Finite Group Databasebeta

← C127×#14232 #44577905

Subgroups — C127×#14232 #44577905

Order 32512.

1618 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#393×C127C211yesmaximal, characteristic
2C2×#391×C127C212yesmaximal, complemented
3C2×#388×C127C212yesmaximal
4C127×#1442C212yesmaximal, complemented
5C127×#1440C211yesmaximal, characteristic
6C127×#1437C211yesmaximal, characteristic
7C127×#1437C212yesmaximal
8C127×#1434C212yesmaximal, complemented
9C4×#95×C127C212yesmaximal, complemented
10C23×Q8×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2212yes—
12C22×C22⋊C4×C127C2212yes—
13C22×C22⋊C4×C127C2211yescharacteristic
14C22×C22⋊C4×C127C2211yescharacteristic
15C22×C22⋊C4×C127C2212yes—
16C22×C22⋊C4×C127C2211yescharacteristic
17C22×C42×C127C2212yes—
18C22×C42×C127C2211yescharacteristic
19C22×C42×C127C2212yes—
20#393×C127C418yescomplemented
21#391×C127—28no—
22#388×C127—28no—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2212yes—
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2212yes—
34C25×C127C2311yescharacteristic
35C22×Q8×C127—24no—
36C22×Q8×C127—24no—
37C22×Q8×C127—41no—
38C22×Q8×C127—41no—
39C22×Q8×C127C2×C414yes—
40C23×C4×C127C2312yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2311yescharacteristic
43C23×C4×C127C2311yescharacteristic
44C23×C4×C127C2312yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2312yes—
47C23×C4×C127C2312yes—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—24no—
50C2×C4⋊C4×C127—42no—
51C2×C22⋊C4×C127—24no—
52C2×C22⋊C4×C127—24no—
53C2×C22⋊C4×C127—24no—
54C2×C22⋊C4×C127—24no—
55C2×C22⋊C4×C127—24no—
56C2×C22⋊C4×C127—24no—
57C2×C22⋊C4×C127—24no—
58C2×C22⋊C4×C127—41no—
59C2×C22⋊C4×C127—41no—
60C2×C22⋊C4×C127—41no—
61C2×C22⋊C4×C127—41no—
62C2×C22⋊C4×C127C2×C418yes—
63C2×C22⋊C4×C127C2×C414yes—
64C2×C42×C127—24no—
65C2×C42×C127—24no—
66C2×C42×C127—24no—
67C2×C42×C127—24no—
68C2×C42×C127—24no—
69C2×C42×C127—24no—
70C2×C42×C127—41no—
71C2×C42×C127—42no—
72#95×C127—24no—
73#95×C127—24no—
74#95×C127—24no—
75#95×C127—24no—
76#95×C127—24no—
77#95×C127—24no—
78#95×C127—24no—
79#95×C127—41no—
80#95×C127C2×C414yes—
81#95×C127C2×C418yes—
82#95×C127D418yes—
83C24×C127—22no—
84C24×C127—22no—
85C24×C127—22no—
86C24×C127—22no—
87C24×C127—22no—
88C24×C127—21no—
89C24×C127—21no—
90C24×C127—22no—
91C24×C127C22×C412yes—
92C24×C127C2411yescharacteristic
93C2×Q8×C127—216no—
94C2×Q8×C127—44no—
95C2×Q8×C127—44no—
96C2×Q8×C127—48no—
97C2×Q8×C127—44no—
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—21no—
125C22×C4×C127—21no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—21no—
129C22×C4×C127—21no—
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×C414yes—
140C22×C4×C127C22×C412yes—
141C22×C4×C127C22×C412yes—
142C22×C4×C127C22×C414yes—
143C22×C4×C127C2×D414yes—
144C22×C4×C127C2×D414yes—
145C22×C4×C127C2×D414yes—
146C22×C4×C127#4114yes—
147C22×C4×C127#4114yes—
148C22×C4×C127#4114yes—
149C22×C4×C127#4114yes—
150C4⋊C4×C127—48no—
151C22⋊C4×C127—216no—
152C22⋊C4×C127—44no—
153C22⋊C4×C127—44no—
154C22⋊C4×C127—44no—
155C22⋊C4×C127—48no—
156C42×C127—48no—
157C42×C127—44no—
158C42×C127—48no—
159C23×C127—24no—
160C23×C127—22no—
161C23×C127—24no—
162C23×C127—22no—
163C23×C127—22no—
164C23×C127—42no—
165C23×C127—42no—
166C23×C127—42no—
167C23×C127—42no—
168C23×C127—42no—
169C23×C127—42no—
170C23×C127—41no—
171C23×C127—42no—
172C23×C127—42no—
173C23×C127—42no—
174C23×C127—41no—
175C23×C127—41no—
176C23×C127—41no—
177C23×C127—42no—
178C23×C127—42no—
179C23×C127—42no—
180C23×C127C23×C411yescharacteristic
181C23×C127C22×D412yes—
182C23×C127C2×#4112yes—
183C23×C127C2×#4112yes—
184C23×C127C2×#4112yes—
185C23×C127C2×#4112yes—
186C23×C127H(5,𝔽2)11yescharacteristic
187C23×C127H(5,𝔽2)11yescharacteristic
188C23×C1272−1+412yes—
189Q8×C127—416no—
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—24no—
201C2×C4×C127—24no—
202C2×C4×C127—24no—
203C2×C4×C127—24no—
204C2×C4×C127—24no—
205C2×C4×C127—24no—
206C2×C4×C127—24no—
207C2×C4×C127—22no—
208C2×C4×C127—22no—
209C2×C4×C127—24no—
210C2×C4×C127—24no—
211C2×C4×C127—24no—
212C2×C4×C127—24no—
213C2×C4×C127—24no—
214C2×C4×C127—24no—
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—41no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127—42no—
227C2×C4×C127—41no—
228C2×C4×C127—41no—
229C2×C4×C127—41no—
230C2×C4×C127—42no—
231C2×C4×C127—42no—
232C2×C4×C127—42no—
233C2×C4×C127—42no—
234C2×C4×C127—42no—
235C2×C4×C127—42no—
236C2×C4×C127—42no—
237C2×C4×C127—42no—
238C2×C4×C127—42no—
239C2×C4×C127—42no—
240C2×C4×C127C4×D418yes—
241C2×C4×C127#12418yes—
242C22×C127—42no—
243C22×C127—42no—
244C22×C127—44no—
245C22×C127—42no—
246C22×C127—44no—
247C22×C127—82no—
248C22×C127—82no—
249C22×C127—82no—
250C22×C127—82no—
251C22×C127C2×C4×D412yes—
252C22×C127C4×#4111yescharacteristic
253C22×C127C4×#4112yes—
254C22×C127#51811yescharacteristic
255C22×C127#51911yescharacteristic
256C22×C127C2×#12412yes—
257C22×C127#52912yes—
258C22×C127#52912yes—
259C22×C127#53212yes—
260C22×C127#53912yes—
261C22×C127#54212yes—
262C22×C127D4211yescharacteristic
263C22×C127#54612yes—
264C22×C127#54712yes—
265C22×C127#54812yes—
266C22×C127#55111yescharacteristic
267C22×C127#55111yescharacteristic
268C22×C127#55111yescharacteristic
269C22×C127#55212yes—
270C22×C127#55512yes—
271C22×C127#55612yes—
272C4×C127—28no—
273C4×C127—28no—
274C4×C127—44no—
275C4×C127—42no—
276C4×C127—42no—
277C4×C127—44no—
278C4×C127—44no—
279C4×C127—82no—
280#14232C12711yesmaximal, characteristic, direct product factor, Sylow
281C2×C127—82no—
282C2×C127C4×#12412yes—
283C2×C127#233211yescharacteristic
284C2×C127#235811yescharacteristic
285C2×C127#236212yes—
286C2×C127#237211yescharacteristic
287C2×C127#248812yes—
288C2×C127#249112yes—
289C2×C127#253212yes—
290C2×C127#256012yes—
291C2×#393C2×C12711yescharacteristic
292C2×#391C2×C12712yescomplemented
293C2×#388C2×C12712yes—
294#1442C2×C12712yescomplemented
295#1440C2×C12711yescharacteristic
296#1437C2×C12711yescharacteristic
297#1437C2×C12712yes—
298#1434C2×C12712yescomplemented
299C4×#95C2×C12712yescomplemented
300C127#1423211yescharacteristic, direct product factor, Sylow
301C23×Q8C22×C12711yescharacteristic
302C22×C4⋊C4C22×C12712yes—
303C22×C22⋊C4C22×C12712yes—
304C22×C22⋊C4C22×C12711yescharacteristic
305C22×C22⋊C4C22×C12711yescharacteristic
306C22×C22⋊C4C22×C12712yes—
307C22×C22⋊C4C22×C12711yescharacteristic
308C22×C42C22×C12712yes—
309C22×C42C22×C12711yescharacteristic
310C22×C42C22×C12712yes—
311#393C4×C12718yescomplemented
312#391—28no—
313#388—28no—
314C2×#95C22×C12712yes—
315C2×#95C22×C12712yes—
316C2×#95C22×C12712yes—
317C2×#95C22×C12712yes—
318C2×#95C22×C12712yes—
319C2×#95C22×C12712yes—
320C2×#95C22×C12712yes—
321C2×#95C22×C12711yescharacteristic
322C2×#95C22×C12712yes—
323C2×#95C22×C12711yescharacteristic
324C2×#95C22×C12712yes—
325C25C23×C12711yescharacteristic
326C22×Q8—24no—
327C22×Q8—24no—
328C22×Q8—41no—
329C22×Q8—41no—
330C22×Q8C2×C4×C12714yes—
331C23×C4C23×C12712yes—
332C23×C4C23×C12711yescharacteristic
333C23×C4C23×C12712yes—
334C23×C4C23×C12711yescharacteristic
335C23×C4C23×C12712yes—
336C23×C4C23×C12712yes—
337C23×C4C23×C12712yes—
338C23×C4C23×C12712yes—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—42no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4C2×C4×C12718yes—
354C2×C22⋊C4C2×C4×C12714yes—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—41no—
362C2×C42—42no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—41no—
371#95C2×C4×C12714yes—
372#95C2×C4×C12718yes—
373#95D4×C12718yes—
374C24—22no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—21no—
380C24—21no—
381C24—22no—
382C24C22×C4×C12712yes—
383C24C24×C12711yescharacteristic
384C2×Q8—216no—
385C2×Q8—44no—
386C2×Q8—44no—
387C2×Q8—48no—
388C2×Q8—44no—
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—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4C22×C4×C12714yes—
431C22×C4C22×C4×C12712yes—
432C22×C4C22×C4×C12712yes—
433C22×C4C22×C4×C12714yes—
434C22×C4C2×D4×C12714yes—
435C22×C4C2×D4×C12714yes—
436C22×C4C2×D4×C12714yes—
437C22×C4#41×C12714yes—
438C22×C4#41×C12714yes—
439C22×C4#41×C12714yes—
440C22×C4#41×C12714yes—
441C4⋊C4—48no—
442C22⋊C4—216no—
443C22⋊C4—44no—
444C22⋊C4—44no—
445C22⋊C4—44no—
446C22⋊C4—48no—
447C42—48no—
448C42—44no—
449C42—48no—
450C23—24no—
451C23—22no—
452C23—24no—
453C23—22no—
454C23—22no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—41no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23C23×C4×C12711yescharacteristic
472C23C22×D4×C12712yes—
473C23C2×#41×C12712yes—
474C23C2×#41×C12712yes—
475C23C2×#41×C12712yes—
476C23C2×#41×C12712yes—
477C23H(5,𝔽2)×C12711yescharacteristic
478C23H(5,𝔽2)×C12711yescharacteristic
479C232−1+4×C12712yes—
480Q8—416no—
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—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
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—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4C4×D4×C12718yes—
532C2×C4#124×C12718yes—
533C22—42no—
534C22—42no—
535C22—44no—
536C22—42no—
537C22—44no—
538C22—82no—
539C22—82no—
540C22—82no—
541C22—82no—
542C22C2×C4×D4×C12712yes—
543C22C4×#41×C12711yescharacteristic
544C22C4×#41×C12712yes—
545C22#518×C12711yescharacteristic
546C22#519×C12711yescharacteristic
547C22C2×#124×C12712yes—
548C22#529×C12712yes—
549C22#529×C12712yes—
550C22#532×C12712yes—
551C22#539×C12712yes—
552C22#542×C12712yes—
553C22D42×C12711yescharacteristic
554C22#546×C12712yes—
555C22#547×C12712yes—
556C22#548×C12712yes—
557C22#551×C12711yescharacteristic
558C22#551×C12711yescharacteristic
559C22#551×C12711yescharacteristic
560C22#552×C12712yes—
561C22#555×C12712yes—
562C22#556×C12712yes—
563C4—28no—
564C4—28no—
565C4—42no—
566C4—42no—
567C4—44no—
568C4—44no—
569C4—44no—
570C4—82no—
571C2—82no—
572C2C4×#124×C12712yes—
573C2C127×#233211yescharacteristic
574C2C127×#235811yescharacteristic
575C2C127×#236212yes—
576C2C127×#237211yescharacteristic
577C2C127×#248812yes—
578C2C127×#249112yes—
579C2C127×#253212yes—
580C2C127×#256012yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#391×C127C2semidirect
4. C127×#1442C2semidirect
8. C127×#1434C2semidirect
9. C4×#95×C127C2semidirect
20. #393×C127C4semidirect
280. #14232C127direct (N × H)
292. C2×#391C2×C127semidirect
294. #1442C2×C127semidirect
298. #1434C2×C127semidirect
299. C4×#95C2×C127semidirect
300. C127#14232direct (N × H)
311. #393C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#393×C1272
C2×#391×C1272
C2×#388×C1272
C127×#14422
C127×#14402
C127×#14372
C127×#14342
C4×#95×C1272
#14232127