Finite Group Databasebeta

← C127×#11325 #44574998

Subgroups — C127×#11325 #44574998

Order 32512.

886 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
1C22×#107×C127C211yesmaximal, characteristic
2C22×#106×C127C211yesmaximal, characteristic
3C2×#382×C127C211yesmaximal, characteristic
4C2×#340×C127C211yesmaximal, characteristic
5C2×#340×C127C211yesmaximal, characteristic
6C2×#336×C127C211yesmaximal, characteristic
7C127×C4⋊#95C211yesmaximal, characteristic
8C23×C8×C127C2211yescharacteristic
9C23×C8×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C42×C127C2211yescharacteristic
15C2×#107×C127—22no—
16C2×#107×C127—22no—
17C2×#107×C127—22no—
18C2×#106×C127—22no—
19C2×#106×C127—22no—
20C2×#106×C127—22no—
21#382×C127—22no—
22#382×C127—22no—
23C2×#95×C127—22no—
24C2×#95×C127—22no—
25#340×C127—22no—
26#340×C127—22no—
27#336×C127C414yescomplemented
28C23×C4×C127—21no—
29C23×C4×C127—21no—
30C23×C4×C127—21no—
31C23×C4×C127—21no—
32C23×C4×C127D412yes—
33C23×C4×C127C2311yescharacteristic
34C22×C8×C127—21no—
35C22×C8×C127—21no—
36C22×C8×C127—21no—
37C22×C8×C127—21no—
38C22×C8×C127—21no—
39C22×C8×C127—21no—
40C22×C8×C127—21no—
41C22×C8×C127—21no—
42C22×C8×C127C2×C412yes—
43C22×C8×C127C2×C412yes—
44C22×C8×C127D412yes—
45C22×C8×C127D412yes—
46C22×C8×C127Q812yes—
47C22×C8×C127Q812yes—
48C2×C4⋊C4×C127—21no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127—21no—
51C2×C4⋊C4×C127—21no—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127—21no—
54C2×C4⋊C4×C127—21no—
55C2×C4⋊C4×C127—21no—
56C2×C4⋊C4×C127—21no—
57C2×C4⋊C4×C127—21no—
58C2×C4⋊C4×C127—21no—
59C2×C4⋊C4×C127—21no—
60C2×C4⋊C4×C127—21no—
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×C127D412yes—
69C2×C4⋊C4×C127D412yes—
70C2×C4⋊C4×C127D412yes—
71C2×C4⋊C4×C127Q812yes—
72C2×C42×C127—21no—
73C2×C42×C127—21no—
74C2×C42×C127—21no—
75C2×C42×C127—21no—
76C2×C42×C127C2×C412yes—
77C2×C42×C127Q812yes—
78#107×C127—28no—
79#106×C127—28no—
80#95×C127—28no—
81#95×C127—44no—
82C24×C127C2×D411yescharacteristic
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—41no—
94C22×C4×C127—41no—
95C22×C4×C127—41no—
96C22×C4×C127—41no—
97C22×C4×C127—41no—
98C22×C4×C127—41no—
99C22×C4×C127—41no—
100C22×C4×C127—41no—
101C22×C4×C127—42no—
102C22×C4×C127—42no—
103C22×C4×C127—42no—
104C22×C4×C127—42no—
105C22×C4×C127—42no—
106C22×C4×C127—42no—
107C22×C4×C127—42no—
108C22×C4×C127—42no—
109C22×C4×C127C4⋊C414yes—
110C22×C4×C127C22×C411yescharacteristic
111C22×C4×C127C2×D411yescharacteristic
112C22×C4×C127C2×D411yescharacteristic
113C22×C4×C127C2×D411yescharacteristic
114C22×C4×C127C2×D411yescharacteristic
115C22×C4×C127C2×D411yescharacteristic
116C22×C4×C127C2×Q811yescharacteristic
117C22×C4×C127C2×Q811yescharacteristic
118C22×C4×C127C2×Q811yescharacteristic
119C22×C4×C127C2×Q811yescharacteristic
120C22×C4×C127#4111yescharacteristic
121C22×C4×C127#4111yescharacteristic
122C22×C4×C127#4111yescharacteristic
123C22×C4×C127#4111yescharacteristic
124C2×C8×C127—22no—
125C2×C8×C127—22no—
126C2×C8×C127—22no—
127C2×C8×C127—22no—
128C2×C8×C127—22no—
129C2×C8×C127—22no—
130C2×C8×C127—22no—
131C2×C8×C127—22no—
132C2×C8×C127—22no—
133C2×C8×C127—22no—
134C2×C8×C127—22no—
135C2×C8×C127—22no—
136C2×C8×C127C4⋊C414yes—
137C2×C8×C127C4⋊C414yes—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—22no—
140C4⋊C4×C127—22no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—22no—
145C4⋊C4×C127—22no—
146C4⋊C4×C127—41no—
147C4⋊C4×C127—41no—
148C4⋊C4×C127—41no—
149C4⋊C4×C127—41no—
150C4⋊C4×C127—41no—
151C4⋊C4×C127—41no—
152C4⋊C4×C127—41no—
153C4⋊C4×C127—41no—
154C42×C127—22no—
155C42×C127—22no—
156C42×C127—22no—
157C42×C127—22no—
158C23×C127C2×C4⋊C411yescharacteristic
159C23×C127#12011yescharacteristic
160C23×C127#12111yescharacteristic
161C23×C127C22⋊Q811yescharacteristic
162C23×C127#12311yescharacteristic
163C23×C127#12711yescharacteristic
164C23×C127C4⋊Q811yescharacteristic
165C23×C127#13512yes—
166C23×C127#13512yes—
167C23×C127AGL(1,ℤ/8)12yes—
168C23×C127#13712yes—
169C2×C4×C127—24no—
170C2×C4×C127—24no—
171C2×C4×C127—24no—
172C2×C4×C127—42no—
173C2×C4×C127—42no—
174C2×C4×C127—42no—
175C2×C4×C127—42no—
176C2×C4×C127—42no—
177C2×C4×C127—42no—
178C2×C4×C127—42no—
179C2×C4×C127—42no—
180C2×C4×C127—44no—
181C2×C4×C127—44no—
182C2×C4×C127—44no—
183C2×C4×C127—44no—
184C2×C4×C127—82no—
185C2×C4×C127—82no—
186C2×C4×C127—82no—
187C2×C4×C127—82no—
188C2×C4×C127—81no—
189C2×C4×C127—81no—
190C2×C4×C127—81no—
191C2×C4×C127—81no—
192C2×C4×C127—81no—
193C2×C4×C127—81no—
194C2×C4×C127—81no—
195C2×C4×C127—81no—
196C2×C4×C127C2×C4⋊C411yescharacteristic
197C2×C4×C127C2×C4⋊C411yescharacteristic
198C2×C4×C127C4×D411yescharacteristic
199C2×C4×C127C4×D411yescharacteristic
200C2×C4×C127C4×D411yescharacteristic
201C2×C4×C127C4×Q811yescharacteristic
202C2×C4×C127#12011yescharacteristic
203C2×C4×C127#12011yescharacteristic
204C2×C4×C127#12111yescharacteristic
205C2×C4×C127#12111yescharacteristic
206C2×C4×C127C22⋊Q811yescharacteristic
207C2×C4×C127C22⋊Q811yescharacteristic
208C2×C4×C127C22⋊Q811yescharacteristic
209C2×C4×C127C22⋊Q811yescharacteristic
210C2×C4×C127C22⋊Q811yescharacteristic
211C2×C4×C127C22⋊Q811yescharacteristic
212C2×C4×C127C22⋊Q811yescharacteristic
213C2×C4×C127C22⋊Q811yescharacteristic
214C2×C4×C127#12311yescharacteristic
215C2×C4×C127#12311yescharacteristic
216C2×C4×C127#12511yescharacteristic
217C2×C4×C127#12511yescharacteristic
218C2×C4×C127#12511yescharacteristic
219C2×C4×C127C4⋊Q811yescharacteristic
220C2×C4×C127C4⋊Q811yescharacteristic
221C2×C4×C127C4⋊Q811yescharacteristic
222C2×C4×C127C4⋊Q811yescharacteristic
223C2×C4×C127C4⋊Q811yescharacteristic
224C8×C127—24no—
225C8×C127—24no—
226C22×C127#38411yescharacteristic
227C22×C127#38511yescharacteristic
228C22×C127#38911yescharacteristic
229C22×C127#39211yescharacteristic
230C22×C127#39511yescharacteristic
231C22×C127#39811yescharacteristic
232C22×C127#39911yescharacteristic
233C22×C127#42712yes—
234C22×C127#42812yes—
235C22×C127#44912yes—
236C22×C127#45212yes—
237C22×C127#46312yes—
238C22×C127#46412yes—
239C22×C127#47812yes—
240C22×C127#47912yes—
241C22×C127#48212yes—
242C22×C127#48512yes—
243C22×C127#49511yescharacteristic
244C22×C127#49511yescharacteristic
245C22×C127#49611yescharacteristic
246C22×C127#49711yescharacteristic
247C22×C127#49912yes—
248C22×C127#50112yes—
249C4×C127—44no—
250C4×C127—82no—
251C4×C127—82no—
252C4×C127—82no—
253C4×C127—82no—
254C4×C127#38511yescharacteristic
255C4×C127#38511yescharacteristic
256C4×C127#38911yescharacteristic
257C4×C127#38911yescharacteristic
258C4×C127#39511yescharacteristic
259C4×C127#39511yescharacteristic
260C4×C127#39811yescharacteristic
261C4×C127#39811yescharacteristic
262#11325C12711yesmaximal, characteristic, direct product factor, Sylow
263C2×C127#144411yescharacteristic
264C2×C127#184611yescharacteristic
265C2×C127#184711yescharacteristic
266C2×C127#185412yes—
267C2×C127#194912yes—
268C2×C127#201211yescharacteristic
269C2×C127#201511yescharacteristic
270C2×C127#205912yes—
271C2×C127#208512yes—
272C2×C127#209211yescharacteristic
273C2×C127#209711yescharacteristic
274C22×#107C2×C12711yescharacteristic
275C22×#106C2×C12711yescharacteristic
276C2×#382C2×C12711yescharacteristic
277C2×#340C2×C12711yescharacteristic
278C2×#340C2×C12711yescharacteristic
279C2×#336C2×C12711yescharacteristic
280C4⋊#95C2×C12711yescharacteristic
281C127#1132511yescharacteristic, direct product factor, Sylow
282C23×C8C22×C12711yescharacteristic
283C23×C8C22×C12711yescharacteristic
284C22×C4⋊C4C22×C12711yescharacteristic
285C22×C4⋊C4C22×C12711yescharacteristic
286C22×C4⋊C4C22×C12711yescharacteristic
287C22×C4⋊C4C22×C12711yescharacteristic
288C22×C42C22×C12711yescharacteristic
289C2×#107—22no—
290C2×#107—22no—
291C2×#107—22no—
292C2×#106—22no—
293C2×#106—22no—
294C2×#106—22no—
295#382—22no—
296#382—22no—
297C2×#95—22no—
298C2×#95—22no—
299#340—22no—
300#340—22no—
301#336C4×C12714yescomplemented
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4D4×C12712yes—
307C23×C4C23×C12711yescharacteristic
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—21no—
311C22×C8—21no—
312C22×C8—21no—
313C22×C8—21no—
314C22×C8—21no—
315C22×C8—21no—
316C22×C8C2×C4×C12712yes—
317C22×C8C2×C4×C12712yes—
318C22×C8D4×C12712yes—
319C22×C8D4×C12712yes—
320C22×C8Q8×C12712yes—
321C22×C8Q8×C12712yes—
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—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4D4×C12712yes—
343C2×C4⋊C4D4×C12712yes—
344C2×C4⋊C4D4×C12712yes—
345C2×C4⋊C4Q8×C12712yes—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42C2×C4×C12712yes—
351C2×C42Q8×C12712yes—
352#107—28no—
353#106—28no—
354#95—28no—
355#95—44no—
356C24C2×D4×C12711yescharacteristic
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4C4⋊C4×C12714yes—
384C22×C4C22×C4×C12711yescharacteristic
385C22×C4C2×D4×C12711yescharacteristic
386C22×C4C2×D4×C12711yescharacteristic
387C22×C4C2×D4×C12711yescharacteristic
388C22×C4C2×D4×C12711yescharacteristic
389C22×C4C2×D4×C12711yescharacteristic
390C22×C4C2×Q8×C12711yescharacteristic
391C22×C4C2×Q8×C12711yescharacteristic
392C22×C4C2×Q8×C12711yescharacteristic
393C22×C4C2×Q8×C12711yescharacteristic
394C22×C4#41×C12711yescharacteristic
395C22×C4#41×C12711yescharacteristic
396C22×C4#41×C12711yescharacteristic
397C22×C4#41×C12711yescharacteristic
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8C4⋊C4×C12714yes—
411C2×C8C4⋊C4×C12714yes—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C42—22no—
429C42—22no—
430C42—22no—
431C42—22no—
432C23C2×C4⋊C4×C12711yescharacteristic
433C23#120×C12711yescharacteristic
434C23#121×C12711yescharacteristic
435C23C22⋊Q8×C12711yescharacteristic
436C23#123×C12711yescharacteristic
437C23#127×C12711yescharacteristic
438C23C4⋊Q8×C12711yescharacteristic
439C23#135×C12712yes—
440C23#135×C12712yes—
441C23AGL(1,ℤ/8)×C12712yes—
442C23#137×C12712yes—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4—44no—
457C2×C4—44no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4C2×C4⋊C4×C12711yescharacteristic
471C2×C4C2×C4⋊C4×C12711yescharacteristic
472C2×C4C4×D4×C12711yescharacteristic
473C2×C4C4×D4×C12711yescharacteristic
474C2×C4C4×D4×C12711yescharacteristic
475C2×C4C4×Q8×C12711yescharacteristic
476C2×C4#120×C12711yescharacteristic
477C2×C4#120×C12711yescharacteristic
478C2×C4#121×C12711yescharacteristic
479C2×C4#121×C12711yescharacteristic
480C2×C4C22⋊Q8×C12711yescharacteristic
481C2×C4C22⋊Q8×C12711yescharacteristic
482C2×C4C22⋊Q8×C12711yescharacteristic
483C2×C4C22⋊Q8×C12711yescharacteristic
484C2×C4C22⋊Q8×C12711yescharacteristic
485C2×C4C22⋊Q8×C12711yescharacteristic
486C2×C4C22⋊Q8×C12711yescharacteristic
487C2×C4C22⋊Q8×C12711yescharacteristic
488C2×C4#123×C12711yescharacteristic
489C2×C4#123×C12711yescharacteristic
490C2×C4#125×C12711yescharacteristic
491C2×C4#125×C12711yescharacteristic
492C2×C4#125×C12711yescharacteristic
493C2×C4C4⋊Q8×C12711yescharacteristic
494C2×C4C4⋊Q8×C12711yescharacteristic
495C2×C4C4⋊Q8×C12711yescharacteristic
496C2×C4C4⋊Q8×C12711yescharacteristic
497C2×C4C4⋊Q8×C12711yescharacteristic
498C8—24no—
499C8—24no—
500C22#384×C12711yescharacteristic
501C22#385×C12711yescharacteristic
502C22#389×C12711yescharacteristic
503C22#392×C12711yescharacteristic
504C22#395×C12711yescharacteristic
505C22#398×C12711yescharacteristic
506C22#399×C12711yescharacteristic
507C22#427×C12712yes—
508C22#428×C12712yes—
509C22#449×C12712yes—
510C22#452×C12712yes—
511C22#463×C12712yes—
512C22#464×C12712yes—
513C22#478×C12712yes—
514C22#479×C12712yes—
515C22#482×C12712yes—
516C22#485×C12712yes—
517C22#495×C12711yescharacteristic
518C22#495×C12711yescharacteristic
519C22#496×C12711yescharacteristic
520C22#497×C12711yescharacteristic
521C22#499×C12712yes—
522C22#501×C12712yes—
523C4—44no—
524C4—82no—
525C4—82no—
526C4—82no—
527C4—82no—
528C4#385×C12711yescharacteristic
529C4#385×C12711yescharacteristic
530C4#389×C12711yescharacteristic
531C4#389×C12711yescharacteristic
532C4#395×C12711yescharacteristic
533C4#395×C12711yescharacteristic
534C4#398×C12711yescharacteristic
535C4#398×C12711yescharacteristic
536C2C127×#144411yescharacteristic
537C2C127×#184611yescharacteristic
538C2C127×#184711yescharacteristic
539C2C127×#185412yes—
540C2C127×#194912yes—
541C2C127×#201211yescharacteristic
542C2C127×#201511yescharacteristic
543C2C127×#205912yes—
544C2C127×#208512yes—
545C2C127×#209211yescharacteristic
546C2C127×#209711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C2×D4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
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
27. #336×C127C4semidirect
262. #11325C127direct (N × H)
281. C127#11325direct (N × H)
301. #336C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#107×C1272
C22×#106×C1272
C2×#382×C1272
C2×#340×C1272
C2×#336×C1272
C127×C4⋊#952
#11325127