Finite Group Databasebeta

← C127×#14236 #44577909

Subgroups — C127×#14236 #44577909

Order 32512.

1554 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#395×C127C211yesmaximal, characteristic
2C2×#391×C127C212yesmaximal
3C2×#389×C127C212yesmaximal
4C127×#1444C212yesmaximal
5C127×#1441C211yesmaximal, characteristic
6C127×#1436C212yesmaximal
7C127×#1436C212yesmaximal
8C127×C4⋊#95C211yesmaximal, characteristic
9C4×#95×C127C212yesmaximal
10C23×Q8×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C42×C127C2212yes—
18C22×C42×C127C2212yes—
19C22×C42×C127C2211yescharacteristic
20#395×C127C418yescomplemented
21#391×C127—28no—
22#389×C127—28no—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C22×Q8×C127—24no—
35C22×Q8×C127—24no—
36C22×Q8×C127—41no—
37C22×Q8×C127—41no—
38C22×Q8×C127C2×C414yes—
39C23×C4×C127C2312yes—
40C23×C4×C127C2311yescharacteristic
41C23×C4×C127C2311yescharacteristic
42C23×C4×C127C2312yes—
43C23×C4×C127C2312yes—
44C23×C4×C127C2312yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2311yescharacteristic
47C23×C4×C127C2312yes—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—24no—
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127—24no—
52C2×C4⋊C4×C127—24no—
53C2×C4⋊C4×C127—24no—
54C2×C4⋊C4×C127—24no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—41no—
57C2×C4⋊C4×C127—41no—
58C2×C4⋊C4×C127—42no—
59C2×C4⋊C4×C127—42no—
60C2×C4⋊C4×C127—41no—
61C2×C4⋊C4×C127—41no—
62C2×C4⋊C4×C127—41no—
63C2×C4⋊C4×C127C2×C418yes—
64C2×C4⋊C4×C127C2×C414yes—
65C2×C42×C127—24no—
66C2×C42×C127—24no—
67C2×C42×C127—24no—
68C2×C42×C127—24no—
69C2×C42×C127—41no—
70C2×C42×C127—41no—
71C2×C42×C127—42no—
72C2×C42×C127—42no—
73C2×C42×C127Q814yescomplemented
74#95×C127—24no—
75#95×C127—24no—
76#95×C127—24no—
77#95×C127—24no—
78#95×C127—24no—
79#95×C127—24no—
80#95×C127—41no—
81#95×C127C2×C414yes—
82#95×C127C2×C418yes—
83#95×C127D418yes—
84#95×C127Q818yescomplemented
85C24×C127C2411yescharacteristic
86C2×Q8×C127—216no—
87C2×Q8×C127—44no—
88C2×Q8×C127—44no—
89C2×Q8×C127—48no—
90C2×Q8×C127—44no—
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—22no—
98C22×C4×C127—22no—
99C22×C4×C127—21no—
100C22×C4×C127—21no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—21no—
104C22×C4×C127—22no—
105C22×C4×C127—21no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—22no—
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—21no—
121C22×C4×C127—22no—
122C22×C4×C127—21no—
123C22×C4×C127—22no—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127C22×C412yes—
135C22×C4×C127C22×C412yes—
136C22×C4×C127C22×C414yes—
137C22×C4×C127C22×C414yes—
138C22×C4×C127C22×C412yes—
139C22×C4×C127C2×D414yes—
140C22×C4×C127C2×D414yes—
141C22×C4×C127C2×D414yes—
142C22×C4×C127C2×Q814yes—
143C22×C4×C127C2×Q814yes—
144C22×C4×C127C2×Q812yes—
145C22×C4×C127C2×Q814yes—
146C22×C4×C127C2×Q814yes—
147C22×C4×C127#4114yes—
148C22×C4×C127#4112yes—
149C22×C4×C127#4114yes—
150C4⋊C4×C127—216no—
151C4⋊C4×C127—44no—
152C4⋊C4×C127—48no—
153C4⋊C4×C127—48no—
154C4⋊C4×C127—44no—
155C4⋊C4×C127—44no—
156C42×C127—44no—
157C42×C127—48no—
158C42×C127—48no—
159C23×C127C23×C411yescharacteristic
160C23×C127C22×D412yes—
161C23×C127C22×Q811yescharacteristic
162C23×C127C22×Q812yes—
163C23×C127C2×#4112yes—
164C23×C127C2×#4111yescharacteristic
165C23×C127C2×#4112yes—
166C23×C127H(5,𝔽2)11yescharacteristic
167C23×C127H(5,𝔽2)11yescharacteristic
168C23×C127H(5,𝔽2)11yescharacteristic
169C23×C1272−1+411yescharacteristic
170Q8×C127—416no—
171C2×C4×C127—24no—
172C2×C4×C127—24no—
173C2×C4×C127—22no—
174C2×C4×C127—24no—
175C2×C4×C127—22no—
176C2×C4×C127—24no—
177C2×C4×C127—24no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—24no—
182C2×C4×C127—22no—
183C2×C4×C127—24no—
184C2×C4×C127—24no—
185C2×C4×C127—24no—
186C2×C4×C127—24no—
187C2×C4×C127—24no—
188C2×C4×C127—24no—
189C2×C4×C127—24no—
190C2×C4×C127—24no—
191C2×C4×C127—24no—
192C2×C4×C127—24no—
193C2×C4×C127—24no—
194C2×C4×C127—24no—
195C2×C4×C127—24no—
196C2×C4×C127—24no—
197C2×C4×C127—22no—
198C2×C4×C127—22no—
199C2×C4×C127—24no—
200C2×C4×C127—24no—
201C2×C4×C127—24no—
202C2×C4×C127—24no—
203C2×C4×C127—24no—
204C2×C4×C127—24no—
205C2×C4×C127—42no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—42no—
209C2×C4×C127—41no—
210C2×C4×C127—41no—
211C2×C4×C127—42no—
212C2×C4×C127—42no—
213C2×C4×C127—42no—
214C2×C4×C127—42no—
215C2×C4×C127—41no—
216C2×C4×C127—41no—
217C2×C4×C127—42no—
218C2×C4×C127—42no—
219C2×C4×C127—42no—
220C2×C4×C127—42no—
221C2×C4×C127—42no—
222C2×C4×C127—42no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127C4×D418yes—
227C2×C4×C127C4×Q814yes—
228C2×C4×C127C4×Q818yes—
229C2×C4×C127C4⋊Q818yes—
230C22×C127C2×C4×D412yes—
231C22×C127C2×C4×Q811yescharacteristic
232C22×C127C2×C4×Q812yes—
233C22×C127#51811yescharacteristic
234C22×C127#52011yescharacteristic
235C22×C127C2×C4⋊Q812yes—
236C22×C127#53212yes—
237C22×C127#53312yes—
238C22×C127#53312yes—
239C22×C127#53811yescharacteristic
240C22×C127#53911yescharacteristic
241C22×C127#54311yescharacteristic
242C22×C127#54411yescharacteristic
243C22×C127D4211yescharacteristic
244C22×C127#54612yes—
245C22×C127#54612yes—
246C22×C127D4×Q812yes—
247C22×C127#55111yescharacteristic
248C22×C127#55212yes—
249C22×C127#55412yes—
250C22×C127#55412yes—
251C22×C127#55511yescharacteristic
252C22×C127Q8211yescharacteristic
253C4×C127—24no—
254C4×C127—28no—
255C4×C127—28no—
256C4×C127—28no—
257C4×C127—42no—
258C4×C127—42no—
259C4×C127—44no—
260C4×C127—44no—
261C4×C127—82no—
262#14236C12711yesmaximal, characteristic, direct product factor, Sylow
263C2×C127C4×C4⋊Q812yes—
264C2×C127#232911yescharacteristic
265C2×C127#235811yescharacteristic
266C2×C127#236012yes—
267C2×C127#236911yescharacteristic
268C2×C127#254912yes—
269C2×C127#255111yescharacteristic
270C2×C127#255511yescharacteristic
271C2×C127#255612yes—
272C2×C127#258611yescharacteristic
273C2×C127#261211yescharacteristic
274C2×#395C2×C12711yescharacteristic
275C2×#391C2×C12712yes—
276C2×#389C2×C12712yes—
277#1444C2×C12712yes—
278#1441C2×C12711yescharacteristic
279#1436C2×C12712yes—
280#1436C2×C12712yes—
281C4⋊#95C2×C12711yescharacteristic
282C4×#95C2×C12712yes—
283C127#1423611yescharacteristic, direct product factor, Sylow
284C23×Q8C22×C12711yescharacteristic
285C22×C4⋊C4C22×C12712yes—
286C22×C4⋊C4C22×C12711yescharacteristic
287C22×C4⋊C4C22×C12712yes—
288C22×C4⋊C4C22×C12712yes—
289C22×C4⋊C4C22×C12711yescharacteristic
290C22×C4⋊C4C22×C12711yescharacteristic
291C22×C42C22×C12712yes—
292C22×C42C22×C12712yes—
293C22×C42C22×C12711yescharacteristic
294#395C4×C12718yescomplemented
295#391—28no—
296#389—28no—
297C2×#95C22×C12712yes—
298C2×#95C22×C12712yes—
299C2×#95C22×C12712yes—
300C2×#95C22×C12712yes—
301C2×#95C22×C12712yes—
302C2×#95C22×C12712yes—
303C2×#95C22×C12711yescharacteristic
304C2×#95C22×C12712yes—
305C2×#95C22×C12711yescharacteristic
306C2×#95C22×C12712yes—
307C2×#95C22×C12712yes—
308C22×Q8—24no—
309C22×Q8—24no—
310C22×Q8—41no—
311C22×Q8—41no—
312C22×Q8C2×C4×C12714yes—
313C23×C4C23×C12712yes—
314C23×C4C23×C12711yescharacteristic
315C23×C4C23×C12711yescharacteristic
316C23×C4C23×C12712yes—
317C23×C4C23×C12712yes—
318C23×C4C23×C12712yes—
319C23×C4C23×C12712yes—
320C23×C4C23×C12711yescharacteristic
321C23×C4C23×C12712yes—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—41no—
331C2×C4⋊C4—41no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—41no—
335C2×C4⋊C4—41no—
336C2×C4⋊C4—41no—
337C2×C4⋊C4C2×C4×C12718yes—
338C2×C4⋊C4C2×C4×C12714yes—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—24no—
342C2×C42—24no—
343C2×C42—41no—
344C2×C42—41no—
345C2×C42—42no—
346C2×C42—42no—
347C2×C42Q8×C12714yescomplemented
348#95—24no—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—41no—
355#95C2×C4×C12714yes—
356#95C2×C4×C12718yes—
357#95D4×C12718yes—
358#95Q8×C12718yescomplemented
359C24C24×C12711yescharacteristic
360C2×Q8—216no—
361C2×Q8—44no—
362C2×Q8—44no—
363C2×Q8—48no—
364C2×Q8—44no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—21no—
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×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4C22×C4×C12712yes—
409C22×C4C22×C4×C12712yes—
410C22×C4C22×C4×C12714yes—
411C22×C4C22×C4×C12714yes—
412C22×C4C22×C4×C12712yes—
413C22×C4C2×D4×C12714yes—
414C22×C4C2×D4×C12714yes—
415C22×C4C2×D4×C12714yes—
416C22×C4C2×Q8×C12714yes—
417C22×C4C2×Q8×C12714yes—
418C22×C4C2×Q8×C12712yes—
419C22×C4C2×Q8×C12714yes—
420C22×C4C2×Q8×C12714yes—
421C22×C4#41×C12714yes—
422C22×C4#41×C12712yes—
423C22×C4#41×C12714yes—
424C4⋊C4—216no—
425C4⋊C4—44no—
426C4⋊C4—48no—
427C4⋊C4—48no—
428C4⋊C4—44no—
429C4⋊C4—44no—
430C42—44no—
431C42—48no—
432C42—48no—
433C23C23×C4×C12711yescharacteristic
434C23C22×D4×C12712yes—
435C23C22×Q8×C12711yescharacteristic
436C23C22×Q8×C12712yes—
437C23C2×#41×C12712yes—
438C23C2×#41×C12711yescharacteristic
439C23C2×#41×C12712yes—
440C23H(5,𝔽2)×C12711yescharacteristic
441C23H(5,𝔽2)×C12711yescharacteristic
442C23H(5,𝔽2)×C12711yescharacteristic
443C232−1+4×C12711yescharacteristic
444Q8—416no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4C4×D4×C12718yes—
501C2×C4C4×Q8×C12714yes—
502C2×C4C4×Q8×C12718yes—
503C2×C4C4⋊Q8×C12718yes—
504C22C2×C4×D4×C12712yes—
505C22C2×C4×Q8×C12711yescharacteristic
506C22C2×C4×Q8×C12712yes—
507C22#518×C12711yescharacteristic
508C22#520×C12711yescharacteristic
509C22C2×C4⋊Q8×C12712yes—
510C22#532×C12712yes—
511C22#533×C12712yes—
512C22#533×C12712yes—
513C22#538×C12711yescharacteristic
514C22#539×C12711yescharacteristic
515C22#543×C12711yescharacteristic
516C22#544×C12711yescharacteristic
517C22D42×C12711yescharacteristic
518C22#546×C12712yes—
519C22#546×C12712yes—
520C22D4×Q8×C12712yes—
521C22#551×C12711yescharacteristic
522C22#552×C12712yes—
523C22#554×C12712yes—
524C22#554×C12712yes—
525C22#555×C12711yescharacteristic
526C22Q82×C12711yescharacteristic
527C4—24no—
528C4—28no—
529C4—28no—
530C4—28no—
531C4—42no—
532C4—42no—
533C4—44no—
534C4—44no—
535C4—82no—
536C2C4×C4⋊Q8×C12712yes—
537C2C127×#232911yescharacteristic
538C2C127×#235811yescharacteristic
539C2C127×#236012yes—
540C2C127×#236911yescharacteristic
541C2C127×#254912yes—
542C2C127×#255111yescharacteristic
543C2C127×#255511yescharacteristic
544C2C127×#255612yes—
545C2C127×#258611yescharacteristic
546C2C127×#261211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
20. #395×C127C4semidirect
73. C2×C42×C127Q8semidirect
84. #95×C127Q8semidirect
262. #14236C127direct (N × H)
283. C127#14236direct (N × H)
294. #395C4×C127semidirect
347. C2×C42Q8×C127semidirect
358. #95Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#395×C1272
C2×#391×C1272
C2×#389×C1272
C127×#14442
C127×#14412
C127×#14362
C127×C4⋊#952
C4×#95×C1272
#14236127