Finite Group Databasebeta

← C127×#8404 #44572077

Subgroups — C127×#8404 #44572077

Order 32512.

1148 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C127C211yesmaximal, characteristic
2C127×#1874C212yesmaximal, complemented
3C2×#327×C127C212yesmaximal, complemented
4C2×#324×C127C211yesmaximal, characteristic, complemented
5C127×#1441C211yesmaximal, characteristic, complemented
6C22×#41×C127—21no—
7#537×C127—24no—
8#537×C127—22no—
9#537×C127C414yescomplemented
10C2×C22⋊Q8×C127—22no—
11C2×#121×C127—22no—
12C2×#121×C127—21no—
13C2×#121×C127C2212yes—
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C2×#102×C127—22no—
17C2×C22⋊C8×C127C2212yes—
18C2×#95×C127—21no—
19C2×#95×C127—21no—
20C2×#95×C127C2211yescharacteristic
21#340×C127—22no—
22#327×C127—24no—
23#324×C127—22no—
24C2×#41×C127—24no—
25C2×#41×C127—24no—
26C2×#41×C127—42no—
27C2×#41×C127—42no—
28C2×#41×C127—42no—
29C2×#41×C127—42no—
30C22×Q8×C127—21no—
31C22×D4×C127—21no—
32C22×D4×C127—22no—
33C22×D4×C127—21no—
34C22×D4×C127D412yes—
35C23×C4×C127—22no—
36C23×C4×C127—21no—
37C23×C4×C127—21no—
38C23×C4×C127D411yescharacteristic
39C23×C4×C127D411yescharacteristic
40C23×C4×C127C2311yescharacteristic
41C22×C8×C127—22no—
42C22⋊Q8×C127—28no—
43C22⋊Q8×C127—28no—
44#121×C127—24no—
45#121×C127—28no—
46#121×C127—28no—
47#121×C127—24no—
48#121×C127—22no—
49#121×C127—22no—
50#121×C127C2×C414yes—
51#121×C127D414yes—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—42no—
57C2×C4⋊C4×C127C2×C412yes—
58C2×C4⋊C4×C127D412yes—
59C2×C4⋊C4×C127D412yes—
60C2×C22⋊C4×C127—22no—
61C2×C22⋊C4×C127—22no—
62#102×C127—44no—
63C22⋊C8×C127—22no—
64C22⋊C8×C127—22no—
65#95×C127—22no—
66#95×C127—42no—
67#95×C127—42no—
68C24×C127—22no—
69C24×C127C2×D411yescharacteristic
70#41×C127—48no—
71#41×C127—48no—
72#41×C127—48no—
73#41×C127—48no—
74C2×Q8×C127—24no—
75C2×Q8×C127—42no—
76C2×Q8×C127—42no—
77C2×D4×C127—24no—
78C2×D4×C127—24no—
79C2×D4×C127—24no—
80C2×D4×C127—24no—
81C2×D4×C127—22no—
82C2×D4×C127—42no—
83C2×D4×C127—42no—
84C2×D4×C127—42no—
85C2×D4×C127—42no—
86C2×D4×C127—42no—
87C2×D4×C127—42no—
88C2×D4×C127—42no—
89C2×D4×C127—42no—
90C2×D4×C127—81no—
91C2×D4×C127—81no—
92C2×D4×C127C22⋊C414yes—
93C22×C4×C127—21no—
94C22×C4×C127—21no—
95C22×C4×C127—21no—
96C22×C4×C127—21no—
97C22×C4×C127—28no—
98C22×C4×C127—21no—
99C22×C4×C127—22no—
100C22×C4×C127—21no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—41no—
104C22×C4×C127—41no—
105C22×C4×C127—44no—
106C22×C4×C127—44no—
107C22×C4×C127—41no—
108C22×C4×C127—41no—
109C22×C4×C127—41no—
110C22×C4×C127—41no—
111C22×C4×C127—41no—
112C22×C4×C127—41no—
113C22×C4×C127—41no—
114C22×C4×C127—41no—
115C22×C4×C127—41no—
116C22×C4×C127—41no—
117C22×C4×C127—41no—
118C22×C4×C127—41no—
119C22×C4×C127—41no—
120C22×C4×C127—41no—
121C22×C4×C127C22⋊C412yes—
122C22×C4×C127C22⋊C412yes—
123C22×C4×C127D812yes—
124C22×C4×C127SD1612yes—
125C22×C4×C127C22×C411yescharacteristic
126C22×C4×C127C2×D412yes—
127C22×C4×C127C2×D412yes—
128C22×C4×C127C2×D411yescharacteristic
129C2×C8×C127—42no—
130C2×C8×C127—42no—
131C2×C8×C127—42no—
132C4⋊C4×C127—24no—
133C4⋊C4×C127—24no—
134C4⋊C4×C127—24no—
135C4⋊C4×C127—22no—
136C4⋊C4×C127—24no—
137C4⋊C4×C127—42no—
138C4⋊C4×C127C22⋊C414yes—
139C22⋊C4×C127—28no—
140C22⋊C4×C127—24no—
141C22⋊C4×C127—24no—
142C23×C127—21no—
143C23×C127—21no—
144C23×C127—21no—
145C23×C127—21no—
146C23×C127—24no—
147C23×C127—42no—
148C23×C127—42no—
149C23×C127—42no—
150C23×C127—42no—
151C23×C127—42no—
152C23×C127—42no—
153C23×C127C2×C22⋊C411yescharacteristic
154C23×C127#12011yescharacteristic
155C23×C127#12011yescharacteristic
156C23×C127C2×D811yescharacteristic
157C23×C127C2×SD1611yescharacteristic
158C23×C127AGL(1,ℤ/8)11yescharacteristic
159C23×C127AGL(1,ℤ/8)11yescharacteristic
160Q8×C127—48no—
161D4×C127—44no—
162D4×C127—48no—
163D4×C127—44no—
164D4×C127—44no—
165D4×C127—44no—
166D4×C127—44no—
167D4×C127—82no—
168D4×C127—84no—
169C2×C4×C127—22no—
170C2×C4×C127—22no—
171C2×C4×C127—22no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—22no—
175C2×C4×C127—22no—
176C2×C4×C127—22no—
177C2×C4×C127—22no—
178C2×C4×C127—24no—
179C2×C4×C127—41no—
180C2×C4×C127—41no—
181C2×C4×C127—42no—
182C2×C4×C127—416no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—41no—
186C2×C4×C127—41no—
187C2×C4×C127—42no—
188C2×C4×C127—42no—
189C2×C4×C127—42no—
190C2×C4×C127—42no—
191C2×C4×C127—42no—
192C2×C4×C127—42no—
193C2×C4×C127—42no—
194C2×C4×C127—81no—
195C2×C4×C127—81no—
196C2×C4×C127—81no—
197C2×C4×C127—81no—
198C2×C4×C127—81no—
199C2×C4×C127—81no—
200C2×C4×C127—81no—
201C2×C4×C127—81no—
202C2×C4×C127—81no—
203C2×C4×C127#10214yescomplemented
204C2×C4×C127C2×C22⋊C412yes—
205C2×C4×C127#12012yes—
206C8×C127—82no—
207C22×C127—21no—
208C22×C127—21no—
209C22×C127—21no—
210C22×C127—21no—
211C22×C127—21no—
212C22×C127—21no—
213C22×C127—21no—
214C22×C127—21no—
215C22×C127—21no—
216C22×C127—21no—
217C22×C127—21no—
218C22×C127—21no—
219C22×C127—44no—
220C22×C127—44no—
221C22×C127—44no—
222C22×C127—82no—
223C22×C127—82no—
224C22×C127—82no—
225C22×C127—82no—
226C22×C127#37911yescharacteristic
227C22×C127C2×#10211yescharacteristic
228C22×C127#41811yescharacteristic
229C22×C127#44711yescharacteristic
230C22×C127#44711yescharacteristic
231C22×C127#45011yescharacteristic
232C22×C127#45011yescharacteristic
233C22×C127#45411yescharacteristic
234C22×C127#45611yescharacteristic
235C22×C127B(4,𝔽2)11yescharacteristic
236C22×C127#45811yescharacteristic
237C4×C127—24no—
238C4×C127—22no—
239C4×C127—22no—
240C4×C127—44no—
241C4×C127—42no—
242C4×C127—82no—
243C4×C127—82no—
244#8404C12711yesmaximal, characteristic, direct product factor, Sylow
245C2×C127—21no—
246C2×C127—21no—
247C2×C127—21no—
248C2×C127—21no—
249C2×C127—84no—
250C2×C127#159811yescharacteristic
251C2×C127#160411yescharacteristic
252C2×C127#161011yescharacteristic
253C2×C127#161611yescharacteristic
254C2×C127#178611yescharacteristic
255C2×C127#179011yescharacteristic
256C2×C127#179311yescharacteristic
257C2×#537C2×C12711yescharacteristic
258#1874C2×C12712yescomplemented
259C2×#327C2×C12712yescomplemented
260C2×#324C2×C12711yescharacteristic, complemented
261#1441C2×C12711yescharacteristic, complemented
262C127#840411yescharacteristic, direct product factor, Sylow
263C22×#41—21no—
264#537—24no—
265#537—22no—
266#537C4×C12714yescomplemented
267C2×C22⋊Q8—22no—
268C2×#121—22no—
269C2×#121—21no—
270C2×#121C22×C12712yes—
271C22×C4⋊C4C22×C12711yescharacteristic
272C22×C4⋊C4C22×C12711yescharacteristic
273C2×#102—22no—
274C2×C22⋊C8C22×C12712yes—
275C2×#95—21no—
276C2×#95—21no—
277C2×#95C22×C12711yescharacteristic
278#340—22no—
279#327—24no—
280#324—22no—
281C2×#41—24no—
282C2×#41—24no—
283C2×#41—42no—
284C2×#41—42no—
285C2×#41—42no—
286C2×#41—42no—
287C22×Q8—21no—
288C22×D4—21no—
289C22×D4—22no—
290C22×D4—21no—
291C22×D4D4×C12712yes—
292C23×C4—22no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4D4×C12711yescharacteristic
296C23×C4D4×C12711yescharacteristic
297C23×C4C23×C12711yescharacteristic
298C22×C8—22no—
299C22⋊Q8—28no—
300C22⋊Q8—28no—
301#121—24no—
302#121—28no—
303#121—28no—
304#121—24no—
305#121—22no—
306#121—22no—
307#121C2×C4×C12714yes—
308#121D4×C12714yes—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4C2×C4×C12712yes—
315C2×C4⋊C4D4×C12712yes—
316C2×C4⋊C4D4×C12712yes—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319#102—44no—
320C22⋊C8—22no—
321C22⋊C8—22no—
322#95—22no—
323#95—42no—
324#95—42no—
325C24—22no—
326C24C2×D4×C12711yescharacteristic
327#41—48no—
328#41—48no—
329#41—48no—
330#41—48no—
331C2×Q8—24no—
332C2×Q8—42no—
333C2×Q8—42no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—24no—
338C2×D4—22no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—42no—
342C2×D4—42no—
343C2×D4—42no—
344C2×D4—42no—
345C2×D4—42no—
346C2×D4—42no—
347C2×D4—81no—
348C2×D4—81no—
349C2×D4C22⋊C4×C12714yes—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—28no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—44no—
363C22×C4—44no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4C22⋊C4×C12712yes—
379C22×C4C22⋊C4×C12712yes—
380C22×C4D8×C12712yes—
381C22×C4SD16×C12712yes—
382C22×C4C22×C4×C12711yescharacteristic
383C22×C4C2×D4×C12712yes—
384C22×C4C2×D4×C12712yes—
385C22×C4C2×D4×C12711yescharacteristic
386C2×C8—42no—
387C2×C8—42no—
388C2×C8—42no—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—22no—
393C4⋊C4—24no—
394C4⋊C4—42no—
395C4⋊C4C22⋊C4×C12714yes—
396C22⋊C4—28no—
397C22⋊C4—24no—
398C22⋊C4—24no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—24no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23C2×C22⋊C4×C12711yescharacteristic
411C23#120×C12711yescharacteristic
412C23#120×C12711yescharacteristic
413C23C2×D8×C12711yescharacteristic
414C23C2×SD16×C12711yescharacteristic
415C23AGL(1,ℤ/8)×C12711yescharacteristic
416C23AGL(1,ℤ/8)×C12711yescharacteristic
417Q8—48no—
418D4—44no—
419D4—48no—
420D4—44no—
421D4—44no—
422D4—44no—
423D4—44no—
424D4—82no—
425D4—84no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—416no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—81no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4#102×C12714yescomplemented
461C2×C4C2×C22⋊C4×C12712yes—
462C2×C4#120×C12712yes—
463C8—82no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—44no—
477C22—44no—
478C22—44no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22—82no—
483C22#379×C12711yescharacteristic
484C22C2×#102×C12711yescharacteristic
485C22#418×C12711yescharacteristic
486C22#447×C12711yescharacteristic
487C22#447×C12711yescharacteristic
488C22#450×C12711yescharacteristic
489C22#450×C12711yescharacteristic
490C22#454×C12711yescharacteristic
491C22#456×C12711yescharacteristic
492C22B(4,𝔽2)×C12711yescharacteristic
493C22#458×C12711yescharacteristic
494C4—24no—
495C4—22no—
496C4—22no—
497C4—44no—
498C4—42no—
499C4—82no—
500C4—82no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—84no—
506C2C127×#159811yescharacteristic
507C2C127×#160411yescharacteristic
508C2C127×#161011yescharacteristic
509C2C127×#161611yescharacteristic
510C2C127×#178611yescharacteristic
511C2C127×#179011yescharacteristic
512C2C127×#179311yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC2×#537×C127C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1874C2semidirect
3. C2×#327×C127C2semidirect
4. C2×#324×C127C2semidirect
5. C127×#1441C2semidirect
9. #537×C127C4semidirect
203. C2×C4×C127#102semidirect
244. #8404C127direct (N × H)
258. #1874C2×C127semidirect
259. C2×#327C2×C127semidirect
260. C2×#324C2×C127semidirect
261. #1441C2×C127semidirect
262. C127#8404direct (N × H)
266. #537C4×C127semidirect
460. C2×C4#102×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1272
C127×#18742
C2×#327×C1272
C2×#324×C1272
C127×#14412
#8404127