Finite Group Databasebeta

← C127×#19447 #44583120

Subgroups — C127×#19447 #44583120

Order 32512.

598 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
1C127×#3209C211yesmaximal, characteristic, complemented
2C127×#3079C211yesmaximal, characteristic
3C127×#3076C211yesmaximal, characteristic
4C127×#2989C211yesmaximal, characteristic
5C127×#1704C212yesmaximal, complemented
6C127×#1703C212yesmaximal, complemented
7C127×#1690C212yesmaximal, complemented
8C127×#1689C212yesmaximal, complemented
9C127×#1570C211yesmaximal, characteristic, complemented
10C127×#1550C211yesmaximal, characteristic, complemented
11C2×#332×C127C211yesmaximal, characteristic, complemented
12#533×C127C2211yescharacteristic
13C2×C4⋊Q8×C127C2211yescharacteristic
14C4×#41×C127C2211yescharacteristic
15#494×C127C2212yes—
16#487×C127C2212yes—
17#479×C127—21no—
18#478×C127—21no—
19#477×C127—21no—
20#477×C127C2211yescharacteristic
21#476×C127—21no—
22#476×C127C2211yescharacteristic
23#475×C127C2211yescharacteristic
24#475×C127C2212yes—
25#474×C127C2211yescharacteristic
26#474×C127C2212yes—
27#462×C127—21no—
28#462×C127—21no—
29#451×C127—22no—
30#446×C127C2212yes—
31#436×C127C2212yes—
32#435×C127—22no—
33#432×C127—21no—
34#431×C127C2211yescharacteristic
35#428×C127—21no—
36#427×C127—21no—
37#423×C127—21no—
38#423×C127C2211yescharacteristic
39C2×C4⋊C8×C127C2211yescharacteristic
40C2×C4⋊C8×C127C2211yescharacteristic
41#417×C127—21no—
42#416×C127—21no—
43#334×C127C2212yes—
44#334×C127C2212yes—
45#333×C127C2212yes—
46#332×C127C2212yes—
47#332×C127C2212yes—
48#332×C127C2212yes—
49C2×#41×C127D411yescharacteristic
50C22×Q8×C127—21no—
51C2×Q16×C127—22no—
52C2×Q16×C127—22no—
53C2×M16×C127—21no—
54C2×M16×C127—22no—
55C22×C8×C127—21no—
56C22×C8×C127—21no—
57C4⋊Q8×C127—21no—
58C4⋊Q8×C127—21no—
59C4⋊Q8×C127—21no—
60C4⋊Q8×C127C2312yes—
61C4⋊Q8×C127C2311yescharacteristic
62C4⋊Q8×C127C2311yescharacteristic
63#125×C127—21no—
64C22⋊Q8×C127—21no—
65C22⋊Q8×C127—21no—
66C4×Q8×C127—21no—
67C4×Q8×C127—21no—
68C4×Q8×C127D411yescharacteristic
69C4×Q8×C127C2311yescharacteristic
70C4×D4×C127—21no—
71C4×D4×C127—21no—
72C4×D4×C127D411yescharacteristic
73C4×D4×C127C2311yescharacteristic
74#117×C127—21no—
75#117×C127—21no—
76#117×C127D411yescharacteristic
77C2×C4⋊C4×C127—21no—
78C2×C4⋊C4×C127—21no—
79C2×C42×C127—21no—
80C2×C42×C127C2311yescharacteristic
81#107×C127—21no—
82#107×C127—21no—
83#107×C127—22no—
84#106×C127—21no—
85#106×C127—21no—
86#106×C127—22no—
87C4⋊C8×C127—22no—
88C4⋊C8×C127—21no—
89C4⋊C8×C127—21no—
90C4⋊C8×C127—21no—
91C4⋊C8×C127D411yescharacteristic
92C4⋊C8×C127D411yescharacteristic
93C4⋊C8×C127C2312yes—
94C4⋊C8×C127C2311yescharacteristic
95C4⋊C8×C127C2311yescharacteristic
96C4⋊C8×C127C2312yes—
97#103×C127—21no—
98#103×C127—21no—
99#103×C127—22no—
100#103×C127—22no—
101#103×C127—22no—
102#102×C127—21no—
103#102×C127—21no—
104#102×C127—22no—
105C22⋊C8×C127—22no—
106C22⋊C8×C127D412yes—
107#97×C127—22no—
108C4×C8×C127C2312yes—
109#41×C127—22no—
110#41×C127—22no—
111C2×Q8×C127—22no—
112C2×Q8×C127—21no—
113C2×Q8×C127—21no—
114C2×Q8×C127—41no—
115C2×Q8×C127—81no—
116C2×Q8×C127—81no—
117C2×Q8×C127C2×D411yescharacteristic
118C2×D4×C127—21no—
119C2×D4×C127C2×D411yescharacteristic
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—21no—
123C22×C4×C127—41no—
124C22×C4×C127C2×D411yescharacteristic
125C22×C4×C127C2×D411yescharacteristic
126C22×C4×C127#4111yescharacteristic
127Q16×C127—82no—
128Q16×C127—82no—
129M16×C127—42no—
130M16×C127—82no—
131C2×C8×C127—22no—
132C2×C8×C127—21no—
133C2×C8×C127—22no—
134C2×C8×C127—21no—
135C2×C8×C127—42no—
136C2×C8×C127—81no—
137C2×C8×C127C2×D412yes—
138C2×C8×C127C2×D412yes—
139C4⋊C4×C127—21no—
140C4⋊C4×C127—21no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—21no—
143C4⋊C4×C127—21no—
144C4⋊C4×C127—21no—
145C4⋊C4×C127—22no—
146C4⋊C4×C127—21no—
147C4⋊C4×C127—41no—
148C4⋊C4×C127—41no—
149C4⋊C4×C127—41no—
150C4⋊C4×C127—41no—
151C4⋊C4×C127C2×D411yescharacteristic
152C4⋊C4×C127C2×D411yescharacteristic
153C22⋊C4×C127—21no—
154C22⋊C4×C127—21no—
155C22⋊C4×C127—21no—
156C22⋊C4×C127—41no—
157C42×C127—21no—
158C42×C127—21no—
159C42×C127—21no—
160C42×C127—41no—
161C42×C127C2×D411yescharacteristic
162C42×C127C2×D411yescharacteristic
163C42×C127#4111yescharacteristic
164C42×C127C2411yescharacteristic
165C23×C127—21no—
166C23×C127#12111yescharacteristic
167Q8×C127—21no—
168Q8×C127—21no—
169Q8×C127—41no—
170Q8×C127—42no—
171Q8×C127—41no—
172Q8×C127—42no—
173Q8×C127—81no—
174Q8×C127—82no—
175D4×C127—21no—
176D4×C127—21no—
177D4×C127—42no—
178C2×C4×C127—21no—
179C2×C4×C127—21no—
180C2×C4×C127—21no—
181C2×C4×C127—21no—
182C2×C4×C127—21no—
183C2×C4×C127—41no—
184C2×C4×C127—41no—
185C2×C4×C127—41no—
186C2×C4×C127—42no—
187C2×C4×C127—41no—
188C2×C4×C127—41no—
189C2×C4×C127—42no—
190C2×C4×C127—81no—
191C2×C4×C127—82no—
192C2×C4×C127#12111yescharacteristic
193C2×C4×C127#12111yescharacteristic
194C2×C4×C127#12111yescharacteristic
195C2×C4×C127#13712yes—
196C2×C4×C127#13712yes—
197C2×C4×C127C22×D411yescharacteristic
198C2×C4×C127C22×D411yescharacteristic
199C2×C4×C127C2×#4111yescharacteristic
200C8×C127—22no—
201C8×C127—22no—
202C8×C127—41no—
203C8×C127—41no—
204C8×C127—42no—
205C8×C127—42no—
206C22×C127—21no—
207C22×C127—21no—
208C22×C127—41no—
209C22×C127—41no—
210C22×C127—41no—
211C22×C127#47012yes—
212C22×C127C2×#12111yescharacteristic
213C4×C127—21no—
214C4×C127—21no—
215C4×C127—21no—
216C4×C127—41no—
217C4×C127—41no—
218C4×C127—41no—
219C4×C127—82no—
220C4×C127—81no—
221C4×C127—81no—
222C4×C127#47012yes—
223C4×C127C2×#13711yescharacteristic
224C4×C127C2×#13711yescharacteristic
225C4×C127#57611yescharacteristic
226C4×C127#57711yescharacteristic
227#19447C12711yesmaximal, characteristic, direct product factor, Sylow
228C2×C127—22no—
229C2×C127—81no—
230C2×C127#304511yescharacteristic
231C2×C127C2×#47011yescharacteristic
232C2×C127#306911yescharacteristic
233#3209C2×C12711yescharacteristic, complemented
234#3079C2×C12711yescharacteristic
235#3076C2×C12711yescharacteristic
236#2989C2×C12711yescharacteristic
237#1704C2×C12712yescomplemented
238#1703C2×C12712yescomplemented
239#1690C2×C12712yescomplemented
240#1689C2×C12712yescomplemented
241#1570C2×C12711yescharacteristic, complemented
242#1550C2×C12711yescharacteristic, complemented
243C2×#332C2×C12711yescharacteristic, complemented
244C127#1944711yescharacteristic, direct product factor, Sylow
245#533C22×C12711yescharacteristic
246C2×C4⋊Q8C22×C12711yescharacteristic
247C4×#41C22×C12711yescharacteristic
248#494C22×C12712yes—
249#487C22×C12712yes—
250#479—21no—
251#478—21no—
252#477—21no—
253#477C22×C12711yescharacteristic
254#476—21no—
255#476C22×C12711yescharacteristic
256#475C22×C12711yescharacteristic
257#475C22×C12712yes—
258#474C22×C12711yescharacteristic
259#474C22×C12712yes—
260#462—21no—
261#462—21no—
262#451—22no—
263#446C22×C12712yes—
264#436C22×C12712yes—
265#435—22no—
266#432—21no—
267#431C22×C12711yescharacteristic
268#428—21no—
269#427—21no—
270#423—21no—
271#423C22×C12711yescharacteristic
272C2×C4⋊C8C22×C12711yescharacteristic
273C2×C4⋊C8C22×C12711yescharacteristic
274#417—21no—
275#416—21no—
276#334C22×C12712yes—
277#334C22×C12712yes—
278#333C22×C12712yes—
279#332C22×C12712yes—
280#332C22×C12712yes—
281#332C22×C12712yes—
282C2×#41D4×C12711yescharacteristic
283C22×Q8—21no—
284C2×Q16—22no—
285C2×Q16—22no—
286C2×M16—21no—
287C2×M16—22no—
288C22×C8—21no—
289C22×C8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8C23×C12712yes—
294C4⋊Q8C23×C12711yescharacteristic
295C4⋊Q8C23×C12711yescharacteristic
296#125—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8D4×C12711yescharacteristic
302C4×Q8C23×C12711yescharacteristic
303C4×D4—21no—
304C4×D4—21no—
305C4×D4D4×C12711yescharacteristic
306C4×D4C23×C12711yescharacteristic
307#117—21no—
308#117—21no—
309#117D4×C12711yescharacteristic
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C42—21no—
313C2×C42C23×C12711yescharacteristic
314#107—21no—
315#107—21no—
316#107—22no—
317#106—21no—
318#106—21no—
319#106—22no—
320C4⋊C8—22no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8D4×C12711yescharacteristic
325C4⋊C8D4×C12711yescharacteristic
326C4⋊C8C23×C12712yes—
327C4⋊C8C23×C12711yescharacteristic
328C4⋊C8C23×C12711yescharacteristic
329C4⋊C8C23×C12712yes—
330#103—21no—
331#103—21no—
332#103—22no—
333#103—22no—
334#103—22no—
335#102—21no—
336#102—21no—
337#102—22no—
338C22⋊C8—22no—
339C22⋊C8D4×C12712yes—
340#97—22no—
341C4×C8C23×C12712yes—
342#41—22no—
343#41—22no—
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—41no—
348C2×Q8—81no—
349C2×Q8—81no—
350C2×Q8C2×D4×C12711yescharacteristic
351C2×D4—21no—
352C2×D4C2×D4×C12711yescharacteristic
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4C2×D4×C12711yescharacteristic
358C22×C4C2×D4×C12711yescharacteristic
359C22×C4#41×C12711yescharacteristic
360Q16—82no—
361Q16—82no—
362M16—42no—
363M16—82no—
364C2×C8—22no—
365C2×C8—21no—
366C2×C8—22no—
367C2×C8—21no—
368C2×C8—42no—
369C2×C8—81no—
370C2×C8C2×D4×C12712yes—
371C2×C8C2×D4×C12712yes—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4C2×D4×C12711yescharacteristic
385C4⋊C4C2×D4×C12711yescharacteristic
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—41no—
390C42—21no—
391C42—21no—
392C42—21no—
393C42—41no—
394C42C2×D4×C12711yescharacteristic
395C42C2×D4×C12711yescharacteristic
396C42#41×C12711yescharacteristic
397C42C24×C12711yescharacteristic
398C23—21no—
399C23#121×C12711yescharacteristic
400Q8—21no—
401Q8—21no—
402Q8—41no—
403Q8—42no—
404Q8—41no—
405Q8—42no—
406Q8—81no—
407Q8—82no—
408D4—21no—
409D4—21no—
410D4—42no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—81no—
424C2×C4—82no—
425C2×C4#121×C12711yescharacteristic
426C2×C4#121×C12711yescharacteristic
427C2×C4#121×C12711yescharacteristic
428C2×C4#137×C12712yes—
429C2×C4#137×C12712yes—
430C2×C4C22×D4×C12711yescharacteristic
431C2×C4C22×D4×C12711yescharacteristic
432C2×C4C2×#41×C12711yescharacteristic
433C8—22no—
434C8—22no—
435C8—41no—
436C8—41no—
437C8—42no—
438C8—42no—
439C22—21no—
440C22—21no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22#470×C12712yes—
445C22C2×#121×C12711yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—41no—
450C4—41no—
451C4—41no—
452C4—82no—
453C4—81no—
454C4—81no—
455C4#470×C12712yes—
456C4C2×#137×C12711yescharacteristic
457C4C2×#137×C12711yescharacteristic
458C4#576×C12711yescharacteristic
459C4#577×C12711yescharacteristic
460C2—22no—
461C2—81no—
462C2C127×#304511yescharacteristic
463C2C2×#470×C12711yescharacteristic
464C2C127×#306911yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×#41×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
1. C127×#3209C2semidirect
5. C127×#1704C2semidirect
6. C127×#1703C2semidirect
7. C127×#1690C2semidirect
8. C127×#1689C2semidirect
9. C127×#1570C2semidirect
10. C127×#1550C2semidirect
11. C2×#332×C127C2semidirect
227. #19447C127direct (N × H)
233. #3209C2×C127semidirect
237. #1704C2×C127semidirect
238. #1703C2×C127semidirect
239. #1690C2×C127semidirect
240. #1689C2×C127semidirect
241. #1570C2×C127semidirect
242. #1550C2×C127semidirect
243. C2×#332C2×C127semidirect
244. C127#19447direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32092
C127×#30792
C127×#30762
C127×#29892
C127×#17042
C127×#17032
C127×#16902
C127×#16892
C127×#15702
C127×#15502
C2×#332×C1272
#19447127