Finite Group Databasebeta

← C127×#20749 #44584422

Subgroups — C127×#20749 #44584422

Order 32512.

1258 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3428C211yesmaximal, characteristic
2C127×#2921C211yesmaximal, characteristic, complemented
3C127×#2298C211yesmaximal, characteristic, complemented
4C127×#1826C212yesmaximal, complemented
5C127×#1806C214yesmaximal, complemented
6C127×#1789C212yesmaximal
7C127×#1759C212yesmaximal, complemented
8C4×#104×C127C212yesmaximal, complemented
9C22×#41×C127C2211yescharacteristic
10#520×C127—22no—
11#520×C127C414yescomplemented
12#519×C127C412yescomplemented
13#518×C127—22no—
14#518×C127C412yescomplemented
15C4×#41×C127—22no—
16C4×#41×C127C2212yes—
17C4×#41×C127C2212yes—
18C2×#117×C127—22no—
19C2×#117×C127C2211yescharacteristic
20C2×#117×C127C2211yescharacteristic
21#433×C127—22no—
22#433×C127—22no—
23#423×C127C2212yescomplemented
24C2×#104×C127C2214yes—
25C2×#104×C127C2214yes—
26#407×C127C2212yes—
27C4×M16×C127C2212yescomplemented
28#388×C127—22no—
29#387×C127—22no—
30C4×C4⋊C4×C127C2212yescomplemented
31C4×C22⋊C4×C127C2212yes—
32#376×C127C2211yescharacteristic, complemented
33C43×C127C2211yescharacteristic, complemented
34#339×C127C2214yescomplemented
35#339×C127C2214yescomplemented
36C2×#41×C127—28no—
37C2×#41×C127—21no—
38C2×#41×C127—21no—
39C2×#41×C127C2×C412yes—
40C2×#41×C127C2312yes—
41C22×Q8×C127C2×C411yescharacteristic
42C22×D4×C127—21no—
43C22×D4×C127C2×C411yescharacteristic
44C23×C4×C127—21no—
45C23×C4×C127C2311yescharacteristic
46C2×M16×C127C2314yes—
47C4×Q8×C127—24no—
48C4×Q8×C127C2×C414yes—
49C4×Q8×C127C2×C414yes—
50C4×D4×C127—24no—
51C4×D4×C127—24no—
52C4×D4×C127—24no—
53C4×D4×C127—24no—
54C4×D4×C127—24no—
55C4×D4×C127C2×C414yes—
56C4×D4×C127C2×C414yes—
57#117×C127—21no—
58#117×C127—21no—
59#117×C127—24no—
60#117×C127—24no—
61#117×C127—22no—
62#117×C127—22no—
63#117×C127C2×C412yes—
64#117×C127C2×C412yes—
65#117×C127C2×C412yes—
66#117×C127D412yes—
67#117×C127D412yes—
68#117×C127C2312yes—
69C2×C4⋊C4×C127—24no—
70C2×C4⋊C4×C127—22no—
71C2×C4⋊C4×C127C2×C412yes—
72C2×C4⋊C4×C127D412yes—
73C2×C22⋊C4×C127—21no—
74C2×C22⋊C4×C127—24no—
75C2×C22⋊C4×C127—22no—
76C2×C22⋊C4×C127D412yes—
77C2×C42×C127—21no—
78C2×C42×C127—22no—
79C2×C42×C127—22no—
80C2×C42×C127—22no—
81C2×C42×C127C2312yes—
82C2×C42×C127C2312yes—
83C2×C42×C127C2311yescharacteristic
84C2×C42×C127C2311yescharacteristic
85C4⋊C8×C127—24no—
86#104×C127—28no—
87#104×C127—28no—
88C22⋊C8×C127—22no—
89C22⋊C8×C127—22no—
90#97×C127—22no—
91C4×C8×C127—22no—
92#95×C127—22no—
93#95×C127—22no—
94#95×C127—22no—
95C24×C127—21no—
96C24×C127C2×D411yescharacteristic
97#41×C127—28no—
98#41×C127—28no—
99#41×C127—24no—
100#41×C127—24no—
101#41×C127—24no—
102#41×C127#4118yes—
103C2×Q8×C127—24no—
104C2×Q8×C127—21no—
105C2×Q8×C127C22×C412yes—
106C2×D4×C127—28no—
107C2×D4×C127—22no—
108C2×D4×C127—22no—
109C2×D4×C127—24no—
110C2×D4×C127—21no—
111C2×D4×C127C22×C412yes—
112C22×C4×C127—28no—
113C22×C4×C127—21no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—24no—
117C22×C4×C127—22no—
118C22×C4×C127—22no—
119C22×C4×C127—24no—
120C22×C4×C127—24no—
121C22×C4×C127—22no—
122C22×C4×C127C22×C411yescharacteristic
123C22×C4×C127C22×C411yescharacteristic
124C22×C4×C127C2×D411yescharacteristic
125C22×C4×C127C2×D411yescharacteristic
126C22×C4×C127C2×D411yescharacteristic
127C22×C4×C127C2×D412yes—
128C22×C4×C127C2×D412yes—
129C22×C4×C127C2411yescharacteristic
130M16×C127—24no—
131M16×C127—24no—
132C2×C8×C127—24no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—24no—
135C4⋊C4×C127—24no—
136C4⋊C4×C127—44no—
137C4⋊C4×C127C22⋊C414yes—
138C4⋊C4×C127C22⋊C414yes—
139C4⋊C4×C127C22×C414yes—
140C22⋊C4×C127—22no—
141C22⋊C4×C127—22no—
142C22⋊C4×C127—24no—
143C22⋊C4×C127—24no—
144C22⋊C4×C127—44no—
145C22⋊C4×C127C22⋊C414yes—
146C22⋊C4×C127C22⋊C414yes—
147C42×C127—24no—
148C42×C127—24no—
149C42×C127—22no—
150C42×C127—22no—
151C42×C127—24no—
152C42×C127—24no—
153C42×C127—44no—
154C42×C127C22×C412yes—
155C42×C127C22×C412yes—
156C42×C127C2×D412yes—
157C42×C127C2×D412yes—
158C23×C127—24no—
159C23×C127—22no—
160C23×C127—22no—
161C23×C127—42no—
162C23×C127—82no—
163C23×C127C2×C22⋊C411yescharacteristic
164C23×C127C2×C22⋊C411yescharacteristic
165C23×C127C22×D411yescharacteristic
166Q8×C127—24no—
167Q8×C127—22no—
168Q8×C127#11714yes—
169D4×C127—28no—
170D4×C127—24no—
171D4×C127—28no—
172D4×C127—22no—
173D4×C127#11714yes—
174C2×C4×C127—24no—
175C2×C4×C127—28no—
176C2×C4×C127—22no—
177C2×C4×C127—22no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—28no—
182C2×C4×C127—22no—
183C2×C4×C127—24no—
184C2×C4×C127—24no—
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—84no—
193C2×C4×C127—84no—
194C2×C4×C127—82no—
195C2×C4×C127C2×C22⋊C411yescharacteristic
196C2×C4×C127C2×C22⋊C414yes—
197C2×C4×C127C2×C22⋊C414yes—
198C2×C4×C127C2×C22⋊C411yescharacteristic
199C2×C4×C127C23×C411yescharacteristic
200C2×C4×C127C22×D411yescharacteristic
201C2×C4×C127C2×#4114yes—
202C8×C127—44no—
203C22×C127—22no—
204C22×C127—22no—
205C22×C127—22no—
206C22×C127—21no—
207C22×C127—21no—
208C22×C127—24no—
209C22×C127—44no—
210C22×C127—82no—
211C22×C127—84no—
212C22×C127C22×C22⋊C411yescharacteristic
213C22×C127#52512yes—
214C4×C127—24no—
215C4×C127—24no—
216C4×C127—21no—
217C4×C127—24no—
218C4×C127—21no—
219C4×C127—44no—
220C4×C127—44no—
221C4×C127—82no—
222C4×C127C2×#11712yes—
223C4×C127#52512yes—
224#20749C12711yesmaximal, characteristic, direct product factor, Sylow
225C2×C127—22no—
226C2×C127—41no—
227C2×C127—41no—
228C2×C127—44no—
229C2×C127#228011yescharacteristic
230C2×C127#290112yes—
231#3428C2×C12711yescharacteristic
232#2921C2×C12711yescharacteristic, complemented
233#2298C2×C12711yescharacteristic, complemented
234#1826C2×C12712yescomplemented
235#1806C2×C12714yescomplemented
236#1789C2×C12712yes—
237#1759C2×C12712yescomplemented
238C4×#104C2×C12712yescomplemented
239C127#2074911yescharacteristic, direct product factor, Sylow
240C22×#41C22×C12711yescharacteristic
241#520—22no—
242#520C4×C12714yescomplemented
243#519C4×C12712yescomplemented
244#518—22no—
245#518C4×C12712yescomplemented
246C4×#41—22no—
247C4×#41C22×C12712yes—
248C4×#41C22×C12712yes—
249C2×#117—22no—
250C2×#117C22×C12711yescharacteristic
251C2×#117C22×C12711yescharacteristic
252#433—22no—
253#433—22no—
254#423C22×C12712yescomplemented
255C2×#104C22×C12714yes—
256C2×#104C22×C12714yes—
257#407C22×C12712yes—
258C4×M16C22×C12712yescomplemented
259#388—22no—
260#387—22no—
261C4×C4⋊C4C22×C12712yescomplemented
262C4×C22⋊C4C22×C12712yes—
263#376C22×C12711yescharacteristic, complemented
264C43C22×C12711yescharacteristic, complemented
265#339C22×C12714yescomplemented
266#339C22×C12714yescomplemented
267C2×#41—28no—
268C2×#41—21no—
269C2×#41—21no—
270C2×#41C2×C4×C12712yes—
271C2×#41C23×C12712yes—
272C22×Q8C2×C4×C12711yescharacteristic
273C22×D4—21no—
274C22×D4C2×C4×C12711yescharacteristic
275C23×C4—21no—
276C23×C4C23×C12711yescharacteristic
277C2×M16C23×C12714yes—
278C4×Q8—24no—
279C4×Q8C2×C4×C12714yes—
280C4×Q8C2×C4×C12714yes—
281C4×D4—24no—
282C4×D4—24no—
283C4×D4—24no—
284C4×D4—24no—
285C4×D4—24no—
286C4×D4C2×C4×C12714yes—
287C4×D4C2×C4×C12714yes—
288#117—21no—
289#117—21no—
290#117—24no—
291#117—24no—
292#117—22no—
293#117—22no—
294#117C2×C4×C12712yes—
295#117C2×C4×C12712yes—
296#117C2×C4×C12712yes—
297#117D4×C12712yes—
298#117D4×C12712yes—
299#117C23×C12712yes—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4C2×C4×C12712yes—
303C2×C4⋊C4D4×C12712yes—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4D4×C12712yes—
308C2×C42—21no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—22no—
312C2×C42C23×C12712yes—
313C2×C42C23×C12712yes—
314C2×C42C23×C12711yescharacteristic
315C2×C42C23×C12711yescharacteristic
316C4⋊C8—24no—
317#104—28no—
318#104—28no—
319C22⋊C8—22no—
320C22⋊C8—22no—
321#97—22no—
322C4×C8—22no—
323#95—22no—
324#95—22no—
325#95—22no—
326C24—21no—
327C24C2×D4×C12711yescharacteristic
328#41—28no—
329#41—28no—
330#41—24no—
331#41—24no—
332#41—24no—
333#41#41×C12718yes—
334C2×Q8—24no—
335C2×Q8—21no—
336C2×Q8C22×C4×C12712yes—
337C2×D4—28no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—24no—
341C2×D4—21no—
342C2×D4C22×C4×C12712yes—
343C22×C4—28no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—22no—
353C22×C4C22×C4×C12711yescharacteristic
354C22×C4C22×C4×C12711yescharacteristic
355C22×C4C2×D4×C12711yescharacteristic
356C22×C4C2×D4×C12711yescharacteristic
357C22×C4C2×D4×C12711yescharacteristic
358C22×C4C2×D4×C12712yes—
359C22×C4C2×D4×C12712yes—
360C22×C4C24×C12711yescharacteristic
361M16—24no—
362M16—24no—
363C2×C8—24no—
364C4⋊C4—22no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—44no—
368C4⋊C4C22⋊C4×C12714yes—
369C4⋊C4C22⋊C4×C12714yes—
370C4⋊C4C22×C4×C12714yes—
371C22⋊C4—22no—
372C22⋊C4—22no—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—44no—
376C22⋊C4C22⋊C4×C12714yes—
377C22⋊C4C22⋊C4×C12714yes—
378C42—24no—
379C42—24no—
380C42—22no—
381C42—22no—
382C42—24no—
383C42—24no—
384C42—44no—
385C42C22×C4×C12712yes—
386C42C22×C4×C12712yes—
387C42C2×D4×C12712yes—
388C42C2×D4×C12712yes—
389C23—24no—
390C23—22no—
391C23—22no—
392C23—42no—
393C23—82no—
394C23C2×C22⋊C4×C12711yescharacteristic
395C23C2×C22⋊C4×C12711yescharacteristic
396C23C22×D4×C12711yescharacteristic
397Q8—24no—
398Q8—22no—
399Q8#117×C12714yes—
400D4—28no—
401D4—24no—
402D4—28no—
403D4—22no—
404D4#117×C12714yes—
405C2×C4—24no—
406C2×C4—28no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—28no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—84no—
424C2×C4—84no—
425C2×C4—82no—
426C2×C4C2×C22⋊C4×C12711yescharacteristic
427C2×C4C2×C22⋊C4×C12714yes—
428C2×C4C2×C22⋊C4×C12714yes—
429C2×C4C2×C22⋊C4×C12711yescharacteristic
430C2×C4C23×C4×C12711yescharacteristic
431C2×C4C22×D4×C12711yescharacteristic
432C2×C4C2×#41×C12714yes—
433C8—44no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—21no—
438C22—21no—
439C22—24no—
440C22—44no—
441C22—82no—
442C22—84no—
443C22C22×C22⋊C4×C12711yescharacteristic
444C22#525×C12712yes—
445C4—24no—
446C4—24no—
447C4—21no—
448C4—24no—
449C4—21no—
450C4—44no—
451C4—44no—
452C4—82no—
453C4C2×#117×C12712yes—
454C4#525×C12712yes—
455C2—22no—
456C2—41no—
457C2—41no—
458C2—44no—
459C2C127×#228011yescharacteristic
460C2C127×#290112yes—
subgroupG/H
centerC2×C4×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC22×C127C22×C22⋊C4
prime radicalC22×#41×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2921C2semidirect
3. C127×#2298C2semidirect
4. C127×#1826C2semidirect
5. C127×#1806C2semidirect
7. C127×#1759C2semidirect
8. C4×#104×C127C2semidirect
11. #520×C127C4semidirect
12. #519×C127C4semidirect
14. #518×C127C4semidirect
23. #423×C127C22semidirect
27. C4×M16×C127C22semidirect
30. C4×C4⋊C4×C127C22semidirect
32. #376×C127C22semidirect
33. C43×C127C22semidirect
34. #339×C127C22semidirect
35. #339×C127C22semidirect
224. #20749C127direct (N × H)
232. #2921C2×C127semidirect
233. #2298C2×C127semidirect
234. #1826C2×C127semidirect
235. #1806C2×C127semidirect
237. #1759C2×C127semidirect
238. C4×#104C2×C127semidirect
239. C127#20749direct (N × H)
242. #520C4×C127semidirect
243. #519C4×C127semidirect
245. #518C4×C127semidirect
254. #423C22×C127semidirect
258. C4×M16C22×C127semidirect
261. C4×C4⋊C4C22×C127semidirect
263. #376C22×C127semidirect
264. C43C22×C127semidirect
265. #339C22×C127semidirect
266. #339C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34282
C127×#29212
C127×#22982
C127×#18262
C127×#18062
C127×#17892
C127×#17592
C4×#104×C1272
#20749127