Finite Group Databasebeta

← C127×#21525 #44585198

Subgroups — C127×#21525 #44585198

Order 32512.

954 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#467×C127C211yesmaximal, characteristic
2C2×C4×Q16×C127C211yesmaximal, characteristic, complemented
3C2×#405×C127C211yesmaximal, characteristic
4C127×#2323C212yesmaximal
5C127×#1969C211yesmaximal, characteristic, complemented
6C127×#1942C211yesmaximal, characteristic, complemented
7C127×#1935C212yesmaximal, complemented
8C127×#1894C212yesmaximal
9C127×#1808C211yesmaximal, characteristic
10C4×#107×C127C211yesmaximal, characteristic, complemented
11C127×#1763C212yesmaximal, complemented
12C22×Q16×C127C2211yescharacteristic
13C22×M16×C127C2211yescharacteristic
14C23×C8×C127C2211yescharacteristic
15C2×C22⋊Q8×C127C2212yes—
16C2×C4×Q8×C127C2212yes—
17C2×#117×C127C2211yescharacteristic
18#467×C127C418yescomplemented
19C4×Q16×C127—24no—
20C2×#107×C127C2211yescharacteristic
21C2×#107×C127C2211yescharacteristic
22C2×#107×C127C2211yescharacteristic
23C2×#103×C127C2212yes—
24C2×#103×C127C2212yes—
25C2×#103×C127C2212yes—
26#405×C127—24no—
27C2×#97×C127C2211yescharacteristic
28C2×#97×C127C2211yescharacteristic
29C2×C4×C8×C127C2211yescharacteristic
30C2×C4×C8×C127C2211yescharacteristic
31#391×C127C2212yes—
32#389×C127—22no—
33#389×C127C2212yes—
34#388×C127—22no—
35#388×C127—22no—
36#387×C127—22no—
37#380×C127C2212yes—
38C4×C4⋊C4×C127C2212yes—
39#340×C127C2212yes—
40#340×C127C2212yes—
41#340×C127C2212yes—
42C22×Q8×C127C2312yes—
43C23×C4×C127C2311yescharacteristic
44C2×Q16×C127—22no—
45C2×Q16×C127—22no—
46C2×Q16×C127C2×C414yes—
47C2×M16×C127—22no—
48C2×M16×C127—22no—
49C2×M16×C127—22no—
50C22×C8×C127—22no—
51C22×C8×C127—22no—
52C22×C8×C127C2×C414yes—
53C22×C8×C127C2311yescharacteristic
54C22×C8×C127C2311yescharacteristic
55C22×C8×C127C2311yescharacteristic
56C22×C8×C127C2311yescharacteristic
57C22⋊Q8×C127—24no—
58C22⋊Q8×C127C2×C418yes—
59C4×Q8×C127—24no—
60C4×Q8×C127—24no—
61#117×C127—22no—
62#117×C127—22no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127D411yescharacteristic
67C2×C4⋊C4×C127D411yescharacteristic
68C2×C4⋊C4×C127C2312yes—
69C2×C4⋊C4×C127C2312yes—
70C2×C4⋊C4×C127C2312yes—
71C2×C22⋊C4×C127—22no—
72C2×C22⋊C4×C127—22no—
73C2×C22⋊C4×C127D411yescharacteristic
74C2×C22⋊C4×C127D411yescharacteristic
75C2×C42×C127—22no—
76C2×C42×C127—22no—
77C2×C42×C127C2311yescharacteristic
78C2×C42×C127C2311yescharacteristic
79#107×C127—22no—
80#107×C127—22no—
81#107×C127C2×C414yes—
82#103×C127—24no—
83#103×C127—24no—
84#103×C127C2×C418yes—
85#97×C127—22no—
86#97×C127—22no—
87C4×C8×C127—22no—
88C4×C8×C127D414yes—
89#95×C127—22no—
90#95×C127—22no—
91#95×C127—22no—
92#95×C127—22no—
93#95×C127—22no—
94C24×C127C2×D411yescharacteristic
95C2×Q8×C127—22no—
96C2×Q8×C127—22no—
97C2×Q8×C127—22no—
98C2×Q8×C127—22no—
99C2×Q8×C127—22no—
100C2×Q8×C127C22×C414yes—
101C22×C4×C127—21no—
102C22×C4×C127—21no—
103C22×C4×C127—21no—
104C22×C4×C127—21no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—22no—
109C22×C4×C127C22×C412yes—
110C22×C4×C127C2×D411yescharacteristic
111C22×C4×C127C2×D411yescharacteristic
112C22×C4×C127C2×D411yescharacteristic
113C22×C4×C127C2×D411yescharacteristic
114C22×C4×C127C2×D411yescharacteristic
115C22×C4×C127#4112yes—
116C22×C4×C127C2411yescharacteristic
117Q16×C127—28no—
118M16×C127—28no—
119C2×C8×C127—21no—
120C2×C8×C127—21no—
121C2×C8×C127—21no—
122C2×C8×C127—21no—
123C2×C8×C127—21no—
124C2×C8×C127—21no—
125C2×C8×C127—28no—
126C2×C8×C127C22×C412yes—
127C2×C8×C127C22×C412yes—
128C2×C8×C127C2×D412yes—
129C2×C8×C127C2×D412yes—
130C2×C8×C127#4112yes—
131C2×C8×C127#4112yes—
132C4⋊C4×C127—28no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—22no—
135C4⋊C4×C127—22no—
136C4⋊C4×C127—22no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—22no—
140C4⋊C4×C127—44no—
141C4⋊C4×C127—82no—
142C4⋊C4×C127C22×C414yes—
143C22⋊C4×C127—28no—
144C22⋊C4×C127—22no—
145C22⋊C4×C127—22no—
146C22⋊C4×C127—82no—
147C42×C127—21no—
148C42×C127—21no—
149C42×C127—44no—
150C42×C127—82no—
151C42×C127C2×D412yes—
152C42×C127#4112yes—
153C23×C127—21no—
154C23×C127—21no—
155C23×C127—21no—
156C23×C127—21no—
157C23×C127—21no—
158C23×C127—21no—
159C23×C127C4×D412yes—
160C23×C127C22×D411yescharacteristic
161Q8×C127—24no—
162Q8×C127—24no—
163Q8×C127—42no—
164Q8×C127—42no—
165C2×C4×C127—21no—
166C2×C4×C127—21no—
167C2×C4×C127—21no—
168C2×C4×C127—21no—
169C2×C4×C127—21no—
170C2×C4×C127—21no—
171C2×C4×C127—22no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—22no—
175C2×C4×C127—24no—
176C2×C4×C127—24no—
177C2×C4×C127—21no—
178C2×C4×C127—21no—
179C2×C4×C127—21no—
180C2×C4×C127—21no—
181C2×C4×C127—21no—
182C2×C4×C127—21no—
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×C127C4×D412yes—
194C2×C4×C127#12112yes—
195C2×C4×C127#12112yes—
196C2×C4×C127C23×C411yescharacteristic
197C2×C4×C127C22×D411yescharacteristic
198C2×C4×C127C2×#4111yescharacteristic
199C2×C4×C127C2×#4111yescharacteristic
200C2×C4×C127C2×#4111yescharacteristic
201C2×C4×C127C2×#4111yescharacteristic
202C8×C127—22no—
203C8×C127—22no—
204C8×C127—22no—
205C8×C127C4×D414yes—
206C22×C127—22no—
207C22×C127—22no—
208C22×C127—22no—
209C22×C127—41no—
210C22×C127—41no—
211C22×C127—41no—
212C22×C127—41no—
213C22×C127C2×C4×D411yescharacteristic
214C22×C127C2×#12111yescharacteristic
215C22×C127#53211yescharacteristic
216C22×C127#57611yescharacteristic
217C22×C127#57811yescharacteristic
218C22×C127#57811yescharacteristic
219C22×C127#57811yescharacteristic
220C4×C127—22no—
221C4×C127—22no—
222C4×C127—22no—
223C4×C127—44no—
224C4×C127—41no—
225C4×C127—41no—
226C4×C127—44no—
227C4×C127—82no—
228C4×C127—82no—
229C4×C127C2×C4×D411yescharacteristic
230C4×C127C4×#4111yescharacteristic
231C4×C127#52511yescharacteristic
232C4×C127#52911yescharacteristic
233#21525C12711yesmaximal, characteristic, direct product factor, Sylow
234C2×C127—42no—
235C2×C127C4×#12111yescharacteristic
236C2×C127#295011yescharacteristic
237C2×C127#295111yescharacteristic
238C2×C127#305911yescharacteristic
239C2×C127#306111yescharacteristic
240C2×C127#317511yescharacteristic
241C2×C127#317711yescharacteristic
242C2×#467C2×C12711yescharacteristic
243C2×C4×Q16C2×C12711yescharacteristic, complemented
244C2×#405C2×C12711yescharacteristic
245#2323C2×C12712yes—
246#1969C2×C12711yescharacteristic, complemented
247#1942C2×C12711yescharacteristic, complemented
248#1935C2×C12712yescomplemented
249#1894C2×C12712yes—
250#1808C2×C12711yescharacteristic
251C4×#107C2×C12711yescharacteristic, complemented
252#1763C2×C12712yescomplemented
253C127#2152511yescharacteristic, direct product factor, Sylow
254C22×Q16C22×C12711yescharacteristic
255C22×M16C22×C12711yescharacteristic
256C23×C8C22×C12711yescharacteristic
257C2×C22⋊Q8C22×C12712yes—
258C2×C4×Q8C22×C12712yes—
259C2×#117C22×C12711yescharacteristic
260#467C4×C12718yescomplemented
261C4×Q16—24no—
262C2×#107C22×C12711yescharacteristic
263C2×#107C22×C12711yescharacteristic
264C2×#107C22×C12711yescharacteristic
265C2×#103C22×C12712yes—
266C2×#103C22×C12712yes—
267C2×#103C22×C12712yes—
268#405—24no—
269C2×#97C22×C12711yescharacteristic
270C2×#97C22×C12711yescharacteristic
271C2×C4×C8C22×C12711yescharacteristic
272C2×C4×C8C22×C12711yescharacteristic
273#391C22×C12712yes—
274#389—22no—
275#389C22×C12712yes—
276#388—22no—
277#388—22no—
278#387—22no—
279#380C22×C12712yes—
280C4×C4⋊C4C22×C12712yes—
281#340C22×C12712yes—
282#340C22×C12712yes—
283#340C22×C12712yes—
284C22×Q8C23×C12712yes—
285C23×C4C23×C12711yescharacteristic
286C2×Q16—22no—
287C2×Q16—22no—
288C2×Q16C2×C4×C12714yes—
289C2×M16—22no—
290C2×M16—22no—
291C2×M16—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8C2×C4×C12714yes—
295C22×C8C23×C12711yescharacteristic
296C22×C8C23×C12711yescharacteristic
297C22×C8C23×C12711yescharacteristic
298C22×C8C23×C12711yescharacteristic
299C22⋊Q8—24no—
300C22⋊Q8C2×C4×C12718yes—
301C4×Q8—24no—
302C4×Q8—24no—
303#117—22no—
304#117—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4D4×C12711yescharacteristic
309C2×C4⋊C4D4×C12711yescharacteristic
310C2×C4⋊C4C23×C12712yes—
311C2×C4⋊C4C23×C12712yes—
312C2×C4⋊C4C23×C12712yes—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4D4×C12711yescharacteristic
316C2×C22⋊C4D4×C12711yescharacteristic
317C2×C42—22no—
318C2×C42—22no—
319C2×C42C23×C12711yescharacteristic
320C2×C42C23×C12711yescharacteristic
321#107—22no—
322#107—22no—
323#107C2×C4×C12714yes—
324#103—24no—
325#103—24no—
326#103C2×C4×C12718yes—
327#97—22no—
328#97—22no—
329C4×C8—22no—
330C4×C8D4×C12714yes—
331#95—22no—
332#95—22no—
333#95—22no—
334#95—22no—
335#95—22no—
336C24C2×D4×C12711yescharacteristic
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8C22×C4×C12714yes—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4C22×C4×C12712yes—
352C22×C4C2×D4×C12711yescharacteristic
353C22×C4C2×D4×C12711yescharacteristic
354C22×C4C2×D4×C12711yescharacteristic
355C22×C4C2×D4×C12711yescharacteristic
356C22×C4C2×D4×C12711yescharacteristic
357C22×C4#41×C12712yes—
358C22×C4C24×C12711yescharacteristic
359Q16—28no—
360M16—28no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—28no—
368C2×C8C22×C4×C12712yes—
369C2×C8C22×C4×C12712yes—
370C2×C8C2×D4×C12712yes—
371C2×C8C2×D4×C12712yes—
372C2×C8#41×C12712yes—
373C2×C8#41×C12712yes—
374C4⋊C4—28no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—44no—
383C4⋊C4—82no—
384C4⋊C4C22×C4×C12714yes—
385C22⋊C4—28no—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—82no—
389C42—21no—
390C42—21no—
391C42—44no—
392C42—82no—
393C42C2×D4×C12712yes—
394C42#41×C12712yes—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23C4×D4×C12712yes—
402C23C22×D4×C12711yescharacteristic
403Q8—24no—
404Q8—24no—
405Q8—42no—
406Q8—42no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
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×C4C4×D4×C12712yes—
436C2×C4#121×C12712yes—
437C2×C4#121×C12712yes—
438C2×C4C23×C4×C12711yescharacteristic
439C2×C4C22×D4×C12711yescharacteristic
440C2×C4C2×#41×C12711yescharacteristic
441C2×C4C2×#41×C12711yescharacteristic
442C2×C4C2×#41×C12711yescharacteristic
443C2×C4C2×#41×C12711yescharacteristic
444C8—22no—
445C8—22no—
446C8—22no—
447C8C4×D4×C12714yes—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22C2×C4×D4×C12711yescharacteristic
456C22C2×#121×C12711yescharacteristic
457C22#532×C12711yescharacteristic
458C22#576×C12711yescharacteristic
459C22#578×C12711yescharacteristic
460C22#578×C12711yescharacteristic
461C22#578×C12711yescharacteristic
462C4—22no—
463C4—22no—
464C4—22no—
465C4—44no—
466C4—41no—
467C4—41no—
468C4—44no—
469C4—82no—
470C4—82no—
471C4C2×C4×D4×C12711yescharacteristic
472C4C4×#41×C12711yescharacteristic
473C4#525×C12711yescharacteristic
474C4#529×C12711yescharacteristic
475C2—42no—
476C2C4×#121×C12711yescharacteristic
477C2C127×#295011yescharacteristic
478C2C127×#295111yescharacteristic
479C2C127×#305911yescharacteristic
480C2C127×#306111yescharacteristic
481C2C127×#317511yescharacteristic
482C2C127×#317711yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC24×C127C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q16×C127C2semidirect
5. C127×#1969C2semidirect
6. C127×#1942C2semidirect
7. C127×#1935C2semidirect
10. C4×#107×C127C2semidirect
11. C127×#1763C2semidirect
18. #467×C127C4semidirect
233. #21525C127direct (N × H)
243. C2×C4×Q16C2×C127semidirect
246. #1969C2×C127semidirect
247. #1942C2×C127semidirect
248. #1935C2×C127semidirect
251. C4×#107C2×C127semidirect
252. #1763C2×C127semidirect
253. C127#21525direct (N × H)
260. #467C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#467×C1272
C2×C4×Q16×C1272
C2×#405×C1272
C127×#23232
C127×#19692
C127×#19422
C127×#19352
C127×#18942
C127×#18082
C4×#107×C1272
C127×#17632
#21525127