Finite Group Databasebeta

← C127×#15521 #44579194

Subgroups — C127×#15521 #44579194

Order 32512.

1218 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#400×C127C212yesmaximal
2C2×#389×C127C212yesmaximal
3C127×#1445C211yesmaximal, characteristic
4C127×#1444C211yesmaximal, characteristic
5C127×#1444C212yesmaximal
6C127×#1442C212yesmaximal
7C127×#1442C211yesmaximal, characteristic
8C127×#1436C212yesmaximal
9C127×#1434C212yesmaximal
10C22×C4⋊C4×C127C2212yes—
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2212yes—
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C42×C127C2212yes—
17#400×C127—28no—
18#389×C127—28no—
19C2×#95×C127C2212yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2212yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2212yes—
32C2×#95×C127C2211yescharacteristic
33C23×C4×C127C2312yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2312yes—
36C23×C4×C127C2312yes—
37C23×C4×C127C2312yes—
38C23×C4×C127C2311yescharacteristic
39C23×C4×C127C2311yescharacteristic
40C23×C4×C127C2311yescharacteristic
41C23×C4×C127C2312yes—
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—24no—
44C2×C4⋊C4×C127—24no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127—24no—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—24no—
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127—22no—
52C2×C4⋊C4×C127—42no—
53C2×C4⋊C4×C127—41no—
54C2×C4⋊C4×C127—41no—
55C2×C4⋊C4×C127—42no—
56C2×C4⋊C4×C127—41no—
57C2×C4⋊C4×C127—41no—
58C2×C42×C127—24no—
59C2×C42×C127—24no—
60C2×C42×C127—42no—
61#95×C127—24no—
62#95×C127—24no—
63#95×C127—24no—
64#95×C127—24no—
65#95×C127—24no—
66#95×C127—24no—
67#95×C127—24no—
68#95×C127—24no—
69#95×C127—22no—
70#95×C127—24no—
71#95×C127—41no—
72#95×C127—41no—
73#95×C127D418yes—
74#95×C127Q814yes—
75C24×C127C2411yescharacteristic
76C22×C4×C127—22no—
77C22×C4×C127—22no—
78C22×C4×C127—22no—
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—21no—
97C22×C4×C127—21no—
98C22×C4×C127—21no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—22no—
104C22×C4×C127—21no—
105C22×C4×C127—21no—
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×C127C2×D414yes—
125C22×C4×C127C2×D414yes—
126C22×C4×C127C2×D414yes—
127C22×C4×C127C2×Q812yes—
128C22×C4×C127C2×Q814yes—
129C22×C4×C127#4112yes—
130C22×C4×C127#4112yes—
131C22×C4×C127#4114yes—
132C22×C4×C127#4114yes—
133C4⋊C4×C127—216no—
134C4⋊C4×C127—48no—
135C4⋊C4×C127—44no—
136C4⋊C4×C127—44no—
137C4⋊C4×C127—48no—
138C4⋊C4×C127—44no—
139C42×C127—48no—
140C23×C127C22×D412yes—
141C23×C127C22×Q811yescharacteristic
142C23×C127C2×#4111yescharacteristic
143C23×C127C2×#4112yes—
144C23×C127C2×#4112yes—
145C23×C127C2×#4111yescharacteristic
146C23×C127H(5,𝔽2)11yescharacteristic
147C23×C127H(5,𝔽2)11yescharacteristic
148C23×C1272−1+411yescharacteristic
149C23×C1272−1+412yes—
150C23×C1272−1+411yescharacteristic
151C2×C4×C127—24no—
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—22no—
163C2×C4×C127—22no—
164C2×C4×C127—24no—
165C2×C4×C127—24no—
166C2×C4×C127—24no—
167C2×C4×C127—24no—
168C2×C4×C127—24no—
169C2×C4×C127—24no—
170C2×C4×C127—24no—
171C2×C4×C127—24no—
172C2×C4×C127—42no—
173C2×C4×C127—42no—
174C2×C4×C127—42no—
175C2×C4×C127—42no—
176C2×C4×C127—42no—
177C2×C4×C127—42no—
178C2×C4×C127—42no—
179C2×C4×C127—42no—
180C2×C4×C127—41no—
181C2×C4×C127—41no—
182C2×C4×C127—42no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—42no—
186C2×C4×C127—42no—
187C2×C4×C127—42no—
188C2×C4×C127—41no—
189C2×C4×C127—41no—
190C2×C4×C127—41no—
191C2×C4×C127—42no—
192C2×C4×C127—41no—
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#12518yes—
208C22×C127#52512yes—
209C22×C127C2×#12512yes—
210C22×C127#53212yes—
211C22×C127#53612yes—
212C22×C127#53811yescharacteristic
213C22×C127#53912yes—
214C22×C127#53911yescharacteristic
215C22×C127#54112yes—
216C22×C127#54411yescharacteristic
217C22×C127D4211yescharacteristic
218C22×C127#54612yes—
219C22×C127#54712yes—
220C22×C127D4×Q812yes—
221C22×C127#55212yes—
222C22×C127#55212yes—
223C22×C127#55411yescharacteristic
224C22×C127#55511yescharacteristic
225C22×C127#55612yes—
226C22×C127#55611yescharacteristic
227C22×C127#55711yescharacteristic
228C22×C127#55911yescharacteristic
229C22×C127#56311yescharacteristic
230C22×C127#56311yescharacteristic
231C4×C127—28no—
232C4×C127—42no—
233C4×C127—44no—
234C4×C127—44no—
235C4×C127—42no—
236C4×C127—42no—
237C4×C127—44no—
238C4×C127—82no—
239C4×C127—82no—
240#15521C12711yesmaximal, characteristic, direct product factor, Sylow
241C2×C127#245511yescharacteristic
242C2×C127#247312yes—
243C2×C127#250612yes—
244C2×C127#255511yescharacteristic
245C2×C127#257111yescharacteristic
246C2×C127#260412yes—
247C2×C127#267711yescharacteristic
248C2×C127#268912yes—
249C2×C127#276911yescharacteristic
250C2×C127#277111yescharacteristic
251C2×C127#280511yescharacteristic
252C2×#400C2×C12712yes—
253C2×#389C2×C12712yes—
254#1445C2×C12711yescharacteristic
255#1444C2×C12711yescharacteristic
256#1444C2×C12712yes—
257#1442C2×C12712yes—
258#1442C2×C12711yescharacteristic
259#1436C2×C12712yes—
260#1434C2×C12712yes—
261C127#1552111yescharacteristic, direct product factor, Sylow
262C22×C4⋊C4C22×C12712yes—
263C22×C4⋊C4C22×C12711yescharacteristic
264C22×C4⋊C4C22×C12712yes—
265C22×C4⋊C4C22×C12712yes—
266C22×C4⋊C4C22×C12711yescharacteristic
267C22×C4⋊C4C22×C12711yescharacteristic
268C22×C42C22×C12712yes—
269#400—28no—
270#389—28no—
271C2×#95C22×C12712yes—
272C2×#95C22×C12712yes—
273C2×#95C22×C12712yes—
274C2×#95C22×C12712yes—
275C2×#95C22×C12712yes—
276C2×#95C22×C12712yes—
277C2×#95C22×C12712yes—
278C2×#95C22×C12712yes—
279C2×#95C22×C12711yescharacteristic
280C2×#95C22×C12712yes—
281C2×#95C22×C12711yescharacteristic
282C2×#95C22×C12711yescharacteristic
283C2×#95C22×C12712yes—
284C2×#95C22×C12711yescharacteristic
285C23×C4C23×C12712yes—
286C23×C4C23×C12712yes—
287C23×C4C23×C12712yes—
288C23×C4C23×C12712yes—
289C23×C4C23×C12712yes—
290C23×C4C23×C12711yescharacteristic
291C23×C4C23×C12711yescharacteristic
292C23×C4C23×C12711yescharacteristic
293C23×C4C23×C12712yes—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—41no—
310C2×C42—24no—
311C2×C42—24no—
312C2×C42—42no—
313#95—24no—
314#95—24no—
315#95—24no—
316#95—24no—
317#95—24no—
318#95—24no—
319#95—24no—
320#95—24no—
321#95—22no—
322#95—24no—
323#95—41no—
324#95—41no—
325#95D4×C12718yes—
326#95Q8×C12714yes—
327C24C24×C12711yescharacteristic
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
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—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—21no—
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×C4C2×D4×C12714yes—
377C22×C4C2×D4×C12714yes—
378C22×C4C2×D4×C12714yes—
379C22×C4C2×Q8×C12712yes—
380C22×C4C2×Q8×C12714yes—
381C22×C4#41×C12712yes—
382C22×C4#41×C12712yes—
383C22×C4#41×C12714yes—
384C22×C4#41×C12714yes—
385C4⋊C4—216no—
386C4⋊C4—48no—
387C4⋊C4—44no—
388C4⋊C4—44no—
389C4⋊C4—48no—
390C4⋊C4—44no—
391C42—48no—
392C23C22×D4×C12712yes—
393C23C22×Q8×C12711yescharacteristic
394C23C2×#41×C12711yescharacteristic
395C23C2×#41×C12712yes—
396C23C2×#41×C12712yes—
397C23C2×#41×C12711yescharacteristic
398C23H(5,𝔽2)×C12711yescharacteristic
399C23H(5,𝔽2)×C12711yescharacteristic
400C232−1+4×C12711yescharacteristic
401C232−1+4×C12712yes—
402C232−1+4×C12711yescharacteristic
403C2×C4—24no—
404C2×C4—24no—
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—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
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#125×C12718yes—
460C22#525×C12712yes—
461C22C2×#125×C12712yes—
462C22#532×C12712yes—
463C22#536×C12712yes—
464C22#538×C12711yescharacteristic
465C22#539×C12712yes—
466C22#539×C12711yescharacteristic
467C22#541×C12712yes—
468C22#544×C12711yescharacteristic
469C22D42×C12711yescharacteristic
470C22#546×C12712yes—
471C22#547×C12712yes—
472C22D4×Q8×C12712yes—
473C22#552×C12712yes—
474C22#552×C12712yes—
475C22#554×C12711yescharacteristic
476C22#555×C12711yescharacteristic
477C22#556×C12712yes—
478C22#556×C12711yescharacteristic
479C22#557×C12711yescharacteristic
480C22#559×C12711yescharacteristic
481C22#563×C12711yescharacteristic
482C22#563×C12711yescharacteristic
483C4—28no—
484C4—42no—
485C4—44no—
486C4—44no—
487C4—42no—
488C4—42no—
489C4—44no—
490C4—82no—
491C4—82no—
492C2C127×#245511yescharacteristic
493C2C127×#247312yes—
494C2C127×#250612yes—
495C2C127×#255511yescharacteristic
496C2C127×#257111yescharacteristic
497C2C127×#260412yes—
498C2C127×#267711yescharacteristic
499C2C127×#268912yes—
500C2C127×#276911yescharacteristic
501C2C127×#277111yescharacteristic
502C2C127×#280511yescharacteristic
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
240. #15521C127direct (N × H)
261. C127#15521direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#400×C1272
C2×#389×C1272
C127×#14452
C127×#14442
C127×#14422
C127×#14362
C127×#14342
#15521127