Finite Group Databasebeta

← C127×#8429 #44572102

Subgroups — C127×#8429 #44572102

Order 32512.

936 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×#3497C211yesmaximal, characteristic
2C127×#1805C211yesmaximal, characteristic, complemented
3C127×#1540C211yesmaximal, characteristic, complemented
4C127×#1517C211yesmaximal, characteristic, complemented
5C127×#1517C211yesmaximal, characteristic, complemented
6C127×#1480C211yesmaximal, characteristic, complemented
7C127×#1479C211yesmaximal, characteristic, complemented
8C2×2−1+4×C127—21no—
9#550×C127—21no—
10#550×C127C412yescomplemented
11D4×Q8×C127—21no—
12D4×Q8×C127C412yescomplemented
13#548×C127—22no—
14#548×C127—22no—
15#537×C127—22no—
16#537×C127—21no—
17#532×C127—22no—
18#532×C127C2211yescharacteristic
19#532×C127C2211yescharacteristic
20C2×C4×Q8×C127C2211yescharacteristic
21#431×C127C2211yescharacteristic
22#431×C127C2211yescharacteristic
23C2×C4⋊C8×C127C2211yescharacteristic
24C2×#103×C127—21no—
25#382×C127C2211yescharacteristic
26#340×C127—21no—
27#332×C127—21no—
28#331×C127—21no—
29#327×C127—22no—
30#327×C127—22no—
31Q8⋊C8×C127—22no—
32D4⋊C8×C127—22no—
332−1+4×C127—42no—
342−1+4×C127—42no—
352−1+4×C127—42no—
362−1+4×C127—42no—
37C2×#41×C127—24no—
38C2×#41×C127—22no—
39C2×#41×C127—22no—
40C2×#41×C127—21no—
41C2×#41×C127—21no—
42C22×Q8×C127—22no—
43C22×Q8×C127—22no—
44C22×Q8×C127D411yescharacteristic
45C22×C8×C127—21no—
46C4⋊Q8×C127—22no—
47C4⋊Q8×C127C2×C411yescharacteristic
48C4⋊Q8×C127D411yescharacteristic
49#127×C127—22no—
50#127×C127C2×C411yescharacteristic
51#127×C127D411yescharacteristic
52#124×C127—24no—
53#124×C127—21no—
54#124×C127—21no—
55C22⋊Q8×C127—22no—
56C22⋊Q8×C127—24no—
57C22⋊Q8×C127—22no—
58C22⋊Q8×C127—24no—
59#121×C127—24no—
60#121×C127—22no—
61#121×C127—24no—
62#121×C127—24no—
63#121×C127—21no—
64#121×C127—21no—
65#121×C127—22no—
66#121×C127D412yes—
67#121×C127D412yes—
68C4×Q8×C127—21no—
69C4×Q8×C127—21no—
70C4×Q8×C127C2×C412yes—
71C4×Q8×C127D412yes—
72C4×D4×C127—24no—
73C4×D4×C127—22no—
74C4×D4×C127—22no—
75C4×D4×C127—21no—
76C4×D4×C127—21no—
77C4×D4×C127C2×C412yes—
78C4×D4×C127D412yes—
79C2×C4⋊C4×C127—21no—
80C2×C4⋊C4×C127—21no—
81C2×C4⋊C4×C127D411yescharacteristic
82C2×C42×C127—21no—
83C2×C42×C127C2311yescharacteristic
84C4⋊C8×C127—21no—
85C4⋊C8×C127—21no—
86C4⋊C8×C127—21no—
87C4⋊C8×C127—21no—
88#103×C127—42no—
89C22⋊C8×C127—21no—
90C22⋊C8×C127—21no—
91C4×C8×C127—21no—
92C4×C8×C127—21no—
93#95×C127—21no—
94#95×C127—21no—
95#41×C127—48no—
96#41×C127—48no—
97#41×C127—44no—
98#41×C127—44no—
99#41×C127—44no—
100#41×C127—44no—
101#41×C127—41no—
102#41×C127—41no—
103#41×C127—41no—
104#41×C127—41no—
105#41×C127—41no—
106#41×C127—41no—
107#41×C127—41no—
108#41×C127—41no—
109C2×Q8×C127—24no—
110C2×Q8×C127—21no—
111C2×Q8×C127—21no—
112C2×Q8×C127—21no—
113C2×Q8×C127—21no—
114C2×Q8×C127—21no—
115C2×Q8×C127—44no—
116C2×Q8×C127—44no—
117C2×Q8×C127—44no—
118C2×Q8×C127—44no—
119C2×Q8×C127C22⋊C412yes—
120C2×Q8×C127D812yes—
121C2×Q8×C127SD1612yes—
122C2×D4×C127—24no—
123C2×D4×C127—22no—
124C2×D4×C127—22no—
125C2×D4×C127—24no—
126C2×D4×C127—21no—
127C2×D4×C127—21no—
128C2×D4×C127—21no—
129C2×D4×C127—21no—
130C2×D4×C127C22⋊C412yes—
131C2×D4×C127C22⋊C412yes—
132C22×C4×C127—21no—
133C22×C4×C127—24no—
134C22×C4×C127—24no—
135C22×C4×C127—21no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—41no—
139C22×C4×C127C2×D411yescharacteristic
140C22×C4×C127C2×D411yescharacteristic
141C22×C4×C127C2×D411yescharacteristic
142C2×C8×C127—41no—
143C2×C8×C127—41no—
144C2×C8×C127—41no—
145C2×C8×C127—41no—
146C2×C8×C127—41no—
147C4⋊C4×C127—24no—
148C4⋊C4×C127—22no—
149C4⋊C4×C127—21no—
150C4⋊C4×C127—22no—
151C4⋊C4×C127—21no—
152C4⋊C4×C127—21no—
153C4⋊C4×C127—41no—
154C4⋊C4×C127—41no—
155C4⋊C4×C127C22⋊C412yes—
156C4⋊C4×C127C22⋊C412yes—
157C4⋊C4×C127C22⋊C412yes—
158C22⋊C4×C127—24no—
159C22⋊C4×C127—24no—
160C22⋊C4×C127—22no—
161C22⋊C4×C127—22no—
162C22⋊C4×C127—22no—
163C22⋊C4×C127—22no—
164C42×C127—22no—
165C42×C127—22no—
166C42×C127C22×C411yescharacteristic
167C42×C127C2×D411yescharacteristic
168C42×C127C2×D411yescharacteristic
169C42×C127C2×D411yescharacteristic
170C23×C127—22no—
171C23×C127—22no—
172C23×C127#12011yescharacteristic
173Q8×C127—22no—
174Q8×C127—22no—
175Q8×C127—22no—
176Q8×C127—48no—
177Q8×C127—41no—
178Q8×C127—41no—
179Q8×C127—41no—
180Q8×C127—41no—
181Q8×C127#10214yes—
182D4×C127—42no—
183D4×C127—42no—
184D4×C127—42no—
185D4×C127—48no—
186D4×C127—42no—
187D4×C127—42no—
188D4×C127—42no—
189D4×C127—42no—
190D4×C127—41no—
191D4×C127—41no—
192D4×C127—41no—
193D4×C127—41no—
194D4×C127—81no—
195D4×C127—84no—
196C2×C4×C127—22no—
197C2×C4×C127—22no—
198C2×C4×C127—22no—
199C2×C4×C127—22no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—41no—
203C2×C4×C127—41no—
204C2×C4×C127—48no—
205C2×C4×C127—48no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—42no—
209C2×C4×C127—42no—
210C2×C4×C127—81no—
211C2×C4×C127—81no—
212C2×C4×C127—81no—
213C2×C4×C127—81no—
214C2×C4×C127C2×C22⋊C411yescharacteristic
215C2×C4×C127C2×C22⋊C411yescharacteristic
216C2×C4×C127C2×C22⋊C411yescharacteristic
217C2×C4×C127#12011yescharacteristic
218C2×C4×C127#12011yescharacteristic
219C2×C4×C127#12011yescharacteristic
220C2×C4×C127C2×D811yescharacteristic
221C2×C4×C127C2×SD1611yescharacteristic
222C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
223C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
224C8×C127—81no—
225C8×C127—81no—
226C8×C127—81no—
227C22×C127—21no—
228C22×C127—21no—
229C22×C127—42no—
230C22×C127—42no—
231C22×C127—42no—
232C22×C127—42no—
233C22×C127—42no—
234C22×C127—42no—
235C22×C127#37911yescharacteristic
236C22×C127#44711yescharacteristic
237C22×C127#45011yescharacteristic
238C4×C127—21no—
239C4×C127—21no—
240C4×C127—21no—
241C4×C127—21no—
242C4×C127—24no—
243C4×C127—42no—
244C4×C127—42no—
245C4×C127—42no—
246C4×C127—161no—
247C4×C127C2×#10211yescharacteristic
248C4×C127#41811yescharacteristic
249C4×C127#44711yescharacteristic
250C4×C127#45011yescharacteristic
251#8429C12711yesmaximal, characteristic, direct product factor, Sylow
252C2×C127—21no—
253C2×C127—21no—
254C2×C127—82no—
255C2×C127—82no—
256C2×C127#178611yescharacteristic
257C2×C127#179411yescharacteristic
258C2×C127#179611yescharacteristic
259#3497C2×C12711yescharacteristic
260#1805C2×C12711yescharacteristic, complemented
261#1540C2×C12711yescharacteristic, complemented
262#1517C2×C12711yescharacteristic, complemented
263#1517C2×C12711yescharacteristic, complemented
264#1480C2×C12711yescharacteristic, complemented
265#1479C2×C12711yescharacteristic, complemented
266C127#842911yescharacteristic, direct product factor, Sylow
267C2×2−1+4—21no—
268#550—21no—
269#550C4×C12712yescomplemented
270D4×Q8—21no—
271D4×Q8C4×C12712yescomplemented
272#548—22no—
273#548—22no—
274#537—22no—
275#537—21no—
276#532—22no—
277#532C22×C12711yescharacteristic
278#532C22×C12711yescharacteristic
279C2×C4×Q8C22×C12711yescharacteristic
280#431C22×C12711yescharacteristic
281#431C22×C12711yescharacteristic
282C2×C4⋊C8C22×C12711yescharacteristic
283C2×#103—21no—
284#382C22×C12711yescharacteristic
285#340—21no—
286#332—21no—
287#331—21no—
288#327—22no—
289#327—22no—
290Q8⋊C8—22no—
291D4⋊C8—22no—
2922−1+4—42no—
2932−1+4—42no—
2942−1+4—42no—
2952−1+4—42no—
296C2×#41—24no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—21no—
300C2×#41—21no—
301C22×Q8—22no—
302C22×Q8—22no—
303C22×Q8D4×C12711yescharacteristic
304C22×C8—21no—
305C4⋊Q8—22no—
306C4⋊Q8C2×C4×C12711yescharacteristic
307C4⋊Q8D4×C12711yescharacteristic
308#127—22no—
309#127C2×C4×C12711yescharacteristic
310#127D4×C12711yescharacteristic
311#124—24no—
312#124—21no—
313#124—21no—
314C22⋊Q8—22no—
315C22⋊Q8—24no—
316C22⋊Q8—22no—
317C22⋊Q8—24no—
318#121—24no—
319#121—22no—
320#121—24no—
321#121—24no—
322#121—21no—
323#121—21no—
324#121—22no—
325#121D4×C12712yes—
326#121D4×C12712yes—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8C2×C4×C12712yes—
330C4×Q8D4×C12712yes—
331C4×D4—24no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4C2×C4×C12712yes—
337C4×D4D4×C12712yes—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4D4×C12711yescharacteristic
341C2×C42—21no—
342C2×C42C23×C12711yescharacteristic
343C4⋊C8—21no—
344C4⋊C8—21no—
345C4⋊C8—21no—
346C4⋊C8—21no—
347#103—42no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C4×C8—21no—
351C4×C8—21no—
352#95—21no—
353#95—21no—
354#41—48no—
355#41—48no—
356#41—44no—
357#41—44no—
358#41—44no—
359#41—44no—
360#41—41no—
361#41—41no—
362#41—41no—
363#41—41no—
364#41—41no—
365#41—41no—
366#41—41no—
367#41—41no—
368C2×Q8—24no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—44no—
375C2×Q8—44no—
376C2×Q8—44no—
377C2×Q8—44no—
378C2×Q8C22⋊C4×C12712yes—
379C2×Q8D8×C12712yes—
380C2×Q8SD16×C12712yes—
381C2×D4—24no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—24no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4C22⋊C4×C12712yes—
390C2×D4C22⋊C4×C12712yes—
391C22×C4—21no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—41no—
398C22×C4C2×D4×C12711yescharacteristic
399C22×C4C2×D4×C12711yescharacteristic
400C22×C4C2×D4×C12711yescharacteristic
401C2×C8—41no—
402C2×C8—41no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C4⋊C4—24no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4C22⋊C4×C12712yes—
415C4⋊C4C22⋊C4×C12712yes—
416C4⋊C4C22⋊C4×C12712yes—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C42—22no—
424C42—22no—
425C42C22×C4×C12711yescharacteristic
426C42C2×D4×C12711yescharacteristic
427C42C2×D4×C12711yescharacteristic
428C42C2×D4×C12711yescharacteristic
429C23—22no—
430C23—22no—
431C23#120×C12711yescharacteristic
432Q8—22no—
433Q8—22no—
434Q8—22no—
435Q8—48no—
436Q8—41no—
437Q8—41no—
438Q8—41no—
439Q8—41no—
440Q8#102×C12714yes—
441D4—42no—
442D4—42no—
443D4—48no—
444D4—42no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—41no—
450D4—41no—
451D4—41no—
452D4—41no—
453D4—81no—
454D4—84no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—48no—
464C2×C4—48no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4C2×C22⋊C4×C12711yescharacteristic
474C2×C4C2×C22⋊C4×C12711yescharacteristic
475C2×C4C2×C22⋊C4×C12711yescharacteristic
476C2×C4#120×C12711yescharacteristic
477C2×C4#120×C12711yescharacteristic
478C2×C4#120×C12711yescharacteristic
479C2×C4C2×D8×C12711yescharacteristic
480C2×C4C2×SD16×C12711yescharacteristic
481C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
482C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
483C8—81no—
484C8—81no—
485C8—81no—
486C22—21no—
487C22—21no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22#379×C12711yescharacteristic
495C22#447×C12711yescharacteristic
496C22#450×C12711yescharacteristic
497C4—24no—
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—42no—
503C4—42no—
504C4—42no—
505C4—161no—
506C4C2×#102×C12711yescharacteristic
507C4#418×C12711yescharacteristic
508C4#447×C12711yescharacteristic
509C4#450×C12711yescharacteristic
510C2—21no—
511C2—21no—
512C2—82no—
513C2—82no—
514C2C127×#178611yescharacteristic
515C2C127×#179411yescharacteristic
516C2C127×#179611yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3497C2
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×#1805C2semidirect
3. C127×#1540C2semidirect
4. C127×#1517C2semidirect
5. C127×#1517C2semidirect
6. C127×#1480C2semidirect
7. C127×#1479C2semidirect
10. #550×C127C4semidirect
12. D4×Q8×C127C4semidirect
251. #8429C127direct (N × H)
260. #1805C2×C127semidirect
261. #1540C2×C127semidirect
262. #1517C2×C127semidirect
263. #1517C2×C127semidirect
264. #1480C2×C127semidirect
265. #1479C2×C127semidirect
266. C127#8429direct (N × H)
269. #550C4×C127semidirect
271. D4×Q8C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34972
C127×#18052
C127×#15402
C127×#15172
C127×#14802
C127×#14792
#8429127