Finite Group Databasebeta

← C127×#21530 #44585203

Subgroups — C127×#21530 #44585203

Order 32512.

954 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#467×C127C211yesmaximal, characteristic
2C2×#441×C127C211yesmaximal, characteristic, complemented
3C2×#405×C127C211yesmaximal, characteristic
4C127×#2323C212yesmaximal
5C127×#1971C211yesmaximal, characteristic, complemented
6C127×#1943C211yesmaximal, characteristic, complemented
7C127×#1933C212yesmaximal, complemented
8C127×#1894C212yesmaximal
9C127×#1807C211yesmaximal, characteristic
10C127×#1776C211yesmaximal, characteristic, complemented
11C4×#103×C127C212yesmaximal, complemented
12C22×Q16×C127C2211yescharacteristic
13C22×M16×C127C2211yescharacteristic
14C23×C8×C127C2211yescharacteristic
15C2×C22⋊Q8×C127C2212yes—
16C2×C4×Q8×C127C2212yes—
17C2×#117×C127C2211yescharacteristic
18#467×C127C418yescomplemented
19#441×C127—24no—
20C2×#107×C127C2211yescharacteristic
21C2×#106×C127C2211yescharacteristic
22C2×#106×C127C2211yescharacteristic
23C2×#103×C127C2212yes—
24C2×#103×C127C2212yes—
25C2×#103×C127C2212yes—
26#405×C127—24no—
27C2×#97×C127C2211yescharacteristic
28C2×#97×C127C2211yescharacteristic
29C2×C4×C8×C127C2211yescharacteristic
30C2×C4×C8×C127C2211yescharacteristic
31#391×C127C2212yes—
32#389×C127—22no—
33#389×C127C2212yes—
34#388×C127—22no—
35#388×C127—22no—
36#387×C127—22no—
37#380×C127C2212yes—
38C4×C4⋊C4×C127C2212yes—
39#340×C127C2212yes—
40#340×C127C2212yes—
41#340×C127C2212yes—
42C22×Q8×C127C2312yes—
43C23×C4×C127C2311yescharacteristic
44C2×Q16×C127—22no—
45C2×Q16×C127—22no—
46C2×Q16×C127C2×C414yes—
47C2×M16×C127—22no—
48C2×M16×C127—22no—
49C2×M16×C127—22no—
50C22×C8×C127—22no—
51C22×C8×C127—22no—
52C22×C8×C127C2×C414yes—
53C22×C8×C127C2311yescharacteristic
54C22×C8×C127C2311yescharacteristic
55C22×C8×C127C2311yescharacteristic
56C22×C8×C127C2311yescharacteristic
57C22⋊Q8×C127—24no—
58C22⋊Q8×C127C2×C418yes—
59C4×Q8×C127—24no—
60C4×Q8×C127—24no—
61#117×C127—22no—
62#117×C127—22no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127D412yes—
67C2×C4⋊C4×C127C2312yes—
68C2×C4⋊C4×C127C2312yes—
69C2×C4⋊C4×C127C2312yes—
70C2×C22⋊C4×C127—22no—
71C2×C22⋊C4×C127—22no—
72C2×C22⋊C4×C127D412yes—
73C2×C42×C127—22no—
74C2×C42×C127—22no—
75C2×C42×C127C2311yescharacteristic
76C2×C42×C127C2311yescharacteristic
77#107×C127C2×C414yes—
78#106×C127—22no—
79#106×C127—22no—
80#103×C127—24no—
81#103×C127—24no—
82#103×C127C2×C418yes—
83#97×C127—22no—
84#97×C127D414yes—
85C4×C8×C127—22no—
86C4×C8×C127—22no—
87#95×C127—22no—
88#95×C127—22no—
89#95×C127—22no—
90#95×C127—22no—
91#95×C127—22no—
92C24×C127C2×D411yescharacteristic
93C2×Q8×C127—22no—
94C2×Q8×C127—22no—
95C2×Q8×C127—22no—
96C2×Q8×C127—22no—
97C2×Q8×C127—22no—
98C2×Q8×C127C22×C414yes—
99C22×C4×C127—21no—
100C22×C4×C127—21no—
101C22×C4×C127—21no—
102C22×C4×C127—21no—
103C22×C4×C127—22no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127C22×C412yes—
108C22×C4×C127C2×D412yes—
109C22×C4×C127C2×D411yescharacteristic
110C22×C4×C127C2×D412yes—
111C22×C4×C127#4112yes—
112C22×C4×C127C2411yescharacteristic
113Q16×C127—28no—
114M16×C127—28no—
115C2×C8×C127—21no—
116C2×C8×C127—21no—
117C2×C8×C127—21no—
118C2×C8×C127—21no—
119C2×C8×C127—21no—
120C2×C8×C127—21no—
121C2×C8×C127—28no—
122C2×C8×C127C22×C412yes—
123C2×C8×C127C22×C412yes—
124C2×C8×C127C2×D412yes—
125C2×C8×C127C2×D412yes—
126C2×C8×C127#4112yes—
127C2×C8×C127#4112yes—
128C4⋊C4×C127—28no—
129C4⋊C4×C127—24no—
130C4⋊C4×C127—22no—
131C4⋊C4×C127—22no—
132C4⋊C4×C127—22no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—22no—
135C4⋊C4×C127—44no—
136C4⋊C4×C127—82no—
137C4⋊C4×C127C22×C414yes—
138C22⋊C4×C127—28no—
139C22⋊C4×C127—24no—
140C22⋊C4×C127—82no—
141C42×C127—21no—
142C42×C127—21no—
143C42×C127—44no—
144C42×C127—82no—
145C42×C127C2×D412yes—
146C42×C127#4112yes—
147C23×C127—21no—
148C23×C127—21no—
149C23×C127—22no—
150C23×C127—22no—
151C23×C127C4×D412yes—
152C23×C127C22×D411yescharacteristic
153Q8×C127—24no—
154Q8×C127—24no—
155Q8×C127—42no—
156Q8×C127—42no—
157C2×C4×C127—21no—
158C2×C4×C127—21no—
159C2×C4×C127—22no—
160C2×C4×C127—22no—
161C2×C4×C127—22no—
162C2×C4×C127—22no—
163C2×C4×C127—22no—
164C2×C4×C127—22no—
165C2×C4×C127—24no—
166C2×C4×C127—24no—
167C2×C4×C127—22no—
168C2×C4×C127—22no—
169C2×C4×C127—22no—
170C2×C4×C127—42no—
171C2×C4×C127—42no—
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—42no—
180C2×C4×C127C4×D412yes—
181C2×C4×C127#12114yes—
182C2×C4×C127C23×C411yescharacteristic
183C2×C4×C127C22×D411yescharacteristic
184C2×C4×C127C2×#4111yescharacteristic
185C2×C4×C127C2×#4111yescharacteristic
186C2×C4×C127C2×#4111yescharacteristic
187C2×C4×C127C2×#4111yescharacteristic
188C8×C127—22no—
189C8×C127—22no—
190C8×C127—22no—
191C8×C127C4×D414yes—
192C22×C127—22no—
193C22×C127—22no—
194C22×C127—22no—
195C22×C127—42no—
196C22×C127—42no—
197C22×C127C2×C4×D411yescharacteristic
198C22×C127C2×#12111yescharacteristic
199C22×C127#53211yescharacteristic
200C22×C127#57712yes—
201C22×C127#57812yes—
202C4×C127—24no—
203C4×C127—22no—
204C4×C127—44no—
205C4×C127—42no—
206C4×C127—44no—
207C4×C127—82no—
208C4×C127—82no—
209C4×C127C2×C4×D411yescharacteristic
210C4×C127C4×#4111yescharacteristic
211C4×C127#52511yescharacteristic
212C4×C127#52911yescharacteristic
213#21530C12711yesmaximal, characteristic, direct product factor, Sylow
214C2×C127—42no—
215C2×C127C4×#12111yescharacteristic
216C2×C127#295011yescharacteristic
217C2×C127#295211yescharacteristic
218C2×C127#306312yes—
219C2×C127#317812yes—
220C2×#467C2×C12711yescharacteristic
221C2×#441C2×C12711yescharacteristic, complemented
222C2×#405C2×C12711yescharacteristic
223#2323C2×C12712yes—
224#1971C2×C12711yescharacteristic, complemented
225#1943C2×C12711yescharacteristic, complemented
226#1933C2×C12712yescomplemented
227#1894C2×C12712yes—
228#1807C2×C12711yescharacteristic
229#1776C2×C12711yescharacteristic, complemented
230C4×#103C2×C12712yescomplemented
231C127#2153011yescharacteristic, direct product factor, Sylow
232C22×Q16C22×C12711yescharacteristic
233C22×M16C22×C12711yescharacteristic
234C23×C8C22×C12711yescharacteristic
235C2×C22⋊Q8C22×C12712yes—
236C2×C4×Q8C22×C12712yes—
237C2×#117C22×C12711yescharacteristic
238#467C4×C12718yescomplemented
239#441—24no—
240C2×#107C22×C12711yescharacteristic
241C2×#106C22×C12711yescharacteristic
242C2×#106C22×C12711yescharacteristic
243C2×#103C22×C12712yes—
244C2×#103C22×C12712yes—
245C2×#103C22×C12712yes—
246#405—24no—
247C2×#97C22×C12711yescharacteristic
248C2×#97C22×C12711yescharacteristic
249C2×C4×C8C22×C12711yescharacteristic
250C2×C4×C8C22×C12711yescharacteristic
251#391C22×C12712yes—
252#389—22no—
253#389C22×C12712yes—
254#388—22no—
255#388—22no—
256#387—22no—
257#380C22×C12712yes—
258C4×C4⋊C4C22×C12712yes—
259#340C22×C12712yes—
260#340C22×C12712yes—
261#340C22×C12712yes—
262C22×Q8C23×C12712yes—
263C23×C4C23×C12711yescharacteristic
264C2×Q16—22no—
265C2×Q16—22no—
266C2×Q16C2×C4×C12714yes—
267C2×M16—22no—
268C2×M16—22no—
269C2×M16—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8C2×C4×C12714yes—
273C22×C8C23×C12711yescharacteristic
274C22×C8C23×C12711yescharacteristic
275C22×C8C23×C12711yescharacteristic
276C22×C8C23×C12711yescharacteristic
277C22⋊Q8—24no—
278C22⋊Q8C2×C4×C12718yes—
279C4×Q8—24no—
280C4×Q8—24no—
281#117—22no—
282#117—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4D4×C12712yes—
287C2×C4⋊C4C23×C12712yes—
288C2×C4⋊C4C23×C12712yes—
289C2×C4⋊C4C23×C12712yes—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4D4×C12712yes—
293C2×C42—22no—
294C2×C42—22no—
295C2×C42C23×C12711yescharacteristic
296C2×C42C23×C12711yescharacteristic
297#107C2×C4×C12714yes—
298#106—22no—
299#106—22no—
300#103—24no—
301#103—24no—
302#103C2×C4×C12718yes—
303#97—22no—
304#97D4×C12714yes—
305C4×C8—22no—
306C4×C8—22no—
307#95—22no—
308#95—22no—
309#95—22no—
310#95—22no—
311#95—22no—
312C24C2×D4×C12711yescharacteristic
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8—22no—
316C2×Q8—22no—
317C2×Q8—22no—
318C2×Q8C22×C4×C12714yes—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4C22×C4×C12712yes—
328C22×C4C2×D4×C12712yes—
329C22×C4C2×D4×C12711yescharacteristic
330C22×C4C2×D4×C12712yes—
331C22×C4#41×C12712yes—
332C22×C4C24×C12711yescharacteristic
333Q16—28no—
334M16—28no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—28no—
342C2×C8C22×C4×C12712yes—
343C2×C8C22×C4×C12712yes—
344C2×C8C2×D4×C12712yes—
345C2×C8C2×D4×C12712yes—
346C2×C8#41×C12712yes—
347C2×C8#41×C12712yes—
348C4⋊C4—28no—
349C4⋊C4—24no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—44no—
356C4⋊C4—82no—
357C4⋊C4C22×C4×C12714yes—
358C22⋊C4—28no—
359C22⋊C4—24no—
360C22⋊C4—82no—
361C42—21no—
362C42—21no—
363C42—44no—
364C42—82no—
365C42C2×D4×C12712yes—
366C42#41×C12712yes—
367C23—21no—
368C23—21no—
369C23—22no—
370C23—22no—
371C23C4×D4×C12712yes—
372C23C22×D4×C12711yescharacteristic
373Q8—24no—
374Q8—24no—
375Q8—42no—
376Q8—42no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4C4×D4×C12712yes—
401C2×C4#121×C12714yes—
402C2×C4C23×C4×C12711yescharacteristic
403C2×C4C22×D4×C12711yescharacteristic
404C2×C4C2×#41×C12711yescharacteristic
405C2×C4C2×#41×C12711yescharacteristic
406C2×C4C2×#41×C12711yescharacteristic
407C2×C4C2×#41×C12711yescharacteristic
408C8—22no—
409C8—22no—
410C8—22no—
411C8C4×D4×C12714yes—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—42no—
416C22—42no—
417C22C2×C4×D4×C12711yescharacteristic
418C22C2×#121×C12711yescharacteristic
419C22#532×C12711yescharacteristic
420C22#577×C12712yes—
421C22#578×C12712yes—
422C4—24no—
423C4—22no—
424C4—44no—
425C4—42no—
426C4—44no—
427C4—82no—
428C4—82no—
429C4C2×C4×D4×C12711yescharacteristic
430C4C4×#41×C12711yescharacteristic
431C4#525×C12711yescharacteristic
432C4#529×C12711yescharacteristic
433C2—42no—
434C2C4×#121×C12711yescharacteristic
435C2C127×#295011yescharacteristic
436C2C127×#295211yescharacteristic
437C2C127×#306312yes—
438C2C127×#317812yes—
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC24×C127C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#441×C127C2semidirect
5. C127×#1971C2semidirect
6. C127×#1943C2semidirect
7. C127×#1933C2semidirect
10. C127×#1776C2semidirect
11. C4×#103×C127C2semidirect
18. #467×C127C4semidirect
213. #21530C127direct (N × H)
221. C2×#441C2×C127semidirect
224. #1971C2×C127semidirect
225. #1943C2×C127semidirect
226. #1933C2×C127semidirect
229. #1776C2×C127semidirect
230. C4×#103C2×C127semidirect
231. C127#21530direct (N × H)
238. #467C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#467×C1272
C2×#441×C1272
C2×#405×C1272
C127×#23232
C127×#19712
C127×#19432
C127×#19332
C127×#18942
C127×#18072
C127×#17762
C4×#103×C1272
#21530127