Finite Group Databasebeta

← C127×#13801 #44577474

Subgroups — C127×#13801 #44577474

Order 32512.

2182 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C127C211yesmaximal, characteristic
2C2×#380×C127C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C127C212yesmaximal, complemented
4C2×C4×C22⋊C4×C127C211yesmaximal, characteristic
5C127×#1437C214yesmaximal
6C127×C4⋊#95C212yesmaximal, complemented
7C127×#1434C212yesmaximal, complemented
8C4×#95×C127C212yesmaximal, complemented
9C24×C4×C127C2211yescharacteristic
10C2×#117×C127—28no—
11C2×#117×C127C418yescomplemented
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C22⋊C4×C127C2212yes—
16C22×C22⋊C4×C127C2212yes—
17C22×C22⋊C4×C127C2212yes—
18C22×C42×C127C2214yes—
19C22×C42×C127C2212yes—
20C22×C42×C127C2212yes—
21#380×C127C418yescomplemented
22C4×C4⋊C4×C127—28no—
23C4×C22⋊C4×C127C418yescomplemented
24C2×#95×C127C2214yes—
25C2×#95×C127C2214yes—
26C2×#95×C127C2214yes—
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C25×C127C2311yescharacteristic
31C23×C4×C127—24no—
32C23×C4×C127—24no—
33C23×C4×C127C2×C414yes—
34C23×C4×C127C2×C414yes—
35C23×C4×C127C2×C414yes—
36C23×C4×C127C2314yes—
37C23×C4×C127C2312yes—
38C23×C4×C127C2312yes—
39C23×C4×C127C2311yescharacteristic
40C23×C4×C127C2312yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2311yescharacteristic
43#117×C127—232no—
44C2×C4⋊C4×C127—24no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127—24no—
47C2×C4⋊C4×C127C2×C414yes—
48C2×C4⋊C4×C127C2×C418yes—
49C2×C4⋊C4×C127C2×C414yes—
50C2×C4⋊C4×C127D418yes—
51C2×C22⋊C4×C127—28no—
52C2×C22⋊C4×C127—24no—
53C2×C22⋊C4×C127—24no—
54C2×C22⋊C4×C127—42no—
55C2×C22⋊C4×C127—42no—
56C2×C22⋊C4×C127C2×C418yes—
57C2×C22⋊C4×C127C2×C418yes—
58C2×C22⋊C4×C127C2×C418yes—
59C2×C42×C127—28no—
60C2×C42×C127—24no—
61C2×C42×C127—24no—
62C2×C42×C127—28no—
63C2×C42×C127—28no—
64C2×C42×C127—44no—
65C2×C42×C127C2×C418yes—
66C2×C42×C127C2×C418yes—
67#95×C127—28no—
68#95×C127—28no—
69#95×C127—44no—
70#95×C127C2×C414yes—
71#95×C127C2×C414yes—
72#95×C127C2×C418yes—
73C24×C127—22no—
74C24×C127—22no—
75C24×C127—22no—
76C24×C127—22no—
77C24×C127—21no—
78C24×C127—21no—
79C24×C127—21no—
80C24×C127—21no—
81C24×C127C22×C412yes—
82C24×C127C22×C412yes—
83C24×C127C22×C412yes—
84C24×C127C2411yescharacteristic
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—24no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—28no—
95C22×C4×C127—28no—
96C22×C4×C127—216no—
97C22×C4×C127—216no—
98C22×C4×C127—22no—
99C22×C4×C127—24no—
100C22×C4×C127—24no—
101C22×C4×C127—24no—
102C22×C4×C127—24no—
103C22×C4×C127—22no—
104C22×C4×C127—24no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—24no—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
110C22×C4×C127—24no—
111C22×C4×C127—24no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127C42116yescomplemented
115C22×C4×C127C22×C414yes—
116C22×C4×C127C22×C418yes—
117C22×C4×C127C22×C414yes—
118C22×C4×C127C22×C412yes—
119C22×C4×C127C22×C412yes—
120C22×C4×C127C22×C412yes—
121C22×C4×C127C22×C414yes—
122C22×C4×C127C22×C414yes—
123C22×C4×C127C22×C412yes—
124C22×C4×C127C22×C412yes—
125C22×C4×C127C22×C412yes—
126C22×C4×C127C2×D418yes—
127C22×C4×C127C2×D414yes—
128C22×C4×C127#4114yes—
129C22×C4×C127#4114yes—
130C22×C4×C127#4114yes—
131C4⋊C4×C127—28no—
132C4⋊C4×C127—216no—
133C4⋊C4×C127C22⋊C4116yescomplemented
134C22⋊C4×C127—216no—
135C22⋊C4×C127—216no—
136C22⋊C4×C127—48no—
137C42×C127—216no—
138C42×C127—216no—
139C42×C127—416no—
140C23×C127—22no—
141C23×C127—24no—
142C23×C127—22no—
143C23×C127—24no—
144C23×C127—24no—
145C23×C127—22no—
146C23×C127—22no—
147C23×C127—24no—
148C23×C127—22no—
149C23×C127—22no—
150C23×C127—22no—
151C23×C127—22no—
152C23×C127—22no—
153C23×C127—22no—
154C23×C127—42no—
155C23×C127—42no—
156C23×C127—42no—
157C23×C127—42no—
158C23×C127—42no—
159C23×C127—42no—
160C23×C127—42no—
161C23×C127—42no—
162C23×C127C2×C4214yes—
163C23×C127C23×C411yescharacteristic
164C23×C127C23×C411yescharacteristic
165C23×C127C23×C411yescharacteristic
166C23×C127C22×D412yes—
167C23×C127C2×#4112yes—
168C23×C127C2×#4112yes—
169C23×C127C2×#4112yes—
170C23×C127H(5,𝔽2)11yescharacteristic
171C23×C127H(5,𝔽2)11yescharacteristic
172C23×C1272−1+411yescharacteristic
173C23×C1272−1+411yescharacteristic
174C2×C4×C127—22no—
175C2×C4×C127—22no—
176C2×C4×C127—24no—
177C2×C4×C127—24no—
178C2×C4×C127—24no—
179C2×C4×C127—24no—
180C2×C4×C127—24no—
181C2×C4×C127—24no—
182C2×C4×C127—24no—
183C2×C4×C127—28no—
184C2×C4×C127—28no—
185C2×C4×C127—24no—
186C2×C4×C127—24no—
187C2×C4×C127—24no—
188C2×C4×C127—232no—
189C2×C4×C127—24no—
190C2×C4×C127—24no—
191C2×C4×C127—24no—
192C2×C4×C127—28no—
193C2×C4×C127—24no—
194C2×C4×C127—28no—
195C2×C4×C127—28no—
196C2×C4×C127—24no—
197C2×C4×C127—24no—
198C2×C4×C127—44no—
199C2×C4×C127—42no—
200C2×C4×C127—44no—
201C2×C4×C127—44no—
202C2×C4×C127—42no—
203C2×C4×C127—44no—
204C2×C4×C127—44no—
205C2×C4×C127—42no—
206C2×C4×C127—44no—
207C2×C4×C127—42no—
208C2×C4×C127C2×C4214yes—
209C2×C4×C127C2×C4214yes—
210C2×C4×C127C2×C22⋊C418yes—
211C2×C4×C127C2×C22⋊C414yes—
212C2×C4×C127#11714yes—
213C2×C4×C127#11718yescomplemented
214C2×C4×C127C4×D418yes—
215C2×C4×C127C4×D418yes—
216C22×C127—24no—
217C22×C127—24no—
218C22×C127—24no—
219C22×C127—42no—
220C22×C127—42no—
221C22×C127—42no—
222C22×C127—42no—
223C22×C127—44no—
224C22×C127—44no—
225C22×C127—44no—
226C22×C127—44no—
227C22×C127C22×C4211yescharacteristic
228C22×C127C22×C22⋊C411yescharacteristic
229C22×C127C2×#11711yescharacteristic
230C22×C127C2×#11712yes—
231C22×C127C2×C4×D412yes—
232C22×C127C2×C4×D412yes—
233C22×C127C4×#4111yescharacteristic
234C22×C127C4×#4111yescharacteristic
235C22×C127C4×#4112yes—
236C22×C127#51811yescharacteristic
237C22×C127#51911yescharacteristic
238C22×C127#52011yescharacteristic
239C22×C127#52011yescharacteristic
240C22×C127#52011yescharacteristic
241C22×C127#52011yescharacteristic
242C22×C127#54612yes—
243C22×C127#54712yes—
244C22×C127#54812yes—
245C22×C127#55012yes—
246C22×C127#55212yes—
247C22×C127#55312yes—
248C22×C127#55512yes—
249C22×C127#55612yes—
250C4×C127—28no—
251C4×C127—28no—
252C4×C127—24no—
253C4×C127—44no—
254C4×C127—44no—
255C4×C127—48no—
256C4×C127C4×C22⋊C418yes—
257#13801C12711yesmaximal, characteristic, direct product factor, Sylow
258C2×C127—44no—
259C2×C127C2×C4×C22⋊C411yescharacteristic
260C2×C127C4×#11711yescharacteristic
261C2×C127#227411yescharacteristic
262C2×C127#233911yescharacteristic
263C2×C127#234111yescharacteristic
264C2×C127#234611yescharacteristic
265C2×C127#234711yescharacteristic
266C2×C127#235212yes—
267C2×C127#235412yes—
268C2×C127#236212yes—
269C2×C127#236312yes—
270C22×#117C2×C12711yescharacteristic
271C2×#380C2×C12711yescharacteristic
272C2×C4×C4⋊C4C2×C12712yescomplemented
273C2×C4×C22⋊C4C2×C12711yescharacteristic
274#1437C2×C12714yes—
275C4⋊#95C2×C12712yescomplemented
276#1434C2×C12712yescomplemented
277C4×#95C2×C12712yescomplemented
278C127#1380111yescharacteristic, direct product factor, Sylow
279C24×C4C22×C12711yescharacteristic
280C2×#117—28no—
281C2×#117C4×C12718yescomplemented
282C22×C4⋊C4C22×C12711yescharacteristic
283C22×C4⋊C4C22×C12712yes—
284C22×C4⋊C4C22×C12711yescharacteristic
285C22×C22⋊C4C22×C12712yes—
286C22×C22⋊C4C22×C12712yes—
287C22×C22⋊C4C22×C12712yes—
288C22×C42C22×C12714yes—
289C22×C42C22×C12712yes—
290C22×C42C22×C12712yes—
291#380C4×C12718yescomplemented
292C4×C4⋊C4—28no—
293C4×C22⋊C4C4×C12718yescomplemented
294C2×#95C22×C12714yes—
295C2×#95C22×C12714yes—
296C2×#95C22×C12714yes—
297C2×#95C22×C12711yescharacteristic
298C2×#95C22×C12712yes—
299C2×#95C22×C12711yescharacteristic
300C25C23×C12711yescharacteristic
301C23×C4—24no—
302C23×C4—24no—
303C23×C4C2×C4×C12714yes—
304C23×C4C2×C4×C12714yes—
305C23×C4C2×C4×C12714yes—
306C23×C4C23×C12714yes—
307C23×C4C23×C12712yes—
308C23×C4C23×C12712yes—
309C23×C4C23×C12711yescharacteristic
310C23×C4C23×C12712yes—
311C23×C4C23×C12712yes—
312C23×C4C23×C12711yescharacteristic
313#117—232no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4C2×C4×C12714yes—
318C2×C4⋊C4C2×C4×C12718yes—
319C2×C4⋊C4C2×C4×C12714yes—
320C2×C4⋊C4D4×C12718yes—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4C2×C4×C12718yes—
327C2×C22⋊C4C2×C4×C12718yes—
328C2×C22⋊C4C2×C4×C12718yes—
329C2×C42—28no—
330C2×C42—24no—
331C2×C42—24no—
332C2×C42—28no—
333C2×C42—28no—
334C2×C42—44no—
335C2×C42C2×C4×C12718yes—
336C2×C42C2×C4×C12718yes—
337#95—28no—
338#95—28no—
339#95—44no—
340#95C2×C4×C12714yes—
341#95C2×C4×C12714yes—
342#95C2×C4×C12718yes—
343C24—22no—
344C24—22no—
345C24—22no—
346C24—22no—
347C24—21no—
348C24—21no—
349C24—21no—
350C24—21no—
351C24C22×C4×C12712yes—
352C24C22×C4×C12712yes—
353C24C22×C4×C12712yes—
354C24C24×C12711yescharacteristic
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—28no—
365C22×C4—28no—
366C22×C4—216no—
367C22×C4—216no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4C42×C127116yescomplemented
385C22×C4C22×C4×C12714yes—
386C22×C4C22×C4×C12718yes—
387C22×C4C22×C4×C12714yes—
388C22×C4C22×C4×C12712yes—
389C22×C4C22×C4×C12712yes—
390C22×C4C22×C4×C12712yes—
391C22×C4C22×C4×C12714yes—
392C22×C4C22×C4×C12714yes—
393C22×C4C22×C4×C12712yes—
394C22×C4C22×C4×C12712yes—
395C22×C4C22×C4×C12712yes—
396C22×C4C2×D4×C12718yes—
397C22×C4C2×D4×C12714yes—
398C22×C4#41×C12714yes—
399C22×C4#41×C12714yes—
400C22×C4#41×C12714yes—
401C4⋊C4—28no—
402C4⋊C4—216no—
403C4⋊C4C22⋊C4×C127116yescomplemented
404C22⋊C4—216no—
405C22⋊C4—216no—
406C22⋊C4—48no—
407C42—216no—
408C42—216no—
409C42—416no—
410C23—22no—
411C23—24no—
412C23—22no—
413C23—24no—
414C23—24no—
415C23—22no—
416C23—22no—
417C23—24no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—22no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23—42no—
429C23—42no—
430C23—42no—
431C23—42no—
432C23C2×C42×C12714yes—
433C23C23×C4×C12711yescharacteristic
434C23C23×C4×C12711yescharacteristic
435C23C23×C4×C12711yescharacteristic
436C23C22×D4×C12712yes—
437C23C2×#41×C12712yes—
438C23C2×#41×C12712yes—
439C23C2×#41×C12712yes—
440C23H(5,𝔽2)×C12711yescharacteristic
441C23H(5,𝔽2)×C12711yescharacteristic
442C232−1+4×C12711yescharacteristic
443C232−1+4×C12711yescharacteristic
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—28no—
454C2×C4—28no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—232no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—28no—
463C2×C4—24no—
464C2×C4—28no—
465C2×C4—28no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—44no—
469C2×C4—42no—
470C2×C4—44no—
471C2×C4—44no—
472C2×C4—42no—
473C2×C4—44no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4—44no—
477C2×C4—42no—
478C2×C4C2×C42×C12714yes—
479C2×C4C2×C42×C12714yes—
480C2×C4C2×C22⋊C4×C12718yes—
481C2×C4C2×C22⋊C4×C12714yes—
482C2×C4#117×C12714yes—
483C2×C4#117×C12718yescomplemented
484C2×C4C4×D4×C12718yes—
485C2×C4C4×D4×C12718yes—
486C22—24no—
487C22—24no—
488C22—24no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—44no—
494C22—44no—
495C22—44no—
496C22—44no—
497C22C22×C42×C12711yescharacteristic
498C22C22×C22⋊C4×C12711yescharacteristic
499C22C2×#117×C12711yescharacteristic
500C22C2×#117×C12712yes—
501C22C2×C4×D4×C12712yes—
502C22C2×C4×D4×C12712yes—
503C22C4×#41×C12711yescharacteristic
504C22C4×#41×C12711yescharacteristic
505C22C4×#41×C12712yes—
506C22#518×C12711yescharacteristic
507C22#519×C12711yescharacteristic
508C22#520×C12711yescharacteristic
509C22#520×C12711yescharacteristic
510C22#520×C12711yescharacteristic
511C22#520×C12711yescharacteristic
512C22#546×C12712yes—
513C22#547×C12712yes—
514C22#548×C12712yes—
515C22#550×C12712yes—
516C22#552×C12712yes—
517C22#553×C12712yes—
518C22#555×C12712yes—
519C22#556×C12712yes—
520C4—28no—
521C4—28no—
522C4—24no—
523C4—44no—
524C4—44no—
525C4—48no—
526C4C4×C22⋊C4×C12718yes—
527C2—44no—
528C2C2×C4×C22⋊C4×C12711yescharacteristic
529C2C4×#117×C12711yescharacteristic
530C2C127×#227411yescharacteristic
531C2C127×#233911yescharacteristic
532C2C127×#234111yescharacteristic
533C2C127×#234611yescharacteristic
534C2C127×#234711yescharacteristic
535C2C127×#235212yes—
536C2C127×#235412yes—
537C2C127×#236212yes—
538C2C127×#236312yes—
subgroupG/H
center, socleC24×C127C24
commutatorC22C22×C42×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C4⋊C4×C127C2semidirect
6. C127×C4⋊#95C2semidirect
7. C127×#1434C2semidirect
8. C4×#95×C127C2semidirect
11. C2×#117×C127C4semidirect
21. #380×C127C4semidirect
23. C4×C22⋊C4×C127C4semidirect
114. C22×C4×C127C42semidirect
133. C4⋊C4×C127C22⋊C4semidirect
213. C2×C4×C127#117semidirect
257. #13801C127direct (N × H)
272. C2×C4×C4⋊C4C2×C127semidirect
275. C4⋊#95C2×C127semidirect
276. #1434C2×C127semidirect
277. C4×#95C2×C127semidirect
278. C127#13801direct (N × H)
281. C2×#117C4×C127semidirect
291. #380C4×C127semidirect
293. C4×C22⋊C4C4×C127semidirect
384. C22×C4C42×C127semidirect
403. C4⋊C4C22⋊C4×C127semidirect
483. C2×C4#117×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#117×C1272
C2×#380×C1272
C2×C4×C4⋊C4×C1272
C2×C4×C22⋊C4×C1272
C127×#14372
C127×C4⋊#952
C127×#14342
C4×#95×C1272
#13801127