Finite Group Databasebeta

← C127×#10992 #44574665

Subgroups — C127×#10992 #44574665

Order 32512.

1658 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C127C211yesmaximal, characteristic
2C22×#99×C127C211yesmaximal, characteristic
3C127×#2308C211yesmaximal, characteristic
4C2×#381×C127C212yesmaximal, complemented
5C2×#342×C127C212yesmaximal, complemented
6C23×D4×C127C2211yescharacteristic
7C24×C4×C127C2211yescharacteristic
8C2×#123×C127—22no—
9C2×#123×C127—24no—
10C2×#123×C127—24no—
11C2×#123×C127C414yescomplemented
12C22×C4⋊C4×C127—21no—
13C22×C22⋊C4×C127—21no—
14C22×C22⋊C4×C127C2212yes—
15C22×C22⋊C4×C127C2212yes—
16C22×C22⋊C4×C127C2211yescharacteristic
17C2×#99×C127—22no—
18C2×#99×C127—24no—
19#386×C127—24no—
20#381×C127—24no—
21#381×C127—21no—
22#381×C127—24no—
23#379×C127—21no—
24C2×#95×C127—24no—
25#342×C127—24no—
26C25×C127D411yescharacteristic
27C25×C127C2311yescharacteristic
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×C127C2×C412yes—
35C22×D4×C127D412yes—
36C23×C4×C127—21no—
37C23×C4×C127—21no—
38C23×C4×C127—21no—
39C23×C4×C127—22no—
40C23×C4×C127—22no—
41C23×C4×C127—22no—
42C23×C4×C127—22no—
43C23×C4×C127—22no—
44C23×C4×C127—22no—
45C23×C4×C127C2×C412yes—
46C23×C4×C127D411yescharacteristic
47C23×C4×C127D414yes—
48C23×C4×C127D414yes—
49#123×C127—216no—
50#123×C127—28no—
51#123×C127—28no—
52C2×C4⋊C4×C127—28no—
53C2×C4⋊C4×C127—24no—
54C2×C22⋊C4×C127—28no—
55C2×C22⋊C4×C127—24no—
56C2×C22⋊C4×C127—22no—
57C2×C22⋊C4×C127—21no—
58C2×C22⋊C4×C127—22no—
59C2×C22⋊C4×C127—22no—
60C2×C22⋊C4×C127—22no—
61C2×C22⋊C4×C127—22no—
62C2×C22⋊C4×C127—22no—
63C2×C22⋊C4×C127—22no—
64C2×C22⋊C4×C127—22no—
65C2×C22⋊C4×C127—22no—
66C2×C22⋊C4×C127—22no—
67C2×C22⋊C4×C127—22no—
68C2×C22⋊C4×C127—22no—
69C2×C22⋊C4×C127—24no—
70C2×C22⋊C4×C127C2×C412yes—
71C2×C22⋊C4×C127D414yes—
72C2×C22⋊C4×C127D414yes—
73#99×C127—28no—
74#95×C127—216no—
75#95×C127—24no—
76C24×C127—22no—
77C24×C127—21no—
78C24×C127—22no—
79C24×C127—21no—
80C24×C127—44no—
81C24×C127—44no—
82C24×C127C22⋊C412yes—
83C24×C127C22×C411yescharacteristic
84C24×C127C2×D411yescharacteristic
85C24×C127C2×D412yes—
86C24×C127C2×D411yescharacteristic
87C24×C127C2×D412yes—
88C24×C127C2×D412yes—
89C24×C127C2×D412yes—
90C24×C127#4112yes—
91C24×C127#4112yes—
92C2×D4×C127—22no—
93C2×D4×C127—22no—
94C2×D4×C127—24no—
95C2×D4×C127—24no—
96C2×D4×C127—22no—
97C2×D4×C127—24no—
98C2×D4×C127—24no—
99C2×D4×C127—22no—
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—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—24no—
112C22×C4×C127—24no—
113C22×C4×C127—24no—
114C22×C4×C127—24no—
115C22×C4×C127—24no—
116C22×C4×C127—22no—
117C22×C4×C127—24no—
118C22×C4×C127—21no—
119C22×C4×C127—24no—
120C22×C4×C127—24no—
121C22×C4×C127—22no—
122C22×C4×C127—24no—
123C22×C4×C127—21no—
124C22×C4×C127—24no—
125C22×C4×C127—24no—
126C22×C4×C127—24no—
127C22×C4×C127—24no—
128C22×C4×C127—44no—
129C22×C4×C127—41no—
130C22×C4×C127—41no—
131C22×C4×C127—42no—
132C22×C4×C127—42no—
133C22×C4×C127—42no—
134C22×C4×C127—42no—
135C22×C4×C127—41no—
136C22×C4×C127—41no—
137C22×C4×C127—42no—
138C22×C4×C127—42no—
139C22×C4×C127—48no—
140C22×C4×C127—48no—
141C22×C4×C127—42no—
142C22×C4×C127—42no—
143C22×C4×C127C22⋊C412yes—
144C22×C4×C127C22⋊C414yescomplemented
145C4⋊C4×C127—216no—
146C22⋊C4×C127—216no—
147C22⋊C4×C127—22no—
148C22⋊C4×C127—24no—
149C22⋊C4×C127—24no—
150C22⋊C4×C127—24no—
151C22⋊C4×C127—42no—
152C22⋊C4×C127—42no—
153C22⋊C4×C127—42no—
154C22⋊C4×C127—42no—
155C22⋊C4×C127—42no—
156C22⋊C4×C127—42no—
157C22⋊C4×C127—84no—
158C22⋊C4×C127C22⋊C414yescomplemented
159C23×C127—28no—
160C23×C127—24no—
161C23×C127—22no—
162C23×C127—22no—
163C23×C127—22no—
164C23×C127—42no—
165C23×C127—42no—
166C23×C127—44no—
167C23×C127—44no—
168C23×C127—44no—
169C23×C127—44no—
170C23×C127—44no—
171C23×C127—44no—
172C23×C127—48no—
173C23×C127—42no—
174C23×C127—42no—
175C23×C127—44no—
176C23×C127—82no—
177C23×C127—84no—
178C23×C127C2×C22⋊C411yescharacteristic
179C23×C127C2×C22⋊C411yescharacteristic
180C23×C127C2×C22⋊C411yescharacteristic
181C23×C127C4×D412yes—
182C23×C127C4×D412yes—
183C23×C127#12012yes—
184C23×C127#12012yes—
185C23×C127#12012yes—
186C23×C127#12011yescharacteristic
187C23×C127#12011yescharacteristic
188C23×C127#12112yes—
189C23×C127#12112yes—
190C23×C127#12112yes—
191C23×C127#12112yes—
192C23×C127#12112yes—
193C23×C127#12112yes—
194C23×C127#12311yescharacteristic
195C23×C127#12312yes—
196C23×C127#12311yescharacteristic
197C23×C127#12412yes—
198C23×C127#12712yes—
199D4×C127—44no—
200D4×C127—44no—
201D4×C127—44no—
202D4×C127—44no—
203C2×C4×C127—24no—
204C2×C4×C127—24no—
205C2×C4×C127—22no—
206C2×C4×C127—28no—
207C2×C4×C127—22no—
208C2×C4×C127—22no—
209C2×C4×C127—44no—
210C2×C4×C127—48no—
211C2×C4×C127—42no—
212C2×C4×C127—42no—
213C2×C4×C127—44no—
214C2×C4×C127—44no—
215C2×C4×C127—44no—
216C2×C4×C127—42no—
217C2×C4×C127—44no—
218C2×C4×C127—44no—
219C2×C4×C127—42no—
220C2×C4×C127—48no—
221C2×C4×C127—48no—
222C2×C4×C127—44no—
223C2×C4×C127—44no—
224C2×C4×C127—48no—
225C2×C4×C127—84no—
226C2×C4×C127—84no—
227C2×C4×C127—84no—
228C22×C127—22no—
229C22×C127—24no—
230C22×C127—22no—
231C22×C127—24no—
232C22×C127—24no—
233C22×C127—24no—
234C22×C127—24no—
235C22×C127—24no—
236C22×C127—24no—
237C22×C127—24no—
238C22×C127—41no—
239C22×C127—41no—
240C22×C127—42no—
241C22×C127—42no—
242C22×C127—41no—
243C22×C127—42no—
244C22×C127—42no—
245C22×C127—41no—
246C22×C127—42no—
247C22×C127—42no—
248C22×C127—44no—
249C22×C127—44no—
250C22×C127—42no—
251C22×C127—82no—
252C22×C127—84no—
253C22×C127—84no—
254C22×C127#37911yescharacteristic
255C22×C127#38612yes—
256C22×C127#38611yescharacteristic
257C22×C127#38611yescharacteristic
258C22×C127#39012yes—
259C22×C127#39212yes—
260C22×C127#39212yes—
261C22×C127#39412yes—
262C22×C127#39412yes—
263C22×C127#45814yes—
264C4×C127—44no—
265C4×C127—44no—
266C4×C127—42no—
267C4×C127—84no—
268C4×C127—84no—
269#10992C12711yesmaximal, characteristic, direct product factor, Sylow
270C2×C127—21no—
271C2×C127—22no—
272C2×C127—21no—
273C2×C127—22no—
274C2×C127—22no—
275C2×C127—22no—
276C2×C127—22no—
277C2×C127—82no—
278C2×C127#143811yescharacteristic
279C2×C127#189012yes—
280C2×C127#202214yes—
281C22×#123C2×C12711yescharacteristic
282C22×#99C2×C12711yescharacteristic
283#2308C2×C12711yescharacteristic
284C2×#381C2×C12712yescomplemented
285C2×#342C2×C12712yescomplemented
286C127#1099211yescharacteristic, direct product factor, Sylow
287C23×D4C22×C12711yescharacteristic
288C24×C4C22×C12711yescharacteristic
289C2×#123—22no—
290C2×#123—24no—
291C2×#123—24no—
292C2×#123C4×C12714yescomplemented
293C22×C4⋊C4—21no—
294C22×C22⋊C4—21no—
295C22×C22⋊C4C22×C12712yes—
296C22×C22⋊C4C22×C12712yes—
297C22×C22⋊C4C22×C12711yescharacteristic
298C2×#99—22no—
299C2×#99—24no—
300#386—24no—
301#381—21no—
302#381—24no—
303#381—24no—
304#379—21no—
305C2×#95—24no—
306#342—24no—
307C25D4×C12711yescharacteristic
308C25C23×C12711yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4C2×C4×C12712yes—
316C22×D4D4×C12712yes—
317C23×C4—21no—
318C23×C4—21no—
319C23×C4—21no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4C2×C4×C12712yes—
327C23×C4D4×C12711yescharacteristic
328C23×C4D4×C12714yes—
329C23×C4D4×C12714yes—
330#123—216no—
331#123—28no—
332#123—28no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—24no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4C2×C4×C12712yes—
352C2×C22⋊C4D4×C12714yes—
353C2×C22⋊C4D4×C12714yes—
354#99—28no—
355#95—216no—
356#95—24no—
357C24—22no—
358C24—21no—
359C24—22no—
360C24—21no—
361C24—44no—
362C24—44no—
363C24C22⋊C4×C12712yes—
364C24C22×C4×C12711yescharacteristic
365C24C2×D4×C12711yescharacteristic
366C24C2×D4×C12712yes—
367C24C2×D4×C12711yescharacteristic
368C24C2×D4×C12712yes—
369C24C2×D4×C12712yes—
370C24C2×D4×C12712yes—
371C24#41×C12712yes—
372C24#41×C12712yes—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—24no—
376C2×D4—24no—
377C2×D4—22no—
378C2×D4—24no—
379C2×D4—24no—
380C2×D4—22no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—21no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—44no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—48no—
421C22×C4—48no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4C22⋊C4×C12712yes—
425C22×C4C22⋊C4×C12714yescomplemented
426C4⋊C4—216no—
427C22⋊C4—216no—
428C22⋊C4—22no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—42no—
433C22⋊C4—42no—
434C22⋊C4—42no—
435C22⋊C4—42no—
436C22⋊C4—42no—
437C22⋊C4—42no—
438C22⋊C4—84no—
439C22⋊C4C22⋊C4×C12714yescomplemented
440C23—28no—
441C23—24no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—42no—
446C23—42no—
447C23—44no—
448C23—44no—
449C23—44no—
450C23—44no—
451C23—44no—
452C23—44no—
453C23—48no—
454C23—42no—
455C23—42no—
456C23—44no—
457C23—82no—
458C23—84no—
459C23C2×C22⋊C4×C12711yescharacteristic
460C23C2×C22⋊C4×C12711yescharacteristic
461C23C2×C22⋊C4×C12711yescharacteristic
462C23C4×D4×C12712yes—
463C23C4×D4×C12712yes—
464C23#120×C12712yes—
465C23#120×C12712yes—
466C23#120×C12712yes—
467C23#120×C12711yescharacteristic
468C23#120×C12711yescharacteristic
469C23#121×C12712yes—
470C23#121×C12712yes—
471C23#121×C12712yes—
472C23#121×C12712yes—
473C23#121×C12712yes—
474C23#121×C12712yes—
475C23#123×C12711yescharacteristic
476C23#123×C12712yes—
477C23#123×C12711yescharacteristic
478C23#124×C12712yes—
479C23#127×C12712yes—
480D4—44no—
481D4—44no—
482D4—44no—
483D4—44no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—28no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—44no—
491C2×C4—48no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—44no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—44no—
499C2×C4—44no—
500C2×C4—42no—
501C2×C4—48no—
502C2×C4—48no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—48no—
506C2×C4—84no—
507C2×C4—84no—
508C2×C4—84no—
509C22—22no—
510C22—24no—
511C22—22no—
512C22—24no—
513C22—24no—
514C22—24no—
515C22—24no—
516C22—24no—
517C22—24no—
518C22—24no—
519C22—41no—
520C22—41no—
521C22—42no—
522C22—42no—
523C22—41no—
524C22—42no—
525C22—42no—
526C22—41no—
527C22—42no—
528C22—42no—
529C22—44no—
530C22—44no—
531C22—42no—
532C22—82no—
533C22—84no—
534C22—84no—
535C22#379×C12711yescharacteristic
536C22#386×C12712yes—
537C22#386×C12711yescharacteristic
538C22#386×C12711yescharacteristic
539C22#390×C12712yes—
540C22#392×C12712yes—
541C22#392×C12712yes—
542C22#394×C12712yes—
543C22#394×C12712yes—
544C22#458×C12714yes—
545C4—44no—
546C4—44no—
547C4—42no—
548C4—84no—
549C4—84no—
550C2—21no—
551C2—22no—
552C2—21no—
553C2—22no—
554C2—22no—
555C2—22no—
556C2—22no—
557C2—82no—
558C2C127×#143811yescharacteristic
559C2C127×#189012yes—
560C2C127×#202214yes—
subgroupG/H
center, socleC23×C127#120
commutatorC24C22×C4×C127
Frattini, cosocleC25C23×C127
prime radicalC23×D4×C127C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C25×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#381×C127C2semidirect
5. C2×#342×C127C2semidirect
11. C2×#123×C127C4semidirect
144. C22×C4×C127C22⋊C4semidirect
158. C22⋊C4×C127C22⋊C4semidirect
269. #10992C127direct (N × H)
284. C2×#381C2×C127semidirect
285. C2×#342C2×C127semidirect
286. C127#10992direct (N × H)
292. C2×#123C4×C127semidirect
425. C22×C4C22⋊C4×C127semidirect
439. C22⋊C4C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1272
C22×#99×C1272
C127×#23082
C2×#381×C1272
C2×#342×C1272
#10992127