Finite Group Databasebeta

← C127×#15267 #44578940

Subgroups — C127×#15267 #44578940

Order 32512.

4234 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C127C212yesmaximal, complemented
2C2×#394×C127C212yesmaximal, complemented
3C2×#392×C127C212yesmaximal, complemented
4C2×#392×C127C211yesmaximal, characteristic, complemented
5C2×#390×C127C212yesmaximal, complemented
6C2×#379×C127C211yesmaximal, characteristic, complemented
7C127×#1439C212yesmaximal, complemented
8C127×#1438C212yesmaximal, complemented
9C127×#1437C211yesmaximal, characteristic, complemented
10C26×C127C2211yescharacteristic
11C23×D4×C127C2212yes—
12C23×D4×C127C2212yes—
13C23×D4×C127C2212yes—
14C23×D4×C127C2211yescharacteristic, complemented
15C2×#120×C127—28no—
16C2×#120×C127—28no—
17C2×#120×C127—28no—
18C22×C4⋊C4×C127C2212yescomplemented
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2212yescomplemented
27C22×C22⋊C4×C127C2212yescomplemented
28C22×C22⋊C4×C127C2212yescomplemented
29C22×C42×C127C2211yescharacteristic, complemented
30#394×C127—28no—
31#392×C127—28no—
32#392×C127—24no—
33#390×C127—28no—
34#379×C127—24no—
35C2×#95×C127C2212yescomplemented
36C2×#95×C127C2211yescharacteristic, complemented
37C2×#95×C127C2212yescomplemented
38C2×#95×C127C2211yescharacteristic, complemented
39C25×C127—24no—
40C25×C127—24no—
41C25×C127—24no—
42C25×C127—22no—
43C25×C127—24no—
44C25×C127—41no—
45C25×C127—41no—
46C25×C127—42no—
47C25×C127—42no—
48C25×C127C2312yes—
49C25×C127C2311yescharacteristic
50C25×C127C2312yes—
51C22×D4×C127—24no—
52C22×D4×C127—24no—
53C22×D4×C127—24no—
54C22×D4×C127—24no—
55C22×D4×C127—24no—
56C22×D4×C127—24no—
57C22×D4×C127—24no—
58C22×D4×C127—24no—
59C22×D4×C127—24no—
60C22×D4×C127—24no—
61C22×D4×C127—24no—
62C22×D4×C127—24no—
63C22×D4×C127—24no—
64C22×D4×C127—24no—
65C22×D4×C127—24no—
66C22×D4×C127—22no—
67C22×D4×C127—42no—
68C22×D4×C127—42no—
69C22×D4×C127—42no—
70C22×D4×C127—42no—
71C22×D4×C127—42no—
72C22×D4×C127—42no—
73C22×D4×C127—42no—
74C22×D4×C127—41no—
75C22×D4×C127—41no—
76C22×D4×C127D418yescomplemented
77C23×C4×C127C2312yes—
78C23×C4×C127C2311yescharacteristic
79C23×C4×C127C2311yescharacteristic
80C23×C4×C127C2312yes—
81C23×C4×C127C2312yes—
82C23×C4×C127C2312yes—
83#120×C127—264no—
84C2×C4⋊C4×C127—24no—
85C2×C4⋊C4×C127—24no—
86C2×C4⋊C4×C127—42no—
87C2×C22⋊C4×C127—24no—
88C2×C22⋊C4×C127—24no—
89C2×C22⋊C4×C127—24no—
90C2×C22⋊C4×C127—24no—
91C2×C22⋊C4×C127—24no—
92C2×C22⋊C4×C127—24no—
93C2×C22⋊C4×C127—24no—
94C2×C22⋊C4×C127—22no—
95C2×C22⋊C4×C127—24no—
96C2×C22⋊C4×C127—24no—
97C2×C22⋊C4×C127—24no—
98C2×C22⋊C4×C127—24no—
99C2×C22⋊C4×C127—24no—
100C2×C22⋊C4×C127—24no—
101C2×C22⋊C4×C127—24no—
102C2×C22⋊C4×C127—24no—
103C2×C22⋊C4×C127—24no—
104C2×C22⋊C4×C127—24no—
105C2×C22⋊C4×C127—24no—
106C2×C22⋊C4×C127—24no—
107C2×C22⋊C4×C127—41no—
108C2×C22⋊C4×C127—41no—
109C2×C22⋊C4×C127—42no—
110C2×C22⋊C4×C127—42no—
111C2×C22⋊C4×C127—42no—
112C2×C22⋊C4×C127—42no—
113C2×C22⋊C4×C127D418yescomplemented
114C2×C22⋊C4×C127D418yescomplemented
115C2×C22⋊C4×C127D414yescomplemented
116C2×C42×C127—24no—
117C2×C42×C127—41no—
118#95×C127—22no—
119#95×C127—24no—
120#95×C127—24no—
121#95×C127—41no—
122C24×C127—22no—
123C24×C127—22no—
124C24×C127—22no—
125C24×C127—22no—
126C24×C127—22no—
127C24×C127—22no—
128C24×C127—22no—
129C24×C127—22no—
130C24×C127—22no—
131C24×C127—21no—
132C24×C127—21no—
133C24×C127—22no—
134C24×C127—22no—
135C24×C127—22no—
136C24×C127—22no—
137C24×C127—22no—
138C24×C127—22no—
139C24×C127—22no—
140C24×C127—22no—
141C24×C127—216no—
142C24×C127—28no—
143C24×C127—22no—
144C24×C127—22no—
145C24×C127—22no—
146C24×C127—22no—
147C24×C127—22no—
148C24×C127—22no—
149C24×C127—22no—
150C24×C127—22no—
151C24×C127—22no—
152C24×C127—22no—
153C24×C127—22no—
154C24×C127—22no—
155C24×C127—22no—
156C24×C127—22no—
157C24×C127—48no—
158C24×C127—48no—
159C24×C127—44no—
160C24×C127—48no—
161C24×C127—44no—
162C24×C127—48no—
163C24×C127—48no—
164C24×C127—48no—
165C24×C127—48no—
166C24×C127—48no—
167C24×C127—44no—
168C24×C127—48no—
169C24×C127—48no—
170C24×C127—48no—
171C24×C127—48no—
172C24×C127—44no—
173C24×C127—44no—
174C24×C127—48no—
175C24×C127—44no—
176C24×C127C2×D414yes—
177C24×C127C2×D414yes—
178C24×C127C2×D414yes—
179C24×C127C2×D414yes—
180C24×C127C2×D412yes—
181C24×C127#4114yes—
182C24×C127C2411yescharacteristic
183C2×D4×C127—216no—
184C2×D4×C127—216no—
185C2×D4×C127—216no—
186C2×D4×C127—216no—
187C2×D4×C127—48no—
188C2×D4×C127—48no—
189C2×D4×C127—48no—
190C2×D4×C127—48no—
191C2×D4×C127—48no—
192C2×D4×C127—48no—
193C2×D4×C127—48no—
194C2×D4×C127—48no—
195C2×D4×C127—48no—
196C2×D4×C127—48no—
197C2×D4×C127—44no—
198C2×D4×C127—48no—
199C2×D4×C127—48no—
200C2×D4×C127—48no—
201C2×D4×C127—44no—
202C2×D4×C127—48no—
203C2×D4×C127—48no—
204C2×D4×C127—48no—
205C2×D4×C127—48no—
206C2×D4×C127—44no—
207C2×D4×C127—48no—
208C2×D4×C127—48no—
209C22×C4×C127—22no—
210C22×C4×C127—22no—
211C22×C4×C127—22no—
212C22×C4×C127—22no—
213C22×C4×C127—22no—
214C22×C4×C127—22no—
215C22×C4×C127—22no—
216C22×C4×C127—22no—
217C22×C4×C127—22no—
218C22×C4×C127—22no—
219C22×C4×C127—22no—
220C22×C4×C127—22no—
221C22×C4×C127—22no—
222C22×C4×C127—22no—
223C22×C4×C127—21no—
224C22×C4×C127—22no—
225C22×C4×C127—21no—
226C22×C4×C127—22no—
227C22×C4×C127—21no—
228C22×C4×C127—21no—
229C22×C4×C127—22no—
230C22×C4×C127—22no—
231C22×C4×C127—22no—
232C22×C4×C127—22no—
233C22×C4×C127—22no—
234C22×C4×C127—22no—
235C22×C4×C127—22no—
236C22×C4×C127—22no—
237C22×C4×C127—22no—
238C22×C4×C127—22no—
239C22×C4×C127—22no—
240C22×C4×C127C2×D414yes—
241C22×C4×C127C2×D412yes—
242C22×C4×C127C2×D412yes—
243C22×C4×C127C2×D414yes—
244C22×C4×C127C2×D414yes—
245C22×C4×C127C2×D414yes—
246C22×C4×C127C2×D414yes—
247C4⋊C4×C127—48no—
248C22⋊C4×C127—216no—
249C22⋊C4×C127—216no—
250C22⋊C4×C127—216no—
251C22⋊C4×C127—44no—
252C22⋊C4×C127—48no—
253C22⋊C4×C127—48no—
254C22⋊C4×C127—48no—
255C22⋊C4×C127—48no—
256C22⋊C4×C127—44no—
257C22⋊C4×C127—48no—
258C42×C127—44no—
259C23×C127—24no—
260C23×C127—24no—
261C23×C127—24no—
262C23×C127—22no—
263C23×C127—24no—
264C23×C127—22no—
265C23×C127—24no—
266C23×C127—24no—
267C23×C127—24no—
268C23×C127—24no—
269C23×C127—24no—
270C23×C127—24no—
271C23×C127—24no—
272C23×C127—24no—
273C23×C127—24no—
274C23×C127—24no—
275C23×C127—24no—
276C23×C127—24no—
277C23×C127—24no—
278C23×C127—24no—
279C23×C127—24no—
280C23×C127—24no—
281C23×C127—24no—
282C23×C127—24no—
283C23×C127—24no—
284C23×C127—24no—
285C23×C127—24no—
286C23×C127—24no—
287C23×C127—24no—
288C23×C127—24no—
289C23×C127—24no—
290C23×C127—24no—
291C23×C127—24no—
292C23×C127—24no—
293C23×C127—24no—
294C23×C127—432no—
295C23×C127—432no—
296C23×C127—432no—
297C23×C127—432no—
298C23×C127—416no—
299C23×C127—416no—
300C23×C127—432no—
301C23×C127—432no—
302C23×C127—416no—
303C23×C127—42no—
304C23×C127—42no—
305C23×C127—42no—
306C23×C127—42no—
307C23×C127—42no—
308C23×C127—42no—
309C23×C127—42no—
310C23×C127—42no—
311C23×C127—42no—
312C23×C127—42no—
313C23×C127—42no—
314C23×C127—42no—
315C23×C127—41no—
316C23×C127—42no—
317C23×C127—41no—
318C23×C127—42no—
319C23×C127—42no—
320C23×C127—42no—
321C23×C127—42no—
322C23×C127—42no—
323C23×C127—42no—
324C23×C127—42no—
325C23×C127—41no—
326C23×C127—42no—
327C23×C127—41no—
328C23×C127—42no—
329C23×C127—42no—
330C23×C127—42no—
331C23×C127—42no—
332C23×C127—42no—
333C23×C127—42no—
334C23×C127—42no—
335C23×C127—42no—
336C23×C127—42no—
337C23×C127—42no—
338C23×C127—42no—
339C23×C127—42no—
340C23×C127—42no—
341C23×C127—42no—
342C23×C127—42no—
343C23×C127—42no—
344C23×C127—42no—
345C23×C127—42no—
346C23×C127—42no—
347C23×C127—42no—
348C23×C127—42no—
349C23×C127—42no—
350C23×C127—42no—
351C23×C127—42no—
352C23×C127—42no—
353C23×C127—42no—
354C23×C127—42no—
355C23×C127—42no—
356C23×C127—42no—
357C23×C127#12118yes—
358C23×C127#12714yes—
359C23×C127C22×D412yes—
360C23×C127C22×D412yes—
361C23×C127C22×D412yes—
362C23×C127C22×D411yescharacteristic
363C23×C127C2×#4112yes—
364C23×C127H(5,𝔽2)11yescharacteristic
365C23×C127H(5,𝔽2)11yescharacteristic
366C23×C127H(5,𝔽2)12yes—
367C23×C127H(5,𝔽2)12yes—
368D4×C127—432no—
369D4×C127—432no—
370D4×C127—432no—
371D4×C127—416no—
372C2×C4×C127—24no—
373C2×C4×C127—24no—
374C2×C4×C127—24no—
375C2×C4×C127—24no—
376C2×C4×C127—24no—
377C2×C4×C127—24no—
378C2×C4×C127—24no—
379C2×C4×C127—24no—
380C2×C4×C127—22no—
381C2×C4×C127—22no—
382C2×C4×C127—24no—
383C2×C4×C127—24no—
384C2×C4×C127—24no—
385C2×C4×C127—24no—
386C2×C4×C127—24no—
387C2×C4×C127—24no—
388C2×C4×C127—42no—
389C2×C4×C127—42no—
390C2×C4×C127—42no—
391C2×C4×C127—42no—
392C2×C4×C127—42no—
393C2×C4×C127—42no—
394C2×C4×C127—41no—
395C2×C4×C127—42no—
396C2×C4×C127—41no—
397C2×C4×C127—42no—
398C2×C4×C127—42no—
399C2×C4×C127—42no—
400C2×C4×C127—41no—
401C2×C4×C127—41no—
402C2×C4×C127—42no—
403C2×C4×C127—42no—
404C2×C4×C127—42no—
405C2×C4×C127—42no—
406C2×C4×C127—42no—
407C2×C4×C127—42no—
408C2×C4×C127—42no—
409C2×C4×C127#12018yescomplemented
410C22×C127—28no—
411C22×C127—28no—
412C22×C127—28no—
413C22×C127—28no—
414C22×C127—24no—
415C22×C127—464no—
416C22×C127—44no—
417C22×C127—44no—
418C22×C127—44no—
419C22×C127—44no—
420C22×C127—42no—
421C22×C127—44no—
422C22×C127—44no—
423C22×C127—44no—
424C22×C127—44no—
425C22×C127—44no—
426C22×C127—44no—
427C22×C127—44no—
428C22×C127—42no—
429C22×C127—44no—
430C22×C127—44no—
431C22×C127—44no—
432C22×C127—44no—
433C22×C127—44no—
434C22×C127—44no—
435C22×C127—44no—
436C22×C127—44no—
437C22×C127—44no—
438C22×C127—44no—
439C22×C127—44no—
440C22×C127—44no—
441C22×C127—44no—
442C22×C127—82no—
443C22×C127—82no—
444C22×C127—82no—
445C22×C127—82no—
446C22×C127—82no—
447C22×C127—82no—
448C22×C127—82no—
449C22×C127—82no—
450C22×C127C2×#12012yes—
451C22×C127C2×#12112yes—
452C22×C127#52511yescharacteristic
453C22×C127C2×#12711yescharacteristic
454C22×C127#53412yes—
455C22×C127#53411yescharacteristic
456C22×C127#53512yes—
457C22×C127#53512yes—
458C22×C127#53812yes—
459C22×C127D4211yescharacteristic
460C22×C127D4212yes—
461C22×C127D4211yescharacteristic
462C22×C127D4212yes—
463C22×C127D4212yes—
464C22×C127D4212yes—
465C22×C127#54612yes—
466C22×C127#54612yes—
467C22×C127#54612yes—
468C22×C127#54612yes—
469C22×C127#56011yescharacteristic
470C22×C127H(3,𝔽4)11yescharacteristic
471C4×C127—28no—
472C4×C127—44no—
473C4×C127—42no—
474C4×C127—42no—
475C4×C127—44no—
476C4×C127—82no—
477#15267C12711yesmaximal, characteristic, direct product factor, Sylow
478C2×C127—48no—
479C2×C127—44no—
480C2×C127—84no—
481C2×C127#240812yes—
482C2×C127#241012yes—
483C2×C127#242412yes—
484C2×C127#243312yes—
485C2×C127#253911yescharacteristic
486C2×C127#266911yescharacteristic
487C2×C127#267012yes—
488C2×C127#267812yes—
489C2×C127#267911yescharacteristic
490C22×#120C2×C12712yescomplemented
491C2×#394C2×C12712yescomplemented
492C2×#392C2×C12712yescomplemented
493C2×#392C2×C12711yescharacteristic, complemented
494C2×#390C2×C12712yescomplemented
495C2×#379C2×C12711yescharacteristic, complemented
496#1439C2×C12712yescomplemented
497#1438C2×C12712yescomplemented
498#1437C2×C12711yescharacteristic, complemented
499C127#1526711yescharacteristic, direct product factor, Sylow
500C26C22×C12711yescharacteristic
501C23×D4C22×C12712yes—
502C23×D4C22×C12712yes—
503C23×D4C22×C12712yes—
504C23×D4C22×C12711yescharacteristic, complemented
505C2×#120—28no—
506C2×#120—28no—
507C2×#120—28no—
508C22×C4⋊C4C22×C12712yescomplemented
509C22×C22⋊C4C22×C12711yescharacteristic
510C22×C22⋊C4C22×C12712yes—
511C22×C22⋊C4C22×C12712yes—
512C22×C22⋊C4C22×C12712yes—
513C22×C22⋊C4C22×C12712yes—
514C22×C22⋊C4C22×C12712yes—
515C22×C22⋊C4C22×C12711yescharacteristic
516C22×C22⋊C4C22×C12712yescomplemented
517C22×C22⋊C4C22×C12712yescomplemented
518C22×C22⋊C4C22×C12712yescomplemented
519C22×C42C22×C12711yescharacteristic, complemented
520#394—28no—
521#392—28no—
522#392—24no—
523#390—28no—
524#379—24no—
525C2×#95C22×C12712yescomplemented
526C2×#95C22×C12711yescharacteristic, complemented
527C2×#95C22×C12712yescomplemented
528C2×#95C22×C12711yescharacteristic, complemented
529C25—24no—
530C25—24no—
531C25—24no—
532C25—22no—
533C25—24no—
534C25—41no—
535C25—41no—
536C25—42no—
537C25—42no—
538C25C23×C12712yes—
539C25C23×C12711yescharacteristic
540C25C23×C12712yes—
541C22×D4—24no—
542C22×D4—24no—
543C22×D4—24no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4—24no—
554C22×D4—24no—
555C22×D4—24no—
556C22×D4—22no—
557C22×D4—42no—
558C22×D4—42no—
559C22×D4—42no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—42no—
564C22×D4—41no—
565C22×D4—41no—
566C22×D4D4×C12718yescomplemented
567C23×C4C23×C12712yes—
568C23×C4C23×C12711yescharacteristic
569C23×C4C23×C12711yescharacteristic
570C23×C4C23×C12712yes—
571C23×C4C23×C12712yes—
572C23×C4C23×C12712yes—
573#120—264no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—42no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—24no—
582C2×C22⋊C4—24no—
583C2×C22⋊C4—24no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—24no—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—42no—
600C2×C22⋊C4—42no—
601C2×C22⋊C4—42no—
602C2×C22⋊C4—42no—
603C2×C22⋊C4D4×C12718yescomplemented
604C2×C22⋊C4D4×C12718yescomplemented
605C2×C22⋊C4D4×C12714yescomplemented
606C2×C42—24no—
607C2×C42—41no—
608#95—22no—
609#95—24no—
610#95—24no—
611#95—41no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—21no—
622C24—21no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—216no—
632C24—28no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—48no—
648C24—48no—
649C24—44no—
650C24—48no—
651C24—44no—
652C24—48no—
653C24—48no—
654C24—48no—
655C24—48no—
656C24—48no—
657C24—44no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—44no—
663C24—44no—
664C24—48no—
665C24—44no—
666C24C2×D4×C12714yes—
667C24C2×D4×C12714yes—
668C24C2×D4×C12714yes—
669C24C2×D4×C12714yes—
670C24C2×D4×C12712yes—
671C24#41×C12714yes—
672C24C24×C12711yescharacteristic
673C2×D4—216no—
674C2×D4—216no—
675C2×D4—216no—
676C2×D4—216no—
677C2×D4—48no—
678C2×D4—48no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—48no—
691C2×D4—44no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—44no—
697C2×D4—48no—
698C2×D4—48no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4C2×D4×C12714yes—
731C22×C4C2×D4×C12712yes—
732C22×C4C2×D4×C12712yes—
733C22×C4C2×D4×C12714yes—
734C22×C4C2×D4×C12714yes—
735C22×C4C2×D4×C12714yes—
736C22×C4C2×D4×C12714yes—
737C4⋊C4—48no—
738C22⋊C4—216no—
739C22⋊C4—216no—
740C22⋊C4—216no—
741C22⋊C4—44no—
742C22⋊C4—48no—
743C22⋊C4—48no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—44no—
747C22⋊C4—48no—
748C42—44no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—22no—
753C23—24no—
754C23—22no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—24no—
766C23—24no—
767C23—24no—
768C23—24no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—432no—
785C23—432no—
786C23—432no—
787C23—432no—
788C23—416no—
789C23—416no—
790C23—432no—
791C23—432no—
792C23—416no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—41no—
806C23—42no—
807C23—41no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—41no—
816C23—42no—
817C23—41no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23#121×C12718yes—
848C23#127×C12714yes—
849C23C22×D4×C12712yes—
850C23C22×D4×C12712yes—
851C23C22×D4×C12712yes—
852C23C22×D4×C12711yescharacteristic
853C23C2×#41×C12712yes—
854C23H(5,𝔽2)×C12711yescharacteristic
855C23H(5,𝔽2)×C12711yescharacteristic
856C23H(5,𝔽2)×C12712yes—
857C23H(5,𝔽2)×C12712yes—
858D4—432no—
859D4—432no—
860D4—432no—
861D4—416no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—41no—
885C2×C4—42no—
886C2×C4—41no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4#120×C12718yescomplemented
900C22—28no—
901C22—28no—
902C22—28no—
903C22—28no—
904C22—24no—
905C22—464no—
906C22—44no—
907C22—44no—
908C22—44no—
909C22—44no—
910C22—42no—
911C22—44no—
912C22—44no—
913C22—44no—
914C22—44no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22—42no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×#120×C12712yes—
941C22C2×#121×C12712yes—
942C22#525×C12711yescharacteristic
943C22C2×#127×C12711yescharacteristic
944C22#534×C12712yes—
945C22#534×C12711yescharacteristic
946C22#535×C12712yes—
947C22#535×C12712yes—
948C22#538×C12712yes—
949C22D42×C12711yescharacteristic
950C22D42×C12712yes—
951C22D42×C12711yescharacteristic
952C22D42×C12712yes—
953C22D42×C12712yes—
954C22D42×C12712yes—
955C22#546×C12712yes—
956C22#546×C12712yes—
957C22#546×C12712yes—
958C22#546×C12712yes—
959C22#560×C12711yescharacteristic
960C22H(3,𝔽4)×C12711yescharacteristic
961C4—28no—
962C4—44no—
963C4—42no—
964C4—42no—
965C4—44no—
966C4—82no—
967C2—48no—
968C2—44no—
969C2—84no—
970C2C127×#240812yes—
971C2C127×#241012yes—
972C2C127×#242412yes—
973C2C127×#243312yes—
974C2C127×#253911yescharacteristic
975C2C127×#266911yescharacteristic
976C2C127×#267012yes—
977C2C127×#267812yes—
978C2C127×#267911yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#120×C127C2semidirect
2. C2×#394×C127C2semidirect
3. C2×#392×C127C2semidirect
4. C2×#392×C127C2semidirect
5. C2×#390×C127C2semidirect
6. C2×#379×C127C2semidirect
7. C127×#1439C2semidirect
8. C127×#1438C2semidirect
9. C127×#1437C2semidirect
14. C23×D4×C127C22semidirect
18. C22×C4⋊C4×C127C22semidirect
26. C22×C22⋊C4×C127C22semidirect
27. C22×C22⋊C4×C127C22semidirect
28. C22×C22⋊C4×C127C22semidirect
29. C22×C42×C127C22semidirect
35. C2×#95×C127C22semidirect
36. C2×#95×C127C22semidirect
37. C2×#95×C127C22semidirect
38. C2×#95×C127C22semidirect
76. C22×D4×C127D4semidirect
113. C2×C22⋊C4×C127D4semidirect
114. C2×C22⋊C4×C127D4semidirect
115. C2×C22⋊C4×C127D4semidirect
409. C2×C4×C127#120semidirect
477. #15267C127direct (N × H)
490. C22×#120C2×C127semidirect
491. C2×#394C2×C127semidirect
492. C2×#392C2×C127semidirect
493. C2×#392C2×C127semidirect
494. C2×#390C2×C127semidirect
495. C2×#379C2×C127semidirect
496. #1439C2×C127semidirect
497. #1438C2×C127semidirect
498. #1437C2×C127semidirect
499. C127#15267direct (N × H)
504. C23×D4C22×C127semidirect
508. C22×C4⋊C4C22×C127semidirect
516. C22×C22⋊C4C22×C127semidirect
517. C22×C22⋊C4C22×C127semidirect
518. C22×C22⋊C4C22×C127semidirect
519. C22×C42C22×C127semidirect
525. C2×#95C22×C127semidirect
526. C2×#95C22×C127semidirect
527. C2×#95C22×C127semidirect
528. C2×#95C22×C127semidirect
566. C22×D4D4×C127semidirect
603. C2×C22⋊C4D4×C127semidirect
604. C2×C22⋊C4D4×C127semidirect
605. C2×C22⋊C4D4×C127semidirect
899. C2×C4#120×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1272
C2×#394×C1272
C2×#392×C1272
C2×#390×C1272
C2×#379×C1272
C127×#14392
C127×#14382
C127×#14372
#15267127