Finite Group Databasebeta

← C127×#18634 #44582307

Subgroups — C127×#18634 #44582307

Order 32512.

1024 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3508C211yesmaximal, characteristic
2C127×#3229C211yesmaximal, characteristic, complemented
3C2×#486×C127C211yesmaximal, characteristic, complemented
4C127×#3039C211yesmaximal, characteristic, complemented
5C127×#1642C214yesmaximal, complemented
6C127×#1640C214yesmaximal, complemented
7C127×#1545C211yesmaximal, characteristic, complemented
8C127×#1493C211yesmaximal, characteristic, complemented
9C127×#1476C211yesmaximal, characteristic, complemented
10C2×#137×C127—21no—
11#559×C127—21no—
12#559×C127C2212yes—
13#550×C127—21no—
14#550×C127C2212yes—
15#546×C127—22no—
16#546×C127—22no—
17#540×C127—22no—
18#535×C127—21no—
19#533×C127C2211yescharacteristic
20#532×C127—21no—
21#532×C127—21no—
22C2×C4⋊Q8×C127C2211yescharacteristic
23C2×#127×C127C2211yescharacteristic
24#518×C127—21no—
25C4×#41×C127C2211yescharacteristic
26#498×C127—21no—
27#487×C127—21no—
28#486×C127—22no—
29#486×C127C2214yes—
30#483×C127—22no—
31#475×C127C2214yescomplemented
32#462×C127—21no—
33#462×C127C2212yescomplemented
34#461×C127—21no—
35#461×C127C2212yescomplemented
36#431×C127C2211yescharacteristic
37#423×C127C2211yescharacteristic
38#419×C127—21no—
39C2×#102×C127—22no—
40C2×C4×C8×C127C2211yescharacteristic
41#331×C127C2214yes—
42Q8⋊C8×C127C2212yescomplemented
43Q8⋊C8×C127C2214yescomplemented
44D4⋊C8×C127C2212yescomplemented
45C2×#41×C127—22no—
46C2×#41×C127—22no—
47C2×#41×C127D411yescharacteristic
48C22×Q8×C127—21no—
49C22×D4×C127—21no—
50C22×D4×C127—21no—
51C22×D4×C127D412yes—
52#137×C127—44no—
53C2×Q16×C127—22no—
54C2×SD16×C127—22no—
55C2×M16×C127—21no—
56C22×C8×C127—21no—
57C4⋊Q8×C127—21no—
58C4⋊Q8×C127—21no—
59C4⋊Q8×C127—21no—
60C4⋊Q8×C127D411yescharacteristic
61C4⋊Q8×C127D411yescharacteristic
62C4⋊Q8×C127C2312yes—
63#127×C127—22no—
64#127×C127—21no—
65#127×C127—21no—
66#127×C127D412yes—
67#127×C127C2312yes—
68#125×C127—21no—
69#124×C127—22no—
70#124×C127—22no—
71#124×C127—22no—
72#123×C127—24no—
73#123×C127—24no—
74C22⋊Q8×C127—21no—
75C22⋊Q8×C127D412yes—
76#121×C127—22no—
77#121×C127—22no—
78#121×C127—22no—
79#121×C127—24no—
80#121×C127—24no—
81#121×C127—22no—
82#120×C127—24no—
83C4×Q8×C127—21no—
84C4×Q8×C127D411yescharacteristic
85C4×Q8×C127C2311yescharacteristic
86C4×Q8×C127C2312yes—
87C4×D4×C127—22no—
88C4×D4×C127—22no—
89C4×D4×C127—22no—
90C4×D4×C127—21no—
91C4×D4×C127—21no—
92C4×D4×C127—22no—
93C4×D4×C127—22no—
94C4×D4×C127—22no—
95C4×D4×C127D411yescharacteristic
96C4×D4×C127C2311yescharacteristic
97#117×C127—21no—
98#117×C127—21no—
99#117×C127D411yescharacteristic
100C2×C4⋊C4×C127—21no—
101C2×C4⋊C4×C127—21no—
102C2×C22⋊C4×C127—24no—
103C2×C42×C127—21no—
104C2×C42×C127C2311yescharacteristic
105#106×C127—24no—
106C4⋊C8×C127—21no—
107C4⋊C8×C127C2312yes—
108C4⋊C8×C127C2312yes—
109#103×C127—24no—
110#103×C127—22no—
111#103×C127—22no—
112#102×C127—28no—
113C22⋊C8×C127—21no—
114C4×C8×C127—21no—
115C4×C8×C127—21no—
116C4×C8×C127C2312yes—
117C24×C127—22no—
118#41×C127—22no—
119#41×C127—22no—
120#41×C127—84no—
121#41×C127—84no—
122C2×Q8×C127—21no—
123C2×Q8×C127—22no—
124C2×Q8×C127—41no—
125C2×Q8×C127—42no—
126C2×Q8×C127—42no—
127C2×Q8×C127C2×D412yes—
128C2×Q8×C127C2×D411yescharacteristic
129C2×D4×C127—21no—
130C2×D4×C127—24no—
131C2×D4×C127—24no—
132C2×D4×C127—22no—
133C2×D4×C127—22no—
134C2×D4×C127—22no—
135C2×D4×C127—22no—
136C2×D4×C127—22no—
137C2×D4×C127—44no—
138C2×D4×C127—42no—
139C2×D4×C127—42no—
140C2×D4×C127—82no—
141C2×D4×C127C2×D411yescharacteristic
142C2×D4×C127C2×D414yes—
143C22×C4×C127—24no—
144C22×C4×C127—24no—
145C22×C4×C127—21no—
146C22×C4×C127—21no—
147C22×C4×C127—21no—
148C22×C4×C127—41no—
149C22×C4×C127C2×D411yescharacteristic
150C22×C4×C127C2×D411yescharacteristic
151C22×C4×C127C2×D411yescharacteristic
152Q16×C127—44no—
153SD16×C127—44no—
154M16×C127—42no—
155C2×C8×C127—22no—
156C2×C8×C127—22no—
157C2×C8×C127—22no—
158C2×C8×C127—42no—
159C4⋊C4×C127—21no—
160C4⋊C4×C127—21no—
161C4⋊C4×C127—21no—
162C4⋊C4×C127—21no—
163C4⋊C4×C127—22no—
164C4⋊C4×C127—21no—
165C4⋊C4×C127—22no—
166C4⋊C4×C127—22no—
167C4⋊C4×C127—22no—
168C4⋊C4×C127—41no—
169C4⋊C4×C127—41no—
170C4⋊C4×C127C2×D411yescharacteristic
171C4⋊C4×C127C2×D411yescharacteristic
172C4⋊C4×C127C2×D412yes—
173C22⋊C4×C127—24no—
174C22⋊C4×C127—24no—
175C22⋊C4×C127—24no—
176C22⋊C4×C127—24no—
177C22⋊C4×C127—21no—
178C22⋊C4×C127—22no—
179C22⋊C4×C127—21no—
180C22⋊C4×C127—21no—
181C42×C127—21no—
182C42×C127—21no—
183C42×C127—21no—
184C42×C127—22no—
185C42×C127C2×D411yescharacteristic
186C42×C127C2×D411yescharacteristic
187C42×C127C2×D411yescharacteristic
188C42×C127C2411yescharacteristic
189C23×C127—24no—
190C23×C127—21no—
191C23×C127—44no—
192C23×C127—82no—
193C23×C127—82no—
194C23×C127#12011yescharacteristic
195Q8×C127—21no—
196Q8×C127—21no—
197Q8×C127—24no—
198Q8×C127—42no—
199Q8×C127—42no—
200Q8×C127—42no—
201Q8×C127—82no—
202D4×C127—21no—
203D4×C127—21no—
204D4×C127—44no—
205D4×C127—42no—
206D4×C127—42no—
207D4×C127—42no—
208D4×C127—44no—
209D4×C127—44no—
210D4×C127—44no—
211D4×C127—82no—
212D4×C127—84no—
213D4×C127—84no—
214C2×C4×C127—22no—
215C2×C4×C127—22no—
216C2×C4×C127—21no—
217C2×C4×C127—21no—
218C2×C4×C127—21no—
219C2×C4×C127—22no—
220C2×C4×C127—22no—
221C2×C4×C127—42no—
222C2×C4×C127—42no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—84no—
226C2×C4×C127—84no—
227C2×C4×C127—82no—
228C2×C4×C127#12011yescharacteristic
229C2×C4×C127#12011yescharacteristic
230C2×C4×C127#12011yescharacteristic
231C2×C4×C127#13512yes—
232C2×C4×C127AGL(1,ℤ/8)12yes—
233C2×C4×C127C22×D411yescharacteristic
234C2×C4×C127C22×D411yescharacteristic
235C2×C4×C127C22×D411yescharacteristic
236C8×C127—42no—
237C8×C127—42no—
238C8×C127—42no—
239C22×C127—21no—
240C22×C127—21no—
241C22×C127—41no—
242C22×C127—44no—
243C22×C127—41no—
244C22×C127—44no—
245C22×C127—41no—
246C22×C127—44no—
247C22×C127—164no—
248C22×C127#44912yes—
249C22×C127C2×#12011yescharacteristic
250C4×C127—21no—
251C4×C127—21no—
252C4×C127—41no—
253C4×C127—41no—
254C4×C127—42no—
255C4×C127—41no—
256C4×C127—42no—
257C4×C127—82no—
258C4×C127#44912yes—
259C4×C127#45512yes—
260C4×C127C2×#13511yescharacteristic
261C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
262C4×C127#57712yes—
263#18634C12711yesmaximal, characteristic, direct product factor, Sylow
264C2×C127—22no—
265C2×C127—81no—
266C2×C127—84no—
267C2×C127C2×#44911yescharacteristic
268C2×C127#300911yescharacteristic
269C2×C127C2×#45511yescharacteristic
270#3508C2×C12711yescharacteristic
271#3229C2×C12711yescharacteristic, complemented
272C2×#486C2×C12711yescharacteristic, complemented
273#3039C2×C12711yescharacteristic, complemented
274#1642C2×C12714yescomplemented
275#1640C2×C12714yescomplemented
276#1545C2×C12711yescharacteristic, complemented
277#1493C2×C12711yescharacteristic, complemented
278#1476C2×C12711yescharacteristic, complemented
279C127#1863411yescharacteristic, direct product factor, Sylow
280C2×#137—21no—
281#559—21no—
282#559C22×C12712yes—
283#550—21no—
284#550C22×C12712yes—
285#546—22no—
286#546—22no—
287#540—22no—
288#535—21no—
289#533C22×C12711yescharacteristic
290#532—21no—
291#532—21no—
292C2×C4⋊Q8C22×C12711yescharacteristic
293C2×#127C22×C12711yescharacteristic
294#518—21no—
295C4×#41C22×C12711yescharacteristic
296#498—21no—
297#487—21no—
298#486—22no—
299#486C22×C12714yes—
300#483—22no—
301#475C22×C12714yescomplemented
302#462—21no—
303#462C22×C12712yescomplemented
304#461—21no—
305#461C22×C12712yescomplemented
306#431C22×C12711yescharacteristic
307#423C22×C12711yescharacteristic
308#419—21no—
309C2×#102—22no—
310C2×C4×C8C22×C12711yescharacteristic
311#331C22×C12714yes—
312Q8⋊C8C22×C12712yescomplemented
313Q8⋊C8C22×C12714yescomplemented
314D4⋊C8C22×C12712yescomplemented
315C2×#41—22no—
316C2×#41—22no—
317C2×#41D4×C12711yescharacteristic
318C22×Q8—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4D4×C12712yes—
322#137—44no—
323C2×Q16—22no—
324C2×SD16—22no—
325C2×M16—21no—
326C22×C8—21no—
327C4⋊Q8—21no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8D4×C12711yescharacteristic
331C4⋊Q8D4×C12711yescharacteristic
332C4⋊Q8C23×C12712yes—
333#127—22no—
334#127—21no—
335#127—21no—
336#127D4×C12712yes—
337#127C23×C12712yes—
338#125—21no—
339#124—22no—
340#124—22no—
341#124—22no—
342#123—24no—
343#123—24no—
344C22⋊Q8—21no—
345C22⋊Q8D4×C12712yes—
346#121—22no—
347#121—22no—
348#121—22no—
349#121—24no—
350#121—24no—
351#121—22no—
352#120—24no—
353C4×Q8—21no—
354C4×Q8D4×C12711yescharacteristic
355C4×Q8C23×C12711yescharacteristic
356C4×Q8C23×C12712yes—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4D4×C12711yescharacteristic
366C4×D4C23×C12711yescharacteristic
367#117—21no—
368#117—21no—
369#117D4×C12711yescharacteristic
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C22⋊C4—24no—
373C2×C42—21no—
374C2×C42C23×C12711yescharacteristic
375#106—24no—
376C4⋊C8—21no—
377C4⋊C8C23×C12712yes—
378C4⋊C8C23×C12712yes—
379#103—24no—
380#103—22no—
381#103—22no—
382#102—28no—
383C22⋊C8—21no—
384C4×C8—21no—
385C4×C8—21no—
386C4×C8C23×C12712yes—
387C24—22no—
388#41—22no—
389#41—22no—
390#41—84no—
391#41—84no—
392C2×Q8—21no—
393C2×Q8—22no—
394C2×Q8—41no—
395C2×Q8—42no—
396C2×Q8—42no—
397C2×Q8C2×D4×C12712yes—
398C2×Q8C2×D4×C12711yescharacteristic
399C2×D4—21no—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—44no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—82no—
411C2×D4C2×D4×C12711yescharacteristic
412C2×D4C2×D4×C12714yes—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—41no—
419C22×C4C2×D4×C12711yescharacteristic
420C22×C4C2×D4×C12711yescharacteristic
421C22×C4C2×D4×C12711yescharacteristic
422Q16—44no—
423SD16—44no—
424M16—42no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—42no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C4⋊C4C2×D4×C12711yescharacteristic
441C4⋊C4C2×D4×C12711yescharacteristic
442C4⋊C4C2×D4×C12712yes—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—21no—
448C22⋊C4—22no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C42—21no—
452C42—21no—
453C42—21no—
454C42—22no—
455C42C2×D4×C12711yescharacteristic
456C42C2×D4×C12711yescharacteristic
457C42C2×D4×C12711yescharacteristic
458C42C24×C12711yescharacteristic
459C23—24no—
460C23—21no—
461C23—44no—
462C23—82no—
463C23—82no—
464C23#120×C12711yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—24no—
468Q8—42no—
469Q8—42no—
470Q8—42no—
471Q8—82no—
472D4—21no—
473D4—21no—
474D4—44no—
475D4—42no—
476D4—42no—
477D4—42no—
478D4—44no—
479D4—44no—
480D4—44no—
481D4—82no—
482D4—84no—
483D4—84no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—84no—
496C2×C4—84no—
497C2×C4—82no—
498C2×C4#120×C12711yescharacteristic
499C2×C4#120×C12711yescharacteristic
500C2×C4#120×C12711yescharacteristic
501C2×C4#135×C12712yes—
502C2×C4AGL(1,ℤ/8)×C12712yes—
503C2×C4C22×D4×C12711yescharacteristic
504C2×C4C22×D4×C12711yescharacteristic
505C2×C4C22×D4×C12711yescharacteristic
506C8—42no—
507C8—42no—
508C8—42no—
509C22—21no—
510C22—21no—
511C22—41no—
512C22—44no—
513C22—41no—
514C22—44no—
515C22—41no—
516C22—44no—
517C22—164no—
518C22#449×C12712yes—
519C22C2×#120×C12711yescharacteristic
520C4—21no—
521C4—21no—
522C4—41no—
523C4—41no—
524C4—42no—
525C4—41no—
526C4—42no—
527C4—82no—
528C4#449×C12712yes—
529C4#455×C12712yes—
530C4C2×#135×C12711yescharacteristic
531C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
532C4#577×C12712yes—
533C2—22no—
534C2—84no—
535C2—81no—
536C2C2×#449×C12711yescharacteristic
537C2C127×#300911yescharacteristic
538C2C2×#455×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3508C2
LCSG ▷ C42 ▷ 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×#3229C2semidirect
3. C2×#486×C127C2semidirect
4. C127×#3039C2semidirect
5. C127×#1642C2semidirect
6. C127×#1640C2semidirect
7. C127×#1545C2semidirect
8. C127×#1493C2semidirect
9. C127×#1476C2semidirect
31. #475×C127C22semidirect
33. #462×C127C22semidirect
35. #461×C127C22semidirect
42. Q8⋊C8×C127C22semidirect
43. Q8⋊C8×C127C22semidirect
44. D4⋊C8×C127C22semidirect
263. #18634C127direct (N × H)
271. #3229C2×C127semidirect
272. C2×#486C2×C127semidirect
273. #3039C2×C127semidirect
274. #1642C2×C127semidirect
275. #1640C2×C127semidirect
276. #1545C2×C127semidirect
277. #1493C2×C127semidirect
278. #1476C2×C127semidirect
279. C127#18634direct (N × H)
301. #475C22×C127semidirect
303. #462C22×C127semidirect
305. #461C22×C127semidirect
312. Q8⋊C8C22×C127semidirect
313. Q8⋊C8C22×C127semidirect
314. D4⋊C8C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35082
C127×#32292
C2×#486×C1272
C127×#30392
C127×#16422
C127×#16402
C127×#15452
C127×#14932
C127×#14762
#18634127