Finite Group Databasebeta

← C127×#17280 #44580953

Subgroups — C127×#17280 #44580953

Order 32512.

990 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#1446C211yesmaximal, characteristic
2C127×#1446C212yesmaximal
3C127×#1445C211yesmaximal, characteristic
4C127×#1443C212yesmaximal
5C127×#1443C212yesmaximal
6C127×#1443C212yesmaximal
7C127×#1442C212yesmaximal
8C127×#1442C211yesmaximal, characteristic
9C127×#1442C212yesmaximal
10C23×Q8×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C2×#95×C127C2212yes—
14C2×#95×C127C2211yescharacteristic
15C2×#95×C127C2212yes—
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×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2211yescharacteristic
31C22×Q8×C127—22no—
32C22×Q8×C127—24no—
33C22×Q8×C127—41no—
34C22×Q8×C127—42no—
35C22×Q8×C127—41no—
36C23×C4×C127C2312yes—
37C23×C4×C127C2312yes—
38C23×C4×C127C2312yes—
39C23×C4×C127C2312yes—
40C23×C4×C127C2312yes—
41C23×C4×C127C2311yescharacteristic
42C23×C4×C127C2311yescharacteristic
43C23×C4×C127C2312yes—
44C23×C4×C127C2311yescharacteristic
45C2×C4⋊C4×C127—22no—
46C2×C4⋊C4×C127—41no—
47C2×C4⋊C4×C127—41no—
48C2×C4⋊C4×C127—41no—
49C2×C4⋊C4×C127—42no—
50#95×C127—24no—
51#95×C127—22no—
52#95×C127—24no—
53#95×C127—24no—
54#95×C127—24no—
55#95×C127—24no—
56#95×C127—41no—
57#95×C127—42no—
58#95×C127—41no—
59#95×C127—42no—
60#95×C127—41no—
61#95×C127—42no—
62#95×C127—42no—
63#95×C127—42no—
64#95×C127—42no—
65#95×C127—42no—
66#95×C127—42no—
67#95×C127—42no—
68C24×C127C2411yescharacteristic
69C2×Q8×C127—48no—
70C2×Q8×C127—44no—
71C2×Q8×C127—48no—
72C2×Q8×C127—44no—
73C2×Q8×C127—44no—
74C22×C4×C127—22no—
75C22×C4×C127—22no—
76C22×C4×C127—22no—
77C22×C4×C127—22no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—21no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
83C22×C4×C127—21no—
84C22×C4×C127—21no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—21no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
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—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#4112yes—
128C22×C4×C127#4112yes—
129C22×C4×C127#4112yes—
130C22×C4×C127#4114yes—
131C4⋊C4×C127—44no—
132C4⋊C4×C127—44no—
133C23×C127C2×#4111yescharacteristic
134C23×C127C2×#4112yes—
135C23×C127C2×#4111yescharacteristic
136C23×C127C2×#4111yescharacteristic
137C23×C127H(5,𝔽2)11yescharacteristic
138C23×C127H(5,𝔽2)11yescharacteristic
139C23×C127H(5,𝔽2)12yes—
140C23×C127H(5,𝔽2)11yescharacteristic
141C23×C1272−1+411yescharacteristic
142C23×C1272−1+412yes—
143C23×C1272−1+412yes—
144Q8×C127—416no—
145C2×C4×C127—22no—
146C2×C4×C127—24no—
147C2×C4×C127—22no—
148C2×C4×C127—24no—
149C2×C4×C127—22no—
150C2×C4×C127—24no—
151C2×C4×C127—24no—
152C2×C4×C127—24no—
153C2×C4×C127—24no—
154C2×C4×C127—42no—
155C2×C4×C127—42no—
156C2×C4×C127—42no—
157C2×C4×C127—42no—
158C2×C4×C127—41no—
159C2×C4×C127—42no—
160C2×C4×C127—41no—
161C2×C4×C127—41no—
162C2×C4×C127—41no—
163C2×C4×C127—42no—
164C2×C4×C127—42no—
165C2×C4×C127—41no—
166C2×C4×C127—41no—
167C2×C4×C127—42no—
168C2×C4×C127—42no—
169C2×C4×C127—42no—
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—42no—
177C2×C4×C127—42no—
178C2×C4×C127—42no—
179C2×C4×C127—42no—
180C2×C4×C127—42no—
181C2×C4×C127—42no—
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—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—
202C22×C127#53812yes—
203C22×C127#53811yescharacteristic
204C22×C127#53811yescharacteristic
205C22×C127#53912yes—
206C22×C127#53911yescharacteristic
207C22×C127#54112yes—
208C22×C127#54112yes—
209C22×C127#54212yes—
210C22×C127#54212yes—
211C22×C127#55112yes—
212C22×C127#55111yescharacteristic
213C22×C127#55212yes—
214C22×C127#55511yescharacteristic
215C22×C127#55611yescharacteristic
216C22×C127#55612yes—
217C22×C127#55911yescharacteristic
218C22×C127H(3,𝔽4)11yescharacteristic
219C22×C127#56211yescharacteristic
220C22×C127#56212yes—
221C22×C127#56312yes—
222C22×C127#56312yes—
223C22×C127#56311yescharacteristic
224C22×C127#56311yescharacteristic
225C4×C127—42no—
226C4×C127—44no—
227C4×C127—42no—
228C4×C127—42no—
229C4×C127—82no—
230C4×C127—82no—
231C4×C127—82no—
232C4×C127—82no—
233C4×C127—82no—
234#17280C12711yesmaximal, characteristic, direct product factor, Sylow
235C2×C127#273611yescharacteristic
236C2×C127#276212yes—
237C2×C127#276411yescharacteristic
238C2×C127#277512yes—
239C2×C127#278911yescharacteristic
240C2×C127#279812yes—
241C2×C127#280811yescharacteristic
242C2×C127#283112yes—
243C2×C127#283211yescharacteristic
244C2×C127#283311yescharacteristic
245C2×C127#283511yescharacteristic
246#1446C2×C12711yescharacteristic
247#1446C2×C12712yes—
248#1445C2×C12711yescharacteristic
249#1443C2×C12712yes—
250#1443C2×C12712yes—
251#1443C2×C12712yes—
252#1442C2×C12712yes—
253#1442C2×C12711yescharacteristic
254#1442C2×C12712yes—
255C127#1728011yescharacteristic, direct product factor, Sylow
256C23×Q8C22×C12711yescharacteristic
257C22×C4⋊C4C22×C12711yescharacteristic
258C22×C4⋊C4C22×C12711yescharacteristic
259C2×#95C22×C12712yes—
260C2×#95C22×C12711yescharacteristic
261C2×#95C22×C12712yes—
262C2×#95C22×C12712yes—
263C2×#95C22×C12712yes—
264C2×#95C22×C12712yes—
265C2×#95C22×C12712yes—
266C2×#95C22×C12712yes—
267C2×#95C22×C12712yes—
268C2×#95C22×C12712yes—
269C2×#95C22×C12712yes—
270C2×#95C22×C12712yes—
271C2×#95C22×C12712yes—
272C2×#95C22×C12712yes—
273C2×#95C22×C12711yescharacteristic
274C2×#95C22×C12712yes—
275C2×#95C22×C12711yescharacteristic
276C2×#95C22×C12711yescharacteristic
277C22×Q8—22no—
278C22×Q8—24no—
279C22×Q8—41no—
280C22×Q8—42no—
281C22×Q8—41no—
282C23×C4C23×C12712yes—
283C23×C4C23×C12712yes—
284C23×C4C23×C12712yes—
285C23×C4C23×C12712yes—
286C23×C4C23×C12712yes—
287C23×C4C23×C12711yescharacteristic
288C23×C4C23×C12711yescharacteristic
289C23×C4C23×C12712yes—
290C23×C4C23×C12711yescharacteristic
291C2×C4⋊C4—22no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—42no—
296#95—24no—
297#95—22no—
298#95—24no—
299#95—24no—
300#95—24no—
301#95—24no—
302#95—41no—
303#95—42no—
304#95—41no—
305#95—42no—
306#95—41no—
307#95—42no—
308#95—42no—
309#95—42no—
310#95—42no—
311#95—42no—
312#95—42no—
313#95—42no—
314C24C24×C12711yescharacteristic
315C2×Q8—48no—
316C2×Q8—44no—
317C2×Q8—48no—
318C2×Q8—44no—
319C2×Q8—44no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—21no—
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—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
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#41×C12712yes—
374C22×C4#41×C12712yes—
375C22×C4#41×C12712yes—
376C22×C4#41×C12714yes—
377C4⋊C4—44no—
378C4⋊C4—44no—
379C23C2×#41×C12711yescharacteristic
380C23C2×#41×C12712yes—
381C23C2×#41×C12711yescharacteristic
382C23C2×#41×C12711yescharacteristic
383C23H(5,𝔽2)×C12711yescharacteristic
384C23H(5,𝔽2)×C12711yescharacteristic
385C23H(5,𝔽2)×C12712yes—
386C23H(5,𝔽2)×C12711yescharacteristic
387C232−1+4×C12711yescharacteristic
388C232−1+4×C12712yes—
389C232−1+4×C12712yes—
390Q8—416no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
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—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
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—
448C22#538×C12712yes—
449C22#538×C12711yescharacteristic
450C22#538×C12711yescharacteristic
451C22#539×C12712yes—
452C22#539×C12711yescharacteristic
453C22#541×C12712yes—
454C22#541×C12712yes—
455C22#542×C12712yes—
456C22#542×C12712yes—
457C22#551×C12712yes—
458C22#551×C12711yescharacteristic
459C22#552×C12712yes—
460C22#555×C12711yescharacteristic
461C22#556×C12711yescharacteristic
462C22#556×C12712yes—
463C22#559×C12711yescharacteristic
464C22H(3,𝔽4)×C12711yescharacteristic
465C22#562×C12711yescharacteristic
466C22#562×C12712yes—
467C22#563×C12712yes—
468C22#563×C12712yes—
469C22#563×C12711yescharacteristic
470C22#563×C12711yescharacteristic
471C4—42no—
472C4—44no—
473C4—42no—
474C4—42no—
475C4—82no—
476C4—82no—
477C4—82no—
478C4—82no—
479C4—82no—
480C2C127×#273611yescharacteristic
481C2C127×#276212yes—
482C2C127×#276411yescharacteristic
483C2C127×#277512yes—
484C2C127×#278911yescharacteristic
485C2C127×#279812yes—
486C2C127×#280811yescharacteristic
487C2C127×#283112yes—
488C2C127×#283211yescharacteristic
489C2C127×#283311yescharacteristic
490C2C127×#283511yescharacteristic
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
234. #17280C127direct (N × H)
255. C127#17280direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#14462
C127×#14452
C127×#14432
C127×#14422
#17280127