Finite Group Databasebeta

← C127×#13967 #44577640

Subgroups — C127×#13967 #44577640

Order 32512.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C127C211yesmaximal, characteristic
2C22×C4×D4×C127C211yesmaximal, characteristic, complemented
3C23×C22⋊C4×C127C211yesmaximal, characteristic, complemented
4C2×#386×C127C212yesmaximal, complemented
5C2×#386×C127C211yesmaximal, characteristic, complemented
6C2×#379×C127C211yesmaximal, characteristic, complemented
7C127×#1439C212yesmaximal, complemented
8C127×#1438C212yesmaximal, complemented
9C127×#1437C212yesmaximal, complemented
10C127×C22⋊#95C211yesmaximal, characteristic, complemented
11C127×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C127C2211yescharacteristic
13C23×D4×C127C2212yes—
14C23×D4×C127C2211yescharacteristic
15C24×C4×C127C2211yescharacteristic
16C24×C4×C127C2211yescharacteristic
17C24×C4×C127C2211yescharacteristic, complemented
18C2×#120×C127—24no—
19C2×#120×C127—24no—
20C2×#120×C127C418yescomplemented
21C2×C4×D4×C127—24no—
22C2×C4×D4×C127—24no—
23C2×C4×D4×C127—24no—
24C22×C4⋊C4×C127C2211yescharacteristic, complemented
25C22×C22⋊C4×C127—24no—
26C22×C22⋊C4×C127—28no—
27C22×C22⋊C4×C127C2212yes—
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2212yes—
30C22×C22⋊C4×C127C2212yes—
31C22×C22⋊C4×C127C2211yescharacteristic
32C22×C22⋊C4×C127C2212yes—
33C22×C22⋊C4×C127C2212yes—
34C22×C22⋊C4×C127C2211yescharacteristic
35C22×C22⋊C4×C127C2211yescharacteristic, complemented
36C22×C22⋊C4×C127C2212yescomplemented
37C22×C42×C127C2211yescharacteristic, complemented
38#386×C127—24no—
39#386×C127—28no—
40#379×C127—24no—
41C2×#95×C127C2212yescomplemented
42C2×#95×C127C2212yescomplemented
43C2×#95×C127C2212yescomplemented
44C2×#95×C127C2212yescomplemented
45C2×#95×C127C2212yescomplemented
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×C414yescomplemented
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—24no—
67C22×D4×C127—24no—
68C22×D4×C127—42no—
69C22×D4×C127—42no—
70C22×D4×C127C2×C414yes—
71C22×D4×C127C2×C418yescomplemented
72C22×D4×C127D414yes—
73C22×D4×C127D414yes—
74C23×C4×C127—22no—
75C23×C4×C127—22no—
76C23×C4×C127—22no—
77C23×C4×C127—22no—
78C23×C4×C127—24no—
79C23×C4×C127—24no—
80C23×C4×C127—22no—
81C23×C4×C127—22no—
82C23×C4×C127—22no—
83C23×C4×C127—22no—
84C23×C4×C127—24no—
85C23×C4×C127—42no—
86C23×C4×C127—42no—
87C23×C4×C127—42no—
88C23×C4×C127D414yescomplemented
89C23×C4×C127C2312yes—
90C23×C4×C127C2312yes—
91C23×C4×C127C2311yescharacteristic
92C23×C4×C127C2311yescharacteristic
93C23×C4×C127C2311yescharacteristic
94C23×C4×C127C2312yes—
95C23×C4×C127C2311yescharacteristic
96C23×C4×C127C2311yescharacteristic
97#120×C127—232no—
98C4×D4×C127—232no—
99C2×C4⋊C4×C127—22no—
100C2×C4⋊C4×C127—22no—
101C2×C4⋊C4×C127—22no—
102C2×C22⋊C4×C127—232no—
103C2×C22⋊C4×C127—24no—
104C2×C22⋊C4×C127—22no—
105C2×C22⋊C4×C127—22no—
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—24no—
115C2×C22⋊C4×C127—22no—
116C2×C22⋊C4×C127—22no—
117C2×C22⋊C4×C127—22no—
118C2×C22⋊C4×C127—24no—
119C2×C22⋊C4×C127—22no—
120C2×C22⋊C4×C127—24no—
121C2×C22⋊C4×C127—24no—
122C2×C22⋊C4×C127—22no—
123C2×C22⋊C4×C127—24no—
124C2×C22⋊C4×C127—24no—
125C2×C22⋊C4×C127—24no—
126C2×C22⋊C4×C127—42no—
127C2×C22⋊C4×C127—42no—
128C2×C22⋊C4×C127—42no—
129C2×C22⋊C4×C127C2×C414yescomplemented
130C2×C22⋊C4×C127C2×C418yescomplemented
131C2×C22⋊C4×C127D418yescomplemented
132C2×C22⋊C4×C127D414yescomplemented
133C2×C42×C127—22no—
134C2×C42×C127—22no—
135C2×C42×C127—22no—
136#95×C127—24no—
137#95×C127—24no—
138#95×C127—24no—
139#95×C127—42no—
140#95×C127—42no—
141C24×C127—22no—
142C24×C127—22no—
143C24×C127—22no—
144C24×C127—22no—
145C24×C127—28no—
146C24×C127—28no—
147C24×C127—216no—
148C24×C127—28no—
149C24×C127—216no—
150C24×C127—22no—
151C24×C127—22no—
152C24×C127—22no—
153C24×C127—21no—
154C24×C127—21no—
155C24×C127—22no—
156C24×C127—22no—
157C24×C127—22no—
158C24×C127—21no—
159C24×C127—21no—
160C24×C127—22no—
161C24×C127—22no—
162C24×C127—22no—
163C24×C127—22no—
164C24×C127—22no—
165C24×C127—22no—
166C24×C127—22no—
167C24×C127—22no—
168C24×C127—22no—
169C24×C127—22no—
170C24×C127—28no—
171C24×C127—28no—
172C24×C127—48no—
173C24×C127—48no—
174C24×C127—48no—
175C24×C127—48no—
176C24×C127—48no—
177C24×C127—48no—
178C24×C127—48no—
179C24×C127—48no—
180C24×C127—48no—
181C24×C127—44no—
182C24×C127—44no—
183C24×C127—48no—
184C24×C127—44no—
185C24×C127—44no—
186C24×C127—44no—
187C24×C127—44no—
188C24×C127C22×C412yes—
189C24×C127C22×C414yes—
190C24×C127C22×C412yes—
191C24×C127C2×D412yes—
192C24×C127C2×D412yes—
193C24×C127C2×D414yes—
194C24×C127C2×D412yes—
195C24×C127C2×D412yes—
196C24×C127C2×D412yes—
197C24×C127C2×D412yes—
198C24×C127#4114yes—
199C24×C127#4112yes—
200C24×C127#4112yes—
201C24×C127C2411yescharacteristic
202C2×D4×C127—28no—
203C2×D4×C127—28no—
204C2×D4×C127—28no—
205C2×D4×C127—28no—
206C2×D4×C127—28no—
207C2×D4×C127—28no—
208C2×D4×C127—216no—
209C2×D4×C127—216no—
210C2×D4×C127—48no—
211C2×D4×C127—48no—
212C2×D4×C127—48no—
213C2×D4×C127—48no—
214C2×D4×C127—48no—
215C2×D4×C127C22⋊C4116yescomplemented
216C22×C4×C127—21no—
217C22×C4×C127—21no—
218C22×C4×C127—21no—
219C22×C4×C127—21no—
220C22×C4×C127—21no—
221C22×C4×C127—21no—
222C22×C4×C127—22no—
223C22×C4×C127—28no—
224C22×C4×C127—28no—
225C22×C4×C127—28no—
226C22×C4×C127—22no—
227C22×C4×C127—22no—
228C22×C4×C127—22no—
229C22×C4×C127—21no—
230C22×C4×C127—21no—
231C22×C4×C127—22no—
232C22×C4×C127—22no—
233C22×C4×C127—22no—
234C22×C4×C127—22no—
235C22×C4×C127—22no—
236C22×C4×C127—21no—
237C22×C4×C127—21no—
238C22×C4×C127—21no—
239C22×C4×C127—21no—
240C22×C4×C127—22no—
241C22×C4×C127—22no—
242C22×C4×C127—22no—
243C22×C4×C127—22no—
244C22×C4×C127—22no—
245C22×C4×C127—22no—
246C22×C4×C127—22no—
247C22×C4×C127—22no—
248C22×C4×C127—22no—
249C22×C4×C127—22no—
250C22×C4×C127—28no—
251C22×C4×C127—22no—
252C22×C4×C127—22no—
253C22×C4×C127—22no—
254C22×C4×C127—22no—
255C22×C4×C127—22no—
256C22×C4×C127—22no—
257C22×C4×C127—22no—
258C22×C4×C127—44no—
259C22×C4×C127—48no—
260C22×C4×C127—48no—
261C22×C4×C127—48no—
262C22×C4×C127—48no—
263C22×C4×C127—48no—
264C22×C4×C127—48no—
265C22×C4×C127—44no—
266C22×C4×C127—44no—
267C22×C4×C127—44no—
268C22×C4×C127—44no—
269C22×C4×C127C22×C414yes—
270C22×C4×C127C22×C412yes—
271C22×C4×C127C2×D414yes—
272C22×C4×C127C2×D412yes—
273C22×C4×C127C2×D412yes—
274C22×C4×C127C2×D412yes—
275C22×C4×C127C2×D412yes—
276C22×C4×C127C2×D412yes—
277C22×C4×C127C2×D414yes—
278C22×C4×C127C2×D412yes—
279C4⋊C4×C127—28no—
280C22⋊C4×C127—216no—
281C22⋊C4×C127—28no—
282C22⋊C4×C127—28no—
283C22⋊C4×C127—28no—
284C22⋊C4×C127—216no—
285C22⋊C4×C127—216no—
286C22⋊C4×C127—48no—
287C22⋊C4×C127—48no—
288C22⋊C4×C127—48no—
289C22⋊C4×C127—44no—
290C42×C127—28no—
291C23×C127—24no—
292C23×C127—24no—
293C23×C127—22no—
294C23×C127—22no—
295C23×C127—24no—
296C23×C127—22no—
297C23×C127—22no—
298C23×C127—24no—
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—232no—
308C23×C127—24no—
309C23×C127—24no—
310C23×C127—22no—
311C23×C127—22no—
312C23×C127—24no—
313C23×C127—24no—
314C23×C127—24no—
315C23×C127—24no—
316C23×C127—24no—
317C23×C127—24no—
318C23×C127—24no—
319C23×C127—22no—
320C23×C127—22no—
321C23×C127—22no—
322C23×C127—22no—
323C23×C127—24no—
324C23×C127—24no—
325C23×C127—24no—
326C23×C127—24no—
327C23×C127—24no—
328C23×C127—24no—
329C23×C127—24no—
330C23×C127—24no—
331C23×C127—24no—
332C23×C127—24no—
333C23×C127—24no—
334C23×C127—24no—
335C23×C127—24no—
336C23×C127—24no—
337C23×C127—24no—
338C23×C127—432no—
339C23×C127—432no—
340C23×C127—416no—
341C23×C127—416no—
342C23×C127—416no—
343C23×C127—416no—
344C23×C127—432no—
345C23×C127—432no—
346C23×C127—416no—
347C23×C127—41no—
348C23×C127—42no—
349C23×C127—42no—
350C23×C127—42no—
351C23×C127—42no—
352C23×C127—41no—
353C23×C127—42no—
354C23×C127—41no—
355C23×C127—42no—
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×C127—42no—
367C23×C127—42no—
368C23×C127—42no—
369C23×C127—42no—
370C23×C127—42no—
371C23×C127—42no—
372C23×C127—42no—
373C23×C127—416no—
374C23×C127C2×C22⋊C414yes—
375C23×C127C2×C22⋊C414yescomplemented
376C23×C127C4×D414yes—
377C23×C127C4×D414yes—
378C23×C127C4×D418yescomplemented
379C23×C127#12014yes—
380C23×C127#12114yes—
381C23×C127#12114yes—
382C23×C127#12314yes—
383C23×C127C23×C411yescharacteristic
384C23×C127C22×D411yescharacteristic
385C23×C127C22×D411yescharacteristic
386C23×C127C22×D411yescharacteristic
387C23×C127C22×D411yescharacteristic
388C23×C127C22×D412yes—
389C23×C127C2×#4111yescharacteristic
390C23×C127C2×#4111yescharacteristic
391C23×C127C2×#4112yes—
392C23×C127H(5,𝔽2)12yes—
393C23×C127H(5,𝔽2)12yes—
394D4×C127—232no—
395D4×C127—432no—
396C2×C4×C127—22no—
397C2×C4×C127—22no—
398C2×C4×C127—22no—
399C2×C4×C127—22no—
400C2×C4×C127—22no—
401C2×C4×C127—22no—
402C2×C4×C127—22no—
403C2×C4×C127—22no—
404C2×C4×C127—24no—
405C2×C4×C127—24no—
406C2×C4×C127—24no—
407C2×C4×C127—24no—
408C2×C4×C127—24no—
409C2×C4×C127—22no—
410C2×C4×C127—22no—
411C2×C4×C127—24no—
412C2×C4×C127—22no—
413C2×C4×C127—22no—
414C2×C4×C127—22no—
415C2×C4×C127—24no—
416C2×C4×C127—24no—
417C2×C4×C127—24no—
418C2×C4×C127—24no—
419C2×C4×C127—416no—
420C2×C4×C127—416no—
421C2×C4×C127—416no—
422C2×C4×C127—41no—
423C2×C4×C127—42no—
424C2×C4×C127—41no—
425C2×C4×C127—41no—
426C2×C4×C127—41no—
427C2×C4×C127—42no—
428C2×C4×C127—42no—
429C2×C4×C127—42no—
430C2×C4×C127—42no—
431C2×C4×C127—42no—
432C2×C4×C127—42no—
433C2×C4×C127—42no—
434C2×C4×C127—42no—
435C2×C4×C127—42no—
436C2×C4×C127—42no—
437C2×C4×C127—42no—
438C2×C4×C127—42no—
439C2×C4×C127—42no—
440C2×C4×C127—42no—
441C2×C4×C127—42no—
442C2×C4×C127—42no—
443C2×C4×C127—42no—
444C2×C4×C127—42no—
445C2×C4×C127C2×C22⋊C414yescomplemented
446C2×C4×C127#12014yescomplemented
447C22×C127—24no—
448C22×C127—28no—
449C22×C127—28no—
450C22×C127—24no—
451C22×C127—24no—
452C22×C127—24no—
453C22×C127—28no—
454C22×C127—28no—
455C22×C127—24no—
456C22×C127—24no—
457C22×C127—28no—
458C22×C127—28no—
459C22×C127—28no—
460C22×C127—24no—
461C22×C127—28no—
462C22×C127—464no—
463C22×C127—42no—
464C22×C127—44no—
465C22×C127—44no—
466C22×C127—44no—
467C22×C127—44no—
468C22×C127—42no—
469C22×C127—44no—
470C22×C127—42no—
471C22×C127—44no—
472C22×C127—42no—
473C22×C127—44no—
474C22×C127—44no—
475C22×C127—44no—
476C22×C127—44no—
477C22×C127—44no—
478C22×C127—44no—
479C22×C127—44no—
480C22×C127—42no—
481C22×C127—44no—
482C22×C127—44no—
483C22×C127—42no—
484C22×C127#38618yescomplemented
485C22×C127C22×C22⋊C411yescharacteristic
486C22×C127C2×C4×D411yescharacteristic
487C22×C127C2×C4×D412yes—
488C22×C127C2×C4×D411yescharacteristic
489C22×C127#51812yes—
490C22×C127C2×#12011yescharacteristic
491C22×C127C2×#12011yescharacteristic
492C22×C127C2×#12111yescharacteristic
493C22×C127C2×#12111yescharacteristic
494C22×C127C2×#12311yescharacteristic
495C22×C127#52511yescharacteristic
496C22×C127#52512yes—
497C22×C127#53411yescharacteristic
498C22×C127#53511yescharacteristic
499C22×C127#53812yes—
500C22×C127D4212yes—
501C22×C127D4212yes—
502C22×C127D4212yes—
503C22×C127#54612yes—
504C22×C127#54612yes—
505C22×C127#54612yes—
506C22×C127#54612yes—
507C22×C127#55112yes—
508C4×C127—24no—
509C4×C127—24no—
510C4×C127—44no—
511C4×C127—42no—
512C4×C127—42no—
513C4×C127—42no—
514C4×C127—44no—
515C4×C127—82no—
516#13967C12711yesmaximal, characteristic, direct product factor, Sylow
517C2×C127—28no—
518C2×C127—44no—
519C2×C127—48no—
520C2×C127C2×#38611yescharacteristic
521C2×C127C4×#12011yescharacteristic
522C2×C127#232111yescharacteristic
523C2×C127D4×C22⋊C412yes—
524C2×C127#235812yes—
525C2×C127#240311yescharacteristic
526C2×C127#240411yescharacteristic
527C2×C127#240811yescharacteristic
528C2×C127#241812yes—
529C2×C127#242412yes—
530C2×C127#253411yescharacteristic
531C22×#120C2×C12711yescharacteristic
532C22×C4×D4C2×C12711yescharacteristic, complemented
533C23×C22⋊C4C2×C12711yescharacteristic, complemented
534C2×#386C2×C12712yescomplemented
535C2×#386C2×C12711yescharacteristic, complemented
536C2×#379C2×C12711yescharacteristic, complemented
537#1439C2×C12712yescomplemented
538#1438C2×C12712yescomplemented
539#1437C2×C12712yescomplemented
540C22⋊#95C2×C12711yescharacteristic, complemented
541C22⋊#95C2×C12711yescharacteristic, complemented
542C127#1396711yescharacteristic, direct product factor, Sylow
543C26C22×C12711yescharacteristic
544C23×D4C22×C12712yes—
545C23×D4C22×C12711yescharacteristic
546C24×C4C22×C12711yescharacteristic
547C24×C4C22×C12711yescharacteristic
548C24×C4C22×C12711yescharacteristic, complemented
549C2×#120—24no—
550C2×#120—24no—
551C2×#120C4×C12718yescomplemented
552C2×C4×D4—24no—
553C2×C4×D4—24no—
554C2×C4×D4—24no—
555C22×C4⋊C4C22×C12711yescharacteristic, complemented
556C22×C22⋊C4—24no—
557C22×C22⋊C4—28no—
558C22×C22⋊C4C22×C12712yes—
559C22×C22⋊C4C22×C12711yescharacteristic
560C22×C22⋊C4C22×C12712yes—
561C22×C22⋊C4C22×C12712yes—
562C22×C22⋊C4C22×C12711yescharacteristic
563C22×C22⋊C4C22×C12712yes—
564C22×C22⋊C4C22×C12712yes—
565C22×C22⋊C4C22×C12711yescharacteristic
566C22×C22⋊C4C22×C12711yescharacteristic, complemented
567C22×C22⋊C4C22×C12712yescomplemented
568C22×C42C22×C12711yescharacteristic, complemented
569#386—24no—
570#386—28no—
571#379—24no—
572C2×#95C22×C12712yescomplemented
573C2×#95C22×C12712yescomplemented
574C2×#95C22×C12712yescomplemented
575C2×#95C22×C12712yescomplemented
576C2×#95C22×C12712yescomplemented
577C25—24no—
578C25—22no—
579C25—24no—
580C25—22no—
581C25—22no—
582C25—22no—
583C25—22no—
584C25—22no—
585C25—42no—
586C25—42no—
587C25C2×C4×C12714yescomplemented
588C25C23×C12711yescharacteristic
589C25C23×C12712yes—
590C25C23×C12711yescharacteristic
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—22no—
595C22×D4—24no—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—42no—
600C22×D4—42no—
601C22×D4C2×C4×C12714yes—
602C22×D4C2×C4×C12718yescomplemented
603C22×D4D4×C12714yes—
604C22×D4D4×C12714yes—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—24no—
610C23×C4—24no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—22no—
615C23×C4—24no—
616C23×C4—42no—
617C23×C4—42no—
618C23×C4—42no—
619C23×C4D4×C12714yescomplemented
620C23×C4C23×C12712yes—
621C23×C4C23×C12712yes—
622C23×C4C23×C12711yescharacteristic
623C23×C4C23×C12711yescharacteristic
624C23×C4C23×C12711yescharacteristic
625C23×C4C23×C12712yes—
626C23×C4C23×C12711yescharacteristic
627C23×C4C23×C12711yescharacteristic
628#120—232no—
629C4×D4—232no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C22⋊C4—232no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—42no—
658C2×C22⋊C4—42no—
659C2×C22⋊C4—42no—
660C2×C22⋊C4C2×C4×C12714yescomplemented
661C2×C22⋊C4C2×C4×C12718yescomplemented
662C2×C22⋊C4D4×C12718yescomplemented
663C2×C22⋊C4D4×C12714yescomplemented
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—22no—
667#95—24no—
668#95—24no—
669#95—24no—
670#95—42no—
671#95—42no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—28no—
677C24—28no—
678C24—216no—
679C24—28no—
680C24—216no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—21no—
685C24—21no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—28no—
702C24—28no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—48no—
711C24—48no—
712C24—44no—
713C24—44no—
714C24—48no—
715C24—44no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24C22×C4×C12712yes—
720C24C22×C4×C12714yes—
721C24C22×C4×C12712yes—
722C24C2×D4×C12712yes—
723C24C2×D4×C12712yes—
724C24C2×D4×C12714yes—
725C24C2×D4×C12712yes—
726C24C2×D4×C12712yes—
727C24C2×D4×C12712yes—
728C24C2×D4×C12712yes—
729C24#41×C12714yes—
730C24#41×C12712yes—
731C24#41×C12712yes—
732C24C24×C12711yescharacteristic
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—216no—
740C2×D4—216no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4C22⋊C4×C127116yescomplemented
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—28no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4C22×C4×C12714yes—
801C22×C4C22×C4×C12712yes—
802C22×C4C2×D4×C12714yes—
803C22×C4C2×D4×C12712yes—
804C22×C4C2×D4×C12712yes—
805C22×C4C2×D4×C12712yes—
806C22×C4C2×D4×C12712yes—
807C22×C4C2×D4×C12712yes—
808C22×C4C2×D4×C12714yes—
809C22×C4C2×D4×C12712yes—
810C4⋊C4—28no—
811C22⋊C4—216no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—216no—
816C22⋊C4—216no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—44no—
821C42—28no—
822C23—24no—
823C23—24no—
824C23—22no—
825C23—22no—
826C23—24no—
827C23—22no—
828C23—22no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—232no—
839C23—24no—
840C23—24no—
841C23—22no—
842C23—22no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—432no—
870C23—432no—
871C23—416no—
872C23—416no—
873C23—416no—
874C23—416no—
875C23—432no—
876C23—432no—
877C23—416no—
878C23—41no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—41no—
884C23—42no—
885C23—41no—
886C23—42no—
887C23—42no—
888C23—41no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—416no—
905C23C2×C22⋊C4×C12714yes—
906C23C2×C22⋊C4×C12714yescomplemented
907C23C4×D4×C12714yes—
908C23C4×D4×C12714yes—
909C23C4×D4×C12718yescomplemented
910C23#120×C12714yes—
911C23#121×C12714yes—
912C23#121×C12714yes—
913C23#123×C12714yes—
914C23C23×C4×C12711yescharacteristic
915C23C22×D4×C12711yescharacteristic
916C23C22×D4×C12711yescharacteristic
917C23C22×D4×C12711yescharacteristic
918C23C22×D4×C12711yescharacteristic
919C23C22×D4×C12712yes—
920C23C2×#41×C12711yescharacteristic
921C23C2×#41×C12711yescharacteristic
922C23C2×#41×C12712yes—
923C23H(5,𝔽2)×C12712yes—
924C23H(5,𝔽2)×C12712yes—
925D4—232no—
926D4—432no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—416no—
951C2×C4—416no—
952C2×C4—416no—
953C2×C4—41no—
954C2×C4—42no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—42no—
958C2×C4—41no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4C2×C22⋊C4×C12714yescomplemented
977C2×C4#120×C12714yescomplemented
978C22—24no—
979C22—28no—
980C22—28no—
981C22—24no—
982C22—24no—
983C22—24no—
984C22—28no—
985C22—28no—
986C22—24no—
987C22—24no—
988C22—28no—
989C22—28no—
990C22—28no—
991C22—24no—
992C22—28no—
993C22—464no—
994C22—44no—
995C22—42no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—42no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—44no—
1004C22—42no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—42no—
1013C22—44no—
1014C22—42no—
1015C22#386×C12718yescomplemented
1016C22C22×C22⋊C4×C12711yescharacteristic
1017C22C2×C4×D4×C12711yescharacteristic
1018C22C2×C4×D4×C12712yes—
1019C22C2×C4×D4×C12711yescharacteristic
1020C22#518×C12712yes—
1021C22C2×#120×C12711yescharacteristic
1022C22C2×#120×C12711yescharacteristic
1023C22C2×#121×C12711yescharacteristic
1024C22C2×#121×C12711yescharacteristic
1025C22C2×#123×C12711yescharacteristic
1026C22#525×C12711yescharacteristic
1027C22#525×C12712yes—
1028C22#534×C12711yescharacteristic
1029C22#535×C12711yescharacteristic
1030C22#538×C12712yes—
1031C22D42×C12712yes—
1032C22D42×C12712yes—
1033C22D42×C12712yes—
1034C22#546×C12712yes—
1035C22#546×C12712yes—
1036C22#546×C12712yes—
1037C22#546×C12712yes—
1038C22#551×C12712yes—
1039C4—24no—
1040C4—24no—
1041C4—44no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—44no—
1046C4—82no—
1047C2—28no—
1048C2—48no—
1049C2—44no—
1050C2C2×#386×C12711yescharacteristic
1051C2C4×#120×C12711yescharacteristic
1052C2C127×#232111yescharacteristic
1053C2D4×C22⋊C4×C12712yes—
1054C2C127×#235812yes—
1055C2C127×#240311yescharacteristic
1056C2C127×#240411yescharacteristic
1057C2C127×#240811yescharacteristic
1058C2C127×#241812yes—
1059C2C127×#242412yes—
1060C2C127×#253411yescharacteristic
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. C22×C4×D4×C127C2semidirect
3. C23×C22⋊C4×C127C2semidirect
4. C2×#386×C127C2semidirect
5. C2×#386×C127C2semidirect
6. C2×#379×C127C2semidirect
7. C127×#1439C2semidirect
8. C127×#1438C2semidirect
9. C127×#1437C2semidirect
10. C127×C22⋊#95C2semidirect
11. C127×C22⋊#95C2semidirect
17. C24×C4×C127C22semidirect
20. C2×#120×C127C4semidirect
24. C22×C4⋊C4×C127C22semidirect
35. C22×C22⋊C4×C127C22semidirect
36. C22×C22⋊C4×C127C22semidirect
37. C22×C42×C127C22semidirect
41. C2×#95×C127C22semidirect
42. C2×#95×C127C22semidirect
43. C2×#95×C127C22semidirect
44. C2×#95×C127C22semidirect
45. C2×#95×C127C22semidirect
56. C25×C127C2×C4semidirect
71. C22×D4×C127C2×C4semidirect
88. C23×C4×C127D4semidirect
129. C2×C22⋊C4×C127C2×C4semidirect
130. C2×C22⋊C4×C127C2×C4semidirect
131. C2×C22⋊C4×C127D4semidirect
132. C2×C22⋊C4×C127D4semidirect
215. C2×D4×C127C22⋊C4semidirect
375. C23×C127C2×C22⋊C4semidirect
378. C23×C127C4×D4semidirect
445. C2×C4×C127C2×C22⋊C4semidirect
446. C2×C4×C127#120semidirect
484. C22×C127#386semidirect
516. #13967C127direct (N × H)
532. C22×C4×D4C2×C127semidirect
533. C23×C22⋊C4C2×C127semidirect
534. C2×#386C2×C127semidirect
535. C2×#386C2×C127semidirect
536. C2×#379C2×C127semidirect
537. #1439C2×C127semidirect
538. #1438C2×C127semidirect
539. #1437C2×C127semidirect
540. C22⋊#95C2×C127semidirect
541. C22⋊#95C2×C127semidirect
542. C127#13967direct (N × H)
548. C24×C4C22×C127semidirect
551. C2×#120C4×C127semidirect
555. C22×C4⋊C4C22×C127semidirect
566. C22×C22⋊C4C22×C127semidirect
567. C22×C22⋊C4C22×C127semidirect
568. C22×C42C22×C127semidirect
572. C2×#95C22×C127semidirect
573. C2×#95C22×C127semidirect
574. C2×#95C22×C127semidirect
575. C2×#95C22×C127semidirect
576. C2×#95C22×C127semidirect
587. C25C2×C4×C127semidirect
602. C22×D4C2×C4×C127semidirect
619. C23×C4D4×C127semidirect
660. C2×C22⋊C4C2×C4×C127semidirect
661. C2×C22⋊C4C2×C4×C127semidirect
662. C2×C22⋊C4D4×C127semidirect
663. C2×C22⋊C4D4×C127semidirect
746. C2×D4C22⋊C4×C127semidirect
906. C23C2×C22⋊C4×C127semidirect
909. C23C4×D4×C127semidirect
976. C2×C4C2×C22⋊C4×C127semidirect
977. C2×C4#120×C127semidirect
1015. C22#386×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1272
C22×C4×D4×C1272
C23×C22⋊C4×C1272
C2×#386×C1272
C2×#379×C1272
C127×#14392
C127×#14382
C127×#14372
C127×C22⋊#952
#13967127