Finite Group Databasebeta

← C127×#21511 #44585184

Subgroups — C127×#21511 #44585184

Order 32512.

980 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#464×C127C211yesmaximal, characteristic
2C2×#441×C127C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C127C211yesmaximal, characteristic
4C127×#2326C211yesmaximal, characteristic
5C127×#2276C211yesmaximal, characteristic, complemented
6C127×#1983C211yesmaximal, characteristic
7C127×#1948C211yesmaximal, characteristic, complemented
8C127×#1927C211yesmaximal, characteristic, complemented
9C127×#1926C211yesmaximal, characteristic
10C127×#1880C211yesmaximal, characteristic
11C127×#1878C211yesmaximal, characteristic, complemented
12C127×#1803C211yesmaximal, characteristic, complemented
13C127×#1768C211yesmaximal, characteristic, complemented
14C127×#1762C211yesmaximal, characteristic
15C4×#103×C127C211yesmaximal, characteristic, complemented
16C22×Q16×C127C2211yescharacteristic
17C22×SD16×C127C2211yescharacteristic
18C2×#124×C127C2211yescharacteristic
19C2×C4×Q8×C127C2211yescharacteristic
20C2×C4×Q8×C127C2211yescharacteristic
21C2×C4×Q8×C127C2211yescharacteristic
22C2×C4×Q8×C127C2211yescharacteristic
23C2×C4×D4×C127C2211yescharacteristic
24#464×C127C418yescomplemented
25#441×C127—24no—
26C4×SD16×C127—24no—
27C2×#106×C127C2211yescharacteristic
28C2×#106×C127C2211yescharacteristic
29C2×C4⋊C8×C127C2211yescharacteristic
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×#103×C127C2211yescharacteristic
32C2×#103×C127C2211yescharacteristic
33C2×#103×C127C2211yescharacteristic
34C2×#103×C127C2211yescharacteristic
35C2×#103×C127C2211yescharacteristic
36C2×#102×C127C2211yescharacteristic
37C2×#102×C127C2211yescharacteristic
38C2×#102×C127C2211yescharacteristic
39C2×#97×C127C2211yescharacteristic
40C2×C4×C8×C127C2211yescharacteristic
41#391×C127C2211yescharacteristic
42#390×C127C2211yescharacteristic
43#388×C127—21no—
44#388×C127—21no—
45#385×C127—21no—
46#385×C127—21no—
47#384×C127C2211yescharacteristic
48C4×C4⋊C4×C127—21no—
49C4×C4⋊C4×C127—21no—
50C4×C4⋊C4×C127—21no—
51C4×C4⋊C4×C127C2211yescharacteristic
52C4×C4⋊C4×C127C2211yescharacteristic
53C4×C4⋊C4×C127C2211yescharacteristic
54#376×C127—21no—
55#376×C127C2211yescharacteristic
56#340×C127C2211yescharacteristic
57#340×C127C2211yescharacteristic
58#340×C127C2211yescharacteristic
59#340×C127C2211yescharacteristic
60#336×C127C2211yescharacteristic
61#336×C127C2211yescharacteristic
62C22×Q8×C127C2311yescharacteristic
63C22×Q8×C127C2311yescharacteristic
64C22×D4×C127C2311yescharacteristic
65C23×C4×C127—21no—
66C2×Q16×C127—22no—
67C2×Q16×C127—22no—
68C2×Q16×C127C2×C414yescomplemented
69C2×SD16×C127—22no—
70C2×SD16×C127—22no—
71C2×SD16×C127C2×C414yes—
72C22×C8×C127C2311yescharacteristic
73C22×C8×C127C2311yescharacteristic
74C22×C8×C127C2311yescharacteristic
75C22×C8×C127C2311yescharacteristic
76#124×C127—22no—
77#124×C127C2×C414yes—
78C4×Q8×C127—22no—
79C4×Q8×C127—22no—
80C4×Q8×C127—22no—
81C4×Q8×C127—22no—
82C4×Q8×C127—22no—
83C4×Q8×C127—22no—
84C4×Q8×C127C2×C414yescomplemented
85C4×Q8×C127D414yes—
86C4×D4×C127—22no—
87C4×D4×C127—22no—
88C2×C4⋊C4×C127—21no—
89C2×C4⋊C4×C127—21no—
90C2×C4⋊C4×C127—21no—
91C2×C4⋊C4×C127—21no—
92C2×C4⋊C4×C127—21no—
93C2×C4⋊C4×C127—21no—
94C2×C4⋊C4×C127C2311yescharacteristic
95C2×C4⋊C4×C127C2311yescharacteristic
96C2×C4⋊C4×C127C2311yescharacteristic
97C2×C4⋊C4×C127C2311yescharacteristic
98C2×C4⋊C4×C127C2311yescharacteristic
99C2×C22⋊C4×C127—21no—
100C2×C22⋊C4×C127—21no—
101C2×C22⋊C4×C127—21no—
102C2×C22⋊C4×C127—21no—
103C2×C22⋊C4×C127—21no—
104C2×C42×C127—21no—
105C2×C42×C127—21no—
106C2×C42×C127—21no—
107C2×C42×C127—21no—
108C2×C42×C127—21no—
109C2×C42×C127—21no—
110C2×C42×C127—21no—
111C2×C42×C127C2311yescharacteristic
112C2×C42×C127C2311yescharacteristic
113C2×C42×C127C2311yescharacteristic
114#106×C127—22no—
115#106×C127—22no—
116C4⋊C8×C127—22no—
117C4⋊C8×C127C2×C414yescomplemented
118#103×C127—22no—
119#103×C127—22no—
120#103×C127—22no—
121#103×C127—22no—
122#103×C127C2×C414yescomplemented
123#102×C127—22no—
124#102×C127—22no—
125#102×C127C2×C414yes—
126#97×C127—22no—
127C4×C8×C127—22no—
128#95×C127—21no—
129#95×C127—21no—
130#95×C127—21no—
131#95×C127—21no—
132#95×C127—21no—
133#95×C127D411yescharacteristic
134#95×C127D411yescharacteristic
135#95×C127D411yescharacteristic
136#95×C127D411yescharacteristic
137C24×C127—21no—
138C2×Q8×C127—21no—
139C2×Q8×C127—21no—
140C2×Q8×C127—21no—
141C2×Q8×C127—21no—
142C2×Q8×C127—21no—
143C2×Q8×C127—21no—
144C2×Q8×C127—21no—
145C2×Q8×C127—21no—
146C2×Q8×C127C22×C412yes—
147C2×Q8×C127C22×C412yes—
148C2×Q8×C127C2×D412yes—
149C2×Q8×C127#4112yes—
150C2×D4×C127—21no—
151C2×D4×C127—21no—
152C2×D4×C127—21no—
153C2×D4×C127—21no—
154C2×D4×C127—21no—
155C2×D4×C127C22×C412yes—
156C22×C4×C127—21no—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—42no—
164C22×C4×C127—81no—
165C22×C4×C127—81no—
166C22×C4×C127C2×D411yescharacteristic
167C22×C4×C127C2×D411yescharacteristic
168C22×C4×C127C2×D411yescharacteristic
169C22×C4×C127C2×D411yescharacteristic
170C22×C4×C127C2×D411yescharacteristic
171C22×C4×C127C2×D411yescharacteristic
172C22×C4×C127C2411yescharacteristic
173Q16×C127—28no—
174SD16×C127—28no—
175C2×C8×C127—21no—
176C2×C8×C127—21no—
177C2×C8×C127—21no—
178C2×C8×C127—21no—
179C2×C8×C127—21no—
180C2×C8×C127—21no—
181C2×C8×C127—21no—
182C2×C8×C127—21no—
183C2×C8×C127—21no—
184C2×C8×C127—21no—
185C2×C8×C127C22×C412yes—
186C2×C8×C127C22×C412yes—
187C4⋊C4×C127—24no—
188C4⋊C4×C127—24no—
189C4⋊C4×C127—24no—
190C4⋊C4×C127—21no—
191C4⋊C4×C127—21no—
192C4⋊C4×C127—21no—
193C4⋊C4×C127—21no—
194C4⋊C4×C127—21no—
195C4⋊C4×C127—21no—
196C4⋊C4×C127—21no—
197C4⋊C4×C127—42no—
198C4⋊C4×C127—81no—
199C4⋊C4×C127—81no—
200C4⋊C4×C127C22×C412yes—
201C4⋊C4×C127C2×D412yes—
202C4⋊C4×C127#4112yes—
203C22⋊C4×C127—24no—
204C22⋊C4×C127—24no—
205C22⋊C4×C127—42no—
206C22⋊C4×C127—81no—
207C22⋊C4×C127—81no—
208C42×C127—24no—
209C42×C127—24no—
210C42×C127—24no—
211C42×C127—21no—
212C42×C127—21no—
213C42×C127—42no—
214C42×C127—81no—
215C42×C127—81no—
216C42×C127—81no—
217C42×C127C22×C412yes—
218C42×C127C2×D412yes—
219C42×C127#4112yes—
220C42×C127#4112yes—
221C23×C127—22no—
222C23×C127—41no—
223C23×C127—41no—
224C23×C127—41no—
225C23×C127—41no—
226C23×C127—41no—
227C23×C127—41no—
228C23×C127C22×D411yescharacteristic
229Q8×C127—22no—
230Q8×C127—22no—
231Q8×C127—22no—
232Q8×C127—22no—
233Q8×C127—22no—
234Q8×C127—41no—
235Q8×C127—41no—
236Q8×C127C4×D414yes—
237D4×C127—22no—
238D4×C127—22no—
239D4×C127—41no—
240D4×C127—41no—
241C2×C4×C127—22no—
242C2×C4×C127—22no—
243C2×C4×C127—22no—
244C2×C4×C127—21no—
245C2×C4×C127—21no—
246C2×C4×C127—21no—
247C2×C4×C127—21no—
248C2×C4×C127—21no—
249C2×C4×C127—21no—
250C2×C4×C127—21no—
251C2×C4×C127—21no—
252C2×C4×C127—22no—
253C2×C4×C127—22no—
254C2×C4×C127—22no—
255C2×C4×C127—21no—
256C2×C4×C127—21no—
257C2×C4×C127—22no—
258C2×C4×C127—21no—
259C2×C4×C127—21no—
260C2×C4×C127—21no—
261C2×C4×C127—21no—
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—41no—
271C2×C4×C127—41no—
272C2×C4×C127—41no—
273C2×C4×C127—41no—
274C2×C4×C127—41no—
275C2×C4×C127—41no—
276C2×C4×C127—84no—
277C2×C4×C127C4×D412yes—
278C2×C4×C127C4×D412yes—
279C2×C4×C127#12112yes—
280C2×C4×C127#12112yes—
281C2×C4×C127C23×C411yescharacteristic
282C2×C4×C127C22×D411yescharacteristic
283C2×C4×C127C2×#4111yescharacteristic
284C2×C4×C127C2×#4111yescharacteristic
285C2×C4×C127C2×#4111yescharacteristic
286C2×C4×C127C2×#4111yescharacteristic
287C8×C127—22no—
288C8×C127—22no—
289C8×C127—41no—
290C8×C127—41no—
291C22×C127—42no—
292C22×C127—42no—
293C22×C127—42no—
294C22×C127—81no—
295C22×C127—81no—
296C22×C127—81no—
297C22×C127—81no—
298C22×C127C2×C4×D411yescharacteristic
299C22×C127C2×#12111yescharacteristic
300C22×C127#52511yescharacteristic
301C22×C127#57711yescharacteristic
302C22×C127#57711yescharacteristic
303C22×C127#57711yescharacteristic
304C22×C127#57811yescharacteristic
305C4×C127—22no—
306C4×C127—22no—
307C4×C127—22no—
308C4×C127—22no—
309C4×C127—24no—
310C4×C127—41no—
311C4×C127—41no—
312C4×C127—42no—
313C4×C127—42no—
314C4×C127—42no—
315C4×C127—42no—
316C4×C127—81no—
317C4×C127—81no—
318C4×C127C2×C4×D411yescharacteristic
319C4×C127C4×#4111yescharacteristic
320C4×C127#52911yescharacteristic
321C4×C127#53211yescharacteristic
322#21511C12711yesmaximal, characteristic, direct product factor, Sylow
323C2×C127—82no—
324C2×C127C4×#12111yescharacteristic
325C2×C127#294711yescharacteristic
326C2×C127#295211yescharacteristic
327C2×C127#304311yescharacteristic
328C2×C127#304611yescharacteristic
329C2×C127#312111yescharacteristic
330C2×C127#312511yescharacteristic
331C2×#464C2×C12711yescharacteristic
332C2×#441C2×C12711yescharacteristic, complemented
333C2×C4×SD16C2×C12711yescharacteristic
334#2326C2×C12711yescharacteristic
335#2276C2×C12711yescharacteristic, complemented
336#1983C2×C12711yescharacteristic
337#1948C2×C12711yescharacteristic, complemented
338#1927C2×C12711yescharacteristic, complemented
339#1926C2×C12711yescharacteristic
340#1880C2×C12711yescharacteristic
341#1878C2×C12711yescharacteristic, complemented
342#1803C2×C12711yescharacteristic, complemented
343#1768C2×C12711yescharacteristic, complemented
344#1762C2×C12711yescharacteristic
345C4×#103C2×C12711yescharacteristic, complemented
346C127#2151111yescharacteristic, direct product factor, Sylow
347C22×Q16C22×C12711yescharacteristic
348C22×SD16C22×C12711yescharacteristic
349C2×#124C22×C12711yescharacteristic
350C2×C4×Q8C22×C12711yescharacteristic
351C2×C4×Q8C22×C12711yescharacteristic
352C2×C4×Q8C22×C12711yescharacteristic
353C2×C4×Q8C22×C12711yescharacteristic
354C2×C4×D4C22×C12711yescharacteristic
355#464C4×C12718yescomplemented
356#441—24no—
357C4×SD16—24no—
358C2×#106C22×C12711yescharacteristic
359C2×#106C22×C12711yescharacteristic
360C2×C4⋊C8C22×C12711yescharacteristic
361C2×C4⋊C8C22×C12711yescharacteristic
362C2×#103C22×C12711yescharacteristic
363C2×#103C22×C12711yescharacteristic
364C2×#103C22×C12711yescharacteristic
365C2×#103C22×C12711yescharacteristic
366C2×#103C22×C12711yescharacteristic
367C2×#102C22×C12711yescharacteristic
368C2×#102C22×C12711yescharacteristic
369C2×#102C22×C12711yescharacteristic
370C2×#97C22×C12711yescharacteristic
371C2×C4×C8C22×C12711yescharacteristic
372#391C22×C12711yescharacteristic
373#390C22×C12711yescharacteristic
374#388—21no—
375#388—21no—
376#385—21no—
377#385—21no—
378#384C22×C12711yescharacteristic
379C4×C4⋊C4—21no—
380C4×C4⋊C4—21no—
381C4×C4⋊C4—21no—
382C4×C4⋊C4C22×C12711yescharacteristic
383C4×C4⋊C4C22×C12711yescharacteristic
384C4×C4⋊C4C22×C12711yescharacteristic
385#376—21no—
386#376C22×C12711yescharacteristic
387#340C22×C12711yescharacteristic
388#340C22×C12711yescharacteristic
389#340C22×C12711yescharacteristic
390#340C22×C12711yescharacteristic
391#336C22×C12711yescharacteristic
392#336C22×C12711yescharacteristic
393C22×Q8C23×C12711yescharacteristic
394C22×Q8C23×C12711yescharacteristic
395C22×D4C23×C12711yescharacteristic
396C23×C4—21no—
397C2×Q16—22no—
398C2×Q16—22no—
399C2×Q16C2×C4×C12714yescomplemented
400C2×SD16—22no—
401C2×SD16—22no—
402C2×SD16C2×C4×C12714yes—
403C22×C8C23×C12711yescharacteristic
404C22×C8C23×C12711yescharacteristic
405C22×C8C23×C12711yescharacteristic
406C22×C8C23×C12711yescharacteristic
407#124—22no—
408#124C2×C4×C12714yes—
409C4×Q8—22no—
410C4×Q8—22no—
411C4×Q8—22no—
412C4×Q8—22no—
413C4×Q8—22no—
414C4×Q8—22no—
415C4×Q8C2×C4×C12714yescomplemented
416C4×Q8D4×C12714yes—
417C4×D4—22no—
418C4×D4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4C23×C12711yescharacteristic
426C2×C4⋊C4C23×C12711yescharacteristic
427C2×C4⋊C4C23×C12711yescharacteristic
428C2×C4⋊C4C23×C12711yescharacteristic
429C2×C4⋊C4C23×C12711yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42C23×C12711yescharacteristic
443C2×C42C23×C12711yescharacteristic
444C2×C42C23×C12711yescharacteristic
445#106—22no—
446#106—22no—
447C4⋊C8—22no—
448C4⋊C8C2×C4×C12714yescomplemented
449#103—22no—
450#103—22no—
451#103—22no—
452#103—22no—
453#103C2×C4×C12714yescomplemented
454#102—22no—
455#102—22no—
456#102C2×C4×C12714yes—
457#97—22no—
458C4×C8—22no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95D4×C12711yescharacteristic
465#95D4×C12711yescharacteristic
466#95D4×C12711yescharacteristic
467#95D4×C12711yescharacteristic
468C24—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8C22×C4×C12712yes—
478C2×Q8C22×C4×C12712yes—
479C2×Q8C2×D4×C12712yes—
480C2×Q8#41×C12712yes—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4C22×C4×C12712yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—42no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4C2×D4×C12711yescharacteristic
498C22×C4C2×D4×C12711yescharacteristic
499C22×C4C2×D4×C12711yescharacteristic
500C22×C4C2×D4×C12711yescharacteristic
501C22×C4C2×D4×C12711yescharacteristic
502C22×C4C2×D4×C12711yescharacteristic
503C22×C4C24×C12711yescharacteristic
504Q16—28no—
505SD16—28no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8C22×C4×C12712yes—
517C2×C8C22×C4×C12712yes—
518C4⋊C4—24no—
519C4⋊C4—24no—
520C4⋊C4—24no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—81no—
530C4⋊C4—81no—
531C4⋊C4C22×C4×C12712yes—
532C4⋊C4C2×D4×C12712yes—
533C4⋊C4#41×C12712yes—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—42no—
537C22⋊C4—81no—
538C22⋊C4—81no—
539C42—24no—
540C42—24no—
541C42—24no—
542C42—21no—
543C42—21no—
544C42—42no—
545C42—81no—
546C42—81no—
547C42—81no—
548C42C22×C4×C12712yes—
549C42C2×D4×C12712yes—
550C42#41×C12712yes—
551C42#41×C12712yes—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23C22×D4×C12711yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—22no—
563Q8—22no—
564Q8—22no—
565Q8—41no—
566Q8—41no—
567Q8C4×D4×C12714yes—
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
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—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—84no—
608C2×C4C4×D4×C12712yes—
609C2×C4C4×D4×C12712yes—
610C2×C4#121×C12712yes—
611C2×C4#121×C12712yes—
612C2×C4C23×C4×C12711yescharacteristic
613C2×C4C22×D4×C12711yescharacteristic
614C2×C4C2×#41×C12711yescharacteristic
615C2×C4C2×#41×C12711yescharacteristic
616C2×C4C2×#41×C12711yescharacteristic
617C2×C4C2×#41×C12711yescharacteristic
618C8—22no—
619C8—22no—
620C8—41no—
621C8—41no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22C2×C4×D4×C12711yescharacteristic
630C22C2×#121×C12711yescharacteristic
631C22#525×C12711yescharacteristic
632C22#577×C12711yescharacteristic
633C22#577×C12711yescharacteristic
634C22#577×C12711yescharacteristic
635C22#578×C12711yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—22no—
640C4—24no—
641C4—41no—
642C4—41no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—42no—
647C4—81no—
648C4—81no—
649C4C2×C4×D4×C12711yescharacteristic
650C4C4×#41×C12711yescharacteristic
651C4#529×C12711yescharacteristic
652C4#532×C12711yescharacteristic
653C2—82no—
654C2C4×#121×C12711yescharacteristic
655C2C127×#294711yescharacteristic
656C2C127×#295211yescharacteristic
657C2C127×#304311yescharacteristic
658C2C127×#304611yescharacteristic
659C2C127×#312111yescharacteristic
660C2C127×#312511yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×D4×C127C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ #376×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#441×C127C2semidirect
5. C127×#2276C2semidirect
7. C127×#1948C2semidirect
8. C127×#1927C2semidirect
11. C127×#1878C2semidirect
12. C127×#1803C2semidirect
13. C127×#1768C2semidirect
15. C4×#103×C127C2semidirect
24. #464×C127C4semidirect
68. C2×Q16×C127C2×C4semidirect
84. C4×Q8×C127C2×C4semidirect
117. C4⋊C8×C127C2×C4semidirect
122. #103×C127C2×C4semidirect
322. #21511C127direct (N × H)
332. C2×#441C2×C127semidirect
335. #2276C2×C127semidirect
337. #1948C2×C127semidirect
338. #1927C2×C127semidirect
341. #1878C2×C127semidirect
342. #1803C2×C127semidirect
343. #1768C2×C127semidirect
345. C4×#103C2×C127semidirect
346. C127#21511direct (N × H)
355. #464C4×C127semidirect
399. C2×Q16C2×C4×C127semidirect
415. C4×Q8C2×C4×C127semidirect
448. C4⋊C8C2×C4×C127semidirect
453. #103C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#464×C1272
C2×#441×C1272
C2×C4×SD16×C1272
C127×#23262
C127×#22762
C127×#19832
C127×#19482
C127×#19272
C127×#19262
C127×#18802
C127×#18782
C127×#18032
C127×#17682
C127×#17622
C4×#103×C1272
#21511127