Finite Group Databasebeta

← C127×#20736 #44584409

Subgroups — C127×#20736 #44584409

Order 32512.

1358 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C127C211yesmaximal, characteristic
2C2×#431×C127C211yesmaximal, characteristic, complemented
3C127×#2283C211yesmaximal, characteristic, complemented
4C127×#1825C212yesmaximal, complemented
5C127×#1805C212yesmaximal, complemented
6C127×#1804C212yesmaximal, complemented
7C127×#1788C212yesmaximal
8C4×#103×C127C212yesmaximal, complemented
9C4×#102×C127C212yesmaximal, complemented
10C22×#41×C127C2211yescharacteristic
11C4×#41×C127—24no—
12C4×#41×C127C418yescomplemented
13C2×C4×Q8×C127C2211yescharacteristic
14C2×C4×Q8×C127C2211yescharacteristic
15C2×C4×D4×C127—21no—
16C2×C4×D4×C127—21no—
17C2×C4×D4×C127C2211yescharacteristic
18C2×C4×D4×C127C2211yescharacteristic
19C2×#117×C127—21no—
20C2×#117×C127C2211yescharacteristic
21C22×C42×C127—21no—
22C22×C42×C127C2211yescharacteristic
23#431×C127—24no—
24C2×C4⋊C8×C127C2212yes—
25C2×#103×C127C2214yes—
26C2×#102×C127C2214yes—
27C2×C22⋊C8×C127C2212yes—
28C2×C4×C8×C127C2212yes—
29#383×C127—21no—
30#382×C127C2212yes—
31#381×C127—21no—
32#380×C127C2212yes—
33C4×C4⋊C4×C127C2212yes—
34C4×C22⋊C4×C127—21no—
35#376×C127—21no—
36#340×C127C2214yes—
37#340×C127C2214yes—
38C2×#41×C127—24no—
39C2×#41×C127—24no—
40C2×#41×C127—22no—
41C2×#41×C127C2×C414yes—
42C22×Q8×C127C2311yescharacteristic
43C22×D4×C127—21no—
44C22×D4×C127C2311yescharacteristic
45C23×C4×C127—21no—
46C23×C4×C127—21no—
47C23×C4×C127—21no—
48C23×C4×C127D411yescharacteristic
49C23×C4×C127D411yescharacteristic
50C23×C4×C127C2311yescharacteristic
51C22×C8×C127C2314yes—
52C4×Q8×C127—22no—
53C4×Q8×C127—22no—
54C4×Q8×C127C2×C414yes—
55C4×Q8×C127C2×C414yes—
56C4×D4×C127—28no—
57C4×D4×C127—28no—
58C4×D4×C127—22no—
59C4×D4×C127—22no—
60C4×D4×C127C2×C414yes—
61C4×D4×C127C2×C414yes—
62#117×C127—22no—
63#117×C127—28no—
64#117×C127C2×C414yes—
65C2×C4⋊C4×C127—21no—
66C2×C4⋊C4×C127—21no—
67C2×C4⋊C4×C127C2314yes—
68C2×C4⋊C4×C127C2311yescharacteristic
69C2×C4⋊C4×C127C2311yescharacteristic
70C2×C22⋊C4×C127—21no—
71C2×C22⋊C4×C127—21no—
72C2×C22⋊C4×C127—21no—
73C2×C22⋊C4×C127—22no—
74C2×C42×C127—21no—
75C2×C42×C127—21no—
76C2×C42×C127—21no—
77C2×C42×C127—28no—
78C2×C42×C127—22no—
79C2×C42×C127C2×C414yes—
80C2×C42×C127D411yescharacteristic
81C2×C42×C127D411yescharacteristic
82C2×C42×C127D414yes—
83C2×C42×C127C2311yescharacteristic
84C2×C42×C127C2311yescharacteristic
85C4⋊C8×C127—24no—
86#103×C127—28no—
87#102×C127—28no—
88C22⋊C8×C127—24no—
89C4×C8×C127—24no—
90#95×C127—22no—
91#95×C127—22no—
92#95×C127—22no—
93#95×C127—22no—
94C24×C127—21no—
95C24×C127C2×D411yescharacteristic
96#41×C127—216no—
97#41×C127—28no—
98#41×C127—28no—
99C2×Q8×C127—21no—
100C2×Q8×C127—22no—
101C2×Q8×C127C22×C412yes—
102C2×Q8×C127#4114yes—
103C2×D4×C127—28no—
104C2×D4×C127—24no—
105C2×D4×C127—21no—
106C2×D4×C127—22no—
107C2×D4×C127C22×C412yes—
108C2×D4×C127#4114yes—
109C22×C4×C127—28no—
110C22×C4×C127—21no—
111C22×C4×C127—24no—
112C22×C4×C127—24no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—24no—
118C22×C4×C127—24no—
119C22×C4×C127—24no—
120C22×C4×C127—42no—
121C22×C4×C127—44no—
122C22×C4×C127—44no—
123C22×C4×C127C22⋊C414yes—
124C22×C4×C127C22⋊C414yes—
125C22×C4×C127C22×C412yes—
126C22×C4×C127C2×D411yescharacteristic
127C22×C4×C127C2×D411yescharacteristic
128C22×C4×C127C2×D411yescharacteristic
129C22×C4×C127C2×D411yescharacteristic
130C22×C4×C127C2×D412yes—
131C22×C4×C127C2×D411yescharacteristic
132C22×C4×C127C2411yescharacteristic
133C2×C8×C127—24no—
134C2×C8×C127—24no—
135C2×C8×C127—24no—
136C4⋊C4×C127—24no—
137C4⋊C4×C127—24no—
138C4⋊C4×C127—21no—
139C4⋊C4×C127—21no—
140C4⋊C4×C127—24no—
141C4⋊C4×C127—24no—
142C4⋊C4×C127C22×C412yes—
143C4⋊C4×C127C22×C412yes—
144C22⋊C4×C127—24no—
145C22⋊C4×C127—24no—
146C22⋊C4×C127—24no—
147C22⋊C4×C127—44no—
148C42×C127—24no—
149C42×C127—24no—
150C42×C127—24no—
151C42×C127—44no—
152C42×C127C22⋊C414yes—
153C42×C127C22⋊C414yes—
154C42×C127C22×C412yes—
155C42×C127C22×C412yes—
156C42×C127C2×D412yes—
157C42×C127C2×D412yes—
158C23×C127—22no—
159C23×C127—22no—
160C23×C127—24no—
161C23×C127—22no—
162C23×C127—22no—
163C23×C127—42no—
164C23×C127—42no—
165C23×C127C2×C22⋊C412yes—
166C23×C127C22×D411yescharacteristic
167Q8×C127—22no—
168Q8×C127—24no—
169Q8×C127#11714yes—
170D4×C127—216no—
171D4×C127—22no—
172D4×C127—24no—
173D4×C127#11714yes—
174C2×C4×C127—216no—
175C2×C4×C127—22no—
176C2×C4×C127—22no—
177C2×C4×C127—24no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
182C2×C4×C127—22no—
183C2×C4×C127—24no—
184C2×C4×C127—28no—
185C2×C4×C127—22no—
186C2×C4×C127—22no—
187C2×C4×C127—44no—
188C2×C4×C127—48no—
189C2×C4×C127—42no—
190C2×C4×C127—42no—
191C2×C4×C127—48no—
192C2×C4×C127—44no—
193C2×C4×C127—44no—
194C2×C4×C127—44no—
195C2×C4×C127C2×C22⋊C412yes—
196C2×C4×C127C2×C22⋊C412yes—
197C2×C4×C127C2×C22⋊C412yes—
198C2×C4×C127C2×C22⋊C412yes—
199C2×C4×C127C2×C22⋊C412yes—
200C2×C4×C127#13514yes—
201C2×C4×C127C23×C411yescharacteristic
202C2×C4×C127C22×D411yescharacteristic
203C2×C4×C127C2×#4112yes—
204C2×C4×C127C2×#4112yes—
205C8×C127—44no—
206C22×C127—22no—
207C22×C127—22no—
208C22×C127—22no—
209C22×C127—24no—
210C22×C127—44no—
211C22×C127—48no—
212C22×C127—42no—
213C22×C127—42no—
214C22×C127C22×C22⋊C411yescharacteristic
215C22×C127#52512yes—
216C22×C127C2×#13512yes—
217C22×C127#57512yes—
218C4×C127—22no—
219C4×C127—22no—
220C4×C127—22no—
221C4×C127—22no—
222C4×C127—24no—
223C4×C127—42no—
224C4×C127—42no—
225C4×C127—84no—
226C4×C127#41614yes—
227C4×C127C2×#11711yescharacteristic
228C4×C127C2×#11711yescharacteristic
229C4×C127#52512yes—
230#20736C12711yesmaximal, characteristic, direct product factor, Sylow
231C2×C127—42no—
232C2×C127—44no—
233C2×C127#228011yescharacteristic
234C2×C127C2×#41611yescharacteristic
235C2×C127#289611yescharacteristic
236C2×C127#310214yes—
237C2×C4×#41C2×C12711yescharacteristic
238C2×#431C2×C12711yescharacteristic, complemented
239#2283C2×C12711yescharacteristic, complemented
240#1825C2×C12712yescomplemented
241#1805C2×C12712yescomplemented
242#1804C2×C12712yescomplemented
243#1788C2×C12712yes—
244C4×#103C2×C12712yescomplemented
245C4×#102C2×C12712yescomplemented
246C127#2073611yescharacteristic, direct product factor, Sylow
247C22×#41C22×C12711yescharacteristic
248C4×#41—24no—
249C4×#41C4×C12718yescomplemented
250C2×C4×Q8C22×C12711yescharacteristic
251C2×C4×Q8C22×C12711yescharacteristic
252C2×C4×D4—21no—
253C2×C4×D4—21no—
254C2×C4×D4C22×C12711yescharacteristic
255C2×C4×D4C22×C12711yescharacteristic
256C2×#117—21no—
257C2×#117C22×C12711yescharacteristic
258C22×C42—21no—
259C22×C42C22×C12711yescharacteristic
260#431—24no—
261C2×C4⋊C8C22×C12712yes—
262C2×#103C22×C12714yes—
263C2×#102C22×C12714yes—
264C2×C22⋊C8C22×C12712yes—
265C2×C4×C8C22×C12712yes—
266#383—21no—
267#382C22×C12712yes—
268#381—21no—
269#380C22×C12712yes—
270C4×C4⋊C4C22×C12712yes—
271C4×C22⋊C4—21no—
272#376—21no—
273#340C22×C12714yes—
274#340C22×C12714yes—
275C2×#41—24no—
276C2×#41—24no—
277C2×#41—22no—
278C2×#41C2×C4×C12714yes—
279C22×Q8C23×C12711yescharacteristic
280C22×D4—21no—
281C22×D4C23×C12711yescharacteristic
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4D4×C12711yescharacteristic
286C23×C4D4×C12711yescharacteristic
287C23×C4C23×C12711yescharacteristic
288C22×C8C23×C12714yes—
289C4×Q8—22no—
290C4×Q8—22no—
291C4×Q8C2×C4×C12714yes—
292C4×Q8C2×C4×C12714yes—
293C4×D4—28no—
294C4×D4—28no—
295C4×D4—22no—
296C4×D4—22no—
297C4×D4C2×C4×C12714yes—
298C4×D4C2×C4×C12714yes—
299#117—22no—
300#117—28no—
301#117C2×C4×C12714yes—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4C23×C12714yes—
305C2×C4⋊C4C23×C12711yescharacteristic
306C2×C4⋊C4C23×C12711yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—22no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—28no—
315C2×C42—22no—
316C2×C42C2×C4×C12714yes—
317C2×C42D4×C12711yescharacteristic
318C2×C42D4×C12711yescharacteristic
319C2×C42D4×C12714yes—
320C2×C42C23×C12711yescharacteristic
321C2×C42C23×C12711yescharacteristic
322C4⋊C8—24no—
323#103—28no—
324#102—28no—
325C22⋊C8—24no—
326C4×C8—24no—
327#95—22no—
328#95—22no—
329#95—22no—
330#95—22no—
331C24—21no—
332C24C2×D4×C12711yescharacteristic
333#41—216no—
334#41—28no—
335#41—28no—
336C2×Q8—21no—
337C2×Q8—22no—
338C2×Q8C22×C4×C12712yes—
339C2×Q8#41×C12714yes—
340C2×D4—28no—
341C2×D4—24no—
342C2×D4—21no—
343C2×D4—22no—
344C2×D4C22×C4×C12712yes—
345C2×D4#41×C12714yes—
346C22×C4—28no—
347C22×C4—21no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—42no—
358C22×C4—44no—
359C22×C4—44no—
360C22×C4C22⋊C4×C12714yes—
361C22×C4C22⋊C4×C12714yes—
362C22×C4C22×C4×C12712yes—
363C22×C4C2×D4×C12711yescharacteristic
364C22×C4C2×D4×C12711yescharacteristic
365C22×C4C2×D4×C12711yescharacteristic
366C22×C4C2×D4×C12711yescharacteristic
367C22×C4C2×D4×C12712yes—
368C22×C4C2×D4×C12711yescharacteristic
369C22×C4C24×C12711yescharacteristic
370C2×C8—24no—
371C2×C8—24no—
372C2×C8—24no—
373C4⋊C4—24no—
374C4⋊C4—24no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—24no—
378C4⋊C4—24no—
379C4⋊C4C22×C4×C12712yes—
380C4⋊C4C22×C4×C12712yes—
381C22⋊C4—24no—
382C22⋊C4—24no—
383C22⋊C4—24no—
384C22⋊C4—44no—
385C42—24no—
386C42—24no—
387C42—24no—
388C42—44no—
389C42C22⋊C4×C12714yes—
390C42C22⋊C4×C12714yes—
391C42C22×C4×C12712yes—
392C42C22×C4×C12712yes—
393C42C2×D4×C12712yes—
394C42C2×D4×C12712yes—
395C23—22no—
396C23—22no—
397C23—24no—
398C23—22no—
399C23—22no—
400C23—42no—
401C23—42no—
402C23C2×C22⋊C4×C12712yes—
403C23C22×D4×C12711yescharacteristic
404Q8—22no—
405Q8—24no—
406Q8#117×C12714yes—
407D4—216no—
408D4—22no—
409D4—24no—
410D4#117×C12714yes—
411C2×C4—216no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—28no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—44no—
425C2×C4—48no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—48no—
429C2×C4—44no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4C2×C22⋊C4×C12712yes—
433C2×C4C2×C22⋊C4×C12712yes—
434C2×C4C2×C22⋊C4×C12712yes—
435C2×C4C2×C22⋊C4×C12712yes—
436C2×C4C2×C22⋊C4×C12712yes—
437C2×C4#135×C12714yes—
438C2×C4C23×C4×C12711yescharacteristic
439C2×C4C22×D4×C12711yescharacteristic
440C2×C4C2×#41×C12712yes—
441C2×C4C2×#41×C12712yes—
442C8—44no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—24no—
447C22—44no—
448C22—48no—
449C22—42no—
450C22—42no—
451C22C22×C22⋊C4×C12711yescharacteristic
452C22#525×C12712yes—
453C22C2×#135×C12712yes—
454C22#575×C12712yes—
455C4—22no—
456C4—22no—
457C4—22no—
458C4—22no—
459C4—24no—
460C4—42no—
461C4—42no—
462C4—84no—
463C4#416×C12714yes—
464C4C2×#117×C12711yescharacteristic
465C4C2×#117×C12711yescharacteristic
466C4#525×C12712yes—
467C2—42no—
468C2—44no—
469C2C127×#228011yescharacteristic
470C2C2×#416×C12711yescharacteristic
471C2C127×#289611yescharacteristic
472C2C127×#310214yes—
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C22×D4
prime radicalC22×#41×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#431×C127C2semidirect
3. C127×#2283C2semidirect
4. C127×#1825C2semidirect
5. C127×#1805C2semidirect
6. C127×#1804C2semidirect
8. C4×#103×C127C2semidirect
9. C4×#102×C127C2semidirect
12. C4×#41×C127C4semidirect
230. #20736C127direct (N × H)
238. C2×#431C2×C127semidirect
239. #2283C2×C127semidirect
240. #1825C2×C127semidirect
241. #1805C2×C127semidirect
242. #1804C2×C127semidirect
244. C4×#103C2×C127semidirect
245. C4×#102C2×C127semidirect
246. C127#20736direct (N × H)
249. C4×#41C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#41×C1272
C2×#431×C1272
C127×#22832
C127×#18252
C127×#18052
C127×#18042
C127×#17882
C4×#103×C1272
C4×#102×C1272
#20736127