Finite Group Databasebeta

← C127×#10995 #44574668

Subgroups — C127×#10995 #44574668

Order 32512.

1934 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#534×C127C211yesmaximal, characteristic
2C22×#99×C127C212yesmaximal, complemented
3C2×#386×C127C212yesmaximal, complemented
4C2×#342×C127C211yesmaximal, characteristic, complemented
5C127×C22⋊#95C211yesmaximal, characteristic, complemented
6C23×D4×C127C2212yes—
7C24×C4×C127C2211yescharacteristic
8#534×C127—24no—
9#534×C127—22no—
10#534×C127C414yescomplemented
11C2×#123×C127—22no—
12C2×#121×C127—22no—
13C2×#120×C127—22no—
14C22×C22⋊C4×C127—22no—
15C22×C22⋊C4×C127C2211yescharacteristic
16C22×C22⋊C4×C127C2212yes—
17C22×C22⋊C4×C127C2211yescharacteristic
18C2×#99×C127—24no—
19C2×#99×C127—24no—
20C2×#99×C127—24no—
21#386×C127—24no—
22#386×C127—24no—
23C2×#95×C127—22no—
24C2×#95×C127—22no—
25#342×C127—22no—
26C25×C127D412yes—
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×C127—22no—
35C22×D4×C127—22no—
36C22×D4×C127—22no—
37C22×D4×C127—22no—
38C22×D4×C127—22no—
39C22×D4×C127—22no—
40C22×D4×C127—22no—
41C22×D4×C127C2×C414yes—
42C22×D4×C127D414yes—
43C23×C4×C127—22no—
44C23×C4×C127—21no—
45C23×C4×C127—22no—
46C23×C4×C127—21no—
47C23×C4×C127—22no—
48C23×C4×C127—21no—
49C23×C4×C127—44no—
50C23×C4×C127D412yes—
51C23×C4×C127D412yes—
52C23×C4×C127D412yescomplemented
53#123×C127—28no—
54#123×C127—28no—
55#121×C127—28no—
56#121×C127—28no—
57#120×C127—28no—
58#120×C127—28no—
59C2×C4⋊C4×C127—22no—
60C2×C22⋊C4×C127—24no—
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—28no—
70C2×C22⋊C4×C127—22no—
71C2×C22⋊C4×C127—21no—
72C2×C22⋊C4×C127—48no—
73C2×C22⋊C4×C127C2×C412yes—
74C2×C22⋊C4×C127D412yes—
75C2×C22⋊C4×C127D414yescomplemented
76C2×C22⋊C4×C127D412yescomplemented
77#99×C127—216no—
78#95×C127—28no—
79#95×C127—44no—
80C24×C127—22no—
81C24×C127—22no—
82C24×C127—22no—
83C24×C127—22no—
84C24×C127—22no—
85C24×C127—22no—
86C24×C127—42no—
87C24×C127—42no—
88C24×C127—44no—
89C24×C127—44no—
90C24×C127C22⋊C414yescomplemented
91C24×C127C22×C411yescharacteristic
92C24×C127C2×D412yes—
93C24×C127C2×D411yescharacteristic
94C24×C127C2×D412yes—
95C24×C127C2×D411yescharacteristic
96C24×C127C2×D411yescharacteristic
97C24×C127C2×D411yescharacteristic
98C24×C127C2×D412yes—
99C24×C127#4112yes—
100C24×C127#4111yescharacteristic
101C24×C127#4111yescharacteristic
102C2×D4×C127—24no—
103C2×D4×C127—24no—
104C2×D4×C127—24no—
105C2×D4×C127—24no—
106C2×D4×C127—24no—
107C2×D4×C127—24no—
108C2×D4×C127—24no—
109C2×D4×C127—24no—
110C2×D4×C127—24no—
111C2×D4×C127—24no—
112C2×D4×C127—24no—
113C2×D4×C127—24no—
114C2×D4×C127—28no—
115C2×D4×C127—42no—
116C2×D4×C127—42no—
117C2×D4×C127—42no—
118C2×D4×C127—42no—
119C2×D4×C127—42no—
120C2×D4×C127—42no—
121C2×D4×C127—42no—
122C2×D4×C127—42no—
123C2×D4×C127—42no—
124C2×D4×C127—42no—
125C2×D4×C127—42no—
126C2×D4×C127—42no—
127C2×D4×C127—42no—
128C2×D4×C127—42no—
129C2×D4×C127—42no—
130C2×D4×C127—42no—
131C2×D4×C127—82no—
132C2×D4×C127—82no—
133C22×C4×C127—24no—
134C22×C4×C127—28no—
135C22×C4×C127—22no—
136C22×C4×C127—24no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—22no—
145C22×C4×C127—24no—
146C22×C4×C127—22no—
147C22×C4×C127—44no—
148C22×C4×C127—48no—
149C22×C4×C127—44no—
150C22×C4×C127—42no—
151C22×C4×C127—44no—
152C22×C4×C127—41no—
153C22×C4×C127—42no—
154C22×C4×C127—41no—
155C22×C4×C127—42no—
156C22×C4×C127—42no—
157C22×C4×C127—42no—
158C22×C4×C127—44no—
159C22×C4×C127—42no—
160C22×C4×C127—44no—
161C22×C4×C127—42no—
162C22×C4×C127—41no—
163C22×C4×C127—42no—
164C22×C4×C127—41no—
165C22×C4×C127C22⋊C414yescomplemented
166C22×C4×C127C22⋊C414yescomplemented
167C4⋊C4×C127—28no—
168C22⋊C4×C127—216no—
169C22⋊C4×C127—24no—
170C22⋊C4×C127—24no—
171C22⋊C4×C127—24no—
172C22⋊C4×C127—24no—
173C22⋊C4×C127—24no—
174C22⋊C4×C127—416no—
175C22⋊C4×C127—42no—
176C22⋊C4×C127—42no—
177C22⋊C4×C127—42no—
178C23×C127—22no—
179C23×C127—24no—
180C23×C127—22no—
181C23×C127—24no—
182C23×C127—24no—
183C23×C127—24no—
184C23×C127—24no—
185C23×C127—41no—
186C23×C127—42no—
187C23×C127—41no—
188C23×C127—42no—
189C23×C127—41no—
190C23×C127—42no—
191C23×C127—42no—
192C23×C127—42no—
193C23×C127—44no—
194C23×C127—41no—
195C23×C127—42no—
196C23×C127—44no—
197C23×C127—48no—
198C23×C127—44no—
199C23×C127—44no—
200C23×C127—48no—
201C23×C127—42no—
202C23×C127—42no—
203C23×C127—42no—
204C23×C127—42no—
205C23×C127—44no—
206C23×C127—44no—
207C23×C127—84no—
208C23×C127—82no—
209C23×C127—82no—
210C23×C127—84no—
211C23×C127C2×C22⋊C412yes—
212C23×C127C2×C22⋊C411yescharacteristic
213C23×C127C4×D411yescharacteristic
214C23×C127C4×D411yescharacteristic
215C23×C127C4×D412yes—
216C23×C127#12012yes—
217C23×C127#12011yescharacteristic
218C23×C127#12012yes—
219C23×C127#12012yes—
220C23×C127#12011yescharacteristic
221C23×C127#12112yes—
222C23×C127#12112yes—
223C23×C127#12111yescharacteristic
224C23×C127#12111yescharacteristic
225C23×C127#12112yes—
226C23×C127#12112yes—
227C23×C127#12112yes—
228C23×C127#12312yes—
229C23×C127#12312yes—
230C23×C127#12411yescharacteristic
231C23×C127#12411yescharacteristic
232C23×C127#12711yescharacteristic
233C23×C127#12711yescharacteristic
234D4×C127—44no—
235D4×C127—44no—
236D4×C127—44no—
237D4×C127—44no—
238D4×C127—44no—
239D4×C127—44no—
240D4×C127—44no—
241D4×C127—44no—
242D4×C127—88no—
243C2×C4×C127—28no—
244C2×C4×C127—24no—
245C2×C4×C127—24no—
246C2×C4×C127—24no—
247C2×C4×C127—24no—
248C2×C4×C127—24no—
249C2×C4×C127—44no—
250C2×C4×C127—42no—
251C2×C4×C127—44no—
252C2×C4×C127—48no—
253C2×C4×C127—42no—
254C2×C4×C127—42no—
255C2×C4×C127—42no—
256C2×C4×C127—42no—
257C2×C4×C127—42no—
258C2×C4×C127—44no—
259C2×C4×C127—42no—
260C2×C4×C127—42no—
261C2×C4×C127—44no—
262C2×C4×C127—44no—
263C2×C4×C127—44no—
264C2×C4×C127—44no—
265C2×C4×C127—44no—
266C2×C4×C127—42no—
267C2×C4×C127—82no—
268C2×C4×C127—81no—
269C2×C4×C127—81no—
270C2×C4×C127—84no—
271C2×C4×C127—82no—
272C2×C4×C127—84no—
273C22×C127—22no—
274C22×C127—21no—
275C22×C127—21no—
276C22×C127—22no—
277C22×C127—22no—
278C22×C127—21no—
279C22×C127—22no—
280C22×C127—21no—
281C22×C127—22no—
282C22×C127—24no—
283C22×C127—24no—
284C22×C127—22no—
285C22×C127—22no—
286C22×C127—22no—
287C22×C127—24no—
288C22×C127—24no—
289C22×C127—41no—
290C22×C127—42no—
291C22×C127—41no—
292C22×C127—42no—
293C22×C127—42no—
294C22×C127—42no—
295C22×C127—42no—
296C22×C127—42no—
297C22×C127—41no—
298C22×C127—41no—
299C22×C127—48no—
300C22×C127—44no—
301C22×C127—48no—
302C22×C127—84no—
303C22×C127—84no—
304C22×C127—84no—
305C22×C127—82no—
306C22×C127—82no—
307C22×C127—84no—
308C22×C127#37911yescharacteristic
309C22×C127#38612yes—
310C22×C127#38612yes—
311C22×C127#39011yescharacteristic
312C22×C127#39011yescharacteristic
313C22×C127#39212yes—
314C22×C127#39211yescharacteristic
315C22×C127#39211yescharacteristic
316C22×C127#39412yes—
317C22×C127#39411yescharacteristic
318C22×C127#39411yescharacteristic
319C22×C127B(4,𝔽2)12yes—
320C22×C127#45812yes—
321C4×C127—44no—
322C4×C127—44no—
323C4×C127—44no—
324C4×C127—84no—
325C4×C127—82no—
326#10995C12711yesmaximal, characteristic, direct product factor, Sylow
327C2×C127—22no—
328C2×C127—21no—
329C2×C127—22no—
330C2×C127—22no—
331C2×C127—22no—
332C2×C127—21no—
333C2×C127—21no—
334C2×C127—21no—
335C2×C127—84no—
336C2×C127#143811yescharacteristic
337C2×C127#179012yes—
338C2×C127#202111yescharacteristic
339C2×C127#202211yescharacteristic
340C2×C127#204412yes—
341C2×#534C2×C12711yescharacteristic
342C22×#99C2×C12712yescomplemented
343C2×#386C2×C12712yescomplemented
344C2×#342C2×C12711yescharacteristic, complemented
345C22⋊#95C2×C12711yescharacteristic, complemented
346C127#1099511yescharacteristic, direct product factor, Sylow
347C23×D4C22×C12712yes—
348C24×C4C22×C12711yescharacteristic
349#534—24no—
350#534—22no—
351#534C4×C12714yescomplemented
352C2×#123—22no—
353C2×#121—22no—
354C2×#120—22no—
355C22×C22⋊C4—22no—
356C22×C22⋊C4C22×C12711yescharacteristic
357C22×C22⋊C4C22×C12712yes—
358C22×C22⋊C4C22×C12711yescharacteristic
359C2×#99—24no—
360C2×#99—24no—
361C2×#99—24no—
362#386—24no—
363#386—24no—
364C2×#95—22no—
365C2×#95—22no—
366#342—22no—
367C25D4×C12712yes—
368C25C23×C12711yescharacteristic
369C22×D4—22no—
370C22×D4—22no—
371C22×D4—22no—
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—22no—
382C22×D4C2×C4×C12714yes—
383C22×D4D4×C12714yes—
384C23×C4—22no—
385C23×C4—21no—
386C23×C4—22no—
387C23×C4—21no—
388C23×C4—22no—
389C23×C4—21no—
390C23×C4—44no—
391C23×C4D4×C12712yes—
392C23×C4D4×C12712yes—
393C23×C4D4×C12712yescomplemented
394#123—28no—
395#123—28no—
396#121—28no—
397#121—28no—
398#120—28no—
399#120—28no—
400C2×C4⋊C4—22no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—28no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—48no—
414C2×C22⋊C4C2×C4×C12712yes—
415C2×C22⋊C4D4×C12712yes—
416C2×C22⋊C4D4×C12714yescomplemented
417C2×C22⋊C4D4×C12712yescomplemented
418#99—216no—
419#95—28no—
420#95—44no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—42no—
428C24—42no—
429C24—44no—
430C24—44no—
431C24C22⋊C4×C12714yescomplemented
432C24C22×C4×C12711yescharacteristic
433C24C2×D4×C12712yes—
434C24C2×D4×C12711yescharacteristic
435C24C2×D4×C12712yes—
436C24C2×D4×C12711yescharacteristic
437C24C2×D4×C12711yescharacteristic
438C24C2×D4×C12711yescharacteristic
439C24C2×D4×C12712yes—
440C24#41×C12712yes—
441C24#41×C12711yescharacteristic
442C24#41×C12711yescharacteristic
443C2×D4—24no—
444C2×D4—24no—
445C2×D4—24no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—24no—
451C2×D4—24no—
452C2×D4—24no—
453C2×D4—24no—
454C2×D4—24no—
455C2×D4—28no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—82no—
473C2×D4—82no—
474C22×C4—24no—
475C22×C4—28no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—44no—
489C22×C4—48no—
490C22×C4—44no—
491C22×C4—42no—
492C22×C4—44no—
493C22×C4—41no—
494C22×C4—42no—
495C22×C4—41no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—44no—
500C22×C4—42no—
501C22×C4—44no—
502C22×C4—42no—
503C22×C4—41no—
504C22×C4—42no—
505C22×C4—41no—
506C22×C4C22⋊C4×C12714yescomplemented
507C22×C4C22⋊C4×C12714yescomplemented
508C4⋊C4—28no—
509C22⋊C4—216no—
510C22⋊C4—24no—
511C22⋊C4—24no—
512C22⋊C4—24no—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—416no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C23—22no—
520C23—24no—
521C23—22no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—41no—
527C23—42no—
528C23—41no—
529C23—42no—
530C23—41no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—44no—
535C23—41no—
536C23—42no—
537C23—44no—
538C23—48no—
539C23—44no—
540C23—44no—
541C23—48no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—44no—
547C23—44no—
548C23—84no—
549C23—82no—
550C23—82no—
551C23—84no—
552C23C2×C22⋊C4×C12712yes—
553C23C2×C22⋊C4×C12711yescharacteristic
554C23C4×D4×C12711yescharacteristic
555C23C4×D4×C12711yescharacteristic
556C23C4×D4×C12712yes—
557C23#120×C12712yes—
558C23#120×C12711yescharacteristic
559C23#120×C12712yes—
560C23#120×C12712yes—
561C23#120×C12711yescharacteristic
562C23#121×C12712yes—
563C23#121×C12712yes—
564C23#121×C12711yescharacteristic
565C23#121×C12711yescharacteristic
566C23#121×C12712yes—
567C23#121×C12712yes—
568C23#121×C12712yes—
569C23#123×C12712yes—
570C23#123×C12712yes—
571C23#124×C12711yescharacteristic
572C23#124×C12711yescharacteristic
573C23#127×C12711yescharacteristic
574C23#127×C12711yescharacteristic
575D4—44no—
576D4—44no—
577D4—44no—
578D4—44no—
579D4—44no—
580D4—44no—
581D4—44no—
582D4—44no—
583D4—88no—
584C2×C4—28no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—44no—
591C2×C4—42no—
592C2×C4—44no—
593C2×C4—48no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—44no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—44no—
603C2×C4—44no—
604C2×C4—44no—
605C2×C4—44no—
606C2×C4—44no—
607C2×C4—42no—
608C2×C4—82no—
609C2×C4—81no—
610C2×C4—81no—
611C2×C4—84no—
612C2×C4—82no—
613C2×C4—84no—
614C22—22no—
615C22—21no—
616C22—21no—
617C22—22no—
618C22—22no—
619C22—21no—
620C22—22no—
621C22—21no—
622C22—22no—
623C22—24no—
624C22—24no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—24no—
629C22—24no—
630C22—41no—
631C22—42no—
632C22—41no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—41no—
639C22—41no—
640C22—48no—
641C22—44no—
642C22—48no—
643C22—84no—
644C22—84no—
645C22—84no—
646C22—82no—
647C22—82no—
648C22—84no—
649C22#379×C12711yescharacteristic
650C22#386×C12712yes—
651C22#386×C12712yes—
652C22#390×C12711yescharacteristic
653C22#390×C12711yescharacteristic
654C22#392×C12712yes—
655C22#392×C12711yescharacteristic
656C22#392×C12711yescharacteristic
657C22#394×C12712yes—
658C22#394×C12711yescharacteristic
659C22#394×C12711yescharacteristic
660C22B(4,𝔽2)×C12712yes—
661C22#458×C12712yes—
662C4—44no—
663C4—44no—
664C4—44no—
665C4—84no—
666C4—82no—
667C2—22no—
668C2—21no—
669C2—22no—
670C2—22no—
671C2—22no—
672C2—21no—
673C2—21no—
674C2—21no—
675C2—84no—
676C2C127×#143811yescharacteristic
677C2C127×#179012yes—
678C2C127×#202111yescharacteristic
679C2C127×#202211yescharacteristic
680C2C127×#204412yes—
subgroupG/H
center, socleC23×C127#120
commutatorC24C22×C4×C127
Frattini, cosocleC25C23×C127
prime radicalC2×#534×C127C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C25×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C127C2semidirect
3. C2×#386×C127C2semidirect
4. C2×#342×C127C2semidirect
5. C127×C22⋊#95C2semidirect
10. #534×C127C4semidirect
52. C23×C4×C127D4semidirect
75. C2×C22⋊C4×C127D4semidirect
76. C2×C22⋊C4×C127D4semidirect
90. C24×C127C22⋊C4semidirect
165. C22×C4×C127C22⋊C4semidirect
166. C22×C4×C127C22⋊C4semidirect
326. #10995C127direct (N × H)
342. C22×#99C2×C127semidirect
343. C2×#386C2×C127semidirect
344. C2×#342C2×C127semidirect
345. C22⋊#95C2×C127semidirect
346. C127#10995direct (N × H)
351. #534C4×C127semidirect
393. C23×C4D4×C127semidirect
416. C2×C22⋊C4D4×C127semidirect
417. C2×C22⋊C4D4×C127semidirect
431. C24C22⋊C4×C127semidirect
506. C22×C4C22⋊C4×C127semidirect
507. C22×C4C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#534×C1272
C22×#99×C1272
C2×#386×C1272
C2×#342×C1272
C127×C22⋊#952
#10995127