Finite Group Databasebeta

← C127×#14699 #44578372

Subgroups — C127×#14699 #44578372

Order 32512.

1566 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C127C211yesmaximal, characteristic
2C2×#389×C127C211yesmaximal, characteristic
3C2×#387×C127C212yesmaximal
4C2×C43×C127C211yesmaximal, characteristic
5C127×#1436C212yesmaximal
6C127×#1436C212yesmaximal
7C127×C4⋊#95C211yesmaximal, characteristic
8C127×C4⋊#95C211yesmaximal, characteristic
9C127×C4⋊#95C211yesmaximal, characteristic
10C127×C4⋊#95C211yesmaximal, characteristic
11C127×#1434C212yesmaximal
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2212yes—
18C22×C42×C127C2211yescharacteristic
19C22×C42×C127C2211yescharacteristic
20C22×C42×C127C2211yescharacteristic
21C22×C42×C127C2211yescharacteristic
22C22×C42×C127C2211yescharacteristic
23C22×C42×C127C2211yescharacteristic
24C22×C42×C127C2211yescharacteristic
25#389×C127—24no—
26#389×C127C418yescomplemented
27#387×C127—28no—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C43×C127—24no—
39C23×C4×C127C2312yes—
40C23×C4×C127C2312yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2311yescharacteristic
44C23×C4×C127C2311yescharacteristic
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2311yescharacteristic
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2311yescharacteristic
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127—22no—
52C2×C4⋊C4×C127—22no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—24no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—24no—
57C2×C4⋊C4×C127—24no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—24no—
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127—22no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127C2×C414yes—
66C2×C4⋊C4×C127C2×C418yes—
67C2×C4⋊C4×C127C2×C414yes—
68C2×C42×C127—22no—
69C2×C42×C127—22no—
70C2×C42×C127—22no—
71C2×C42×C127—22no—
72C2×C42×C127—22no—
73C2×C42×C127—22no—
74C2×C42×C127—22no—
75C2×C42×C127—22no—
76C2×C42×C127—22no—
77C2×C42×C127—22no—
78C2×C42×C127—22no—
79C2×C42×C127—22no—
80C2×C42×C127—22no—
81C2×C42×C127—22no—
82C2×C42×C127—22no—
83C2×C42×C127—22no—
84C2×C42×C127C2×C414yes—
85C2×C42×C127D414yes—
86C2×C42×C127D414yes—
87C2×C42×C127Q814yes—
88C2×C42×C127Q814yes—
89#95×C127—24no—
90#95×C127—24no—
91#95×C127—24no—
92#95×C127—24no—
93#95×C127—24no—
94#95×C127—24no—
95#95×C127—24no—
96#95×C127—24no—
97#95×C127—24no—
98#95×C127C2×C418yes—
99C24×C127C2411yescharacteristic
100C22×C4×C127—21no—
101C22×C4×C127—21no—
102C22×C4×C127—21no—
103C22×C4×C127—21no—
104C22×C4×C127—21no—
105C22×C4×C127—21no—
106C22×C4×C127—21no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—21no—
112C22×C4×C127—21no—
113C22×C4×C127—21no—
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—21no—
119C22×C4×C127—21no—
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—21no—
123C22×C4×C127—21no—
124C22×C4×C127—22no—
125C22×C4×C127—22no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127—22no—
136C22×C4×C127—22no—
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—22no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127C22×C414yes—
151C22×C4×C127C22×C414yes—
152C22×C4×C127C22×C412yes—
153C22×C4×C127C22×C412yes—
154C22×C4×C127C22×C412yes—
155C22×C4×C127C2×D412yes—
156C22×C4×C127C2×D412yes—
157C22×C4×C127C2×D412yes—
158C22×C4×C127C2×D412yes—
159C22×C4×C127C2×D412yes—
160C22×C4×C127C2×D412yes—
161C22×C4×C127C2×Q812yes—
162C22×C4×C127C2×Q812yes—
163C22×C4×C127C2×Q812yes—
164C22×C4×C127C2×Q812yes—
165C22×C4×C127C2×Q812yes—
166C22×C4×C127C2×Q812yes—
167C22×C4×C127#4112yes—
168C22×C4×C127#4112yes—
169C22×C4×C127#4112yes—
170C22×C4×C127#4112yes—
171C22×C4×C127#4112yes—
172C22×C4×C127#4112yes—
173C22×C4×C127#4112yes—
174C22×C4×C127#4112yes—
175C22×C4×C127#4112yes—
176C22×C4×C127#4112yes—
177C4⋊C4×C127—28no—
178C4⋊C4×C127—216no—
179C4⋊C4×C127—28no—
180C4⋊C4×C127—48no—
181C4⋊C4×C127—44no—
182C4⋊C4×C127—44no—
183C42×C127—28no—
184C42×C127—28no—
185C42×C127—28no—
186C42×C127—28no—
187C42×C127—28no—
188C42×C127—28no—
189C42×C127—28no—
190C23×C127C23×C411yescharacteristic
191C23×C127C22×D411yescharacteristic
192C23×C127C22×D411yescharacteristic
193C23×C127C22×Q811yescharacteristic
194C23×C127C22×Q811yescharacteristic
195C23×C127C2×#4111yescharacteristic
196C23×C127C2×#4111yescharacteristic
197C23×C127C2×#4111yescharacteristic
198C23×C127C2×#4111yescharacteristic
199C23×C127C2×#4111yescharacteristic
200C23×C127C2×#4111yescharacteristic
201C23×C127C2×#4111yescharacteristic
202C23×C127C2×#4111yescharacteristic
203C23×C127C2×#4111yescharacteristic
204C23×C127C2×#4111yescharacteristic
205C2×C4×C127—22no—
206C2×C4×C127—22no—
207C2×C4×C127—22no—
208C2×C4×C127—22no—
209C2×C4×C127—22no—
210C2×C4×C127—22no—
211C2×C4×C127—22no—
212C2×C4×C127—22no—
213C2×C4×C127—22no—
214C2×C4×C127—22no—
215C2×C4×C127—22no—
216C2×C4×C127—22no—
217C2×C4×C127—22no—
218C2×C4×C127—22no—
219C2×C4×C127—22no—
220C2×C4×C127—22no—
221C2×C4×C127—22no—
222C2×C4×C127—22no—
223C2×C4×C127—22no—
224C2×C4×C127—22no—
225C2×C4×C127—22no—
226C2×C4×C127—22no—
227C2×C4×C127—22no—
228C2×C4×C127—22no—
229C2×C4×C127—22no—
230C2×C4×C127—22no—
231C2×C4×C127—22no—
232C2×C4×C127—22no—
233C2×C4×C127—22no—
234C2×C4×C127—22no—
235C2×C4×C127—22no—
236C2×C4×C127—22no—
237C2×C4×C127—22no—
238C2×C4×C127—22no—
239C2×C4×C127—22no—
240C2×C4×C127—22no—
241C2×C4×C127—24no—
242C2×C4×C127—24no—
243C2×C4×C127—24no—
244C2×C4×C127—24no—
245C2×C4×C127—24no—
246C2×C4×C127—24no—
247C2×C4×C127—42no—
248C2×C4×C127—42no—
249C2×C4×C127—42no—
250C2×C4×C127—42no—
251C2×C4×C127—42no—
252C2×C4×C127—42no—
253C2×C4×C127—42no—
254C2×C4×C127—42no—
255C2×C4×C127—42no—
256C2×C4×C127—42no—
257C2×C4×C127—42no—
258C2×C4×C127—42no—
259C2×C4×C127—42no—
260C2×C4×C127—42no—
261C2×C4×C127—42no—
262C2×C4×C127—42no—
263C2×C4×C127—42no—
264C2×C4×C127—42no—
265C2×C4×C127—42no—
266C2×C4×C127—42no—
267C2×C4×C127—42no—
268C2×C4×C127—42no—
269C2×C4×C127#11714yes—
270C2×C4×C127C4×D414yes—
271C2×C4×C127C4×D414yes—
272C2×C4×C127C4×Q814yes—
273C2×C4×C127C4×Q814yes—
274C2×C4×C127#12114yes—
275C2×C4×C127C22⋊Q814yes—
276C2×C4×C127C22⋊Q814yes—
277C2×C4×C127#12314yes—
278C2×C4×C127#12514yes—
279C2×C4×C127#12514yes—
280C2×C4×C127#12614yes—
281C2×C4×C127C4⋊Q814yes—
282C22×C127C2×#11711yescharacteristic
283C22×C127C2×C4×D411yescharacteristic
284C22×C127C2×C4×D411yescharacteristic
285C22×C127C2×C4×Q811yescharacteristic
286C22×C127C2×C4×Q811yescharacteristic
287C22×C127C4×#4111yescharacteristic
288C22×C127C4×#4111yescharacteristic
289C22×C127C2×#12111yescharacteristic
290C22×C127C2×C22⋊Q811yescharacteristic
291C22×C127C2×C22⋊Q811yescharacteristic
292C22×C127C2×#12311yescharacteristic
293C22×C127#52511yescharacteristic
294C22×C127#52511yescharacteristic
295C22×C127C2×#12511yescharacteristic
296C22×C127C2×#12511yescharacteristic
297C22×C127C2×#12611yescharacteristic
298C22×C127#52911yescharacteristic
299C22×C127#52911yescharacteristic
300C22×C127#52911yescharacteristic
301C22×C127#52911yescharacteristic
302C22×C127#52911yescharacteristic
303C22×C127#52911yescharacteristic
304C22×C127#52911yescharacteristic
305C22×C127#52911yescharacteristic
306C22×C127C2×C4⋊Q811yescharacteristic
307C22×C127#53211yescharacteristic
308C22×C127#53211yescharacteristic
309C22×C127#53211yescharacteristic
310C22×C127#53211yescharacteristic
311C22×C127#53311yescharacteristic
312C22×C127#53311yescharacteristic
313C22×C127#53311yescharacteristic
314C22×C127#53311yescharacteristic
315C22×C127#53311yescharacteristic
316C22×C127#53311yescharacteristic
317C4×C127—24no—
318C4×C127—24no—
319C4×C127—24no—
320C4×C127—24no—
321C4×C127—24no—
322C4×C127—24no—
323C4×C127—44no—
324C4×C127—44no—
325C4×C127—82no—
326C4×C127—82no—
327C4×C127#38718yescomplemented
328#14699C12711yesmaximal, characteristic, direct product factor, Sylow
329C2×C127C2×#38711yescharacteristic
330C2×C127#229311yescharacteristic
331C2×C127#229511yescharacteristic
332C2×C127C4×#12111yescharacteristic
333C2×C127C4×C22⋊Q811yescharacteristic
334C2×C127C4×#12511yescharacteristic
335C2×C127C4×C4⋊Q811yescharacteristic
336C2×C127#285111yescharacteristic
337C2×C127#285411yescharacteristic
338C2×C127#285511yescharacteristic
339C2×C127#285711yescharacteristic
340C2×C127#285911yescharacteristic
341C2×C127#286011yescharacteristic
342C2×C127#286311yescharacteristic
343C2×C127#286411yescharacteristic
344C2×#389C2×C12711yescharacteristic
345C2×#389C2×C12711yescharacteristic
346C2×#387C2×C12712yes—
347C2×C43C2×C12711yescharacteristic
348#1436C2×C12712yes—
349#1436C2×C12712yes—
350C4⋊#95C2×C12711yescharacteristic
351C4⋊#95C2×C12711yescharacteristic
352C4⋊#95C2×C12711yescharacteristic
353C4⋊#95C2×C12711yescharacteristic
354#1434C2×C12712yes—
355C127#1469911yescharacteristic, direct product factor, Sylow
356C22×C4⋊C4C22×C12711yescharacteristic
357C22×C4⋊C4C22×C12711yescharacteristic
358C22×C4⋊C4C22×C12712yes—
359C22×C4⋊C4C22×C12711yescharacteristic
360C22×C4⋊C4C22×C12711yescharacteristic
361C22×C4⋊C4C22×C12712yes—
362C22×C42C22×C12711yescharacteristic
363C22×C42C22×C12711yescharacteristic
364C22×C42C22×C12711yescharacteristic
365C22×C42C22×C12711yescharacteristic
366C22×C42C22×C12711yescharacteristic
367C22×C42C22×C12711yescharacteristic
368C22×C42C22×C12711yescharacteristic
369#389—24no—
370#389C4×C12718yescomplemented
371#387—28no—
372C2×#95C22×C12712yes—
373C2×#95C22×C12712yes—
374C2×#95C22×C12712yes—
375C2×#95C22×C12712yes—
376C2×#95C22×C12712yes—
377C2×#95C22×C12712yes—
378C2×#95C22×C12712yes—
379C2×#95C22×C12712yes—
380C2×#95C22×C12712yes—
381C2×#95C22×C12712yes—
382C43—24no—
383C23×C4C23×C12712yes—
384C23×C4C23×C12712yes—
385C23×C4C23×C12712yes—
386C23×C4C23×C12712yes—
387C23×C4C23×C12711yescharacteristic
388C23×C4C23×C12711yescharacteristic
389C23×C4C23×C12711yescharacteristic
390C23×C4C23×C12711yescharacteristic
391C23×C4C23×C12711yescharacteristic
392C23×C4C23×C12711yescharacteristic
393C23×C4C23×C12711yescharacteristic
394C2×C4⋊C4—24no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4C2×C4×C12714yes—
410C2×C4⋊C4C2×C4×C12718yes—
411C2×C4⋊C4C2×C4×C12714yes—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42C2×C4×C12714yes—
429C2×C42D4×C12714yes—
430C2×C42D4×C12714yes—
431C2×C42Q8×C12714yes—
432C2×C42Q8×C12714yes—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95C2×C4×C12718yes—
443C24C24×C12711yescharacteristic
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
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—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4C22×C4×C12714yes—
495C22×C4C22×C4×C12714yes—
496C22×C4C22×C4×C12712yes—
497C22×C4C22×C4×C12712yes—
498C22×C4C22×C4×C12712yes—
499C22×C4C2×D4×C12712yes—
500C22×C4C2×D4×C12712yes—
501C22×C4C2×D4×C12712yes—
502C22×C4C2×D4×C12712yes—
503C22×C4C2×D4×C12712yes—
504C22×C4C2×D4×C12712yes—
505C22×C4C2×Q8×C12712yes—
506C22×C4C2×Q8×C12712yes—
507C22×C4C2×Q8×C12712yes—
508C22×C4C2×Q8×C12712yes—
509C22×C4C2×Q8×C12712yes—
510C22×C4C2×Q8×C12712yes—
511C22×C4#41×C12712yes—
512C22×C4#41×C12712yes—
513C22×C4#41×C12712yes—
514C22×C4#41×C12712yes—
515C22×C4#41×C12712yes—
516C22×C4#41×C12712yes—
517C22×C4#41×C12712yes—
518C22×C4#41×C12712yes—
519C22×C4#41×C12712yes—
520C22×C4#41×C12712yes—
521C4⋊C4—28no—
522C4⋊C4—216no—
523C4⋊C4—28no—
524C4⋊C4—48no—
525C4⋊C4—44no—
526C4⋊C4—44no—
527C42—28no—
528C42—28no—
529C42—28no—
530C42—28no—
531C42—28no—
532C42—28no—
533C42—28no—
534C23C23×C4×C12711yescharacteristic
535C23C22×D4×C12711yescharacteristic
536C23C22×D4×C12711yescharacteristic
537C23C22×Q8×C12711yescharacteristic
538C23C22×Q8×C12711yescharacteristic
539C23C2×#41×C12711yescharacteristic
540C23C2×#41×C12711yescharacteristic
541C23C2×#41×C12711yescharacteristic
542C23C2×#41×C12711yescharacteristic
543C23C2×#41×C12711yescharacteristic
544C23C2×#41×C12711yescharacteristic
545C23C2×#41×C12711yescharacteristic
546C23C2×#41×C12711yescharacteristic
547C23C2×#41×C12711yescharacteristic
548C23C2×#41×C12711yescharacteristic
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4#117×C12714yes—
614C2×C4C4×D4×C12714yes—
615C2×C4C4×D4×C12714yes—
616C2×C4C4×Q8×C12714yes—
617C2×C4C4×Q8×C12714yes—
618C2×C4#121×C12714yes—
619C2×C4C22⋊Q8×C12714yes—
620C2×C4C22⋊Q8×C12714yes—
621C2×C4#123×C12714yes—
622C2×C4#125×C12714yes—
623C2×C4#125×C12714yes—
624C2×C4#126×C12714yes—
625C2×C4C4⋊Q8×C12714yes—
626C22C2×#117×C12711yescharacteristic
627C22C2×C4×D4×C12711yescharacteristic
628C22C2×C4×D4×C12711yescharacteristic
629C22C2×C4×Q8×C12711yescharacteristic
630C22C2×C4×Q8×C12711yescharacteristic
631C22C4×#41×C12711yescharacteristic
632C22C4×#41×C12711yescharacteristic
633C22C2×#121×C12711yescharacteristic
634C22C2×C22⋊Q8×C12711yescharacteristic
635C22C2×C22⋊Q8×C12711yescharacteristic
636C22C2×#123×C12711yescharacteristic
637C22#525×C12711yescharacteristic
638C22#525×C12711yescharacteristic
639C22C2×#125×C12711yescharacteristic
640C22C2×#125×C12711yescharacteristic
641C22C2×#126×C12711yescharacteristic
642C22#529×C12711yescharacteristic
643C22#529×C12711yescharacteristic
644C22#529×C12711yescharacteristic
645C22#529×C12711yescharacteristic
646C22#529×C12711yescharacteristic
647C22#529×C12711yescharacteristic
648C22#529×C12711yescharacteristic
649C22#529×C12711yescharacteristic
650C22C2×C4⋊Q8×C12711yescharacteristic
651C22#532×C12711yescharacteristic
652C22#532×C12711yescharacteristic
653C22#532×C12711yescharacteristic
654C22#532×C12711yescharacteristic
655C22#533×C12711yescharacteristic
656C22#533×C12711yescharacteristic
657C22#533×C12711yescharacteristic
658C22#533×C12711yescharacteristic
659C22#533×C12711yescharacteristic
660C22#533×C12711yescharacteristic
661C4—24no—
662C4—24no—
663C4—24no—
664C4—24no—
665C4—24no—
666C4—24no—
667C4—44no—
668C4—44no—
669C4—82no—
670C4—82no—
671C4#387×C12718yescomplemented
672C2C2×#387×C12711yescharacteristic
673C2C127×#229311yescharacteristic
674C2C127×#229511yescharacteristic
675C2C4×#121×C12711yescharacteristic
676C2C4×C22⋊Q8×C12711yescharacteristic
677C2C4×#125×C12711yescharacteristic
678C2C4×C4⋊Q8×C12711yescharacteristic
679C2C127×#285111yescharacteristic
680C2C127×#285411yescharacteristic
681C2C127×#285511yescharacteristic
682C2C127×#285711yescharacteristic
683C2C127×#285911yescharacteristic
684C2C127×#286011yescharacteristic
685C2C127×#286311yescharacteristic
686C2C127×#286411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
26. #389×C127C4semidirect
327. C4×C127#387semidirect
328. #14699C127direct (N × H)
355. C127#14699direct (N × H)
370. #389C4×C127semidirect
671. C4#387×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1272
C2×#387×C1272
C2×C43×C1272
C127×#14362
C127×C4⋊#952
C127×#14342
#14699127