Finite Group Databasebeta

← C127×#19640 #44583313

Subgroups — C127×#19640 #44583313

Order 32512.

742 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
1C127×#3227C211yesmaximal, characteristic, complemented
2C127×#3206C211yesmaximal, characteristic, complemented
3C127×#3169C211yesmaximal, characteristic
4C127×#3141C211yesmaximal, characteristic, complemented
5C127×#3141C211yesmaximal, characteristic, complemented
6C2×#487×C127C211yesmaximal, characteristic, complemented
7C127×#1718C212yesmaximal, complemented
8C127×#1717C212yesmaximal, complemented
9C127×#1711C212yesmaximal, complemented
10C127×#1708C212yesmaximal, complemented
11C8×M16×C127C211yesmaximal, characteristic, complemented
12#532×C127C2211yescharacteristic
13#532×C127C2211yescharacteristic
14C2×C4⋊Q8×C127C2211yescharacteristic
15C2×C4⋊Q8×C127C2211yescharacteristic
16#500×C127C2211yescharacteristic
17#498×C127C2212yes—
18#493×C127C2211yescharacteristic
19#492×C127C2212yes—
20#489×C127—22no—
21#489×C127—22no—
22#487×C127—22no—
23#487×C127C2212yes—
24#487×C127C2212yes—
25#487×C127C2212yes—
26#487×C127C2212yes—
27#487×C127C2212yes—
28#486×C127C2212yes—
29#486×C127C2212yes—
30#486×C127C2211yescharacteristic
31#486×C127C2211yescharacteristic
32#486×C127C2212yes—
33#481×C127—22no—
34#476×C127—22no—
35#466×C127—22no—
36#461×C127—22no—
37#448×C127—22no—
38C4×D8×C127—22no—
39#431×C127C2211yescharacteristic
40#417×C127—22no—
41#417×C127—22no—
42C2×#103×C127—22no—
43C4×M16×C127C2211yescharacteristic
44C2×C4×C8×C127C2211yescharacteristic
45#322×C127C2212yes—
46C82×C127C2212yes—
47C2×#41×C127—21no—
48C2×#41×C127—21no—
49C22×Q8×C127—21no—
50C22×Q8×C127—21no—
51C2×SD16×C127—24no—
52C2×D8×C127—22no—
53C2×M16×C127D412yes—
54C22×C8×C127D412yes—
55C4⋊Q8×C127—21no—
56C4⋊Q8×C127—21no—
57C4⋊Q8×C127—21no—
58C4⋊Q8×C127—21no—
59C4⋊Q8×C127—21no—
60C4⋊Q8×C127—21no—
61C4⋊Q8×C127C2311yescharacteristic
62C4⋊Q8×C127C2312yes—
63C4⋊Q8×C127C2311yescharacteristic
64C4⋊Q8×C127C2312yes—
65#127×C127C2311yescharacteristic
66#127×C127C2311yescharacteristic
67#124×C127—21no—
68#124×C127—21no—
69#121×C127—21no—
70#121×C127—21no—
71#121×C127—21no—
72#121×C127—21no—
73C4×D4×C127—21no—
74C4×D4×C127—21no—
75C4×D4×C127—21no—
76C4×D4×C127—21no—
77C2×C4⋊C4×C127—21no—
78C2×C4⋊C4×C127—21no—
79C2×C4⋊C4×C127—21no—
80C2×C4⋊C4×C127—21no—
81C2×C42×C127C2311yescharacteristic
82#107×C127—22no—
83#106×C127—24no—
84C4⋊C8×C127D412yes—
85#103×C127—24no—
86#103×C127—24no—
87#103×C127—24no—
88#103×C127—24no—
89#103×C127—24no—
90#102×C127—24no—
91#102×C127—24no—
92#102×C127—22no—
93#102×C127—22no—
94#102×C127—24no—
95C22⋊C8×C127D412yes—
96#97×C127D412yes—
97C4×C8×C127D412yes—
98C4×C8×C127C2312yes—
99C4×C8×C127C2311yescharacteristic
100C4×C8×C127C2311yescharacteristic
101C4×C8×C127C2312yes—
102#41×C127—44no—
103#41×C127—44no—
104C2×Q8×C127—21no—
105C2×Q8×C127—21no—
106C2×Q8×C127—22no—
107C2×Q8×C127—22no—
108C2×Q8×C127—44no—
109C2×Q8×C127—41no—
110C2×Q8×C127—41no—
111C2×Q8×C127—82no—
112C2×D4×C127—21no—
113C2×D4×C127—21no—
114C2×D4×C127—21no—
115C2×D4×C127—21no—
116C2×D4×C127—21no—
117C2×D4×C127—21no—
118C2×D4×C127—41no—
119C2×D4×C127—41no—
120C22×C4×C127—41no—
121C22×C4×C127—41no—
122C22×C4×C127—41no—
123C22×C4×C127—41no—
124C22×C4×C127C2×D411yescharacteristic
125C22×C4×C127C2×D411yescharacteristic
126C22×C4×C127C2×D411yescharacteristic
127SD16×C127—84no—
128D8×C127—44no—
129M16×C127—24no—
130C2×C8×C127—42no—
131C2×C8×C127C2×D412yes—
132C2×C8×C127C2×D412yes—
133C2×C8×C127C2×D414yes—
134C2×C8×C127C2×D414yes—
135C4⋊C4×C127—22no—
136C4⋊C4×C127—22no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—21no—
139C4⋊C4×C127—21no—
140C4⋊C4×C127—22no—
141C4⋊C4×C127—21no—
142C4⋊C4×C127—21no—
143C4⋊C4×C127—41no—
144C4⋊C4×C127—41no—
145C4⋊C4×C127—41no—
146C4⋊C4×C127—41no—
147C22⋊C4×C127—41no—
148C22⋊C4×C127—41no—
149C22⋊C4×C127—41no—
150C22⋊C4×C127—41no—
151C42×C127C2×D411yescharacteristic
152C42×C127C2×D411yescharacteristic
153C42×C127C2×D411yescharacteristic
154C42×C127C2411yescharacteristic
155C23×C127—41no—
156C23×C127—41no—
157C23×C127#12711yescharacteristic
158Q8×C127—42no—
159Q8×C127—42no—
160Q8×C127—44no—
161Q8×C127—44no—
162Q8×C127—82no—
163Q8×C127—82no—
164D4×C127—42no—
165D4×C127—42no—
166D4×C127—42no—
167D4×C127—42no—
168D4×C127—42no—
169D4×C127—42no—
170D4×C127—82no—
171D4×C127—82no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—41no—
175C2×C4×C127—41no—
176C2×C4×C127—42no—
177C2×C4×C127—42no—
178C2×C4×C127—82no—
179C2×C4×C127—82no—
180C2×C4×C127—82no—
181C2×C4×C127—82no—
182C2×C4×C127#12711yescharacteristic
183C2×C4×C127#12711yescharacteristic
184C2×C4×C127#12711yescharacteristic
185C2×C4×C127#13514yes—
186C2×C4×C127C22×D411yescharacteristic
187C2×C4×C127C22×D411yescharacteristic
188C2×C4×C127C22×D411yescharacteristic
189C8×C127—24no—
190C8×C127—22no—
191C8×C127—22no—
192C8×C127—24no—
193C22×C127—21no—
194C22×C127—21no—
195C22×C127—81no—
196C22×C127—81no—
197C22×C127—81no—
198C22×C127—81no—
199C22×C127—81no—
200C22×C127—81no—
201C22×C127#49512yes—
202C22×C127C2×#12711yescharacteristic
203C4×C127—21no—
204C4×C127—21no—
205C4×C127—81no—
206C4×C127—81no—
207C4×C127—82no—
208C4×C127—82no—
209C4×C127#49512yes—
210C4×C127C2×#13512yes—
211C4×C127#57512yes—
212C4×C127#57712yes—
213#19640C12711yesmaximal, characteristic, direct product factor, Sylow
214C2×C127—22no—
215C2×C127—161no—
216C2×C127—161no—
217C2×C127C2×#49511yescharacteristic
218C2×C127#315311yescharacteristic
219C2×C127#315411yescharacteristic
220#3227C2×C12711yescharacteristic, complemented
221#3206C2×C12711yescharacteristic, complemented
222#3169C2×C12711yescharacteristic
223#3141C2×C12711yescharacteristic, complemented
224#3141C2×C12711yescharacteristic, complemented
225C2×#487C2×C12711yescharacteristic, complemented
226#1718C2×C12712yescomplemented
227#1717C2×C12712yescomplemented
228#1711C2×C12712yescomplemented
229#1708C2×C12712yescomplemented
230C8×M16C2×C12711yescharacteristic, complemented
231C127#1964011yescharacteristic, direct product factor, Sylow
232#532C22×C12711yescharacteristic
233#532C22×C12711yescharacteristic
234C2×C4⋊Q8C22×C12711yescharacteristic
235C2×C4⋊Q8C22×C12711yescharacteristic
236#500C22×C12711yescharacteristic
237#498C22×C12712yes—
238#493C22×C12711yescharacteristic
239#492C22×C12712yes—
240#489—22no—
241#489—22no—
242#487—22no—
243#487C22×C12712yes—
244#487C22×C12712yes—
245#487C22×C12712yes—
246#487C22×C12712yes—
247#487C22×C12712yes—
248#486C22×C12712yes—
249#486C22×C12712yes—
250#486C22×C12711yescharacteristic
251#486C22×C12711yescharacteristic
252#486C22×C12712yes—
253#481—22no—
254#476—22no—
255#466—22no—
256#461—22no—
257#448—22no—
258C4×D8—22no—
259#431C22×C12711yescharacteristic
260#417—22no—
261#417—22no—
262C2×#103—22no—
263C4×M16C22×C12711yescharacteristic
264C2×C4×C8C22×C12711yescharacteristic
265#322C22×C12712yes—
266C82C22×C12712yes—
267C2×#41—21no—
268C2×#41—21no—
269C22×Q8—21no—
270C22×Q8—21no—
271C2×SD16—24no—
272C2×D8—22no—
273C2×M16D4×C12712yes—
274C22×C8D4×C12712yes—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8C23×C12712yes—
282C4⋊Q8C23×C12712yes—
283C4⋊Q8C23×C12711yescharacteristic
284C4⋊Q8C23×C12711yescharacteristic
285#127C23×C12711yescharacteristic
286#127C23×C12711yescharacteristic
287#124—21no—
288#124—21no—
289#121—21no—
290#121—21no—
291#121—21no—
292#121—21no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—21no—
296C4×D4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C42C23×C12711yescharacteristic
302#107—22no—
303#106—24no—
304C4⋊C8D4×C12712yes—
305#103—24no—
306#103—24no—
307#103—24no—
308#103—24no—
309#103—24no—
310#102—24no—
311#102—24no—
312#102—22no—
313#102—22no—
314#102—24no—
315C22⋊C8D4×C12712yes—
316#97D4×C12712yes—
317C4×C8D4×C12712yes—
318C4×C8C23×C12711yescharacteristic
319C4×C8C23×C12712yes—
320C4×C8C23×C12712yes—
321C4×C8C23×C12711yescharacteristic
322#41—44no—
323#41—44no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—22no—
327C2×Q8—22no—
328C2×Q8—44no—
329C2×Q8—41no—
330C2×Q8—41no—
331C2×Q8—82no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4C2×D4×C12711yescharacteristic
345C22×C4C2×D4×C12711yescharacteristic
346C22×C4C2×D4×C12711yescharacteristic
347SD16—84no—
348D8—44no—
349M16—24no—
350C2×C8—42no—
351C2×C8C2×D4×C12712yes—
352C2×C8C2×D4×C12712yes—
353C2×C8C2×D4×C12714yes—
354C2×C8C2×D4×C12714yes—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C42C2×D4×C12711yescharacteristic
372C42C2×D4×C12711yescharacteristic
373C42C2×D4×C12711yescharacteristic
374C42C24×C12711yescharacteristic
375C23—41no—
376C23—41no—
377C23#127×C12711yescharacteristic
378Q8—42no—
379Q8—42no—
380Q8—44no—
381Q8—44no—
382Q8—82no—
383Q8—82no—
384D4—42no—
385D4—42no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—42no—
390D4—82no—
391D4—82no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4#127×C12711yescharacteristic
403C2×C4#127×C12711yescharacteristic
404C2×C4#127×C12711yescharacteristic
405C2×C4#135×C12714yes—
406C2×C4C22×D4×C12711yescharacteristic
407C2×C4C22×D4×C12711yescharacteristic
408C2×C4C22×D4×C12711yescharacteristic
409C8—24no—
410C8—22no—
411C8—22no—
412C8—24no—
413C22—21no—
414C22—21no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22#495×C12712yes—
422C22C2×#127×C12711yescharacteristic
423C4—21no—
424C4—21no—
425C4—81no—
426C4—81no—
427C4—82no—
428C4—82no—
429C4#495×C12712yes—
430C4C2×#135×C12712yes—
431C4#575×C12712yes—
432C4#577×C12712yes—
433C2—22no—
434C2—161no—
435C2—161no—
436C2C2×#495×C12711yescharacteristic
437C2C127×#315311yescharacteristic
438C2C127×#315411yescharacteristic
subgroupG/H
center, socleC22×C127C2×#127
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3169C2
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
1. C127×#3227C2semidirect
2. C127×#3206C2semidirect
4. C127×#3141C2semidirect
5. C127×#3141C2semidirect
6. C2×#487×C127C2semidirect
7. C127×#1718C2semidirect
8. C127×#1717C2semidirect
9. C127×#1711C2semidirect
10. C127×#1708C2semidirect
11. C8×M16×C127C2semidirect
213. #19640C127direct (N × H)
220. #3227C2×C127semidirect
221. #3206C2×C127semidirect
223. #3141C2×C127semidirect
224. #3141C2×C127semidirect
225. C2×#487C2×C127semidirect
226. #1718C2×C127semidirect
227. #1717C2×C127semidirect
228. #1711C2×C127semidirect
229. #1708C2×C127semidirect
230. C8×M16C2×C127semidirect
231. C127#19640direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32272
C127×#32062
C127×#31692
C127×#31412
C2×#487×C1272
C127×#17182
C127×#17172
C127×#17112
C127×#17082
C8×M16×C1272
#19640127