Finite Group Databasebeta

← C127×#13995 #44577668

Subgroups — C127×#13995 #44577668

Order 32512.

4210 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C127C211yesmaximal, characteristic
2C23×C22⋊C4×C127C211yesmaximal, characteristic, complemented
3C2×#390×C127C212yesmaximal, complemented
4C2×#386×C127C211yesmaximal, characteristic, complemented
5C2×#386×C127C211yesmaximal, characteristic, complemented
6C2×#385×C127C211yesmaximal, characteristic, complemented
7C2×#379×C127C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
9C127×#1439C212yesmaximal, complemented
10C127×#1438C212yesmaximal, complemented
11C127×#1437C212yesmaximal, complemented
12C26×C127C2211yescharacteristic
13C23×D4×C127C2211yescharacteristic
14C23×D4×C127C2212yes—
15C24×C4×C127C2211yescharacteristic
16C24×C4×C127C2211yescharacteristic
17C2×#120×C127—24no—
18C2×#120×C127—24no—
19C2×#120×C127C418yescomplemented
20C22×C4⋊C4×C127C2212yescomplemented
21C22×C22⋊C4×C127—24no—
22C22×C22⋊C4×C127—28no—
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2212yes—
27C22×C22⋊C4×C127C2212yes—
28C22×C22⋊C4×C127C2212yes—
29C22×C22⋊C4×C127C2211yescharacteristic
30C22×C22⋊C4×C127C2211yescharacteristic
31C22×C22⋊C4×C127C2211yescharacteristic, complemented
32C22×C22⋊C4×C127C2212yescomplemented
33C22×C22⋊C4×C127C2211yescharacteristic, complemented
34C22×C42×C127C2212yescomplemented
35#390×C127—28no—
36#386×C127—24no—
37#386×C127—24no—
38#385×C127—24no—
39#379×C127—24no—
40C4×C22⋊C4×C127—24no—
41C2×#95×C127C2211yescharacteristic, complemented
42C2×#95×C127C2212yescomplemented
43C2×#95×C127C2212yescomplemented
44C2×#95×C127C2212yescomplemented
45C2×#95×C127C2211yescharacteristic, complemented
46C25×C127—24no—
47C25×C127—22no—
48C25×C127—24no—
49C25×C127—22no—
50C25×C127—22no—
51C25×C127—22no—
52C25×C127—22no—
53C25×C127—22no—
54C25×C127—42no—
55C25×C127—42no—
56C25×C127C2×C414yes—
57C25×C127C2311yescharacteristic
58C25×C127C2312yes—
59C25×C127C2311yescharacteristic
60C22×D4×C127—22no—
61C22×D4×C127—22no—
62C22×D4×C127—22no—
63C22×D4×C127—22no—
64C22×D4×C127—24no—
65C22×D4×C127—24no—
66C22×D4×C127—22no—
67C22×D4×C127—22no—
68C22×D4×C127—24no—
69C22×D4×C127—24no—
70C22×D4×C127—42no—
71C22×D4×C127—42no—
72C22×D4×C127C2×C414yes—
73C22×D4×C127C2×C418yescomplemented
74C23×C4×C127—22no—
75C23×C4×C127—22no—
76C23×C4×C127—22no—
77C23×C4×C127—24no—
78C23×C4×C127—24no—
79C23×C4×C127—22no—
80C23×C4×C127—22no—
81C23×C4×C127—42no—
82C23×C4×C127—42no—
83C23×C4×C127D414yescomplemented
84C23×C4×C127C2311yescharacteristic
85C23×C4×C127C2311yescharacteristic
86C23×C4×C127C2311yescharacteristic
87C23×C4×C127C2312yes—
88C23×C4×C127C2312yes—
89C23×C4×C127C2311yescharacteristic
90C23×C4×C127C2312yes—
91C23×C4×C127C2311yescharacteristic
92#120×C127—232no—
93C2×C4⋊C4×C127—24no—
94C2×C4⋊C4×C127—24no—
95C2×C4⋊C4×C127—42no—
96C2×C22⋊C4×C127—232no—
97C2×C22⋊C4×C127—24no—
98C2×C22⋊C4×C127—22no—
99C2×C22⋊C4×C127—22no—
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—22no—
107C2×C22⋊C4×C127—22no—
108C2×C22⋊C4×C127—22no—
109C2×C22⋊C4×C127—24no—
110C2×C22⋊C4×C127—24no—
111C2×C22⋊C4×C127—24no—
112C2×C22⋊C4×C127—24no—
113C2×C22⋊C4×C127—24no—
114C2×C22⋊C4×C127—22no—
115C2×C22⋊C4×C127—22no—
116C2×C22⋊C4×C127—24no—
117C2×C22⋊C4×C127—24no—
118C2×C22⋊C4×C127—42no—
119C2×C22⋊C4×C127—42no—
120C2×C22⋊C4×C127—42no—
121C2×C22⋊C4×C127—42no—
122C2×C22⋊C4×C127C2×C414yes—
123C2×C22⋊C4×C127C2×C418yescomplemented
124C2×C22⋊C4×C127D414yes—
125C2×C22⋊C4×C127D414yes—
126C2×C22⋊C4×C127D418yescomplemented
127C2×C22⋊C4×C127D414yescomplemented
128C2×C42×C127—24no—
129C2×C42×C127—24no—
130C2×C42×C127—42no—
131#95×C127—24no—
132#95×C127—24no—
133#95×C127—24no—
134#95×C127—22no—
135#95×C127—22no—
136C24×C127—22no—
137C24×C127—22no—
138C24×C127—22no—
139C24×C127—22no—
140C24×C127—28no—
141C24×C127—28no—
142C24×C127—216no—
143C24×C127—216no—
144C24×C127—28no—
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—28no—
158C24×C127—28no—
159C24×C127—21no—
160C24×C127—22no—
161C24×C127—21no—
162C24×C127—21no—
163C24×C127—21no—
164C24×C127—21no—
165C24×C127—21no—
166C24×C127—22no—
167C24×C127—22no—
168C24×C127—22no—
169C24×C127—48no—
170C24×C127—48no—
171C24×C127—48no—
172C24×C127—48no—
173C24×C127—48no—
174C24×C127—48no—
175C24×C127—48no—
176C24×C127—48no—
177C24×C127—48no—
178C24×C127—44no—
179C24×C127—44no—
180C24×C127—48no—
181C24×C127—44no—
182C24×C127—44no—
183C24×C127—44no—
184C24×C127—44no—
185C24×C127C22×C412yes—
186C24×C127C22×C414yes—
187C24×C127C22×C412yes—
188C24×C127C2×D414yes—
189C24×C127C2×D412yes—
190C24×C127C2×D412yes—
191C24×C127C2×D412yes—
192C24×C127C2×D412yes—
193C24×C127#4114yes—
194C24×C127#4112yes—
195C24×C127#4112yes—
196C24×C127C2411yescharacteristic
197C2×D4×C127—28no—
198C2×D4×C127—28no—
199C2×D4×C127—28no—
200C2×D4×C127—216no—
201C2×D4×C127—216no—
202C2×D4×C127—48no—
203C2×D4×C127—48no—
204C2×D4×C127—48no—
205C2×D4×C127—48no—
206C2×D4×C127—48no—
207C2×D4×C127—44no—
208C2×D4×C127—44no—
209C2×D4×C127—44no—
210C2×D4×C127—44no—
211C22×C4×C127—21no—
212C22×C4×C127—22no—
213C22×C4×C127—21no—
214C22×C4×C127—22no—
215C22×C4×C127—22no—
216C22×C4×C127—22no—
217C22×C4×C127—22no—
218C22×C4×C127—28no—
219C22×C4×C127—28no—
220C22×C4×C127—21no—
221C22×C4×C127—21no—
222C22×C4×C127—21no—
223C22×C4×C127—22no—
224C22×C4×C127—22no—
225C22×C4×C127—22no—
226C22×C4×C127—22no—
227C22×C4×C127—22no—
228C22×C4×C127—22no—
229C22×C4×C127—22no—
230C22×C4×C127—21no—
231C22×C4×C127—21no—
232C22×C4×C127—22no—
233C22×C4×C127—22no—
234C22×C4×C127—21no—
235C22×C4×C127—21no—
236C22×C4×C127—21no—
237C22×C4×C127—22no—
238C22×C4×C127—22no—
239C22×C4×C127—22no—
240C22×C4×C127—22no—
241C22×C4×C127—22no—
242C22×C4×C127—28no—
243C22×C4×C127—21no—
244C22×C4×C127—21no—
245C22×C4×C127—21no—
246C22×C4×C127—21no—
247C22×C4×C127—21no—
248C22×C4×C127—22no—
249C22×C4×C127—21no—
250C22×C4×C127—22no—
251C22×C4×C127—22no—
252C22×C4×C127—22no—
253C22×C4×C127—44no—
254C22×C4×C127—48no—
255C22×C4×C127—48no—
256C22×C4×C127—48no—
257C22×C4×C127—48no—
258C22×C4×C127—44no—
259C22×C4×C127—44no—
260C22×C4×C127C22×C412yes—
261C22×C4×C127C22×C414yes—
262C22×C4×C127C2×D414yes—
263C22×C4×C127C2×D412yes—
264C22×C4×C127C2×D414yes—
265C22×C4×C127C2×D414yes—
266C22×C4×C127C2×D414yes—
267C22×C4×C127C2×D412yes—
268C22×C4×C127C2×D414yes—
269C4⋊C4×C127—48no—
270C22⋊C4×C127—216no—
271C22⋊C4×C127—28no—
272C22⋊C4×C127—216no—
273C22⋊C4×C127—216no—
274C22⋊C4×C127—48no—
275C22⋊C4×C127—48no—
276C22⋊C4×C127—48no—
277C22⋊C4×C127—44no—
278C22⋊C4×C127—44no—
279C22⋊C4×C127—44no—
280C22⋊C4×C127C22⋊C4116yescomplemented
281C42×C127—48no—
282C23×C127—24no—
283C23×C127—24no—
284C23×C127—22no—
285C23×C127—22no—
286C23×C127—24no—
287C23×C127—22no—
288C23×C127—22no—
289C23×C127—24no—
290C23×C127—24no—
291C23×C127—24no—
292C23×C127—24no—
293C23×C127—24no—
294C23×C127—24no—
295C23×C127—24no—
296C23×C127—24no—
297C23×C127—24no—
298C23×C127—232no—
299C23×C127—24no—
300C23×C127—24no—
301C23×C127—24no—
302C23×C127—24no—
303C23×C127—24no—
304C23×C127—24no—
305C23×C127—24no—
306C23×C127—24no—
307C23×C127—24no—
308C23×C127—24no—
309C23×C127—24no—
310C23×C127—24no—
311C23×C127—24no—
312C23×C127—24no—
313C23×C127—24no—
314C23×C127—24no—
315C23×C127—24no—
316C23×C127—24no—
317C23×C127—22no—
318C23×C127—22no—
319C23×C127—24no—
320C23×C127—22no—
321C23×C127—24no—
322C23×C127—432no—
323C23×C127—432no—
324C23×C127—416no—
325C23×C127—416no—
326C23×C127—416no—
327C23×C127—432no—
328C23×C127—416no—
329C23×C127—432no—
330C23×C127—416no—
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—416no—
348C23×C127—41no—
349C23×C127—41no—
350C23×C127—41no—
351C23×C127—41no—
352C23×C127—42no—
353C23×C127—41no—
354C23×C127—41no—
355C23×C127—41no—
356C23×C127—41no—
357C23×C127—42no—
358C23×C127—42no—
359C23×C127—42no—
360C23×C127—42no—
361C23×C127—42no—
362C23×C127—42no—
363C23×C127—42no—
364C23×C127—42no—
365C23×C127—42no—
366C23×C127C2×C22⋊C414yes—
367C23×C127C4×D418yes—
368C23×C127C4×D414yes—
369C23×C127C4×D414yes—
370C23×C127#12114yes—
371C23×C127#12114yes—
372C23×C127#12414yes—
373C23×C127#12714yes—
374C23×C127C23×C411yescharacteristic
375C23×C127C22×D411yescharacteristic
376C23×C127C22×D411yescharacteristic
377C23×C127C22×D411yescharacteristic
378C23×C127C22×D412yes—
379C23×C127C22×D411yescharacteristic
380C23×C127C2×#4111yescharacteristic
381C23×C127C2×#4111yescharacteristic
382C23×C127C2×#4112yes—
383C23×C127H(5,𝔽2)12yes—
384C23×C127H(5,𝔽2)12yes—
385D4×C127—432no—
386D4×C127—416no—
387C2×C4×C127—24no—
388C2×C4×C127—24no—
389C2×C4×C127—22no—
390C2×C4×C127—22no—
391C2×C4×C127—24no—
392C2×C4×C127—24no—
393C2×C4×C127—24no—
394C2×C4×C127—24no—
395C2×C4×C127—24no—
396C2×C4×C127—24no—
397C2×C4×C127—22no—
398C2×C4×C127—22no—
399C2×C4×C127—22no—
400C2×C4×C127—22no—
401C2×C4×C127—24no—
402C2×C4×C127—24no—
403C2×C4×C127—22no—
404C2×C4×C127—22no—
405C2×C4×C127—24no—
406C2×C4×C127—24no—
407C2×C4×C127—24no—
408C2×C4×C127—24no—
409C2×C4×C127—416no—
410C2×C4×C127—416no—
411C2×C4×C127—41no—
412C2×C4×C127—41no—
413C2×C4×C127—42no—
414C2×C4×C127—41no—
415C2×C4×C127—42no—
416C2×C4×C127—41no—
417C2×C4×C127—42no—
418C2×C4×C127—42no—
419C2×C4×C127—42no—
420C2×C4×C127—42no—
421C2×C4×C127—42no—
422C2×C4×C127—42no—
423C2×C4×C127—42no—
424C2×C4×C127—42no—
425C2×C4×C127—41no—
426C2×C4×C127—41no—
427C2×C4×C127—41no—
428C2×C4×C127—41no—
429C2×C4×C127—41no—
430C2×C4×C127—41no—
431C2×C4×C127—42no—
432C2×C4×C127—42no—
433C2×C4×C127—42no—
434C2×C4×C127—42no—
435C2×C4×C127C2×C22⋊C418yescomplemented
436C2×C4×C127#12014yescomplemented
437C22×C127—24no—
438C22×C127—28no—
439C22×C127—28no—
440C22×C127—24no—
441C22×C127—24no—
442C22×C127—28no—
443C22×C127—24no—
444C22×C127—28no—
445C22×C127—24no—
446C22×C127—24no—
447C22×C127—28no—
448C22×C127—28no—
449C22×C127—28no—
450C22×C127—464no—
451C22×C127—44no—
452C22×C127—44no—
453C22×C127—44no—
454C22×C127—44no—
455C22×C127—44no—
456C22×C127—44no—
457C22×C127—44no—
458C22×C127—44no—
459C22×C127—44no—
460C22×C127—44no—
461C22×C127—44no—
462C22×C127—44no—
463C22×C127—42no—
464C22×C127—44no—
465C22×C127—44no—
466C22×C127—42no—
467C22×C127—42no—
468C22×C127—81no—
469C22×C127—81no—
470C22×C127—82no—
471C22×C127—81no—
472C22×C127—82no—
473C22×C127—81no—
474C22×C127#39018yescomplemented
475C22×C127C22×C22⋊C411yescharacteristic
476C22×C127C2×C4×D411yescharacteristic
477C22×C127C2×C4×D412yes—
478C22×C127C2×C4×D411yescharacteristic
479C22×C127#51812yes—
480C22×C127C2×#12011yescharacteristic
481C22×C127C2×#12111yescharacteristic
482C22×C127C2×#12111yescharacteristic
483C22×C127#52511yescharacteristic
484C22×C127#52512yes—
485C22×C127C2×#12411yescharacteristic
486C22×C127C2×#12711yescharacteristic
487C22×C127#53411yescharacteristic
488C22×C127#53511yescharacteristic
489C22×C127#53812yes—
490C22×C127D4212yes—
491C22×C127D4212yes—
492C22×C127D4212yes—
493C22×C127#54612yes—
494C22×C127#54612yes—
495C22×C127#54612yes—
496C22×C127#54612yes—
497C22×C127#55112yes—
498C4×C127—28no—
499C4×C127—24no—
500C4×C127—42no—
501C4×C127—44no—
502C4×C127—44no—
503C4×C127—42no—
504C4×C127—81no—
505C4×C127—81no—
506#13995C12711yesmaximal, characteristic, direct product factor, Sylow
507C2×C127—28no—
508C2×C127—48no—
509C2×C127—82no—
510C2×C127C2×#39011yescharacteristic
511C2×C127C4×#12011yescharacteristic
512C2×C127#232111yescharacteristic
513C2×C127D4×C22⋊C412yes—
514C2×C127#235812yes—
515C2×C127#241011yescharacteristic
516C2×C127#241111yescharacteristic
517C2×C127#242412yes—
518C2×C127#243311yescharacteristic
519C2×C127#247212yes—
520C2×C127#253911yescharacteristic
521C22×#120C2×C12711yescharacteristic
522C23×C22⋊C4C2×C12711yescharacteristic, complemented
523C2×#390C2×C12712yescomplemented
524C2×#386C2×C12711yescharacteristic, complemented
525C2×#386C2×C12711yescharacteristic, complemented
526C2×#385C2×C12711yescharacteristic, complemented
527C2×#379C2×C12711yescharacteristic, complemented
528C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
529#1439C2×C12712yescomplemented
530#1438C2×C12712yescomplemented
531#1437C2×C12712yescomplemented
532C127#1399511yescharacteristic, direct product factor, Sylow
533C26C22×C12711yescharacteristic
534C23×D4C22×C12711yescharacteristic
535C23×D4C22×C12712yes—
536C24×C4C22×C12711yescharacteristic
537C24×C4C22×C12711yescharacteristic
538C2×#120—24no—
539C2×#120—24no—
540C2×#120C4×C12718yescomplemented
541C22×C4⋊C4C22×C12712yescomplemented
542C22×C22⋊C4—24no—
543C22×C22⋊C4—28no—
544C22×C22⋊C4C22×C12712yes—
545C22×C22⋊C4C22×C12711yescharacteristic
546C22×C22⋊C4C22×C12712yes—
547C22×C22⋊C4C22×C12712yes—
548C22×C22⋊C4C22×C12712yes—
549C22×C22⋊C4C22×C12712yes—
550C22×C22⋊C4C22×C12711yescharacteristic
551C22×C22⋊C4C22×C12711yescharacteristic
552C22×C22⋊C4C22×C12711yescharacteristic, complemented
553C22×C22⋊C4C22×C12712yescomplemented
554C22×C22⋊C4C22×C12711yescharacteristic, complemented
555C22×C42C22×C12712yescomplemented
556#390—28no—
557#386—24no—
558#386—24no—
559#385—24no—
560#379—24no—
561C4×C22⋊C4—24no—
562C2×#95C22×C12711yescharacteristic, complemented
563C2×#95C22×C12712yescomplemented
564C2×#95C22×C12712yescomplemented
565C2×#95C22×C12712yescomplemented
566C2×#95C22×C12711yescharacteristic, complemented
567C25—24no—
568C25—22no—
569C25—24no—
570C25—22no—
571C25—22no—
572C25—22no—
573C25—22no—
574C25—22no—
575C25—42no—
576C25—42no—
577C25C2×C4×C12714yes—
578C25C23×C12711yescharacteristic
579C25C23×C12712yes—
580C25C23×C12711yescharacteristic
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—22no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—42no—
592C22×D4—42no—
593C22×D4C2×C4×C12714yes—
594C22×D4C2×C4×C12718yescomplemented
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—24no—
599C23×C4—24no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—42no—
603C23×C4—42no—
604C23×C4D4×C12714yescomplemented
605C23×C4C23×C12711yescharacteristic
606C23×C4C23×C12711yescharacteristic
607C23×C4C23×C12711yescharacteristic
608C23×C4C23×C12712yes—
609C23×C4C23×C12712yes—
610C23×C4C23×C12711yescharacteristic
611C23×C4C23×C12712yes—
612C23×C4C23×C12711yescharacteristic
613#120—232no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—42no—
617C2×C22⋊C4—232no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—24no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—24no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4—42no—
643C2×C22⋊C4C2×C4×C12714yes—
644C2×C22⋊C4C2×C4×C12718yescomplemented
645C2×C22⋊C4D4×C12714yes—
646C2×C22⋊C4D4×C12714yes—
647C2×C22⋊C4D4×C12718yescomplemented
648C2×C22⋊C4D4×C12714yescomplemented
649C2×C42—24no—
650C2×C42—24no—
651C2×C42—42no—
652#95—24no—
653#95—24no—
654#95—24no—
655#95—22no—
656#95—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—28no—
662C24—28no—
663C24—216no—
664C24—216no—
665C24—28no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—28no—
679C24—28no—
680C24—21no—
681C24—22no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—44no—
700C24—44no—
701C24—48no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24C22×C4×C12712yes—
707C24C22×C4×C12714yes—
708C24C22×C4×C12712yes—
709C24C2×D4×C12714yes—
710C24C2×D4×C12712yes—
711C24C2×D4×C12712yes—
712C24C2×D4×C12712yes—
713C24C2×D4×C12712yes—
714C24#41×C12714yes—
715C24#41×C12712yes—
716C24#41×C12712yes—
717C24C24×C12711yescharacteristic
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—216no—
722C2×D4—216no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—28no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—44no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4C22×C4×C12712yes—
782C22×C4C22×C4×C12714yes—
783C22×C4C2×D4×C12714yes—
784C22×C4C2×D4×C12712yes—
785C22×C4C2×D4×C12714yes—
786C22×C4C2×D4×C12714yes—
787C22×C4C2×D4×C12714yes—
788C22×C4C2×D4×C12712yes—
789C22×C4C2×D4×C12714yes—
790C4⋊C4—48no—
791C22⋊C4—216no—
792C22⋊C4—28no—
793C22⋊C4—216no—
794C22⋊C4—216no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4C22⋊C4×C127116yescomplemented
802C42—48no—
803C23—24no—
804C23—24no—
805C23—22no—
806C23—22no—
807C23—24no—
808C23—22no—
809C23—22no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—232no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—24no—
841C23—22no—
842C23—24no—
843C23—432no—
844C23—432no—
845C23—416no—
846C23—416no—
847C23—416no—
848C23—432no—
849C23—416no—
850C23—432no—
851C23—416no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—416no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—42no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23C2×C22⋊C4×C12714yes—
888C23C4×D4×C12718yes—
889C23C4×D4×C12714yes—
890C23C4×D4×C12714yes—
891C23#121×C12714yes—
892C23#121×C12714yes—
893C23#124×C12714yes—
894C23#127×C12714yes—
895C23C23×C4×C12711yescharacteristic
896C23C22×D4×C12711yescharacteristic
897C23C22×D4×C12711yescharacteristic
898C23C22×D4×C12711yescharacteristic
899C23C22×D4×C12712yes—
900C23C22×D4×C12711yescharacteristic
901C23C2×#41×C12711yescharacteristic
902C23C2×#41×C12711yescharacteristic
903C23C2×#41×C12712yes—
904C23H(5,𝔽2)×C12712yes—
905C23H(5,𝔽2)×C12712yes—
906D4—432no—
907D4—416no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—416no—
931C2×C4—416no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—42no—
937C2×C4—41no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4C2×C22⋊C4×C12718yescomplemented
957C2×C4#120×C12714yescomplemented
958C22—24no—
959C22—28no—
960C22—28no—
961C22—24no—
962C22—24no—
963C22—28no—
964C22—24no—
965C22—28no—
966C22—24no—
967C22—24no—
968C22—28no—
969C22—28no—
970C22—28no—
971C22—464no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—44no—
986C22—44no—
987C22—42no—
988C22—42no—
989C22—81no—
990C22—81no—
991C22—82no—
992C22—81no—
993C22—82no—
994C22—81no—
995C22#390×C12718yescomplemented
996C22C22×C22⋊C4×C12711yescharacteristic
997C22C2×C4×D4×C12711yescharacteristic
998C22C2×C4×D4×C12712yes—
999C22C2×C4×D4×C12711yescharacteristic
1000C22#518×C12712yes—
1001C22C2×#120×C12711yescharacteristic
1002C22C2×#121×C12711yescharacteristic
1003C22C2×#121×C12711yescharacteristic
1004C22#525×C12711yescharacteristic
1005C22#525×C12712yes—
1006C22C2×#124×C12711yescharacteristic
1007C22C2×#127×C12711yescharacteristic
1008C22#534×C12711yescharacteristic
1009C22#535×C12711yescharacteristic
1010C22#538×C12712yes—
1011C22D42×C12712yes—
1012C22D42×C12712yes—
1013C22D42×C12712yes—
1014C22#546×C12712yes—
1015C22#546×C12712yes—
1016C22#546×C12712yes—
1017C22#546×C12712yes—
1018C22#551×C12712yes—
1019C4—28no—
1020C4—24no—
1021C4—42no—
1022C4—44no—
1023C4—44no—
1024C4—42no—
1025C4—81no—
1026C4—81no—
1027C2—28no—
1028C2—48no—
1029C2—82no—
1030C2C2×#390×C12711yescharacteristic
1031C2C4×#120×C12711yescharacteristic
1032C2C127×#232111yescharacteristic
1033C2D4×C22⋊C4×C12712yes—
1034C2C127×#235812yes—
1035C2C127×#241011yescharacteristic
1036C2C127×#241111yescharacteristic
1037C2C127×#242412yes—
1038C2C127×#243311yescharacteristic
1039C2C127×#247212yes—
1040C2C127×#253911yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC22×#120×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C127C2semidirect
3. C2×#390×C127C2semidirect
4. C2×#386×C127C2semidirect
5. C2×#386×C127C2semidirect
6. C2×#385×C127C2semidirect
7. C2×#379×C127C2semidirect
8. C2×C4×C22⋊C4×C127C2semidirect
9. C127×#1439C2semidirect
10. C127×#1438C2semidirect
11. C127×#1437C2semidirect
19. C2×#120×C127C4semidirect
20. C22×C4⋊C4×C127C22semidirect
31. C22×C22⋊C4×C127C22semidirect
32. C22×C22⋊C4×C127C22semidirect
33. C22×C22⋊C4×C127C22semidirect
34. C22×C42×C127C22semidirect
41. C2×#95×C127C22semidirect
42. C2×#95×C127C22semidirect
43. C2×#95×C127C22semidirect
44. C2×#95×C127C22semidirect
45. C2×#95×C127C22semidirect
73. C22×D4×C127C2×C4semidirect
83. C23×C4×C127D4semidirect
123. C2×C22⋊C4×C127C2×C4semidirect
126. C2×C22⋊C4×C127D4semidirect
127. C2×C22⋊C4×C127D4semidirect
280. C22⋊C4×C127C22⋊C4semidirect
435. C2×C4×C127C2×C22⋊C4semidirect
436. C2×C4×C127#120semidirect
474. C22×C127#390semidirect
506. #13995C127direct (N × H)
522. C23×C22⋊C4C2×C127semidirect
523. C2×#390C2×C127semidirect
524. C2×#386C2×C127semidirect
525. C2×#386C2×C127semidirect
526. C2×#385C2×C127semidirect
527. C2×#379C2×C127semidirect
528. C2×C4×C22⋊C4C2×C127semidirect
529. #1439C2×C127semidirect
530. #1438C2×C127semidirect
531. #1437C2×C127semidirect
532. C127#13995direct (N × H)
540. C2×#120C4×C127semidirect
541. C22×C4⋊C4C22×C127semidirect
552. C22×C22⋊C4C22×C127semidirect
553. C22×C22⋊C4C22×C127semidirect
554. C22×C22⋊C4C22×C127semidirect
555. C22×C42C22×C127semidirect
562. C2×#95C22×C127semidirect
563. C2×#95C22×C127semidirect
564. C2×#95C22×C127semidirect
565. C2×#95C22×C127semidirect
566. C2×#95C22×C127semidirect
594. C22×D4C2×C4×C127semidirect
604. C23×C4D4×C127semidirect
644. C2×C22⋊C4C2×C4×C127semidirect
647. C2×C22⋊C4D4×C127semidirect
648. C2×C22⋊C4D4×C127semidirect
801. C22⋊C4C22⋊C4×C127semidirect
956. C2×C4C2×C22⋊C4×C127semidirect
957. C2×C4#120×C127semidirect
995. C22#390×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1272
C23×C22⋊C4×C1272
C2×#390×C1272
C2×#386×C1272
C2×#385×C1272
C2×#379×C1272
C2×C4×C22⋊C4×C1272
C127×#14392
C127×#14382
C127×#14372
#13995127