Finite Group Databasebeta

← C127×#21655 #44585328

Subgroups — C127×#21655 #44585328

Order 32512.

886 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×#489×C127C211yesmaximal, characteristic
2C4×C4⋊Q8×C127C211yesmaximal, characteristic, complemented
3C4×#124×C127C211yesmaximal, characteristic
4C127×#1993C211yesmaximal, characteristic, complemented
5C127×#1959C211yesmaximal, characteristic
6C127×#1934C212yesmaximal
7C127×#1933C212yesmaximal, complemented
8C127×#1836C211yesmaximal, characteristic, complemented
9C127×#1763C212yesmaximal, complemented
10C127×#1762C212yesmaximal
11C4×#97×C127C211yesmaximal, characteristic, complemented
12C2×C4⋊Q8×C127C2211yescharacteristic
13C2×#124×C127C2211yescharacteristic
14C2×C4×Q8×C127—21no—
15C2×C4×Q8×C127C2211yescharacteristic
16C2×C4×D4×C127C2211yescharacteristic
17#489×C127C418yescomplemented
18C2×#103×C127C2212yes—
19C2×#103×C127C2212yes—
20C2×#102×C127C2212yes—
21C2×#102×C127C2212yes—
22C2×#97×C127C2211yescharacteristic
23C2×#97×C127C2212yes—
24C2×#97×C127C2211yescharacteristic
25C2×C4×C8×C127C2212yes—
26#391×C127—21no—
27#391×C127C2211yescharacteristic
28#390×C127C2211yescharacteristic
29#389×C127—21no—
30#389×C127C2212yes—
31#388×C127—21no—
32#388×C127—21no—
33#384×C127C2211yescharacteristic
34#382×C127C2211yescharacteristic
35C4×C4⋊C4×C127—21no—
36C4×C4⋊C4×C127C2212yes—
37C4×C22⋊C4×C127—21no—
38C4×C22⋊C4×C127—21no—
39C43×C127C2211yescharacteristic
40#340×C127C2212yes—
41#340×C127C2212yes—
42#340×C127C2212yes—
43#340×C127C2212yes—
44C22×Q8×C127—21no—
45C22×Q8×C127C2311yescharacteristic
46C22×D4×C127C2311yescharacteristic
47C23×C4×C127—21no—
48C22×C8×C127C2312yes—
49C22×C8×C127C2312yes—
50C4⋊Q8×C127—22no—
51C4⋊Q8×C127C2×C414yescomplemented
52#124×C127—22no—
53#124×C127C2×C414yes—
54C4×Q8×C127—24no—
55C4×Q8×C127—44no—
56C4×D4×C127—24no—
57C2×C4⋊C4×C127—21no—
58C2×C4⋊C4×C127—21no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—21no—
61C2×C4⋊C4×C127—21no—
62C2×C4⋊C4×C127C2311yescharacteristic
63C2×C4⋊C4×C127C2311yescharacteristic
64C2×C4⋊C4×C127C2312yes—
65C2×C4⋊C4×C127C2312yes—
66C2×C22⋊C4×C127—21no—
67C2×C22⋊C4×C127—21no—
68C2×C22⋊C4×C127—21no—
69C2×C22⋊C4×C127—21no—
70C2×C22⋊C4×C127—21no—
71C2×C42×C127—22no—
72C2×C42×C127—21no—
73C2×C42×C127D411yescharacteristic
74C2×C42×C127D411yescharacteristic
75C2×C42×C127D411yescharacteristic
76C2×C42×C127D411yescharacteristic
77C2×C42×C127C2311yescharacteristic
78C2×C42×C127C2311yescharacteristic
79C2×C42×C127C2311yescharacteristic
80#103×C127—24no—
81#103×C127C2×C418yescomplemented
82#102×C127—24no—
83#102×C127C2×C418yes—
84#97×C127—22no—
85#97×C127—24no—
86#97×C127C2×C414yescomplemented
87C4×C8×C127—24no—
88#95×C127—21no—
89#95×C127—21no—
90#95×C127—21no—
91#95×C127—21no—
92#95×C127—22no—
93#95×C127—22no—
94C24×C127—21no—
95C2×Q8×C127—24no—
96C2×Q8×C127—21no—
97C2×Q8×C127—22no—
98C2×Q8×C127—22no—
99C2×Q8×C127—42no—
100C2×Q8×C127—42no—
101C2×Q8×C127C22×C412yes—
102C2×D4×C127—22no—
103C2×D4×C127—22no—
104C2×D4×C127—21no—
105C2×D4×C127C22×C412yes—
106C22×C4×C127—21no—
107C22×C4×C127—22no—
108C22×C4×C127—21no—
109C22×C4×C127—21no—
110C22×C4×C127—22no—
111C22×C4×C127—42no—
112C22×C4×C127—42no—
113C22×C4×C127—42no—
114C22×C4×C127C2×D411yescharacteristic
115C22×C4×C127C2×D411yescharacteristic
116C22×C4×C127C2×D411yescharacteristic
117C22×C4×C127C2×D411yescharacteristic
118C22×C4×C127C2×D411yescharacteristic
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127C2411yescharacteristic
121C2×C8×C127—22no—
122C2×C8×C127—22no—
123C2×C8×C127—22no—
124C2×C8×C127—22no—
125C2×C8×C127C22×C414yes—
126C2×C8×C127#4114yes—
127C4⋊C4×C127—24no—
128C4⋊C4×C127—22no—
129C4⋊C4×C127—22no—
130C4⋊C4×C127—22no—
131C4⋊C4×C127—22no—
132C4⋊C4×C127—22no—
133C4⋊C4×C127—42no—
134C4⋊C4×C127—42no—
135C4⋊C4×C127—42no—
136C4⋊C4×C127—44no—
137C4⋊C4×C127C22×C414yes—
138C22⋊C4×C127—24no—
139C22⋊C4×C127—24no—
140C22⋊C4×C127—42no—
141C22⋊C4×C127—42no—
142C22⋊C4×C127—42no—
143C42×C127—22no—
144C42×C127—22no—
145C42×C127—22no—
146C42×C127—41no—
147C42×C127—41no—
148C42×C127—44no—
149C42×C127—42no—
150C42×C127C22×C412yes—
151C42×C127#4112yes—
152C42×C127#4114yes—
153C23×C127—22no—
154C23×C127—41no—
155C23×C127—41no—
156C23×C127—41no—
157C23×C127—41no—
158C23×C127—41no—
159C23×C127—41no—
160C23×C127C22×D411yescharacteristic
161Q8×C127—24no—
162Q8×C127—48no—
163Q8×C127—42no—
164D4×C127—24no—
165D4×C127—42no—
166C2×C4×C127—21no—
167C2×C4×C127—21no—
168C2×C4×C127—21no—
169C2×C4×C127—21no—
170C2×C4×C127—21no—
171C2×C4×C127—21no—
172C2×C4×C127—21no—
173C2×C4×C127—21no—
174C2×C4×C127—21no—
175C2×C4×C127—21no—
176C2×C4×C127—21no—
177C2×C4×C127—21no—
178C2×C4×C127—22no—
179C2×C4×C127—24no—
180C2×C4×C127—41no—
181C2×C4×C127—41no—
182C2×C4×C127—42no—
183C2×C4×C127—42no—
184C2×C4×C127—41no—
185C2×C4×C127—41no—
186C2×C4×C127—42no—
187C2×C4×C127—42no—
188C2×C4×C127—41no—
189C2×C4×C127—41no—
190C2×C4×C127—42no—
191C2×C4×C127—41no—
192C2×C4×C127—41no—
193C2×C4×C127—84no—
194C2×C4×C127C4×D412yes—
195C2×C4×C127C4×D412yes—
196C2×C4×C127#12412yes—
197C2×C4×C127#12412yes—
198C2×C4×C127AGL(1,ℤ/8)12yes—
199C2×C4×C127#13712yes—
200C2×C4×C127C23×C411yescharacteristic
201C2×C4×C127C2×#4112yes—
202C2×C4×C127C2×#4112yes—
203C2×C4×C127C2×#4111yescharacteristic
204C8×C127—24no—
205C8×C127—24no—
206C22×C127—42no—
207C22×C127—42no—
208C22×C127—42no—
209C22×C127—81no—
210C22×C127—81no—
211C22×C127—81no—
212C22×C127—81no—
213C22×C127C2×C4×D411yescharacteristic
214C22×C127C2×#12411yescharacteristic
215C22×C127#53211yescharacteristic
216C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
217C22×C127C2×#13711yescharacteristic
218C22×C127#57511yescharacteristic
219C22×C127#57511yescharacteristic
220C4×C127—22no—
221C4×C127—22no—
222C4×C127—22no—
223C4×C127—22no—
224C4×C127—22no—
225C4×C127—22no—
226C4×C127—44no—
227C4×C127—42no—
228C4×C127—81no—
229C4×C127—81no—
230C4×C127—82no—
231C4×C127C4×#4112yes—
232C4×C127#52912yes—
233#21655C12711yesmaximal, characteristic, direct product factor, Sylow
234C2×C127—82no—
235C2×C127C4×#12411yescharacteristic
236C2×C127C4×AGL(1,ℤ/8)11yescharacteristic
237C2×C127C4×#13711yescharacteristic
238C2×C127#314011yescharacteristic
239C2×C127#314111yescharacteristic
240C2×C127#318011yescharacteristic
241C2×C127#318111yescharacteristic
242C2×#489C2×C12711yescharacteristic
243C4×C4⋊Q8C2×C12711yescharacteristic, complemented
244C4×#124C2×C12711yescharacteristic
245#1993C2×C12711yescharacteristic, complemented
246#1959C2×C12711yescharacteristic
247#1934C2×C12712yes—
248#1933C2×C12712yescomplemented
249#1836C2×C12711yescharacteristic, complemented
250#1763C2×C12712yescomplemented
251#1762C2×C12712yes—
252C4×#97C2×C12711yescharacteristic, complemented
253C127#2165511yescharacteristic, direct product factor, Sylow
254C2×C4⋊Q8C22×C12711yescharacteristic
255C2×#124C22×C12711yescharacteristic
256C2×C4×Q8—21no—
257C2×C4×Q8C22×C12711yescharacteristic
258C2×C4×D4C22×C12711yescharacteristic
259#489C4×C12718yescomplemented
260C2×#103C22×C12712yes—
261C2×#103C22×C12712yes—
262C2×#102C22×C12712yes—
263C2×#102C22×C12712yes—
264C2×#97C22×C12711yescharacteristic
265C2×#97C22×C12712yes—
266C2×#97C22×C12711yescharacteristic
267C2×C4×C8C22×C12712yes—
268#391—21no—
269#391C22×C12711yescharacteristic
270#390C22×C12711yescharacteristic
271#389—21no—
272#389C22×C12712yes—
273#388—21no—
274#388—21no—
275#384C22×C12711yescharacteristic
276#382C22×C12711yescharacteristic
277C4×C4⋊C4—21no—
278C4×C4⋊C4C22×C12712yes—
279C4×C22⋊C4—21no—
280C4×C22⋊C4—21no—
281C43C22×C12711yescharacteristic
282#340C22×C12712yes—
283#340C22×C12712yes—
284#340C22×C12712yes—
285#340C22×C12712yes—
286C22×Q8—21no—
287C22×Q8C23×C12711yescharacteristic
288C22×D4C23×C12711yescharacteristic
289C23×C4—21no—
290C22×C8C23×C12712yes—
291C22×C8C23×C12712yes—
292C4⋊Q8—22no—
293C4⋊Q8C2×C4×C12714yescomplemented
294#124—22no—
295#124C2×C4×C12714yes—
296C4×Q8—24no—
297C4×Q8—44no—
298C4×D4—24no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4C23×C12711yescharacteristic
305C2×C4⋊C4C23×C12711yescharacteristic
306C2×C4⋊C4C23×C12712yes—
307C2×C4⋊C4C23×C12712yes—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C42—22no—
314C2×C42—21no—
315C2×C42D4×C12711yescharacteristic
316C2×C42D4×C12711yescharacteristic
317C2×C42D4×C12711yescharacteristic
318C2×C42D4×C12711yescharacteristic
319C2×C42C23×C12711yescharacteristic
320C2×C42C23×C12711yescharacteristic
321C2×C42C23×C12711yescharacteristic
322#103—24no—
323#103C2×C4×C12718yescomplemented
324#102—24no—
325#102C2×C4×C12718yes—
326#97—22no—
327#97—24no—
328#97C2×C4×C12714yescomplemented
329C4×C8—24no—
330#95—21no—
331#95—21no—
332#95—21no—
333#95—21no—
334#95—22no—
335#95—22no—
336C24—21no—
337C2×Q8—24no—
338C2×Q8—21no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—42no—
342C2×Q8—42no—
343C2×Q8C22×C4×C12712yes—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—21no—
347C2×D4C22×C4×C12712yes—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4C2×D4×C12711yescharacteristic
357C22×C4C2×D4×C12711yescharacteristic
358C22×C4C2×D4×C12711yescharacteristic
359C22×C4C2×D4×C12711yescharacteristic
360C22×C4C2×D4×C12711yescharacteristic
361C22×C4C2×D4×C12711yescharacteristic
362C22×C4C24×C12711yescharacteristic
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8C22×C4×C12714yes—
368C2×C8#41×C12714yes—
369C4⋊C4—24no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—42no—
378C4⋊C4—44no—
379C4⋊C4C22×C4×C12714yes—
380C22⋊C4—24no—
381C22⋊C4—24no—
382C22⋊C4—42no—
383C22⋊C4—42no—
384C22⋊C4—42no—
385C42—22no—
386C42—22no—
387C42—22no—
388C42—41no—
389C42—41no—
390C42—44no—
391C42—42no—
392C42C22×C4×C12712yes—
393C42#41×C12712yes—
394C42#41×C12714yes—
395C23—22no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23C22×D4×C12711yescharacteristic
403Q8—24no—
404Q8—48no—
405Q8—42no—
406D4—24no—
407D4—42no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—84no—
436C2×C4C4×D4×C12712yes—
437C2×C4C4×D4×C12712yes—
438C2×C4#124×C12712yes—
439C2×C4#124×C12712yes—
440C2×C4AGL(1,ℤ/8)×C12712yes—
441C2×C4#137×C12712yes—
442C2×C4C23×C4×C12711yescharacteristic
443C2×C4C2×#41×C12712yes—
444C2×C4C2×#41×C12712yes—
445C2×C4C2×#41×C12711yescharacteristic
446C8—24no—
447C8—24no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22C2×C4×D4×C12711yescharacteristic
456C22C2×#124×C12711yescharacteristic
457C22#532×C12711yescharacteristic
458C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
459C22C2×#137×C12711yescharacteristic
460C22#575×C12711yescharacteristic
461C22#575×C12711yescharacteristic
462C4—22no—
463C4—22no—
464C4—22no—
465C4—22no—
466C4—22no—
467C4—22no—
468C4—44no—
469C4—42no—
470C4—81no—
471C4—81no—
472C4—82no—
473C4C4×#41×C12712yes—
474C4#529×C12712yes—
475C2—82no—
476C2C4×#124×C12711yescharacteristic
477C2C4×AGL(1,ℤ/8)×C12711yescharacteristic
478C2C4×#137×C12711yescharacteristic
479C2C127×#314011yescharacteristic
480C2C127×#314111yescharacteristic
481C2C127×#318011yescharacteristic
482C2C127×#318111yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×D4×C127C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C43×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊Q8×C127C2semidirect
4. C127×#1993C2semidirect
7. C127×#1933C2semidirect
8. C127×#1836C2semidirect
9. C127×#1763C2semidirect
11. C4×#97×C127C2semidirect
17. #489×C127C4semidirect
51. C4⋊Q8×C127C2×C4semidirect
81. #103×C127C2×C4semidirect
86. #97×C127C2×C4semidirect
233. #21655C127direct (N × H)
243. C4×C4⋊Q8C2×C127semidirect
245. #1993C2×C127semidirect
248. #1933C2×C127semidirect
249. #1836C2×C127semidirect
250. #1763C2×C127semidirect
252. C4×#97C2×C127semidirect
253. C127#21655direct (N × H)
259. #489C4×C127semidirect
293. C4⋊Q8C2×C4×C127semidirect
323. #103C2×C4×C127semidirect
328. #97C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#489×C1272
C4×C4⋊Q8×C1272
C4×#124×C1272
C127×#19932
C127×#19592
C127×#19342
C127×#19332
C127×#18362
C127×#17632
C127×#17622
C4×#97×C1272
#21655127