Finite Group Databasebeta

← C127×#18259 #44581932

Subgroups — C127×#18259 #44581932

Order 32512.

1132 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3538C211yesmaximal, characteristic
2C127×#3004C211yesmaximal, characteristic
3C2×#451×C127C211yesmaximal, characteristic, complemented
4C127×#2434C211yesmaximal, characteristic, complemented
5C127×#1605C214yesmaximal, complemented
6C127×#1603C214yesmaximal, complemented
7C127×#1508C211yesmaximal, characteristic, complemented
8C127×#1501C211yesmaximal, characteristic
9C127×#1472C211yesmaximal, characteristic, complemented
10C23×Q8×C127C2211yescharacteristic
11C2×#137×C127—21no—
12C22×Q16×C127—21no—
13#563×C127—22no—
14#552×C127—21no—
15#552×C127—21no—
16#551×C127—22no—
17D4×Q8×C127—21no—
18D4×Q8×C127—21no—
19#544×C127—21no—
20#544×C127C2212yes—
21#541×C127—21no—
22#539×C127—21no—
23#539×C127C2212yes—
24#536×C127—21no—
25C2×C4⋊Q8×C127—21no—
26#525×C127C2211yescharacteristic
27C2×C22⋊Q8×C127C2211yescharacteristic
28C2×C22⋊Q8×C127C2211yescharacteristic
29#451×C127—22no—
30#451×C127—21no—
31#451×C127C2214yes—
32#451×C127C2212yes—
33#448×C127—21no—
34#448×C127C2212yes—
35#419×C127—21no—
36C2×#103×C127—21no—
37#407×C127C2211yescharacteristic
38C2×C22⋊C8×C127C2211yescharacteristic
39#395×C127C2214yes—
40#391×C127—21no—
41#385×C127—22no—
42C4×C22⋊C4×C127C2211yescharacteristic
43#328×C127C2214yes—
44#328×C127C2212yes—
45#327×C127C2212yes—
46#324×C127C2214yes—
47C2×#41×C127D411yescharacteristic
48C22×Q8×C127—21no—
49C22×Q8×C127—21no—
50C22×Q8×C127—21no—
51C22×Q8×C127—21no—
52C22×Q8×C127—21no—
53C22×Q8×C127—21no—
54C22×Q8×C127—44no—
55C22×Q8×C127D411yescharacteristic
56C22×Q8×C127D411yescharacteristic
57C22×Q8×C127C2312yes—
58C23×C4×C127—21no—
59C23×C4×C127C2311yescharacteristic
60#137×C127—44no—
61C2×Q16×C127—24no—
62C2×Q16×C127—22no—
63C2×Q16×C127—44no—
64C2×SD16×C127—22no—
65C2×M16×C127—21no—
66C22×C8×C127—21no—
67C4⋊Q8×C127—21no—
68C4⋊Q8×C127—22no—
69C4⋊Q8×C127—22no—
70C4⋊Q8×C127—22no—
71C4⋊Q8×C127—44no—
72#126×C127—22no—
73#126×C127—22no—
74#126×C127—22no—
75#126×C127—22no—
76#125×C127—21no—
77#125×C127—22no—
78#125×C127—22no—
79#125×C127—22no—
80#125×C127—22no—
81#124×C127—22no—
82#123×C127—22no—
83#123×C127—22no—
84#123×C127—22no—
85#123×C127—21no—
86#123×C127—22no—
87C22⋊Q8×C127—21no—
88C22⋊Q8×C127—21no—
89C22⋊Q8×C127—22no—
90C22⋊Q8×C127—22no—
91C22⋊Q8×C127—22no—
92C22⋊Q8×C127—21no—
93C22⋊Q8×C127—21no—
94C22⋊Q8×C127—21no—
95C22⋊Q8×C127—21no—
96C22⋊Q8×C127—21no—
97C22⋊Q8×C127—21no—
98C22⋊Q8×C127—22no—
99C22⋊Q8×C127D412yes—
100C22⋊Q8×C127D411yescharacteristic
101C22⋊Q8×C127C2312yes—
102C22⋊Q8×C127C2311yescharacteristic
103#121×C127D411yescharacteristic
104#121×C127C2311yescharacteristic
105#120×C127—21no—
106C4×Q8×C127—21no—
107C4×Q8×C127—21no—
108C4×D4×C127—22no—
109C4×D4×C127—21no—
110C4×D4×C127—21no—
111C4×D4×C127—22no—
112#117×C127—21no—
113#117×C127—22no—
114#117×C127—22no—
115#117×C127D411yescharacteristic
116C2×C4⋊C4×C127—21no—
117C2×C4⋊C4×C127—24no—
118C2×C4⋊C4×C127D411yescharacteristic
119C2×C4⋊C4×C127D411yescharacteristic
120C2×C4⋊C4×C127C2312yes—
121C2×C22⋊C4×C127—21no—
122C2×C22⋊C4×C127—21no—
123C2×C22⋊C4×C127D412yes—
124C2×C42×C127—21no—
125#103×C127—24no—
126#103×C127—22no—
127#103×C127—22no—
128C22⋊C8×C127—21no—
129C22⋊C8×C127—21no—
130C22⋊C8×C127C2312yes—
131C22⋊C8×C127C2312yes—
132#95×C127—24no—
133#95×C127C2312yes—
134C24×C127C2×D411yescharacteristic
135#41×C127—42no—
136C2×Q8×C127—24no—
137C2×Q8×C127—22no—
138C2×Q8×C127—21no—
139C2×Q8×C127—21no—
140C2×Q8×C127—21no—
141C2×Q8×C127—24no—
142C2×Q8×C127—24no—
143C2×Q8×C127—22no—
144C2×Q8×C127—22no—
145C2×Q8×C127—44no—
146C2×Q8×C127—42no—
147C2×Q8×C127—42no—
148C2×Q8×C127—42no—
149C2×Q8×C127—42no—
150C2×Q8×C127—42no—
151C2×Q8×C127—44no—
152C2×Q8×C127—44no—
153C2×Q8×C127—41no—
154C2×Q8×C127—41no—
155C2×Q8×C127—82no—
156C2×Q8×C127C2×D412yes—
157C2×Q8×C127C2×D411yescharacteristic
158C2×D4×C127—21no—
159C2×D4×C127—21no—
160C2×D4×C127—21no—
161C2×D4×C127C2×D411yescharacteristic
162C22×C4×C127—21no—
163C22×C4×C127—22no—
164C22×C4×C127—22no—
165C22×C4×C127—22no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—42no—
169C22×C4×C127—44no—
170C22×C4×C127—41no—
171C22×C4×C127—41no—
172C22×C4×C127C2×D412yes—
173C22×C4×C127C2×D411yescharacteristic
174C22×C4×C127C2×D411yescharacteristic
175C22×C4×C127C2×D411yescharacteristic
176C22×C4×C127C2×D412yes—
177C22×C4×C127C2×D411yescharacteristic
178C22×C4×C127C2×D411yescharacteristic
179C22×C4×C127C2411yescharacteristic
180Q16×C127—48no—
181Q16×C127—44no—
182SD16×C127—44no—
183M16×C127—42no—
184C2×C8×C127—22no—
185C2×C8×C127—22no—
186C2×C8×C127—42no—
187C4⋊C4×C127—22no—
188C4⋊C4×C127—22no—
189C4⋊C4×C127—22no—
190C4⋊C4×C127—22no—
191C4⋊C4×C127—22no—
192C4⋊C4×C127—22no—
193C4⋊C4×C127—22no—
194C4⋊C4×C127—22no—
195C4⋊C4×C127—22no—
196C4⋊C4×C127—21no—
197C4⋊C4×C127—21no—
198C4⋊C4×C127—21no—
199C4⋊C4×C127—21no—
200C4⋊C4×C127—22no—
201C4⋊C4×C127—22no—
202C4⋊C4×C127—22no—
203C4⋊C4×C127—21no—
204C4⋊C4×C127—48no—
205C4⋊C4×C127C2×D412yes—
206C4⋊C4×C127C2×D411yescharacteristic
207C4⋊C4×C127C2×D411yescharacteristic
208C22⋊C4×C127—24no—
209C22⋊C4×C127—22no—
210C22⋊C4×C127—22no—
211C22⋊C4×C127—22no—
212C22⋊C4×C127—22no—
213C22⋊C4×C127—22no—
214C22⋊C4×C127—22no—
215C22⋊C4×C127—21no—
216C22⋊C4×C127—21no—
217C22⋊C4×C127—22no—
218C22⋊C4×C127—21no—
219C22⋊C4×C127—21no—
220C22⋊C4×C127—21no—
221C42×C127—22no—
222C42×C127—22no—
223C42×C127—22no—
224C42×C127—21no—
225C42×C127—42no—
226C23×C127—22no—
227C23×C127—22no—
228C23×C127—21no—
229C23×C127—41no—
230C23×C127#12011yescharacteristic
231C23×C127#12011yescharacteristic
232C23×C127C22×D411yescharacteristic
233Q8×C127—24no—
234Q8×C127—24no—
235Q8×C127—42no—
236Q8×C127—41no—
237Q8×C127—42no—
238Q8×C127—42no—
239Q8×C127—44no—
240Q8×C127—44no—
241Q8×C127—42no—
242Q8×C127—42no—
243Q8×C127—81no—
244Q8×C127—82no—
245D4×C127—41no—
246D4×C127—42no—
247D4×C127—42no—
248D4×C127—81no—
249C2×C4×C127—22no—
250C2×C4×C127—22no—
251C2×C4×C127—22no—
252C2×C4×C127—24no—
253C2×C4×C127—24no—
254C2×C4×C127—21no—
255C2×C4×C127—21no—
256C2×C4×C127—22no—
257C2×C4×C127—22no—
258C2×C4×C127—21no—
259C2×C4×C127—22no—
260C2×C4×C127—22no—
261C2×C4×C127—24no—
262C2×C4×C127—41no—
263C2×C4×C127—41no—
264C2×C4×C127—41no—
265C2×C4×C127—42no—
266C2×C4×C127—42no—
267C2×C4×C127—44no—
268C2×C4×C127—44no—
269C2×C4×C127—42no—
270C2×C4×C127—42no—
271C2×C4×C127—42no—
272C2×C4×C127—42no—
273C2×C4×C127—42no—
274C2×C4×C127—81no—
275C2×C4×C127—82no—
276C2×C4×C127#12011yescharacteristic
277C2×C4×C127#12011yescharacteristic
278C2×C4×C127C22×D411yescharacteristic
279C2×C4×C127C22×D411yescharacteristic
280C8×C127—42no—
281C8×C127—42no—
282C22×C127—21no—
283C22×C127—21no—
284C22×C127—21no—
285C22×C127—21no—
286C22×C127—21no—
287C22×C127—21no—
288C22×C127—21no—
289C22×C127—44no—
290C22×C127—41no—
291C22×C127—41no—
292C22×C127—41no—
293C22×C127#45612yes—
294C22×C127C2×#12011yescharacteristic
295C22×C127#57812yes—
296C4×C127—21no—
297C4×C127—21no—
298C4×C127—21no—
299C4×C127—44no—
300C4×C127—42no—
301C4×C127—41no—
302C4×C127—42no—
303C4×C127—41no—
304C4×C127—44no—
305C4×C127—41no—
306C4×C127—42no—
307C4×C127—42no—
308C4×C127B(4,𝔽2)12yes—
309#18259C12711yesmaximal, characteristic, direct product factor, Sylow
310C2×C127—22no—
311C2×C127—22no—
312C2×C127—41no—
313C2×C127—81no—
314C2×C127#301111yescharacteristic
315C2×C127C2×#45611yescharacteristic
316C2×C127C2×B(4,𝔽2)11yescharacteristic
317#3538C2×C12711yescharacteristic
318#3004C2×C12711yescharacteristic
319C2×#451C2×C12711yescharacteristic, complemented
320#2434C2×C12711yescharacteristic, complemented
321#1605C2×C12714yescomplemented
322#1603C2×C12714yescomplemented
323#1508C2×C12711yescharacteristic, complemented
324#1501C2×C12711yescharacteristic
325#1472C2×C12711yescharacteristic, complemented
326C127#1825911yescharacteristic, direct product factor, Sylow
327C23×Q8C22×C12711yescharacteristic
328C2×#137—21no—
329C22×Q16—21no—
330#563—22no—
331#552—21no—
332#552—21no—
333#551—22no—
334D4×Q8—21no—
335D4×Q8—21no—
336#544—21no—
337#544C22×C12712yes—
338#541—21no—
339#539—21no—
340#539C22×C12712yes—
341#536—21no—
342C2×C4⋊Q8—21no—
343#525C22×C12711yescharacteristic
344C2×C22⋊Q8C22×C12711yescharacteristic
345C2×C22⋊Q8C22×C12711yescharacteristic
346#451—22no—
347#451—21no—
348#451C22×C12714yes—
349#451C22×C12712yes—
350#448—21no—
351#448C22×C12712yes—
352#419—21no—
353C2×#103—21no—
354#407C22×C12711yescharacteristic
355C2×C22⋊C8C22×C12711yescharacteristic
356#395C22×C12714yes—
357#391—21no—
358#385—22no—
359C4×C22⋊C4C22×C12711yescharacteristic
360#328C22×C12714yes—
361#328C22×C12712yes—
362#327C22×C12712yes—
363#324C22×C12714yes—
364C2×#41D4×C12711yescharacteristic
365C22×Q8—21no—
366C22×Q8—21no—
367C22×Q8—21no—
368C22×Q8—21no—
369C22×Q8—21no—
370C22×Q8—21no—
371C22×Q8—44no—
372C22×Q8D4×C12711yescharacteristic
373C22×Q8D4×C12711yescharacteristic
374C22×Q8C23×C12712yes—
375C23×C4—21no—
376C23×C4C23×C12711yescharacteristic
377#137—44no—
378C2×Q16—24no—
379C2×Q16—22no—
380C2×Q16—44no—
381C2×SD16—22no—
382C2×M16—21no—
383C22×C8—21no—
384C4⋊Q8—21no—
385C4⋊Q8—22no—
386C4⋊Q8—22no—
387C4⋊Q8—22no—
388C4⋊Q8—44no—
389#126—22no—
390#126—22no—
391#126—22no—
392#126—22no—
393#125—21no—
394#125—22no—
395#125—22no—
396#125—22no—
397#125—22no—
398#124—22no—
399#123—22no—
400#123—22no—
401#123—22no—
402#123—21no—
403#123—22no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415C22⋊Q8—22no—
416C22⋊Q8D4×C12712yes—
417C22⋊Q8D4×C12711yescharacteristic
418C22⋊Q8C23×C12712yes—
419C22⋊Q8C23×C12711yescharacteristic
420#121D4×C12711yescharacteristic
421#121C23×C12711yescharacteristic
422#120—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×D4—22no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—22no—
429#117—21no—
430#117—22no—
431#117—22no—
432#117D4×C12711yescharacteristic
433C2×C4⋊C4—21no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4D4×C12711yescharacteristic
436C2×C4⋊C4D4×C12711yescharacteristic
437C2×C4⋊C4C23×C12712yes—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4D4×C12712yes—
441C2×C42—21no—
442#103—24no—
443#103—22no—
444#103—22no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8C23×C12712yes—
448C22⋊C8C23×C12712yes—
449#95—24no—
450#95C23×C12712yes—
451C24C2×D4×C12711yescharacteristic
452#41—42no—
453C2×Q8—24no—
454C2×Q8—22no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—24no—
459C2×Q8—24no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—44no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—41no—
471C2×Q8—41no—
472C2×Q8—82no—
473C2×Q8C2×D4×C12712yes—
474C2×Q8C2×D4×C12711yescharacteristic
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4C2×D4×C12711yescharacteristic
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—42no—
486C22×C4—44no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4C2×D4×C12712yes—
490C22×C4C2×D4×C12711yescharacteristic
491C22×C4C2×D4×C12711yescharacteristic
492C22×C4C2×D4×C12711yescharacteristic
493C22×C4C2×D4×C12712yes—
494C22×C4C2×D4×C12711yescharacteristic
495C22×C4C2×D4×C12711yescharacteristic
496C22×C4C24×C12711yescharacteristic
497Q16—48no—
498Q16—44no—
499SD16—44no—
500M16—42no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—42no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—48no—
522C4⋊C4C2×D4×C12712yes—
523C4⋊C4C2×D4×C12711yescharacteristic
524C4⋊C4C2×D4×C12711yescharacteristic
525C22⋊C4—24no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C42—22no—
539C42—22no—
540C42—22no—
541C42—21no—
542C42—42no—
543C23—22no—
544C23—22no—
545C23—21no—
546C23—41no—
547C23#120×C12711yescharacteristic
548C23#120×C12711yescharacteristic
549C23C22×D4×C12711yescharacteristic
550Q8—24no—
551Q8—24no—
552Q8—42no—
553Q8—41no—
554Q8—42no—
555Q8—42no—
556Q8—44no—
557Q8—44no—
558Q8—42no—
559Q8—42no—
560Q8—81no—
561Q8—82no—
562D4—41no—
563D4—42no—
564D4—42no—
565D4—81no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—81no—
592C2×C4—82no—
593C2×C4#120×C12711yescharacteristic
594C2×C4#120×C12711yescharacteristic
595C2×C4C22×D4×C12711yescharacteristic
596C2×C4C22×D4×C12711yescharacteristic
597C8—42no—
598C8—42no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—44no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22#456×C12712yes—
611C22C2×#120×C12711yescharacteristic
612C22#578×C12712yes—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—44no—
617C4—42no—
618C4—41no—
619C4—42no—
620C4—41no—
621C4—44no—
622C4—41no—
623C4—42no—
624C4—42no—
625C4B(4,𝔽2)×C12712yes—
626C2—22no—
627C2—22no—
628C2—41no—
629C2—81no—
630C2C127×#301111yescharacteristic
631C2C2×#456×C12711yescharacteristic
632C2C2×B(4,𝔽2)×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radical#525×C127C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#451×C127C2semidirect
4. C127×#2434C2semidirect
5. C127×#1605C2semidirect
6. C127×#1603C2semidirect
7. C127×#1508C2semidirect
9. C127×#1472C2semidirect
309. #18259C127direct (N × H)
319. C2×#451C2×C127semidirect
320. #2434C2×C127semidirect
321. #1605C2×C127semidirect
322. #1603C2×C127semidirect
323. #1508C2×C127semidirect
325. #1472C2×C127semidirect
326. C127#18259direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35382
C127×#30042
C2×#451×C1272
C127×#24342
C127×#16052
C127×#16032
C127×#15082
C127×#15012
C127×#14722
#18259127