Finite Group Databasebeta

← C127×#14016 #44577689

Subgroups — C127×#14016 #44577689

Order 32512.

2590 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic
2C2×#386×C127C211yesmaximal, characteristic
3C2×#386×C127C211yesmaximal, characteristic
4C2×#385×C127C211yesmaximal, characteristic, complemented
5C22×#95×C127C211yesmaximal, characteristic, complemented
6C127×#1442C212yesmaximal, complemented
7C127×#1439C212yesmaximal, complemented
8C127×#1436C212yesmaximal, complemented
9C127×C22⋊#95C211yesmaximal, characteristic, complemented
10C127×C22⋊#95C211yesmaximal, characteristic, complemented
11C127×C22⋊#95C212yesmaximal, complemented
12C23×D4×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C24×C4×C127C2211yescharacteristic
15C24×C4×C127C2211yescharacteristic
16C24×C4×C127C2211yescharacteristic
17C2×C4×D4×C127—24no—
18C2×C4×D4×C127—24no—
19C2×C4×D4×C127—24no—
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2212yes—
28C22×C42×C127C2211yescharacteristic
29#386×C127—24no—
30#386×C127C418yescomplemented
31#385×C127—24no—
32C2×#95×C127—24no—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2212yes—
40C2×#95×C127C2212yes—
41C2×#95×C127C2212yes—
42C25×C127C2311yescharacteristic
43C25×C127C2311yescharacteristic
44C22×D4×C127—22no—
45C22×D4×C127—22no—
46C22×D4×C127—22no—
47C22×D4×C127—22no—
48C22×D4×C127C2×C414yes—
49C22×D4×C127D414yes—
50C22×D4×C127Q814yes—
51C23×C4×C127—22no—
52C23×C4×C127—22no—
53C23×C4×C127—22no—
54C23×C4×C127—22no—
55C23×C4×C127—22no—
56C23×C4×C127—22no—
57C23×C4×C127—22no—
58C23×C4×C127—22no—
59C23×C4×C127—24no—
60C23×C4×C127—24no—
61C23×C4×C127—22no—
62C23×C4×C127—22no—
63C23×C4×C127—24no—
64C23×C4×C127—42no—
65C23×C4×C127—42no—
66C23×C4×C127—42no—
67C23×C4×C127—42no—
68C23×C4×C127—42no—
69C23×C4×C127C2×C414yescomplemented
70C23×C4×C127D414yes—
71C23×C4×C127C2312yes—
72C23×C4×C127C2312yes—
73C23×C4×C127C2312yes—
74C23×C4×C127C2311yescharacteristic
75C23×C4×C127C2311yescharacteristic
76C23×C4×C127C2311yescharacteristic
77C23×C4×C127C2312yes—
78C23×C4×C127C2311yescharacteristic
79C23×C4×C127C2311yescharacteristic
80C4×D4×C127—232no—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—22no—
83C2×C4⋊C4×C127—22no—
84C2×C4⋊C4×C127—24no—
85C2×C4⋊C4×C127—24no—
86C2×C4⋊C4×C127—42no—
87C2×C22⋊C4×C127—22no—
88C2×C22⋊C4×C127—22no—
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—22no—
91C2×C22⋊C4×C127—22no—
92C2×C22⋊C4×C127—22no—
93C2×C22⋊C4×C127—22no—
94C2×C22⋊C4×C127—24no—
95C2×C22⋊C4×C127—22no—
96C2×C22⋊C4×C127—22no—
97C2×C22⋊C4×C127—22no—
98C2×C22⋊C4×C127—24no—
99C2×C22⋊C4×C127—42no—
100C2×C22⋊C4×C127—42no—
101C2×C22⋊C4×C127—42no—
102C2×C22⋊C4×C127C2×C414yescomplemented
103C2×C22⋊C4×C127C2×C418yescomplemented
104C2×C22⋊C4×C127D414yes—
105C2×C42×C127—22no—
106C2×C42×C127—22no—
107C2×C42×C127—22no—
108#95×C127—24no—
109#95×C127—24no—
110#95×C127—24no—
111#95×C127—24no—
112#95×C127—24no—
113#95×C127—42no—
114#95×C127—42no—
115#95×C127—42no—
116#95×C127C2×C418yescomplemented
117C24×C127—22no—
118C24×C127—22no—
119C24×C127—22no—
120C24×C127—22no—
121C24×C127—21no—
122C24×C127—21no—
123C24×C127—22no—
124C24×C127—22no—
125C24×C127—21no—
126C24×C127—21no—
127C24×C127—22no—
128C24×C127—22no—
129C24×C127C22×C412yes—
130C24×C127C22×C412yes—
131C24×C127C2×D412yes—
132C24×C127C2×D412yes—
133C24×C127C2×D412yes—
134C24×C127C2×D412yes—
135C24×C127C2×Q812yes—
136C24×C127C2×Q812yes—
137C24×C127#4112yes—
138C24×C127#4112yes—
139C24×C127C2411yescharacteristic
140C2×D4×C127—28no—
141C2×D4×C127—28no—
142C2×D4×C127—28no—
143C2×D4×C127—28no—
144C2×D4×C127—28no—
145C2×D4×C127—28no—
146C2×D4×C127C4⋊C4116yescomplemented
147C22×C4×C127—21no—
148C22×C4×C127—21no—
149C22×C4×C127—21no—
150C22×C4×C127—21no—
151C22×C4×C127—21no—
152C22×C4×C127—21no—
153C22×C4×C127—22no—
154C22×C4×C127—28no—
155C22×C4×C127—28no—
156C22×C4×C127—28no—
157C22×C4×C127—28no—
158C22×C4×C127—22no—
159C22×C4×C127—22no—
160C22×C4×C127—22no—
161C22×C4×C127—22no—
162C22×C4×C127—22no—
163C22×C4×C127—21no—
164C22×C4×C127—21no—
165C22×C4×C127—21no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
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—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—28no—
189C22×C4×C127—22no—
190C22×C4×C127—22no—
191C22×C4×C127—22no—
192C22×C4×C127—22no—
193C22×C4×C127—22no—
194C22×C4×C127—22no—
195C22×C4×C127—22no—
196C22×C4×C127—48no—
197C22×C4×C127—44no—
198C22×C4×C127—48no—
199C22×C4×C127—48no—
200C22×C4×C127—48no—
201C22×C4×C127—48no—
202C22×C4×C127—48no—
203C22×C4×C127—48no—
204C22×C4×C127—44no—
205C22×C4×C127—44no—
206C22×C4×C127—44no—
207C22×C4×C127—44no—
208C22×C4×C127—48no—
209C22×C4×C127—44no—
210C22×C4×C127—44no—
211C22×C4×C127C22×C414yes—
212C22×C4×C127C22×C414yes—
213C22×C4×C127C22×C412yes—
214C22×C4×C127C2×D412yes—
215C22×C4×C127C2×D412yes—
216C22×C4×C127C2×D412yes—
217C22×C4×C127C2×D412yes—
218C22×C4×C127C2×D412yes—
219C22×C4×C127C2×Q812yes—
220C22×C4×C127#4114yes—
221C22×C4×C127#4114yes—
222C4⋊C4×C127—28no—
223C4⋊C4×C127—48no—
224C22⋊C4×C127—28no—
225C22⋊C4×C127—28no—
226C22⋊C4×C127—28no—
227C22⋊C4×C127—48no—
228C22⋊C4×C127—48no—
229C22⋊C4×C127—44no—
230C42×C127—28no—
231C23×C127—24no—
232C23×C127—24no—
233C23×C127—22no—
234C23×C127—22no—
235C23×C127—24no—
236C23×C127—22no—
237C23×C127—22no—
238C23×C127—24no—
239C23×C127—24no—
240C23×C127—24no—
241C23×C127—24no—
242C23×C127—24no—
243C23×C127—24no—
244C23×C127—24no—
245C23×C127—24no—
246C23×C127—24no—
247C23×C127—22no—
248C23×C127—22no—
249C23×C127—24no—
250C23×C127—24no—
251C23×C127—22no—
252C23×C127—22no—
253C23×C127—22no—
254C23×C127—22no—
255C23×C127—24no—
256C23×C127—24no—
257C23×C127—24no—
258C23×C127—24no—
259C23×C127—41no—
260C23×C127—41no—
261C23×C127—42no—
262C23×C127—41no—
263C23×C127—41no—
264C23×C127—42no—
265C23×C127—42no—
266C23×C127—42no—
267C23×C127—42no—
268C23×C127—42no—
269C23×C127C2×C4⋊C414yes—
270C23×C127C2×C4⋊C414yes—
271C23×C127C4×D414yes—
272C23×C127C4×D414yes—
273C23×C127#12014yes—
274C23×C127C22⋊Q814yes—
275C23×C127C22⋊Q814yes—
276C23×C127#12314yes—
277C23×C127C23×C411yescharacteristic
278C23×C127C22×D411yescharacteristic
279C23×C127C22×D411yescharacteristic
280C23×C127C22×D411yescharacteristic
281C23×C127C22×Q811yescharacteristic
282C23×C127C2×#4111yescharacteristic
283C23×C127C2×#4111yescharacteristic
284C23×C127C2×#4112yes—
285C23×C127C2×#4112yes—
286C23×C127H(5,𝔽2)12yes—
287C23×C127H(5,𝔽2)12yes—
288D4×C127—232no—
289C2×C4×C127—22no—
290C2×C4×C127—22no—
291C2×C4×C127—22no—
292C2×C4×C127—22no—
293C2×C4×C127—22no—
294C2×C4×C127—22no—
295C2×C4×C127—22no—
296C2×C4×C127—22no—
297C2×C4×C127—24no—
298C2×C4×C127—24no—
299C2×C4×C127—24no—
300C2×C4×C127—24no—
301C2×C4×C127—24no—
302C2×C4×C127—24no—
303C2×C4×C127—24no—
304C2×C4×C127—24no—
305C2×C4×C127—22no—
306C2×C4×C127—22no—
307C2×C4×C127—22no—
308C2×C4×C127—22no—
309C2×C4×C127—24no—
310C2×C4×C127—22no—
311C2×C4×C127—24no—
312C2×C4×C127—24no—
313C2×C4×C127—24no—
314C2×C4×C127—24no—
315C2×C4×C127—416no—
316C2×C4×C127—416no—
317C2×C4×C127—416no—
318C2×C4×C127—416no—
319C2×C4×C127—42no—
320C2×C4×C127—41no—
321C2×C4×C127—41no—
322C2×C4×C127—42no—
323C2×C4×C127—41no—
324C2×C4×C127—41no—
325C2×C4×C127—42no—
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—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×C127C2×C4⋊C414yes—
347C2×C4×C127#12314yes—
348C22×C127—24no—
349C22×C127—24no—
350C22×C127—28no—
351C22×C127—28no—
352C22×C127—24no—
353C22×C127—24no—
354C22×C127—28no—
355C22×C127—28no—
356C22×C127—24no—
357C22×C127—24no—
358C22×C127—28no—
359C22×C127—24no—
360C22×C127—42no—
361C22×C127—42no—
362C22×C127—44no—
363C22×C127—42no—
364C22×C127—42no—
365C22×C127—44no—
366C22×C127—44no—
367C22×C127—42no—
368C22×C127—42no—
369C22×C127#38518yes—
370C22×C127C22×C4⋊C411yescharacteristic
371C22×C127C2×C4×D411yescharacteristic
372C22×C127C2×C4×D411yescharacteristic
373C22×C127C4×#4112yes—
374C22×C127#51812yes—
375C22×C127C2×#12011yescharacteristic
376C22×C127C2×C22⋊Q811yescharacteristic
377C22×C127C2×C22⋊Q811yescharacteristic
378C22×C127C2×#12311yescharacteristic
379C22×C127C2×#12311yescharacteristic
380C22×C127#52511yescharacteristic
381C22×C127#52912yes—
382C22×C127#53411yescharacteristic
383C22×C127#53511yescharacteristic
384C22×C127#53812yes—
385C22×C127#54612yes—
386C22×C127#54612yes—
387C22×C127#54612yes—
388C22×C127#54612yes—
389C22×C127#55312yes—
390C22×C127#55312yes—
391C22×C127#55412yes—
392C22×C127#55412yes—
393C4×C127—24no—
394C4×C127—24no—
395C4×C127—44no—
396C4×C127—44no—
397C4×C127—42no—
398C4×C127—44no—
399C4×C127—42no—
400C4×C127—42no—
401C4×C127—82no—
402#14016C12711yesmaximal, characteristic, direct product factor, Sylow
403C2×C127—28no—
404C2×C127—44no—
405C2×C127C2×#38511yescharacteristic
406C2×C127C4×#12311yescharacteristic
407C2×C127#232111yescharacteristic
408C2×C127#234912yes—
409C2×C127#236412yes—
410C2×C127#240411yescharacteristic
411C2×C127#240511yescharacteristic
412C2×C127#244412yes—
413C2×C127#245012yes—
414C2×C127#248711yescharacteristic
415C2×C127#257911yescharacteristic
416C22×C4×D4C2×C12711yescharacteristic
417C2×#386C2×C12711yescharacteristic
418C2×#386C2×C12711yescharacteristic
419C2×#385C2×C12711yescharacteristic, complemented
420C22×#95C2×C12711yescharacteristic, complemented
421#1442C2×C12712yescomplemented
422#1439C2×C12712yescomplemented
423#1436C2×C12712yescomplemented
424C22⋊#95C2×C12711yescharacteristic, complemented
425C22⋊#95C2×C12711yescharacteristic, complemented
426C22⋊#95C2×C12712yescomplemented
427C127#1401611yescharacteristic, direct product factor, Sylow
428C23×D4C22×C12711yescharacteristic
429C24×C4C22×C12711yescharacteristic
430C24×C4C22×C12711yescharacteristic
431C24×C4C22×C12711yescharacteristic
432C24×C4C22×C12711yescharacteristic
433C2×C4×D4—24no—
434C2×C4×D4—24no—
435C2×C4×D4—24no—
436C22×C4⋊C4C22×C12711yescharacteristic
437C22×C4⋊C4C22×C12712yes—
438C22×C22⋊C4C22×C12711yescharacteristic
439C22×C22⋊C4C22×C12711yescharacteristic
440C22×C22⋊C4C22×C12712yes—
441C22×C22⋊C4C22×C12711yescharacteristic
442C22×C22⋊C4C22×C12711yescharacteristic
443C22×C22⋊C4C22×C12712yes—
444C22×C42C22×C12711yescharacteristic
445#386—24no—
446#386C4×C12718yescomplemented
447#385—24no—
448C2×#95—24no—
449C2×#95C22×C12712yes—
450C2×#95C22×C12712yes—
451C2×#95C22×C12712yes—
452C2×#95C22×C12712yes—
453C2×#95C22×C12712yes—
454C2×#95C22×C12712yes—
455C2×#95C22×C12712yes—
456C2×#95C22×C12712yes—
457C2×#95C22×C12712yes—
458C25C23×C12711yescharacteristic
459C25C23×C12711yescharacteristic
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4C2×C4×C12714yes—
465C22×D4D4×C12714yes—
466C22×D4Q8×C12714yes—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—42no—
482C23×C4—42no—
483C23×C4—42no—
484C23×C4—42no—
485C23×C4C2×C4×C12714yescomplemented
486C23×C4D4×C12714yes—
487C23×C4C23×C12712yes—
488C23×C4C23×C12712yes—
489C23×C4C23×C12712yes—
490C23×C4C23×C12711yescharacteristic
491C23×C4C23×C12711yescharacteristic
492C23×C4C23×C12711yescharacteristic
493C23×C4C23×C12712yes—
494C23×C4C23×C12711yescharacteristic
495C23×C4C23×C12711yescharacteristic
496C4×D4—232no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—24no—
502C2×C4⋊C4—42no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
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×C12714yes—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—22no—
524#95—24no—
525#95—24no—
526#95—24no—
527#95—24no—
528#95—24no—
529#95—42no—
530#95—42no—
531#95—42no—
532#95C2×C4×C12718yescomplemented
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—21no—
538C24—21no—
539C24—22no—
540C24—22no—
541C24—21no—
542C24—21no—
543C24—22no—
544C24—22no—
545C24C22×C4×C12712yes—
546C24C22×C4×C12712yes—
547C24C2×D4×C12712yes—
548C24C2×D4×C12712yes—
549C24C2×D4×C12712yes—
550C24C2×D4×C12712yes—
551C24C2×Q8×C12712yes—
552C24C2×Q8×C12712yes—
553C24#41×C12712yes—
554C24#41×C12712yes—
555C24C24×C12711yescharacteristic
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4C4⋊C4×C127116yescomplemented
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
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—22no—
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—28no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—48no—
613C22×C4—44no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—48no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4C22×C4×C12714yes—
628C22×C4C22×C4×C12714yes—
629C22×C4C22×C4×C12712yes—
630C22×C4C2×D4×C12712yes—
631C22×C4C2×D4×C12712yes—
632C22×C4C2×D4×C12712yes—
633C22×C4C2×D4×C12712yes—
634C22×C4C2×D4×C12712yes—
635C22×C4C2×Q8×C12712yes—
636C22×C4#41×C12714yes—
637C22×C4#41×C12714yes—
638C4⋊C4—28no—
639C4⋊C4—48no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—44no—
646C42—28no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—24no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—41no—
676C23—41no—
677C23—42no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23C2×C4⋊C4×C12714yes—
686C23C2×C4⋊C4×C12714yes—
687C23C4×D4×C12714yes—
688C23C4×D4×C12714yes—
689C23#120×C12714yes—
690C23C22⋊Q8×C12714yes—
691C23C22⋊Q8×C12714yes—
692C23#123×C12714yes—
693C23C23×C4×C12711yescharacteristic
694C23C22×D4×C12711yescharacteristic
695C23C22×D4×C12711yescharacteristic
696C23C22×D4×C12711yescharacteristic
697C23C22×Q8×C12711yescharacteristic
698C23C2×#41×C12711yescharacteristic
699C23C2×#41×C12711yescharacteristic
700C23C2×#41×C12712yes—
701C23C2×#41×C12712yes—
702C23H(5,𝔽2)×C12712yes—
703C23H(5,𝔽2)×C12712yes—
704D4—232no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—416no—
732C2×C4—416no—
733C2×C4—416no—
734C2×C4—416no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
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×C4C2×C4⋊C4×C12714yes—
763C2×C4#123×C12714yes—
764C22—24no—
765C22—24no—
766C22—28no—
767C22—28no—
768C22—24no—
769C22—24no—
770C22—28no—
771C22—28no—
772C22—24no—
773C22—24no—
774C22—28no—
775C22—24no—
776C22—42no—
777C22—42no—
778C22—44no—
779C22—42no—
780C22—42no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22#385×C12718yes—
786C22C22×C4⋊C4×C12711yescharacteristic
787C22C2×C4×D4×C12711yescharacteristic
788C22C2×C4×D4×C12711yescharacteristic
789C22C4×#41×C12712yes—
790C22#518×C12712yes—
791C22C2×#120×C12711yescharacteristic
792C22C2×C22⋊Q8×C12711yescharacteristic
793C22C2×C22⋊Q8×C12711yescharacteristic
794C22C2×#123×C12711yescharacteristic
795C22C2×#123×C12711yescharacteristic
796C22#525×C12711yescharacteristic
797C22#529×C12712yes—
798C22#534×C12711yescharacteristic
799C22#535×C12711yescharacteristic
800C22#538×C12712yes—
801C22#546×C12712yes—
802C22#546×C12712yes—
803C22#546×C12712yes—
804C22#546×C12712yes—
805C22#553×C12712yes—
806C22#553×C12712yes—
807C22#554×C12712yes—
808C22#554×C12712yes—
809C4—24no—
810C4—24no—
811C4—44no—
812C4—44no—
813C4—44no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—82no—
818C2—28no—
819C2—44no—
820C2C2×#385×C12711yescharacteristic
821C2C4×#123×C12711yescharacteristic
822C2C127×#232111yescharacteristic
823C2C127×#234912yes—
824C2C127×#236412yes—
825C2C127×#240411yescharacteristic
826C2C127×#240511yescharacteristic
827C2C127×#244412yes—
828C2C127×#245012yes—
829C2C127×#248711yescharacteristic
830C2C127×#257911yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#385×C127C2semidirect
5. C22×#95×C127C2semidirect
6. C127×#1442C2semidirect
7. C127×#1439C2semidirect
8. C127×#1436C2semidirect
9. C127×C22⋊#95C2semidirect
10. C127×C22⋊#95C2semidirect
11. C127×C22⋊#95C2semidirect
30. #386×C127C4semidirect
69. C23×C4×C127C2×C4semidirect
102. C2×C22⋊C4×C127C2×C4semidirect
103. C2×C22⋊C4×C127C2×C4semidirect
116. #95×C127C2×C4semidirect
146. C2×D4×C127C4⋊C4semidirect
402. #14016C127direct (N × H)
419. C2×#385C2×C127semidirect
420. C22×#95C2×C127semidirect
421. #1442C2×C127semidirect
422. #1439C2×C127semidirect
423. #1436C2×C127semidirect
424. C22⋊#95C2×C127semidirect
425. C22⋊#95C2×C127semidirect
426. C22⋊#95C2×C127semidirect
427. C127#14016direct (N × H)
446. #386C4×C127semidirect
485. C23×C4C2×C4×C127semidirect
518. C2×C22⋊C4C2×C4×C127semidirect
519. C2×C22⋊C4C2×C4×C127semidirect
532. #95C2×C4×C127semidirect
562. C2×D4C4⋊C4×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×#386×C1272
C2×#385×C1272
C22×#95×C1272
C127×#14422
C127×#14392
C127×#14362
C127×C22⋊#952
#14016127