Finite Group Databasebeta

← C2×C127×#1799 #44584304

Subgroups — C2×C127×#1799 #44584304

Order 32512.

2066 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic
2C22×#99×C127C212yesmaximal
3C2×#380×C127C212yesmaximal, complemented
4C127×#1799C218yesmaximal, direct product factor
5C2×#342×C127C212yesmaximal, complemented
6C23×D4×C127C2211yescharacteristic
7C24×C4×C127C411yescharacteristic, complemented
8C24×C4×C127C2211yescharacteristic
9C2×C4×D4×C127—22no—
10C2×C4×D4×C127—22no—
11C2×C4×D4×C127—24no—
12C2×C4×D4×C127C414yescomplemented
13C2×C4×D4×C127C2214yes—
14C22×C4⋊C4×C127—22no—
15C22×C4⋊C4×C127C411yescharacteristic, complemented
16C22×C22⋊C4×C127C411yescharacteristic, complemented
17C22×C22⋊C4×C127C2214yes—
18C22×C22⋊C4×C127C2211yescharacteristic
19C22×C42×C127C411yescharacteristic, complemented
20C2×#99×C127—28no—
21C2×#99×C127C2218yes—
22#380×C127—24no—
23#380×C127C2218yescomplemented
24C2×#95×C127—22no—
25#342×C127C2218yescomplemented
26C25×C127C2×C411yescharacteristic
27C25×C127C2311yescharacteristic
28C22×D4×C127—22no—
29C22×D4×C127—22no—
30C22×D4×C127—24no—
31C22×D4×C127C2×C412yes—
32C22×D4×C127D414yes—
33C22×D4×C127Q814yes—
34C22×D4×C127C2312yes—
35C23×C4×C127—22no—
36C23×C4×C127—21no—
37C23×C4×C127—21no—
38C23×C4×C127—24no—
39C23×C4×C127—44no—
40C23×C4×C127—44no—
41C23×C4×C127C2×C411yescharacteristic
42C23×C4×C127C2×C411yescharacteristic
43C23×C4×C127C2×C411yescharacteristic
44C23×C4×C127C2×C411yescharacteristic
45C23×C4×C127C2×C411yescharacteristic
46C23×C4×C127C2×C412yes—
47C23×C4×C127C2×C414yescomplemented
48C23×C4×C127D412yes—
49C23×C4×C127D412yes—
50C23×C4×C127D414yes—
51C23×C4×C127C2312yes—
52C4×D4×C127—28no—
53C4×D4×C127—28no—
54C4×D4×C127—28no—
55C4×D4×C127—28no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—28no—
59C2×C4⋊C4×C127—48no—
60C2×C4⋊C4×C127C2×C414yescomplemented
61C2×C22⋊C4×C127—22no—
62C2×C22⋊C4×C127—22no—
63C2×C22⋊C4×C127—22no—
64C2×C22⋊C4×C127—22no—
65C2×C22⋊C4×C127—28no—
66C2×C22⋊C4×C127—28no—
67C2×C22⋊C4×C127—24no—
68C2×C22⋊C4×C127C2×C412yes—
69C2×C22⋊C4×C127C2×C414yescomplemented
70C2×C22⋊C4×C127C2318yes—
71C2×C22⋊C4×C127C2312yes—
72C2×C42×C127—22no—
73C2×C42×C127—21no—
74C2×C42×C127—21no—
75C2×C42×C127C2×C414yescomplemented
76#99×C127—216no—
77#95×C127—28no—
78C24×C127—21no—
79C24×C127—21no—
80C24×C127—22no—
81C24×C127—42no—
82C24×C127—42no—
83C24×C127—42no—
84C24×C127—42no—
85C24×C127C4⋊C414yescomplemented
86C24×C127C22×C411yescharacteristic
87C24×C127C22×C412yes—
88C24×C127C22×C411yescharacteristic
89C24×C127C2×D412yes—
90C24×C127C2×D412yes—
91C24×C127C2×D412yes—
92C24×C127C2×Q812yes—
93C24×C127#4114yes—
94C24×C127C2411yescharacteristic
95C2×D4×C127—24no—
96C2×D4×C127—24no—
97C2×D4×C127—28no—
98C2×D4×C127—28no—
99C2×D4×C127—28no—
100C2×D4×C127—28no—
101C2×D4×C127—24no—
102C2×D4×C127—24no—
103C2×D4×C127C4⋊C418yescomplemented
104C2×D4×C127C2×D414yes—
105C2×D4×C127C2×Q814yes—
106C22×C4×C127—21no—
107C22×C4×C127—21no—
108C22×C4×C127—22no—
109C22×C4×C127—28no—
110C22×C4×C127—24no—
111C22×C4×C127—21no—
112C22×C4×C127—21no—
113C22×C4×C127—21no—
114C22×C4×C127—21no—
115C22×C4×C127—24no—
116C22×C4×C127—24no—
117C22×C4×C127—28no—
118C22×C4×C127—44no—
119C22×C4×C127—48no—
120C22×C4×C127—44no—
121C22×C4×C127—42no—
122C22×C4×C127—44no—
123C22×C4×C127—44no—
124C22×C4×C127—48no—
125C22×C4×C127—48no—
126C22×C4×C127—44no—
127C22×C4×C127—42no—
128C22×C4×C127—42no—
129C22×C4×C127—48no—
130C22×C4×C127—48no—
131C22×C4×C127—48no—
132C22×C4×C127C22⋊C412yes—
133C22×C4×C127C22⋊C414yes—
134C22×C4×C127C22⋊C411yescharacteristic
135C22×C4×C127C22⋊C412yes—
136C22×C4×C127C22⋊C412yes—
137C22×C4×C127C22⋊C414yes—
138C22×C4×C127C22⋊C411yescharacteristic
139C22×C4×C127C4⋊C414yescomplemented
140C22×C4×C127C22×C412yes—
141C22×C4×C127C22×C412yes—
142C22×C4×C127C22×C412yes—
143C22×C4×C127C22×C412yes—
144C22×C4×C127C22×C412yes—
145C22×C4×C127C2×D414yes—
146C22×C4×C127C2×D414yes—
147C4⋊C4×C127—28no—
148C4⋊C4×C127—416no—
149C22⋊C4×C127—24no—
150C22⋊C4×C127—24no—
151C22⋊C4×C127—28no—
152C22⋊C4×C127—28no—
153C22⋊C4×C127—28no—
154C22⋊C4×C127—48no—
155C42×C127—24no—
156C42×C127—24no—
157C23×C127—24no—
158C23×C127—22no—
159C23×C127—24no—
160C23×C127—22no—
161C23×C127—22no—
162C23×C127—22no—
163C23×C127—24no—
164C23×C127—24no—
165C23×C127—41no—
166C23×C127—42no—
167C23×C127—41no—
168C23×C127—41no—
169C23×C127—44no—
170C23×C127—42no—
171C23×C127—44no—
172C23×C127—48no—
173C23×C127—41no—
174C23×C127—42no—
175C23×C127—48no—
176C23×C127—42no—
177C23×C127—42no—
178C23×C127—48no—
179C23×C127—42no—
180C23×C127—42no—
181C23×C127—42no—
182C23×C127C2×C22⋊C412yes—
183C23×C127C2×C22⋊C411yescharacteristic
184C23×C127C2×C22⋊C411yescharacteristic
185C23×C127C2×C4⋊C412yes—
186C23×C127C2×C4⋊C412yes—
187C23×C127C2×C4⋊C414yescomplemented
188C23×C127#11712yes—
189C23×C127#11712yes—
190C23×C127#12114yes—
191C23×C127#12114yes—
192C23×C127C22⋊Q814yes—
193C23×C127C22⋊Q814yes—
194C23×C127C23×C411yescharacteristic
195C23×C127C22×D412yes—
196C23×C127C22×D411yescharacteristic
197C23×C127C22×Q811yescharacteristic
198C23×C127C2×#4112yes—
199D4×C127—28no—
200D4×C127—28no—
201D4×C127—216no—
202C2×C4×C127—22no—
203C2×C4×C127—22no—
204C2×C4×C127—24no—
205C2×C4×C127—24no—
206C2×C4×C127—22no—
207C2×C4×C127—24no—
208C2×C4×C127—28no—
209C2×C4×C127—24no—
210C2×C4×C127—24no—
211C2×C4×C127—28no—
212C2×C4×C127—22no—
213C2×C4×C127—22no—
214C2×C4×C127—44no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—44no—
218C2×C4×C127—48no—
219C2×C4×C127—42no—
220C2×C4×C127—42no—
221C2×C4×C127—42no—
222C2×C4×C127—42no—
223C2×C4×C127—48no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127—48no—
227C2×C4×C127—48no—
228C2×C4×C127—48no—
229C2×C4×C127—816no—
230C2×C4×C127#9914yescomplemented
231C2×C4×C127C2×C22⋊C412yes—
232C2×C4×C127C2×C22⋊C414yes—
233C2×C4×C127C2×C22⋊C412yes—
234C2×C4×C127C2×C4⋊C414yescomplemented
235C22×C127—28no—
236C22×C127—24no—
237C22×C127—24no—
238C22×C127—28no—
239C22×C127—22no—
240C22×C127—21no—
241C22×C127—21no—
242C22×C127—22no—
243C22×C127—22no—
244C22×C127—21no—
245C22×C127—21no—
246C22×C127—22no—
247C22×C127—24no—
248C22×C127—42no—
249C22×C127—42no—
250C22×C127—44no—
251C22×C127—44no—
252C22×C127—41no—
253C22×C127—41no—
254C22×C127—42no—
255C22×C127—44no—
256C22×C127—44no—
257C22×C127—48no—
258C22×C127—48no—
259C22×C127—42no—
260C22×C127—42no—
261C22×C127#38012yes—
262C22×C127#38014yes—
263C22×C127#38012yes—
264C22×C127C2×#9912yes—
265C22×C127#41012yes—
266C22×C127C22×C22⋊C411yescharacteristic
267C22×C127C22×C4⋊C411yescharacteristic
268C22×C127C2×#11711yescharacteristic
269C22×C127C2×#12112yes—
270C22×C127C2×C22⋊Q812yes—
271C4×C127—22no—
272C4×C127—24no—
273C4×C127—24no—
274C4×C127—42no—
275C4×C127—42no—
276C4×C127—88no—
277C4×C127C2×#9914yescomplemented
278C2×#1799C12711yesmaximal, characteristic, direct product factor, Sylow
279C2×C127—22no—
280C2×C127—21no—
281C2×C127—21no—
282C2×C127—22no—
283C2×C127—22no—
284C2×C127—24no—
285C2×C127—44no—
286C2×C127#179914yesdirect product factor
287C2×C127C2×#38011yescharacteristic
288C2×C127C22×#9911yescharacteristic
289C2×C127C2×#41011yescharacteristic
290C22×C4×D4C2×C12711yescharacteristic
291C22×#99C2×C12712yes—
292C2×#380C2×C12712yescomplemented
293#1799C2×C12718yesdirect product factor
294C2×#342C2×C12712yescomplemented
295C127C2×#179911yescharacteristic, direct product factor, Sylow
296C23×D4C22×C12711yescharacteristic
297C24×C4C4×C12711yescharacteristic, complemented
298C24×C4C22×C12711yescharacteristic
299C2×C4×D4—22no—
300C2×C4×D4—22no—
301C2×C4×D4—24no—
302C2×C4×D4C4×C12714yescomplemented
303C2×C4×D4C22×C12714yes—
304C22×C4⋊C4—22no—
305C22×C4⋊C4C4×C12711yescharacteristic, complemented
306C22×C22⋊C4C4×C12711yescharacteristic, complemented
307C22×C22⋊C4C22×C12714yes—
308C22×C22⋊C4C22×C12711yescharacteristic
309C22×C42C4×C12711yescharacteristic, complemented
310C2×#99—28no—
311C2×#99C22×C12718yes—
312#380—24no—
313#380C22×C12718yescomplemented
314C2×#95—22no—
315#342C22×C12718yescomplemented
316C25C2×C4×C12711yescharacteristic
317C25C23×C12711yescharacteristic
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—24no—
321C22×D4C2×C4×C12712yes—
322C22×D4D4×C12714yes—
323C22×D4Q8×C12714yes—
324C22×D4C23×C12712yes—
325C23×C4—22no—
326C23×C4—21no—
327C23×C4—21no—
328C23×C4—24no—
329C23×C4—44no—
330C23×C4—44no—
331C23×C4C2×C4×C12711yescharacteristic
332C23×C4C2×C4×C12711yescharacteristic
333C23×C4C2×C4×C12711yescharacteristic
334C23×C4C2×C4×C12711yescharacteristic
335C23×C4C2×C4×C12711yescharacteristic
336C23×C4C2×C4×C12712yes—
337C23×C4C2×C4×C12714yescomplemented
338C23×C4D4×C12712yes—
339C23×C4D4×C12712yes—
340C23×C4D4×C12714yes—
341C23×C4C23×C12712yes—
342C4×D4—28no—
343C4×D4—28no—
344C4×D4—28no—
345C4×D4—28no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—48no—
350C2×C4⋊C4C2×C4×C12714yescomplemented
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4C2×C4×C12712yes—
359C2×C22⋊C4C2×C4×C12714yescomplemented
360C2×C22⋊C4C23×C12718yes—
361C2×C22⋊C4C23×C12712yes—
362C2×C42—21no—
363C2×C42—22no—
364C2×C42—21no—
365C2×C42C2×C4×C12714yescomplemented
366#99—216no—
367#95—28no—
368C24—21no—
369C24—21no—
370C24—22no—
371C24—42no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24C4⋊C4×C12714yescomplemented
376C24C22×C4×C12711yescharacteristic
377C24C22×C4×C12712yes—
378C24C22×C4×C12711yescharacteristic
379C24C2×D4×C12712yes—
380C24C2×D4×C12712yes—
381C24C2×D4×C12712yes—
382C24C2×Q8×C12712yes—
383C24#41×C12714yes—
384C24C24×C12711yescharacteristic
385C2×D4—24no—
386C2×D4—24no—
387C2×D4—28no—
388C2×D4—28no—
389C2×D4—28no—
390C2×D4—28no—
391C2×D4—24no—
392C2×D4—24no—
393C2×D4C4⋊C4×C12718yescomplemented
394C2×D4C2×D4×C12714yes—
395C2×D4C2×Q8×C12714yes—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—28no—
400C22×C4—24no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—28no—
408C22×C4—44no—
409C22×C4—48no—
410C22×C4—44no—
411C22×C4—42no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—48no—
415C22×C4—48no—
416C22×C4—44no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—48no—
420C22×C4—48no—
421C22×C4—48no—
422C22×C4C22⋊C4×C12711yescharacteristic
423C22×C4C22⋊C4×C12712yes—
424C22×C4C22⋊C4×C12712yes—
425C22×C4C22⋊C4×C12714yes—
426C22×C4C22⋊C4×C12712yes—
427C22×C4C22⋊C4×C12714yes—
428C22×C4C22⋊C4×C12711yescharacteristic
429C22×C4C4⋊C4×C12714yescomplemented
430C22×C4C22×C4×C12712yes—
431C22×C4C22×C4×C12712yes—
432C22×C4C22×C4×C12712yes—
433C22×C4C22×C4×C12712yes—
434C22×C4C22×C4×C12712yes—
435C22×C4C2×D4×C12714yes—
436C22×C4C2×D4×C12714yes—
437C4⋊C4—28no—
438C4⋊C4—416no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—28no—
442C22⋊C4—28no—
443C22⋊C4—28no—
444C22⋊C4—48no—
445C42—24no—
446C42—24no—
447C23—24no—
448C23—22no—
449C23—24no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—24no—
454C23—24no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—42no—
460C23—44no—
461C23—44no—
462C23—48no—
463C23—41no—
464C23—42no—
465C23—48no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—48no—
470C23—42no—
471C23—42no—
472C23C2×C22⋊C4×C12712yes—
473C23C2×C22⋊C4×C12711yescharacteristic
474C23C2×C22⋊C4×C12711yescharacteristic
475C23C2×C4⋊C4×C12712yes—
476C23C2×C4⋊C4×C12712yes—
477C23C2×C4⋊C4×C12714yescomplemented
478C23#117×C12712yes—
479C23#117×C12712yes—
480C23#121×C12714yes—
481C23#121×C12714yes—
482C23C22⋊Q8×C12714yes—
483C23C22⋊Q8×C12714yes—
484C23C23×C4×C12711yescharacteristic
485C23C22×D4×C12712yes—
486C23C22×D4×C12711yescharacteristic
487C23C22×Q8×C12711yescharacteristic
488C23C2×#41×C12712yes—
489D4—28no—
490D4—28no—
491D4—216no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—28no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—28no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—44no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—44no—
508C2×C4—48no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—48no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—48no—
517C2×C4—48no—
518C2×C4—48no—
519C2×C4—816no—
520C2×C4#99×C12714yescomplemented
521C2×C4C2×C22⋊C4×C12712yes—
522C2×C4C2×C22⋊C4×C12714yes—
523C2×C4C2×C22⋊C4×C12712yes—
524C2×C4C2×C4⋊C4×C12714yescomplemented
525C22—22no—
526C22—21no—
527C22—21no—
528C22—22no—
529C22—22no—
530C22—21no—
531C22—21no—
532C22—22no—
533C22—28no—
534C22—24no—
535C22—24no—
536C22—28no—
537C22—24no—
538C22—42no—
539C22—42no—
540C22—44no—
541C22—44no—
542C22—41no—
543C22—41no—
544C22—42no—
545C22—44no—
546C22—44no—
547C22—48no—
548C22—42no—
549C22—42no—
550C22—48no—
551C22#380×C12712yes—
552C22#380×C12714yes—
553C22#380×C12712yes—
554C22C2×#99×C12712yes—
555C22#410×C12712yes—
556C22C22×C22⋊C4×C12711yescharacteristic
557C22C22×C4⋊C4×C12711yescharacteristic
558C22C2×#117×C12711yescharacteristic
559C22C2×#121×C12712yes—
560C22C2×C22⋊Q8×C12712yes—
561C4—22no—
562C4—24no—
563C4—24no—
564C4—42no—
565C4—42no—
566C4—88no—
567C4C2×#99×C12714yescomplemented
568C2—22no—
569C2—21no—
570C2—21no—
571C2—22no—
572C2—22no—
573C2—24no—
574C2—44no—
575C2C127×#179914yesdirect product factor
576C2C2×#380×C12711yescharacteristic
577C2C22×#99×C12711yescharacteristic
578C2C2×#410×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#380×C127C2semidirect
4. C127×#1799C2direct (N × H)
5. C2×#342×C127C2semidirect
7. C24×C4×C127C4semidirect
12. C2×C4×D4×C127C4semidirect
15. C22×C4⋊C4×C127C4semidirect
16. C22×C22⋊C4×C127C4semidirect
19. C22×C42×C127C4semidirect
23. #380×C127C22semidirect
25. #342×C127C22semidirect
47. C23×C4×C127C2×C4semidirect
60. C2×C4⋊C4×C127C2×C4semidirect
69. C2×C22⋊C4×C127C2×C4semidirect
75. C2×C42×C127C2×C4semidirect
85. C24×C127C4⋊C4semidirect
103. C2×D4×C127C4⋊C4semidirect
139. C22×C4×C127C4⋊C4semidirect
187. C23×C127C2×C4⋊C4semidirect
230. C2×C4×C127#99semidirect
234. C2×C4×C127C2×C4⋊C4semidirect
277. C4×C127C2×#99semidirect
278. C2×#1799C127direct (N × H)
286. C2×C127#1799direct (N × H)
292. C2×#380C2×C127semidirect
293. #1799C2×C127direct (N × H)
294. C2×#342C2×C127semidirect
295. C127C2×#1799direct (N × H)
297. C24×C4C4×C127semidirect
302. C2×C4×D4C4×C127semidirect
305. C22×C4⋊C4C4×C127semidirect
306. C22×C22⋊C4C4×C127semidirect
309. C22×C42C4×C127semidirect
313. #380C22×C127semidirect
315. #342C22×C127semidirect
337. C23×C4C2×C4×C127semidirect
350. C2×C4⋊C4C2×C4×C127semidirect
359. C2×C22⋊C4C2×C4×C127semidirect
365. C2×C42C2×C4×C127semidirect
375. C24C4⋊C4×C127semidirect
393. C2×D4C4⋊C4×C127semidirect
429. C22×C4C4⋊C4×C127semidirect
477. C23C2×C4⋊C4×C127semidirect
520. C2×C4#99×C127semidirect
524. C2×C4C2×C4⋊C4×C127semidirect
567. C4C2×#99×C127semidirect
575. C2C127×#1799direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1272
C22×#99×C1272
C2×#380×C1272
C127×#17992
C2×#342×C1272
C2×#1799127