Finite Group Databasebeta

← C127×#16109 #44579782

Subgroups — C127×#16109 #44579782

Order 32512.

1198 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#391×C127C212yesmaximal
2C127×#1446C211yesmaximal, characteristic
3C127×#1445C212yesmaximal
4C127×#1445C212yesmaximal
5C127×#1445C211yesmaximal, characteristic
6C127×#1443C212yesmaximal
7C127×#1442C211yesmaximal, characteristic
8C127×#1436C212yesmaximal
9C127×#1436C212yesmaximal
10C23×Q8×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C42×C127C2212yes—
15#391×C127—28no—
16C2×#95×C127C2212yes—
17C2×#95×C127C2212yes—
18C2×#95×C127C2212yes—
19C2×#95×C127C2212yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2212yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2211yescharacteristic
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2211yescharacteristic
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2211yescharacteristic
32C22×Q8×C127—24no—
33C22×Q8×C127—24no—
34C22×Q8×C127—41no—
35C22×Q8×C127—41no—
36C22×Q8×C127D414yes—
37C23×C4×C127C2312yes—
38C23×C4×C127C2312yes—
39C23×C4×C127C2312yes—
40C23×C4×C127C2311yescharacteristic
41C23×C4×C127C2312yes—
42C23×C4×C127C2311yescharacteristic
43C23×C4×C127C2312yes—
44C23×C4×C127C2311yescharacteristic
45C23×C4×C127C2312yes—
46C2×C4⋊C4×C127—24no—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—24no—
50C2×C4⋊C4×C127—41no—
51C2×C4⋊C4×C127—41no—
52C2×C4⋊C4×C127—41no—
53C2×C4⋊C4×C127Q814yescomplemented
54C2×C42×C127—24no—
55C2×C42×C127—42no—
56C2×C42×C127—42no—
57#95×C127—24no—
58#95×C127—24no—
59#95×C127—24no—
60#95×C127—24no—
61#95×C127—24no—
62#95×C127—24no—
63#95×C127—24no—
64#95×C127—24no—
65#95×C127—22no—
66#95×C127—24no—
67#95×C127—42no—
68#95×C127—41no—
69#95×C127—42no—
70#95×C127—41no—
71#95×C127—41no—
72#95×C127—42no—
73C24×C127C2411yescharacteristic
74C2×Q8×C127—216no—
75C2×Q8×C127—44no—
76C2×Q8×C127—48no—
77C2×Q8×C127—44no—
78C2×Q8×C127—44no—
79C22×C4×C127—22no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—21no—
96C22×C4×C127—22no—
97C22×C4×C127—21no—
98C22×C4×C127—21no—
99C22×C4×C127—21no—
100C22×C4×C127—21no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—22no—
104C22×C4×C127—21no—
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×C127C2×D412yes—
129C22×C4×C127C2×D414yes—
130C22×C4×C127C2×Q812yes—
131C22×C4×C127C2×Q814yes—
132C22×C4×C127#4112yes—
133C22×C4×C127#4114yes—
134C22×C4×C127#4114yes—
135C22×C4×C127#4114yes—
136C4⋊C4×C127—44no—
137C4⋊C4×C127—44no—
138C4⋊C4×C127—48no—
139C42×C127—48no—
140C23×C127C22×D411yescharacteristic
141C23×C127C22×Q811yescharacteristic
142C23×C127C2×#4112yes—
143C23×C127C2×#4112yes—
144C23×C127C2×#4111yescharacteristic
145C23×C127C2×#4112yes—
146C23×C127H(5,𝔽2)11yescharacteristic
147C23×C127H(5,𝔽2)11yescharacteristic
148C23×C127H(5,𝔽2)11yescharacteristic
149C23×C1272−1+411yescharacteristic
150C23×C1272−1+412yes—
151Q8×C127—416no—
152C2×C4×C127—24no—
153C2×C4×C127—24no—
154C2×C4×C127—24no—
155C2×C4×C127—24no—
156C2×C4×C127—24no—
157C2×C4×C127—24no—
158C2×C4×C127—24no—
159C2×C4×C127—24no—
160C2×C4×C127—24no—
161C2×C4×C127—22no—
162C2×C4×C127—24no—
163C2×C4×C127—22no—
164C2×C4×C127—22no—
165C2×C4×C127—24no—
166C2×C4×C127—24no—
167C2×C4×C127—24no—
168C2×C4×C127—24no—
169C2×C4×C127—24no—
170C2×C4×C127—42no—
171C2×C4×C127—42no—
172C2×C4×C127—42no—
173C2×C4×C127—42no—
174C2×C4×C127—42no—
175C2×C4×C127—42no—
176C2×C4×C127—41no—
177C2×C4×C127—41no—
178C2×C4×C127—41no—
179C2×C4×C127—41no—
180C2×C4×C127—42no—
181C2×C4×C127—41no—
182C2×C4×C127—41no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—42no—
186C2×C4×C127—42no—
187C2×C4×C127—42no—
188C2×C4×C127—42no—
189C2×C4×C127—42no—
190C2×C4×C127—42no—
191C2×C4×C127—42no—
192C2×C4×C127—42no—
193C2×C4×C127—42no—
194C2×C4×C127—42no—
195C2×C4×C127—42no—
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—42no—
205C2×C4×C127—42no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127#12318yes—
209C22×C127C2×#12312yes—
210C22×C127#52912yes—
211C22×C127#53312yes—
212C22×C127#53411yescharacteristic
213C22×C127#53912yes—
214C22×C127#53911yescharacteristic
215C22×C127#54112yes—
216C22×C127#54212yes—
217C22×C127#54311yescharacteristic
218C22×C127#54812yes—
219C22×C127D4×Q811yescharacteristic
220C22×C127#55011yescharacteristic
221C22×C127#55112yes—
222C22×C127#55111yescharacteristic
223C22×C127#55111yescharacteristic
224C22×C127#55111yescharacteristic
225C22×C127#55411yescharacteristic
226C22×C127#55612yes—
227C22×C127#55612yes—
228C22×C127#55712yes—
229C22×C127#55912yes—
230C22×C127#56211yescharacteristic
231C22×C127#56311yescharacteristic
232C4×C127—28no—
233C4×C127—42no—
234C4×C127—44no—
235C4×C127—44no—
236C4×C127—42no—
237C4×C127—42no—
238C4×C127—82no—
239C4×C127—82no—
240C4×C127—82no—
241#16109C12711yesmaximal, characteristic, direct product factor, Sylow
242C2×C127#244612yes—
243C2×C127#244812yes—
244C2×C127#248311yescharacteristic
245C2×C127#252311yescharacteristic
246C2×C127#258812yes—
247C2×C127#260711yescharacteristic
248C2×C127#272811yescharacteristic
249C2×C127#273211yescharacteristic
250C2×C127#278911yescharacteristic
251C2×C127#279812yes—
252C2×C127#279911yescharacteristic
253C2×#391C2×C12712yes—
254#1446C2×C12711yescharacteristic
255#1445C2×C12712yes—
256#1445C2×C12712yes—
257#1445C2×C12711yescharacteristic
258#1443C2×C12712yes—
259#1442C2×C12711yescharacteristic
260#1436C2×C12712yes—
261#1436C2×C12712yes—
262C127#1610911yescharacteristic, direct product factor, Sylow
263C23×Q8C22×C12711yescharacteristic
264C22×C4⋊C4C22×C12712yes—
265C22×C4⋊C4C22×C12711yescharacteristic
266C22×C4⋊C4C22×C12711yescharacteristic
267C22×C42C22×C12712yes—
268#391—28no—
269C2×#95C22×C12712yes—
270C2×#95C22×C12712yes—
271C2×#95C22×C12712yes—
272C2×#95C22×C12712yes—
273C2×#95C22×C12712yes—
274C2×#95C22×C12712yes—
275C2×#95C22×C12712yes—
276C2×#95C22×C12712yes—
277C2×#95C22×C12711yescharacteristic
278C2×#95C22×C12712yes—
279C2×#95C22×C12712yes—
280C2×#95C22×C12712yes—
281C2×#95C22×C12711yescharacteristic
282C2×#95C22×C12711yescharacteristic
283C2×#95C22×C12712yes—
284C2×#95C22×C12711yescharacteristic
285C22×Q8—24no—
286C22×Q8—24no—
287C22×Q8—41no—
288C22×Q8—41no—
289C22×Q8D4×C12714yes—
290C23×C4C23×C12712yes—
291C23×C4C23×C12712yes—
292C23×C4C23×C12712yes—
293C23×C4C23×C12711yescharacteristic
294C23×C4C23×C12711yescharacteristic
295C23×C4C23×C12712yes—
296C23×C4C23×C12711yescharacteristic
297C23×C4C23×C12712yes—
298C23×C4C23×C12712yes—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4Q8×C12714yescomplemented
307C2×C42—24no—
308C2×C42—42no—
309C2×C42—42no—
310#95—24no—
311#95—24no—
312#95—24no—
313#95—24no—
314#95—24no—
315#95—24no—
316#95—24no—
317#95—24no—
318#95—22no—
319#95—24no—
320#95—42no—
321#95—41no—
322#95—42no—
323#95—41no—
324#95—41no—
325#95—42no—
326C24C24×C12711yescharacteristic
327C2×Q8—216no—
328C2×Q8—44no—
329C2×Q8—48no—
330C2×Q8—44no—
331C2×Q8—44no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
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×C4C2×D4×C12712yes—
382C22×C4C2×D4×C12714yes—
383C22×C4C2×Q8×C12712yes—
384C22×C4C2×Q8×C12714yes—
385C22×C4#41×C12712yes—
386C22×C4#41×C12714yes—
387C22×C4#41×C12714yes—
388C22×C4#41×C12714yes—
389C4⋊C4—44no—
390C4⋊C4—44no—
391C4⋊C4—48no—
392C42—48no—
393C23C22×D4×C12711yescharacteristic
394C23C22×Q8×C12711yescharacteristic
395C23C2×#41×C12712yes—
396C23C2×#41×C12712yes—
397C23C2×#41×C12711yescharacteristic
398C23C2×#41×C12712yes—
399C23H(5,𝔽2)×C12711yescharacteristic
400C23H(5,𝔽2)×C12711yescharacteristic
401C23H(5,𝔽2)×C12711yescharacteristic
402C232−1+4×C12711yescharacteristic
403C232−1+4×C12712yes—
404Q8—416no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4#123×C12718yes—
462C22C2×#123×C12712yes—
463C22#529×C12712yes—
464C22#533×C12712yes—
465C22#534×C12711yescharacteristic
466C22#539×C12712yes—
467C22#539×C12711yescharacteristic
468C22#541×C12712yes—
469C22#542×C12712yes—
470C22#543×C12711yescharacteristic
471C22#548×C12712yes—
472C22D4×Q8×C12711yescharacteristic
473C22#550×C12711yescharacteristic
474C22#551×C12712yes—
475C22#551×C12711yescharacteristic
476C22#551×C12711yescharacteristic
477C22#551×C12711yescharacteristic
478C22#554×C12711yescharacteristic
479C22#556×C12712yes—
480C22#556×C12712yes—
481C22#557×C12712yes—
482C22#559×C12712yes—
483C22#562×C12711yescharacteristic
484C22#563×C12711yescharacteristic
485C4—28no—
486C4—42no—
487C4—44no—
488C4—44no—
489C4—42no—
490C4—42no—
491C4—82no—
492C4—82no—
493C4—82no—
494C2C127×#244612yes—
495C2C127×#244812yes—
496C2C127×#248311yescharacteristic
497C2C127×#252311yescharacteristic
498C2C127×#258812yes—
499C2C127×#260711yescharacteristic
500C2C127×#272811yescharacteristic
501C2C127×#273211yescharacteristic
502C2C127×#278911yescharacteristic
503C2C127×#279812yes—
504C2C127×#279911yescharacteristic
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
53. C2×C4⋊C4×C127Q8semidirect
241. #16109C127direct (N × H)
262. C127#16109direct (N × H)
306. C2×C4⋊C4Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#391×C1272
C127×#14462
C127×#14452
C127×#14432
C127×#14422
C127×#14362
#16109127