Finite Group Databasebeta

← C127×#11340 #44575013

Subgroups — C127×#11340 #44575013

Order 32512.

894 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#428×C127C211yesmaximal, characteristic
2C127×#2317C211yesmaximal, characteristic
3C2×#384×C127C211yesmaximal, characteristic
4C2×#343×C127C211yesmaximal, characteristic
5C127×#1736C211yesmaximal, characteristic
6C2×#339×C127C211yesmaximal, characteristic
7C2×#339×C127C211yesmaximal, characteristic
8C22×M16×C127C2211yescharacteristic
9C22×M16×C127C2211yescharacteristic
10C2×#117×C127C2211yescharacteristic
11C2×#117×C127C2211yescharacteristic
12C22×C4⋊C4×C127—22no—
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C42×C127C2211yescharacteristic
16#428×C127—22no—
17#428×C127—22no—
18C2×#107×C127—21no—
19C2×#106×C127—21no—
20#389×C127—22no—
21#385×C127—22no—
22#384×C127—21no—
23#384×C127—22no—
24#384×C127—22no—
25#382×C127—21no—
26#343×C127—22no—
27#340×C127—22no—
28#339×C127—22no—
29#339×C127C414yescomplemented
30C23×C4×C127—21no—
31C23×C4×C127—21no—
32C23×C4×C127D412yes—
33C23×C4×C127C2311yescharacteristic
34C2×M16×C127—21no—
35C2×M16×C127—21no—
36C2×M16×C127—21no—
37C2×M16×C127—21no—
38C2×M16×C127—21no—
39C2×M16×C127—21no—
40C2×M16×C127—21no—
41C2×M16×C127—21no—
42C2×M16×C127C2×C412yes—
43C2×M16×C127D412yes—
44C2×M16×C127Q812yes—
45C2×M16×C127Q812yes—
46C22×C8×C127—21no—
47C22×C8×C127—21no—
48#117×C127—21no—
49#117×C127—21no—
50#117×C127—21no—
51#117×C127—21no—
52#117×C127—21no—
53#117×C127—21no—
54#117×C127C2×C412yes—
55#117×C127Q812yes—
56C2×C4⋊C4×C127—21no—
57C2×C4⋊C4×C127—21no—
58C2×C4⋊C4×C127—21no—
59C2×C4⋊C4×C127—21no—
60C2×C4⋊C4×C127—28no—
61C2×C4⋊C4×C127—21no—
62C2×C4⋊C4×C127—21no—
63C2×C4⋊C4×C127—21no—
64C2×C4⋊C4×C127—21no—
65C2×C4⋊C4×C127—21no—
66C2×C4⋊C4×C127—21no—
67C2×C4⋊C4×C127—21no—
68C2×C4⋊C4×C127—24no—
69C2×C4⋊C4×C127—48no—
70C2×C4⋊C4×C127D412yes—
71C2×C4⋊C4×C127D411yescharacteristic
72C2×C4⋊C4×C127D411yescharacteristic
73C2×C4⋊C4×C127D412yes—
74C2×C22⋊C4×C127—21no—
75C2×C22⋊C4×C127—21no—
76C2×C42×C127—21no—
77C2×C42×C127—21no—
78C2×C42×C127—21no—
79C2×C42×C127—21no—
80C2×C42×C127—21no—
81C2×C42×C127C2×C412yes—
82C2×C42×C127D412yes—
83C2×C42×C127Q812yes—
84#107×C127—24no—
85#106×C127—24no—
86#95×C127—24no—
87C24×C127C2×D411yescharacteristic
88C22×C4×C127—24no—
89C22×C4×C127—24no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—21no—
97C22×C4×C127—22no—
98C22×C4×C127—21no—
99C22×C4×C127—22no—
100C22×C4×C127—44no—
101C22×C4×C127—44no—
102C22×C4×C127—41no—
103C22×C4×C127—41no—
104C22×C4×C127C22×C411yescharacteristic
105C22×C4×C127C2×D411yescharacteristic
106C22×C4×C127C2×D411yescharacteristic
107C22×C4×C127C2×D411yescharacteristic
108C22×C4×C127C2×D411yescharacteristic
109C22×C4×C127C2×D411yescharacteristic
110C22×C4×C127C2×Q811yescharacteristic
111C22×C4×C127C2×Q811yescharacteristic
112C22×C4×C127C2×Q811yescharacteristic
113C22×C4×C127C2×Q811yescharacteristic
114C22×C4×C127#4111yescharacteristic
115C22×C4×C127#4111yescharacteristic
116C22×C4×C127#4111yescharacteristic
117C22×C4×C127#4111yescharacteristic
118M16×C127—22no—
119M16×C127—22no—
120M16×C127—22no—
121M16×C127—22no—
122M16×C127—22no—
123M16×C127—41no—
124M16×C127—41no—
125M16×C127C4⋊C414yescomplemented
126C2×C8×C127—22no—
127C2×C8×C127—22no—
128C2×C8×C127—22no—
129C2×C8×C127—22no—
130C2×C8×C127—41no—
131C2×C8×C127—41no—
132C4⋊C4×C127—22no—
133C4⋊C4×C127—21no—
134C4⋊C4×C127—22no—
135C4⋊C4×C127—21no—
136C4⋊C4×C127—22no—
137C4⋊C4×C127—21no—
138C4⋊C4×C127—21no—
139C4⋊C4×C127—416no—
140C4⋊C4×C127—41no—
141C4⋊C4×C127—41no—
142C4⋊C4×C127—41no—
143C4⋊C4×C127—41no—
144C4⋊C4×C127—41no—
145C4⋊C4×C127—41no—
146C4⋊C4×C127—84no—
147C4⋊C4×C127C4⋊C414yescomplemented
148C22⋊C4×C127—22no—
149C22⋊C4×C127—22no—
150C22⋊C4×C127—41no—
151C22⋊C4×C127—41no—
152C42×C127—22no—
153C42×C127—22no—
154C42×C127—22no—
155C42×C127—22no—
156C42×C127—22no—
157C42×C127—41no—
158C42×C127—41no—
159C42×C127C4⋊C414yescomplemented
160C23×C127—22no—
161C23×C127—22no—
162C23×C127C4×D411yescharacteristic
163C23×C127#12011yescharacteristic
164C23×C127#12011yescharacteristic
165C23×C127#12111yescharacteristic
166C23×C127C22⋊Q811yescharacteristic
167C23×C127C22⋊Q811yescharacteristic
168C23×C127C4⋊Q811yescharacteristic
169C2×C4×C127—24no—
170C2×C4×C127—28no—
171C2×C4×C127—28no—
172C2×C4×C127—24no—
173C2×C4×C127—24no—
174C2×C4×C127—24no—
175C2×C4×C127—42no—
176C2×C4×C127—42no—
177C2×C4×C127—44no—
178C2×C4×C127—44no—
179C2×C4×C127—41no—
180C2×C4×C127—41no—
181C2×C4×C127—42no—
182C2×C4×C127—42no—
183C2×C4×C127—42no—
184C2×C4×C127—44no—
185C2×C4×C127—42no—
186C2×C4×C127—82no—
187C2×C4×C127—82no—
188C2×C4×C127—82no—
189C2×C4×C127C2×C4⋊C411yescharacteristic
190C2×C4×C127C2×C4⋊C411yescharacteristic
191C2×C4×C127C2×C4⋊C411yescharacteristic
192C2×C4×C127C4×D411yescharacteristic
193C2×C4×C127C4×D411yescharacteristic
194C2×C4×C127C4×Q811yescharacteristic
195C2×C4×C127#12011yescharacteristic
196C2×C4×C127#12111yescharacteristic
197C2×C4×C127#12111yescharacteristic
198C2×C4×C127C22⋊Q811yescharacteristic
199C2×C4×C127C22⋊Q811yescharacteristic
200C2×C4×C127C22⋊Q811yescharacteristic
201C2×C4×C127C22⋊Q811yescharacteristic
202C2×C4×C127C22⋊Q811yescharacteristic
203C2×C4×C127C22⋊Q811yescharacteristic
204C2×C4×C127C22⋊Q811yescharacteristic
205C2×C4×C127#12311yescharacteristic
206C2×C4×C127#12311yescharacteristic
207C2×C4×C127#12311yescharacteristic
208C2×C4×C127#12511yescharacteristic
209C2×C4×C127#12511yescharacteristic
210C2×C4×C127#12511yescharacteristic
211C2×C4×C127#12711yescharacteristic
212C2×C4×C127C4⋊Q811yescharacteristic
213C2×C4×C127C4⋊Q811yescharacteristic
214C2×C4×C127C4⋊Q811yescharacteristic
215C2×C4×C127C4⋊Q811yescharacteristic
216C2×C4×C127C4⋊Q811yescharacteristic
217C8×C127—24no—
218C8×C127—42no—
219C22×C127—22no—
220C22×C127—22no—
221C22×C127—22no—
222C22×C127—22no—
223C22×C127—21no—
224C22×C127—21no—
225C22×C127—21no—
226C22×C127—21no—
227C22×C127#38511yescharacteristic
228C22×C127#38511yescharacteristic
229C22×C127#38911yescharacteristic
230C22×C127#39211yescharacteristic
231C22×C127#39511yescharacteristic
232C22×C127#39511yescharacteristic
233C22×C127#39811yescharacteristic
234C22×C127#45312yes—
235C22×C127#45612yes—
236C4×C127—28no—
237C4×C127—44no—
238C4×C127—81no—
239C4×C127—82no—
240C4×C127—82no—
241C4×C127—81no—
242C4×C127#38411yescharacteristic
243C4×C127#38511yescharacteristic
244C4×C127#38911yescharacteristic
245C4×C127#38911yescharacteristic
246C4×C127#39511yescharacteristic
247C4×C127#39811yescharacteristic
248C4×C127#39811yescharacteristic
249C4×C127#39911yescharacteristic
250#11340C12711yesmaximal, characteristic, direct product factor, Sylow
251C2×C127—21no—
252C2×C127—21no—
253C2×C127—21no—
254C2×C127—21no—
255C2×C127#144411yescharacteristic
256C2×C127#185912yes—
257C2×C127#200211yescharacteristic
258C2×C127#200511yescharacteristic
259C2×C127#206012yes—
260C2×#428C2×C12711yescharacteristic
261#2317C2×C12711yescharacteristic
262C2×#384C2×C12711yescharacteristic
263C2×#343C2×C12711yescharacteristic
264#1736C2×C12711yescharacteristic
265C2×#339C2×C12711yescharacteristic
266C2×#339C2×C12711yescharacteristic
267C127#1134011yescharacteristic, direct product factor, Sylow
268C22×M16C22×C12711yescharacteristic
269C22×M16C22×C12711yescharacteristic
270C2×#117C22×C12711yescharacteristic
271C2×#117C22×C12711yescharacteristic
272C22×C4⋊C4—22no—
273C22×C4⋊C4C22×C12711yescharacteristic
274C22×C4⋊C4C22×C12711yescharacteristic
275C22×C42C22×C12711yescharacteristic
276#428—22no—
277#428—22no—
278C2×#107—21no—
279C2×#106—21no—
280#389—22no—
281#385—22no—
282#384—21no—
283#384—22no—
284#384—22no—
285#382—21no—
286#343—22no—
287#340—22no—
288#339—22no—
289#339C4×C12714yescomplemented
290C23×C4—21no—
291C23×C4—21no—
292C23×C4D4×C12712yes—
293C23×C4C23×C12711yescharacteristic
294C2×M16—21no—
295C2×M16—21no—
296C2×M16—21no—
297C2×M16—21no—
298C2×M16—21no—
299C2×M16—21no—
300C2×M16—21no—
301C2×M16—21no—
302C2×M16C2×C4×C12712yes—
303C2×M16D4×C12712yes—
304C2×M16Q8×C12712yes—
305C2×M16Q8×C12712yes—
306C22×C8—21no—
307C22×C8—21no—
308#117—21no—
309#117—21no—
310#117—21no—
311#117—21no—
312#117—21no—
313#117—21no—
314#117C2×C4×C12712yes—
315#117Q8×C12712yes—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—48no—
330C2×C4⋊C4D4×C12712yes—
331C2×C4⋊C4D4×C12711yescharacteristic
332C2×C4⋊C4D4×C12711yescharacteristic
333C2×C4⋊C4D4×C12712yes—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42C2×C4×C12712yes—
342C2×C42D4×C12712yes—
343C2×C42Q8×C12712yes—
344#107—24no—
345#106—24no—
346#95—24no—
347C24C2×D4×C12711yescharacteristic
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—44no—
361C22×C4—44no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4C22×C4×C12711yescharacteristic
365C22×C4C2×D4×C12711yescharacteristic
366C22×C4C2×D4×C12711yescharacteristic
367C22×C4C2×D4×C12711yescharacteristic
368C22×C4C2×D4×C12711yescharacteristic
369C22×C4C2×D4×C12711yescharacteristic
370C22×C4C2×Q8×C12711yescharacteristic
371C22×C4C2×Q8×C12711yescharacteristic
372C22×C4C2×Q8×C12711yescharacteristic
373C22×C4C2×Q8×C12711yescharacteristic
374C22×C4#41×C12711yescharacteristic
375C22×C4#41×C12711yescharacteristic
376C22×C4#41×C12711yescharacteristic
377C22×C4#41×C12711yescharacteristic
378M16—22no—
379M16—22no—
380M16—22no—
381M16—22no—
382M16—22no—
383M16—41no—
384M16—41no—
385M16C4⋊C4×C12714yescomplemented
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—41no—
391C2×C8—41no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—416no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—84no—
407C4⋊C4C4⋊C4×C12714yescomplemented
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C42—22no—
413C42—22no—
414C42—22no—
415C42—22no—
416C42—22no—
417C42—41no—
418C42—41no—
419C42C4⋊C4×C12714yescomplemented
420C23—22no—
421C23—22no—
422C23C4×D4×C12711yescharacteristic
423C23#120×C12711yescharacteristic
424C23#120×C12711yescharacteristic
425C23#121×C12711yescharacteristic
426C23C22⋊Q8×C12711yescharacteristic
427C23C22⋊Q8×C12711yescharacteristic
428C23C4⋊Q8×C12711yescharacteristic
429C2×C4—24no—
430C2×C4—28no—
431C2×C4—28no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4C2×C4⋊C4×C12711yescharacteristic
450C2×C4C2×C4⋊C4×C12711yescharacteristic
451C2×C4C2×C4⋊C4×C12711yescharacteristic
452C2×C4C4×D4×C12711yescharacteristic
453C2×C4C4×D4×C12711yescharacteristic
454C2×C4C4×Q8×C12711yescharacteristic
455C2×C4#120×C12711yescharacteristic
456C2×C4#121×C12711yescharacteristic
457C2×C4#121×C12711yescharacteristic
458C2×C4C22⋊Q8×C12711yescharacteristic
459C2×C4C22⋊Q8×C12711yescharacteristic
460C2×C4C22⋊Q8×C12711yescharacteristic
461C2×C4C22⋊Q8×C12711yescharacteristic
462C2×C4C22⋊Q8×C12711yescharacteristic
463C2×C4C22⋊Q8×C12711yescharacteristic
464C2×C4C22⋊Q8×C12711yescharacteristic
465C2×C4#123×C12711yescharacteristic
466C2×C4#123×C12711yescharacteristic
467C2×C4#123×C12711yescharacteristic
468C2×C4#125×C12711yescharacteristic
469C2×C4#125×C12711yescharacteristic
470C2×C4#125×C12711yescharacteristic
471C2×C4#127×C12711yescharacteristic
472C2×C4C4⋊Q8×C12711yescharacteristic
473C2×C4C4⋊Q8×C12711yescharacteristic
474C2×C4C4⋊Q8×C12711yescharacteristic
475C2×C4C4⋊Q8×C12711yescharacteristic
476C2×C4C4⋊Q8×C12711yescharacteristic
477C8—24no—
478C8—42no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22#385×C12711yescharacteristic
488C22#385×C12711yescharacteristic
489C22#389×C12711yescharacteristic
490C22#392×C12711yescharacteristic
491C22#395×C12711yescharacteristic
492C22#395×C12711yescharacteristic
493C22#398×C12711yescharacteristic
494C22#453×C12712yes—
495C22#456×C12712yes—
496C4—28no—
497C4—44no—
498C4—82no—
499C4—82no—
500C4—81no—
501C4—81no—
502C4#384×C12711yescharacteristic
503C4#385×C12711yescharacteristic
504C4#389×C12711yescharacteristic
505C4#389×C12711yescharacteristic
506C4#395×C12711yescharacteristic
507C4#398×C12711yescharacteristic
508C4#398×C12711yescharacteristic
509C4#399×C12711yescharacteristic
510C2—21no—
511C2—21no—
512C2—21no—
513C2—21no—
514C2C127×#144411yescharacteristic
515C2C127×#185912yes—
516C2C127×#200211yescharacteristic
517C2C127×#200511yescharacteristic
518C2C127×#206012yes—
subgroupG/H
center, socleC23×C127#120
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
29. #339×C127C4semidirect
125. M16×C127C4⋊C4semidirect
147. C4⋊C4×C127C4⋊C4semidirect
159. C42×C127C4⋊C4semidirect
250. #11340C127direct (N × H)
267. C127#11340direct (N × H)
289. #339C4×C127semidirect
385. M16C4⋊C4×C127semidirect
407. C4⋊C4C4⋊C4×C127semidirect
419. C42C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#428×C1272
C127×#23172
C2×#384×C1272
C2×#343×C1272
C127×#17362
C2×#339×C1272
#11340127