Finite Group Databasebeta

← C127×#18339 #44582012

Subgroups — C127×#18339 #44582012

Order 32512.

1156 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3449C211yesmaximal, characteristic
2C127×#3234C212yesmaximal, complemented
3C127×#2611C211yesmaximal, characteristic, complemented
4C127×#1616C212yesmaximal, complemented
5C127×#1613C212yesmaximal, complemented
6C127×#1610C212yesmaximal, complemented
7C127×#1607C212yesmaximal, complemented
8C127×#1505C212yesmaximal, complemented
9C127×#1464C211yesmaximal, characteristic, complemented
10C22×#41×C127—21no—
11#537×C127—21no—
12#537×C127C2212yes—
13#536×C127—22no—
14#535×C127—22no—
15#534×C127—21no—
16#534×C127C2212yes—
17#532×C127—21no—
18#532×C127C2212yes—
19C2×#125×C127C2211yescharacteristic, complemented
20#525×C127—24no—
21C2×#117×C127C2211yescharacteristic
22#501×C127—22no—
23#490×C127—22no—
24#481×C127C2214yescomplemented
25#480×C127C2214yescomplemented
26#478×C127—24no—
27#432×C127C2212yescomplemented
28#400×C127C2211yescharacteristic, complemented
29#399×C127C2211yescharacteristic
30#398×C127C2211yescharacteristic, complemented
31#397×C127C2211yescharacteristic
32#389×C127—21no—
33#388×C127—21no—
34#387×C127—21no—
35#385×C127—21no—
36#376×C127C2211yescharacteristic, complemented
37#327×C127C2214yescomplemented
38#327×C127C2214yescomplemented
39#324×C127C2212yescomplemented
40#323×C127C2212yes—
41C2×#41×C127—22no—
42C2×#41×C127—22no—
43C2×#41×C127—22no—
44C2×#41×C127—22no—
45C2×#41×C127—44no—
46C2×#41×C127—44no—
47C22×Q8×C127—21no—
48C22×D4×C127—21no—
49C22×D4×C127—22no—
50C23×C4×C127—22no—
51C23×C4×C127D411yescharacteristic
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127D412yes—
54#127×C127—21no—
55#127×C127D412yes—
56#125×C127—22no—
57#125×C127—22no—
58#124×C127—22no—
59#124×C127—22no—
60#123×C127—24no—
61#123×C127—24no—
62C22⋊Q8×C127—24no—
63C22⋊Q8×C127—24no—
64#121×C127—24no—
65#121×C127—24no—
66#121×C127—22no—
67#121×C127—22no—
68#121×C127—22no—
69#121×C127C2314yes—
70#120×C127—24no—
71#120×C127—24no—
72C4×D4×C127—22no—
73C4×D4×C127—22no—
74C4×D4×C127—22no—
75C4×D4×C127D414yes—
76#117×C127—22no—
77#117×C127—22no—
78C2×C4⋊C4×C127—21no—
79C2×C4⋊C4×C127—21no—
80C2×C4⋊C4×C127—21no—
81C2×C4⋊C4×C127—21no—
82C2×C4⋊C4×C127D411yescharacteristic
83C2×C4⋊C4×C127C2311yescharacteristic
84C2×C4⋊C4×C127C2311yescharacteristic
85C2×C4⋊C4×C127C2311yescharacteristic
86C2×C22⋊C4×C127—21no—
87C2×C22⋊C4×C127—21no—
88C2×C22⋊C4×C127D411yescharacteristic
89C2×C22⋊C4×C127C2311yescharacteristic
90C2×C42×C127—21no—
91C2×C42×C127D411yescharacteristic
92C2×C42×C127C2311yescharacteristic
93#107×C127—24no—
94#106×C127—24no—
95C4⋊C8×C127—22no—
96#102×C127—24no—
97#102×C127—24no—
98C22⋊C8×C127C2314yes—
99#97×C127—22no—
100#95×C127—21no—
101#95×C127—21no—
102#95×C127—21no—
103#95×C127—21no—
104#95×C127—21no—
105#95×C127C2311yescharacteristic
106#95×C127C2311yescharacteristic
107C24×C127—22no—
108C24×C127C2×D411yescharacteristic
109#41×C127—48no—
110#41×C127—48no—
111#41×C127—44no—
112#41×C127—44no—
113#41×C127—44no—
114#41×C127—44no—
115C2×Q8×C127—22no—
116C2×Q8×C127—22no—
117C2×Q8×C127—44no—
118C2×D4×C127—24no—
119C2×D4×C127—22no—
120C2×D4×C127—24no—
121C2×D4×C127—22no—
122C2×D4×C127—22no—
123C2×D4×C127—22no—
124C2×D4×C127—22no—
125C2×D4×C127—44no—
126C2×D4×C127—44no—
127C2×D4×C127—44no—
128C2×D4×C127C2×D414yes—
129C22×C4×C127—22no—
130C22×C4×C127—21no—
131C22×C4×C127—21no—
132C22×C4×C127—22no—
133C22×C4×C127—24no—
134C22×C4×C127—22no—
135C22×C4×C127—21no—
136C22×C4×C127—24no—
137C22×C4×C127—21no—
138C22×C4×C127—21no—
139C22×C4×C127—21no—
140C22×C4×C127—48no—
141C22×C4×C127C2×D411yescharacteristic
142C22×C4×C127C2×D411yescharacteristic
143C22×C4×C127C2×D411yescharacteristic
144C22×C4×C127C2×D411yescharacteristic
145C22×C4×C127C2×D411yescharacteristic
146C22×C4×C127C2411yescharacteristic
147C2×C8×C127—24no—
148C4⋊C4×C127—22no—
149C4⋊C4×C127—22no—
150C4⋊C4×C127—22no—
151C4⋊C4×C127—22no—
152C4⋊C4×C127—22no—
153C4⋊C4×C127—22no—
154C4⋊C4×C127—22no—
155C4⋊C4×C127—42no—
156C4⋊C4×C127—41no—
157C4⋊C4×C127—41no—
158C4⋊C4×C127—42no—
159C4⋊C4×C127—42no—
160C4⋊C4×C127C2×D414yes—
161C22⋊C4×C127—24no—
162C22⋊C4×C127—24no—
163C22⋊C4×C127—22no—
164C22⋊C4×C127—24no—
165C22⋊C4×C127—22no—
166C22⋊C4×C127—24no—
167C22⋊C4×C127—42no—
168C22⋊C4×C127—42no—
169C42×C127—21no—
170C42×C127—21no—
171C42×C127—42no—
172C42×C127C2×D412yes—
173C42×C127C2×D412yes—
174C23×C127—21no—
175C23×C127—21no—
176C23×C127—24no—
177C23×C127—41no—
178C23×C127—41no—
179C23×C127—44no—
180C23×C127—82no—
181C23×C127—82no—
182C23×C127AGL(1,ℤ/8)12yes—
183C23×C127C22×D411yescharacteristic
184Q8×C127—44no—
185Q8×C127—44no—
186D4×C127—44no—
187D4×C127—44no—
188D4×C127—44no—
189D4×C127—48no—
190D4×C127—44no—
191D4×C127—44no—
192D4×C127—82no—
193D4×C127—82no—
194D4×C127—82no—
195C2×C4×C127—24no—
196C2×C4×C127—24no—
197C2×C4×C127—21no—
198C2×C4×C127—21no—
199C2×C4×C127—21no—
200C2×C4×C127—21no—
201C2×C4×C127—22no—
202C2×C4×C127—21no—
203C2×C4×C127—21no—
204C2×C4×C127—24no—
205C2×C4×C127—41no—
206C2×C4×C127—41no—
207C2×C4×C127—48no—
208C2×C4×C127—48no—
209C2×C4×C127—41no—
210C2×C4×C127—44no—
211C2×C4×C127—41no—
212C2×C4×C127—41no—
213C2×C4×C127—41no—
214C2×C4×C127—41no—
215C2×C4×C127—41no—
216C2×C4×C127—41no—
217C2×C4×C127—41no—
218C2×C4×C127—41no—
219C2×C4×C127—41no—
220C2×C4×C127—41no—
221C2×C4×C127—41no—
222C2×C4×C127—41no—
223C2×C4×C127#12011yescharacteristic
224C2×C4×C127#12011yescharacteristic
225C2×C4×C127#12012yes—
226C2×C4×C127AGL(1,ℤ/8)12yes—
227C2×C4×C127C22×D412yes—
228C8×C127—44no—
229C22×C127—21no—
230C22×C127—21no—
231C22×C127—22no—
232C22×C127—42no—
233C22×C127—41no—
234C22×C127—41no—
235C22×C127—44no—
236C22×C127—44no—
237C22×C127—44no—
238C22×C127—81no—
239C22×C127—88no—
240C22×C127C2×#12011yescharacteristic
241C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
242C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
243C4×C127—21no—
244C4×C127—22no—
245C4×C127—21no—
246C4×C127—22no—
247C4×C127—22no—
248C4×C127—42no—
249C4×C127—44no—
250C4×C127—41no—
251C4×C127—41no—
252C4×C127—81no—
253C4×C127—81no—
254C4×C127—81no—
255#18339C12711yesmaximal, characteristic, direct product factor, Sylow
256C2×C127—21no—
257C2×C127—21no—
258C2×C127—42no—
259C2×C127—84no—
260C2×C127#300311yescharacteristic
261C2×C127#301811yescharacteristic
262C2×C127#302811yescharacteristic
263#3449C2×C12711yescharacteristic
264#3234C2×C12712yescomplemented
265#2611C2×C12711yescharacteristic, complemented
266#1616C2×C12712yescomplemented
267#1613C2×C12712yescomplemented
268#1610C2×C12712yescomplemented
269#1607C2×C12712yescomplemented
270#1505C2×C12712yescomplemented
271#1464C2×C12711yescharacteristic, complemented
272C127#1833911yescharacteristic, direct product factor, Sylow
273C22×#41—21no—
274#537—21no—
275#537C22×C12712yes—
276#536—22no—
277#535—22no—
278#534—21no—
279#534C22×C12712yes—
280#532—21no—
281#532C22×C12712yes—
282C2×#125C22×C12711yescharacteristic, complemented
283#525—24no—
284C2×#117C22×C12711yescharacteristic
285#501—22no—
286#490—22no—
287#481C22×C12714yescomplemented
288#480C22×C12714yescomplemented
289#478—24no—
290#432C22×C12712yescomplemented
291#400C22×C12711yescharacteristic, complemented
292#399C22×C12711yescharacteristic
293#398C22×C12711yescharacteristic, complemented
294#397C22×C12711yescharacteristic
295#389—21no—
296#388—21no—
297#387—21no—
298#385—21no—
299#376C22×C12711yescharacteristic, complemented
300#327C22×C12714yescomplemented
301#327C22×C12714yescomplemented
302#324C22×C12712yescomplemented
303#323C22×C12712yes—
304C2×#41—22no—
305C2×#41—22no—
306C2×#41—22no—
307C2×#41—22no—
308C2×#41—44no—
309C2×#41—44no—
310C22×Q8—21no—
311C22×D4—21no—
312C22×D4—22no—
313C23×C4—22no—
314C23×C4D4×C12711yescharacteristic
315C4⋊Q8—21no—
316C4⋊Q8D4×C12712yes—
317#127—21no—
318#127D4×C12712yes—
319#125—22no—
320#125—22no—
321#124—22no—
322#124—22no—
323#123—24no—
324#123—24no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327#121—24no—
328#121—24no—
329#121—22no—
330#121—22no—
331#121—22no—
332#121C23×C12714yes—
333#120—24no—
334#120—24no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4D4×C12714yes—
339#117—22no—
340#117—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4D4×C12711yescharacteristic
346C2×C4⋊C4C23×C12711yescharacteristic
347C2×C4⋊C4C23×C12711yescharacteristic
348C2×C4⋊C4C23×C12711yescharacteristic
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4D4×C12711yescharacteristic
352C2×C22⋊C4C23×C12711yescharacteristic
353C2×C42—21no—
354C2×C42D4×C12711yescharacteristic
355C2×C42C23×C12711yescharacteristic
356#107—24no—
357#106—24no—
358C4⋊C8—22no—
359#102—24no—
360#102—24no—
361C22⋊C8C23×C12714yes—
362#97—22no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95C23×C12711yescharacteristic
369#95C23×C12711yescharacteristic
370C24—22no—
371C24C2×D4×C12711yescharacteristic
372#41—48no—
373#41—48no—
374#41—44no—
375#41—44no—
376#41—44no—
377#41—44no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—44no—
381C2×D4—24no—
382C2×D4—22no—
383C2×D4—24no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—44no—
389C2×D4—44no—
390C2×D4—44no—
391C2×D4C2×D4×C12714yes—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—24no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—48no—
404C22×C4C2×D4×C12711yescharacteristic
405C22×C4C2×D4×C12711yescharacteristic
406C22×C4C2×D4×C12711yescharacteristic
407C22×C4C2×D4×C12711yescharacteristic
408C22×C4C2×D4×C12711yescharacteristic
409C22×C4C24×C12711yescharacteristic
410C2×C8—24no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—42no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—42no—
422C4⋊C4—42no—
423C4⋊C4C2×D4×C12714yes—
424C22⋊C4—24no—
425C22⋊C4—24no—
426C22⋊C4—22no—
427C22⋊C4—24no—
428C22⋊C4—22no—
429C22⋊C4—24no—
430C22⋊C4—42no—
431C22⋊C4—42no—
432C42—21no—
433C42—21no—
434C42—42no—
435C42C2×D4×C12712yes—
436C42C2×D4×C12712yes—
437C23—21no—
438C23—21no—
439C23—24no—
440C23—41no—
441C23—41no—
442C23—44no—
443C23—82no—
444C23—82no—
445C23AGL(1,ℤ/8)×C12712yes—
446C23C22×D4×C12711yescharacteristic
447Q8—44no—
448Q8—44no—
449D4—44no—
450D4—44no—
451D4—44no—
452D4—48no—
453D4—44no—
454D4—44no—
455D4—82no—
456D4—82no—
457D4—82no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—24no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—48no—
471C2×C4—48no—
472C2×C4—44no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4#120×C12711yescharacteristic
487C2×C4#120×C12711yescharacteristic
488C2×C4#120×C12712yes—
489C2×C4AGL(1,ℤ/8)×C12712yes—
490C2×C4C22×D4×C12712yes—
491C8—44no—
492C22—21no—
493C22—21no—
494C22—22no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—44no—
499C22—44no—
500C22—44no—
501C22—81no—
502C22—88no—
503C22C2×#120×C12711yescharacteristic
504C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
505C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
506C4—21no—
507C4—22no—
508C4—21no—
509C4—22no—
510C4—22no—
511C4—42no—
512C4—44no—
513C4—41no—
514C4—41no—
515C4—81no—
516C4—81no—
517C4—81no—
518C2—21no—
519C2—21no—
520C2—42no—
521C2—84no—
522C2C127×#300311yescharacteristic
523C2C127×#301811yescharacteristic
524C2C127×#302811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radicalC127×#3449C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#3234C2semidirect
3. C127×#2611C2semidirect
4. C127×#1616C2semidirect
5. C127×#1613C2semidirect
6. C127×#1610C2semidirect
7. C127×#1607C2semidirect
8. C127×#1505C2semidirect
9. C127×#1464C2semidirect
19. C2×#125×C127C22semidirect
24. #481×C127C22semidirect
25. #480×C127C22semidirect
27. #432×C127C22semidirect
28. #400×C127C22semidirect
30. #398×C127C22semidirect
36. #376×C127C22semidirect
37. #327×C127C22semidirect
38. #327×C127C22semidirect
39. #324×C127C22semidirect
255. #18339C127direct (N × H)
264. #3234C2×C127semidirect
265. #2611C2×C127semidirect
266. #1616C2×C127semidirect
267. #1613C2×C127semidirect
268. #1610C2×C127semidirect
269. #1607C2×C127semidirect
270. #1505C2×C127semidirect
271. #1464C2×C127semidirect
272. C127#18339direct (N × H)
282. C2×#125C22×C127semidirect
287. #481C22×C127semidirect
288. #480C22×C127semidirect
290. #432C22×C127semidirect
291. #400C22×C127semidirect
293. #398C22×C127semidirect
299. #376C22×C127semidirect
300. #327C22×C127semidirect
301. #327C22×C127semidirect
302. #324C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34492
C127×#32342
C127×#26112
C127×#16162
C127×#16132
C127×#16102
C127×#16072
C127×#15052
C127×#14642
#18339127