Finite Group Databasebeta

← C127×#8426 #44572099

Subgroups — C127×#8426 #44572099

Order 32512.

836 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3508C211yesmaximal, characteristic
2C127×#1982C211yesmaximal, characteristic, complemented
3C127×#1806C211yesmaximal, characteristic, complemented
4C127×#1550C211yesmaximal, characteristic, complemented
5C127×#1545C211yesmaximal, characteristic, complemented
6C127×#1503C211yesmaximal, characteristic, complemented
7C127×#1477C211yesmaximal, characteristic, complemented
8#559×C127—21no—
9#559×C127C412yescomplemented
10#550×C127—21no—
11#550×C127C412yescomplemented
12#546×C127—22no—
13#546×C127—22no—
14#540×C127—22no—
15#535×C127—21no—
16#533×C127C2211yescharacteristic
17#532×C127—21no—
18#532×C127—21no—
19C2×#127×C127C2211yescharacteristic
20#518×C127—21no—
21C4×#41×C127C2211yescharacteristic
22#431×C127C2211yescharacteristic
23#423×C127C2211yescharacteristic
24C2×C4⋊C8×C127C2211yescharacteristic
25C2×#104×C127—21no—
26C2×#102×C127—22no—
27C4×C4⋊C4×C127C2211yescharacteristic
28#339×C127—21no—
29#333×C127—21no—
30#332×C127—21no—
31#331×C127—22no—
32#328×C127—22no—
33Q8⋊C8×C127—21no—
34D4⋊C8×C127—21no—
35C2×#41×C127—22no—
36C2×#41×C127—22no—
37C2×#41×C127D411yescharacteristic
38C22×D4×C127—21no—
39C22×D4×C127—21no—
40C22×D4×C127D412yes—
41C2×M16×C127—21no—
42C22×C8×C127—21no—
43C4⋊Q8×C127D411yescharacteristic
44C4⋊Q8×C127D411yescharacteristic
45#127×C127—22no—
46#127×C127—21no—
47#127×C127—21no—
48#127×C127C2×C412yes—
49#127×C127D412yes—
50#125×C127—21no—
51#124×C127—22no—
52#124×C127—22no—
53#124×C127—22no—
54#123×C127—24no—
55#123×C127—24no—
56C22⋊Q8×C127—21no—
57C22⋊Q8×C127D412yes—
58#121×C127—22no—
59#121×C127—22no—
60#121×C127—22no—
61#121×C127—24no—
62#121×C127—24no—
63#121×C127—22no—
64#120×C127—24no—
65C4×Q8×C127—21no—
66C4×Q8×C127C2×C411yescharacteristic
67C4×Q8×C127C2×C412yes—
68C4×Q8×C127D411yescharacteristic
69C4×D4×C127—22no—
70C4×D4×C127—22no—
71C4×D4×C127—22no—
72C4×D4×C127—21no—
73C4×D4×C127—21no—
74C4×D4×C127—22no—
75C4×D4×C127—22no—
76C4×D4×C127—22no—
77C4×D4×C127C2×C411yescharacteristic
78C4×D4×C127D411yescharacteristic
79#117×C127—21no—
80#117×C127—21no—
81#117×C127D411yescharacteristic
82C2×C4⋊C4×C127—21no—
83C2×C22⋊C4×C127—24no—
84C2×C42×C127—21no—
85C2×C42×C127—21no—
86C2×C42×C127C2311yescharacteristic
87C4⋊C8×C127—21no—
88C4⋊C8×C127—21no—
89C4⋊C8×C127—21no—
90C4⋊C8×C127—21no—
91C4⋊C8×C127—21no—
92#104×C127—42no—
93#102×C127—44no—
94C22⋊C8×C127—21no—
95C4×C8×C127—21no—
96#95×C127—21no—
97C24×C127—22no—
98#41×C127—21no—
99#41×C127—21no—
100#41×C127—21no—
101#41×C127—21no—
102#41×C127—84no—
103#41×C127—82no—
104#41×C127—82no—
105C2×Q8×C127—21no—
106C2×Q8×C127C22⋊C411yescharacteristic
107C2×Q8×C127C22⋊C412yes—
108C2×D4×C127—21no—
109C2×D4×C127—24no—
110C2×D4×C127—24no—
111C2×D4×C127—22no—
112C2×D4×C127—22no—
113C2×D4×C127—22no—
114C2×D4×C127—22no—
115C2×D4×C127—22no—
116C2×D4×C127—42no—
117C2×D4×C127—42no—
118C2×D4×C127—41no—
119C2×D4×C127—41no—
120C2×D4×C127—41no—
121C2×D4×C127—41no—
122C2×D4×C127—82no—
123C2×D4×C127C22⋊C411yescharacteristic
124C2×D4×C127C22⋊C414yes—
125C22×C4×C127—24no—
126C22×C4×C127—24no—
127C22×C4×C127—21no—
128C22×C4×C127—21no—
129C22×C4×C127—21no—
130C22×C4×C127—41no—
131C22×C4×C127C2×D411yescharacteristic
132C22×C4×C127C2×D411yescharacteristic
133C22×C4×C127C2×D411yescharacteristic
134M16×C127—41no—
135M16×C127—41no—
136C2×C8×C127—42no—
137C2×C8×C127—41no—
138C2×C8×C127—41no—
139C2×C8×C127—41no—
140C4⋊C4×C127—21no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—21no—
143C4⋊C4×C127—21no—
144C4⋊C4×C127—21no—
145C4⋊C4×C127—21no—
146C4⋊C4×C127—22no—
147C4⋊C4×C127—22no—
148C4⋊C4×C127—41no—
149C4⋊C4×C127C22⋊C411yescharacteristic
150C4⋊C4×C127C22⋊C411yescharacteristic
151C4⋊C4×C127C22⋊C412yes—
152C22⋊C4×C127—24no—
153C22⋊C4×C127—24no—
154C22⋊C4×C127—24no—
155C22⋊C4×C127—24no—
156C22⋊C4×C127—21no—
157C22⋊C4×C127—22no—
158C22⋊C4×C127—21no—
159C22⋊C4×C127—21no—
160C42×C127—21no—
161C42×C127—22no—
162C42×C127—21no—
163C42×C127—21no—
164C42×C127—41no—
165C42×C127—41no—
166C42×C127C22×C411yescharacteristic
167C42×C127C2×D411yescharacteristic
168C42×C127C2×D411yescharacteristic
169C42×C127C2×D411yescharacteristic
170C23×C127—24no—
171C23×C127—21no—
172C23×C127—42no—
173C23×C127—42no—
174C23×C127—82no—
175C23×C127—82no—
176C23×C127#12011yescharacteristic
177Q8×C127—21no—
178Q8×C127—21no—
179Q8×C127—42no—
180Q8×C127—41no—
181Q8×C127—41no—
182D4×C127—21no—
183D4×C127—21no—
184D4×C127—44no—
185D4×C127—44no—
186D4×C127—41no—
187D4×C127—41no—
188D4×C127—42no—
189D4×C127—42no—
190D4×C127—42no—
191D4×C127—42no—
192D4×C127—42no—
193D4×C127—42no—
194D4×C127—82no—
195D4×C127—84no—
196D4×C127—84no—
197C2×C4×C127—21no—
198C2×C4×C127—21no—
199C2×C4×C127—21no—
200C2×C4×C127—21no—
201C2×C4×C127—21no—
202C2×C4×C127—22no—
203C2×C4×C127—22no—
204C2×C4×C127—41no—
205C2×C4×C127—42no—
206C2×C4×C127—41no—
207C2×C4×C127—41no—
208C2×C4×C127—41no—
209C2×C4×C127—41no—
210C2×C4×C127—42no—
211C2×C4×C127—84no—
212C2×C4×C127—84no—
213C2×C4×C127—81no—
214C2×C4×C127—81no—
215C2×C4×C127C2×C22⋊C411yescharacteristic
216C2×C4×C127C2×C22⋊C411yescharacteristic
217C2×C4×C127C2×C22⋊C411yescharacteristic
218C2×C4×C127#12011yescharacteristic
219C2×C4×C127#12011yescharacteristic
220C2×C4×C127#12011yescharacteristic
221C2×C4×C127#13511yescharacteristic
222C2×C4×C127#13511yescharacteristic
223C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
224C2×C4×C127#13711yescharacteristic
225C8×C127—81no—
226C8×C127—81no—
227C8×C127—81no—
228C22×C127—21no—
229C22×C127—21no—
230C22×C127—41no—
231C22×C127—44no—
232C22×C127—41no—
233C22×C127—44no—
234C22×C127—41no—
235C22×C127—44no—
236C22×C127—162no—
237C22×C127—162no—
238C22×C127#37911yescharacteristic
239C22×C127#44911yescharacteristic
240C22×C127#45211yescharacteristic
241C4×C127—21no—
242C4×C127—21no—
243C4×C127—21no—
244C4×C127—41no—
245C4×C127—42no—
246C4×C127—41no—
247C4×C127—42no—
248C4×C127—41no—
249C4×C127—82no—
250C4×C127#41611yescharacteristic
251C4×C127#41711yescharacteristic
252C4×C127#44911yescharacteristic
253C4×C127#45211yescharacteristic
254C4×C127#45311yescharacteristic
255C4×C127#45511yescharacteristic
256#8426C12711yesmaximal, characteristic, direct product factor, Sylow
257C2×C127—21no—
258C2×C127—21no—
259C2×C127—81no—
260C2×C127—84no—
261C2×C127#178811yescharacteristic
262C2×C127#179211yescharacteristic
263C2×C127#179511yescharacteristic
264#3508C2×C12711yescharacteristic
265#1982C2×C12711yescharacteristic, complemented
266#1806C2×C12711yescharacteristic, complemented
267#1550C2×C12711yescharacteristic, complemented
268#1545C2×C12711yescharacteristic, complemented
269#1503C2×C12711yescharacteristic, complemented
270#1477C2×C12711yescharacteristic, complemented
271C127#842611yescharacteristic, direct product factor, Sylow
272#559—21no—
273#559C4×C12712yescomplemented
274#550—21no—
275#550C4×C12712yescomplemented
276#546—22no—
277#546—22no—
278#540—22no—
279#535—21no—
280#533C22×C12711yescharacteristic
281#532—21no—
282#532—21no—
283C2×#127C22×C12711yescharacteristic
284#518—21no—
285C4×#41C22×C12711yescharacteristic
286#431C22×C12711yescharacteristic
287#423C22×C12711yescharacteristic
288C2×C4⋊C8C22×C12711yescharacteristic
289C2×#104—21no—
290C2×#102—22no—
291C4×C4⋊C4C22×C12711yescharacteristic
292#339—21no—
293#333—21no—
294#332—21no—
295#331—22no—
296#328—22no—
297Q8⋊C8—21no—
298D4⋊C8—21no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41D4×C12711yescharacteristic
302C22×D4—21no—
303C22×D4—21no—
304C22×D4D4×C12712yes—
305C2×M16—21no—
306C22×C8—21no—
307C4⋊Q8D4×C12711yescharacteristic
308C4⋊Q8D4×C12711yescharacteristic
309#127—22no—
310#127—21no—
311#127—21no—
312#127C2×C4×C12712yes—
313#127D4×C12712yes—
314#125—21no—
315#124—22no—
316#124—22no—
317#124—22no—
318#123—24no—
319#123—24no—
320C22⋊Q8—21no—
321C22⋊Q8D4×C12712yes—
322#121—22no—
323#121—22no—
324#121—22no—
325#121—24no—
326#121—24no—
327#121—22no—
328#120—24no—
329C4×Q8—21no—
330C4×Q8C2×C4×C12711yescharacteristic
331C4×Q8C2×C4×C12712yes—
332C4×Q8D4×C12711yescharacteristic
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4C2×C4×C12711yescharacteristic
342C4×D4D4×C12711yescharacteristic
343#117—21no—
344#117—21no—
345#117D4×C12711yescharacteristic
346C2×C4⋊C4—21no—
347C2×C22⋊C4—24no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42C23×C12711yescharacteristic
351C4⋊C8—21no—
352C4⋊C8—21no—
353C4⋊C8—21no—
354C4⋊C8—21no—
355C4⋊C8—21no—
356#104—42no—
357#102—44no—
358C22⋊C8—21no—
359C4×C8—21no—
360#95—21no—
361C24—22no—
362#41—21no—
363#41—21no—
364#41—21no—
365#41—21no—
366#41—84no—
367#41—82no—
368#41—82no—
369C2×Q8—21no—
370C2×Q8C22⋊C4×C12711yescharacteristic
371C2×Q8C22⋊C4×C12712yes—
372C2×D4—21no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—82no—
387C2×D4C22⋊C4×C12711yescharacteristic
388C2×D4C22⋊C4×C12714yes—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—41no—
395C22×C4C2×D4×C12711yescharacteristic
396C22×C4C2×D4×C12711yescharacteristic
397C22×C4C2×D4×C12711yescharacteristic
398M16—41no—
399M16—41no—
400C2×C8—42no—
401C2×C8—41no—
402C2×C8—41no—
403C2×C8—41no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—41no—
413C4⋊C4C22⋊C4×C12711yescharacteristic
414C4⋊C4C22⋊C4×C12711yescharacteristic
415C4⋊C4C22⋊C4×C12712yes—
416C22⋊C4—24no—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—21no—
421C22⋊C4—22no—
422C22⋊C4—21no—
423C22⋊C4—21no—
424C42—21no—
425C42—22no—
426C42—21no—
427C42—21no—
428C42—41no—
429C42—41no—
430C42C22×C4×C12711yescharacteristic
431C42C2×D4×C12711yescharacteristic
432C42C2×D4×C12711yescharacteristic
433C42C2×D4×C12711yescharacteristic
434C23—24no—
435C23—21no—
436C23—42no—
437C23—42no—
438C23—82no—
439C23—82no—
440C23#120×C12711yescharacteristic
441Q8—21no—
442Q8—21no—
443Q8—42no—
444Q8—41no—
445Q8—41no—
446D4—21no—
447D4—21no—
448D4—44no—
449D4—44no—
450D4—41no—
451D4—41no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—82no—
459D4—84no—
460D4—84no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—84no—
476C2×C4—84no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4C2×C22⋊C4×C12711yescharacteristic
480C2×C4C2×C22⋊C4×C12711yescharacteristic
481C2×C4C2×C22⋊C4×C12711yescharacteristic
482C2×C4#120×C12711yescharacteristic
483C2×C4#120×C12711yescharacteristic
484C2×C4#120×C12711yescharacteristic
485C2×C4#135×C12711yescharacteristic
486C2×C4#135×C12711yescharacteristic
487C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
488C2×C4#137×C12711yescharacteristic
489C8—81no—
490C8—81no—
491C8—81no—
492C22—21no—
493C22—21no—
494C22—41no—
495C22—44no—
496C22—41no—
497C22—44no—
498C22—41no—
499C22—44no—
500C22—162no—
501C22—162no—
502C22#379×C12711yescharacteristic
503C22#449×C12711yescharacteristic
504C22#452×C12711yescharacteristic
505C4—21no—
506C4—21no—
507C4—21no—
508C4—41no—
509C4—41no—
510C4—42no—
511C4—41no—
512C4—42no—
513C4—82no—
514C4#416×C12711yescharacteristic
515C4#417×C12711yescharacteristic
516C4#449×C12711yescharacteristic
517C4#452×C12711yescharacteristic
518C4#453×C12711yescharacteristic
519C4#455×C12711yescharacteristic
520C2—21no—
521C2—21no—
522C2—84no—
523C2—81no—
524C2C127×#178811yescharacteristic
525C2C127×#179211yescharacteristic
526C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×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×#1982C2semidirect
3. C127×#1806C2semidirect
4. C127×#1550C2semidirect
5. C127×#1545C2semidirect
6. C127×#1503C2semidirect
7. C127×#1477C2semidirect
9. #559×C127C4semidirect
11. #550×C127C4semidirect
256. #8426C127direct (N × H)
265. #1982C2×C127semidirect
266. #1806C2×C127semidirect
267. #1550C2×C127semidirect
268. #1545C2×C127semidirect
269. #1503C2×C127semidirect
270. #1477C2×C127semidirect
271. C127#8426direct (N × H)
273. #559C4×C127semidirect
275. #550C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35082
C127×#19822
C127×#18062
C127×#15502
C127×#15452
C127×#15032
C127×#14772
#8426127