Finite Group Databasebeta

← C127×#14189 #44577862

Subgroups — C127×#14189 #44577862

Order 32512.

2830 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic, complemented
2C2×#392×C127C211yesmaximal, characteristic
3C2×#390×C127C212yesmaximal, complemented
4C2×#388×C127C211yesmaximal, characteristic, complemented
5C2×#386×C127C212yesmaximal, complemented
6C2×#385×C127C212yesmaximal, complemented
7C127×#1444C211yesmaximal, characteristic, complemented
8C127×#1439C211yesmaximal, characteristic, complemented
9C127×#1438C211yesmaximal, characteristic, complemented
10C127×#1437C212yesmaximal, complemented
11C4×#95×C127C211yesmaximal, characteristic, complemented
12C23×D4×C127C2211yescharacteristic
13C23×D4×C127C2212yes—
14C24×C4×C127C2212yes—
15C2×C4×D4×C127—28no—
16C2×C4×D4×C127—24no—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2212yes—
28C22×C42×C127C2212yes—
29C22×C42×C127C2211yescharacteristic
30#392×C127C418yescomplemented
31#390×C127—28no—
32#388×C127—24no—
33#386×C127—28no—
34#385×C127—28no—
35C2×#95×C127C2211yescharacteristic
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2211yescharacteristic
41C2×#95×C127C2212yes—
42C25×C127C2311yescharacteristic
43C25×C127C2312yes—
44C22×D4×C127—24no—
45C22×D4×C127—24no—
46C22×D4×C127—24no—
47C22×D4×C127—24no—
48C22×D4×C127—22no—
49C22×D4×C127—24no—
50C22×D4×C127—22no—
51C22×D4×C127—24no—
52C22×D4×C127—42no—
53C22×D4×C127—42no—
54C22×D4×C127C2×C414yes—
55C22×D4×C127C2×C418yescomplemented
56C23×C4×C127—24no—
57C23×C4×C127—24no—
58C23×C4×C127—24no—
59C23×C4×C127—24no—
60C23×C4×C127—24no—
61C23×C4×C127—42no—
62C23×C4×C127—42no—
63C23×C4×C127C2311yescharacteristic
64C23×C4×C127C2311yescharacteristic
65C23×C4×C127C2311yescharacteristic
66C23×C4×C127C2312yes—
67C23×C4×C127C2312yes—
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2312yes—
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2311yescharacteristic
72C4×D4×C127—232no—
73C2×C4⋊C4×C127—24no—
74C2×C4⋊C4×C127—22no—
75C2×C4⋊C4×C127—24no—
76C2×C4⋊C4×C127—24no—
77C2×C4⋊C4×C127—22no—
78C2×C4⋊C4×C127—24no—
79C2×C4⋊C4×C127—42no—
80C2×C22⋊C4×C127—24no—
81C2×C22⋊C4×C127—24no—
82C2×C22⋊C4×C127—24no—
83C2×C22⋊C4×C127—22no—
84C2×C22⋊C4×C127—22no—
85C2×C22⋊C4×C127—24no—
86C2×C22⋊C4×C127—24no—
87C2×C22⋊C4×C127—24no—
88C2×C22⋊C4×C127—24no—
89C2×C22⋊C4×C127—24no—
90C2×C22⋊C4×C127—24no—
91C2×C22⋊C4×C127—24no—
92C2×C22⋊C4×C127—22no—
93C2×C22⋊C4×C127—22no—
94C2×C22⋊C4×C127—24no—
95C2×C22⋊C4×C127—24no—
96C2×C22⋊C4×C127—42no—
97C2×C22⋊C4×C127—42no—
98C2×C22⋊C4×C127—42no—
99C2×C22⋊C4×C127C2×C414yescomplemented
100C2×C22⋊C4×C127C2×C418yescomplemented
101C2×C22⋊C4×C127D418yescomplemented
102C2×C42×C127—24no—
103C2×C42×C127—24no—
104C2×C42×C127—24no—
105C2×C42×C127—42no—
106C2×C42×C127D414yescomplemented
107#95×C127—24no—
108#95×C127—24no—
109#95×C127—22no—
110#95×C127—22no—
111#95×C127—22no—
112#95×C127C2×C414yescomplemented
113#95×C127D418yescomplemented
114C24×C127—22no—
115C24×C127—22no—
116C24×C127—22no—
117C24×C127—22no—
118C24×C127—22no—
119C24×C127—22no—
120C24×C127—22no—
121C24×C127—22no—
122C24×C127—22no—
123C24×C127—22no—
124C24×C127—22no—
125C24×C127—22no—
126C24×C127—21no—
127C24×C127—22no—
128C24×C127—22no—
129C24×C127—21no—
130C24×C127—22no—
131C24×C127—22no—
132C24×C127—21no—
133C24×C127—21no—
134C24×C127—21no—
135C24×C127—21no—
136C24×C127C22×C412yes—
137C24×C127C22×C414yes—
138C24×C127C2×D414yes—
139C24×C127#4114yes—
140C24×C127C2411yescharacteristic
141C2×D4×C127—28no—
142C2×D4×C127—28no—
143C2×D4×C127—216no—
144C2×D4×C127—216no—
145C2×D4×C127—216no—
146C2×D4×C127—28no—
147C2×D4×C127—216no—
148C2×D4×C127—48no—
149C2×D4×C127—48no—
150C2×D4×C127—48no—
151C2×D4×C127—48no—
152C2×D4×C127—48no—
153C22×C4×C127—22no—
154C22×C4×C127—22no—
155C22×C4×C127—22no—
156C22×C4×C127—22no—
157C22×C4×C127—22no—
158C22×C4×C127—22no—
159C22×C4×C127—21no—
160C22×C4×C127—22no—
161C22×C4×C127—22no—
162C22×C4×C127—21no—
163C22×C4×C127—21no—
164C22×C4×C127—21no—
165C22×C4×C127—216no—
166C22×C4×C127—21no—
167C22×C4×C127—22no—
168C22×C4×C127—22no—
169C22×C4×C127—22no—
170C22×C4×C127—22no—
171C22×C4×C127—22no—
172C22×C4×C127—22no—
173C22×C4×C127—22no—
174C22×C4×C127—22no—
175C22×C4×C127—21no—
176C22×C4×C127—22no—
177C22×C4×C127—22no—
178C22×C4×C127—22no—
179C22×C4×C127—22no—
180C22×C4×C127—22no—
181C22×C4×C127—22no—
182C22×C4×C127—21no—
183C22×C4×C127—22no—
184C22×C4×C127—21no—
185C22×C4×C127—22no—
186C22×C4×C127—22no—
187C22×C4×C127—22no—
188C22×C4×C127—21no—
189C22×C4×C127—21no—
190C22×C4×C127—21no—
191C22×C4×C127—21no—
192C22×C4×C127—48no—
193C22×C4×C127—48no—
194C22×C4×C127—48no—
195C22×C4×C127—48no—
196C22×C4×C127—48no—
197C22×C4×C127—48no—
198C22×C4×C127C22×C412yes—
199C22×C4×C127C22×C412yes—
200C22×C4×C127C22×C414yes—
201C22×C4×C127C2×D414yes—
202C22×C4×C127C2×D414yes—
203C22×C4×C127C2×D412yes—
204C22×C4×C127C2×D414yes—
205C22×C4×C127C2×D412yes—
206C22×C4×C127C2×D414yes—
207C22×C4×C127C2×D414yes—
208C22×C4×C127C2×D412yes—
209C22×C4×C127#4112yes—
210C22×C4×C127#4114yes—
211C4⋊C4×C127—28no—
212C4⋊C4×C127—48no—
213C4⋊C4×C127—44no—
214C22⋊C4×C127—28no—
215C22⋊C4×C127—216no—
216C22⋊C4×C127—216no—
217C22⋊C4×C127—48no—
218C22⋊C4×C127—48no—
219C22⋊C4×C127—48no—
220C22⋊C4×C127—44no—
221C22⋊C4×C127—44no—
222C42×C127—28no—
223C42×C127—48no—
224C23×C127—24no—
225C23×C127—24no—
226C23×C127—24no—
227C23×C127—24no—
228C23×C127—24no—
229C23×C127—24no—
230C23×C127—24no—
231C23×C127—24no—
232C23×C127—24no—
233C23×C127—24no—
234C23×C127—24no—
235C23×C127—24no—
236C23×C127—24no—
237C23×C127—24no—
238C23×C127—24no—
239C23×C127—24no—
240C23×C127—24no—
241C23×C127—24no—
242C23×C127—22no—
243C23×C127—24no—
244C23×C127—24no—
245C23×C127—22no—
246C23×C127—22no—
247C23×C127—42no—
248C23×C127—42no—
249C23×C127—42no—
250C23×C127—42no—
251C23×C127—42no—
252C23×C127—42no—
253C23×C127—42no—
254C23×C127—42no—
255C23×C127—42no—
256C23×C127—42no—
257C23×C127—42no—
258C23×C127—42no—
259C23×C127—42no—
260C23×C127—42no—
261C23×C127—42no—
262C23×C127—42no—
263C23×C127—41no—
264C23×C127—41no—
265C23×C127—42no—
266C23×C127—41no—
267C23×C127—41no—
268C23×C127—42no—
269C23×C127—41no—
270C23×C127—41no—
271C23×C127—41no—
272C23×C127—41no—
273C23×C127—42no—
274C23×C127—42no—
275C23×C127—42no—
276C23×C127—42no—
277C23×C127—42no—
278C23×C127—42no—
279C23×C127—42no—
280C23×C127—42no—
281C23×C127C4×D418yes—
282C23×C127C23×C411yescharacteristic
283C23×C127C22×D411yescharacteristic
284C23×C127C22×D412yes—
285C23×C127C22×D412yes—
286C23×C127C2×#4111yescharacteristic
287C23×C127C2×#4112yes—
288C23×C127C2×#4112yes—
289C23×C127H(5,𝔽2)11yescharacteristic
290C23×C127H(5,𝔽2)11yescharacteristic
291C23×C127H(5,𝔽2)11yescharacteristic
292C23×C1272−1+411yescharacteristic
293D4×C127—232no—
294D4×C127—432no—
295C2×C4×C127—24no—
296C2×C4×C127—24no—
297C2×C4×C127—24no—
298C2×C4×C127—22no—
299C2×C4×C127—22no—
300C2×C4×C127—22no—
301C2×C4×C127—24no—
302C2×C4×C127—22no—
303C2×C4×C127—22no—
304C2×C4×C127—22no—
305C2×C4×C127—24no—
306C2×C4×C127—24no—
307C2×C4×C127—24no—
308C2×C4×C127—24no—
309C2×C4×C127—24no—
310C2×C4×C127—24no—
311C2×C4×C127—24no—
312C2×C4×C127—24no—
313C2×C4×C127—22no—
314C2×C4×C127—24no—
315C2×C4×C127—24no—
316C2×C4×C127—24no—
317C2×C4×C127—24no—
318C2×C4×C127—24no—
319C2×C4×C127—24no—
320C2×C4×C127—24no—
321C2×C4×C127—432no—
322C2×C4×C127—42no—
323C2×C4×C127—41no—
324C2×C4×C127—42no—
325C2×C4×C127—41no—
326C2×C4×C127—42no—
327C2×C4×C127—42no—
328C2×C4×C127—42no—
329C2×C4×C127—42no—
330C2×C4×C127—42no—
331C2×C4×C127—42no—
332C2×C4×C127—42no—
333C2×C4×C127—41no—
334C2×C4×C127—41no—
335C2×C4×C127—41no—
336C2×C4×C127—41no—
337C2×C4×C127—41no—
338C2×C4×C127—41no—
339C2×C4×C127—42no—
340C2×C4×C127—42no—
341C2×C4×C127—42no—
342C2×C4×C127—42no—
343C2×C4×C127C4×D414yes—
344C2×C4×C127C4×D418yescomplemented
345C2×C4×C127#12014yes—
346C2×C4×C127#12714yes—
347C22×C127—28no—
348C22×C127—28no—
349C22×C127—28no—
350C22×C127—44no—
351C22×C127—44no—
352C22×C127—44no—
353C22×C127—44no—
354C22×C127—44no—
355C22×C127—44no—
356C22×C127—44no—
357C22×C127—44no—
358C22×C127—44no—
359C22×C127—44no—
360C22×C127—44no—
361C22×C127—44no—
362C22×C127—42no—
363C22×C127—42no—
364C22×C127—44no—
365C22×C127—44no—
366C22×C127—42no—
367C22×C127—81no—
368C22×C127—81no—
369C22×C127—81no—
370C22×C127—82no—
371C22×C127—82no—
372C22×C127—81no—
373C22×C127C2×C4×D411yescharacteristic
374C22×C127C2×C4×D412yes—
375C22×C127C2×C4×D412yes—
376C22×C127#51811yescharacteristic
377C22×C127#52011yescharacteristic
378C22×C127C2×#12011yescharacteristic
379C22×C127#52511yescharacteristic
380C22×C127#52512yes—
381C22×C127C2×#12711yescharacteristic
382C22×C127#53211yescharacteristic
383C22×C127#53212yes—
384C22×C127#53511yescharacteristic
385C22×C127#53711yescharacteristic
386C22×C127#54011yescharacteristic
387C22×C127#54211yescharacteristic
388C22×C127D4212yes—
389C22×C127D4212yes—
390C22×C127#54612yes—
391C22×C127#54612yes—
392C22×C127#54712yes—
393C22×C127#54812yes—
394C22×C127#55112yes—
395C22×C127#55312yes—
396C4×C127—28no—
397C4×C127—24no—
398C4×C127—24no—
399C4×C127—24no—
400C4×C127—42no—
401C4×C127—44no—
402C4×C127—44no—
403C4×C127—81no—
404C4×C127—81no—
405#14189C12711yesmaximal, characteristic, direct product factor, Sylow
406C2×C127—48no—
407C2×C127—82no—
408C2×C127C4×#12011yescharacteristic
409C2×C127C4×#12711yescharacteristic
410C2×C127#232411yescharacteristic
411C2×C127#235812yes—
412C2×C127#236112yes—
413C2×C127#243011yescharacteristic
414C2×C127#243311yescharacteristic
415C2×C127#246112yes—
416C2×C127#246412yes—
417C2×C127#254011yescharacteristic
418C2×C127#260311yescharacteristic
419C22×C4×D4C2×C12711yescharacteristic, complemented
420C2×#392C2×C12711yescharacteristic
421C2×#390C2×C12712yescomplemented
422C2×#388C2×C12711yescharacteristic, complemented
423C2×#386C2×C12712yescomplemented
424C2×#385C2×C12712yescomplemented
425#1444C2×C12711yescharacteristic, complemented
426#1439C2×C12711yescharacteristic, complemented
427#1438C2×C12711yescharacteristic, complemented
428#1437C2×C12712yescomplemented
429C4×#95C2×C12711yescharacteristic, complemented
430C127#1418911yescharacteristic, direct product factor, Sylow
431C23×D4C22×C12711yescharacteristic
432C23×D4C22×C12712yes—
433C24×C4C22×C12712yes—
434C2×C4×D4—28no—
435C2×C4×D4—24no—
436C22×C4⋊C4C22×C12711yescharacteristic
437C22×C4⋊C4C22×C12711yescharacteristic
438C22×C4⋊C4C22×C12712yes—
439C22×C22⋊C4C22×C12711yescharacteristic
440C22×C22⋊C4C22×C12711yescharacteristic
441C22×C22⋊C4C22×C12712yes—
442C22×C22⋊C4C22×C12712yes—
443C22×C22⋊C4C22×C12712yes—
444C22×C22⋊C4C22×C12712yes—
445C22×C22⋊C4C22×C12711yescharacteristic
446C22×C22⋊C4C22×C12712yes—
447C22×C42C22×C12712yes—
448C22×C42C22×C12711yescharacteristic
449#392C4×C12718yescomplemented
450#390—28no—
451#388—24no—
452#386—28no—
453#385—28no—
454C2×#95C22×C12711yescharacteristic
455C2×#95C22×C12711yescharacteristic
456C2×#95C22×C12712yes—
457C2×#95C22×C12712yes—
458C2×#95C22×C12711yescharacteristic
459C2×#95C22×C12711yescharacteristic
460C2×#95C22×C12712yes—
461C25C23×C12711yescharacteristic
462C25C23×C12712yes—
463C22×D4—24no—
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—24no—
467C22×D4—22no—
468C22×D4—24no—
469C22×D4—22no—
470C22×D4—24no—
471C22×D4—42no—
472C22×D4—42no—
473C22×D4C2×C4×C12714yes—
474C22×D4C2×C4×C12718yescomplemented
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—42no—
482C23×C4C23×C12711yescharacteristic
483C23×C4C23×C12711yescharacteristic
484C23×C4C23×C12711yescharacteristic
485C23×C4C23×C12712yes—
486C23×C4C23×C12712yes—
487C23×C4C23×C12711yescharacteristic
488C23×C4C23×C12712yes—
489C23×C4C23×C12711yescharacteristic
490C23×C4C23×C12711yescharacteristic
491C4×D4—232no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—42no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4C2×C4×C12714yescomplemented
519C2×C22⋊C4C2×C4×C12718yescomplemented
520C2×C22⋊C4D4×C12718yescomplemented
521C2×C42—24no—
522C2×C42—24no—
523C2×C42—24no—
524C2×C42—42no—
525C2×C42D4×C12714yescomplemented
526#95—24no—
527#95—24no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95C2×C4×C12714yescomplemented
532#95D4×C12718yescomplemented
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—21no—
546C24—22no—
547C24—22no—
548C24—21no—
549C24—22no—
550C24—22no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24C22×C4×C12712yes—
556C24C22×C4×C12714yes—
557C24C2×D4×C12714yes—
558C24#41×C12714yes—
559C24C24×C12711yescharacteristic
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—216no—
563C2×D4—216no—
564C2×D4—216no—
565C2×D4—28no—
566C2×D4—216no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—48no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—216no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4C22×C4×C12712yes—
618C22×C4C22×C4×C12712yes—
619C22×C4C22×C4×C12714yes—
620C22×C4C2×D4×C12714yes—
621C22×C4C2×D4×C12714yes—
622C22×C4C2×D4×C12712yes—
623C22×C4C2×D4×C12714yes—
624C22×C4C2×D4×C12712yes—
625C22×C4C2×D4×C12714yes—
626C22×C4C2×D4×C12714yes—
627C22×C4C2×D4×C12712yes—
628C22×C4#41×C12712yes—
629C22×C4#41×C12714yes—
630C4⋊C4—28no—
631C4⋊C4—48no—
632C4⋊C4—44no—
633C22⋊C4—28no—
634C22⋊C4—216no—
635C22⋊C4—216no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C42—28no—
642C42—48no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—22no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—41no—
684C23—42no—
685C23—41no—
686C23—41no—
687C23—42no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23C4×D4×C12718yes—
701C23C23×C4×C12711yescharacteristic
702C23C22×D4×C12711yescharacteristic
703C23C22×D4×C12712yes—
704C23C22×D4×C12712yes—
705C23C2×#41×C12711yescharacteristic
706C23C2×#41×C12712yes—
707C23C2×#41×C12712yes—
708C23H(5,𝔽2)×C12711yescharacteristic
709C23H(5,𝔽2)×C12711yescharacteristic
710C23H(5,𝔽2)×C12711yescharacteristic
711C232−1+4×C12711yescharacteristic
712D4—232no—
713D4—432no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—432no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4C4×D4×C12714yes—
763C2×C4C4×D4×C12718yescomplemented
764C2×C4#120×C12714yes—
765C2×C4#127×C12714yes—
766C22—28no—
767C22—28no—
768C22—28no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—42no—
782C22—44no—
783C22—44no—
784C22—42no—
785C22—42no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—82no—
790C22—82no—
791C22—81no—
792C22C2×C4×D4×C12711yescharacteristic
793C22C2×C4×D4×C12712yes—
794C22C2×C4×D4×C12712yes—
795C22#518×C12711yescharacteristic
796C22#520×C12711yescharacteristic
797C22C2×#120×C12711yescharacteristic
798C22#525×C12711yescharacteristic
799C22#525×C12712yes—
800C22C2×#127×C12711yescharacteristic
801C22#532×C12711yescharacteristic
802C22#532×C12712yes—
803C22#535×C12711yescharacteristic
804C22#537×C12711yescharacteristic
805C22#540×C12711yescharacteristic
806C22#542×C12711yescharacteristic
807C22D42×C12712yes—
808C22D42×C12712yes—
809C22#546×C12712yes—
810C22#546×C12712yes—
811C22#547×C12712yes—
812C22#548×C12712yes—
813C22#551×C12712yes—
814C22#553×C12712yes—
815C4—28no—
816C4—24no—
817C4—24no—
818C4—24no—
819C4—44no—
820C4—44no—
821C4—42no—
822C4—81no—
823C4—81no—
824C2—48no—
825C2—82no—
826C2C4×#120×C12711yescharacteristic
827C2C4×#127×C12711yescharacteristic
828C2C127×#232411yescharacteristic
829C2C127×#235812yes—
830C2C127×#236112yes—
831C2C127×#243011yescharacteristic
832C2C127×#243311yescharacteristic
833C2C127×#246112yes—
834C2C127×#246412yes—
835C2C127×#254011yescharacteristic
836C2C127×#260311yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC2×#392×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×D4×C127C2semidirect
3. C2×#390×C127C2semidirect
4. C2×#388×C127C2semidirect
5. C2×#386×C127C2semidirect
6. C2×#385×C127C2semidirect
7. C127×#1444C2semidirect
8. C127×#1439C2semidirect
9. C127×#1438C2semidirect
10. C127×#1437C2semidirect
11. C4×#95×C127C2semidirect
30. #392×C127C4semidirect
55. C22×D4×C127C2×C4semidirect
99. C2×C22⋊C4×C127C2×C4semidirect
100. C2×C22⋊C4×C127C2×C4semidirect
101. C2×C22⋊C4×C127D4semidirect
106. C2×C42×C127D4semidirect
112. #95×C127C2×C4semidirect
113. #95×C127D4semidirect
344. C2×C4×C127C4×D4semidirect
405. #14189C127direct (N × H)
419. C22×C4×D4C2×C127semidirect
421. C2×#390C2×C127semidirect
422. C2×#388C2×C127semidirect
423. C2×#386C2×C127semidirect
424. C2×#385C2×C127semidirect
425. #1444C2×C127semidirect
426. #1439C2×C127semidirect
427. #1438C2×C127semidirect
428. #1437C2×C127semidirect
429. C4×#95C2×C127semidirect
430. C127#14189direct (N × H)
449. #392C4×C127semidirect
474. C22×D4C2×C4×C127semidirect
518. C2×C22⋊C4C2×C4×C127semidirect
519. C2×C22⋊C4C2×C4×C127semidirect
520. C2×C22⋊C4D4×C127semidirect
525. C2×C42D4×C127semidirect
531. #95C2×C4×C127semidirect
532. #95D4×C127semidirect
763. C2×C4C4×D4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1272
C2×#392×C1272
C2×#390×C1272
C2×#388×C1272
C2×#386×C1272
C2×#385×C1272
C127×#14442
C127×#14392
C127×#14382
C127×#14372
C4×#95×C1272
#14189127