Finite Group Databasebeta

← C127×#14626 #44578299

Subgroups — C127×#14626 #44578299

Order 32512.

1194 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#395×C127C211yesmaximal, characteristic
2C2×#391×C127C211yesmaximal, characteristic
3C2×#387×C127C211yesmaximal, characteristic
4C127×#1446C211yesmaximal, characteristic
5C127×#1445C212yesmaximal
6C127×#1443C212yesmaximal
7C127×#1443C212yesmaximal
8C127×#1442C211yesmaximal, characteristic
9C127×#1441C211yesmaximal, characteristic
10C127×#1441C212yesmaximal
11C127×#1434C211yesmaximal, characteristic
12C23×Q8×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2212yes—
17C22×C42×C127C2211yescharacteristic
18#395×C127C418yescomplemented
19#391×C127—24no—
20#387×C127—24no—
21C2×#95×C127C2211yescharacteristic
22C2×#95×C127C2212yes—
23C2×#95×C127C2211yescharacteristic
24C2×#95×C127C2211yescharacteristic
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—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2212yes—
38C22×Q8×C127—22no—
39C22×Q8×C127—22no—
40C22×Q8×C127—42no—
41C22×Q8×C127—42no—
42C22×Q8×C127C2×C414yes—
43C23×C4×C127C2311yescharacteristic
44C23×C4×C127C2312yes—
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2312yes—
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2312yes—
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2312yes—
51C23×C4×C127C2311yescharacteristic
52C23×C4×C127C2311yescharacteristic
53C23×C4×C127C2311yescharacteristic
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—42no—
59C2×C4⋊C4×C127—42no—
60C2×C4⋊C4×C127—42no—
61C2×C4⋊C4×C127—42no—
62C2×C4⋊C4×C127C2×C414yes—
63C2×C4⋊C4×C127C2×C418yes—
64C2×C42×C127—42no—
65C2×C42×C127D414yes—
66#95×C127—22no—
67#95×C127—22no—
68#95×C127—22no—
69#95×C127—22no—
70#95×C127—24no—
71#95×C127—24no—
72#95×C127—22no—
73#95×C127—42no—
74#95×C127—42no—
75#95×C127—42no—
76#95×C127—42no—
77#95×C127—42no—
78#95×C127—42no—
79#95×C127—42no—
80#95×C127—42no—
81#95×C127C2×C418yes—
82#95×C127C2×C414yes—
83C24×C127C2411yescharacteristic
84C2×Q8×C127—28no—
85C2×Q8×C127—48no—
86C2×Q8×C127—44no—
87C2×Q8×C127—44no—
88C2×Q8×C127—48no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—21no—
92C22×C4×C127—22no—
93C22×C4×C127—21no—
94C22×C4×C127—21no—
95C22×C4×C127—21no—
96C22×C4×C127—22no—
97C22×C4×C127—21no—
98C22×C4×C127—22no—
99C22×C4×C127—21no—
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—22no—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
110C22×C4×C127—21no—
111C22×C4×C127—21no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—21no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—22no—
118C22×C4×C127—21no—
119C22×C4×C127—21no—
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—21no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—22no—
126C22×C4×C127—22no—
127C22×C4×C127—21no—
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×C127—22no—
135C22×C4×C127—22no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—21no—
139C22×C4×C127—21no—
140C22×C4×C127—22no—
141C22×C4×C127—21no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—22no—
145C22×C4×C127C22×C412yes—
146C22×C4×C127C22×C414yes—
147C22×C4×C127C22×C414yes—
148C22×C4×C127C22×C412yes—
149C22×C4×C127C22×C412yes—
150C22×C4×C127C2×D412yes—
151C22×C4×C127C2×D412yes—
152C22×C4×C127C2×D412yes—
153C22×C4×C127#4112yes—
154C4⋊C4×C127—28no—
155C4⋊C4×C127—48no—
156C4⋊C4×C127—44no—
157C4⋊C4×C127—44no—
158C42×C127—44no—
159C23×C127C23×C411yescharacteristic
160C23×C127C22×D411yescharacteristic
161C23×C127C2×#4111yescharacteristic
162C23×C127H(5,𝔽2)12yes—
163C23×C127H(5,𝔽2)12yes—
164C23×C127H(5,𝔽2)11yescharacteristic
165C23×C1272−1+412yes—
166C23×C1272−1+412yes—
167C23×C1272−1+411yescharacteristic
168C23×C1272−1+411yescharacteristic
169C23×C1272−1+411yescharacteristic
170Q8×C127—416no—
171C2×C4×C127—24no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—24no—
175C2×C4×C127—22no—
176C2×C4×C127—22no—
177C2×C4×C127—24no—
178C2×C4×C127—24no—
179C2×C4×C127—24no—
180C2×C4×C127—24no—
181C2×C4×C127—24no—
182C2×C4×C127—22no—
183C2×C4×C127—24no—
184C2×C4×C127—22no—
185C2×C4×C127—24no—
186C2×C4×C127—22no—
187C2×C4×C127—22no—
188C2×C4×C127—22no—
189C2×C4×C127—22no—
190C2×C4×C127—22no—
191C2×C4×C127—22no—
192C2×C4×C127—41no—
193C2×C4×C127—42no—
194C2×C4×C127—41no—
195C2×C4×C127—42no—
196C2×C4×C127—41no—
197C2×C4×C127—41no—
198C2×C4×C127—42no—
199C2×C4×C127—42no—
200C2×C4×C127—42no—
201C2×C4×C127—41no—
202C2×C4×C127—41no—
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—41no—
212C2×C4×C127—42no—
213C2×C4×C127—41no—
214C2×C4×C127—42no—
215C2×C4×C127—41no—
216C2×C4×C127—41no—
217C2×C4×C127—41no—
218C2×C4×C127—42no—
219C2×C4×C127—41no—
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×C127—42no—
227C2×C4×C127—42no—
228C2×C4×C127—42no—
229C2×C4×C127—42no—
230C2×C4×C127—42no—
231C2×C4×C127—42no—
232C2×C4×C127—42no—
233C2×C4×C127—42no—
234C2×C4×C127—42no—
235C2×C4×C127C4×D414yes—
236C22×C127C2×C4×D411yescharacteristic
237C22×C127#51812yes—
238C22×C127#51911yescharacteristic
239C22×C127#51912yes—
240C22×C127#52011yescharacteristic
241C22×C127#53411yescharacteristic
242C22×C127#53511yescharacteristic
243C22×C127#53611yescharacteristic
244C22×C127#53611yescharacteristic
245C22×C127#53611yescharacteristic
246C22×C127#53711yescharacteristic
247C22×C127#53812yes—
248C22×C127#54112yes—
249C22×C127#54111yescharacteristic
250C22×C127#54211yescharacteristic
251C22×C127#56212yes—
252C22×C127#56212yes—
253C22×C127#56312yes—
254C22×C127#56312yes—
255C22×C127#56312yes—
256C22×C127#56312yes—
257C22×C127#56312yes—
258C22×C127#56312yes—
259C4×C127—24no—
260C4×C127—42no—
261C4×C127—42no—
262C4×C127—44no—
263C4×C127—42no—
264C4×C127—44no—
265C4×C127—42no—
266C4×C127—82no—
267C4×C127—81no—
268C4×C127—82no—
269C4×C127—81no—
270#14626C12711yesmaximal, characteristic, direct product factor, Sylow
271C2×C127#232111yescharacteristic
272C2×C127#232311yescharacteristic
273C2×C127#232711yescharacteristic
274C2×C127#237812yes—
275C2×C127#238112yes—
276C2×C127#281411yescharacteristic
277C2×C127#281711yescharacteristic
278C2×C127#282011yescharacteristic
279C2×C127#282111yescharacteristic
280C2×C127#283112yes—
281C2×C127#283312yes—
282C2×#395C2×C12711yescharacteristic
283C2×#391C2×C12711yescharacteristic
284C2×#387C2×C12711yescharacteristic
285#1446C2×C12711yescharacteristic
286#1445C2×C12712yes—
287#1443C2×C12712yes—
288#1443C2×C12712yes—
289#1442C2×C12711yescharacteristic
290#1441C2×C12711yescharacteristic
291#1441C2×C12712yes—
292#1434C2×C12711yescharacteristic
293C127#1462611yescharacteristic, direct product factor, Sylow
294C23×Q8C22×C12711yescharacteristic
295C22×C4⋊C4C22×C12711yescharacteristic
296C22×C4⋊C4C22×C12711yescharacteristic
297C22×C4⋊C4C22×C12711yescharacteristic
298C22×C4⋊C4C22×C12712yes—
299C22×C42C22×C12711yescharacteristic
300#395C4×C12718yescomplemented
301#391—24no—
302#387—24no—
303C2×#95C22×C12711yescharacteristic
304C2×#95C22×C12712yes—
305C2×#95C22×C12711yescharacteristic
306C2×#95C22×C12711yescharacteristic
307C2×#95C22×C12711yescharacteristic
308C2×#95C22×C12712yes—
309C2×#95C22×C12711yescharacteristic
310C2×#95C22×C12712yes—
311C2×#95C22×C12712yes—
312C2×#95C22×C12712yes—
313C2×#95C22×C12712yes—
314C2×#95C22×C12712yes—
315C2×#95C22×C12712yes—
316C2×#95C22×C12712yes—
317C2×#95C22×C12712yes—
318C2×#95C22×C12711yescharacteristic
319C2×#95C22×C12712yes—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—42no—
323C22×Q8—42no—
324C22×Q8C2×C4×C12714yes—
325C23×C4C23×C12711yescharacteristic
326C23×C4C23×C12712yes—
327C23×C4C23×C12711yescharacteristic
328C23×C4C23×C12712yes—
329C23×C4C23×C12711yescharacteristic
330C23×C4C23×C12712yes—
331C23×C4C23×C12711yescharacteristic
332C23×C4C23×C12712yes—
333C23×C4C23×C12711yescharacteristic
334C23×C4C23×C12711yescharacteristic
335C23×C4C23×C12711yescharacteristic
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4C2×C4×C12714yes—
345C2×C4⋊C4C2×C4×C12718yes—
346C2×C42—42no—
347C2×C42D4×C12714yes—
348#95—22no—
349#95—22no—
350#95—22no—
351#95—22no—
352#95—24no—
353#95—24no—
354#95—22no—
355#95—42no—
356#95—42no—
357#95—42no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—42no—
363#95C2×C4×C12718yes—
364#95C2×C4×C12714yes—
365C24C24×C12711yescharacteristic
366C2×Q8—28no—
367C2×Q8—48no—
368C2×Q8—44no—
369C2×Q8—44no—
370C2×Q8—48no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
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—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4C22×C4×C12712yes—
428C22×C4C22×C4×C12714yes—
429C22×C4C22×C4×C12714yes—
430C22×C4C22×C4×C12712yes—
431C22×C4C22×C4×C12712yes—
432C22×C4C2×D4×C12712yes—
433C22×C4C2×D4×C12712yes—
434C22×C4C2×D4×C12712yes—
435C22×C4#41×C12712yes—
436C4⋊C4—28no—
437C4⋊C4—48no—
438C4⋊C4—44no—
439C4⋊C4—44no—
440C42—44no—
441C23C23×C4×C12711yescharacteristic
442C23C22×D4×C12711yescharacteristic
443C23C2×#41×C12711yescharacteristic
444C23H(5,𝔽2)×C12712yes—
445C23H(5,𝔽2)×C12712yes—
446C23H(5,𝔽2)×C12711yescharacteristic
447C232−1+4×C12712yes—
448C232−1+4×C12712yes—
449C232−1+4×C12711yescharacteristic
450C232−1+4×C12711yescharacteristic
451C232−1+4×C12711yescharacteristic
452Q8—416no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
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—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4C4×D4×C12714yes—
518C22C2×C4×D4×C12711yescharacteristic
519C22#518×C12712yes—
520C22#519×C12711yescharacteristic
521C22#519×C12712yes—
522C22#520×C12711yescharacteristic
523C22#534×C12711yescharacteristic
524C22#535×C12711yescharacteristic
525C22#536×C12711yescharacteristic
526C22#536×C12711yescharacteristic
527C22#536×C12711yescharacteristic
528C22#537×C12711yescharacteristic
529C22#538×C12712yes—
530C22#541×C12712yes—
531C22#541×C12711yescharacteristic
532C22#542×C12711yescharacteristic
533C22#562×C12712yes—
534C22#562×C12712yes—
535C22#563×C12712yes—
536C22#563×C12712yes—
537C22#563×C12712yes—
538C22#563×C12712yes—
539C22#563×C12712yes—
540C22#563×C12712yes—
541C4—24no—
542C4—44no—
543C4—42no—
544C4—42no—
545C4—44no—
546C4—42no—
547C4—42no—
548C4—82no—
549C4—81no—
550C4—82no—
551C4—81no—
552C2C127×#232111yescharacteristic
553C2C127×#232311yescharacteristic
554C2C127×#232711yescharacteristic
555C2C127×#237812yes—
556C2C127×#238112yes—
557C2C127×#281411yescharacteristic
558C2C127×#281711yescharacteristic
559C2C127×#282011yescharacteristic
560C2C127×#282111yescharacteristic
561C2C127×#283112yes—
562C2C127×#283312yes—
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
18. #395×C127C4semidirect
270. #14626C127direct (N × H)
293. C127#14626direct (N × H)
300. #395C4×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×#387×C1272
C127×#14462
C127×#14452
C127×#14432
C127×#14422
C127×#14412
C127×#14342
#14626127