Finite Group Databasebeta

← C127×#13996 #44577669

Subgroups — C127×#13996 #44577669

Order 32512.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C127C211yesmaximal, characteristic
2C2×#386×C127C211yesmaximal, characteristic
3C2×#386×C127C211yesmaximal, characteristic
4C2×#385×C127C211yesmaximal, characteristic, complemented
5C2×#381×C127C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
7C22×#95×C127C211yesmaximal, characteristic, complemented
8C127×#1445C212yesmaximal, complemented
9C127×#1439C212yesmaximal, complemented
10C127×#1437C212yesmaximal, complemented
11C127×C4⋊#95C212yesmaximal, complemented
12C23×D4×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C24×C4×C127C2211yescharacteristic
15C24×C4×C127C2211yescharacteristic
16C2×#123×C127—24no—
17C2×#123×C127—24no—
18C2×#123×C127C418yescomplemented
19C22×C4⋊C4×C127C2212yes—
20C22×C4⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2211yescharacteristic
28C22×C42×C127C2212yes—
29#386×C127—24no—
30#386×C127—24no—
31#385×C127—24no—
32#381×C127—24no—
33C4×C22⋊C4×C127—24no—
34C2×#95×C127—24no—
35C2×#95×C127C2211yescharacteristic
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2212yes—
40C2×#95×C127C2212yes—
41C2×#95×C127C2212yes—
42C2×#95×C127C2212yes—
43C2×#95×C127C2211yescharacteristic
44C25×C127C2311yescharacteristic
45C25×C127C2311yescharacteristic
46C22×D4×C127—22no—
47C22×D4×C127—22no—
48C22×D4×C127—22no—
49C22×D4×C127—22no—
50C22×D4×C127—22no—
51C22×D4×C127—22no—
52C22×D4×C127C2×C414yes—
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—22no—
60C23×C4×C127—22no—
61C23×C4×C127—22no—
62C23×C4×C127—24no—
63C23×C4×C127—24no—
64C23×C4×C127—22no—
65C23×C4×C127—22no—
66C23×C4×C127—42no—
67C23×C4×C127—42no—
68C23×C4×C127C2×C414yes—
69C23×C4×C127D414yes—
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2311yescharacteristic
72C23×C4×C127C2312yes—
73C23×C4×C127C2311yescharacteristic
74C23×C4×C127C2312yes—
75C23×C4×C127C2311yescharacteristic
76C23×C4×C127C2312yes—
77C23×C4×C127C2312yes—
78C23×C4×C127C2311yescharacteristic
79#123×C127—232no—
80C2×C4⋊C4×C127—24no—
81C2×C4⋊C4×C127—24no—
82C2×C4⋊C4×C127—24no—
83C2×C4⋊C4×C127—24no—
84C2×C4⋊C4×C127—42no—
85C2×C4⋊C4×C127C2×C418yescomplemented
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—22no—
88C2×C22⋊C4×C127—24no—
89C2×C22⋊C4×C127—24no—
90C2×C22⋊C4×C127—22no—
91C2×C22⋊C4×C127—22no—
92C2×C22⋊C4×C127—22no—
93C2×C22⋊C4×C127—24no—
94C2×C22⋊C4×C127—22no—
95C2×C22⋊C4×C127—22no—
96C2×C22⋊C4×C127—24no—
97C2×C22⋊C4×C127—24no—
98C2×C22⋊C4×C127—42no—
99C2×C22⋊C4×C127—42no—
100C2×C22⋊C4×C127C2×C414yes—
101C2×C22⋊C4×C127C2×C418yescomplemented
102C2×C22⋊C4×C127D414yes—
103C2×C22⋊C4×C127D414yes—
104C2×C22⋊C4×C127D414yes—
105C2×C42×C127—24no—
106C2×C42×C127—24no—
107C2×C42×C127—42no—
108#95×C127—24no—
109#95×C127—24no—
110#95×C127—24no—
111#95×C127—24no—
112#95×C127—24no—
113#95×C127—24no—
114#95×C127—24no—
115#95×C127—22no—
116#95×C127—22no—
117C24×C127—22no—
118C24×C127—22no—
119C24×C127—22no—
120C24×C127—22no—
121C24×C127—21no—
122C24×C127—21no—
123C24×C127—21no—
124C24×C127—21no—
125C24×C127—22no—
126C24×C127—22no—
127C24×C127—21no—
128C24×C127—21no—
129C24×C127—22no—
130C24×C127—22no—
131C24×C127C22×C412yes—
132C24×C127C22×C412yes—
133C24×C127C2×D412yes—
134C24×C127C2×D412yes—
135C24×C127C2×D412yes—
136C24×C127C2×D412yes—
137C24×C127#4112yes—
138C24×C127#4112yes—
139C24×C127C2411yescharacteristic
140C2×D4×C127—28no—
141C2×D4×C127—28no—
142C2×D4×C127—28no—
143C2×D4×C127—44no—
144C2×D4×C127—44no—
145C2×D4×C127—44no—
146C2×D4×C127—44no—
147C22×C4×C127—21no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127—21no—
151C22×C4×C127—22no—
152C22×C4×C127—22no—
153C22×C4×C127—22no—
154C22×C4×C127—28no—
155C22×C4×C127—28no—
156C22×C4×C127—28no—
157C22×C4×C127—28no—
158C22×C4×C127—28no—
159C22×C4×C127—22no—
160C22×C4×C127—22no—
161C22×C4×C127—21no—
162C22×C4×C127—22no—
163C22×C4×C127—21no—
164C22×C4×C127—21no—
165C22×C4×C127—22no—
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—22no—
174C22×C4×C127—22no—
175C22×C4×C127—22no—
176C22×C4×C127—22no—
177C22×C4×C127—21no—
178C22×C4×C127—22no—
179C22×C4×C127—22no—
180C22×C4×C127—21no—
181C22×C4×C127—21no—
182C22×C4×C127—22no—
183C22×C4×C127—22no—
184C22×C4×C127—22no—
185C22×C4×C127—22no—
186C22×C4×C127—22no—
187C22×C4×C127—28no—
188C22×C4×C127—21no—
189C22×C4×C127—21no—
190C22×C4×C127—21no—
191C22×C4×C127—21no—
192C22×C4×C127—21no—
193C22×C4×C127—21no—
194C22×C4×C127—22no—
195C22×C4×C127—22no—
196C22×C4×C127—22no—
197C22×C4×C127—22no—
198C22×C4×C127—44no—
199C22×C4×C127—48no—
200C22×C4×C127—48no—
201C22×C4×C127—48no—
202C22×C4×C127—48no—
203C22×C4×C127—44no—
204C22×C4×C127—44no—
205C22×C4×C127—44no—
206C22×C4×C127—44no—
207C22×C4×C127—44no—
208C22×C4×C127—44no—
209C22×C4×C127C22×C414yes—
210C22×C4×C127C22×C412yes—
211C22×C4×C127C22×C414yes—
212C22×C4×C127C2×D414yes—
213C22×C4×C127C2×D412yes—
214C22×C4×C127C2×D414yes—
215C22×C4×C127C2×D414yes—
216C22×C4×C127C2×D412yes—
217C22×C4×C127#4114yes—
218C22×C4×C127#4114yes—
219C4⋊C4×C127—216no—
220C4⋊C4×C127—48no—
221C22⋊C4×C127—28no—
222C22⋊C4×C127—216no—
223C22⋊C4×C127—48no—
224C22⋊C4×C127—44no—
225C22⋊C4×C127—44no—
226C22⋊C4×C127—44no—
227C22⋊C4×C127C22⋊C4116yescomplemented
228C42×C127—48no—
229C23×C127—24no—
230C23×C127—24no—
231C23×C127—22no—
232C23×C127—22no—
233C23×C127—24no—
234C23×C127—22no—
235C23×C127—22no—
236C23×C127—24no—
237C23×C127—24no—
238C23×C127—24no—
239C23×C127—24no—
240C23×C127—24no—
241C23×C127—24no—
242C23×C127—24no—
243C23×C127—24no—
244C23×C127—24no—
245C23×C127—22no—
246C23×C127—22no—
247C23×C127—22no—
248C23×C127—24no—
249C23×C127—24no—
250C23×C127—41no—
251C23×C127—41no—
252C23×C127—41no—
253C23×C127—41no—
254C23×C127—41no—
255C23×C127—42no—
256C23×C127—41no—
257C23×C127—41no—
258C23×C127—41no—
259C23×C127—42no—
260C23×C127—42no—
261C23×C127—42no—
262C23×C127—42no—
263C23×C127—42no—
264C23×C127—42no—
265C23×C127—42no—
266C23×C127—42no—
267C23×C127—42no—
268C23×C127C2×C22⋊C414yes—
269C23×C127C4×D414yes—
270C23×C127C4×D414yes—
271C23×C127#12114yes—
272C23×C127#12114yes—
273C23×C127#12414yes—
274C23×C127#12714yes—
275C23×C127C23×C411yescharacteristic
276C23×C127C22×D411yescharacteristic
277C23×C127C22×D411yescharacteristic
278C23×C127C22×D411yescharacteristic
279C23×C127C22×D411yescharacteristic
280C23×C127C2×#4111yescharacteristic
281C23×C127C2×#4111yescharacteristic
282C23×C127C2×#4112yes—
283C23×C127C2×#4112yes—
284C23×C127H(5,𝔽2)12yes—
285C23×C1272−1+412yes—
286D4×C127—416no—
287C2×C4×C127—24no—
288C2×C4×C127—24no—
289C2×C4×C127—22no—
290C2×C4×C127—22no—
291C2×C4×C127—24no—
292C2×C4×C127—24no—
293C2×C4×C127—24no—
294C2×C4×C127—24no—
295C2×C4×C127—24no—
296C2×C4×C127—24no—
297C2×C4×C127—24no—
298C2×C4×C127—22no—
299C2×C4×C127—24no—
300C2×C4×C127—24no—
301C2×C4×C127—22no—
302C2×C4×C127—22no—
303C2×C4×C127—24no—
304C2×C4×C127—22no—
305C2×C4×C127—22no—
306C2×C4×C127—24no—
307C2×C4×C127—22no—
308C2×C4×C127—24no—
309C2×C4×C127—24no—
310C2×C4×C127—24no—
311C2×C4×C127—24no—
312C2×C4×C127—416no—
313C2×C4×C127—416no—
314C2×C4×C127—42no—
315C2×C4×C127—42no—
316C2×C4×C127—41no—
317C2×C4×C127—41no—
318C2×C4×C127—42no—
319C2×C4×C127—41no—
320C2×C4×C127—42no—
321C2×C4×C127—42no—
322C2×C4×C127—42no—
323C2×C4×C127—41no—
324C2×C4×C127—42no—
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—416no—
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×C127C2×C22⋊C418yes—
344C2×C4×C127#12314yescomplemented
345C22×C127—24no—
346C22×C127—28no—
347C22×C127—28no—
348C22×C127—24no—
349C22×C127—24no—
350C22×C127—28no—
351C22×C127—28no—
352C22×C127—24no—
353C22×C127—24no—
354C22×C127—24no—
355C22×C127—42no—
356C22×C127—44no—
357C22×C127—44no—
358C22×C127—42no—
359C22×C127—42no—
360C22×C127—81no—
361C22×C127—81no—
362C22×C127—82no—
363C22×C127—82no—
364C22×C127—81no—
365C22×C127—81no—
366C22×C127#39018yes—
367C22×C127C22×C22⋊C411yescharacteristic
368C22×C127C2×C4×D411yescharacteristic
369C22×C127C2×C4×D411yescharacteristic
370C22×C127C4×#4112yes—
371C22×C127#52012yes—
372C22×C127C2×#12111yescharacteristic
373C22×C127C2×#12111yescharacteristic
374C22×C127C2×#12311yescharacteristic
375C22×C127#52511yescharacteristic
376C22×C127C2×#12411yescharacteristic
377C22×C127#52912yes—
378C22×C127C2×#12711yescharacteristic
379C22×C127#53411yescharacteristic
380C22×C127#53611yescharacteristic
381C22×C127#53912yes—
382C22×C127#54612yes—
383C22×C127#54612yes—
384C22×C127#54612yes—
385C22×C127#54712yes—
386C22×C127#54712yes—
387C22×C127#54712yes—
388C22×C127#55112yes—
389C22×C127#55212yes—
390C4×C127—28no—
391C4×C127—24no—
392C4×C127—42no—
393C4×C127—44no—
394C4×C127—44no—
395C4×C127—44no—
396C4×C127—42no—
397C4×C127—81no—
398C4×C127—81no—
399#13996C12711yesmaximal, characteristic, direct product factor, Sylow
400C2×C127—28no—
401C2×C127—82no—
402C2×C127C2×#39011yescharacteristic
403C2×C127C4×#12311yescharacteristic
404C2×C127#232211yescharacteristic
405C2×C127#233912yes—
406C2×C127#235912yes—
407C2×C127#241211yescharacteristic
408C2×C127#241311yescharacteristic
409C2×C127#242512yes—
410C2×C127#248812yes—
411C2×C127#250111yescharacteristic
412C2×C127#253911yescharacteristic
413C22×#123C2×C12711yescharacteristic
414C2×#386C2×C12711yescharacteristic
415C2×#386C2×C12711yescharacteristic
416C2×#385C2×C12711yescharacteristic, complemented
417C2×#381C2×C12711yescharacteristic, complemented
418C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
419C22×#95C2×C12711yescharacteristic, complemented
420#1445C2×C12712yescomplemented
421#1439C2×C12712yescomplemented
422#1437C2×C12712yescomplemented
423C4⋊#95C2×C12712yescomplemented
424C127#1399611yescharacteristic, direct product factor, Sylow
425C23×D4C22×C12711yescharacteristic
426C24×C4C22×C12711yescharacteristic
427C24×C4C22×C12711yescharacteristic
428C24×C4C22×C12711yescharacteristic
429C2×#123—24no—
430C2×#123—24no—
431C2×#123C4×C12718yescomplemented
432C22×C4⋊C4C22×C12712yes—
433C22×C4⋊C4C22×C12712yes—
434C22×C22⋊C4C22×C12711yescharacteristic
435C22×C22⋊C4C22×C12711yescharacteristic
436C22×C22⋊C4C22×C12712yes—
437C22×C22⋊C4C22×C12712yes—
438C22×C22⋊C4C22×C12711yescharacteristic
439C22×C22⋊C4C22×C12711yescharacteristic
440C22×C22⋊C4C22×C12711yescharacteristic
441C22×C42C22×C12712yes—
442#386—24no—
443#386—24no—
444#385—24no—
445#381—24no—
446C4×C22⋊C4—24no—
447C2×#95—24no—
448C2×#95C22×C12711yescharacteristic
449C2×#95C22×C12712yes—
450C2×#95C22×C12712yes—
451C2×#95C22×C12712yes—
452C2×#95C22×C12712yes—
453C2×#95C22×C12712yes—
454C2×#95C22×C12712yes—
455C2×#95C22×C12712yes—
456C2×#95C22×C12711yescharacteristic
457C25C23×C12711yescharacteristic
458C25C23×C12711yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C2×C4×C12714yes—
466C23×C4—22no—
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—42no—
480C23×C4—42no—
481C23×C4C2×C4×C12714yes—
482C23×C4D4×C12714yes—
483C23×C4C23×C12711yescharacteristic
484C23×C4C23×C12711yescharacteristic
485C23×C4C23×C12712yes—
486C23×C4C23×C12711yescharacteristic
487C23×C4C23×C12712yes—
488C23×C4C23×C12711yescharacteristic
489C23×C4C23×C12712yes—
490C23×C4C23×C12712yes—
491C23×C4C23×C12711yescharacteristic
492#123—232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4C2×C4×C12718yescomplemented
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4C2×C4×C12714yes—
514C2×C22⋊C4C2×C4×C12718yescomplemented
515C2×C22⋊C4D4×C12714yes—
516C2×C22⋊C4D4×C12714yes—
517C2×C22⋊C4D4×C12714yes—
518C2×C42—24no—
519C2×C42—24no—
520C2×C42—42no—
521#95—24no—
522#95—24no—
523#95—24no—
524#95—24no—
525#95—24no—
526#95—24no—
527#95—24no—
528#95—22no—
529#95—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24C22×C4×C12712yes—
545C24C22×C4×C12712yes—
546C24C2×D4×C12712yes—
547C24C2×D4×C12712yes—
548C24C2×D4×C12712yes—
549C24C2×D4×C12712yes—
550C24#41×C12712yes—
551C24#41×C12712yes—
552C24C24×C12711yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4C22×C4×C12714yes—
623C22×C4C22×C4×C12712yes—
624C22×C4C22×C4×C12714yes—
625C22×C4C2×D4×C12714yes—
626C22×C4C2×D4×C12712yes—
627C22×C4C2×D4×C12714yes—
628C22×C4C2×D4×C12714yes—
629C22×C4C2×D4×C12712yes—
630C22×C4#41×C12714yes—
631C22×C4#41×C12714yes—
632C4⋊C4—216no—
633C4⋊C4—48no—
634C22⋊C4—28no—
635C22⋊C4—216no—
636C22⋊C4—48no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4C22⋊C4×C127116yescomplemented
641C42—48no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C2×C22⋊C4×C12714yes—
682C23C4×D4×C12714yes—
683C23C4×D4×C12714yes—
684C23#121×C12714yes—
685C23#121×C12714yes—
686C23#124×C12714yes—
687C23#127×C12714yes—
688C23C23×C4×C12711yescharacteristic
689C23C22×D4×C12711yescharacteristic
690C23C22×D4×C12711yescharacteristic
691C23C22×D4×C12711yescharacteristic
692C23C22×D4×C12711yescharacteristic
693C23C2×#41×C12711yescharacteristic
694C23C2×#41×C12711yescharacteristic
695C23C2×#41×C12712yes—
696C23C2×#41×C12712yes—
697C23H(5,𝔽2)×C12712yes—
698C232−1+4×C12712yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—416no—
726C2×C4—416no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—416no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4C2×C22⋊C4×C12718yes—
757C2×C4#123×C12714yescomplemented
758C22—24no—
759C22—28no—
760C22—28no—
761C22—24no—
762C22—24no—
763C22—28no—
764C22—28no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—42no—
769C22—44no—
770C22—44no—
771C22—42no—
772C22—42no—
773C22—81no—
774C22—81no—
775C22—82no—
776C22—82no—
777C22—81no—
778C22—81no—
779C22#390×C12718yes—
780C22C22×C22⋊C4×C12711yescharacteristic
781C22C2×C4×D4×C12711yescharacteristic
782C22C2×C4×D4×C12711yescharacteristic
783C22C4×#41×C12712yes—
784C22#520×C12712yes—
785C22C2×#121×C12711yescharacteristic
786C22C2×#121×C12711yescharacteristic
787C22C2×#123×C12711yescharacteristic
788C22#525×C12711yescharacteristic
789C22C2×#124×C12711yescharacteristic
790C22#529×C12712yes—
791C22C2×#127×C12711yescharacteristic
792C22#534×C12711yescharacteristic
793C22#536×C12711yescharacteristic
794C22#539×C12712yes—
795C22#546×C12712yes—
796C22#546×C12712yes—
797C22#546×C12712yes—
798C22#547×C12712yes—
799C22#547×C12712yes—
800C22#547×C12712yes—
801C22#551×C12712yes—
802C22#552×C12712yes—
803C4—28no—
804C4—24no—
805C4—42no—
806C4—44no—
807C4—44no—
808C4—44no—
809C4—42no—
810C4—81no—
811C4—81no—
812C2—28no—
813C2—82no—
814C2C2×#390×C12711yescharacteristic
815C2C4×#123×C12711yescharacteristic
816C2C127×#232211yescharacteristic
817C2C127×#233912yes—
818C2C127×#235912yes—
819C2C127×#241211yescharacteristic
820C2C127×#241311yescharacteristic
821C2C127×#242512yes—
822C2C127×#248812yes—
823C2C127×#250111yescharacteristic
824C2C127×#253911yescharacteristic
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. C2×#381×C127C2semidirect
6. C2×C4×C22⋊C4×C127C2semidirect
7. C22×#95×C127C2semidirect
8. C127×#1445C2semidirect
9. C127×#1439C2semidirect
10. C127×#1437C2semidirect
11. C127×C4⋊#95C2semidirect
18. C2×#123×C127C4semidirect
85. C2×C4⋊C4×C127C2×C4semidirect
101. C2×C22⋊C4×C127C2×C4semidirect
227. C22⋊C4×C127C22⋊C4semidirect
344. C2×C4×C127#123semidirect
399. #13996C127direct (N × H)
416. C2×#385C2×C127semidirect
417. C2×#381C2×C127semidirect
418. C2×C4×C22⋊C4C2×C127semidirect
419. C22×#95C2×C127semidirect
420. #1445C2×C127semidirect
421. #1439C2×C127semidirect
422. #1437C2×C127semidirect
423. C4⋊#95C2×C127semidirect
424. C127#13996direct (N × H)
431. C2×#123C4×C127semidirect
498. C2×C4⋊C4C2×C4×C127semidirect
514. C2×C22⋊C4C2×C4×C127semidirect
640. C22⋊C4C22⋊C4×C127semidirect
757. C2×C4#123×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1272
C2×#386×C1272
C2×#385×C1272
C2×#381×C1272
C2×C4×C22⋊C4×C1272
C22×#95×C1272
C127×#14452
C127×#14392
C127×#14372
C127×C4⋊#952
#13996127