—22no—
439C23—22no—
440C23—22no—
441C23—21no—
442C23—41no—
443C23C4×D4×C12711yescharacteristic
444C23C4×D4×C12711yescharacteristic
445C23C2×#41×C12711yescharacteristic
446Q8—22no—
447D4—22no—
448D4—42no—
449D4—42no—
450D4—42no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4C4×D4×C12711yescharacteristic
471C2×C4C4×D4×C12711yescharacteristic
472C2×C4C23×C4×C12711yescharacteristic
473C2×C4C22×D4×C12711yescharacteristic
474C2×C4C2×#41×C12712yes—
475C2×C4C2×#41×C12712yes—
476C8—22no—
477C8—22no—
478C8—21no—
479C8—21no—
480C8—24no—
481C8—41no—
482C8—41no—
483C8#123×C12712yes—
484C8#123×C12712yes—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—44no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22#444×C12712yes—
497C22C2×C4×D4×C12711yescharacteristic
498C22#529×C12712yes—
499C4—21no—
500C4—21no—
501C4—42no—
502C4—41no—
503C4—42no—
504C4—41no—
505C4—41no—
506C4—82no—
507C4C4×#41×C12712yes—
508C4C2×#123×C12711yescharacteristic
509C4#525×C12711yescharacteristic
510C2—22no—
511C2—22no—
512C2—41no—
513C2—81no—
514C2C4×#123×C12711yescharacteristic
515C2C2×#444×C12711yescharacteristic
516C2C127×#295511yescharacteristic
subgroupG/H
centerC2×C4×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC22×C127C2×C4×D4
prime radical#525×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#405×C127C2semidirect
4. C127×#1929C2semidirect
5. C127×#1922C2semidirect
7. C127×#1855C2semidirect
8. C127×#1826C2semidirect
9. C127×#1773C2semidirect
10. C127×#1765C2semidirect
11. C127×#1752C2semidirect
17. #485×C127C4semidirect
18. #484×C127C4semidirect
19. #483×C127C4semidirect
20. #482×C127C4semidirect
21. #481×C127C4semidirect
22. #480×C127C4semidirect
251. #21593C127direct (N × H)
261. C2×#405C2×C127semidirect
262. #1929C2×C127semidirect
263. #1922C2×C127semidirect
265. #1855C2×C127semidirect
266. #1826C2×C127semidirect
267. #1773C2×C127semidirect
268. #1765C2×C127semidirect
269. #1752C2×C127semidirect
270. C127#21593direct (N × H)
276. #485C4×C127semidirect
277. #484C4×C127semidirect
278. #483C4×C127semidirect
279. #482C4×C127semidirect
280. #481C4×C127semidirect
281. #480C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#30912
C127×#29292
C2×#405×C1272
C127×#19292
C127×#19222
C127×#18712
C127×#18552
C127×#18262
C127×#17732
C127×#17652
C127×#17522
#21593127