Finite Group Databasebeta

← C127×#21136 #44584809

Subgroups — C127×#21136 #44584809

Order 32512.

862 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×SD16×C127C211yesmaximal, characteristic
2C127×#2319C211yesmaximal, characteristic
3C127×#2276C211yesmaximal, characteristic, complemented
4C127×#1925C212yesmaximal
5C127×#1919C212yesmaximal, complemented
6C127×#1880C212yesmaximal
7C127×#1863C212yesmaximal, complemented
8C4×#107×C127C211yesmaximal, characteristic, complemented
9C127×#1763C211yesmaximal, characteristic, complemented
10C127×#1762C211yesmaximal, characteristic
11C127×#1746C211yesmaximal, characteristic, complemented
12C22×SD16×C127C2211yescharacteristic
13C2×C4×Q8×C127C2212yes—
14C2×C4×Q8×C127C2211yescharacteristic
15C2×C4×D4×C127C2211yescharacteristic
16C4×SD16×C127C418yescomplemented
17C2×#107×C127C2212yes—
18C2×#106×C127C2211yescharacteristic
19C2×#103×C127C2212yes—
20C2×#103×C127C2211yescharacteristic
21C2×#102×C127C2212yes—
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×C127—21no—
31C4×C4⋊C4×C127—22no—
32C4×C4⋊C4×C127C2211yescharacteristic
33C4×C4⋊C4×C127C2212yes—
34C4×C4⋊C4×C127C2211yescharacteristic
35#376×C127—21no—
36#376×C127C2211yescharacteristic
37#340×C127C2212yes—
38#340×C127C2212yes—
39#340×C127C2212yes—
40#336×C127C2212yes—
41#336×C127C2212yes—
42C22×Q8×C127C2311yescharacteristic
43C22×D4×C127C2311yescharacteristic
44C23×C4×C127—21no—
45C2×SD16×C127—24no—
46C2×SD16×C127C2×C414yes—
47C22×C8×C127C2312yes—
48C22×C8×C127C2311yescharacteristic
49C22×C8×C127C2311yescharacteristic
50C4×Q8×C127—24no—
51C4×Q8×C127—24no—
52C4×Q8×C127—22no—
53C4×Q8×C127C2×C414yes—
54C4×D4×C127—22no—
55C4×D4×C127C2×C414yes—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—21no—
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—21no—
64C2×C22⋊C4×C127—22no—
65C2×C22⋊C4×C127—22no—
66C2×C42×C127—22no—
67C2×C42×C127—21no—
68C2×C42×C127—22no—
69C2×C42×C127—21no—
70C2×C42×C127—21no—
71C2×C42×C127C2312yes—
72C2×C42×C127C2311yescharacteristic
73#107×C127—24no—
74#106×C127C2×C414yes—
75#103×C127—24no—
76#103×C127C2×C414yes—
77#102×C127—24no—
78#102×C127C2×C414yes—
79#97×C127—22no—
80C4×C8×C127C2×C414yes—
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—
89C2×Q8×C127—21no—
90C2×Q8×C127—22no—
91C2×Q8×C127C22×C412yes—
92C2×Q8×C127#4114yes—
93C2×D4×C127—22no—
94C2×D4×C127—22no—
95C2×D4×C127—21no—
96C2×D4×C127C22×C412yes—
97C22×C4×C127—21no—
98C22×C4×C127—21no—
99C22×C4×C127—22no—
100C22×C4×C127—21no—
101C22×C4×C127—24no—
102C22×C4×C127—22no—
103C22×C4×C127—82no—
104C22×C4×C127C2×D412yes—
105C22×C4×C127C2×D412yes—
106C22×C4×C127C2×D411yescharacteristic
107C22×C4×C127C2×D411yescharacteristic
108C22×C4×C127C2411yescharacteristic
109SD16×C127—28no—
110C2×C8×C127—22no—
111C2×C8×C127—22no—
112C2×C8×C127—22no—
113C2×C8×C127—22no—
114C2×C8×C127—22no—
115C2×C8×C127C22×C412yes—
116C2×C8×C127C22×C412yes—
117C4⋊C4×C127—28no—
118C4⋊C4×C127—24no—
119C4⋊C4×C127—21no—
120C4⋊C4×C127—21no—
121C4⋊C4×C127—22no—
122C4⋊C4×C127—22no—
123C4⋊C4×C127—22no—
124C4⋊C4×C127—82no—
125C4⋊C4×C127C22×C412yes—
126C4⋊C4×C127C22×C412yes—
127C4⋊C4×C127#4114yes—
128C22⋊C4×C127—24no—
129C22⋊C4×C127—82no—
130C22⋊C4×C127—82no—
131C42×C127—28no—
132C42×C127—24no—
133C42×C127—22no—
134C42×C127—22no—
135C42×C127—81no—
136C42×C127—81no—
137C42×C127—82no—
138C42×C127C22×C412yes—
139C42×C127#4112yes—
140C23×C127—22no—
141C23×C127—42no—
142C23×C127—41no—
143C23×C127—42no—
144C23×C127—41no—
145C23×C127C22×D411yescharacteristic
146Q8×C127—22no—
147Q8×C127—24no—
148Q8×C127#11714yes—
149D4×C127—22no—
150D4×C127—22no—
151D4×C127—42no—
152C2×C4×C127—22no—
153C2×C4×C127—24no—
154C2×C4×C127—21no—
155C2×C4×C127—22no—
156C2×C4×C127—21no—
157C2×C4×C127—22no—
158C2×C4×C127—22no—
159C2×C4×C127—22no—
160C2×C4×C127—22no—
161C2×C4×C127—24no—
162C2×C4×C127—22no—
163C2×C4×C127—22no—
164C2×C4×C127—22no—
165C2×C4×C127—22no—
166C2×C4×C127—42no—
167C2×C4×C127—41no—
168C2×C4×C127—42no—
169C2×C4×C127—42no—
170C2×C4×C127—41no—
171C2×C4×C127—42no—
172C2×C4×C127—42no—
173C2×C4×C127—42no—
174C2×C4×C127—84no—
175C2×C4×C127C4×D412yes—
176C2×C4×C127C4×D412yes—
177C2×C4×C127C23×C411yescharacteristic
178C2×C4×C127C2×#4112yes—
179C2×C4×C127C2×#4112yes—
180C2×C4×C127C2×#4111yescharacteristic
181C8×C127—22no—
182C8×C127—22no—
183C8×C127—42no—
184C22×C127—42no—
185C22×C127—42no—
186C22×C127—42no—
187C22×C127—82no—
188C22×C127—82no—
189C22×C127C2×C4×D411yescharacteristic
190C22×C127#52512yes—
191C22×C127#57611yescharacteristic
192C22×C127#57712yes—
193C22×C127#57811yescharacteristic
194C4×C127—22no—
195C4×C127—22no—
196C4×C127—24no—
197C4×C127—42no—
198C4×C127—44no—
199C4×C127—42no—
200C4×C127—42no—
201C4×C127—42no—
202C4×C127—82no—
203C4×C127C2×#11711yescharacteristic
204C4×C127C4×#4111yescharacteristic
205C4×C127#52912yes—
206#21136C12711yesmaximal, characteristic, direct product factor, Sylow
207C2×C127—82no—
208C2×C127#229011yescharacteristic
209C2×C127#294911yescharacteristic
210C2×C127#295111yescharacteristic
211C2×C127#311912yes—
212C2×C127#312112yes—
213C2×C4×SD16C2×C12711yescharacteristic
214#2319C2×C12711yescharacteristic
215#2276C2×C12711yescharacteristic, complemented
216#1925C2×C12712yes—
217#1919C2×C12712yescomplemented
218#1880C2×C12712yes—
219#1863C2×C12712yescomplemented
220C4×#107C2×C12711yescharacteristic, complemented
221#1763C2×C12711yescharacteristic, complemented
222#1762C2×C12711yescharacteristic
223#1746C2×C12711yescharacteristic, complemented
224C127#2113611yescharacteristic, direct product factor, Sylow
225C22×SD16C22×C12711yescharacteristic
226C2×C4×Q8C22×C12712yes—
227C2×C4×Q8C22×C12711yescharacteristic
228C2×C4×D4C22×C12711yescharacteristic
229C4×SD16C4×C12718yescomplemented
230C2×#107C22×C12712yes—
231C2×#106C22×C12711yescharacteristic
232C2×#103C22×C12712yes—
233C2×#103C22×C12711yescharacteristic
234C2×#102C22×C12712yes—
235C2×#102C22×C12711yescharacteristic
236C2×#97C22×C12711yescharacteristic
237C2×C4×C8C22×C12711yescharacteristic
238#390C22×C12712yes—
239#389C22×C12712yes—
240#388—22no—
241#381—21no—
242#380—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—22no—
245C4×C4⋊C4C22×C12711yescharacteristic
246C4×C4⋊C4C22×C12712yes—
247C4×C4⋊C4C22×C12711yescharacteristic
248#376—21no—
249#376C22×C12711yescharacteristic
250#340C22×C12712yes—
251#340C22×C12712yes—
252#340C22×C12712yes—
253#336C22×C12712yes—
254#336C22×C12712yes—
255C22×Q8C23×C12711yescharacteristic
256C22×D4C23×C12711yescharacteristic
257C23×C4—21no—
258C2×SD16—24no—
259C2×SD16C2×C4×C12714yes—
260C22×C8C23×C12712yes—
261C22×C8C23×C12711yescharacteristic
262C22×C8C23×C12711yescharacteristic
263C4×Q8—24no—
264C4×Q8—24no—
265C4×Q8—22no—
266C4×Q8C2×C4×C12714yes—
267C4×D4—22no—
268C4×D4C2×C4×C12714yes—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4C23×C12712yes—
273C2×C4⋊C4C23×C12711yescharacteristic
274C2×C4⋊C4C23×C12711yescharacteristic
275C2×C4⋊C4C23×C12712yes—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279C2×C42—22no—
280C2×C42—21no—
281C2×C42—22no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42C23×C12712yes—
285C2×C42C23×C12711yescharacteristic
286#107—24no—
287#106C2×C4×C12714yes—
288#103—24no—
289#103C2×C4×C12714yes—
290#102—24no—
291#102C2×C4×C12714yes—
292#97—22no—
293C4×C8C2×C4×C12714yes—
294#95—22no—
295#95—21no—
296#95—21no—
297#95—22no—
298#95D4×C12711yescharacteristic
299#95D4×C12711yescharacteristic
300#95D4×C12712yes—
301C24—21no—
302C2×Q8—21no—
303C2×Q8—22no—
304C2×Q8C22×C4×C12712yes—
305C2×Q8#41×C12714yes—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4C22×C4×C12712yes—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—24no—
315C22×C4—22no—
316C22×C4—82no—
317C22×C4C2×D4×C12712yes—
318C22×C4C2×D4×C12712yes—
319C22×C4C2×D4×C12711yescharacteristic
320C22×C4C2×D4×C12711yescharacteristic
321C22×C4C24×C12711yescharacteristic
322SD16—28no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8C22×C4×C12712yes—
329C2×C8C22×C4×C12712yes—
330C4⋊C4—28no—
331C4⋊C4—24no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—82no—
338C4⋊C4C22×C4×C12712yes—
339C4⋊C4C22×C4×C12712yes—
340C4⋊C4#41×C12714yes—
341C22⋊C4—24no—
342C22⋊C4—82no—
343C22⋊C4—82no—
344C42—28no—
345C42—24no—
346C42—22no—
347C42—22no—
348C42—81no—
349C42—81no—
350C42—82no—
351C42C22×C4×C12712yes—
352C42#41×C12712yes—
353C23—22no—
354C23—42no—
355C23—41no—
356C23—42no—
357C23—41no—
358C23C22×D4×C12711yescharacteristic
359Q8—22no—
360Q8—24no—
361Q8#117×C12714yes—
362D4—22no—
363D4—22no—
364D4—42no—
365C2×C4—22no—
366C2×C4—24no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—84no—
388C2×C4C4×D4×C12712yes—
389C2×C4C4×D4×C12712yes—
390C2×C4C23×C4×C12711yescharacteristic
391C2×C4C2×#41×C12712yes—
392C2×C4C2×#41×C12712yes—
393C2×C4C2×#41×C12711yescharacteristic
394C8—22no—
395C8—22no—
396C8—42no—
397C22—42no—
398C22—42no—
399C22—42no—
400C22—82no—
401C22—82no—
402C22C2×C4×D4×C12711yescharacteristic
403C22#525×C12712yes—
404C22#576×C12711yescharacteristic
405C22#577×C12712yes—
406C22#578×C12711yescharacteristic
407C4—22no—
408C4—22no—
409C4—24no—
410C4—42no—
411C4—44no—
412C4—42no—
413C4—42no—
414C4—42no—
415C4—82no—
416C4C2×#117×C12711yescharacteristic
417C4C4×#41×C12711yescharacteristic
418C4#529×C12712yes—
419C2—82no—
420C2C127×#229011yescharacteristic
421C2C127×#294911yescharacteristic
422C2C127×#295111yescharacteristic
423C2C127×#311912yes—
424C2C127×#312112yes—
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 ◁ #376×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#2276C2semidirect
5. C127×#1919C2semidirect
7. C127×#1863C2semidirect
8. C4×#107×C127C2semidirect
9. C127×#1763C2semidirect
11. C127×#1746C2semidirect
16. C4×SD16×C127C4semidirect
206. #21136C127direct (N × H)
215. #2276C2×C127semidirect
217. #1919C2×C127semidirect
219. #1863C2×C127semidirect
220. C4×#107C2×C127semidirect
221. #1763C2×C127semidirect
223. #1746C2×C127semidirect
224. C127#21136direct (N × H)
229. C4×SD16C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C4×SD16×C1272
C127×#23192
C127×#22762
C127×#19252
C127×#19192
C127×#18802
C127×#18632
C4×#107×C1272
C127×#17632
C127×#17622
C127×#17462
#21136127