Finite Group Databasebeta

← C127×#13927 #44577600

Subgroups — C127×#13927 #44577600

Order 32512.

1650 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C127C211yesmaximal, characteristic
2C2×#387×C127C212yesmaximal
3C127×#1446C212yesmaximal
4C127×#1441C212yesmaximal
5C127×#1436C212yesmaximal
6C127×C4⋊#95C211yesmaximal, characteristic
7C127×#1434C211yesmaximal, characteristic
8C127×#1434C211yesmaximal, characteristic
9C127×#1434C211yesmaximal, characteristic
10C127×#1434C211yesmaximal, characteristic
11C4×#95×C127C211yesmaximal, characteristic
12C23×Q8×C127C2211yescharacteristic
13C2×C4×Q8×C127—28no—
14C2×C4×Q8×C127C418yescomplemented
15C22×C4⋊C4×C127C2212yes—
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C42×C127C2212yes—
20C22×C42×C127C2211yescharacteristic
21C22×C42×C127C2211yescharacteristic
22C22×C42×C127C2211yescharacteristic
23#387×C127—28no—
24C2×#95×C127C2211yescharacteristic
25C2×#95×C127C2212yes—
26C2×#95×C127C2211yescharacteristic
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2211yescharacteristic
38C22×Q8×C127—24no—
39C22×Q8×C127—24no—
40C22×Q8×C127—22no—
41C22×Q8×C127—22no—
42C22×Q8×C127C2×C414yes—
43C23×C4×C127C2312yes—
44C23×C4×C127C2312yes—
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2312yes—
47C23×C4×C127C2312yes—
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2311yescharacteristic
51C23×C4×C127C2311yescharacteristic
52C23×C4×C127C2311yescharacteristic
53C23×C4×C127C2311yescharacteristic
54C4×Q8×C127—232no—
55C2×C4⋊C4×C127—24no—
56C2×C4⋊C4×C127—24no—
57C2×C4⋊C4×C127—24no—
58C2×C4⋊C4×C127—24no—
59C2×C4⋊C4×C127—42no—
60C2×C4⋊C4×C127C2×C414yes—
61C2×C4⋊C4×C127C2×C414yes—
62C2×C4⋊C4×C127C2×C414yes—
63C2×C4⋊C4×C127D418yes—
64C2×C42×C127—24no—
65C2×C42×C127—24no—
66C2×C42×C127—24no—
67C2×C42×C127—24no—
68C2×C42×C127—24no—
69C2×C42×C127—42no—
70C2×C42×C127C2×C414yes—
71C2×C42×C127C2×C414yes—
72C2×C42×C127C2×C414yes—
73#95×C127—24no—
74#95×C127—24no—
75#95×C127—24no—
76#95×C127—24no—
77#95×C127—24no—
78#95×C127—22no—
79#95×C127—24no—
80#95×C127—24no—
81#95×C127—24no—
82#95×C127—24no—
83#95×C127—22no—
84#95×C127—22no—
85#95×C127—42no—
86#95×C127Q814yescomplemented
87C24×C127C2411yescharacteristic
88C2×Q8×C127—216no—
89C2×Q8×C127—216no—
90C2×Q8×C127—28no—
91C2×Q8×C127—28no—
92C2×Q8×C127—28no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—22no—
98C22×C4×C127—22no—
99C22×C4×C127—21no—
100C22×C4×C127—21no—
101C22×C4×C127—22no—
102C22×C4×C127—21no—
103C22×C4×C127—21no—
104C22×C4×C127—21no—
105C22×C4×C127—21no—
106C22×C4×C127—22no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—22no—
118C22×C4×C127—22no—
119C22×C4×C127—21no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—21no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—22no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127—22no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127C22×C412yes—
140C22×C4×C127C22×C412yes—
141C22×C4×C127C22×C412yes—
142C22×C4×C127C22×C412yes—
143C22×C4×C127C22×C412yes—
144C22×C4×C127C22×C412yes—
145C22×C4×C127C22×C412yes—
146C22×C4×C127C2×D414yes—
147C22×C4×C127C2×D414yes—
148C22×C4×C127C2×D414yes—
149C22×C4×C127C2×Q814yes—
150C22×C4×C127C2×Q812yes—
151C22×C4×C127#4114yes—
152C22×C4×C127#4114yes—
153C22×C4×C127#4112yes—
154C22×C4×C127#4112yes—
155C22×C4×C127#4112yes—
156C4⋊C4×C127—28no—
157C4⋊C4×C127—28no—
158C4⋊C4×C127—48no—
159C4⋊C4×C127C22⋊C4116yes—
160C42×C127—28no—
161C42×C127—28no—
162C42×C127—28no—
163C42×C127—48no—
164C23×C127C23×C411yescharacteristic
165C23×C127C22×D412yes—
166C23×C127C22×Q811yescharacteristic
167C23×C127C2×#4112yes—
168C23×C127C2×#4111yescharacteristic
169C23×C127C2×#4111yescharacteristic
170C23×C127C2×#4111yescharacteristic
171C23×C127C2×#4112yes—
172C23×C127H(5,𝔽2)11yescharacteristic
173C23×C1272−1+412yes—
174C23×C1272−1+411yescharacteristic
175Q8×C127—232no—
176C2×C4×C127—22no—
177C2×C4×C127—22no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
182C2×C4×C127—22no—
183C2×C4×C127—22no—
184C2×C4×C127—22no—
185C2×C4×C127—22no—
186C2×C4×C127—22no—
187C2×C4×C127—22no—
188C2×C4×C127—24no—
189C2×C4×C127—24no—
190C2×C4×C127—24no—
191C2×C4×C127—24no—
192C2×C4×C127—24no—
193C2×C4×C127—24no—
194C2×C4×C127—24no—
195C2×C4×C127—24no—
196C2×C4×C127—24no—
197C2×C4×C127—24no—
198C2×C4×C127—24no—
199C2×C4×C127—24no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—22no—
203C2×C4×C127—24no—
204C2×C4×C127—24no—
205C2×C4×C127—24no—
206C2×C4×C127—24no—
207C2×C4×C127—24no—
208C2×C4×C127—24no—
209C2×C4×C127—42no—
210C2×C4×C127—42no—
211C2×C4×C127—42no—
212C2×C4×C127—42no—
213C2×C4×C127—42no—
214C2×C4×C127—42no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—42no—
218C2×C4×C127—42no—
219C2×C4×C127—42no—
220C2×C4×C127—42no—
221C2×C4×C127—42no—
222C2×C4×C127—42no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127—42no—
227C2×C4×C127—42no—
228C2×C4×C127—42no—
229C2×C4×C127—42no—
230C2×C4×C127—42no—
231C2×C4×C127—42no—
232C2×C4×C127—42no—
233C2×C4×C127C2×C22⋊C414yes—
234C2×C4×C127C2×C22⋊C414yes—
235C2×C4×C127C2×C22⋊C414yes—
236C2×C4×C127#11714yes—
237C2×C4×C127#11714yes—
238C2×C4×C127C4×Q814yes—
239C22×C127C22×C22⋊C411yescharacteristic
240C22×C127C2×#11711yescharacteristic
241C22×C127C2×#11711yescharacteristic
242C22×C127C2×C4×Q811yescharacteristic
243C22×C127C4×#4111yescharacteristic
244C22×C127#51911yescharacteristic
245C22×C127#52011yescharacteristic
246C22×C127#52512yes—
247C22×C127#52512yes—
248C22×C127#52912yes—
249C22×C127#53312yes—
250C22×C127#54112yes—
251C22×C127#54212yes—
252C22×C127#54612yes—
253C22×C127#54712yes—
254C22×C127#54812yes—
255C22×C127D4×Q812yes—
256C22×C127#55212yes—
257C22×C127#55411yescharacteristic
258C22×C127#55611yescharacteristic
259C22×C127#55612yes—
260C22×C127#55711yescharacteristic
261C22×C127#55911yescharacteristic
262C4×C127—24no—
263C4×C127—24no—
264C4×C127—24no—
265C4×C127—24no—
266C4×C127—24no—
267C4×C127—24no—
268C4×C127—42no—
269C4×C127—44no—
270C4×C127—44no—
271C4×C127—82no—
272C4×C127—82no—
273#13927C12711yesmaximal, characteristic, direct product factor, Sylow
274C2×C127#228011yescharacteristic
275C2×C127#229511yescharacteristic
276C2×C127#232011yescharacteristic
277C2×C127#233911yescharacteristic
278C2×C127Q8×C22⋊C411yescharacteristic
279C2×C127#235511yescharacteristic
280C2×C127#235611yescharacteristic
281C2×C127#245812yes—
282C2×C127#246212yes—
283C2×C127#246512yes—
284C2×C127#246912yes—
285C22×C4×Q8C2×C12711yescharacteristic
286C2×#387C2×C12712yes—
287#1446C2×C12712yes—
288#1441C2×C12712yes—
289#1436C2×C12712yes—
290C4⋊#95C2×C12711yescharacteristic
291#1434C2×C12711yescharacteristic
292#1434C2×C12711yescharacteristic
293#1434C2×C12711yescharacteristic
294#1434C2×C12711yescharacteristic
295C4×#95C2×C12711yescharacteristic
296C127#1392711yescharacteristic, direct product factor, Sylow
297C23×Q8C22×C12711yescharacteristic
298C2×C4×Q8—28no—
299C2×C4×Q8C4×C12718yescomplemented
300C22×C4⋊C4C22×C12712yes—
301C22×C4⋊C4C22×C12711yescharacteristic
302C22×C4⋊C4C22×C12711yescharacteristic
303C22×C4⋊C4C22×C12711yescharacteristic
304C22×C42C22×C12712yes—
305C22×C42C22×C12711yescharacteristic
306C22×C42C22×C12711yescharacteristic
307C22×C42C22×C12711yescharacteristic
308#387—28no—
309C2×#95C22×C12711yescharacteristic
310C2×#95C22×C12712yes—
311C2×#95C22×C12711yescharacteristic
312C2×#95C22×C12711yescharacteristic
313C2×#95C22×C12712yes—
314C2×#95C22×C12712yes—
315C2×#95C22×C12712yes—
316C2×#95C22×C12712yes—
317C2×#95C22×C12712yes—
318C2×#95C22×C12712yes—
319C2×#95C22×C12712yes—
320C2×#95C22×C12712yes—
321C2×#95C22×C12712yes—
322C2×#95C22×C12711yescharacteristic
323C22×Q8—24no—
324C22×Q8—24no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8C2×C4×C12714yes—
328C23×C4C23×C12712yes—
329C23×C4C23×C12712yes—
330C23×C4C23×C12711yescharacteristic
331C23×C4C23×C12712yes—
332C23×C4C23×C12712yes—
333C23×C4C23×C12711yescharacteristic
334C23×C4C23×C12711yescharacteristic
335C23×C4C23×C12711yescharacteristic
336C23×C4C23×C12711yescharacteristic
337C23×C4C23×C12711yescharacteristic
338C23×C4C23×C12711yescharacteristic
339C4×Q8—232no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4C2×C4×C12714yes—
346C2×C4⋊C4C2×C4×C12714yes—
347C2×C4⋊C4C2×C4×C12714yes—
348C2×C4⋊C4D4×C12718yes—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—42no—
355C2×C42C2×C4×C12714yes—
356C2×C42C2×C4×C12714yes—
357C2×C42C2×C4×C12714yes—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—22no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—22no—
369#95—22no—
370#95—42no—
371#95Q8×C12714yescomplemented
372C24C24×C12711yescharacteristic
373C2×Q8—216no—
374C2×Q8—216no—
375C2×Q8—28no—
376C2×Q8—28no—
377C2×Q8—28no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4C22×C4×C12712yes—
425C22×C4C22×C4×C12712yes—
426C22×C4C22×C4×C12712yes—
427C22×C4C22×C4×C12712yes—
428C22×C4C22×C4×C12712yes—
429C22×C4C22×C4×C12712yes—
430C22×C4C22×C4×C12712yes—
431C22×C4C2×D4×C12714yes—
432C22×C4C2×D4×C12714yes—
433C22×C4C2×D4×C12714yes—
434C22×C4C2×Q8×C12714yes—
435C22×C4C2×Q8×C12712yes—
436C22×C4#41×C12714yes—
437C22×C4#41×C12714yes—
438C22×C4#41×C12712yes—
439C22×C4#41×C12712yes—
440C22×C4#41×C12712yes—
441C4⋊C4—28no—
442C4⋊C4—28no—
443C4⋊C4—48no—
444C4⋊C4C22⋊C4×C127116yes—
445C42—28no—
446C42—28no—
447C42—28no—
448C42—48no—
449C23C23×C4×C12711yescharacteristic
450C23C22×D4×C12712yes—
451C23C22×Q8×C12711yescharacteristic
452C23C2×#41×C12712yes—
453C23C2×#41×C12711yescharacteristic
454C23C2×#41×C12711yescharacteristic
455C23C2×#41×C12711yescharacteristic
456C23C2×#41×C12712yes—
457C23H(5,𝔽2)×C12711yescharacteristic
458C232−1+4×C12712yes—
459C232−1+4×C12711yescharacteristic
460Q8—232no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4C2×C22⋊C4×C12714yes—
519C2×C4C2×C22⋊C4×C12714yes—
520C2×C4C2×C22⋊C4×C12714yes—
521C2×C4#117×C12714yes—
522C2×C4#117×C12714yes—
523C2×C4C4×Q8×C12714yes—
524C22C22×C22⋊C4×C12711yescharacteristic
525C22C2×#117×C12711yescharacteristic
526C22C2×#117×C12711yescharacteristic
527C22C2×C4×Q8×C12711yescharacteristic
528C22C4×#41×C12711yescharacteristic
529C22#519×C12711yescharacteristic
530C22#520×C12711yescharacteristic
531C22#525×C12712yes—
532C22#525×C12712yes—
533C22#529×C12712yes—
534C22#533×C12712yes—
535C22#541×C12712yes—
536C22#542×C12712yes—
537C22#546×C12712yes—
538C22#547×C12712yes—
539C22#548×C12712yes—
540C22D4×Q8×C12712yes—
541C22#552×C12712yes—
542C22#554×C12711yescharacteristic
543C22#556×C12711yescharacteristic
544C22#556×C12712yes—
545C22#557×C12711yescharacteristic
546C22#559×C12711yescharacteristic
547C4—24no—
548C4—24no—
549C4—24no—
550C4—24no—
551C4—24no—
552C4—24no—
553C4—42no—
554C4—44no—
555C4—44no—
556C4—82no—
557C4—82no—
558C2C127×#228011yescharacteristic
559C2C127×#229511yescharacteristic
560C2C127×#232011yescharacteristic
561C2C127×#233911yescharacteristic
562C2Q8×C22⋊C4×C12711yescharacteristic
563C2C127×#235511yescharacteristic
564C2C127×#235611yescharacteristic
565C2C127×#245812yes—
566C2C127×#246212yes—
567C2C127×#246512yes—
568C2C127×#246912yes—
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
14. C2×C4×Q8×C127C4semidirect
86. #95×C127Q8semidirect
273. #13927C127direct (N × H)
296. C127#13927direct (N × H)
299. C2×C4×Q8C4×C127semidirect
371. #95Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C1272
C2×#387×C1272
C127×#14462
C127×#14412
C127×#14362
C127×C4⋊#952
C127×#14342
C4×#95×C1272
#13927127