Finite Group Databasebeta

← C127×#15930 #44579603

Subgroups — C127×#15930 #44579603

Order 32512.

1450 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#393×C127C211yesmaximal, characteristic
2C2×#381×C127C211yesmaximal, characteristic
3C127×#1446C212yesmaximal, complemented
4C127×#1443C212yesmaximal, complemented
5C127×#1443C212yesmaximal, complemented
6C127×#1440C212yesmaximal
7C127×#1437C211yesmaximal, characteristic
8C127×#1434C212yesmaximal, complemented
9C127×C22⋊#95C212yesmaximal
10C23×Q8×C127C2211yescharacteristic
11C24×C4×C127C2211yescharacteristic
12C22×C22⋊C4×C127C2211yescharacteristic
13C22×C22⋊C4×C127C2212yes—
14C22×C22⋊C4×C127C2212yes—
15C22×C22⋊C4×C127C2211yescharacteristic
16C22×C42×C127C2211yescharacteristic
17#393×C127—24no—
18#381×C127—24no—
19C2×#95×C127C2212yes—
20C2×#95×C127C2211yescharacteristic
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×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C25×C127C2311yescharacteristic
34C22×Q8×C127—22no—
35C22×Q8×C127—24no—
36C22×Q8×C127—42no—
37C22×Q8×C127—41no—
38C22×Q8×C127—41no—
39C23×C4×C127—22no—
40C23×C4×C127—24no—
41C23×C4×C127—24no—
42C23×C4×C127—41no—
43C23×C4×C127—41no—
44C23×C4×C127C2312yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2312yes—
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2312yes—
50C23×C4×C127C2312yes—
51C23×C4×C127C2312yes—
52C2×C22⋊C4×C127—22no—
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—42no—
61C2×C22⋊C4×C127—42no—
62C2×C22⋊C4×C127D414yes—
63C2×C42×C127—24no—
64C2×C42×C127—41no—
65#95×C127—24no—
66#95×C127—24no—
67#95×C127—24no—
68#95×C127—22no—
69#95×C127—24no—
70#95×C127—24no—
71#95×C127—24no—
72#95×C127—24no—
73#95×C127—42no—
74#95×C127—42no—
75#95×C127—41no—
76#95×C127—42no—
77#95×C127—42no—
78#95×C127—42no—
79C24×C127—22no—
80C24×C127—22no—
81C24×C127—22no—
82C24×C127—22no—
83C24×C127—21no—
84C24×C127—21no—
85C24×C127—22no—
86C24×C127C2×D412yes—
87C24×C127#4114yes—
88C24×C127C2411yescharacteristic
89C2×Q8×C127—48no—
90C2×Q8×C127—44no—
91C2×Q8×C127—44no—
92C2×Q8×C127—48no—
93C2×Q8×C127—44no—
94C22×C4×C127—28no—
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—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—21no—
117C22×C4×C127—21no—
118C22×C4×C127—21no—
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×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×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—48no—
143C22×C4×C127—48no—
144C22×C4×C127—44no—
145C22×C4×C127—44no—
146C22×C4×C127C2×D412yes—
147C22×C4×C127C2×D412yes—
148C22×C4×C127#4114yes—
149C22×C4×C127#4114yes—
150C22×C4×C127#4114yes—
151C22⋊C4×C127—44no—
152C22⋊C4×C127—48no—
153C22⋊C4×C127—48no—
154C22⋊C4×C127—44no—
155C42×C127—44no—
156C23×C127—22no—
157C23×C127—24no—
158C23×C127—22no—
159C23×C127—24no—
160C23×C127—24no—
161C23×C127—24no—
162C23×C127—24no—
163C23×C127—24no—
164C23×C127—24no—
165C23×C127—24no—
166C23×C127—42no—
167C23×C127—42no—
168C23×C127—42no—
169C23×C127—42no—
170C23×C127—41no—
171C23×C127—41no—
172C23×C127—42no—
173C23×C127—42no—
174C23×C127—41no—
175C23×C127—41no—
176C23×C127#12414yes—
177C23×C127C22×D411yescharacteristic
178C23×C127C2×#4112yes—
179C23×C127C2×#4112yes—
180C23×C127C2×#4112yes—
181C23×C127C2×#4112yes—
182C23×C127H(5,𝔽2)11yescharacteristic
183C23×C127H(5,𝔽2)11yescharacteristic
184C23×C127H(5,𝔽2)12yes—
185C23×C1272−1+412yes—
186Q8×C127—416no—
187C2×C4×C127—24no—
188C2×C4×C127—24no—
189C2×C4×C127—22no—
190C2×C4×C127—22no—
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—416no—
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—41no—
211C2×C4×C127—42no—
212C2×C4×C127—42no—
213C2×C4×C127—42no—
214C2×C4×C127—41no—
215C2×C4×C127—42no—
216C2×C4×C127—41no—
217C2×C4×C127—42no—
218C2×C4×C127—41no—
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×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—
240C22×C127—24no—
241C22×C127—28no—
242C22×C127—44no—
243C22×C127—42no—
244C22×C127—42no—
245C22×C127—44no—
246C22×C127—44no—
247C22×C127—44no—
248C22×C127—44no—
249C22×C127#52511yescharacteristic
250C22×C127C2×#12411yescharacteristic
251C22×C127#52912yes—
252C22×C127#52912yes—
253C22×C127#53411yescharacteristic
254C22×C127#53812yes—
255C22×C127#53912yes—
256C22×C127#54212yes—
257C22×C127#54212yes—
258C22×C127#54612yes—
259C22×C127#54712yes—
260C22×C127#55112yes—
261C22×C127#55112yes—
262C22×C127#55111yescharacteristic
263C22×C127#55112yes—
264C22×C127#55111yescharacteristic
265C22×C127#55212yes—
266C22×C127#55512yes—
267C22×C127#55612yes—
268C22×C127#56011yescharacteristic
269C22×C127#56311yescharacteristic
270C4×C127—44no—
271C4×C127—44no—
272C4×C127—42no—
273C4×C127—44no—
274C4×C127—42no—
275C4×C127—82no—
276C4×C127—82no—
277C4×C127—82no—
278#15930C12711yesmaximal, characteristic, direct product factor, Sylow
279C2×C127—44no—
280C2×C127#247412yes—
281C2×C127#248812yes—
282C2×C127#252712yes—
283C2×C127#256111yescharacteristic
284C2×C127#257212yes—
285C2×C127#269711yescharacteristic
286C2×C127#271711yescharacteristic
287C2×C127#273712yes—
288C2×C127#274512yes—
289C2×#393C2×C12711yescharacteristic
290C2×#381C2×C12711yescharacteristic
291#1446C2×C12712yescomplemented
292#1443C2×C12712yescomplemented
293#1443C2×C12712yescomplemented
294#1440C2×C12712yes—
295#1437C2×C12711yescharacteristic
296#1434C2×C12712yescomplemented
297C22⋊#95C2×C12712yes—
298C127#1593011yescharacteristic, direct product factor, Sylow
299C23×Q8C22×C12711yescharacteristic
300C24×C4C22×C12711yescharacteristic
301C22×C22⋊C4C22×C12711yescharacteristic
302C22×C22⋊C4C22×C12712yes—
303C22×C22⋊C4C22×C12712yes—
304C22×C22⋊C4C22×C12711yescharacteristic
305C22×C42C22×C12711yescharacteristic
306#393—24no—
307#381—24no—
308C2×#95C22×C12712yes—
309C2×#95C22×C12711yescharacteristic
310C2×#95C22×C12712yes—
311C2×#95C22×C12712yes—
312C2×#95C22×C12712yes—
313C2×#95C22×C12712yes—
314C2×#95C22×C12712yes—
315C2×#95C22×C12712yes—
316C2×#95C22×C12712yes—
317C2×#95C22×C12712yes—
318C2×#95C22×C12711yescharacteristic
319C2×#95C22×C12712yes—
320C2×#95C22×C12712yes—
321C2×#95C22×C12712yes—
322C25C23×C12711yescharacteristic
323C22×Q8—22no—
324C22×Q8—24no—
325C22×Q8—42no—
326C22×Q8—41no—
327C22×Q8—41no—
328C23×C4—22no—
329C23×C4—24no—
330C23×C4—24no—
331C23×C4—41no—
332C23×C4—41no—
333C23×C4C23×C12712yes—
334C23×C4C23×C12712yes—
335C23×C4C23×C12712yes—
336C23×C4C23×C12711yescharacteristic
337C23×C4C23×C12711yescharacteristic
338C23×C4C23×C12712yes—
339C23×C4C23×C12712yes—
340C23×C4C23×C12712yes—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—41no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4D4×C12714yes—
352C2×C42—24no—
353C2×C42—41no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—22no—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—24no—
362#95—42no—
363#95—42no—
364#95—41no—
365#95—42no—
366#95—42no—
367#95—42no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—21no—
373C24—21no—
374C24—22no—
375C24C2×D4×C12712yes—
376C24#41×C12714yes—
377C24C24×C12711yescharacteristic
378C2×Q8—48no—
379C2×Q8—44no—
380C2×Q8—44no—
381C2×Q8—48no—
382C2×Q8—44no—
383C22×C4—28no—
384C22×C4—22no—
385C22×C4—22no—
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—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
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×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4C2×D4×C12712yes—
436C22×C4C2×D4×C12712yes—
437C22×C4#41×C12714yes—
438C22×C4#41×C12714yes—
439C22×C4#41×C12714yes—
440C22⋊C4—44no—
441C22⋊C4—48no—
442C22⋊C4—48no—
443C22⋊C4—44no—
444C42—44no—
445C23—22no—
446C23—24no—
447C23—22no—
448C23—24no—
449C23—24no—
450C23—24no—
451C23—24no—
452C23—24no—
453C23—24no—
454C23—24no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—41no—
460C23—41no—
461C23—42no—
462C23—42no—
463C23—41no—
464C23—41no—
465C23#124×C12714yes—
466C23C22×D4×C12711yescharacteristic
467C23C2×#41×C12712yes—
468C23C2×#41×C12712yes—
469C23C2×#41×C12712yes—
470C23C2×#41×C12712yes—
471C23H(5,𝔽2)×C12711yescharacteristic
472C23H(5,𝔽2)×C12711yescharacteristic
473C23H(5,𝔽2)×C12712yes—
474C232−1+4×C12712yes—
475Q8—416no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
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—416no—
490C2×C4—42no—
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—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
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—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C22—28no—
530C22—24no—
531C22—44no—
532C22—42no—
533C22—42no—
534C22—44no—
535C22—44no—
536C22—44no—
537C22—44no—
538C22#525×C12711yescharacteristic
539C22C2×#124×C12711yescharacteristic
540C22#529×C12712yes—
541C22#529×C12712yes—
542C22#534×C12711yescharacteristic
543C22#538×C12712yes—
544C22#539×C12712yes—
545C22#542×C12712yes—
546C22#542×C12712yes—
547C22#546×C12712yes—
548C22#547×C12712yes—
549C22#551×C12711yescharacteristic
550C22#551×C12712yes—
551C22#551×C12712yes—
552C22#551×C12711yescharacteristic
553C22#551×C12712yes—
554C22#552×C12712yes—
555C22#555×C12712yes—
556C22#556×C12712yes—
557C22#560×C12711yescharacteristic
558C22#563×C12711yescharacteristic
559C4—44no—
560C4—42no—
561C4—44no—
562C4—42no—
563C4—44no—
564C4—82no—
565C4—82no—
566C4—82no—
567C2—44no—
568C2C127×#247412yes—
569C2C127×#248812yes—
570C2C127×#252712yes—
571C2C127×#256111yescharacteristic
572C2C127×#257212yes—
573C2C127×#269711yescharacteristic
574C2C127×#271711yescharacteristic
575C2C127×#273712yes—
576C2C127×#274512yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1446C2semidirect
4. C127×#1443C2semidirect
5. C127×#1443C2semidirect
8. C127×#1434C2semidirect
278. #15930C127direct (N × H)
291. #1446C2×C127semidirect
292. #1443C2×C127semidirect
293. #1443C2×C127semidirect
296. #1434C2×C127semidirect
298. C127#15930direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#393×C1272
C2×#381×C1272
C127×#14462
C127×#14432
C127×#14402
C127×#14372
C127×#14342
C127×C22⋊#952
#15930127