Finite Group Databasebeta

← C127×#21508 #44585181

Subgroups — C127×#21508 #44585181

Order 32512.

1004 conjugacy classes of subgroups.

The subgroup lattice has 666 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×#440×C127C211yesmaximal, characteristic
4C4×#124×C127C211yesmaximal, characteristic
5C42×Q8×C127C211yesmaximal, characteristic, complemented
6C127×#1983C211yesmaximal, characteristic
7C127×#1949C211yesmaximal, characteristic, complemented
8C127×#1928C211yesmaximal, characteristic, complemented
9C127×#1926C211yesmaximal, characteristic
10C127×#1880C211yesmaximal, characteristic
11C127×#1878C211yesmaximal, characteristic, complemented
12C127×#1805C211yesmaximal, characteristic, complemented
13C127×#1767C211yesmaximal, characteristic, complemented
14C127×#1763C211yesmaximal, characteristic, complemented
15C127×#1762C211yesmaximal, characteristic
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—
26#440×C127—24no—
27C2×#107×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×#97×C127C2211yescharacteristic
41#391×C127C2211yescharacteristic
42#390×C127C2211yescharacteristic
43#388×C127—21no—
44#388×C127—21no—
45#382×C127C2211yescharacteristic
46C4×C4⋊C4×C127—21no—
47C4×C4⋊C4×C127—21no—
48C4×C4⋊C4×C127—21no—
49C4×C4⋊C4×C127C2211yescharacteristic
50C4×C4⋊C4×C127C2211yescharacteristic
51C4×C4⋊C4×C127C2211yescharacteristic
52C4×C22⋊C4×C127—21no—
53C4×C22⋊C4×C127—21no—
54C43×C127—21no—
55C43×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×C127C2311yescharacteristic
93C2×C4⋊C4×C127C2311yescharacteristic
94C2×C4⋊C4×C127C2311yescharacteristic
95C2×C4⋊C4×C127C2311yescharacteristic
96C2×C4⋊C4×C127C2311yescharacteristic
97C2×C22⋊C4×C127—21no—
98C2×C22⋊C4×C127—21no—
99C2×C22⋊C4×C127—21no—
100C2×C22⋊C4×C127—21no—
101C2×C22⋊C4×C127—21no—
102C2×C42×C127—21no—
103C2×C42×C127—21no—
104C2×C42×C127—21no—
105C2×C42×C127—21no—
106C2×C42×C127—21no—
107C2×C42×C127—21no—
108C2×C42×C127—21no—
109C2×C42×C127D411yescharacteristic
110C2×C42×C127D411yescharacteristic
111C2×C42×C127D411yescharacteristic
112C2×C42×C127D411yescharacteristic
113C2×C42×C127C2311yescharacteristic
114C2×C42×C127C2311yescharacteristic
115C2×C42×C127C2311yescharacteristic
116#107×C127—22no—
117#106×C127—22no—
118C4⋊C8×C127—22no—
119C4⋊C8×C127C2×C414yescomplemented
120#103×C127—22no—
121#103×C127—22no—
122#103×C127—22no—
123#103×C127—22no—
124#103×C127C2×C414yescomplemented
125#102×C127—22no—
126#102×C127—22no—
127#102×C127C2×C414yes—
128#97×C127—22no—
129#97×C127—22no—
130#95×C127—21no—
131#95×C127—21no—
132#95×C127—21no—
133#95×C127—21no—
134#95×C127—21no—
135#95×C127—21no—
136#95×C127—21no—
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—42no—
165C22×C4×C127—42no—
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×C127C22×C412yes—
199C4⋊C4×C127C2×D412yes—
200C4⋊C4×C127#4112yes—
201C22⋊C4×C127—24no—
202C22⋊C4×C127—24no—
203C22⋊C4×C127—42no—
204C22⋊C4×C127—42no—
205C22⋊C4×C127—42no—
206C42×C127—24no—
207C42×C127—24no—
208C42×C127—24no—
209C42×C127—22no—
210C42×C127—21no—
211C42×C127—21no—
212C42×C127—41no—
213C42×C127—41no—
214C42×C127—41no—
215C42×C127—42no—
216C42×C127—42no—
217C42×C127—42no—
218C42×C127—42no—
219C42×C127C22×C412yes—
220C42×C127C2×D412yes—
221C42×C127#4112yes—
222C42×C127#4112yes—
223C23×C127—22no—
224C23×C127—41no—
225C23×C127—41no—
226C23×C127—41no—
227C23×C127—41no—
228C23×C127—41no—
229C23×C127—41no—
230C23×C127C22×D411yescharacteristic
231Q8×C127—22no—
232Q8×C127—22no—
233Q8×C127—22no—
234Q8×C127—22no—
235Q8×C127—22no—
236Q8×C127—41no—
237Q8×C127—41no—
238Q8×C127C4×D414yes—
239D4×C127—22no—
240D4×C127—22no—
241D4×C127—41no—
242D4×C127—41no—
243C2×C4×C127—22no—
244C2×C4×C127—22no—
245C2×C4×C127—21no—
246C2×C4×C127—22no—
247C2×C4×C127—21no—
248C2×C4×C127—21no—
249C2×C4×C127—21no—
250C2×C4×C127—21no—
251C2×C4×C127—21no—
252C2×C4×C127—21no—
253C2×C4×C127—21no—
254C2×C4×C127—21no—
255C2×C4×C127—21no—
256C2×C4×C127—22no—
257C2×C4×C127—22no—
258C2×C4×C127—22no—
259C2×C4×C127—21no—
260C2×C4×C127—22no—
261C2×C4×C127—21no—
262C2×C4×C127—21no—
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—41no—
277C2×C4×C127—84no—
278C2×C4×C127C4×D412yes—
279C2×C4×C127C4×D412yes—
280C2×C4×C127#12112yes—
281C2×C4×C127#12112yes—
282C2×C4×C127#13712yes—
283C2×C4×C127C23×C411yescharacteristic
284C2×C4×C127C22×D411yescharacteristic
285C2×C4×C127C2×#4111yescharacteristic
286C2×C4×C127C2×#4111yescharacteristic
287C2×C4×C127C2×#4111yescharacteristic
288C2×C4×C127C2×#4111yescharacteristic
289C8×C127—22no—
290C8×C127—22no—
291C8×C127—41no—
292C8×C127—41no—
293C22×C127—42no—
294C22×C127—42no—
295C22×C127—42no—
296C22×C127—81no—
297C22×C127—81no—
298C22×C127—81no—
299C22×C127—81no—
300C22×C127C2×C4×D411yescharacteristic
301C22×C127C2×#12111yescharacteristic
302C22×C127#52511yescharacteristic
303C22×C127C2×#13711yescharacteristic
304C22×C127#57511yescharacteristic
305C22×C127#57511yescharacteristic
306C22×C127#57511yescharacteristic
307C4×C127—22no—
308C4×C127—22no—
309C4×C127—22no—
310C4×C127—22no—
311C4×C127—22no—
312C4×C127—24no—
313C4×C127—41no—
314C4×C127—42no—
315C4×C127—42no—
316C4×C127—42no—
317C4×C127—42no—
318C4×C127—81no—
319C4×C127—81no—
320C4×C127C2×C4×D411yescharacteristic
321C4×C127C4×#4111yescharacteristic
322C4×C127#52911yescharacteristic
323C4×C127#53211yescharacteristic
324#21508C12711yesmaximal, characteristic, direct product factor, Sylow
325C2×C127—82no—
326C2×C127C4×#12111yescharacteristic
327C2×C127#294311yescharacteristic
328C2×C127C4×#13711yescharacteristic
329C2×C127#303711yescharacteristic
330C2×C127#304011yescharacteristic
331C2×C127#311111yescharacteristic
332C2×C127#311711yescharacteristic
333C2×#464C2×C12711yescharacteristic
334C2×#441C2×C12711yescharacteristic, complemented
335C2×#440C2×C12711yescharacteristic
336C4×#124C2×C12711yescharacteristic
337C42×Q8C2×C12711yescharacteristic, complemented
338#1983C2×C12711yescharacteristic
339#1949C2×C12711yescharacteristic, complemented
340#1928C2×C12711yescharacteristic, complemented
341#1926C2×C12711yescharacteristic
342#1880C2×C12711yescharacteristic
343#1878C2×C12711yescharacteristic, complemented
344#1805C2×C12711yescharacteristic, complemented
345#1767C2×C12711yescharacteristic, complemented
346#1763C2×C12711yescharacteristic, complemented
347#1762C2×C12711yescharacteristic
348C127#2150811yescharacteristic, direct product factor, Sylow
349C22×Q16C22×C12711yescharacteristic
350C22×SD16C22×C12711yescharacteristic
351C2×#124C22×C12711yescharacteristic
352C2×C4×Q8C22×C12711yescharacteristic
353C2×C4×Q8C22×C12711yescharacteristic
354C2×C4×Q8C22×C12711yescharacteristic
355C2×C4×Q8C22×C12711yescharacteristic
356C2×C4×D4C22×C12711yescharacteristic
357#464C4×C12718yescomplemented
358#441—24no—
359#440—24no—
360C2×#107C22×C12711yescharacteristic
361C2×#106C22×C12711yescharacteristic
362C2×C4⋊C8C22×C12711yescharacteristic
363C2×C4⋊C8C22×C12711yescharacteristic
364C2×#103C22×C12711yescharacteristic
365C2×#103C22×C12711yescharacteristic
366C2×#103C22×C12711yescharacteristic
367C2×#103C22×C12711yescharacteristic
368C2×#103C22×C12711yescharacteristic
369C2×#102C22×C12711yescharacteristic
370C2×#102C22×C12711yescharacteristic
371C2×#102C22×C12711yescharacteristic
372C2×#97C22×C12711yescharacteristic
373C2×#97C22×C12711yescharacteristic
374#391C22×C12711yescharacteristic
375#390C22×C12711yescharacteristic
376#388—21no—
377#388—21no—
378#382C22×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
385C4×C22⋊C4—21no—
386C4×C22⋊C4—21no—
387C43—21no—
388C43C22×C12711yescharacteristic
389#340C22×C12711yescharacteristic
390#340C22×C12711yescharacteristic
391#340C22×C12711yescharacteristic
392#340C22×C12711yescharacteristic
393#336C22×C12711yescharacteristic
394#336C22×C12711yescharacteristic
395C22×Q8C23×C12711yescharacteristic
396C22×Q8C23×C12711yescharacteristic
397C22×D4C23×C12711yescharacteristic
398C23×C4—21no—
399C2×Q16—22no—
400C2×Q16—22no—
401C2×Q16C2×C4×C12714yescomplemented
402C2×SD16—22no—
403C2×SD16—22no—
404C2×SD16C2×C4×C12714yes—
405C22×C8C23×C12711yescharacteristic
406C22×C8C23×C12711yescharacteristic
407C22×C8C23×C12711yescharacteristic
408C22×C8C23×C12711yescharacteristic
409#124—22no—
410#124C2×C4×C12714yes—
411C4×Q8—22no—
412C4×Q8—22no—
413C4×Q8—22no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×Q8—22no—
417C4×Q8C2×C4×C12714yescomplemented
418C4×Q8D4×C12714yes—
419C4×D4—22no—
420C4×D4—22no—
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×C42D4×C12711yescharacteristic
443C2×C42D4×C12711yescharacteristic
444C2×C42D4×C12711yescharacteristic
445C2×C42D4×C12711yescharacteristic
446C2×C42C23×C12711yescharacteristic
447C2×C42C23×C12711yescharacteristic
448C2×C42C23×C12711yescharacteristic
449#107—22no—
450#106—22no—
451C4⋊C8—22no—
452C4⋊C8C2×C4×C12714yescomplemented
453#103—22no—
454#103—22no—
455#103—22no—
456#103—22no—
457#103C2×C4×C12714yescomplemented
458#102—22no—
459#102—22no—
460#102C2×C4×C12714yes—
461#97—22no—
462#97—22no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470C24—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8C22×C4×C12712yes—
480C2×Q8C22×C4×C12712yes—
481C2×Q8C2×D4×C12712yes—
482C2×Q8#41×C12712yes—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4C22×C4×C12712yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4C2×D4×C12711yescharacteristic
500C22×C4C2×D4×C12711yescharacteristic
501C22×C4C2×D4×C12711yescharacteristic
502C22×C4C2×D4×C12711yescharacteristic
503C22×C4C2×D4×C12711yescharacteristic
504C22×C4C2×D4×C12711yescharacteristic
505C22×C4C24×C12711yescharacteristic
506Q16—28no—
507SD16—28no—
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×C8—21no—
517C2×C8—21no—
518C2×C8C22×C4×C12712yes—
519C2×C8C22×C4×C12712yes—
520C4⋊C4—24no—
521C4⋊C4—24no—
522C4⋊C4—24no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4C22×C4×C12712yes—
532C4⋊C4C2×D4×C12712yes—
533C4⋊C4#41×C12712yes—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—42no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C42—24no—
540C42—24no—
541C42—24no—
542C42—22no—
543C42—21no—
544C42—21no—
545C42—41no—
546C42—41no—
547C42—41no—
548C42—42no—
549C42—42no—
550C42—42no—
551C42—42no—
552C42C22×C4×C12712yes—
553C42C2×D4×C12712yes—
554C42#41×C12712yes—
555C42#41×C12712yes—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23C22×D4×C12711yescharacteristic
564Q8—22no—
565Q8—22no—
566Q8—22no—
567Q8—22no—
568Q8—22no—
569Q8—41no—
570Q8—41no—
571Q8C4×D4×C12714yes—
572D4—22no—
573D4—22no—
574D4—41no—
575D4—41no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
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—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—84no—
611C2×C4C4×D4×C12712yes—
612C2×C4C4×D4×C12712yes—
613C2×C4#121×C12712yes—
614C2×C4#121×C12712yes—
615C2×C4#137×C12712yes—
616C2×C4C23×C4×C12711yescharacteristic
617C2×C4C22×D4×C12711yescharacteristic
618C2×C4C2×#41×C12711yescharacteristic
619C2×C4C2×#41×C12711yescharacteristic
620C2×C4C2×#41×C12711yescharacteristic
621C2×C4C2×#41×C12711yescharacteristic
622C8—22no—
623C8—22no—
624C8—41no—
625C8—41no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22C2×C4×D4×C12711yescharacteristic
634C22C2×#121×C12711yescharacteristic
635C22#525×C12711yescharacteristic
636C22C2×#137×C12711yescharacteristic
637C22#575×C12711yescharacteristic
638C22#575×C12711yescharacteristic
639C22#575×C12711yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—22no—
645C4—24no—
646C4—41no—
647C4—42no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4C2×C4×D4×C12711yescharacteristic
654C4C4×#41×C12711yescharacteristic
655C4#529×C12711yescharacteristic
656C4#532×C12711yescharacteristic
657C2—82no—
658C2C4×#121×C12711yescharacteristic
659C2C127×#294311yescharacteristic
660C2C4×#137×C12711yescharacteristic
661C2C127×#303711yescharacteristic
662C2C127×#304011yescharacteristic
663C2C127×#311111yescharacteristic
664C2C127×#311711yescharacteristic
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 ◁ C43×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#441×C127C2semidirect
5. C42×Q8×C127C2semidirect
7. C127×#1949C2semidirect
8. C127×#1928C2semidirect
11. C127×#1878C2semidirect
12. C127×#1805C2semidirect
13. C127×#1767C2semidirect
14. C127×#1763C2semidirect
24. #464×C127C4semidirect
68. C2×Q16×C127C2×C4semidirect
84. C4×Q8×C127C2×C4semidirect
119. C4⋊C8×C127C2×C4semidirect
124. #103×C127C2×C4semidirect
324. #21508C127direct (N × H)
334. C2×#441C2×C127semidirect
337. C42×Q8C2×C127semidirect
339. #1949C2×C127semidirect
340. #1928C2×C127semidirect
343. #1878C2×C127semidirect
344. #1805C2×C127semidirect
345. #1767C2×C127semidirect
346. #1763C2×C127semidirect
348. C127#21508direct (N × H)
357. #464C4×C127semidirect
401. C2×Q16C2×C4×C127semidirect
417. C4×Q8C2×C4×C127semidirect
452. C4⋊C8C2×C4×C127semidirect
457. #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×#440×C1272
C4×#124×C1272
C42×Q8×C1272
C127×#19832
C127×#19492
C127×#19282
C127×#19262
C127×#18802
C127×#18782
C127×#18052
C127×#17672
C127×#17632
C127×#17622
#21508127