Finite Group Databasebeta

← C127×#17235 #44580908

Subgroups — C127×#17235 #44580908

Order 32512.

1034 conjugacy classes of subgroups.

The subgroup lattice has 500 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×#1445C211yesmaximal, characteristic
5C127×#1443C212yesmaximal
6C127×#1442C212yesmaximal
7C127×#1442C212yesmaximal
8C127×#1442C212yesmaximal
9C127×#1441C212yesmaximal
10C23×Q8×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2212yes—
13C22×C4⋊C4×C127C2211yescharacteristic
14C2×#95×C127C2212yes—
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×C127C2211yescharacteristic
26C2×#95×C127C2211yescharacteristic
27C2×#95×C127C2212yes—
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—41no—
50C2×C4⋊C4×C127—42no—
51C2×C4⋊C4×C127—42no—
52C2×C4⋊C4×C127—42no—
53C2×C4⋊C4×C127Q814yescomplemented
54#95×C127—24no—
55#95×C127—24no—
56#95×C127—24no—
57#95×C127—24no—
58#95×C127—42no—
59#95×C127—42no—
60#95×C127—41no—
61#95×C127—42no—
62#95×C127—42no—
63#95×C127—41no—
64#95×C127—42no—
65#95×C127—41no—
66#95×C127—42no—
67#95×C127—42no—
68#95×C127—41no—
69#95×C127—42no—
70#95×C127—42no—
71C24×C127C2411yescharacteristic
72C2×Q8×C127—48no—
73C2×Q8×C127—44no—
74C2×Q8×C127—48no—
75C2×Q8×C127—44no—
76C2×Q8×C127—44no—
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—21no—
85C22×C4×C127—21no—
86C22×C4×C127—22no—
87C22×C4×C127—21no—
88C22×C4×C127—21no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—21no—
93C22×C4×C127—21no—
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—22no—
128C22×C4×C127—22no—
129C22×C4×C127C2×Q812yes—
130C22×C4×C127C2×Q814yes—
131C22×C4×C127#4112yes—
132C22×C4×C127#4112yes—
133C22×C4×C127#4114yes—
134C4⋊C4×C127—44no—
135C4⋊C4×C127—44no—
136C4⋊C4×C127—48no—
137C23×C127C22×Q811yescharacteristic
138C23×C127C2×#4111yescharacteristic
139C23×C127C2×#4112yes—
140C23×C127C2×#4111yescharacteristic
141C23×C127H(5,𝔽2)11yescharacteristic
142C23×C127H(5,𝔽2)11yescharacteristic
143C23×C127H(5,𝔽2)11yescharacteristic
144C23×C127H(5,𝔽2)12yes—
145C23×C127H(5,𝔽2)11yescharacteristic
146C23×C1272−1+412yes—
147C23×C1272−1+412yes—
148Q8×C127—416no—
149C2×C4×C127—22no—
150C2×C4×C127—24no—
151C2×C4×C127—22no—
152C2×C4×C127—22no—
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—42no—
162C2×C4×C127—42no—
163C2×C4×C127—42no—
164C2×C4×C127—42no—
165C2×C4×C127—42no—
166C2×C4×C127—42no—
167C2×C4×C127—41no—
168C2×C4×C127—42no—
169C2×C4×C127—41no—
170C2×C4×C127—42no—
171C2×C4×C127—41no—
172C2×C4×C127—41no—
173C2×C4×C127—42no—
174C2×C4×C127—42no—
175C2×C4×C127—42no—
176C2×C4×C127—41no—
177C2×C4×C127—41no—
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—
202C2×C4×C127—42no—
203C2×C4×C127—42no—
204C2×C4×C127—42no—
205C2×C4×C127—42no—
206C22×C127#53811yescharacteristic
207C22×C127#53812yes—
208C22×C127#53811yescharacteristic
209C22×C127#54112yes—
210C22×C127#54212yes—
211C22×C127#54212yes—
212C22×C127#54212yes—
213C22×C127#54311yescharacteristic
214C22×C127#54412yes—
215C22×C127#55112yes—
216C22×C127#55111yescharacteristic
217C22×C127#55212yes—
218C22×C127#55411yescharacteristic
219C22×C127#55411yescharacteristic
220C22×C127#55712yes—
221C22×C127#55911yescharacteristic
222C22×C127#56011yescharacteristic
223C22×C127H(3,𝔽4)11yescharacteristic
224C22×C127#56212yes—
225C22×C127#56212yes—
226C22×C127#56311yescharacteristic
227C22×C127#56312yes—
228C22×C127#56311yescharacteristic
229C4×C127—42no—
230C4×C127—44no—
231C4×C127—42no—
232C4×C127—42no—
233C4×C127—44no—
234C4×C127—82no—
235C4×C127—82no—
236C4×C127—82no—
237C4×C127—82no—
238#17235C12711yesmaximal, characteristic, direct product factor, Sylow
239C2×C127#273511yescharacteristic
240C2×C127#275412yes—
241C2×C127#275512yes—
242C2×C127#276411yescharacteristic
243C2×C127#277412yes—
244C2×C127#279911yescharacteristic
245C2×C127#280411yescharacteristic
246C2×C127#283011yescharacteristic
247C2×C127#283212yes—
248C2×C127#283311yescharacteristic
249C2×C127#284111yescharacteristic
250#1446C2×C12711yescharacteristic
251#1446C2×C12712yes—
252#1445C2×C12711yescharacteristic
253#1445C2×C12711yescharacteristic
254#1443C2×C12712yes—
255#1442C2×C12712yes—
256#1442C2×C12712yes—
257#1442C2×C12712yes—
258#1441C2×C12712yes—
259C127#1723511yescharacteristic, direct product factor, Sylow
260C23×Q8C22×C12711yescharacteristic
261C22×C4⋊C4C22×C12711yescharacteristic
262C22×C4⋊C4C22×C12712yes—
263C22×C4⋊C4C22×C12711yescharacteristic
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×C12712yes—
274C2×#95C22×C12712yes—
275C2×#95C22×C12711yescharacteristic
276C2×#95C22×C12711yescharacteristic
277C2×#95C22×C12712yes—
278C2×#95C22×C12712yes—
279C2×#95C22×C12711yescharacteristic
280C2×#95C22×C12711yescharacteristic
281C22×Q8—22no—
282C22×Q8—24no—
283C22×Q8—41no—
284C22×Q8—42no—
285C22×Q8—41no—
286C23×C4C23×C12712yes—
287C23×C4C23×C12712yes—
288C23×C4C23×C12712yes—
289C23×C4C23×C12712yes—
290C23×C4C23×C12712yes—
291C23×C4C23×C12711yescharacteristic
292C23×C4C23×C12711yescharacteristic
293C23×C4C23×C12712yes—
294C23×C4C23×C12711yescharacteristic
295C2×C4⋊C4—22no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4Q8×C12714yescomplemented
304#95—24no—
305#95—24no—
306#95—24no—
307#95—24no—
308#95—42no—
309#95—42no—
310#95—41no—
311#95—42no—
312#95—42no—
313#95—41no—
314#95—42no—
315#95—41no—
316#95—42no—
317#95—42no—
318#95—41no—
319#95—42no—
320#95—42no—
321C24C24×C12711yescharacteristic
322C2×Q8—48no—
323C2×Q8—44no—
324C2×Q8—48no—
325C2×Q8—44no—
326C2×Q8—44no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
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—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4C2×Q8×C12712yes—
380C22×C4C2×Q8×C12714yes—
381C22×C4#41×C12712yes—
382C22×C4#41×C12712yes—
383C22×C4#41×C12714yes—
384C4⋊C4—44no—
385C4⋊C4—44no—
386C4⋊C4—48no—
387C23C22×Q8×C12711yescharacteristic
388C23C2×#41×C12711yescharacteristic
389C23C2×#41×C12712yes—
390C23C2×#41×C12711yescharacteristic
391C23H(5,𝔽2)×C12711yescharacteristic
392C23H(5,𝔽2)×C12711yescharacteristic
393C23H(5,𝔽2)×C12711yescharacteristic
394C23H(5,𝔽2)×C12712yes—
395C23H(5,𝔽2)×C12711yescharacteristic
396C232−1+4×C12712yes—
397C232−1+4×C12712yes—
398Q8—416no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—22no—
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—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
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—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C22#538×C12711yescharacteristic
457C22#538×C12712yes—
458C22#538×C12711yescharacteristic
459C22#541×C12712yes—
460C22#542×C12712yes—
461C22#542×C12712yes—
462C22#542×C12712yes—
463C22#543×C12711yescharacteristic
464C22#544×C12712yes—
465C22#551×C12712yes—
466C22#551×C12711yescharacteristic
467C22#552×C12712yes—
468C22#554×C12711yescharacteristic
469C22#554×C12711yescharacteristic
470C22#557×C12712yes—
471C22#559×C12711yescharacteristic
472C22#560×C12711yescharacteristic
473C22H(3,𝔽4)×C12711yescharacteristic
474C22#562×C12712yes—
475C22#562×C12712yes—
476C22#563×C12711yescharacteristic
477C22#563×C12712yes—
478C22#563×C12711yescharacteristic
479C4—42no—
480C4—44no—
481C4—42no—
482C4—42no—
483C4—44no—
484C4—82no—
485C4—82no—
486C4—82no—
487C4—82no—
488C2C127×#273511yescharacteristic
489C2C127×#275412yes—
490C2C127×#275512yes—
491C2C127×#276411yescharacteristic
492C2C127×#277412yes—
493C2C127×#279911yescharacteristic
494C2C127×#280411yescharacteristic
495C2C127×#283011yescharacteristic
496C2C127×#283212yes—
497C2C127×#283311yescharacteristic
498C2C127×#284111yescharacteristic
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
238. #17235C127direct (N × H)
259. C127#17235direct (N × H)
303. C2×C4⋊C4Q8×C127semidirect

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
C127×#14412
#17235127