Finite Group Databasebeta

← C127×#11022 #44574695

Subgroups — C127×#11022 #44574695

Order 32512.

1822 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
1C23×D8×C127C211yesmaximal, characteristic
2C22×#102×C127C212yesmaximal, complemented
3C2×#390×C127C212yesmaximal, complemented
4C2×#340×C127C211yesmaximal, characteristic, complemented
5C2×#336×C127C211yesmaximal, characteristic, complemented
6C23×D4×C127C2212yes—
7C22×D8×C127—24no—
8C22×D8×C127—24no—
9C22×D8×C127—22no—
10C22×D8×C127—22no—
11C22×D8×C127C414yescomplemented
12C23×C8×C127C2211yescharacteristic
13C23×C8×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2212yes—
15C22×C22⋊C4×C127—24no—
16C22×C42×C127C2211yescharacteristic
17C2×#102×C127—24no—
18C2×#102×C127—24no—
19C2×#102×C127—24no—
20#390×C127—24no—
21#390×C127—24no—
22#340×C127—22no—
23#336×C127—22no—
24C25×C127—22no—
25C22×D4×C127—22no—
26C22×D4×C127—22no—
27C22×D4×C127—22no—
28C22×D4×C127—22no—
29C22×D4×C127—22no—
30C22×D4×C127—22no—
31C22×D4×C127—22no—
32C22×D4×C127—22no—
33C22×D4×C127—22no—
34C22×D4×C127—22no—
35C22×D4×C127—22no—
36C22×D4×C127C2×C414yes—
37C22×D4×C127D414yes—
38C22×D4×C127D414yes—
39C23×C4×C127—22no—
40C23×C4×C127D412yes—
41C23×C4×C127C2311yescharacteristic
42C2×D8×C127—28no—
43C2×D8×C127—28no—
44C2×D8×C127—216no—
45C2×D8×C127—216no—
46C2×D8×C127—28no—
47C22×C8×C127—22no—
48C22×C8×C127—22no—
49C22×C8×C127—21no—
50C22×C8×C127—22no—
51C22×C8×C127—22no—
52C22×C8×C127—21no—
53C22×C8×C127C2×C412yes—
54C22×C8×C127D412yes—
55C22×C8×C127D412yes—
56C22×C8×C127D412yes—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127D414yes—
63C2×C22⋊C4×C127—216no—
64C2×C22⋊C4×C127—48no—
65C2×C22⋊C4×C127—48no—
66C2×C42×C127—21no—
67C2×C42×C127—22no—
68C2×C42×C127—22no—
69C2×C42×C127—21no—
70#102×C127—216no—
71C24×C127—24no—
72C24×C127—24no—
73C24×C127—24no—
74C24×C127—42no—
75C24×C127—42no—
76C24×C127—42no—
77C24×C127—42no—
78C24×C127—44no—
79C24×C127—44no—
80C24×C127—44no—
81C24×C127—44no—
82C24×C127C2×D411yescharacteristic
83C2×D4×C127—24no—
84C2×D4×C127—24no—
85C2×D4×C127—24no—
86C2×D4×C127—24no—
87C2×D4×C127—24no—
88C2×D4×C127—24no—
89C2×D4×C127—24no—
90C2×D4×C127—24no—
91C2×D4×C127—24no—
92C2×D4×C127—24no—
93C2×D4×C127—24no—
94C2×D4×C127—24no—
95C2×D4×C127—24no—
96C2×D4×C127—24no—
97C2×D4×C127—24no—
98C2×D4×C127—42no—
99C2×D4×C127—42no—
100C2×D4×C127—42no—
101C2×D4×C127—42no—
102C2×D4×C127—42no—
103C2×D4×C127—42no—
104C2×D4×C127—42no—
105C2×D4×C127—42no—
106C2×D4×C127—42no—
107C2×D4×C127—42no—
108C2×D4×C127—42no—
109C2×D4×C127—42no—
110C2×D4×C127C22⋊C418yescomplemented
111C22×C4×C127—24no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—24no—
115C22×C4×C127—24no—
116C22×C4×C127—42no—
117C22×C4×C127—42no—
118C22×C4×C127—44no—
119C22×C4×C127—44no—
120C22×C4×C127D814yescomplemented
121C22×C4×C127C22×C411yescharacteristic
122C22×C4×C127C2×D412yes—
123C22×C4×C127C2×D412yes—
124C22×C4×C127C2×D411yescharacteristic
125C22×C4×C127C2×D411yescharacteristic
126C22×C4×C127C2×D411yescharacteristic
127C22×C4×C127C2×D412yes—
128C22×C4×C127#4111yescharacteristic
129C22×C4×C127#4112yes—
130C22×C4×C127#4111yescharacteristic
131D8×C127—232no—
132C2×C8×C127—24no—
133C2×C8×C127—22no—
134C2×C8×C127—22no—
135C2×C8×C127—24no—
136C2×C8×C127—24no—
137C2×C8×C127—22no—
138C2×C8×C127—41no—
139C2×C8×C127—42no—
140C2×C8×C127—41no—
141C2×C8×C127C22⋊C414yescomplemented
142C4⋊C4×C127—24no—
143C4⋊C4×C127—24no—
144C4⋊C4×C127—42no—
145C4⋊C4×C127—42no—
146C22⋊C4×C127—432no—
147C42×C127—41no—
148C42×C127—42no—
149C42×C127—41no—
150C23×C127—28no—
151C23×C127—44no—
152C23×C127—44no—
153C23×C127—44no—
154C23×C127—44no—
155C23×C127—44no—
156C23×C127—44no—
157C23×C127—48no—
158C23×C127—48no—
159C23×C127—48no—
160C23×C127—48no—
161C23×C127—48no—
162C23×C127—48no—
163C23×C127—84no—
164C23×C127—84no—
165C23×C127—84no—
166C23×C127—84no—
167C23×C127—84no—
168C23×C127—84no—
169C23×C127—82no—
170C23×C127—82no—
171C23×C127—82no—
172C23×C127—82no—
173C23×C127C4×D411yescharacteristic
174C23×C127#12012yes—
175C23×C127#12112yes—
176C23×C127#12111yescharacteristic
177C23×C127#12711yescharacteristic
178C23×C127C2×D812yes—
179C23×C127#13512yes—
180C23×C127AGL(1,ℤ/8)14yes—
181D4×C127—28no—
182D4×C127—28no—
183D4×C127—44no—
184D4×C127—44no—
185D4×C127—44no—
186D4×C127—44no—
187D4×C127—44no—
188D4×C127—44no—
189C2×C4×C127—28no—
190C2×C4×C127—24no—
191C2×C4×C127—42no—
192C2×C4×C127—44no—
193C2×C4×C127—42no—
194C2×C4×C127—44no—
195C2×C4×C127—48no—
196C2×C4×C127—84no—
197C2×C4×C127—82no—
198C2×C4×C127—82no—
199C2×C4×C127C2×C22⋊C412yes—
200C2×C4×C127C2×C22⋊C411yescharacteristic
201C2×C4×C127C4×D411yescharacteristic
202C2×C4×C127C4×D412yes—
203C2×C4×C127#12011yescharacteristic
204C2×C4×C127#12011yescharacteristic
205C2×C4×C127#12012yes—
206C2×C4×C127#12012yes—
207C2×C4×C127#12112yes—
208C2×C4×C127#12112yes—
209C2×C4×C127#12112yes—
210C2×C4×C127#12112yes—
211C2×C4×C127#12111yescharacteristic
212C2×C4×C127#12312yes—
213C2×C4×C127#12312yes—
214C2×C4×C127#12411yescharacteristic
215C2×C4×C127#12411yescharacteristic
216C2×C4×C127#12711yescharacteristic
217C8×C127—24no—
218C8×C127—42no—
219C22×C127—416no—
220C22×C127—48no—
221C22×C127—88no—
222C22×C127—88no—
223C22×C127—84no—
224C22×C127—84no—
225C22×C127—88no—
226C22×C127—84no—
227C22×C127—84no—
228C22×C127—84no—
229C22×C127—84no—
230C22×C127#38612yes—
231C22×C127#39011yescharacteristic
232C22×C127#39211yescharacteristic
233C22×C127#39212yes—
234C22×C127#39411yescharacteristic
235C22×C127C4×D812yes—
236C22×C127#44212yes—
237C22×C127#44714yes—
238C22×C127#44914yes—
239C22×C127#45914yes—
240C22×C127#46314yes—
241C22×C127#46612yes—
242C22×C127#46912yes—
243C22×C127#49311yescharacteristic
244C22×C127#49511yescharacteristic
245C22×C127#49612yes—
246C4×C127—44no—
247C4×C127—84no—
248C4×C127#37911yescharacteristic
249C4×C127#38612yes—
250C4×C127#39011yescharacteristic
251C4×C127#39211yescharacteristic
252C4×C127#39411yescharacteristic
253C4×C127#39412yes—
254#11022C12711yesmaximal, characteristic, direct product factor, Sylow
255C2×C127—88no—
256C2×C127#143811yescharacteristic
257C2×C127#187914yes—
258C2×C127#197011yescharacteristic
259C2×C127#197211yescharacteristic
260C2×C127#199912yes—
261C2×C127#201112yes—
262C2×C127#201212yes—
263C2×C127#205412yes—
264C23×D8C2×C12711yescharacteristic
265C22×#102C2×C12712yescomplemented
266C2×#390C2×C12712yescomplemented
267C2×#340C2×C12711yescharacteristic, complemented
268C2×#336C2×C12711yescharacteristic, complemented
269C127#1102211yescharacteristic, direct product factor, Sylow
270C23×D4C22×C12712yes—
271C22×D8—24no—
272C22×D8—24no—
273C22×D8—22no—
274C22×D8—22no—
275C22×D8C4×C12714yescomplemented
276C23×C8C22×C12711yescharacteristic
277C23×C8C22×C12711yescharacteristic
278C22×C4⋊C4C22×C12712yes—
279C22×C22⋊C4—24no—
280C22×C42C22×C12711yescharacteristic
281C2×#102—24no—
282C2×#102—24no—
283C2×#102—24no—
284#390—24no—
285#390—24no—
286#340—22no—
287#336—22no—
288C25—22no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4C2×C4×C12714yes—
301C22×D4D4×C12714yes—
302C22×D4D4×C12714yes—
303C23×C4—22no—
304C23×C4D4×C12712yes—
305C23×C4C23×C12711yescharacteristic
306C2×D8—28no—
307C2×D8—28no—
308C2×D8—216no—
309C2×D8—216no—
310C2×D8—28no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—21no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—21no—
317C22×C8C2×C4×C12712yes—
318C22×C8D4×C12712yes—
319C22×C8D4×C12712yes—
320C22×C8D4×C12712yes—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4D4×C12714yes—
327C2×C22⋊C4—216no—
328C2×C22⋊C4—48no—
329C2×C22⋊C4—48no—
330C2×C42—21no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—21no—
334#102—216no—
335C24—24no—
336C24—24no—
337C24—24no—
338C24—42no—
339C24—42no—
340C24—42no—
341C24—42no—
342C24—44no—
343C24—44no—
344C24—44no—
345C24—44no—
346C24C2×D4×C12711yescharacteristic
347C2×D4—24no—
348C2×D4—24no—
349C2×D4—24no—
350C2×D4—24no—
351C2×D4—24no—
352C2×D4—24no—
353C2×D4—24no—
354C2×D4—24no—
355C2×D4—24no—
356C2×D4—24no—
357C2×D4—24no—
358C2×D4—24no—
359C2×D4—24no—
360C2×D4—24no—
361C2×D4—24no—
362C2×D4—42no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4C22⋊C4×C12718yescomplemented
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—44no—
383C22×C4—44no—
384C22×C4D8×C12714yescomplemented
385C22×C4C22×C4×C12711yescharacteristic
386C22×C4C2×D4×C12712yes—
387C22×C4C2×D4×C12712yes—
388C22×C4C2×D4×C12711yescharacteristic
389C22×C4C2×D4×C12711yescharacteristic
390C22×C4C2×D4×C12711yescharacteristic
391C22×C4C2×D4×C12712yes—
392C22×C4#41×C12711yescharacteristic
393C22×C4#41×C12712yes—
394C22×C4#41×C12711yescharacteristic
395D8—232no—
396C2×C8—24no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—24no—
400C2×C8—24no—
401C2×C8—22no—
402C2×C8—41no—
403C2×C8—42no—
404C2×C8—41no—
405C2×C8C22⋊C4×C12714yescomplemented
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C22⋊C4—432no—
411C42—41no—
412C42—42no—
413C42—41no—
414C23—28no—
415C23—44no—
416C23—44no—
417C23—44no—
418C23—44no—
419C23—44no—
420C23—44no—
421C23—48no—
422C23—48no—
423C23—48no—
424C23—48no—
425C23—48no—
426C23—48no—
427C23—82no—
428C23—82no—
429C23—84no—
430C23—84no—
431C23—84no—
432C23—84no—
433C23—84no—
434C23—84no—
435C23—82no—
436C23—82no—
437C23C4×D4×C12711yescharacteristic
438C23#120×C12712yes—
439C23#121×C12712yes—
440C23#121×C12711yescharacteristic
441C23#127×C12711yescharacteristic
442C23C2×D8×C12712yes—
443C23#135×C12712yes—
444C23AGL(1,ℤ/8)×C12714yes—
445D4—28no—
446D4—28no—
447D4—44no—
448D4—44no—
449D4—44no—
450D4—44no—
451D4—44no—
452D4—44no—
453C2×C4—28no—
454C2×C4—24no—
455C2×C4—42no—
456C2×C4—44no—
457C2×C4—42no—
458C2×C4—44no—
459C2×C4—48no—
460C2×C4—82no—
461C2×C4—84no—
462C2×C4—82no—
463C2×C4C2×C22⋊C4×C12712yes—
464C2×C4C2×C22⋊C4×C12711yescharacteristic
465C2×C4C4×D4×C12711yescharacteristic
466C2×C4C4×D4×C12712yes—
467C2×C4#120×C12711yescharacteristic
468C2×C4#120×C12711yescharacteristic
469C2×C4#120×C12712yes—
470C2×C4#120×C12712yes—
471C2×C4#121×C12712yes—
472C2×C4#121×C12712yes—
473C2×C4#121×C12712yes—
474C2×C4#121×C12712yes—
475C2×C4#121×C12711yescharacteristic
476C2×C4#123×C12712yes—
477C2×C4#123×C12712yes—
478C2×C4#124×C12711yescharacteristic
479C2×C4#124×C12711yescharacteristic
480C2×C4#127×C12711yescharacteristic
481C8—24no—
482C8—42no—
483C22—416no—
484C22—48no—
485C22—88no—
486C22—84no—
487C22—84no—
488C22—88no—
489C22—84no—
490C22—84no—
491C22—84no—
492C22—84no—
493C22—88no—
494C22#386×C12712yes—
495C22#390×C12711yescharacteristic
496C22#392×C12711yescharacteristic
497C22#392×C12712yes—
498C22#394×C12711yescharacteristic
499C22C4×D8×C12712yes—
500C22#442×C12712yes—
501C22#447×C12714yes—
502C22#449×C12714yes—
503C22#459×C12714yes—
504C22#463×C12714yes—
505C22#466×C12712yes—
506C22#469×C12712yes—
507C22#493×C12711yescharacteristic
508C22#495×C12711yescharacteristic
509C22#496×C12712yes—
510C4—44no—
511C4—84no—
512C4#379×C12711yescharacteristic
513C4#386×C12712yes—
514C4#390×C12711yescharacteristic
515C4#392×C12711yescharacteristic
516C4#394×C12711yescharacteristic
517C4#394×C12712yes—
518C2—88no—
519C2C127×#143811yescharacteristic
520C2C127×#187914yes—
521C2C127×#197011yescharacteristic
522C2C127×#197211yescharacteristic
523C2C127×#199912yes—
524C2C127×#201112yes—
525C2C127×#201212yes—
526C2C127×#205412yes—
subgroupG/H
center, socleC24×C127C2×D4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC23×D8×C127C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#102×C127C2semidirect
3. C2×#390×C127C2semidirect
4. C2×#340×C127C2semidirect
5. C2×#336×C127C2semidirect
11. C22×D8×C127C4semidirect
110. C2×D4×C127C22⋊C4semidirect
120. C22×C4×C127D8semidirect
141. C2×C8×C127C22⋊C4semidirect
254. #11022C127direct (N × H)
265. C22×#102C2×C127semidirect
266. C2×#390C2×C127semidirect
267. C2×#340C2×C127semidirect
268. C2×#336C2×C127semidirect
269. C127#11022direct (N × H)
275. C22×D8C4×C127semidirect
374. C2×D4C22⋊C4×C127semidirect
384. C22×C4D8×C127semidirect
405. C2×C8C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C23×D8×C1272
C22×#102×C1272
C2×#390×C1272
C2×#340×C1272
C2×#336×C1272
#11022127