Finite Group Databasebeta

← C127×#9343 #44573016

Subgroups — C127×#9343 #44573016

Order 32512.

576 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×#3192C211yesmaximal, characteristic
2C127×#2377C211yesmaximal, characteristic, complemented
3C127×#1964C211yesmaximal, characteristic, complemented
4C127×#1510C211yesmaximal, characteristic, complemented
5C127×#1507C211yesmaximal, characteristic, complemented
6C127×#1305C211yesmaximal, characteristic, complemented
7C127×#1284C211yesmaximal, characteristic, complemented
8C2×#121×C127C2211yescharacteristic
9C2×#121×C127C2211yescharacteristic
10#481×C127—21no—
11#481×C127C412yescomplemented
12#469×C127—22no—
13#447×C127—21no—
14#447×C127C412yescomplemented
15C2×#99×C127—21no—
16C2×#99×C127—21no—
17#407×C127C2211yescharacteristic
18#407×C127C2211yescharacteristic
19#390×C127—21no—
20#388×C127—21no—
21#387×C127—21no—
22#386×C127—21no—
23#386×C127—21no—
24#385×C127—21no—
25#381×C127C2211yescharacteristic
26#380×C127C2211yescharacteristic
27C4×C22⋊C4×C127C2211yescharacteristic
28#327×C127—22no—
29#327×C127—21no—
30#327×C127—21no—
31C22×D4×C127—21no—
32C22×D4×C127—21no—
33C22×D4×C127C2×C411yescharacteristic, complemented
34C22×D4×C127D411yescharacteristic
35C23×C4×C127—21no—
36C23×C4×C127C2311yescharacteristic
37C2×D8×C127—22no—
38C2×M16×C127—21no—
39C2×M16×C127—21no—
40#121×C127—21no—
41#121×C127—21no—
42#121×C127—21no—
43#121×C127—21no—
44#121×C127—21no—
45#121×C127—21no—
46#121×C127C2×C412yes—
47#121×C127D412yes—
48C2×C4⋊C4×C127—21no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127C2×C411yescharacteristic, complemented
51C2×C4⋊C4×C127D411yescharacteristic
52C2×C22⋊C4×C127—21no—
53C2×C22⋊C4×C127—21no—
54C2×C22⋊C4×C127—21no—
55C2×C22⋊C4×C127—21no—
56C2×C22⋊C4×C127—21no—
57C2×C22⋊C4×C127—21no—
58C2×C22⋊C4×C127—21no—
59C2×C22⋊C4×C127D411yescharacteristic
60C2×C22⋊C4×C127D411yescharacteristic
61C2×C42×C127—21no—
62C2×C42×C127—21no—
63#106×C127—22no—
64#102×C127—22no—
65#102×C127—22no—
66#99×C127—42no—
67#99×C127—42no—
68C22⋊C8×C127—21no—
69C22⋊C8×C127—21no—
70C22⋊C8×C127—21no—
71C22⋊C8×C127C2×C412yescomplemented
72#95×C127—21no—
73#95×C127—21no—
74#95×C127—21no—
75#95×C127—21no—
76#95×C127—21no—
77#95×C127D411yescharacteristic
78#95×C127D411yescharacteristic
79C24×C127—21no—
80C24×C127—21no—
81C24×C127C2×D411yescharacteristic
82C2×D4×C127—22no—
83C2×D4×C127—22no—
84C2×D4×C127—21no—
85C2×D4×C127—21no—
86C2×D4×C127—21no—
87C2×D4×C127—41no—
88C2×D4×C127—41no—
89C2×D4×C127—41no—
90C2×D4×C127—41no—
91C2×D4×C127—41no—
92C2×D4×C127—41no—
93C2×D4×C127—81no—
94C2×D4×C127—81no—
95C2×D4×C127—81no—
96C2×D4×C127—81no—
97C2×D4×C127C22⋊C412yes—
98C22×C4×C127—21no—
99C22×C4×C127—21no—
100C22×C4×C127—21no—
101C22×C4×C127—21no—
102C22×C4×C127—21no—
103C22×C4×C127—21no—
104C22×C4×C127—41no—
105C22×C4×C127—81no—
106C22×C4×C127—81no—
107C22×C4×C127—81no—
108C22×C4×C127—81no—
109C22×C4×C127C22×C411yescharacteristic
110C22×C4×C127C2×D411yescharacteristic
111C22×C4×C127C2×D411yescharacteristic
112C22×C4×C127C2×D411yescharacteristic
113C22×C4×C127#4111yescharacteristic
114C22×C4×C127#4111yescharacteristic
115D8×C127—82no—
116M16×C127—81no—
117M16×C127—81no—
118C2×C8×C127—22no—
119C2×C8×C127—41no—
120C4⋊C4×C127—21no—
121C4⋊C4×C127—21no—
122C4⋊C4×C127—21no—
123C4⋊C4×C127—81no—
124C4⋊C4×C127—81no—
125C4⋊C4×C127C22⋊C412yes—
126C22⋊C4×C127—22no—
127C22⋊C4×C127—22no—
128C22⋊C4×C127—22no—
129C22⋊C4×C127—41no—
130C22⋊C4×C127—41no—
131C22⋊C4×C127—41no—
132C22⋊C4×C127—41no—
133C22⋊C4×C127—41no—
134C22⋊C4×C127—81no—
135C22⋊C4×C127—81no—
136C22⋊C4×C127—81no—
137C22⋊C4×C127—81no—
138C42×C127—81no—
139C42×C127—81no—
140C23×C127—21no—
141C23×C127—21no—
142C23×C127—22no—
143C23×C127—41no—
144C23×C127—41no—
145C23×C127—41no—
146C23×C127—41no—
147C23×C127—41no—
148C23×C127—41no—
149C23×C127—41no—
150C23×C127—41no—
151C23×C127—41no—
152C23×C127—41no—
153C23×C127—41no—
154C23×C127—81no—
155C23×C127—81no—
156C23×C127C4×D411yescharacteristic
157C23×C127#12011yescharacteristic
158C23×C127#12111yescharacteristic
159D4×C127—42no—
160D4×C127—42no—
161D4×C127—81no—
162D4×C127—81no—
163D4×C127—82no—
164D4×C127—82no—
165D4×C127—81no—
166D4×C127—81no—
167D4×C127—81no—
168D4×C127—81no—
169C2×C4×C127—22no—
170C2×C4×C127—41no—
171C2×C4×C127—41no—
172C2×C4×C127—41no—
173C2×C4×C127—41no—
174C2×C4×C127—41no—
175C2×C4×C127—41no—
176C2×C4×C127—41no—
177C2×C4×C127—41no—
178C2×C4×C127—41no—
179C2×C4×C127—41no—
180C2×C4×C127—42no—
181C2×C4×C127—41no—
182C2×C4×C127—41no—
183C2×C4×C127—41no—
184C2×C4×C127—41no—
185C2×C4×C127—41no—
186C2×C4×C127—41no—
187C2×C4×C127—41no—
188C2×C4×C127—41no—
189C2×C4×C127—41no—
190C2×C4×C127—41no—
191C2×C4×C127—41no—
192C2×C4×C127—41no—
193C2×C4×C127—41no—
194C2×C4×C127—81no—
195C2×C4×C127—81no—
196C2×C4×C127—84no—
197C2×C4×C127C2×C22⋊C411yescharacteristic
198C2×C4×C127C4×D411yescharacteristic
199C2×C4×C127#12111yescharacteristic
200C2×C4×C127#12311yescharacteristic
201C8×C127—42no—
202C8×C127—81no—
203C22×C127—21no—
204C22×C127—21no—
205C22×C127—21no—
206C22×C127—21no—
207C22×C127—21no—
208C22×C127—21no—
209C22×C127—21no—
210C22×C127—21no—
211C22×C127—42no—
212C22×C127—42no—
213C22×C127—42no—
214C22×C127—81no—
215C22×C127—81no—
216C22×C127—81no—
217C22×C127—81no—
218C22×C127—81no—
219C22×C127—81no—
220C22×C127—81no—
221C22×C127—81no—
222C22×C127—81no—
223C22×C127—161no—
224C22×C127—161no—
225C22×C127#38611yescharacteristic
226C22×C127#45311yescharacteristic
227C22×C127#45411yescharacteristic
228C4×C127—21no—
229C4×C127—21no—
230C4×C127—21no—
231C4×C127—21no—
232C4×C127—42no—
233C4×C127—81no—
234C4×C127—81no—
235C4×C127—81no—
236C4×C127—81no—
237C4×C127—82no—
238C4×C127—81no—
239#9343C12711yesmaximal, characteristic, direct product factor, Sylow
240C2×C127—21no—
241C2×C127—21no—
242C2×C127—41no—
243C2×C127—41no—
244C2×C127—82no—
245C2×C127—161no—
246C2×C127#188311yescharacteristic
247C2×C127#190411yescharacteristic
248C2×C127#191311yescharacteristic
249#3192C2×C12711yescharacteristic
250#2377C2×C12711yescharacteristic, complemented
251#1964C2×C12711yescharacteristic, complemented
252#1510C2×C12711yescharacteristic, complemented
253#1507C2×C12711yescharacteristic, complemented
254#1305C2×C12711yescharacteristic, complemented
255#1284C2×C12711yescharacteristic, complemented
256C127#934311yescharacteristic, direct product factor, Sylow
257C2×#121C22×C12711yescharacteristic
258C2×#121C22×C12711yescharacteristic
259#481—21no—
260#481C4×C12712yescomplemented
261#469—22no—
262#447—21no—
263#447C4×C12712yescomplemented
264C2×#99—21no—
265C2×#99—21no—
266#407C22×C12711yescharacteristic
267#407C22×C12711yescharacteristic
268#390—21no—
269#388—21no—
270#387—21no—
271#386—21no—
272#386—21no—
273#385—21no—
274#381C22×C12711yescharacteristic
275#380C22×C12711yescharacteristic
276C4×C22⋊C4C22×C12711yescharacteristic
277#327—22no—
278#327—21no—
279#327—21no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4C2×C4×C12711yescharacteristic, complemented
283C22×D4D4×C12711yescharacteristic
284C23×C4—21no—
285C23×C4C23×C12711yescharacteristic
286C2×D8—22no—
287C2×M16—21no—
288C2×M16—21no—
289#121—21no—
290#121—21no—
291#121—21no—
292#121—21no—
293#121—21no—
294#121—21no—
295#121C2×C4×C12712yes—
296#121D4×C12712yes—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4C2×C4×C12711yescharacteristic, complemented
300C2×C4⋊C4D4×C12711yescharacteristic
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4D4×C12711yescharacteristic
309C2×C22⋊C4D4×C12711yescharacteristic
310C2×C42—21no—
311C2×C42—21no—
312#106—22no—
313#102—22no—
314#102—22no—
315#99—42no—
316#99—42no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8C2×C4×C12712yescomplemented
321#95—21no—
322#95—21no—
323#95—21no—
324#95—21no—
325#95—21no—
326#95D4×C12711yescharacteristic
327#95D4×C12711yescharacteristic
328C24—21no—
329C24—21no—
330C24C2×D4×C12711yescharacteristic
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—81no—
343C2×D4—81no—
344C2×D4—81no—
345C2×D4—81no—
346C2×D4C22⋊C4×C12712yes—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—41no—
354C22×C4—81no—
355C22×C4—81no—
356C22×C4—81no—
357C22×C4—81no—
358C22×C4C22×C4×C12711yescharacteristic
359C22×C4C2×D4×C12711yescharacteristic
360C22×C4C2×D4×C12711yescharacteristic
361C22×C4C2×D4×C12711yescharacteristic
362C22×C4#41×C12711yescharacteristic
363C22×C4#41×C12711yescharacteristic
364D8—82no—
365M16—81no—
366M16—81no—
367C2×C8—22no—
368C2×C8—41no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—81no—
373C4⋊C4—81no—
374C4⋊C4C22⋊C4×C12712yes—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—81no—
384C22⋊C4—81no—
385C22⋊C4—81no—
386C22⋊C4—81no—
387C42—81no—
388C42—81no—
389C23—21no—
390C23—21no—
391C23—22no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—81no—
404C23—81no—
405C23C4×D4×C12711yescharacteristic
406C23#120×C12711yescharacteristic
407C23#121×C12711yescharacteristic
408D4—42no—
409D4—42no—
410D4—81no—
411D4—81no—
412D4—82no—
413D4—82no—
414D4—81no—
415D4—81no—
416D4—81no—
417D4—81no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—84no—
446C2×C4C2×C22⋊C4×C12711yescharacteristic
447C2×C4C4×D4×C12711yescharacteristic
448C2×C4#121×C12711yescharacteristic
449C2×C4#123×C12711yescharacteristic
450C8—42no—
451C8—81no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—161no—
473C22—161no—
474C22#386×C12711yescharacteristic
475C22#453×C12711yescharacteristic
476C22#454×C12711yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—42no—
482C4—81no—
483C4—81no—
484C4—81no—
485C4—81no—
486C4—82no—
487C4—81no—
488C2—21no—
489C2—21no—
490C2—41no—
491C2—41no—
492C2—82no—
493C2—161no—
494C2C127×#188311yescharacteristic
495C2C127×#190411yescharacteristic
496C2C127×#191311yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC127×#3192C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C127×#2377C2semidirect
3. C127×#1964C2semidirect
4. C127×#1510C2semidirect
5. C127×#1507C2semidirect
6. C127×#1305C2semidirect
7. C127×#1284C2semidirect
11. #481×C127C4semidirect
14. #447×C127C4semidirect
33. C22×D4×C127C2×C4semidirect
50. C2×C4⋊C4×C127C2×C4semidirect
71. C22⋊C8×C127C2×C4semidirect
239. #9343C127direct (N × H)
250. #2377C2×C127semidirect
251. #1964C2×C127semidirect
252. #1510C2×C127semidirect
253. #1507C2×C127semidirect
254. #1305C2×C127semidirect
255. #1284C2×C127semidirect
256. C127#9343direct (N × H)
260. #481C4×C127semidirect
263. #447C4×C127semidirect
282. C22×D4C2×C4×C127semidirect
299. C2×C4⋊C4C2×C4×C127semidirect
320. C22⋊C8C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31922
C127×#23772
C127×#19642
C127×#15102
C127×#15072
C127×#13052
C127×#12842
#9343127