Finite Group Databasebeta

← C127×#14175 #44577848

Subgroups — C127×#14175 #44577848

Order 32512.

2854 conjugacy classes of subgroups.

The subgroup lattice has 842 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×#386×C127C212yesmaximal, complemented
4C2×#386×C127C212yesmaximal, complemented
5C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
6C127×#1442C211yesmaximal, characteristic, complemented
7C127×#1439C211yesmaximal, characteristic, complemented
8C127×#1438C211yesmaximal, characteristic, complemented
9C127×#1437C212yesmaximal, complemented
10C127×#1434C211yesmaximal, characteristic, complemented
11C127×C22⋊#95C212yesmaximal, complemented
12C23×D4×C127C2211yescharacteristic
13C23×D4×C127C2212yes—
14C24×C4×C127C2212yes—
15C24×C4×C127C2211yescharacteristic
16C2×C4×D4×C127—28no—
17C2×C4×D4×C127—24no—
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C22⋊C4×C127C2212yes—
26C22×C42×C127C2211yescharacteristic
27C22×C42×C127C2211yescharacteristic
28#392×C127C418yescomplemented
29#386×C127—28no—
30#386×C127—28no—
31C4×C22⋊C4×C127—24no—
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2212yes—
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2212yes—
40C2×#95×C127C2211yescharacteristic
41C25×C127C2311yescharacteristic
42C25×C127C2312yes—
43C22×D4×C127—24no—
44C22×D4×C127—24no—
45C22×D4×C127—24no—
46C22×D4×C127—24no—
47C22×D4×C127—24no—
48C22×D4×C127—24no—
49C22×D4×C127—22no—
50C22×D4×C127—22no—
51C22×D4×C127—42no—
52C22×D4×C127—42no—
53C22×D4×C127C2×C414yescomplemented
54C22×D4×C127C2×C418yescomplemented
55C23×C4×C127—24no—
56C23×C4×C127—22no—
57C23×C4×C127—24no—
58C23×C4×C127—24no—
59C23×C4×C127—22no—
60C23×C4×C127—22no—
61C23×C4×C127—24no—
62C23×C4×C127—24no—
63C23×C4×C127—24no—
64C23×C4×C127—42no—
65C23×C4×C127—42no—
66C23×C4×C127—42no—
67C23×C4×C127C2312yes—
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2312yes—
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2312yes—
72C23×C4×C127C2311yescharacteristic
73C23×C4×C127C2311yescharacteristic
74C23×C4×C127C2311yescharacteristic
75C23×C4×C127C2311yescharacteristic
76C4×D4×C127—232no—
77C2×C4⋊C4×C127—24no—
78C2×C4⋊C4×C127—22no—
79C2×C22⋊C4×C127—24no—
80C2×C22⋊C4×C127—24no—
81C2×C22⋊C4×C127—22no—
82C2×C22⋊C4×C127—22no—
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—42no—
92C2×C22⋊C4×C127—42no—
93C2×C22⋊C4×C127—42no—
94C2×C22⋊C4×C127—42no—
95C2×C22⋊C4×C127—42no—
96C2×C22⋊C4×C127C2×C414yescomplemented
97C2×C22⋊C4×C127C2×C418yescomplemented
98C2×C22⋊C4×C127D418yescomplemented
99C2×C22⋊C4×C127D414yescomplemented
100C2×C42×C127—24no—
101C2×C42×C127—22no—
102C2×C42×C127—42no—
103C2×C42×C127D414yescomplemented
104#95×C127—22no—
105#95×C127—22no—
106#95×C127—24no—
107#95×C127—24no—
108#95×C127—24no—
109#95×C127—24no—
110#95×C127—22no—
111#95×C127—42no—
112#95×C127C2×C414yescomplemented
113C24×C127—21no—
114C24×C127—22no—
115C24×C127—22no—
116C24×C127—22no—
117C24×C127—22no—
118C24×C127—21no—
119C24×C127—21no—
120C24×C127—22no—
121C24×C127—21no—
122C24×C127—22no—
123C24×C127—22no—
124C24×C127—22no—
125C24×C127—22no—
126C24×C127—22no—
127C24×C127—22no—
128C24×C127—22no—
129C24×C127—22no—
130C24×C127—22no—
131C24×C127—22no—
132C24×C127—22no—
133C24×C127C22×C414yes—
134C24×C127C22×C412yes—
135C24×C127C2×D414yes—
136C24×C127C2×D412yes—
137C24×C127#4114yes—
138C24×C127#4112yes—
139C24×C127C2411yescharacteristic
140C2×D4×C127—28no—
141C2×D4×C127—28no—
142C2×D4×C127—216no—
143C2×D4×C127—216no—
144C2×D4×C127—216no—
145C2×D4×C127—216no—
146C2×D4×C127—28no—
147C2×D4×C127—48no—
148C2×D4×C127—48no—
149C2×D4×C127—48no—
150C2×D4×C127—48no—
151C2×D4×C127—48no—
152C22×C4×C127—22no—
153C22×C4×C127—22no—
154C22×C4×C127—21no—
155C22×C4×C127—21no—
156C22×C4×C127—22no—
157C22×C4×C127—22no—
158C22×C4×C127—22no—
159C22×C4×C127—216no—
160C22×C4×C127—28no—
161C22×C4×C127—21no—
162C22×C4×C127—22no—
163C22×C4×C127—22no—
164C22×C4×C127—21no—
165C22×C4×C127—21no—
166C22×C4×C127—22no—
167C22×C4×C127—22no—
168C22×C4×C127—22no—
169C22×C4×C127—22no—
170C22×C4×C127—21no—
171C22×C4×C127—21no—
172C22×C4×C127—22no—
173C22×C4×C127—21no—
174C22×C4×C127—22no—
175C22×C4×C127—22no—
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—22no—
183C22×C4×C127—22no—
184C22×C4×C127—22no—
185C22×C4×C127—22no—
186C22×C4×C127—22no—
187C22×C4×C127—22no—
188C22×C4×C127—22no—
189C22×C4×C127—22no—
190C22×C4×C127—22no—
191C22×C4×C127—22no—
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×C127—44no—
199C22×C4×C127—48no—
200C22×C4×C127—44no—
201C22×C4×C127—48no—
202C22×C4×C127C22×C414yes—
203C22×C4×C127C22×C412yes—
204C22×C4×C127C22×C412yes—
205C22×C4×C127C2×D412yes—
206C22×C4×C127C2×D414yes—
207C22×C4×C127C2×D412yes—
208C22×C4×C127C2×D414yes—
209C22×C4×C127C2×D412yes—
210C22×C4×C127C2×D412yes—
211C22×C4×C127C2×D412yes—
212C22×C4×C127#4112yes—
213C22×C4×C127#4112yes—
214C22×C4×C127#4112yes—
215C4⋊C4×C127—28no—
216C22⋊C4×C127—28no—
217C22⋊C4×C127—216no—
218C22⋊C4×C127—28no—
219C22⋊C4×C127—48no—
220C22⋊C4×C127—48no—
221C22⋊C4×C127—48no—
222C22⋊C4×C127—48no—
223C42×C127—28no—
224C42×C127—44no—
225C23×C127—22no—
226C23×C127—24no—
227C23×C127—24no—
228C23×C127—24no—
229C23×C127—24no—
230C23×C127—24no—
231C23×C127—22no—
232C23×C127—24no—
233C23×C127—24no—
234C23×C127—24no—
235C23×C127—24no—
236C23×C127—22no—
237C23×C127—22no—
238C23×C127—24no—
239C23×C127—24no—
240C23×C127—24no—
241C23×C127—22no—
242C23×C127—22no—
243C23×C127—24no—
244C23×C127—24no—
245C23×C127—24no—
246C23×C127—24no—
247C23×C127—24no—
248C23×C127—24no—
249C23×C127—24no—
250C23×C127—24no—
251C23×C127—24no—
252C23×C127—24no—
253C23×C127—24no—
254C23×C127—24no—
255C23×C127—41no—
256C23×C127—42no—
257C23×C127—42no—
258C23×C127—41no—
259C23×C127—42no—
260C23×C127—42no—
261C23×C127—42no—
262C23×C127—42no—
263C23×C127—41no—
264C23×C127—41no—
265C23×C127—42no—
266C23×C127—42no—
267C23×C127—42no—
268C23×C127—42no—
269C23×C127—42no—
270C23×C127—42no—
271C23×C127—42no—
272C23×C127—42no—
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×C127C4×D414yescomplemented
283C23×C127C23×C411yescharacteristic
284C23×C127C22×D411yescharacteristic
285C23×C127C22×D412yes—
286C23×C127C22×D411yescharacteristic
287C23×C127C2×#4111yescharacteristic
288C23×C127C2×#4112yes—
289C23×C127C2×#4111yescharacteristic
290C23×C127C2×#4111yescharacteristic
291C23×C127C2×#4111yescharacteristic
292C23×C127H(5,𝔽2)12yes—
293C23×C127H(5,𝔽2)12yes—
294D4×C127—232no—
295D4×C127—432no—
296C2×C4×C127—24no—
297C2×C4×C127—22no—
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—24no—
305C2×C4×C127—24no—
306C2×C4×C127—24no—
307C2×C4×C127—24no—
308C2×C4×C127—22no—
309C2×C4×C127—24no—
310C2×C4×C127—24no—
311C2×C4×C127—24no—
312C2×C4×C127—24no—
313C2×C4×C127—24no—
314C2×C4×C127—22no—
315C2×C4×C127—22no—
316C2×C4×C127—24no—
317C2×C4×C127—24no—
318C2×C4×C127—24no—
319C2×C4×C127—24no—
320C2×C4×C127—416no—
321C2×C4×C127—432no—
322C2×C4×C127—41no—
323C2×C4×C127—42no—
324C2×C4×C127—41no—
325C2×C4×C127—41no—
326C2×C4×C127—41no—
327C2×C4×C127—41no—
328C2×C4×C127—41no—
329C2×C4×C127—42no—
330C2×C4×C127—42no—
331C2×C4×C127—42no—
332C2×C4×C127—42no—
333C2×C4×C127—42no—
334C2×C4×C127—42no—
335C2×C4×C127—42no—
336C2×C4×C127—42no—
337C2×C4×C127—42no—
338C2×C4×C127—42no—
339C2×C4×C127—42no—
340C2×C4×C127—42no—
341C2×C4×C127—42no—
342C2×C4×C127—42no—
343C2×C4×C127—42no—
344C2×C4×C127—42no—
345C2×C4×C127—42no—
346C2×C4×C127C4×D414yes—
347C2×C4×C127#12014yes—
348C2×C4×C127#12114yes—
349C22×C127—28no—
350C22×C127—28no—
351C22×C127—28no—
352C22×C127—28no—
353C22×C127—24no—
354C22×C127—42no—
355C22×C127—44no—
356C22×C127—42no—
357C22×C127—44no—
358C22×C127—44no—
359C22×C127—44no—
360C22×C127—44no—
361C22×C127—42no—
362C22×C127—44no—
363C22×C127—44no—
364C22×C127—42no—
365C22×C127—44no—
366C22×C127—44no—
367C22×C127—44no—
368C22×C127—44no—
369C22×C127—44no—
370C22×C127—44no—
371C22×C127—42no—
372C22×C127—44no—
373C22×C127—42no—
374C22×C127—44no—
375C22×C127C2×C4×D411yescharacteristic
376C22×C127C2×C4×D411yescharacteristic
377C22×C127C2×C4×D412yes—
378C22×C127C4×#4111yescharacteristic
379C22×C127#51812yes—
380C22×C127C2×#12011yescharacteristic
381C22×C127C2×#12111yescharacteristic
382C22×C127#52511yescharacteristic
383C22×C127#52511yescharacteristic
384C22×C127#52512yes—
385C22×C127#52911yescharacteristic
386C22×C127#53211yescharacteristic
387C22×C127#53511yescharacteristic
388C22×C127#53511yescharacteristic
389C22×C127#54012yes—
390C22×C127D4212yes—
391C22×C127#54612yes—
392C22×C127#54612yes—
393C22×C127#54612yes—
394C22×C127#54612yes—
395C22×C127#55112yes—
396C22×C127#55312yes—
397C22×C127#55312yes—
398C4×C127—24no—
399C4×C127—24no—
400C4×C127—24no—
401C4×C127—42no—
402C4×C127—44no—
403C4×C127—42no—
404C4×C127—44no—
405C4×C127—42no—
406C4×C127—82no—
407#14175C12711yesmaximal, characteristic, direct product factor, Sylow
408C2×C127—48no—
409C2×C127—44no—
410C2×C127C4×#12011yescharacteristic
411C2×C127C4×#12111yescharacteristic
412C2×C127#232811yescharacteristic
413C2×C127#235812yes—
414C2×C127#236412yes—
415C2×C127#240411yescharacteristic
416C2×C127#240811yescharacteristic
417C2×C127#245712yes—
418C2×C127#246412yes—
419C2×C127#253511yescharacteristic
420C2×C127#259811yescharacteristic
421C22×C4×D4C2×C12711yescharacteristic, complemented
422C2×#392C2×C12711yescharacteristic
423C2×#386C2×C12712yescomplemented
424C2×#386C2×C12712yescomplemented
425C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
426#1442C2×C12711yescharacteristic, complemented
427#1439C2×C12711yescharacteristic, complemented
428#1438C2×C12711yescharacteristic, complemented
429#1437C2×C12712yescomplemented
430#1434C2×C12711yescharacteristic, complemented
431C22⋊#95C2×C12712yescomplemented
432C127#1417511yescharacteristic, direct product factor, Sylow
433C23×D4C22×C12711yescharacteristic
434C23×D4C22×C12712yes—
435C24×C4C22×C12712yes—
436C24×C4C22×C12711yescharacteristic
437C2×C4×D4—28no—
438C2×C4×D4—24no—
439C22×C4⋊C4C22×C12711yescharacteristic
440C22×C22⋊C4C22×C12712yes—
441C22×C22⋊C4C22×C12712yes—
442C22×C22⋊C4C22×C12712yes—
443C22×C22⋊C4C22×C12711yescharacteristic
444C22×C22⋊C4C22×C12712yes—
445C22×C22⋊C4C22×C12711yescharacteristic
446C22×C22⋊C4C22×C12712yes—
447C22×C42C22×C12711yescharacteristic
448C22×C42C22×C12711yescharacteristic
449#392C4×C12718yescomplemented
450#386—28no—
451#386—28no—
452C4×C22⋊C4—24no—
453C2×#95C22×C12711yescharacteristic
454C2×#95C22×C12712yes—
455C2×#95C22×C12712yes—
456C2×#95C22×C12712yes—
457C2×#95C22×C12711yescharacteristic
458C2×#95C22×C12712yes—
459C2×#95C22×C12711yescharacteristic
460C2×#95C22×C12712yes—
461C2×#95C22×C12711yescharacteristic
462C25C23×C12711yescharacteristic
463C25C23×C12712yes—
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—42no—
473C22×D4—42no—
474C22×D4C2×C4×C12714yescomplemented
475C22×D4C2×C4×C12718yescomplemented
476C23×C4—24no—
477C23×C4—22no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—24no—
483C23×C4—24no—
484C23×C4—24no—
485C23×C4—42no—
486C23×C4—42no—
487C23×C4—42no—
488C23×C4C23×C12712yes—
489C23×C4C23×C12711yescharacteristic
490C23×C4C23×C12712yes—
491C23×C4C23×C12711yescharacteristic
492C23×C4C23×C12712yes—
493C23×C4C23×C12711yescharacteristic
494C23×C4C23×C12711yescharacteristic
495C23×C4C23×C12711yescharacteristic
496C23×C4C23×C12711yescharacteristic
497C4×D4—232no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4C2×C4×C12714yescomplemented
518C2×C22⋊C4C2×C4×C12718yescomplemented
519C2×C22⋊C4D4×C12718yescomplemented
520C2×C22⋊C4D4×C12714yescomplemented
521C2×C42—24no—
522C2×C42—22no—
523C2×C42—42no—
524C2×C42D4×C12714yescomplemented
525#95—22no—
526#95—22no—
527#95—24no—
528#95—24no—
529#95—24no—
530#95—24no—
531#95—22no—
532#95—42no—
533#95C2×C4×C12714yescomplemented
534C24—21no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—21no—
540C24—21no—
541C24—22no—
542C24—21no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24C22×C4×C12714yes—
555C24C22×C4×C12712yes—
556C24C2×D4×C12714yes—
557C24C2×D4×C12712yes—
558C24#41×C12714yes—
559C24#41×C12712yes—
560C24C24×C12711yescharacteristic
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—216no—
564C2×D4—216no—
565C2×D4—216no—
566C2×D4—216no—
567C2×D4—28no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—48no—
572C2×D4—48no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—216no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
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—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—44no—
620C22×C4—48no—
621C22×C4—44no—
622C22×C4—48no—
623C22×C4C22×C4×C12714yes—
624C22×C4C22×C4×C12712yes—
625C22×C4C22×C4×C12712yes—
626C22×C4C2×D4×C12712yes—
627C22×C4C2×D4×C12714yes—
628C22×C4C2×D4×C12712yes—
629C22×C4C2×D4×C12714yes—
630C22×C4C2×D4×C12712yes—
631C22×C4C2×D4×C12712yes—
632C22×C4C2×D4×C12712yes—
633C22×C4#41×C12712yes—
634C22×C4#41×C12712yes—
635C22×C4#41×C12712yes—
636C4⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—216no—
639C22⋊C4—28no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C42—28no—
645C42—44no—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—41no—
685C23—41no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23C4×D4×C12718yes—
703C23C4×D4×C12714yescomplemented
704C23C23×C4×C12711yescharacteristic
705C23C22×D4×C12711yescharacteristic
706C23C22×D4×C12712yes—
707C23C22×D4×C12711yescharacteristic
708C23C2×#41×C12711yescharacteristic
709C23C2×#41×C12712yes—
710C23C2×#41×C12711yescharacteristic
711C23C2×#41×C12711yescharacteristic
712C23C2×#41×C12711yescharacteristic
713C23H(5,𝔽2)×C12712yes—
714C23H(5,𝔽2)×C12712yes—
715D4—232no—
716D4—432no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—416no—
742C2×C4—432no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4C4×D4×C12714yes—
768C2×C4#120×C12714yes—
769C2×C4#121×C12714yes—
770C22—28no—
771C22—28no—
772C22—28no—
773C22—28no—
774C22—24no—
775C22—42no—
776C22—44no—
777C22—42no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—42no—
783C22—44no—
784C22—44no—
785C22—42no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—42no—
793C22—44no—
794C22—42no—
795C22—44no—
796C22C2×C4×D4×C12711yescharacteristic
797C22C2×C4×D4×C12711yescharacteristic
798C22C2×C4×D4×C12712yes—
799C22C4×#41×C12711yescharacteristic
800C22#518×C12712yes—
801C22C2×#120×C12711yescharacteristic
802C22C2×#121×C12711yescharacteristic
803C22#525×C12711yescharacteristic
804C22#525×C12711yescharacteristic
805C22#525×C12712yes—
806C22#529×C12711yescharacteristic
807C22#532×C12711yescharacteristic
808C22#535×C12711yescharacteristic
809C22#535×C12711yescharacteristic
810C22#540×C12712yes—
811C22D42×C12712yes—
812C22#546×C12712yes—
813C22#546×C12712yes—
814C22#546×C12712yes—
815C22#546×C12712yes—
816C22#551×C12712yes—
817C22#553×C12712yes—
818C22#553×C12712yes—
819C4—24no—
820C4—24no—
821C4—24no—
822C4—42no—
823C4—44no—
824C4—42no—
825C4—44no—
826C4—42no—
827C4—82no—
828C2—48no—
829C2—44no—
830C2C4×#120×C12711yescharacteristic
831C2C4×#121×C12711yescharacteristic
832C2C127×#232811yescharacteristic
833C2C127×#235812yes—
834C2C127×#236412yes—
835C2C127×#240411yescharacteristic
836C2C127×#240811yescharacteristic
837C2C127×#245712yes—
838C2C127×#246412yes—
839C2C127×#253511yescharacteristic
840C2C127×#259811yescharacteristic
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×#386×C127C2semidirect
4. C2×#386×C127C2semidirect
5. C2×C4×C22⋊C4×C127C2semidirect
6. C127×#1442C2semidirect
7. C127×#1439C2semidirect
8. C127×#1438C2semidirect
9. C127×#1437C2semidirect
10. C127×#1434C2semidirect
11. C127×C22⋊#95C2semidirect
28. #392×C127C4semidirect
53. C22×D4×C127C2×C4semidirect
54. C22×D4×C127C2×C4semidirect
96. C2×C22⋊C4×C127C2×C4semidirect
97. C2×C22⋊C4×C127C2×C4semidirect
98. C2×C22⋊C4×C127D4semidirect
99. C2×C22⋊C4×C127D4semidirect
103. C2×C42×C127D4semidirect
112. #95×C127C2×C4semidirect
282. C23×C127C4×D4semidirect
407. #14175C127direct (N × H)
421. C22×C4×D4C2×C127semidirect
423. C2×#386C2×C127semidirect
424. C2×#386C2×C127semidirect
425. C2×C4×C22⋊C4C2×C127semidirect
426. #1442C2×C127semidirect
427. #1439C2×C127semidirect
428. #1438C2×C127semidirect
429. #1437C2×C127semidirect
430. #1434C2×C127semidirect
431. C22⋊#95C2×C127semidirect
432. C127#14175direct (N × H)
449. #392C4×C127semidirect
474. C22×D4C2×C4×C127semidirect
475. C22×D4C2×C4×C127semidirect
517. C2×C22⋊C4C2×C4×C127semidirect
518. C2×C22⋊C4C2×C4×C127semidirect
519. C2×C22⋊C4D4×C127semidirect
520. C2×C22⋊C4D4×C127semidirect
524. C2×C42D4×C127semidirect
533. #95C2×C4×C127semidirect
703. C23C4×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×#386×C1272
C2×C4×C22⋊C4×C1272
C127×#14422
C127×#14392
C127×#14382
C127×#14372
C127×#14342
C127×C22⋊#952
#14175127