Finite Group Databasebeta

← C127×#15510 #44579183

Subgroups — C127×#15510 #44579183

Order 32512.

1478 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#395×C127C212yesmaximal
2C2×#391×C127C212yesmaximal
3C127×#1446C211yesmaximal, characteristic
4C127×#1446C211yesmaximal, characteristic
5C127×#1444C211yesmaximal, characteristic
6C127×#1444C212yesmaximal
7C127×#1441C212yesmaximal
8C127×#1436C212yesmaximal
9C127×C4⋊#95C212yesmaximal
10C23×Q8×C127C2211yescharacteristic
11C23×Q8×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2212yes—
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2212yes—
17C22×C42×C127C2212yes—
18#395×C127—28no—
19#391×C127—28no—
20C2×#95×C127C2212yes—
21C2×#95×C127C2212yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2211yescharacteristic
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2212yes—
32C2×#95×C127C2211yescharacteristic
33C22×Q8×C127—24no—
34C22×Q8×C127—24no—
35C22×Q8×C127—24no—
36C22×Q8×C127—22no—
37C22×Q8×C127—41no—
38C22×Q8×C127—41no—
39C22×Q8×C127—41no—
40C22×Q8×C127—42no—
41C22×Q8×C127—41no—
42C22×Q8×C127Q814yescomplemented
43C23×C4×C127C2312yes—
44C23×C4×C127C2312yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2312yes—
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2312yes—
51C23×C4×C127C2312yes—
52C2×C4⋊C4×C127—24no—
53C2×C4⋊C4×C127—24no—
54C2×C4⋊C4×C127—24no—
55C2×C4⋊C4×C127—24no—
56C2×C4⋊C4×C127—24no—
57C2×C4⋊C4×C127—42no—
58C2×C4⋊C4×C127—42no—
59C2×C4⋊C4×C127—42no—
60C2×C4⋊C4×C127—42no—
61C2×C4⋊C4×C127—42no—
62C2×C4⋊C4×C127—42no—
63C2×C4⋊C4×C127—41no—
64C2×C4⋊C4×C127—42no—
65C2×C4⋊C4×C127Q818yescomplemented
66C2×C42×C127—24no—
67C2×C42×C127—24no—
68C2×C42×C127—42no—
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—41no—
76#95×C127—42no—
77#95×C127—42no—
78#95×C127—41no—
79#95×C127—41no—
80#95×C127D418yes—
81#95×C127Q814yescomplemented
82C24×C127C2411yescharacteristic
83C2×Q8×C127—216no—
84C2×Q8×C127—44no—
85C2×Q8×C127—44no—
86C2×Q8×C127—48no—
87C2×Q8×C127—44no—
88C2×Q8×C127—44no—
89C2×Q8×C127—48no—
90C2×Q8×C127—48no—
91C2×Q8×C127—44no—
92C2×Q8×C127—44no—
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—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—21no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—21no—
118C22×C4×C127—21no—
119C22×C4×C127—21no—
120C22×C4×C127—21no—
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—21no—
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×C127C2×D414yes—
139C22×C4×C127C2×D414yes—
140C22×C4×C127C2×D414yes—
141C22×C4×C127C2×Q812yes—
142C22×C4×C127C2×Q814yes—
143C22×C4×C127C2×Q814yes—
144C22×C4×C127C2×Q812yes—
145C22×C4×C127C2×Q814yes—
146C22×C4×C127C2×Q814yes—
147C22×C4×C127C2×Q814yes—
148C22×C4×C127#4112yes—
149C22×C4×C127#4114yes—
150C4⋊C4×C127—48no—
151C4⋊C4×C127—48no—
152C4⋊C4×C127—48no—
153C4⋊C4×C127—48no—
154C4⋊C4×C127—44no—
155C42×C127—48no—
156C23×C127C22×D412yes—
157C23×C127C22×Q811yescharacteristic
158C23×C127C22×Q811yescharacteristic
159C23×C127C22×Q812yes—
160C23×C127C2×#4112yes—
161C23×C127C2×#4111yescharacteristic
162C23×C127H(5,𝔽2)11yescharacteristic
163C23×C127H(5,𝔽2)12yes—
164C23×C127H(5,𝔽2)11yescharacteristic
165C23×C127H(5,𝔽2)11yescharacteristic
166C23×C1272−1+411yescharacteristic
167Q8×C127—416no—
168Q8×C127—416no—
169C2×C4×C127—24no—
170C2×C4×C127—24no—
171C2×C4×C127—24no—
172C2×C4×C127—24no—
173C2×C4×C127—24no—
174C2×C4×C127—24no—
175C2×C4×C127—24no—
176C2×C4×C127—24no—
177C2×C4×C127—24no—
178C2×C4×C127—24no—
179C2×C4×C127—24no—
180C2×C4×C127—24no—
181C2×C4×C127—24no—
182C2×C4×C127—24no—
183C2×C4×C127—22no—
184C2×C4×C127—24no—
185C2×C4×C127—24no—
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—42no—
197C2×C4×C127—42no—
198C2×C4×C127—42no—
199C2×C4×C127—42no—
200C2×C4×C127—42no—
201C2×C4×C127—42no—
202C2×C4×C127—42no—
203C2×C4×C127—42no—
204C2×C4×C127—41no—
205C2×C4×C127—41no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—42no—
209C2×C4×C127—42no—
210C2×C4×C127—41no—
211C2×C4×C127—41no—
212C2×C4×C127—41no—
213C2×C4×C127—42no—
214C2×C4×C127—41no—
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×C127C22⋊Q818yes—
225C2×C4×C127C4⋊Q818yes—
226C22×C127C2×C22⋊Q812yes—
227C22×C127C2×C4⋊Q812yes—
228C22×C127#53312yes—
229C22×C127#53512yes—
230C22×C127#53811yescharacteristic
231C22×C127#54212yes—
232C22×C127#54312yes—
233C22×C127#54311yescharacteristic
234C22×C127#54411yescharacteristic
235C22×C127D4211yescharacteristic
236C22×C127#54612yes—
237C22×C127#54612yes—
238C22×C127D4×Q812yes—
239C22×C127#55111yescharacteristic
240C22×C127#55412yes—
241C22×C127#55412yes—
242C22×C127#55411yescharacteristic
243C22×C127#55711yescharacteristic
244C22×C127Q8211yescharacteristic
245C22×C127Q8212yes—
246C22×C127Q8211yescharacteristic
247C22×C127H(3,𝔽4)11yescharacteristic
248C22×C127#56211yescharacteristic
249C4×C127—28no—
250C4×C127—28no—
251C4×C127—44no—
252C4×C127—42no—
253C4×C127—44no—
254C4×C127—44no—
255C4×C127—42no—
256C4×C127—42no—
257C4×C127—82no—
258#15510C12711yesmaximal, characteristic, direct product factor, Sylow
259C2×C127#243711yescharacteristic
260C2×C127#245112yes—
261C2×C127#254912yes—
262C2×C127#255111yescharacteristic
263C2×C127#256712yes—
264C2×C127#258611yescharacteristic
265C2×C127#267011yescharacteristic
266C2×C127#269212yes—
267C2×C127#276311yescharacteristic
268C2×C127#280611yescharacteristic
269C2×C127#281111yescharacteristic
270C2×#395C2×C12712yes—
271C2×#391C2×C12712yes—
272#1446C2×C12711yescharacteristic
273#1446C2×C12711yescharacteristic
274#1444C2×C12711yescharacteristic
275#1444C2×C12712yes—
276#1441C2×C12712yes—
277#1436C2×C12712yes—
278C4⋊#95C2×C12712yes—
279C127#1551011yescharacteristic, direct product factor, Sylow
280C23×Q8C22×C12711yescharacteristic
281C23×Q8C22×C12711yescharacteristic
282C22×C4⋊C4C22×C12712yes—
283C22×C4⋊C4C22×C12712yes—
284C22×C4⋊C4C22×C12712yes—
285C22×C4⋊C4C22×C12711yescharacteristic
286C22×C4⋊C4C22×C12712yes—
287C22×C42C22×C12712yes—
288#395—28no—
289#391—28no—
290C2×#95C22×C12712yes—
291C2×#95C22×C12712yes—
292C2×#95C22×C12712yes—
293C2×#95C22×C12712yes—
294C2×#95C22×C12712yes—
295C2×#95C22×C12712yes—
296C2×#95C22×C12711yescharacteristic
297C2×#95C22×C12712yes—
298C2×#95C22×C12712yes—
299C2×#95C22×C12711yescharacteristic
300C2×#95C22×C12711yescharacteristic
301C2×#95C22×C12712yes—
302C2×#95C22×C12711yescharacteristic
303C22×Q8—24no—
304C22×Q8—24no—
305C22×Q8—24no—
306C22×Q8—22no—
307C22×Q8—41no—
308C22×Q8—41no—
309C22×Q8—41no—
310C22×Q8—42no—
311C22×Q8—41no—
312C22×Q8Q8×C12714yescomplemented
313C23×C4C23×C12712yes—
314C23×C4C23×C12712yes—
315C23×C4C23×C12712yes—
316C23×C4C23×C12711yescharacteristic
317C23×C4C23×C12712yes—
318C23×C4C23×C12711yescharacteristic
319C23×C4C23×C12711yescharacteristic
320C23×C4C23×C12712yes—
321C23×C4C23×C12712yes—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—41no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4Q8×C12718yescomplemented
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—42no—
339#95—24no—
340#95—24no—
341#95—24no—
342#95—24no—
343#95—24no—
344#95—24no—
345#95—41no—
346#95—42no—
347#95—42no—
348#95—41no—
349#95—41no—
350#95D4×C12718yes—
351#95Q8×C12714yescomplemented
352C24C24×C12711yescharacteristic
353C2×Q8—216no—
354C2×Q8—44no—
355C2×Q8—44no—
356C2×Q8—48no—
357C2×Q8—44no—
358C2×Q8—44no—
359C2×Q8—48no—
360C2×Q8—48no—
361C2×Q8—44no—
362C2×Q8—44no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
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×C4C2×D4×C12714yes—
409C22×C4C2×D4×C12714yes—
410C22×C4C2×D4×C12714yes—
411C22×C4C2×Q8×C12712yes—
412C22×C4C2×Q8×C12714yes—
413C22×C4C2×Q8×C12714yes—
414C22×C4C2×Q8×C12712yes—
415C22×C4C2×Q8×C12714yes—
416C22×C4C2×Q8×C12714yes—
417C22×C4C2×Q8×C12714yes—
418C22×C4#41×C12712yes—
419C22×C4#41×C12714yes—
420C4⋊C4—48no—
421C4⋊C4—48no—
422C4⋊C4—48no—
423C4⋊C4—48no—
424C4⋊C4—44no—
425C42—48no—
426C23C22×D4×C12712yes—
427C23C22×Q8×C12711yescharacteristic
428C23C22×Q8×C12711yescharacteristic
429C23C22×Q8×C12712yes—
430C23C2×#41×C12712yes—
431C23C2×#41×C12711yescharacteristic
432C23H(5,𝔽2)×C12711yescharacteristic
433C23H(5,𝔽2)×C12712yes—
434C23H(5,𝔽2)×C12711yescharacteristic
435C23H(5,𝔽2)×C12711yescharacteristic
436C232−1+4×C12711yescharacteristic
437Q8—416no—
438Q8—416no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4C22⋊Q8×C12718yes—
495C2×C4C4⋊Q8×C12718yes—
496C22C2×C22⋊Q8×C12712yes—
497C22C2×C4⋊Q8×C12712yes—
498C22#533×C12712yes—
499C22#535×C12712yes—
500C22#538×C12711yescharacteristic
501C22#542×C12712yes—
502C22#543×C12712yes—
503C22#543×C12711yescharacteristic
504C22#544×C12711yescharacteristic
505C22D42×C12711yescharacteristic
506C22#546×C12712yes—
507C22#546×C12712yes—
508C22D4×Q8×C12712yes—
509C22#551×C12711yescharacteristic
510C22#554×C12712yes—
511C22#554×C12712yes—
512C22#554×C12711yescharacteristic
513C22#557×C12711yescharacteristic
514C22Q82×C12711yescharacteristic
515C22Q82×C12712yes—
516C22Q82×C12711yescharacteristic
517C22H(3,𝔽4)×C12711yescharacteristic
518C22#562×C12711yescharacteristic
519C4—28no—
520C4—28no—
521C4—44no—
522C4—42no—
523C4—44no—
524C4—44no—
525C4—42no—
526C4—42no—
527C4—82no—
528C2C127×#243711yescharacteristic
529C2C127×#245112yes—
530C2C127×#254912yes—
531C2C127×#255111yescharacteristic
532C2C127×#256712yes—
533C2C127×#258611yescharacteristic
534C2C127×#267011yescharacteristic
535C2C127×#269212yes—
536C2C127×#276311yescharacteristic
537C2C127×#280611yescharacteristic
538C2C127×#281111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
42. C22×Q8×C127Q8semidirect
65. C2×C4⋊C4×C127Q8semidirect
81. #95×C127Q8semidirect
258. #15510C127direct (N × H)
279. C127#15510direct (N × H)
312. C22×Q8Q8×C127semidirect
335. C2×C4⋊C4Q8×C127semidirect
351. #95Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#395×C1272
C2×#391×C1272
C127×#14462
C127×#14442
C127×#14412
C127×#14362
C127×C4⋊#952
#15510127