Finite Group Databasebeta

← C127×#13790 #44577463

Subgroups — C127×#13790 #44577463

Order 32512.

1522 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
1C2×#389×C127C211yesmaximal, characteristic
2C2×#387×C127C212yesmaximal
3C2×C4×C4⋊C4×C127C212yesmaximal
4C127×#1436C212yesmaximal
5C127×#1436C212yesmaximal
6C127×#1436C212yesmaximal
7C127×#1434C212yesmaximal
8C127×#1434C211yesmaximal, characteristic
9C4×#95×C127C211yesmaximal, characteristic
10C22×C4⋊C4×C127C2212yes—
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C42×C127C2212yes—
15C22×C42×C127C2211yescharacteristic
16C22×C42×C127C2212yes—
17C22×C42×C127C2211yescharacteristic
18C22×C42×C127C2211yescharacteristic
19#389×C127C418yescomplemented
20#387×C127C4116yescomplemented
21C4×C4⋊C4×C127—28no—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2211yescharacteristic
26C2×#95×C127C2212yes—
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2312yes—
36C23×C4×C127C2312yes—
37C23×C4×C127C2311yescharacteristic
38C23×C4×C127C2312yes—
39C23×C4×C127C2312yes—
40C23×C4×C127C2311yescharacteristic
41C23×C4×C127C2311yescharacteristic
42C23×C4×C127C2312yes—
43C2×C4⋊C4×C127—24no—
44C2×C4⋊C4×C127—24no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127—24no—
47C2×C4⋊C4×C127—41no—
48C2×C4⋊C4×C127—41no—
49C2×C4⋊C4×C127C2×C418yes—
50C2×C4⋊C4×C127C2×C418yes—
51C2×C4⋊C4×C127C2×C414yes—
52C2×C4⋊C4×C127C2×C418yes—
53C2×C4⋊C4×C127C2×C414yes—
54C2×C42×C127—24no—
55C2×C42×C127—24no—
56C2×C42×C127—24no—
57C2×C42×C127—22no—
58C2×C42×C127—41no—
59C2×C42×C127—41no—
60C2×C42×C127—41no—
61C2×C42×C127—41no—
62C2×C42×C127—41no—
63C2×C42×C127—41no—
64C2×C42×C127—42no—
65C2×C42×C127—42no—
66C2×C42×C127C2×C418yes—
67C2×C42×C127C2×C414yes—
68C2×C42×C127D414yes—
69#95×C127—24no—
70#95×C127—24no—
71#95×C127—24no—
72#95×C127—41no—
73#95×C127—42no—
74#95×C127—41no—
75#95×C127—42no—
76#95×C127C2×C418yes—
77#95×C127C2×C418yes—
78#95×C127C2×C418yes—
79#95×C127C2×C418yes—
80#95×C127C2×C418yes—
81C24×C127C2411yescharacteristic
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
86C22×C4×C127—21no—
87C22×C4×C127—21no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—21no—
91C22×C4×C127—21no—
92C22×C4×C127—21no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—21no—
97C22×C4×C127—22no—
98C22×C4×C127—22no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—22no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—22no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127C22×C414yes—
126C22×C4×C127C22×C414yes—
127C22×C4×C127C22×C412yes—
128C22×C4×C127C22×C414yes—
129C22×C4×C127C22×C414yes—
130C22×C4×C127C22×C414yes—
131C22×C4×C127C22×C414yes—
132C22×C4×C127C22×C414yes—
133C22×C4×C127C22×C414yes—
134C22×C4×C127C22×C412yes—
135C22×C4×C127C22×C414yes—
136C22×C4×C127C22×C412yes—
137C22×C4×C127C2×D412yes—
138C22×C4×C127C2×D414yes—
139C22×C4×C127#4114yes—
140C22×C4×C127#4112yes—
141C4⋊C4×C127—216no—
142C4⋊C4×C127—216no—
143C4⋊C4×C127—44no—
144C4⋊C4×C127C42116yescomplemented
145C42×C127—216no—
146C42×C127—44no—
147C42×C127—44no—
148C42×C127—48no—
149C42×C127—44no—
150C23×C127C23×C411yescharacteristic
151C23×C127C23×C412yes—
152C23×C127C22×D411yescharacteristic
153C23×C127C2×#4111yescharacteristic
154C23×C127C2×#4112yes—
155C23×C127H(5,𝔽2)11yescharacteristic
156C23×C127H(5,𝔽2)11yescharacteristic
157C23×C127H(5,𝔽2)11yescharacteristic
158C23×C1272−1+412yes—
159C23×C1272−1+411yescharacteristic
160C23×C1272−1+412yes—
161C2×C4×C127—24no—
162C2×C4×C127—24no—
163C2×C4×C127—24no—
164C2×C4×C127—24no—
165C2×C4×C127—24no—
166C2×C4×C127—24no—
167C2×C4×C127—22no—
168C2×C4×C127—22no—
169C2×C4×C127—22no—
170C2×C4×C127—24no—
171C2×C4×C127—24no—
172C2×C4×C127—22no—
173C2×C4×C127—24no—
174C2×C4×C127—24no—
175C2×C4×C127—24no—
176C2×C4×C127—22no—
177C2×C4×C127—24no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—24no—
181C2×C4×C127—24no—
182C2×C4×C127—22no—
183C2×C4×C127—24no—
184C2×C4×C127—24no—
185C2×C4×C127—24no—
186C2×C4×C127—22no—
187C2×C4×C127—24no—
188C2×C4×C127—22no—
189C2×C4×C127—24no—
190C2×C4×C127—24no—
191C2×C4×C127—22no—
192C2×C4×C127—24no—
193C2×C4×C127—24no—
194C2×C4×C127—24no—
195C2×C4×C127—24no—
196C2×C4×C127—24no—
197C2×C4×C127—24no—
198C2×C4×C127—42no—
199C2×C4×C127—42no—
200C2×C4×C127—42no—
201C2×C4×C127—42no—
202C2×C4×C127—42no—
203C2×C4×C127—42no—
204C2×C4×C127—42no—
205C2×C4×C127—42no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—42no—
209C2×C4×C127—42no—
210C2×C4×C127—42no—
211C2×C4×C127—42no—
212C2×C4×C127—42no—
213C2×C4×C127—42no—
214C2×C4×C127—42no—
215C2×C4×C127—42no—
216C2×C4×C127C2×C4218yes—
217C2×C4×C127C2×C4214yes—
218C2×C4×C127C4×D418yes—
219C2×C4×C127C4×D414yes—
220C22×C127C22×C4211yescharacteristic
221C22×C127C2×C4×D412yes—
222C22×C127C2×C4×D411yescharacteristic
223C22×C127C4×#4111yescharacteristic
224C22×C127C4×#4112yes—
225C22×C127#51811yescharacteristic
226C22×C127#51912yes—
227C22×C127#51911yescharacteristic
228C22×C127#51911yescharacteristic
229C22×C127#52012yes—
230C22×C127#52012yes—
231C22×C127#52012yes—
232C22×C127#52011yescharacteristic
233C22×C127#53411yescharacteristic
234C22×C127#53612yes—
235C22×C127#53711yescharacteristic
236C22×C127#53811yescharacteristic
237C22×C127#53912yes—
238C22×C127#53912yes—
239C22×C127#53911yescharacteristic
240C22×C127#54112yes—
241C22×C127#54112yes—
242C22×C127#54212yes—
243C4×C127—28no—
244C4×C127—24no—
245C4×C127—28no—
246C4×C127—24no—
247C4×C127—44no—
248C4×C127—44no—
249C4×C127—44no—
250C4×C127—42no—
251C4×C127—44no—
252#13790C12711yesmaximal, characteristic, direct product factor, Sylow
253C2×C127C42×D411yescharacteristic
254C2×C127#227411yescharacteristic
255C2×C127#227611yescharacteristic
256C2×C127#232212yes—
257C2×C127#232312yes—
258C2×C127#232511yescharacteristic
259C2×C127#232711yescharacteristic
260C2×C127#233211yescharacteristic
261C2×C127#233412yes—
262C2×C127#233611yescharacteristic
263C2×C127#233612yes—
264C2×#389C2×C12711yescharacteristic
265C2×#387C2×C12712yes—
266C2×C4×C4⋊C4C2×C12712yes—
267#1436C2×C12712yes—
268#1436C2×C12712yes—
269#1436C2×C12712yes—
270#1434C2×C12712yes—
271#1434C2×C12711yescharacteristic
272C4×#95C2×C12711yescharacteristic
273C127#1379011yescharacteristic, direct product factor, Sylow
274C22×C4⋊C4C22×C12712yes—
275C22×C4⋊C4C22×C12712yes—
276C22×C4⋊C4C22×C12711yescharacteristic
277C22×C4⋊C4C22×C12711yescharacteristic
278C22×C42C22×C12712yes—
279C22×C42C22×C12711yescharacteristic
280C22×C42C22×C12712yes—
281C22×C42C22×C12711yescharacteristic
282C22×C42C22×C12711yescharacteristic
283#389C4×C12718yescomplemented
284#387C4×C127116yescomplemented
285C4×C4⋊C4—28no—
286C2×#95C22×C12712yes—
287C2×#95C22×C12712yes—
288C2×#95C22×C12712yes—
289C2×#95C22×C12711yescharacteristic
290C2×#95C22×C12712yes—
291C2×#95C22×C12711yescharacteristic
292C2×#95C22×C12712yes—
293C2×#95C22×C12712yes—
294C2×#95C22×C12712yes—
295C2×#95C22×C12712yes—
296C2×#95C22×C12712yes—
297C2×#95C22×C12712yes—
298C23×C4C23×C12712yes—
299C23×C4C23×C12712yes—
300C23×C4C23×C12712yes—
301C23×C4C23×C12711yescharacteristic
302C23×C4C23×C12712yes—
303C23×C4C23×C12712yes—
304C23×C4C23×C12711yescharacteristic
305C23×C4C23×C12711yescharacteristic
306C23×C4C23×C12712yes—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4C2×C4×C12718yes—
314C2×C4⋊C4C2×C4×C12718yes—
315C2×C4⋊C4C2×C4×C12714yes—
316C2×C4⋊C4C2×C4×C12718yes—
317C2×C4⋊C4C2×C4×C12714yes—
318C2×C42—24no—
319C2×C42—24no—
320C2×C42—24no—
321C2×C42—22no—
322C2×C42—41no—
323C2×C42—41no—
324C2×C42—41no—
325C2×C42—41no—
326C2×C42—41no—
327C2×C42—41no—
328C2×C42—42no—
329C2×C42—42no—
330C2×C42C2×C4×C12718yes—
331C2×C42C2×C4×C12714yes—
332C2×C42D4×C12714yes—
333#95—24no—
334#95—24no—
335#95—24no—
336#95—41no—
337#95—42no—
338#95—41no—
339#95—42no—
340#95C2×C4×C12718yes—
341#95C2×C4×C12718yes—
342#95C2×C4×C12718yes—
343#95C2×C4×C12718yes—
344#95C2×C4×C12718yes—
345C24C24×C12711yescharacteristic
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4C22×C4×C12714yes—
390C22×C4C22×C4×C12714yes—
391C22×C4C22×C4×C12712yes—
392C22×C4C22×C4×C12714yes—
393C22×C4C22×C4×C12714yes—
394C22×C4C22×C4×C12714yes—
395C22×C4C22×C4×C12714yes—
396C22×C4C22×C4×C12714yes—
397C22×C4C22×C4×C12714yes—
398C22×C4C22×C4×C12712yes—
399C22×C4C22×C4×C12714yes—
400C22×C4C22×C4×C12712yes—
401C22×C4C2×D4×C12712yes—
402C22×C4C2×D4×C12714yes—
403C22×C4#41×C12714yes—
404C22×C4#41×C12712yes—
405C4⋊C4—216no—
406C4⋊C4—216no—
407C4⋊C4—44no—
408C4⋊C4C42×C127116yescomplemented
409C42—216no—
410C42—44no—
411C42—44no—
412C42—48no—
413C42—44no—
414C23C23×C4×C12711yescharacteristic
415C23C23×C4×C12712yes—
416C23C22×D4×C12711yescharacteristic
417C23C2×#41×C12711yescharacteristic
418C23C2×#41×C12712yes—
419C23H(5,𝔽2)×C12711yescharacteristic
420C23H(5,𝔽2)×C12711yescharacteristic
421C23H(5,𝔽2)×C12711yescharacteristic
422C232−1+4×C12712yes—
423C232−1+4×C12711yescharacteristic
424C232−1+4×C12712yes—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4C2×C42×C12718yes—
481C2×C4C2×C42×C12714yes—
482C2×C4C4×D4×C12718yes—
483C2×C4C4×D4×C12714yes—
484C22C22×C42×C12711yescharacteristic
485C22C2×C4×D4×C12712yes—
486C22C2×C4×D4×C12711yescharacteristic
487C22C4×#41×C12711yescharacteristic
488C22C4×#41×C12712yes—
489C22#518×C12711yescharacteristic
490C22#519×C12712yes—
491C22#519×C12711yescharacteristic
492C22#519×C12711yescharacteristic
493C22#520×C12712yes—
494C22#520×C12712yes—
495C22#520×C12712yes—
496C22#520×C12711yescharacteristic
497C22#534×C12711yescharacteristic
498C22#536×C12712yes—
499C22#537×C12711yescharacteristic
500C22#538×C12711yescharacteristic
501C22#539×C12712yes—
502C22#539×C12712yes—
503C22#539×C12711yescharacteristic
504C22#541×C12712yes—
505C22#541×C12712yes—
506C22#542×C12712yes—
507C4—28no—
508C4—24no—
509C4—28no—
510C4—24no—
511C4—44no—
512C4—44no—
513C4—44no—
514C4—42no—
515C4—44no—
516C2C42×D4×C12711yescharacteristic
517C2C127×#227411yescharacteristic
518C2C127×#227611yescharacteristic
519C2C127×#232212yes—
520C2C127×#232312yes—
521C2C127×#232511yescharacteristic
522C2C127×#232711yescharacteristic
523C2C127×#233211yescharacteristic
524C2C127×#233412yes—
525C2C127×#233611yescharacteristic
526C2C127×#233612yes—
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC22C22×C42×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
19. #389×C127C4semidirect
20. #387×C127C4semidirect
144. C4⋊C4×C127C42semidirect
252. #13790C127direct (N × H)
273. C127#13790direct (N × H)
283. #389C4×C127semidirect
284. #387C4×C127semidirect
408. C4⋊C4C42×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1272
C2×#387×C1272
C2×C4×C4⋊C4×C1272
C127×#14362
C127×#14342
C4×#95×C1272
#13790127