Finite Group Databasebeta

← C127×#18530 #44582203

Subgroups — C127×#18530 #44582203

Order 32512.

962 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C127C211yesmaximal, characteristic
2C127×#3139C211yesmaximal, characteristic, complemented
3C127×#3113C211yesmaximal, characteristic, complemented
4C127×#3110C211yesmaximal, characteristic
5C127×#1644C214yesmaximal, complemented
6C127×#1643C214yesmaximal, complemented
7C127×#1558C211yesmaximal, characteristic, complemented
8C127×#1491C211yesmaximal, characteristic, complemented
9C127×#1490C211yesmaximal, characteristic
10#554×C127—22no—
11#554×C127—22no—
12#554×C127—22no—
13#554×C127C2214yes—
14#533×C127C2211yescharacteristic
15C2×C4⋊Q8×C127C2211yescharacteristic
16C2×#125×C127—21no—
17C2×C22⋊Q8×C127—21no—
18C2×C22⋊Q8×C127—22no—
19C2×C4×Q8×C127C2211yescharacteristic
20C2×C4×D4×C127—21no—
21C2×C4×D4×C127C2211yescharacteristic
22C22×C4⋊C4×C127—21no—
23#491×C127—22no—
24#487×C127C2212yescomplemented
25#487×C127C2212yescomplemented
26#484×C127—21no—
27#483×C127—21no—
28#475×C127C2212yescomplemented
29#474×C127C2212yes—
30#462×C127C2212yescomplemented
31#461×C127C2212yes—
32#451×C127—21no—
33#450×C127—21no—
34#441×C127—22no—
35#440×C127—22no—
36#432×C127C2211yescharacteristic
37#432×C127C2211yescharacteristic
38#419×C127—22no—
39C4×M16×C127C2211yescharacteristic
40#333×C127C2214yescomplemented
41Q8⋊C8×C127C2214yescomplemented
42D4⋊C8×C127C2214yes—
43C22×Q8×C127D411yescharacteristic
44C22×Q8×C127D412yes—
45C22×D4×C127D411yescharacteristic
46C23×C4×C127—22no—
47C23×C4×C127—21no—
48C2×Q16×C127—22no—
49C2×SD16×C127—22no—
50C2×M16×C127—21no—
51C4⋊Q8×C127—21no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127D412yes—
54C4⋊Q8×C127C2311yescharacteristic
55C4⋊Q8×C127C2311yescharacteristic
56C4⋊Q8×C127C2312yes—
57#125×C127—24no—
58#125×C127—24no—
59#125×C127—21no—
60C22⋊Q8×C127—24no—
61C22⋊Q8×C127—28no—
62C22⋊Q8×C127—24no—
63C22⋊Q8×C127—28no—
64C22⋊Q8×C127—21no—
65C22⋊Q8×C127—21no—
66C4×Q8×C127—21no—
67C4×Q8×C127—21no—
68C4×Q8×C127—21no—
69C4×Q8×C127—21no—
70C4×Q8×C127D412yes—
71C4×Q8×C127C2312yes—
72C4×D4×C127—24no—
73C4×D4×C127—24no—
74C4×D4×C127—21no—
75C4×D4×C127—21no—
76C4×D4×C127D412yes—
77C4×D4×C127C2312yes—
78#117×C127—21no—
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—24no—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—21no—
83C2×C4⋊C4×C127—21no—
84C2×C4⋊C4×C127—21no—
85C2×C4⋊C4×C127—24no—
86C2×C4⋊C4×C127D411yescharacteristic
87C2×C4⋊C4×C127D411yescharacteristic
88C2×C22⋊C4×C127—22no—
89C2×C22⋊C4×C127—21no—
90C2×C42×C127—21no—
91C2×C42×C127C2311yescharacteristic
92#107×C127—22no—
93#106×C127—22no—
94C4⋊C8×C127C2312yes—
95C4⋊C8×C127C2312yes—
96#103×C127—24no—
97#103×C127—24no—
98#103×C127—22no—
99#103×C127—22no—
100#103×C127—22no—
101#102×C127—22no—
102C22⋊C8×C127—21no—
103C22⋊C8×C127—21no—
104#97×C127—21no—
105#97×C127—21no—
106#97×C127—21no—
107C4×C8×C127C2312yes—
108C24×C127—21no—
109C2×Q8×C127—21no—
110C2×Q8×C127—22no—
111C2×Q8×C127—21no—
112C2×Q8×C127—21no—
113C2×Q8×C127—42no—
114C2×Q8×C127—44no—
115C2×Q8×C127C2×D412yes—
116C2×Q8×C127C2×D414yes—
117C2×D4×C127—24no—
118C2×D4×C127—21no—
119C2×D4×C127C2×D412yes—
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—21no—
123C22×C4×C127—22no—
124C22×C4×C127—28no—
125C22×C4×C127—22no—
126C22×C4×C127—22no—
127C22×C4×C127—44no—
128C22×C4×C127—84no—
129C22×C4×C127C2×D411yescharacteristic
130C22×C4×C127C2×D411yescharacteristic
131C22×C4×C127C2×D411yescharacteristic
132Q16×C127—44no—
133SD16×C127—44no—
134M16×C127—42no—
135C2×C8×C127—22no—
136C2×C8×C127—22no—
137C2×C8×C127—22no—
138C4⋊C4×C127—28no—
139C4⋊C4×C127—28no—
140C4⋊C4×C127—21no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—21no—
145C4⋊C4×C127—22no—
146C4⋊C4×C127—22no—
147C4⋊C4×C127—22no—
148C4⋊C4×C127—21no—
149C4⋊C4×C127—21no—
150C4⋊C4×C127—21no—
151C4⋊C4×C127—21no—
152C4⋊C4×C127—41no—
153C4⋊C4×C127—41no—
154C4⋊C4×C127C2×D412yes—
155C4⋊C4×C127C2×D412yes—
156C22⋊C4×C127—28no—
157C22⋊C4×C127—22no—
158C22⋊C4×C127—22no—
159C22⋊C4×C127—41no—
160C42×C127—22no—
161C42×C127—22no—
162C42×C127—41no—
163C42×C127C2×D411yescharacteristic
164C42×C127C2×D411yescharacteristic
165C42×C127C2×D411yescharacteristic
166C42×C127C2411yescharacteristic
167C23×C127—24no—
168C23×C127—22no—
169C23×C127—42no—
170C23×C127—42no—
171C23×C127#12011yescharacteristic
172Q8×C127—22no—
173Q8×C127—22no—
174Q8×C127—44no—
175Q8×C127—42no—
176Q8×C127—42no—
177Q8×C127—42no—
178Q8×C127—82no—
179D4×C127—24no—
180D4×C127—22no—
181D4×C127#13714yes—
182C2×C4×C127—22no—
183C2×C4×C127—22no—
184C2×C4×C127—22no—
185C2×C4×C127—22no—
186C2×C4×C127—22no—
187C2×C4×C127—22no—
188C2×C4×C127—24no—
189C2×C4×C127—44no—
190C2×C4×C127—42no—
191C2×C4×C127—42no—
192C2×C4×C127—42no—
193C2×C4×C127—44no—
194C2×C4×C127—44no—
195C2×C4×C127—41no—
196C2×C4×C127—41no—
197C2×C4×C127—88no—
198C2×C4×C127#12011yescharacteristic
199C2×C4×C127#12011yescharacteristic
200C2×C4×C127#12011yescharacteristic
201C2×C4×C127C22×D411yescharacteristic
202C2×C4×C127C22×D411yescharacteristic
203C2×C4×C127C22×D411yescharacteristic
204C8×C127—42no—
205C8×C127—42no—
206C8×C127—42no—
207C22×C127—21no—
208C22×C127—21no—
209C22×C127—24no—
210C22×C127—48no—
211C22×C127—42no—
212C22×C127—42no—
213C22×C127#45512yes—
214C22×C127C2×#12011yescharacteristic
215C4×C127—21no—
216C4×C127—21no—
217C4×C127—21no—
218C4×C127—21no—
219C4×C127—42no—
220C4×C127—42no—
221C4×C127—42no—
222C4×C127—44no—
223C4×C127—81no—
224C4×C127—81no—
225C4×C127C2×#13712yes—
226C4×C127#57512yes—
227#18530C12711yesmaximal, characteristic, direct product factor, Sylow
228C2×C127—22no—
229C2×C127—44no—
230C2×C127#300411yescharacteristic
231C2×C127#300511yescharacteristic
232C2×C127C2×#45511yescharacteristic
233C2×#554C2×C12711yescharacteristic
234#3139C2×C12711yescharacteristic, complemented
235#3113C2×C12711yescharacteristic, complemented
236#3110C2×C12711yescharacteristic
237#1644C2×C12714yescomplemented
238#1643C2×C12714yescomplemented
239#1558C2×C12711yescharacteristic, complemented
240#1491C2×C12711yescharacteristic, complemented
241#1490C2×C12711yescharacteristic
242C127#1853011yescharacteristic, direct product factor, Sylow
243#554—22no—
244#554—22no—
245#554—22no—
246#554C22×C12714yes—
247#533C22×C12711yescharacteristic
248C2×C4⋊Q8C22×C12711yescharacteristic
249C2×#125—21no—
250C2×C22⋊Q8—21no—
251C2×C22⋊Q8—22no—
252C2×C4×Q8C22×C12711yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4C22×C12711yescharacteristic
255C22×C4⋊C4—21no—
256#491—22no—
257#487C22×C12712yescomplemented
258#487C22×C12712yescomplemented
259#484—21no—
260#483—21no—
261#475C22×C12712yescomplemented
262#474C22×C12712yes—
263#462C22×C12712yescomplemented
264#461C22×C12712yes—
265#451—21no—
266#450—21no—
267#441—22no—
268#440—22no—
269#432C22×C12711yescharacteristic
270#432C22×C12711yescharacteristic
271#419—22no—
272C4×M16C22×C12711yescharacteristic
273#333C22×C12714yescomplemented
274Q8⋊C8C22×C12714yescomplemented
275D4⋊C8C22×C12714yes—
276C22×Q8D4×C12711yescharacteristic
277C22×Q8D4×C12712yes—
278C22×D4D4×C12711yescharacteristic
279C23×C4—22no—
280C23×C4—21no—
281C2×Q16—22no—
282C2×SD16—22no—
283C2×M16—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8D4×C12712yes—
287C4⋊Q8C23×C12711yescharacteristic
288C4⋊Q8C23×C12711yescharacteristic
289C4⋊Q8C23×C12712yes—
290#125—24no—
291#125—24no—
292#125—21no—
293C22⋊Q8—24no—
294C22⋊Q8—28no—
295C22⋊Q8—24no—
296C22⋊Q8—28no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8D4×C12712yes—
304C4×Q8C23×C12712yes—
305C4×D4—24no—
306C4×D4—24no—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4D4×C12712yes—
310C4×D4C23×C12712yes—
311#117—21no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4D4×C12711yescharacteristic
320C2×C4⋊C4D4×C12711yescharacteristic
321C2×C22⋊C4—22no—
322C2×C22⋊C4—21no—
323C2×C42—21no—
324C2×C42C23×C12711yescharacteristic
325#107—22no—
326#106—22no—
327C4⋊C8C23×C12712yes—
328C4⋊C8C23×C12712yes—
329#103—24no—
330#103—24no—
331#103—22no—
332#103—22no—
333#103—22no—
334#102—22no—
335C22⋊C8—21no—
336C22⋊C8—21no—
337#97—21no—
338#97—21no—
339#97—21no—
340C4×C8C23×C12712yes—
341C24—21no—
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—21no—
345C2×Q8—21no—
346C2×Q8—42no—
347C2×Q8—44no—
348C2×Q8C2×D4×C12712yes—
349C2×Q8C2×D4×C12714yes—
350C2×D4—24no—
351C2×D4—21no—
352C2×D4C2×D4×C12712yes—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—28no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—44no—
361C22×C4—84no—
362C22×C4C2×D4×C12711yescharacteristic
363C22×C4C2×D4×C12711yescharacteristic
364C22×C4C2×D4×C12711yescharacteristic
365Q16—44no—
366SD16—44no—
367M16—42no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—22no—
371C4⋊C4—28no—
372C4⋊C4—28no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4C2×D4×C12712yes—
388C4⋊C4C2×D4×C12712yes—
389C22⋊C4—28no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—41no—
393C42—22no—
394C42—22no—
395C42—41no—
396C42C2×D4×C12711yescharacteristic
397C42C2×D4×C12711yescharacteristic
398C42C2×D4×C12711yescharacteristic
399C42C24×C12711yescharacteristic
400C23—24no—
401C23—22no—
402C23—42no—
403C23—42no—
404C23#120×C12711yescharacteristic
405Q8—22no—
406Q8—22no—
407Q8—44no—
408Q8—42no—
409Q8—42no—
410Q8—42no—
411Q8—82no—
412D4—24no—
413D4—22no—
414D4#137×C12714yes—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—44no—
427C2×C4—44no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—88no—
431C2×C4#120×C12711yescharacteristic
432C2×C4#120×C12711yescharacteristic
433C2×C4#120×C12711yescharacteristic
434C2×C4C22×D4×C12711yescharacteristic
435C2×C4C22×D4×C12711yescharacteristic
436C2×C4C22×D4×C12711yescharacteristic
437C8—42no—
438C8—42no—
439C8—42no—
440C22—21no—
441C22—21no—
442C22—24no—
443C22—48no—
444C22—42no—
445C22—42no—
446C22#455×C12712yes—
447C22C2×#120×C12711yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—42no—
453C4—42no—
454C4—42no—
455C4—44no—
456C4—81no—
457C4—81no—
458C4C2×#137×C12712yes—
459C4#575×C12712yes—
460C2—22no—
461C2—44no—
462C2C127×#300411yescharacteristic
463C2C127×#300511yescharacteristic
464C2C2×#455×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC22×D4×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#3139C2semidirect
3. C127×#3113C2semidirect
5. C127×#1644C2semidirect
6. C127×#1643C2semidirect
7. C127×#1558C2semidirect
8. C127×#1491C2semidirect
24. #487×C127C22semidirect
25. #487×C127C22semidirect
28. #475×C127C22semidirect
30. #462×C127C22semidirect
40. #333×C127C22semidirect
41. Q8⋊C8×C127C22semidirect
227. #18530C127direct (N × H)
234. #3139C2×C127semidirect
235. #3113C2×C127semidirect
237. #1644C2×C127semidirect
238. #1643C2×C127semidirect
239. #1558C2×C127semidirect
240. #1491C2×C127semidirect
242. C127#18530direct (N × H)
257. #487C22×C127semidirect
258. #487C22×C127semidirect
261. #475C22×C127semidirect
263. #462C22×C127semidirect
273. #333C22×C127semidirect
274. Q8⋊C8C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1272
C127×#31392
C127×#31132
C127×#31102
C127×#16442
C127×#16432
C127×#15582
C127×#14912
C127×#14902
#18530127