Finite Group Databasebeta

← C127×#14446 #44578119

Subgroups — C127×#14446 #44578119

Order 32512.

1246 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C127C211yesmaximal, characteristic
2C2×#387×C127C212yesmaximal
3C127×#1445C212yesmaximal
4C127×#1442C212yesmaximal
5C127×#1441C212yesmaximal
6C127×#1436C212yesmaximal
7C127×#1436C212yesmaximal
8C127×C4⋊#95C211yesmaximal, characteristic
9C127×C4⋊#95C211yesmaximal, characteristic
10C22×C4⋊C4×C127C2212yes—
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C42×C127C2212yes—
18C22×C42×C127C2211yescharacteristic
19#389×C127C418yescomplemented
20#387×C127—28no—
21C2×#95×C127C2212yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C23×C4×C127C2312yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2312yes—
36C23×C4×C127C2312yes—
37C23×C4×C127C2312yes—
38C23×C4×C127C2312yes—
39C23×C4×C127C2311yescharacteristic
40C23×C4×C127C2311yescharacteristic
41C23×C4×C127C2311yescharacteristic
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—22no—
44C2×C4⋊C4×C127—22no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127—22no—
47C2×C4⋊C4×C127—22no—
48C2×C4⋊C4×C127—41no—
49C2×C4⋊C4×C127—41no—
50C2×C4⋊C4×C127—41no—
51C2×C4⋊C4×C127—41no—
52C2×C4⋊C4×C127—41no—
53C2×C4⋊C4×C127—41no—
54C2×C4⋊C4×C127—41no—
55C2×C4⋊C4×C127—41no—
56C2×C4⋊C4×C127—41no—
57C2×C4⋊C4×C127—41no—
58C2×C4⋊C4×C127C2×C414yes—
59C2×C4⋊C4×C127C2×C418yes—
60C2×C4⋊C4×C127C2×C414yes—
61C2×C4⋊C4×C127D414yes—
62C2×C4⋊C4×C127Q814yes—
63C2×C42×C127—24no—
64C2×C42×C127—41no—
65C2×C42×C127—41no—
66C2×C42×C127—42no—
67C2×C42×C127—42no—
68C2×C42×C127C2×C414yes—
69#95×C127—24no—
70#95×C127—24no—
71#95×C127—24no—
72#95×C127—24no—
73#95×C127—24no—
74#95×C127—24no—
75#95×C127—24no—
76#95×C127—42no—
77#95×C127—42no—
78#95×C127—42no—
79#95×C127—42no—
80#95×C127C2×C418yes—
81C24×C127C2411yescharacteristic
82C22×C4×C127—21no—
83C22×C4×C127—21no—
84C22×C4×C127—21no—
85C22×C4×C127—21no—
86C22×C4×C127—21no—
87C22×C4×C127—21no—
88C22×C4×C127—21no—
89C22×C4×C127—21no—
90C22×C4×C127—21no—
91C22×C4×C127—21no—
92C22×C4×C127—21no—
93C22×C4×C127—21no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—22no—
98C22×C4×C127—22no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—22no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—22no—
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—22no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
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×C127C22×C414yes—
133C22×C4×C127C22×C414yes—
134C22×C4×C127C22×C412yes—
135C22×C4×C127C22×C412yes—
136C22×C4×C127C22×C412yes—
137C22×C4×C127C2×D414yes—
138C22×C4×C127C2×D412yes—
139C22×C4×C127C2×Q814yes—
140C22×C4×C127C2×Q812yes—
141C22×C4×C127#4112yes—
142C22×C4×C127#4112yes—
143C22×C4×C127#4112yes—
144C22×C4×C127#4112yes—
145C4⋊C4×C127—28no—
146C4⋊C4×C127—216no—
147C4⋊C4×C127—44no—
148C4⋊C4×C127—44no—
149C4⋊C4×C127—44no—
150C4⋊C4×C127—44no—
151C4⋊C4×C127—44no—
152C42×C127—44no—
153C42×C127—48no—
154C23×C127C23×C411yescharacteristic
155C23×C127C22×D411yescharacteristic
156C23×C127C22×Q811yescharacteristic
157C23×C127C2×#4111yescharacteristic
158C23×C127C2×#4111yescharacteristic
159C23×C127C2×#4111yescharacteristic
160C23×C127C2×#4111yescharacteristic
161C23×C127H(5,𝔽2)11yescharacteristic
162C23×C127H(5,𝔽2)11yescharacteristic
163C23×C127H(5,𝔽2)11yescharacteristic
164C23×C127H(5,𝔽2)11yescharacteristic
165C23×C1272−1+411yescharacteristic
166C23×C1272−1+411yescharacteristic
167C23×C1272−1+411yescharacteristic
168C23×C1272−1+411yescharacteristic
169C2×C4×C127—22no—
170C2×C4×C127—22no—
171C2×C4×C127—22no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—22no—
175C2×C4×C127—22no—
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—24no—
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—42no—
200C2×C4×C127—42no—
201C2×C4×C127—42no—
202C2×C4×C127—42no—
203C2×C4×C127—42no—
204C2×C4×C127—42no—
205C2×C4×C127—42no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—42no—
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#11714yes—
230C2×C4×C127C4×D414yes—
231C2×C4×C127C4×Q814yes—
232C22×C127C2×#11711yescharacteristic
233C22×C127C2×C4×D411yescharacteristic
234C22×C127C2×C4×Q811yescharacteristic
235C22×C127#51811yescharacteristic
236C22×C127#51911yescharacteristic
237C22×C127#52011yescharacteristic
238C22×C127#52011yescharacteristic
239C22×C127#53411yescharacteristic
240C22×C127#53711yescharacteristic
241C22×C127#53811yescharacteristic
242C22×C127#53811yescharacteristic
243C22×C127#53911yescharacteristic
244C22×C127#53911yescharacteristic
245C22×C127#53911yescharacteristic
246C22×C127#53911yescharacteristic
247C22×C127#53911yescharacteristic
248C22×C127#53911yescharacteristic
249C22×C127#54311yescharacteristic
250C22×C127#54411yescharacteristic
251C22×C127#54711yescharacteristic
252C22×C127#54711yescharacteristic
253C22×C127D4×Q811yescharacteristic
254C22×C127#55011yescharacteristic
255C22×C127#55411yescharacteristic
256C22×C127#55511yescharacteristic
257C22×C127#55611yescharacteristic
258C22×C127#55611yescharacteristic
259C22×C127#55611yescharacteristic
260C22×C127#55711yescharacteristic
261C22×C127#55711yescharacteristic
262C22×C127#55911yescharacteristic
263C22×C127#56211yescharacteristic
264C22×C127#56311yescharacteristic
265C22×C127#56311yescharacteristic
266C22×C127#56411yescharacteristic
267C4×C127—24no—
268C4×C127—24no—
269C4×C127—24no—
270C4×C127—44no—
271C4×C127—44no—
272C4×C127—44no—
273C4×C127—44no—
274C4×C127—82no—
275C4×C127—82no—
276#14446C12711yesmaximal, characteristic, direct product factor, Sylow
277C2×C127#231311yescharacteristic
278C2×C127#232511yescharacteristic
279C2×C127#232911yescharacteristic
280C2×C127#235411yescharacteristic
281C2×C127#235511yescharacteristic
282C2×C127#236511yescharacteristic
283C2×C127#238211yescharacteristic
284C2×C127#272411yescharacteristic
285C2×C127#272611yescharacteristic
286C2×C127#272711yescharacteristic
287C2×C127#273211yescharacteristic
288C2×C127#280511yescharacteristic
289C2×C127#280811yescharacteristic
290C2×C127#280911yescharacteristic
291C2×C127#281011yescharacteristic
292C2×#389C2×C12711yescharacteristic
293C2×#387C2×C12712yes—
294#1445C2×C12712yes—
295#1442C2×C12712yes—
296#1441C2×C12712yes—
297#1436C2×C12712yes—
298#1436C2×C12712yes—
299C4⋊#95C2×C12711yescharacteristic
300C4⋊#95C2×C12711yescharacteristic
301C127#1444611yescharacteristic, direct product factor, Sylow
302C22×C4⋊C4C22×C12712yes—
303C22×C4⋊C4C22×C12711yescharacteristic
304C22×C4⋊C4C22×C12711yescharacteristic
305C22×C4⋊C4C22×C12711yescharacteristic
306C22×C4⋊C4C22×C12711yescharacteristic
307C22×C4⋊C4C22×C12711yescharacteristic
308C22×C4⋊C4C22×C12711yescharacteristic
309C22×C42C22×C12712yes—
310C22×C42C22×C12711yescharacteristic
311#389C4×C12718yescomplemented
312#387—28no—
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×C12712yes—
323C2×#95C22×C12712yes—
324C2×#95C22×C12712yes—
325C23×C4C23×C12712yes—
326C23×C4C23×C12712yes—
327C23×C4C23×C12712yes—
328C23×C4C23×C12712yes—
329C23×C4C23×C12712yes—
330C23×C4C23×C12712yes—
331C23×C4C23×C12711yescharacteristic
332C23×C4C23×C12711yescharacteristic
333C23×C4C23×C12711yescharacteristic
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—41no—
343C2×C4⋊C4—41no—
344C2×C4⋊C4—41no—
345C2×C4⋊C4—41no—
346C2×C4⋊C4—41no—
347C2×C4⋊C4—41no—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4C2×C4×C12714yes—
351C2×C4⋊C4C2×C4×C12718yes—
352C2×C4⋊C4C2×C4×C12714yes—
353C2×C4⋊C4D4×C12714yes—
354C2×C4⋊C4Q8×C12714yes—
355C2×C42—24no—
356C2×C42—41no—
357C2×C42—41no—
358C2×C42—42no—
359C2×C42—42no—
360C2×C42C2×C4×C12714yes—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95C2×C4×C12718yes—
373C24C24×C12711yescharacteristic
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
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—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
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×C12714yes—
425C22×C4C22×C4×C12714yes—
426C22×C4C22×C4×C12712yes—
427C22×C4C22×C4×C12712yes—
428C22×C4C22×C4×C12712yes—
429C22×C4C2×D4×C12714yes—
430C22×C4C2×D4×C12712yes—
431C22×C4C2×Q8×C12714yes—
432C22×C4C2×Q8×C12712yes—
433C22×C4#41×C12712yes—
434C22×C4#41×C12712yes—
435C22×C4#41×C12712yes—
436C22×C4#41×C12712yes—
437C4⋊C4—28no—
438C4⋊C4—216no—
439C4⋊C4—44no—
440C4⋊C4—44no—
441C4⋊C4—44no—
442C4⋊C4—44no—
443C4⋊C4—44no—
444C42—44no—
445C42—48no—
446C23C23×C4×C12711yescharacteristic
447C23C22×D4×C12711yescharacteristic
448C23C22×Q8×C12711yescharacteristic
449C23C2×#41×C12711yescharacteristic
450C23C2×#41×C12711yescharacteristic
451C23C2×#41×C12711yescharacteristic
452C23C2×#41×C12711yescharacteristic
453C23H(5,𝔽2)×C12711yescharacteristic
454C23H(5,𝔽2)×C12711yescharacteristic
455C23H(5,𝔽2)×C12711yescharacteristic
456C23H(5,𝔽2)×C12711yescharacteristic
457C232−1+4×C12711yescharacteristic
458C232−1+4×C12711yescharacteristic
459C232−1+4×C12711yescharacteristic
460C232−1+4×C12711yescharacteristic
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—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
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×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4#117×C12714yes—
522C2×C4C4×D4×C12714yes—
523C2×C4C4×Q8×C12714yes—
524C22C2×#117×C12711yescharacteristic
525C22C2×C4×D4×C12711yescharacteristic
526C22C2×C4×Q8×C12711yescharacteristic
527C22#518×C12711yescharacteristic
528C22#519×C12711yescharacteristic
529C22#520×C12711yescharacteristic
530C22#520×C12711yescharacteristic
531C22#534×C12711yescharacteristic
532C22#537×C12711yescharacteristic
533C22#538×C12711yescharacteristic
534C22#538×C12711yescharacteristic
535C22#539×C12711yescharacteristic
536C22#539×C12711yescharacteristic
537C22#539×C12711yescharacteristic
538C22#539×C12711yescharacteristic
539C22#539×C12711yescharacteristic
540C22#539×C12711yescharacteristic
541C22#543×C12711yescharacteristic
542C22#544×C12711yescharacteristic
543C22#547×C12711yescharacteristic
544C22#547×C12711yescharacteristic
545C22D4×Q8×C12711yescharacteristic
546C22#550×C12711yescharacteristic
547C22#554×C12711yescharacteristic
548C22#555×C12711yescharacteristic
549C22#556×C12711yescharacteristic
550C22#556×C12711yescharacteristic
551C22#556×C12711yescharacteristic
552C22#557×C12711yescharacteristic
553C22#557×C12711yescharacteristic
554C22#559×C12711yescharacteristic
555C22#562×C12711yescharacteristic
556C22#563×C12711yescharacteristic
557C22#563×C12711yescharacteristic
558C22#564×C12711yescharacteristic
559C4—24no—
560C4—24no—
561C4—24no—
562C4—44no—
563C4—44no—
564C4—44no—
565C4—44no—
566C4—82no—
567C4—82no—
568C2C127×#231311yescharacteristic
569C2C127×#232511yescharacteristic
570C2C127×#232911yescharacteristic
571C2C127×#235411yescharacteristic
572C2C127×#235511yescharacteristic
573C2C127×#236511yescharacteristic
574C2C127×#238211yescharacteristic
575C2C127×#272411yescharacteristic
576C2C127×#272611yescharacteristic
577C2C127×#272711yescharacteristic
578C2C127×#273211yescharacteristic
579C2C127×#280511yescharacteristic
580C2C127×#280811yescharacteristic
581C2C127×#280911yescharacteristic
582C2C127×#281011yescharacteristic
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
19. #389×C127C4semidirect
276. #14446C127direct (N × H)
301. C127#14446direct (N × H)
311. #389C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1272
C2×#387×C1272
C127×#14452
C127×#14422
C127×#14412
C127×#14362
C127×C4⋊#952
#14446127