Finite Group Databasebeta

← C127×#21582 #44585255

Subgroups — C127×#21582 #44585255

Order 32512.

960 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C127C211yesmaximal, characteristic
2C4×#121×C127C211yesmaximal, characteristic
3C4×#117×C127C211yesmaximal, characteristic, complemented
4C127×#1926C211yesmaximal, characteristic, complemented
5C127×#1925C211yesmaximal, characteristic, complemented
6C127×#1919C211yesmaximal, characteristic, complemented
7C127×#1918C211yesmaximal, characteristic, complemented
8C127×#1875C211yesmaximal, characteristic
9C127×#1854C211yesmaximal, characteristic, complemented
10C127×#1825C211yesmaximal, characteristic, complemented
11C127×#1776C211yesmaximal, characteristic, complemented
12C127×#1776C211yesmaximal, characteristic, complemented
13C127×#1762C211yesmaximal, characteristic, complemented
14C127×#1762C211yesmaximal, characteristic, complemented
15C127×#1749C211yesmaximal, characteristic, complemented
16C2×#121×C127C2211yescharacteristic
17C2×C4×D4×C127—21no—
18C2×C4×D4×C127C2211yescharacteristic
19C2×#117×C127C2211yescharacteristic
20C2×#117×C127C2211yescharacteristic
21C22×C42×C127C2211yescharacteristic
22#482×C127C418yescomplemented
23C2×#107×C127C2211yescharacteristic
24C2×#107×C127C2211yescharacteristic
25C2×#106×C127C2211yescharacteristic
26C2×#106×C127C2211yescharacteristic
27C2×#102×C127C2211yescharacteristic
28C2×#102×C127C2211yescharacteristic
29C2×#102×C127C2211yescharacteristic
30C2×#102×C127C2211yescharacteristic
31C2×C22⋊C8×C127C2211yescharacteristic
32C2×C22⋊C8×C127C2211yescharacteristic
33C2×#97×C127C2211yescharacteristic
34C2×#97×C127C2211yescharacteristic
35#390×C127C2211yescharacteristic
36#389×C127C2211yescharacteristic
37#388×C127—21no—
38#386×C127—21no—
39#380×C127C2211yescharacteristic
40C4×C4⋊C4×C127C2211yescharacteristic
41C4×C4⋊C4×C127C2211yescharacteristic
42C4×C4⋊C4×C127C2211yescharacteristic
43C4×C4⋊C4×C127C2211yescharacteristic
44C4×C4⋊C4×C127C2211yescharacteristic
45C4×C22⋊C4×C127—21no—
46C4×C22⋊C4×C127—21no—
47C4×C22⋊C4×C127—21no—
48#376×C127—21no—
49C43×C127—21no—
50#340×C127C2211yescharacteristic
51#340×C127C2211yescharacteristic
52#340×C127C2211yescharacteristic
53#340×C127C2211yescharacteristic
54#340×C127C2211yescharacteristic
55#340×C127C2211yescharacteristic
56#340×C127C2211yescharacteristic
57#340×C127C2211yescharacteristic
58#336×C127C2211yescharacteristic
59#336×C127C2211yescharacteristic
60C22×D4×C127—21no—
61C22×D4×C127C2311yescharacteristic
62C23×C4×C127—21no—
63C23×C4×C127D411yescharacteristic
64C23×C4×C127D411yescharacteristic
65C23×C4×C127C2311yescharacteristic
66C22×C8×C127C2311yescharacteristic
67C22×C8×C127C2311yescharacteristic
68C22×C8×C127C2311yescharacteristic
69C22×C8×C127C2311yescharacteristic
70#121×C127—22no—
71#121×C127C2×C414yes—
72C4×D4×C127—22no—
73C4×D4×C127—22no—
74C4×D4×C127—44no—
75#117×C127—22no—
76#117×C127—22no—
77#117×C127—22no—
78#117×C127C2×C414yescomplemented
79C2×C4⋊C4×C127—21no—
80C2×C4⋊C4×C127C2311yescharacteristic
81C2×C4⋊C4×C127C2311yescharacteristic
82C2×C4⋊C4×C127C2311yescharacteristic
83C2×C4⋊C4×C127C2311yescharacteristic
84C2×C4⋊C4×C127C2311yescharacteristic
85C2×C4⋊C4×C127C2311yescharacteristic
86C2×C4⋊C4×C127C2311yescharacteristic
87C2×C22⋊C4×C127—21no—
88C2×C22⋊C4×C127—21no—
89C2×C22⋊C4×C127—21no—
90C2×C22⋊C4×C127—21no—
91C2×C22⋊C4×C127—21no—
92C2×C22⋊C4×C127—21no—
93C2×C22⋊C4×C127—21no—
94C2×C42×C127—21no—
95C2×C42×C127—21no—
96C2×C42×C127—22no—
97C2×C42×C127—22no—
98C2×C42×C127—21no—
99C2×C42×C127—21no—
100C2×C42×C127—21no—
101C2×C42×C127—21no—
102C2×C42×C127—21no—
103C2×C42×C127D411yescharacteristic
104C2×C42×C127D411yescharacteristic
105C2×C42×C127C2311yescharacteristic
106C2×C42×C127C2311yescharacteristic
107#107×C127—22no—
108#107×C127C2×C414yescomplemented
109#106×C127—22no—
110#106×C127C2×C414yescomplemented
111#102×C127—22no—
112#102×C127—22no—
113#102×C127C2×C414yescomplemented
114#102×C127C2×C414yescomplemented
115C22⋊C8×C127—22no—
116C22⋊C8×C127C2×C414yescomplemented
117#97×C127—22no—
118#97×C127—22no—
119#95×C127—21no—
120#95×C127—21no—
121#95×C127—21no—
122#95×C127—21no—
123#95×C127—21no—
124#95×C127—21no—
125#95×C127—21no—
126C24×C127—21no—
127C24×C127C2×D411yescharacteristic
128C2×D4×C127—24no—
129C2×D4×C127—21no—
130C2×D4×C127—21no—
131C2×D4×C127—21no—
132C2×D4×C127—21no—
133C2×D4×C127—21no—
134C2×D4×C127—42no—
135C2×D4×C127—42no—
136C2×D4×C127C22×C412yes—
137C22×C4×C127—21no—
138C22×C4×C127—21no—
139C22×C4×C127—21no—
140C22×C4×C127—21no—
141C22×C4×C127—21no—
142C22×C4×C127—21no—
143C22×C4×C127—21no—
144C22×C4×C127—21no—
145C22×C4×C127—21no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—21no—
150C22×C4×C127—21no—
151C22×C4×C127—41no—
152C22×C4×C127—41no—
153C22×C4×C127—41no—
154C22×C4×C127—42no—
155C22×C4×C127—42no—
156C22×C4×C127—42no—
157C22×C4×C127C22×C412yes—
158C22×C4×C127C2×D411yescharacteristic
159C22×C4×C127C2×D411yescharacteristic
160C22×C4×C127C2×D411yescharacteristic
161C22×C4×C127C2×D411yescharacteristic
162C22×C4×C127C2×D411yescharacteristic
163C22×C4×C127#4112yes—
164C22×C4×C127C2411yescharacteristic
165C2×C8×C127—21no—
166C2×C8×C127—21no—
167C2×C8×C127—21no—
168C2×C8×C127—21no—
169C2×C8×C127—21no—
170C2×C8×C127—21no—
171C2×C8×C127—21no—
172C2×C8×C127—21no—
173C2×C8×C127—21no—
174C2×C8×C127—21no—
175C2×C8×C127C22×C412yes—
176C2×C8×C127C22×C412yes—
177C4⋊C4×C127—21no—
178C4⋊C4×C127—21no—
179C4⋊C4×C127—21no—
180C4⋊C4×C127—21no—
181C4⋊C4×C127—21no—
182C4⋊C4×C127—21no—
183C4⋊C4×C127—21no—
184C4⋊C4×C127—21no—
185C4⋊C4×C127—21no—
186C4⋊C4×C127—42no—
187C4⋊C4×C127C22×C412yes—
188C4⋊C4×C127C22×C412yes—
189C4⋊C4×C127C22×C412yes—
190C4⋊C4×C127#4112yes—
191C4⋊C4×C127#4112yes—
192C22⋊C4×C127—24no—
193C22⋊C4×C127—24no—
194C22⋊C4×C127—24no—
195C22⋊C4×C127—42no—
196C22⋊C4×C127—42no—
197C22⋊C4×C127—42no—
198C22⋊C4×C127—42no—
199C42×C127—24no—
200C42×C127—24no—
201C42×C127—22no—
202C42×C127—22no—
203C42×C127—21no—
204C42×C127—21no—
205C42×C127—42no—
206C42×C127—42no—
207C42×C127—42no—
208C42×C127—42no—
209C42×C127—42no—
210C42×C127#4112yes—
211C42×C127#4112yes—
212C23×C127—21no—
213C23×C127—21no—
214C23×C127—21no—
215C23×C127—21no—
216C23×C127—21no—
217C23×C127—21no—
218C23×C127—22no—
219C23×C127—41no—
220C23×C127—41no—
221C23×C127—41no—
222C23×C127—41no—
223C23×C127—41no—
224C23×C127—41no—
225C23×C127C4×D412yes—
226C23×C127C22×D411yescharacteristic
227D4×C127—22no—
228D4×C127—22no—
229D4×C127—48no—
230D4×C127—41no—
231D4×C127—41no—
232C2×C4×C127—21no—
233C2×C4×C127—21no—
234C2×C4×C127—21no—
235C2×C4×C127—21no—
236C2×C4×C127—21no—
237C2×C4×C127—21no—
238C2×C4×C127—21no—
239C2×C4×C127—21no—
240C2×C4×C127—22no—
241C2×C4×C127—22no—
242C2×C4×C127—22no—
243C2×C4×C127—22no—
244C2×C4×C127—22no—
245C2×C4×C127—22no—
246C2×C4×C127—22no—
247C2×C4×C127—21no—
248C2×C4×C127—22no—
249C2×C4×C127—22no—
250C2×C4×C127—21no—
251C2×C4×C127—21no—
252C2×C4×C127—44no—
253C2×C4×C127—44no—
254C2×C4×C127—41no—
255C2×C4×C127—41no—
256C2×C4×C127—41no—
257C2×C4×C127—41no—
258C2×C4×C127—41no—
259C2×C4×C127—41no—
260C2×C4×C127—41no—
261C2×C4×C127—41no—
262C2×C4×C127—41no—
263C2×C4×C127—41no—
264C2×C4×C127—41no—
265C2×C4×C127—41no—
266C2×C4×C127—41no—
267C2×C4×C127—41no—
268C2×C4×C127—41no—
269C2×C4×C127—41no—
270C2×C4×C127—84no—
271C2×C4×C127C4×D412yes—
272C2×C4×C127#12312yes—
273C2×C4×C127#12312yes—
274C2×C4×C127AGL(1,ℤ/8)12yes—
275C2×C4×C127C23×C411yescharacteristic
276C2×C4×C127C2×#4111yescharacteristic
277C2×C4×C127C2×#4111yescharacteristic
278C2×C4×C127C2×#4111yescharacteristic
279C2×C4×C127C2×#4111yescharacteristic
280C2×C4×C127C2×#4111yescharacteristic
281C8×C127—22no—
282C8×C127—22no—
283C8×C127—41no—
284C8×C127—41no—
285C22×C127—22no—
286C22×C127—22no—
287C22×C127—22no—
288C22×C127—41no—
289C22×C127—41no—
290C22×C127—41no—
291C22×C127—41no—
292C22×C127—42no—
293C22×C127—42no—
294C22×C127—42no—
295C22×C127—81no—
296C22×C127—81no—
297C22×C127—81no—
298C22×C127—81no—
299C22×C127C2×C4×D411yescharacteristic
300C22×C127C2×#12311yescharacteristic
301C22×C127#52511yescharacteristic
302C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
303C22×C127#57511yescharacteristic
304C22×C127#57511yescharacteristic
305C22×C127#57511yescharacteristic
306C4×C127—22no—
307C4×C127—22no—
308C4×C127—22no—
309C4×C127—22no—
310C4×C127—41no—
311C4×C127—42no—
312C4×C127—42no—
313C4×C127—42no—
314C4×C127—42no—
315C4×C127—42no—
316C4×C127—81no—
317C4×C127—81no—
318C4×C127C4×#4111yescharacteristic
319C4×C127C4×#4111yescharacteristic
320C4×C127#52911yescharacteristic
321C4×C127#52911yescharacteristic
322#21582C12711yesmaximal, characteristic, direct product factor, Sylow
323C2×C127—42no—
324C2×C127—82no—
325C2×C127C4×#12311yescharacteristic
326C2×C127#294311yescharacteristic
327C2×C127C4×AGL(1,ℤ/8)11yescharacteristic
328C2×C127#309311yescharacteristic
329C2×C127#309411yescharacteristic
330C2×C127#311111yescharacteristic
331C2×C127#311511yescharacteristic
332C2×#482C2×C12711yescharacteristic
333C4×#121C2×C12711yescharacteristic
334C4×#117C2×C12711yescharacteristic, complemented
335#1926C2×C12711yescharacteristic, complemented
336#1925C2×C12711yescharacteristic, complemented
337#1919C2×C12711yescharacteristic, complemented
338#1918C2×C12711yescharacteristic, complemented
339#1875C2×C12711yescharacteristic
340#1854C2×C12711yescharacteristic, complemented
341#1825C2×C12711yescharacteristic, complemented
342#1776C2×C12711yescharacteristic, complemented
343#1776C2×C12711yescharacteristic, complemented
344#1762C2×C12711yescharacteristic, complemented
345#1762C2×C12711yescharacteristic, complemented
346#1749C2×C12711yescharacteristic, complemented
347C127#2158211yescharacteristic, direct product factor, Sylow
348C2×#121C22×C12711yescharacteristic
349C2×C4×D4—21no—
350C2×C4×D4C22×C12711yescharacteristic
351C2×#117C22×C12711yescharacteristic
352C2×#117C22×C12711yescharacteristic
353C22×C42C22×C12711yescharacteristic
354#482C4×C12718yescomplemented
355C2×#107C22×C12711yescharacteristic
356C2×#107C22×C12711yescharacteristic
357C2×#106C22×C12711yescharacteristic
358C2×#106C22×C12711yescharacteristic
359C2×#102C22×C12711yescharacteristic
360C2×#102C22×C12711yescharacteristic
361C2×#102C22×C12711yescharacteristic
362C2×#102C22×C12711yescharacteristic
363C2×C22⋊C8C22×C12711yescharacteristic
364C2×C22⋊C8C22×C12711yescharacteristic
365C2×#97C22×C12711yescharacteristic
366C2×#97C22×C12711yescharacteristic
367#390C22×C12711yescharacteristic
368#389C22×C12711yescharacteristic
369#388—21no—
370#386—21no—
371#380C22×C12711yescharacteristic
372C4×C4⋊C4C22×C12711yescharacteristic
373C4×C4⋊C4C22×C12711yescharacteristic
374C4×C4⋊C4C22×C12711yescharacteristic
375C4×C4⋊C4C22×C12711yescharacteristic
376C4×C4⋊C4C22×C12711yescharacteristic
377C4×C22⋊C4—21no—
378C4×C22⋊C4—21no—
379C4×C22⋊C4—21no—
380#376—21no—
381C43—21no—
382#340C22×C12711yescharacteristic
383#340C22×C12711yescharacteristic
384#340C22×C12711yescharacteristic
385#340C22×C12711yescharacteristic
386#340C22×C12711yescharacteristic
387#340C22×C12711yescharacteristic
388#340C22×C12711yescharacteristic
389#340C22×C12711yescharacteristic
390#336C22×C12711yescharacteristic
391#336C22×C12711yescharacteristic
392C22×D4—21no—
393C22×D4C23×C12711yescharacteristic
394C23×C4—21no—
395C23×C4D4×C12711yescharacteristic
396C23×C4D4×C12711yescharacteristic
397C23×C4C23×C12711yescharacteristic
398C22×C8C23×C12711yescharacteristic
399C22×C8C23×C12711yescharacteristic
400C22×C8C23×C12711yescharacteristic
401C22×C8C23×C12711yescharacteristic
402#121—22no—
403#121C2×C4×C12714yes—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—44no—
407#117—22no—
408#117—22no—
409#117—22no—
410#117C2×C4×C12714yescomplemented
411C2×C4⋊C4—21no—
412C2×C4⋊C4C23×C12711yescharacteristic
413C2×C4⋊C4C23×C12711yescharacteristic
414C2×C4⋊C4C23×C12711yescharacteristic
415C2×C4⋊C4C23×C12711yescharacteristic
416C2×C4⋊C4C23×C12711yescharacteristic
417C2×C4⋊C4C23×C12711yescharacteristic
418C2×C4⋊C4C23×C12711yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42D4×C12711yescharacteristic
436C2×C42D4×C12711yescharacteristic
437C2×C42C23×C12711yescharacteristic
438C2×C42C23×C12711yescharacteristic
439#107—22no—
440#107C2×C4×C12714yescomplemented
441#106—22no—
442#106C2×C4×C12714yescomplemented
443#102—22no—
444#102—22no—
445#102C2×C4×C12714yescomplemented
446#102C2×C4×C12714yescomplemented
447C22⋊C8—22no—
448C22⋊C8C2×C4×C12714yescomplemented
449#97—22no—
450#97—22no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458C24—21no—
459C24C2×D4×C12711yescharacteristic
460C2×D4—24no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4C22×C4×C12712yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4C22×C4×C12712yes—
490C22×C4C2×D4×C12711yescharacteristic
491C22×C4C2×D4×C12711yescharacteristic
492C22×C4C2×D4×C12711yescharacteristic
493C22×C4C2×D4×C12711yescharacteristic
494C22×C4C2×D4×C12711yescharacteristic
495C22×C4#41×C12712yes—
496C22×C4C24×C12711yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8C22×C4×C12712yes—
508C2×C8C22×C4×C12712yes—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4C22×C4×C12712yes—
520C4⋊C4C22×C4×C12712yes—
521C4⋊C4C22×C4×C12712yes—
522C4⋊C4#41×C12712yes—
523C4⋊C4#41×C12712yes—
524C22⋊C4—24no—
525C22⋊C4—24no—
526C22⋊C4—24no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C42—24no—
532C42—24no—
533C42—22no—
534C42—22no—
535C42—21no—
536C42—21no—
537C42—42no—
538C42—42no—
539C42—42no—
540C42—42no—
541C42—42no—
542C42#41×C12712yes—
543C42#41×C12712yes—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23C4×D4×C12712yes—
558C23C22×D4×C12711yescharacteristic
559D4—22no—
560D4—22no—
561D4—48no—
562D4—41no—
563D4—41no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—84no—
603C2×C4C4×D4×C12712yes—
604C2×C4#123×C12712yes—
605C2×C4#123×C12712yes—
606C2×C4AGL(1,ℤ/8)×C12712yes—
607C2×C4C23×C4×C12711yescharacteristic
608C2×C4C2×#41×C12711yescharacteristic
609C2×C4C2×#41×C12711yescharacteristic
610C2×C4C2×#41×C12711yescharacteristic
611C2×C4C2×#41×C12711yescharacteristic
612C2×C4C2×#41×C12711yescharacteristic
613C8—22no—
614C8—22no—
615C8—41no—
616C8—41no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22C2×C4×D4×C12711yescharacteristic
632C22C2×#123×C12711yescharacteristic
633C22#525×C12711yescharacteristic
634C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
635C22#575×C12711yescharacteristic
636C22#575×C12711yescharacteristic
637C22#575×C12711yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—22no—
642C4—41no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—42no—
647C4—42no—
648C4—81no—
649C4—81no—
650C4C4×#41×C12711yescharacteristic
651C4C4×#41×C12711yescharacteristic
652C4#529×C12711yescharacteristic
653C4#529×C12711yescharacteristic
654C2—42no—
655C2—82no—
656C2C4×#123×C12711yescharacteristic
657C2C127×#294311yescharacteristic
658C2C4×AGL(1,ℤ/8)×C12711yescharacteristic
659C2C127×#309311yescharacteristic
660C2C127×#309411yescharacteristic
661C2C127×#311111yescharacteristic
662C2C127×#311511yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC2×#121×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C4×#117×C127C2semidirect
4. C127×#1926C2semidirect
5. C127×#1925C2semidirect
6. C127×#1919C2semidirect
7. C127×#1918C2semidirect
9. C127×#1854C2semidirect
10. C127×#1825C2semidirect
11. C127×#1776C2semidirect
12. C127×#1776C2semidirect
13. C127×#1762C2semidirect
14. C127×#1762C2semidirect
15. C127×#1749C2semidirect
22. #482×C127C4semidirect
78. #117×C127C2×C4semidirect
108. #107×C127C2×C4semidirect
110. #106×C127C2×C4semidirect
113. #102×C127C2×C4semidirect
114. #102×C127C2×C4semidirect
116. C22⋊C8×C127C2×C4semidirect
322. #21582C127direct (N × H)
334. C4×#117C2×C127semidirect
335. #1926C2×C127semidirect
336. #1925C2×C127semidirect
337. #1919C2×C127semidirect
338. #1918C2×C127semidirect
340. #1854C2×C127semidirect
341. #1825C2×C127semidirect
342. #1776C2×C127semidirect
343. #1776C2×C127semidirect
344. #1762C2×C127semidirect
345. #1762C2×C127semidirect
346. #1749C2×C127semidirect
347. C127#21582direct (N × H)
354. #482C4×C127semidirect
410. #117C2×C4×C127semidirect
440. #107C2×C4×C127semidirect
442. #106C2×C4×C127semidirect
445. #102C2×C4×C127semidirect
446. #102C2×C4×C127semidirect
448. C22⋊C8C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C1272
C4×#121×C1272
C4×#117×C1272
C127×#19262
C127×#19252
C127×#19192
C127×#19182
C127×#18752
C127×#18542
C127×#18252
C127×#17762
C127×#17622
C127×#17492
#21582127