Finite Group Databasebeta

← C127×#8329 #44572002

Subgroups — C127×#8329 #44572002

Order 32512.

1276 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C127C211yesmaximal, characteristic
2C127×#1779C211yesmaximal, characteristic
3C2×#328×C127C214yesmaximal, complemented
4C127×C22⋊#95C211yesmaximal, characteristic
5C23×Q8×C127C411yescharacteristic, complemented
6C24×C4×C127C2211yescharacteristic
7C2×C22⋊Q8×C127—21no—
8C2×C22⋊Q8×C127—21no—
9C2×C22⋊Q8×C127—28no—
10C2×C22⋊Q8×C127C412yescomplemented
11C2×C22⋊Q8×C127C2212yes—
12C22×C4⋊C4×C127—21no—
13C22×C4⋊C4×C127C411yescharacteristic, complemented
14C22×C22⋊C4×C127—21no—
15C22×C22⋊C4×C127—21no—
16C2×C22⋊C8×C127—21no—
17C2×C22⋊C8×C127—21no—
18C2×C22⋊C8×C127C2212yes—
19C2×#95×C127—21no—
20C2×#95×C127C2212yes—
21#328×C127—28no—
22C25×C127D411yescharacteristic
23C22×Q8×C127—24no—
24C22×Q8×C127—21no—
25C22×Q8×C127—42no—
26C22×Q8×C127—42no—
27C22×Q8×C127C2×C412yes—
28C23×C4×C127—21no—
29C23×C4×C127—21no—
30C23×C4×C127—24no—
31C23×C4×C127—22no—
32C23×C4×C127—42no—
33C23×C4×C127—42no—
34C23×C4×C127C2×C411yescharacteristic
35C23×C4×C127C2×C411yescharacteristic
36C23×C4×C127D411yescharacteristic
37C23×C4×C127D411yescharacteristic
38C23×C4×C127D411yescharacteristic
39C23×C4×C127C2311yescharacteristic
40C22×C8×C127—22no—
41C22⋊Q8×C127—28no—
42C22⋊Q8×C127—28no—
43C22⋊Q8×C127—24no—
44C22⋊Q8×C127—24no—
45C22⋊Q8×C127—24no—
46C22⋊Q8×C127D418yes—
47C2×C4⋊C4×C127—28no—
48C2×C4⋊C4×C127—22no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127—22no—
51C2×C4⋊C4×C127—24no—
52C2×C4⋊C4×C127C2×C412yes—
53C2×C22⋊C4×C127—28no—
54C2×C22⋊C4×C127—22no—
55C2×C22⋊C4×C127—22no—
56C2×C22⋊C4×C127—24no—
57C2×C22⋊C4×C127—42no—
58C2×C22⋊C4×C127—42no—
59C22⋊C8×C127—24no—
60C22⋊C8×C127—42no—
61C22⋊C8×C127—42no—
62#95×C127—24no—
63#95×C127—42no—
64C24×C127—22no—
65C24×C127—22no—
66C24×C127—22no—
67C24×C127—22no—
68C24×C127—41no—
69C24×C127—41no—
70C24×C127C22⋊C411yescharacteristic
71C24×C127C22⋊C411yescharacteristic
72C24×C127SD1612yes—
73C24×C127Q1612yes—
74C24×C127C2×D411yescharacteristic
75C2×Q8×C127—24no—
76C2×Q8×C127—22no—
77C2×Q8×C127—416no—
78C2×Q8×C127—42no—
79C2×Q8×C127—42no—
80C2×Q8×C127—42no—
81C2×Q8×C127—42no—
82C2×Q8×C127C22⋊C414yescomplemented
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
86C22×C4×C127—24no—
87C22×C4×C127—24no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—24no—
98C22×C4×C127—41no—
99C22×C4×C127—41no—
100C22×C4×C127—41no—
101C22×C4×C127—41no—
102C22×C4×C127—41no—
103C22×C4×C127—41no—
104C22×C4×C127—41no—
105C22×C4×C127—416no—
106C22×C4×C127—42no—
107C22×C4×C127—42no—
108C22×C4×C127—42no—
109C22×C4×C127—42no—
110C22×C4×C127—42no—
111C22×C4×C127—42no—
112C22×C4×C127—42no—
113C22×C4×C127—42no—
114C22×C4×C127—42no—
115C22×C4×C127—42no—
116C22×C4×C127C22⋊C411yescharacteristic
117C22×C4×C127C22⋊C411yescharacteristic
118C22×C4×C127C22×C411yescharacteristic
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127C2×D414yes—
121C2×C8×C127—42no—
122C2×C8×C127—42no—
123C2×C8×C127—42no—
124C4⋊C4×C127—24no—
125C4⋊C4×C127—28no—
126C4⋊C4×C127—22no—
127C4⋊C4×C127—28no—
128C4⋊C4×C127C22⋊C414yescomplemented
129C22⋊C4×C127—28no—
130C22⋊C4×C127—28no—
131C22⋊C4×C127—48no—
132C23×C127—21no—
133C23×C127—21no—
134C23×C127—21no—
135C23×C127—21no—
136C23×C127—21no—
137C23×C127—21no—
138C23×C127—21no—
139C23×C127—21no—
140C23×C127—24no—
141C23×C127—24no—
142C23×C127—21no—
143C23×C127—21no—
144C23×C127—21no—
145C23×C127—21no—
146C23×C127—21no—
147C23×C127—21no—
148C23×C127—24no—
149C23×C127—24no—
150C23×C127—42no—
151C23×C127—42no—
152C23×C127—44no—
153C23×C127—44no—
154C23×C127—44no—
155C23×C127—44no—
156C23×C127#9912yes—
157C23×C127#10312yes—
158C23×C127#10312yes—
159C23×C127#10412yes—
160C23×C127C2×C22⋊C411yescharacteristic
161C23×C127#12012yes—
162C23×C127C2×SD1611yescharacteristic
163C23×C127C2×Q1611yescharacteristic
164C23×C127#13712yes—
165Q8×C127—44no—
166Q8×C127—48no—
167Q8×C127—44no—
168C2×C4×C127—28no—
169C2×C4×C127—21no—
170C2×C4×C127—21no—
171C2×C4×C127—21no—
172C2×C4×C127—21no—
173C2×C4×C127—21no—
174C2×C4×C127—21no—
175C2×C4×C127—24no—
176C2×C4×C127—24no—
177C2×C4×C127—21no—
178C2×C4×C127—21no—
179C2×C4×C127—21no—
180C2×C4×C127—44no—
181C2×C4×C127—44no—
182C2×C4×C127—44no—
183C2×C4×C127—44no—
184C2×C4×C127—44no—
185C2×C4×C127—48no—
186C2×C4×C127—48no—
187C2×C4×C127—42no—
188C2×C4×C127—42no—
189C2×C4×C127—42no—
190C2×C4×C127—42no—
191C2×C4×C127—44no—
192C2×C4×C127—44no—
193C2×C4×C127—44no—
194C2×C4×C127—82no—
195C2×C4×C127—82no—
196C2×C4×C127—82no—
197C2×C4×C127—82no—
198C2×C4×C127#9912yes—
199C2×C4×C127C2×C22⋊C412yes—
200C2×C4×C127#12012yes—
201C8×C127—82no—
202C22×C127—21no—
203C22×C127—21no—
204C22×C127—22no—
205C22×C127—22no—
206C22×C127—22no—
207C22×C127—22no—
208C22×C127—21no—
209C22×C127—22no—
210C22×C127—21no—
211C22×C127—22no—
212C22×C127—22no—
213C22×C127—22no—
214C22×C127—22no—
215C22×C127—22no—
216C22×C127—22no—
217C22×C127—22no—
218C22×C127—22no—
219C22×C127—48no—
220C22×C127—48no—
221C22×C127—41no—
222C22×C127—41no—
223C22×C127—41no—
224C22×C127—41no—
225C22×C127#32814yescomplemented
226C22×C127#37911yescharacteristic
227C22×C127C2×#9911yescharacteristic
228C22×C127C2×#9911yescharacteristic
229C22×C127C2×#10311yescharacteristic
230C22×C127#41911yescharacteristic
231C22×C127C2×#10411yescharacteristic
232C22×C127#42111yescharacteristic
233C22×C127#44812yes—
234C22×C127#45112yes—
235C4×C127—22no—
236C4×C127—22no—
237C4×C127—22no—
238C4×C127—41no—
239C4×C127—44no—
240C4×C127—44no—
241C4×C127—84no—
242#8329C12711yesmaximal, characteristic, direct product factor, Sylow
243C2×C127—22no—
244C2×C127—24no—
245C2×C127—22no—
246C2×C127—42no—
247C2×C127C2×#32811yescharacteristic
248C2×C127#150811yescharacteristic
249C2×C127#151111yescharacteristic
250C2×C127#152011yescharacteristic
251C2×C127#178111yescharacteristic
252C2×C127#178711yescharacteristic
253C2×C127#178911yescharacteristic
254C22×C22⋊Q8C2×C12711yescharacteristic
255#1779C2×C12711yescharacteristic
256C2×#328C2×C12714yescomplemented
257C22⋊#95C2×C12711yescharacteristic
258C127#832911yescharacteristic, direct product factor, Sylow
259C23×Q8C4×C12711yescharacteristic, complemented
260C24×C4C22×C12711yescharacteristic
261C2×C22⋊Q8—21no—
262C2×C22⋊Q8—21no—
263C2×C22⋊Q8—28no—
264C2×C22⋊Q8C4×C12712yescomplemented
265C2×C22⋊Q8C22×C12712yes—
266C22×C4⋊C4—21no—
267C22×C4⋊C4C4×C12711yescharacteristic, complemented
268C22×C22⋊C4—21no—
269C22×C22⋊C4—21no—
270C2×C22⋊C8—21no—
271C2×C22⋊C8—21no—
272C2×C22⋊C8C22×C12712yes—
273C2×#95—21no—
274C2×#95C22×C12712yes—
275#328—28no—
276C25D4×C12711yescharacteristic
277C22×Q8—24no—
278C22×Q8—21no—
279C22×Q8—42no—
280C22×Q8—42no—
281C22×Q8C2×C4×C12712yes—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—24no—
285C23×C4—22no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4C2×C4×C12711yescharacteristic
289C23×C4C2×C4×C12711yescharacteristic
290C23×C4D4×C12711yescharacteristic
291C23×C4D4×C12711yescharacteristic
292C23×C4D4×C12711yescharacteristic
293C23×C4C23×C12711yescharacteristic
294C22×C8—22no—
295C22⋊Q8—28no—
296C22⋊Q8—28no—
297C22⋊Q8—24no—
298C22⋊Q8—24no—
299C22⋊Q8—24no—
300C22⋊Q8D4×C12718yes—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4C2×C4×C12712yes—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C22⋊C8—24no—
314C22⋊C8—42no—
315C22⋊C8—42no—
316#95—24no—
317#95—42no—
318C24—22no—
319C24—22no—
320C24—22no—
321C24—22no—
322C24—41no—
323C24—41no—
324C24C22⋊C4×C12711yescharacteristic
325C24C22⋊C4×C12711yescharacteristic
326C24SD16×C12712yes—
327C24Q16×C12712yes—
328C24C2×D4×C12711yescharacteristic
329C2×Q8—24no—
330C2×Q8—22no—
331C2×Q8—416no—
332C2×Q8—42no—
333C2×Q8—42no—
334C2×Q8—42no—
335C2×Q8—42no—
336C2×Q8C22⋊C4×C12714yescomplemented
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—416no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4C22⋊C4×C12711yescharacteristic
371C22×C4C22⋊C4×C12711yescharacteristic
372C22×C4C22×C4×C12711yescharacteristic
373C22×C4C2×D4×C12711yescharacteristic
374C22×C4C2×D4×C12714yes—
375C2×C8—42no—
376C2×C8—42no—
377C2×C8—42no—
378C4⋊C4—24no—
379C4⋊C4—28no—
380C4⋊C4—22no—
381C4⋊C4—28no—
382C4⋊C4C22⋊C4×C12714yescomplemented
383C22⋊C4—28no—
384C22⋊C4—28no—
385C22⋊C4—48no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—24no—
395C23—24no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—24no—
403C23—24no—
404C23—42no—
405C23—42no—
406C23—44no—
407C23—44no—
408C23—44no—
409C23—44no—
410C23#99×C12712yes—
411C23#103×C12712yes—
412C23#103×C12712yes—
413C23#104×C12712yes—
414C23C2×C22⋊C4×C12711yescharacteristic
415C23#120×C12712yes—
416C23C2×SD16×C12711yescharacteristic
417C23C2×Q16×C12711yescharacteristic
418C23#137×C12712yes—
419Q8—44no—
420Q8—48no—
421Q8—44no—
422C2×C4—28no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—44no—
435C2×C4—44no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—48no—
440C2×C4—48no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—82no—
451C2×C4—82no—
452C2×C4#99×C12712yes—
453C2×C4C2×C22⋊C4×C12712yes—
454C2×C4#120×C12712yes—
455C8—82no—
456C22—21no—
457C22—21no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—21no—
463C22—22no—
464C22—21no—
465C22—22no—
466C22—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—22no—
473C22—48no—
474C22—48no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22#328×C12714yescomplemented
480C22#379×C12711yescharacteristic
481C22C2×#99×C12711yescharacteristic
482C22C2×#99×C12711yescharacteristic
483C22C2×#103×C12711yescharacteristic
484C22#419×C12711yescharacteristic
485C22C2×#104×C12711yescharacteristic
486C22#421×C12711yescharacteristic
487C22#448×C12712yes—
488C22#451×C12712yes—
489C4—22no—
490C4—22no—
491C4—22no—
492C4—41no—
493C4—44no—
494C4—44no—
495C4—84no—
496C2—22no—
497C2—24no—
498C2—22no—
499C2—42no—
500C2C2×#328×C12711yescharacteristic
501C2C127×#150811yescharacteristic
502C2C127×#151111yescharacteristic
503C2C127×#152011yescharacteristic
504C2C127×#178111yescharacteristic
505C2C127×#178711yescharacteristic
506C2C127×#178911yescharacteristic
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC25×C127D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#328×C127C2semidirect
5. C23×Q8×C127C4semidirect
10. C2×C22⋊Q8×C127C4semidirect
13. C22×C4⋊C4×C127C4semidirect
82. C2×Q8×C127C22⋊C4semidirect
128. C4⋊C4×C127C22⋊C4semidirect
225. C22×C127#328semidirect
242. #8329C127direct (N × H)
256. C2×#328C2×C127semidirect
258. C127#8329direct (N × H)
259. C23×Q8C4×C127semidirect
264. C2×C22⋊Q8C4×C127semidirect
267. C22×C4⋊C4C4×C127semidirect
336. C2×Q8C22⋊C4×C127semidirect
382. C4⋊C4C22⋊C4×C127semidirect
479. C22#328×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1272
C127×#17792
C2×#328×C1272
C127×C22⋊#952
#8329127