Finite Group Databasebeta

← C127×#18337 #44582010

Subgroups — C127×#18337 #44582010

Order 32512.

1016 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3461C211yesmaximal, characteristic, complemented
2C127×#3217C212yesmaximal, complemented
3C127×#2548C211yesmaximal, characteristic, complemented
4C127×#1599C212yesmaximal, complemented
5C127×#1598C212yesmaximal, complemented
6C127×#1597C214yesmaximal, complemented
7C127×#1509C212yesmaximal, complemented
8C127×#1467C211yesmaximal, characteristic, complemented
9#544×C127C2211yescharacteristic
10#542×C127—22no—
11#541×C127—22no—
12#539×C127—21no—
13#539×C127C2212yes—
14#537×C127C2211yescharacteristic
15#536×C127—21no—
16#533×C127—22no—
17C2×#127×C127C2211yescharacteristic
18#529×C127—22no—
19#529×C127—21no—
20#529×C127C2212yes—
21C2×#124×C127—21no—
22C4×#41×C127—21no—
23C2×C4×Q8×C127C2211yescharacteristic
24#496×C127—22no—
25#490×C127—22no—
26#460×C127—22no—
27#459×C127—22no—
28#450×C127C2214yes—
29#447×C127C2214yes—
30#432×C127C2212yes—
31#394×C127C2212yes—
32#394×C127C2212yes—
33#390×C127—21no—
34#390×C127—21no—
35#390×C127—21no—
36C4×C4⋊C4×C127C2211yescharacteristic
37#328×C127C2214yes—
38#327×C127C2214yes—
39#324×C127C2212yes—
40#324×C127C2212yes—
41C2×#41×C127—21no—
42C22×Q8×C127D411yescharacteristic
43C22×D4×C127—21no—
44C22×D4×C127—21no—
45C22×D4×C127C2312yes—
46C2×SD16×C127—24no—
47C2×D8×C127—24no—
48C4⋊Q8×C127—22no—
49C4⋊Q8×C127—22no—
50#127×C127—22no—
51#127×C127—22no—
52#126×C127—22no—
53#126×C127—22no—
54#126×C127—22no—
55#126×C127—22no—
56#125×C127—21no—
57#125×C127—22no—
58#125×C127—22no—
59#125×C127—22no—
60#125×C127D412yes—
61#124×C127—22no—
62#124×C127—21no—
63#124×C127—44no—
64#124×C127D412yes—
65#123×C127—22no—
66#123×C127—22no—
67#123×C127—22no—
68#123×C127—22no—
69C22⋊Q8×C127—22no—
70C22⋊Q8×C127—22no—
71C22⋊Q8×C127—22no—
72C22⋊Q8×C127—22no—
73C22⋊Q8×C127—21no—
74C22⋊Q8×C127—22no—
75C22⋊Q8×C127C2312yes—
76#121×C127—22no—
77#121×C127—21no—
78#121×C127C2312yes—
79C4×Q8×C127—21no—
80C4×Q8×C127—21no—
81C4×Q8×C127—21no—
82C4×Q8×C127—22no—
83C4×Q8×C127—22no—
84C4×Q8×C127D412yes—
85C4×D4×C127—21no—
86C4×D4×C127—21no—
87C4×D4×C127—21no—
88C4×D4×C127—22no—
89C4×D4×C127—22no—
90C4×D4×C127D412yes—
91#117×C127—22no—
92#117×C127—22no—
93#117×C127—21no—
94#117×C127—22no—
95C2×C4⋊C4×C127—21no—
96C2×C4⋊C4×C127D411yescharacteristic
97C2×C4⋊C4×C127C2311yescharacteristic
98C2×C4⋊C4×C127C2311yescharacteristic
99C2×C22⋊C4×C127—22no—
100C2×C22⋊C4×C127—22no—
101C2×C22⋊C4×C127—22no—
102C2×C22⋊C4×C127—22no—
103C2×C42×C127—22no—
104C2×C42×C127—21no—
105C2×C42×C127D411yescharacteristic
106C2×C42×C127D411yescharacteristic
107C2×C42×C127C2311yescharacteristic
108C4⋊C8×C127—22no—
109#102×C127—24no—
110#102×C127—24no—
111C22⋊C8×C127C2314yes—
112#97×C127—22no—
113#95×C127C2312yes—
114C24×C127—22no—
115#41×C127—42no—
116#41×C127—42no—
117C2×Q8×C127—21no—
118C2×Q8×C127—21no—
119C2×Q8×C127—22no—
120C2×Q8×C127—22no—
121C2×Q8×C127—41no—
122C2×Q8×C127C2×D412yes—
123C2×D4×C127—21no—
124C2×D4×C127—22no—
125C2×D4×C127—21no—
126C2×D4×C127—24no—
127C2×D4×C127—42no—
128C2×D4×C127—42no—
129C2×D4×C127—42no—
130C2×D4×C127—42no—
131C2×D4×C127—41no—
132C2×D4×C127—42no—
133C2×D4×C127—41no—
134C2×D4×C127—82no—
135C2×D4×C127C2×D412yes—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127C2×D411yescharacteristic
141C22×C4×C127C2×D411yescharacteristic
142C22×C4×C127C2×D411yescharacteristic
143C22×C4×C127C2×D411yescharacteristic
144C22×C4×C127C2×D411yescharacteristic
145C22×C4×C127C2×D411yescharacteristic
146C22×C4×C127C2411yescharacteristic
147SD16×C127—84no—
148D8×C127—84no—
149C2×C8×C127—24no—
150C4⋊C4×C127—21no—
151C4⋊C4×C127—22no—
152C4⋊C4×C127—21no—
153C4⋊C4×C127—22no—
154C4⋊C4×C127—22no—
155C4⋊C4×C127—21no—
156C4⋊C4×C127—21no—
157C4⋊C4×C127—22no—
158C4⋊C4×C127—22no—
159C4⋊C4×C127—22no—
160C4⋊C4×C127—22no—
161C4⋊C4×C127—22no—
162C4⋊C4×C127—22no—
163C4⋊C4×C127—22no—
164C4⋊C4×C127—22no—
165C4⋊C4×C127—42no—
166C4⋊C4×C127C2×D412yes—
167C4⋊C4×C127C2×D412yes—
168C22⋊C4×C127—22no—
169C22⋊C4×C127—22no—
170C22⋊C4×C127—22no—
171C22⋊C4×C127—22no—
172C22⋊C4×C127—22no—
173C22⋊C4×C127—22no—
174C22⋊C4×C127—22no—
175C22⋊C4×C127—22no—
176C22⋊C4×C127—22no—
177C22⋊C4×C127—44no—
178C22⋊C4×C127—44no—
179C22⋊C4×C127—82no—
180C22⋊C4×C127—82no—
181C42×C127—22no—
182C42×C127—22no—
183C42×C127—21no—
184C42×C127—22no—
185C42×C127—21no—
186C42×C127—21no—
187C42×C127—21no—
188C42×C127—42no—
189C42×C127C2×D412yes—
190C42×C127C2×D412yes—
191C23×C127—22no—
192C23×C127—42no—
193C23×C127—42no—
194C23×C127—42no—
195C23×C127—42no—
196C23×C127—42no—
197C23×C127—42no—
198C23×C127—42no—
199C23×C127C22×D411yescharacteristic
200Q8×C127—44no—
201Q8×C127—42no—
202Q8×C127—42no—
203Q8×C127—81no—
204D4×C127—42no—
205D4×C127—42no—
206D4×C127—44no—
207D4×C127—44no—
208D4×C127—42no—
209D4×C127—42no—
210D4×C127—84no—
211D4×C127—82no—
212D4×C127—81no—
213D4×C127—82no—
214C2×C4×C127—21no—
215C2×C4×C127—21no—
216C2×C4×C127—21no—
217C2×C4×C127—21no—
218C2×C4×C127—22no—
219C2×C4×C127—21no—
220C2×C4×C127—22no—
221C2×C4×C127—22no—
222C2×C4×C127—21no—
223C2×C4×C127—21no—
224C2×C4×C127—22no—
225C2×C4×C127—21no—
226C2×C4×C127—21no—
227C2×C4×C127—41no—
228C2×C4×C127—44no—
229C2×C4×C127—44no—
230C2×C4×C127—41no—
231C2×C4×C127—41no—
232C2×C4×C127—42no—
233C2×C4×C127—42no—
234C2×C4×C127—42no—
235C2×C4×C127—82no—
236C2×C4×C127#12011yescharacteristic
237C2×C4×C127#12012yes—
238C2×C4×C127#12011yescharacteristic
239C2×C4×C127AGL(1,ℤ/8)12yes—
240C2×C4×C127C22×D412yes—
241C8×C127—44no—
242C22×C127—21no—
243C22×C127—21no—
244C22×C127—42no—
245C22×C127—42no—
246C22×C127—42no—
247C22×C127—82no—
248C22×C127—82no—
249C22×C127—82no—
250C22×C127—82no—
251C22×C127—82no—
252C22×C127—82no—
253C22×C127—82no—
254C22×C127C2×#12011yescharacteristic
255C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
256C22×C127#57511yescharacteristic
257C4×C127—22no—
258C4×C127—22no—
259C4×C127—21no—
260C4×C127—22no—
261C4×C127—41no—
262C4×C127—42no—
263C4×C127—42no—
264C4×C127—41no—
265C4×C127—41no—
266C4×C127—42no—
267C4×C127—82no—
268C4×C127#45412yes—
269#18337C12711yesmaximal, characteristic, direct product factor, Sylow
270C2×C127—21no—
271C2×C127—21no—
272C2×C127—82no—
273C2×C127—162no—
274C2×C127#300611yescharacteristic
275C2×C127C2×#45411yescharacteristic
276C2×C127#302711yescharacteristic
277#3461C2×C12711yescharacteristic, complemented
278#3217C2×C12712yescomplemented
279#2548C2×C12711yescharacteristic, complemented
280#1599C2×C12712yescomplemented
281#1598C2×C12712yescomplemented
282#1597C2×C12714yescomplemented
283#1509C2×C12712yescomplemented
284#1467C2×C12711yescharacteristic, complemented
285C127#1833711yescharacteristic, direct product factor, Sylow
286#544C22×C12711yescharacteristic
287#542—22no—
288#541—22no—
289#539—21no—
290#539C22×C12712yes—
291#537C22×C12711yescharacteristic
292#536—21no—
293#533—22no—
294C2×#127C22×C12711yescharacteristic
295#529—22no—
296#529—21no—
297#529C22×C12712yes—
298C2×#124—21no—
299C4×#41—21no—
300C2×C4×Q8C22×C12711yescharacteristic
301#496—22no—
302#490—22no—
303#460—22no—
304#459—22no—
305#450C22×C12714yes—
306#447C22×C12714yes—
307#432C22×C12712yes—
308#394C22×C12712yes—
309#394C22×C12712yes—
310#390—21no—
311#390—21no—
312#390—21no—
313C4×C4⋊C4C22×C12711yescharacteristic
314#328C22×C12714yes—
315#327C22×C12714yes—
316#324C22×C12712yes—
317#324C22×C12712yes—
318C2×#41—21no—
319C22×Q8D4×C12711yescharacteristic
320C22×D4—21no—
321C22×D4—21no—
322C22×D4C23×C12712yes—
323C2×SD16—24no—
324C2×D8—24no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327#127—22no—
328#127—22no—
329#126—22no—
330#126—22no—
331#126—22no—
332#126—22no—
333#125—21no—
334#125—22no—
335#125—22no—
336#125—22no—
337#125D4×C12712yes—
338#124—22no—
339#124—21no—
340#124—44no—
341#124D4×C12712yes—
342#123—22no—
343#123—22no—
344#123—22no—
345#123—22no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8—21no—
351C22⋊Q8—22no—
352C22⋊Q8C23×C12712yes—
353#121—22no—
354#121—21no—
355#121C23×C12712yes—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8—22no—
360C4×Q8—22no—
361C4×Q8D4×C12712yes—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4D4×C12712yes—
368#117—22no—
369#117—22no—
370#117—21no—
371#117—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4D4×C12711yescharacteristic
374C2×C4⋊C4C23×C12711yescharacteristic
375C2×C4⋊C4C23×C12711yescharacteristic
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C42—22no—
381C2×C42—21no—
382C2×C42D4×C12711yescharacteristic
383C2×C42D4×C12711yescharacteristic
384C2×C42C23×C12711yescharacteristic
385C4⋊C8—22no—
386#102—24no—
387#102—24no—
388C22⋊C8C23×C12714yes—
389#97—22no—
390#95C23×C12712yes—
391C24—22no—
392#41—42no—
393#41—42no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—41no—
399C2×Q8C2×D4×C12712yes—
400C2×D4—21no—
401C2×D4—22no—
402C2×D4—21no—
403C2×D4—24no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4—42no—
408C2×D4—41no—
409C2×D4—42no—
410C2×D4—41no—
411C2×D4—82no—
412C2×D4C2×D4×C12712yes—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4C2×D4×C12711yescharacteristic
418C22×C4C2×D4×C12711yescharacteristic
419C22×C4C2×D4×C12711yescharacteristic
420C22×C4C2×D4×C12711yescharacteristic
421C22×C4C2×D4×C12711yescharacteristic
422C22×C4C2×D4×C12711yescharacteristic
423C22×C4C24×C12711yescharacteristic
424SD16—84no—
425D8—84no—
426C2×C8—24no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—42no—
443C4⋊C4C2×D4×C12712yes—
444C4⋊C4C2×D4×C12712yes—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—44no—
455C22⋊C4—44no—
456C22⋊C4—82no—
457C22⋊C4—82no—
458C42—22no—
459C42—22no—
460C42—21no—
461C42—22no—
462C42—21no—
463C42—21no—
464C42—21no—
465C42—42no—
466C42C2×D4×C12712yes—
467C42C2×D4×C12712yes—
468C23—22no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23C22×D4×C12711yescharacteristic
477Q8—44no—
478Q8—42no—
479Q8—42no—
480Q8—81no—
481D4—42no—
482D4—42no—
483D4—44no—
484D4—44no—
485D4—42no—
486D4—42no—
487D4—84no—
488D4—82no—
489D4—81no—
490D4—82no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—82no—
513C2×C4#120×C12711yescharacteristic
514C2×C4#120×C12712yes—
515C2×C4#120×C12711yescharacteristic
516C2×C4AGL(1,ℤ/8)×C12712yes—
517C2×C4C22×D4×C12712yes—
518C8—44no—
519C22—21no—
520C22—21no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—82no—
525C22—82no—
526C22—82no—
527C22—82no—
528C22—82no—
529C22—82no—
530C22—82no—
531C22C2×#120×C12711yescharacteristic
532C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
533C22#575×C12711yescharacteristic
534C4—22no—
535C4—22no—
536C4—21no—
537C4—22no—
538C4—41no—
539C4—42no—
540C4—42no—
541C4—41no—
542C4—41no—
543C4—42no—
544C4—82no—
545C4#454×C12712yes—
546C2—21no—
547C2—21no—
548C2—82no—
549C2—162no—
550C2C127×#300611yescharacteristic
551C2C2×#454×C12711yescharacteristic
552C2C127×#302711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
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
1. C127×#3461C2semidirect
2. C127×#3217C2semidirect
3. C127×#2548C2semidirect
4. C127×#1599C2semidirect
5. C127×#1598C2semidirect
6. C127×#1597C2semidirect
7. C127×#1509C2semidirect
8. C127×#1467C2semidirect
269. #18337C127direct (N × H)
277. #3461C2×C127semidirect
278. #3217C2×C127semidirect
279. #2548C2×C127semidirect
280. #1599C2×C127semidirect
281. #1598C2×C127semidirect
282. #1597C2×C127semidirect
283. #1509C2×C127semidirect
284. #1467C2×C127semidirect
285. C127#18337direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34612
C127×#32172
C127×#25482
C127×#15992
C127×#15982
C127×#15972
C127×#15092
C127×#14672
#18337127