Finite Group Databasebeta

← C127×#21134 #44584807

Subgroups — C127×#21134 #44584807

Order 32512.

938 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D8×C127C211yesmaximal, characteristic
2C127×#2319C211yesmaximal, characteristic, complemented
3C127×#2275C211yesmaximal, characteristic, complemented
4C127×#1926C212yesmaximal, complemented
5C127×#1918C212yesmaximal, complemented
6C127×#1879C212yesmaximal
7C127×#1864C212yesmaximal, complemented
8C4×#106×C127C211yesmaximal, characteristic, complemented
9C127×#1762C211yesmaximal, characteristic, complemented
10C127×#1762C211yesmaximal, characteristic, complemented
11C127×#1746C211yesmaximal, characteristic, complemented
12C22×D8×C127C2211yescharacteristic
13C2×C4×D4×C127C2212yes—
14C2×C4×D4×C127C2211yescharacteristic
15C2×C4×D4×C127C2211yescharacteristic
16C4×D8×C127C418yescomplemented
17C2×#107×C127C2211yescharacteristic
18C2×#106×C127C2212yes—
19C2×#102×C127C2212yes—
20C2×#102×C127C2212yes—
21C2×#102×C127C2211yescharacteristic
22C2×#102×C127C2211yescharacteristic
23C2×#97×C127C2211yescharacteristic
24C2×C4×C8×C127C2211yescharacteristic
25#390×C127C2212yes—
26#389×C127C2212yes—
27#388×C127—22no—
28#381×C127—21no—
29#380×C127—21no—
30C4×C4⋊C4×C127C2211yescharacteristic
31C4×C4⋊C4×C127C2212yes—
32C4×C4⋊C4×C127C2211yescharacteristic
33C4×C22⋊C4×C127—21no—
34C4×C22⋊C4×C127—22no—
35#376×C127C2211yescharacteristic
36C2×#95×C127—21no—
37#340×C127C2212yes—
38#340×C127C2212yes—
39#340×C127C2212yes—
40#336×C127C2212yes—
41#336×C127C2212yes—
42C22×D4×C127C2311yescharacteristic
43C22×D4×C127C2311yescharacteristic
44C23×C4×C127—22no—
45C23×C4×C127—21no—
46C23×C4×C127—21no—
47C2×D8×C127—24no—
48C2×D8×C127C2×C414yes—
49C22×C8×C127C2312yes—
50C22×C8×C127C2311yescharacteristic
51C22×C8×C127C2311yescharacteristic
52C4×D4×C127—24no—
53C4×D4×C127—24no—
54C4×D4×C127—22no—
55C4×D4×C127—22no—
56C4×D4×C127C2×C414yes—
57C4×D4×C127C2×C414yescomplemented
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127C2312yes—
60C2×C4⋊C4×C127C2311yescharacteristic
61C2×C4⋊C4×C127C2311yescharacteristic
62C2×C4⋊C4×C127C2312yes—
63C2×C22⋊C4×C127—22no—
64C2×C22⋊C4×C127—21no—
65C2×C22⋊C4×C127—21no—
66C2×C22⋊C4×C127—22no—
67C2×C22⋊C4×C127—22no—
68C2×C42×C127—22no—
69C2×C42×C127—21no—
70C2×C42×C127—21no—
71C2×C42×C127C2312yes—
72C2×C42×C127C2311yescharacteristic
73#107×C127C2×C414yescomplemented
74#106×C127—24no—
75#102×C127—24no—
76#102×C127—24no—
77#102×C127C2×C414yes—
78#102×C127C2×C414yescomplemented
79#97×C127—22no—
80C4×C8×C127C2×C414yescomplemented
81#95×C127—22no—
82#95×C127—21no—
83#95×C127—21no—
84#95×C127—22no—
85#95×C127D411yescharacteristic
86#95×C127D411yescharacteristic
87#95×C127D412yes—
88C24×C127—21no—
89C24×C127—21no—
90C2×D4×C127—22no—
91C2×D4×C127—21no—
92C2×D4×C127—22no—
93C2×D4×C127—22no—
94C2×D4×C127—21no—
95C2×D4×C127C22×C412yes—
96C2×D4×C127C22×C412yes—
97C2×D4×C127#4114yes—
98C22×C4×C127—21no—
99C22×C4×C127—22no—
100C22×C4×C127—21no—
101C22×C4×C127—28no—
102C22×C4×C127—24no—
103C22×C4×C127—24no—
104C22×C4×C127—22no—
105C22×C4×C127—82no—
106C22×C4×C127—82no—
107C22×C4×C127—82no—
108C22×C4×C127—82no—
109C22×C4×C127C2×D412yes—
110C22×C4×C127C2×D412yes—
111C22×C4×C127C2×D411yescharacteristic
112C22×C4×C127C2×D411yescharacteristic
113C22×C4×C127C2411yescharacteristic
114D8×C127—28no—
115C2×C8×C127—22no—
116C2×C8×C127—22no—
117C2×C8×C127—22no—
118C2×C8×C127—22no—
119C2×C8×C127—22no—
120C2×C8×C127C22×C412yes—
121C2×C8×C127C22×C412yes—
122C4⋊C4×C127—21no—
123C4⋊C4×C127—21no—
124C4⋊C4×C127—22no—
125C4⋊C4×C127—22no—
126C4⋊C4×C127—22no—
127C4⋊C4×C127—82no—
128C4⋊C4×C127C22×C412yes—
129C4⋊C4×C127C22×C412yes—
130C4⋊C4×C127#4114yes—
131C22⋊C4×C127—28no—
132C22⋊C4×C127—24no—
133C22⋊C4×C127—24no—
134C22⋊C4×C127—82no—
135C22⋊C4×C127—82no—
136C42×C127—22no—
137C42×C127—22no—
138C42×C127—81no—
139C42×C127—81no—
140C42×C127—82no—
141C42×C127C22×C412yes—
142C42×C127#4112yes—
143C23×C127—22no—
144C23×C127—24no—
145C23×C127—22no—
146C23×C127—42no—
147C23×C127—41no—
148C23×C127—41no—
149C23×C127—42no—
150C23×C127—42no—
151C23×C127—41no—
152C23×C127—41no—
153C23×C127C22×D411yescharacteristic
154D4×C127—22no—
155D4×C127—22no—
156D4×C127—22no—
157D4×C127—24no—
158D4×C127—42no—
159D4×C127#11714yes—
160C2×C4×C127—22no—
161C2×C4×C127—21no—
162C2×C4×C127—21no—
163C2×C4×C127—22no—
164C2×C4×C127—22no—
165C2×C4×C127—22no—
166C2×C4×C127—22no—
167C2×C4×C127—24no—
168C2×C4×C127—22no—
169C2×C4×C127—22no—
170C2×C4×C127—22no—
171C2×C4×C127—22no—
172C2×C4×C127—42no—
173C2×C4×C127—42no—
174C2×C4×C127—42no—
175C2×C4×C127—42no—
176C2×C4×C127—42no—
177C2×C4×C127—42no—
178C2×C4×C127—42no—
179C2×C4×C127—84no—
180C2×C4×C127—84no—
181C2×C4×C127—88no—
182C2×C4×C127C4×D412yes—
183C2×C4×C127C4×D412yes—
184C2×C4×C127C23×C411yescharacteristic
185C2×C4×C127C2×#4112yes—
186C2×C4×C127C2×#4112yes—
187C2×C4×C127C2×#4111yescharacteristic
188C8×C127—22no—
189C8×C127—22no—
190C8×C127—42no—
191C22×C127—24no—
192C22×C127—44no—
193C22×C127—44no—
194C22×C127—42no—
195C22×C127—42no—
196C22×C127—42no—
197C22×C127—42no—
198C22×C127—42no—
199C22×C127—82no—
200C22×C127—82no—
201C22×C127C2×C4×D411yescharacteristic
202C22×C127#52512yes—
203C22×C127#57612yes—
204C22×C127#57711yescharacteristic
205C22×C127#57711yescharacteristic
206C4×C127—22no—
207C4×C127—22no—
208C4×C127—42no—
209C4×C127—44no—
210C4×C127—42no—
211C4×C127—42no—
212C4×C127—42no—
213C4×C127—82no—
214C4×C127C2×#11711yescharacteristic
215C4×C127C4×#4111yescharacteristic
216C4×C127#52912yes—
217#21134C12711yesmaximal, characteristic, direct product factor, Sylow
218C2×C127—44no—
219C2×C127—82no—
220C2×C127#229011yescharacteristic
221C2×C127#294811yescharacteristic
222C2×C127#295211yescharacteristic
223C2×C127#311812yes—
224C2×C127#311912yes—
225C2×C4×D8C2×C12711yescharacteristic
226#2319C2×C12711yescharacteristic, complemented
227#2275C2×C12711yescharacteristic, complemented
228#1926C2×C12712yescomplemented
229#1918C2×C12712yescomplemented
230#1879C2×C12712yes—
231#1864C2×C12712yescomplemented
232C4×#106C2×C12711yescharacteristic, complemented
233#1762C2×C12711yescharacteristic, complemented
234#1762C2×C12711yescharacteristic, complemented
235#1746C2×C12711yescharacteristic, complemented
236C127#2113411yescharacteristic, direct product factor, Sylow
237C22×D8C22×C12711yescharacteristic
238C2×C4×D4C22×C12712yes—
239C2×C4×D4C22×C12711yescharacteristic
240C2×C4×D4C22×C12711yescharacteristic
241C4×D8C4×C12718yescomplemented
242C2×#107C22×C12711yescharacteristic
243C2×#106C22×C12712yes—
244C2×#102C22×C12712yes—
245C2×#102C22×C12712yes—
246C2×#102C22×C12711yescharacteristic
247C2×#102C22×C12711yescharacteristic
248C2×#97C22×C12711yescharacteristic
249C2×C4×C8C22×C12711yescharacteristic
250#390C22×C12712yes—
251#389C22×C12712yes—
252#388—22no—
253#381—21no—
254#380—21no—
255C4×C4⋊C4C22×C12711yescharacteristic
256C4×C4⋊C4C22×C12712yes—
257C4×C4⋊C4C22×C12711yescharacteristic
258C4×C22⋊C4—21no—
259C4×C22⋊C4—22no—
260#376C22×C12711yescharacteristic
261C2×#95—21no—
262#340C22×C12712yes—
263#340C22×C12712yes—
264#340C22×C12712yes—
265#336C22×C12712yes—
266#336C22×C12712yes—
267C22×D4C23×C12711yescharacteristic
268C22×D4C23×C12711yescharacteristic
269C23×C4—22no—
270C23×C4—21no—
271C23×C4—21no—
272C2×D8—24no—
273C2×D8C2×C4×C12714yes—
274C22×C8C23×C12712yes—
275C22×C8C23×C12711yescharacteristic
276C22×C8C23×C12711yescharacteristic
277C4×D4—24no—
278C4×D4—24no—
279C4×D4—22no—
280C4×D4—22no—
281C4×D4C2×C4×C12714yes—
282C4×D4C2×C4×C12714yescomplemented
283C2×C4⋊C4—22no—
284C2×C4⋊C4C23×C12712yes—
285C2×C4⋊C4C23×C12711yescharacteristic
286C2×C4⋊C4C23×C12711yescharacteristic
287C2×C4⋊C4C23×C12712yes—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C42—22no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42C23×C12712yes—
297C2×C42C23×C12711yescharacteristic
298#107C2×C4×C12714yescomplemented
299#106—24no—
300#102—24no—
301#102—24no—
302#102C2×C4×C12714yes—
303#102C2×C4×C12714yescomplemented
304#97—22no—
305C4×C8C2×C4×C12714yescomplemented
306#95—22no—
307#95—21no—
308#95—21no—
309#95—22no—
310#95D4×C12711yescharacteristic
311#95D4×C12711yescharacteristic
312#95D4×C12712yes—
313C24—21no—
314C24—21no—
315C2×D4—22no—
316C2×D4—21no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—21no—
320C2×D4C22×C4×C12712yes—
321C2×D4C22×C4×C12712yes—
322C2×D4#41×C12714yes—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—28no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—22no—
330C22×C4—82no—
331C22×C4—82no—
332C22×C4—82no—
333C22×C4—82no—
334C22×C4C2×D4×C12712yes—
335C22×C4C2×D4×C12712yes—
336C22×C4C2×D4×C12711yescharacteristic
337C22×C4C2×D4×C12711yescharacteristic
338C22×C4C24×C12711yescharacteristic
339D8—28no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8C22×C4×C12712yes—
346C2×C8C22×C4×C12712yes—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—82no—
353C4⋊C4C22×C4×C12712yes—
354C4⋊C4C22×C4×C12712yes—
355C4⋊C4#41×C12714yes—
356C22⋊C4—28no—
357C22⋊C4—24no—
358C22⋊C4—24no—
359C22⋊C4—82no—
360C22⋊C4—82no—
361C42—22no—
362C42—22no—
363C42—81no—
364C42—81no—
365C42—82no—
366C42C22×C4×C12712yes—
367C42#41×C12712yes—
368C23—22no—
369C23—24no—
370C23—22no—
371C23—42no—
372C23—41no—
373C23—41no—
374C23—42no—
375C23—42no—
376C23—41no—
377C23—41no—
378C23C22×D4×C12711yescharacteristic
379D4—22no—
380D4—22no—
381D4—22no—
382D4—24no—
383D4—42no—
384D4#117×C12714yes—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—84no—
405C2×C4—84no—
406C2×C4—88no—
407C2×C4C4×D4×C12712yes—
408C2×C4C4×D4×C12712yes—
409C2×C4C23×C4×C12711yescharacteristic
410C2×C4C2×#41×C12712yes—
411C2×C4C2×#41×C12712yes—
412C2×C4C2×#41×C12711yescharacteristic
413C8—22no—
414C8—22no—
415C8—42no—
416C22—24no—
417C22—44no—
418C22—44no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22—82no—
425C22—82no—
426C22C2×C4×D4×C12711yescharacteristic
427C22#525×C12712yes—
428C22#576×C12712yes—
429C22#577×C12711yescharacteristic
430C22#577×C12711yescharacteristic
431C4—22no—
432C4—22no—
433C4—42no—
434C4—44no—
435C4—42no—
436C4—42no—
437C4—42no—
438C4—82no—
439C4C2×#117×C12711yescharacteristic
440C4C4×#41×C12711yescharacteristic
441C4#529×C12712yes—
442C2—44no—
443C2—82no—
444C2C127×#229011yescharacteristic
445C2C127×#294811yescharacteristic
446C2C127×#295211yescharacteristic
447C2C127×#311812yes—
448C2C127×#311912yes—
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×D8×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ #376×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2319C2semidirect
3. C127×#2275C2semidirect
4. C127×#1926C2semidirect
5. C127×#1918C2semidirect
7. C127×#1864C2semidirect
8. C4×#106×C127C2semidirect
9. C127×#1762C2semidirect
10. C127×#1762C2semidirect
11. C127×#1746C2semidirect
16. C4×D8×C127C4semidirect
57. C4×D4×C127C2×C4semidirect
73. #107×C127C2×C4semidirect
78. #102×C127C2×C4semidirect
80. C4×C8×C127C2×C4semidirect
217. #21134C127direct (N × H)
226. #2319C2×C127semidirect
227. #2275C2×C127semidirect
228. #1926C2×C127semidirect
229. #1918C2×C127semidirect
231. #1864C2×C127semidirect
232. C4×#106C2×C127semidirect
233. #1762C2×C127semidirect
234. #1762C2×C127semidirect
235. #1746C2×C127semidirect
236. C127#21134direct (N × H)
241. C4×D8C4×C127semidirect
282. C4×D4C2×C4×C127semidirect
298. #107C2×C4×C127semidirect
303. #102C2×C4×C127semidirect
305. C4×C8C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D8×C1272
C127×#23192
C127×#22752
C127×#19262
C127×#19182
C127×#18792
C127×#18642
C4×#106×C1272
C127×#17622
C127×#17462
#21134127