Finite Group Databasebeta

← C127×#8486 #44572159

Subgroups — C127×#8486 #44572159

Order 32512.

686 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3559C211yesmaximal, characteristic
2C127×#1998C211yesmaximal, characteristic, complemented
3C127×#1557C211yesmaximal, characteristic, complemented
4C127×#1529C211yesmaximal, characteristic, complemented
5C127×#1495C211yesmaximal, characteristic, complemented
6C127×#1484C211yesmaximal, characteristic, complemented
7C127×#1470C211yesmaximal, characteristic, complemented
8#563×C127—21no—
9#562×C127—21no—
10#554×C127—21no—
11#553×C127—21no—
12#553×C127—21no—
13#547×C127—22no—
14#547×C127—21no—
15#544×C127—21no—
16#540×C127—21no—
17#539×C127—22no—
18#539×C127C412yes—
19#537×C127C412yes—
20#532×C127C2211yescharacteristic
21#529×C127C2211yescharacteristic
22C2×#125×C127C2211yescharacteristic
23#432×C127C2211yescharacteristic
24#431×C127C2211yescharacteristic
25#423×C127C2211yescharacteristic
26C4×M16×C127C2211yescharacteristic
27#343×C127—21no—
28#343×C127—21no—
29#332×C127—21no—
30#331×C127—21no—
31#330×C127—21no—
32#329×C127—21no—
33Q8⋊C8×C127—21no—
34D4⋊C8×C127—22no—
35D4⋊C8×C127—21no—
36#324×C127—22no—
37C2×#41×C127—22no—
38C2×#41×C127—21no—
39C2×M16×C127—21no—
40C2×M16×C127—21no—
41C4⋊Q8×C127—21no—
42C4⋊Q8×C127—22no—
43C4⋊Q8×C127D411yescharacteristic
44#127×C127D411yescharacteristic
45#126×C127—22no—
46#126×C127—22no—
47#126×C127—21no—
48#125×C127—21no—
49#125×C127—22no—
50#125×C127—21no—
51#125×C127—21no—
52#125×C127—21no—
53#125×C127—21no—
54#125×C127D411yescharacteristic
55#124×C127—21no—
56#124×C127D411yescharacteristic
57#123×C127—22no—
58#123×C127—22no—
59#123×C127—22no—
60#123×C127—22no—
61#123×C127—22no—
62#123×C127—22no—
63#123×C127—21no—
64C22⋊Q8×C127—22no—
65C22⋊Q8×C127—22no—
66C22⋊Q8×C127—22no—
67C22⋊Q8×C127—22no—
68C22⋊Q8×C127—22no—
69C22⋊Q8×C127—22no—
70C22⋊Q8×C127C2×C411yescharacteristic
71#121×C127—21no—
72#121×C127—22no—
73#121×C127—21no—
74#121×C127—22no—
75#121×C127—22no—
76#121×C127—22no—
77#121×C127—21no—
78#121×C127C2×C411yescharacteristic
79#121×C127C2×C412yes—
80C4×Q8×C127D411yescharacteristic
81C4×D4×C127—22no—
82C4×D4×C127—21no—
83C4×D4×C127—21no—
84C4×D4×C127—22no—
85C4×D4×C127—21no—
86C4×D4×C127—21no—
87C4×D4×C127D411yescharacteristic
88C4×D4×C127D412yes—
89#117×C127—21no—
90#117×C127—21no—
91C2×C4⋊C4×C127—22no—
92C2×C4⋊C4×C127—21no—
93C2×C4⋊C4×C127C2×C412yes—
94C2×C4⋊C4×C127D412yes—
95C2×C4⋊C4×C127D411yescharacteristic
96C2×C4⋊C4×C127D411yescharacteristic
97C2×C42×C127C2311yescharacteristic
98C4⋊C8×C127—21no—
99C4⋊C8×C127—21no—
100C4⋊C8×C127—21no—
101C4⋊C8×C127—21no—
102C22⋊C8×C127—21no—
103C22⋊C8×C127—21no—
104#97×C127—21no—
105#97×C127—21no—
106C4×C8×C127—21no—
107C4×C8×C127—21no—
108#41×C127—82no—
109#41×C127—84no—
110C2×Q8×C127—22no—
111C2×Q8×C127—21no—
112C2×Q8×C127C22⋊C411yescharacteristic
113C2×D4×C127—22no—
114C2×D4×C127—21no—
115C2×D4×C127—22no—
116C2×D4×C127—22no—
117C2×D4×C127—21no—
118C2×D4×C127—21no—
119C2×D4×C127C22⋊C411yescharacteristic
120C2×D4×C127C22⋊C412yes—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—21no—
125C22×C4×C127—22no—
126C22×C4×C127C22⋊C412yes—
127C22×C4×C127C22⋊C412yes—
128C22×C4×C127C22×C411yescharacteristic
129C22×C4×C127C2×D411yescharacteristic
130C22×C4×C127C2×D411yescharacteristic
131M16×C127—22no—
132M16×C127—41no—
133M16×C127—42no—
134C2×C8×C127—41no—
135C2×C8×C127—41no—
136C2×C8×C127—41no—
137C2×C8×C127—41no—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—22no—
140C4⋊C4×C127—22no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—21no—
145C4⋊C4×C127—21no—
146C4⋊C4×C127—21no—
147C4⋊C4×C127—22no—
148C4⋊C4×C127—21no—
149C4⋊C4×C127—21no—
150C4⋊C4×C127—22no—
151C4⋊C4×C127—21no—
152C4⋊C4×C127—21no—
153C4⋊C4×C127—21no—
154C4⋊C4×C127—21no—
155C4⋊C4×C127C22⋊C412yes—
156C4⋊C4×C127C22⋊C411yescharacteristic
157C4⋊C4×C127C22⋊C411yescharacteristic
158C22⋊C4×C127—22no—
159C22⋊C4×C127—22no—
160C22⋊C4×C127—22no—
161C22⋊C4×C127—22no—
162C22⋊C4×C127—22no—
163C22⋊C4×C127—21no—
164C22⋊C4×C127—21no—
165C22⋊C4×C127—22no—
166C22⋊C4×C127—21no—
167C22⋊C4×C127—21no—
168C22⋊C4×C127—21no—
169C22⋊C4×C127—22no—
170C42×C127—22no—
171C42×C127—21no—
172C42×C127C2×D411yescharacteristic
173C42×C127C2×D411yescharacteristic
174C42×C127C2×D411yescharacteristic
175C42×C127C2×D411yescharacteristic
176C23×C127—21no—
177C23×C127—22no—
178C23×C127C2×C22⋊C411yescharacteristic
179Q8×C127—41no—
180Q8×C127—81no—
181Q8×C127—82no—
182D4×C127—42no—
183D4×C127—41no—
184D4×C127—44no—
185D4×C127—42no—
186D4×C127—41no—
187D4×C127—41no—
188D4×C127—81no—
189D4×C127—82no—
190D4×C127—82no—
191C2×C4×C127—21no—
192C2×C4×C127—21no—
193C2×C4×C127—21no—
194C2×C4×C127—21no—
195C2×C4×C127—22no—
196C2×C4×C127—22no—
197C2×C4×C127—21no—
198C2×C4×C127—22no—
199C2×C4×C127—41no—
200C2×C4×C127—41no—
201C2×C4×C127—41no—
202C2×C4×C127—41no—
203C2×C4×C127—42no—
204C2×C4×C127—42no—
205C2×C4×C127—82no—
206C2×C4×C127—82no—
207C2×C4×C127—82no—
208C2×C4×C127—82no—
209C2×C4×C127C2×C22⋊C411yescharacteristic
210C2×C4×C127C2×C22⋊C411yescharacteristic
211C2×C4×C127#12011yescharacteristic
212C2×C4×C127#12011yescharacteristic
213C2×C4×C127#12011yescharacteristic
214C2×C4×C127#12011yescharacteristic
215C8×C127—42no—
216C8×C127—81no—
217C8×C127—81no—
218C8×C127—81no—
219C22×C127—21no—
220C22×C127—21no—
221C22×C127—21no—
222C22×C127—41no—
223C22×C127—42no—
224C22×C127—42no—
225C22×C127—41no—
226C22×C127—42no—
227C22×C127—41no—
228C22×C127#37911yescharacteristic
229C4×C127—21no—
230C4×C127—21no—
231C4×C127—21no—
232C4×C127—21no—
233C4×C127—21no—
234C4×C127—41no—
235C4×C127—42no—
236C4×C127—42no—
237C4×C127—41no—
238C4×C127—42no—
239C4×C127—41no—
240C4×C127#45411yescharacteristic
241C4×C127#45611yescharacteristic
242#8486C12711yesmaximal, characteristic, direct product factor, Sylow
243C2×C127—41no—
244C2×C127—81no—
245C2×C127—82no—
246C2×C127#179111yescharacteristic
247C2×C127#179311yescharacteristic
248C2×C127#179511yescharacteristic
249#3559C2×C12711yescharacteristic
250#1998C2×C12711yescharacteristic, complemented
251#1557C2×C12711yescharacteristic, complemented
252#1529C2×C12711yescharacteristic, complemented
253#1495C2×C12711yescharacteristic, complemented
254#1484C2×C12711yescharacteristic, complemented
255#1470C2×C12711yescharacteristic, complemented
256C127#848611yescharacteristic, direct product factor, Sylow
257#563—21no—
258#562—21no—
259#554—21no—
260#553—21no—
261#553—21no—
262#547—22no—
263#547—21no—
264#544—21no—
265#540—21no—
266#539—22no—
267#539C4×C12712yes—
268#537C4×C12712yes—
269#532C22×C12711yescharacteristic
270#529C22×C12711yescharacteristic
271C2×#125C22×C12711yescharacteristic
272#432C22×C12711yescharacteristic
273#431C22×C12711yescharacteristic
274#423C22×C12711yescharacteristic
275C4×M16C22×C12711yescharacteristic
276#343—21no—
277#343—21no—
278#332—21no—
279#331—21no—
280#330—21no—
281#329—21no—
282Q8⋊C8—21no—
283D4⋊C8—22no—
284D4⋊C8—21no—
285#324—22no—
286C2×#41—22no—
287C2×#41—21no—
288C2×M16—21no—
289C2×M16—21no—
290C4⋊Q8—21no—
291C4⋊Q8—22no—
292C4⋊Q8D4×C12711yescharacteristic
293#127D4×C12711yescharacteristic
294#126—22no—
295#126—22no—
296#126—21no—
297#125—21no—
298#125—22no—
299#125—21no—
300#125—21no—
301#125—21no—
302#125—21no—
303#125D4×C12711yescharacteristic
304#124—21no—
305#124D4×C12711yescharacteristic
306#123—22no—
307#123—22no—
308#123—22no—
309#123—22no—
310#123—22no—
311#123—22no—
312#123—21no—
313C22⋊Q8—22no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C22⋊Q8—22no—
319C22⋊Q8C2×C4×C12711yescharacteristic
320#121—21no—
321#121—22no—
322#121—21no—
323#121—22no—
324#121—22no—
325#121—22no—
326#121—21no—
327#121C2×C4×C12711yescharacteristic
328#121C2×C4×C12712yes—
329C4×Q8D4×C12711yescharacteristic
330C4×D4—22no—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—22no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4D4×C12711yescharacteristic
337C4×D4D4×C12712yes—
338#117—21no—
339#117—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4C2×C4×C12712yes—
343C2×C4⋊C4D4×C12712yes—
344C2×C4⋊C4D4×C12711yescharacteristic
345C2×C4⋊C4D4×C12711yescharacteristic
346C2×C42C23×C12711yescharacteristic
347C4⋊C8—21no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353#97—21no—
354#97—21no—
355C4×C8—21no—
356C4×C8—21no—
357#41—82no—
358#41—84no—
359C2×Q8—22no—
360C2×Q8—21no—
361C2×Q8C22⋊C4×C12711yescharacteristic
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4C22⋊C4×C12711yescharacteristic
369C2×D4C22⋊C4×C12712yes—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4C22⋊C4×C12712yes—
376C22×C4C22⋊C4×C12712yes—
377C22×C4C22×C4×C12711yescharacteristic
378C22×C4C2×D4×C12711yescharacteristic
379C22×C4C2×D4×C12711yescharacteristic
380M16—22no—
381M16—41no—
382M16—42no—
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—41no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4C22⋊C4×C12712yes—
405C4⋊C4C22⋊C4×C12711yescharacteristic
406C4⋊C4C22⋊C4×C12711yescharacteristic
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—22no—
415C22⋊C4—21no—
416C22⋊C4—21no—
417C22⋊C4—21no—
418C22⋊C4—22no—
419C42—22no—
420C42—21no—
421C42C2×D4×C12711yescharacteristic
422C42C2×D4×C12711yescharacteristic
423C42C2×D4×C12711yescharacteristic
424C42C2×D4×C12711yescharacteristic
425C23—22no—
426C23—21no—
427C23C2×C22⋊C4×C12711yescharacteristic
428Q8—41no—
429Q8—81no—
430Q8—82no—
431D4—42no—
432D4—41no—
433D4—44no—
434D4—42no—
435D4—41no—
436D4—41no—
437D4—81no—
438D4—82no—
439D4—82no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4C2×C22⋊C4×C12711yescharacteristic
459C2×C4C2×C22⋊C4×C12711yescharacteristic
460C2×C4#120×C12711yescharacteristic
461C2×C4#120×C12711yescharacteristic
462C2×C4#120×C12711yescharacteristic
463C2×C4#120×C12711yescharacteristic
464C8—42no—
465C8—81no—
466C8—81no—
467C8—81no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—42no—
472C22—41no—
473C22—41no—
474C22—42no—
475C22—42no—
476C22—41no—
477C22#379×C12711yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—41no—
485C4—41no—
486C4—42no—
487C4—42no—
488C4—41no—
489C4#454×C12711yescharacteristic
490C4#456×C12711yescharacteristic
491C2—41no—
492C2—82no—
493C2—81no—
494C2C127×#179111yescharacteristic
495C2C127×#179311yescharacteristic
496C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3559C2
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×#1998C2semidirect
3. C127×#1557C2semidirect
4. C127×#1529C2semidirect
5. C127×#1495C2semidirect
6. C127×#1484C2semidirect
7. C127×#1470C2semidirect
242. #8486C127direct (N × H)
250. #1998C2×C127semidirect
251. #1557C2×C127semidirect
252. #1529C2×C127semidirect
253. #1495C2×C127semidirect
254. #1484C2×C127semidirect
255. #1470C2×C127semidirect
256. C127#8486direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35592
C127×#19982
C127×#15572
C127×#15292
C127×#14952
C127×#14842
C127×#14702
#8486127