Finite Group Databasebeta

← C127×#8425 #44572098

Subgroups — C127×#8425 #44572098

Order 32512.

750 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3503C211yesmaximal, characteristic
2C127×#1981C211yesmaximal, characteristic, complemented
3C127×#1806C211yesmaximal, characteristic
4C127×#1550C211yesmaximal, characteristic, complemented
5C127×#1548C211yesmaximal, characteristic, complemented
6C127×#1503C211yesmaximal, characteristic, complemented
7C127×#1477C211yesmaximal, characteristic
8Q82×C127C412yescomplemented
9#557×C127—21no—
10#554×C127—22no—
11#554×C127C412yescomplemented
12D4×Q8×C127—22no—
13D4×Q8×C127—21no—
14#544×C127—22no—
15#544×C127—21no—
16#533×C127—21no—
17#533×C127C2211yescharacteristic
18C2×C4⋊Q8×C127—21no—
19C2×C4⋊Q8×C127C2211yescharacteristic
20#520×C127—21no—
21C4×#41×C127C2211yescharacteristic
22#431×C127C2211yescharacteristic
23#423×C127C2211yescharacteristic
24C2×C4⋊C8×C127C2211yescharacteristic
25C2×#104×C127—21no—
26C2×#103×C127—22no—
27C4×C4⋊C4×C127C2211yescharacteristic
28#339×C127—21no—
29#333×C127—22no—
30#333×C127—21no—
31#332×C127—21no—
32#328×C127—22no—
33Q8⋊C8×C127—21no—
34D4⋊C8×C127—21no—
35C2×#41×C127D411yescharacteristic
36C22×Q8×C127—22no—
37C22×Q8×C127D412yes—
38C2×M16×C127—21no—
39C22×C8×C127—21no—
40C4⋊Q8×C127—22no—
41C4⋊Q8×C127—22no—
42C4⋊Q8×C127—24no—
43C4⋊Q8×C127—22no—
44C4⋊Q8×C127—22no—
45C4⋊Q8×C127—21no—
46C4⋊Q8×C127—21no—
47C4⋊Q8×C127C2×C412yes—
48C4⋊Q8×C127D412yes—
49C4⋊Q8×C127D411yescharacteristic
50C4⋊Q8×C127D411yescharacteristic
51#125×C127—22no—
52#125×C127—24no—
53#125×C127—22no—
54#125×C127—21no—
55C22⋊Q8×C127—22no—
56C22⋊Q8×C127—24no—
57C22⋊Q8×C127—24no—
58C22⋊Q8×C127—22no—
59C22⋊Q8×C127—24no—
60C22⋊Q8×C127—21no—
61C22⋊Q8×C127D412yes—
62C4×Q8×C127—22no—
63C4×Q8×C127—22no—
64C4×Q8×C127—22no—
65C4×Q8×C127—21no—
66C4×Q8×C127C2×C411yescharacteristic
67C4×Q8×C127C2×C412yes—
68C4×Q8×C127D411yescharacteristic
69C4×D4×C127—24no—
70C4×D4×C127—22no—
71C4×D4×C127—21no—
72C4×D4×C127—21no—
73C4×D4×C127C2×C411yescharacteristic
74C4×D4×C127D411yescharacteristic
75#117×C127—22no—
76#117×C127—21no—
77#117×C127—21no—
78#117×C127D411yescharacteristic
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—21no—
81C2×C4⋊C4×C127—21no—
82C2×C4⋊C4×C127—22no—
83C2×C4⋊C4×C127—21no—
84C2×C42×C127—21no—
85C2×C42×C127—21no—
86C2×C42×C127C2311yescharacteristic
87C4⋊C8×C127—21no—
88C4⋊C8×C127—21no—
89C4⋊C8×C127—21no—
90C4⋊C8×C127—21no—
91C4⋊C8×C127—21no—
92#104×C127—42no—
93#103×C127—44no—
94C22⋊C8×C127—21no—
95C4×C8×C127—21no—
96#95×C127—21no—
97#41×C127—21no—
98#41×C127—21no—
99#41×C127SD1612yes—
100#41×C127Q1612yes—
101C2×Q8×C127—24no—
102C2×Q8×C127—22no—
103C2×Q8×C127—21no—
104C2×Q8×C127—42no—
105C2×Q8×C127—42no—
106C2×Q8×C127—82no—
107C2×Q8×C127—82no—
108C2×Q8×C127C22⋊C411yescharacteristic
109C2×Q8×C127C22⋊C412yes—
110C2×Q8×C127C22⋊C414yes—
111C2×D4×C127—21no—
112C2×D4×C127C22⋊C411yescharacteristic
113C22×C4×C127—21no—
114C22×C4×C127—24no—
115C22×C4×C127—22no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—41no—
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127C2×D411yescharacteristic
121C22×C4×C127C2×D411yescharacteristic
122M16×C127—41no—
123M16×C127—41no—
124C2×C8×C127—42no—
125C2×C8×C127—41no—
126C2×C8×C127—41no—
127C2×C8×C127—41no—
128C4⋊C4×C127—24no—
129C4⋊C4×C127—24no—
130C4⋊C4×C127—24no—
131C4⋊C4×C127—24no—
132C4⋊C4×C127—22no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—21no—
135C4⋊C4×C127—22no—
136C4⋊C4×C127—22no—
137C4⋊C4×C127—21no—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—21no—
140C4⋊C4×C127—21no—
141C4⋊C4×C127—21no—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—41no—
145C4⋊C4×C127C22⋊C412yes—
146C4⋊C4×C127C22⋊C411yescharacteristic
147C4⋊C4×C127C22⋊C411yescharacteristic
148C22⋊C4×C127—24no—
149C22⋊C4×C127—22no—
150C22⋊C4×C127—21no—
151C22⋊C4×C127—21no—
152C22⋊C4×C127—21no—
153C42×C127—24no—
154C42×C127—21no—
155C42×C127—22no—
156C42×C127—21no—
157C42×C127—21no—
158C42×C127—41no—
159C42×C127—41no—
160C42×C127C22×C411yescharacteristic
161C42×C127C2×D411yescharacteristic
162C42×C127C2×D411yescharacteristic
163C42×C127C2×D411yescharacteristic
164C23×C127—21no—
165C23×C127#12011yescharacteristic
166Q8×C127—21no—
167Q8×C127—44no—
168Q8×C127—42no—
169Q8×C127—42no—
170Q8×C127—41no—
171Q8×C127—42no—
172Q8×C127—41no—
173Q8×C127—84no—
174Q8×C127#10312yescomplemented
175D4×C127—22no—
176D4×C127—22no—
177D4×C127—21no—
178D4×C127#10312yescomplemented
179C2×C4×C127—21no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
182C2×C4×C127—21no—
183C2×C4×C127—21no—
184C2×C4×C127—22no—
185C2×C4×C127—21no—
186C2×C4×C127—21no—
187C2×C4×C127—24no—
188C2×C4×C127—22no—
189C2×C4×C127—41no—
190C2×C4×C127—42no—
191C2×C4×C127—41no—
192C2×C4×C127—41no—
193C2×C4×C127—42no—
194C2×C4×C127—82no—
195C2×C4×C127—84no—
196C2×C4×C127—81no—
197C2×C4×C127—81no—
198C2×C4×C127C2×C22⋊C411yescharacteristic
199C2×C4×C127C2×C22⋊C411yescharacteristic
200C2×C4×C127C2×C22⋊C411yescharacteristic
201C2×C4×C127#12011yescharacteristic
202C2×C4×C127#12011yescharacteristic
203C2×C4×C127#12011yescharacteristic
204C2×C4×C127C2×SD1611yescharacteristic
205C2×C4×C127C2×Q1611yescharacteristic
206C2×C4×C127#13711yescharacteristic
207C2×C4×C127#13711yescharacteristic
208C8×C127—81no—
209C8×C127—81no—
210C8×C127—81no—
211C22×C127—21no—
212C22×C127—21no—
213C22×C127—22no—
214C22×C127—41no—
215C22×C127—41no—
216C22×C127#37911yescharacteristic
217C22×C127#44811yescharacteristic
218C22×C127#45111yescharacteristic
219C4×C127—21no—
220C4×C127—21no—
221C4×C127—21no—
222C4×C127—22no—
223C4×C127—41no—
224C4×C127—44no—
225C4×C127—42no—
226C4×C127—41no—
227C4×C127—42no—
228C4×C127—82no—
229C4×C127C2×#10311yescharacteristic
230C4×C127#41911yescharacteristic
231C4×C127#44811yescharacteristic
232C4×C127#45111yescharacteristic
233C4×C127#45311yescharacteristic
234C4×C127#45511yescharacteristic
235#8425C12711yesmaximal, characteristic, direct product factor, Sylow
236C2×C127—21no—
237C2×C127—21no—
238C2×C127—42no—
239C2×C127#178711yescharacteristic
240C2×C127#179211yescharacteristic
241C2×C127#179611yescharacteristic
242#3503C2×C12711yescharacteristic
243#1981C2×C12711yescharacteristic, complemented
244#1806C2×C12711yescharacteristic
245#1550C2×C12711yescharacteristic, complemented
246#1548C2×C12711yescharacteristic, complemented
247#1503C2×C12711yescharacteristic, complemented
248#1477C2×C12711yescharacteristic
249C127#842511yescharacteristic, direct product factor, Sylow
250Q82C4×C12712yescomplemented
251#557—21no—
252#554—22no—
253#554C4×C12712yescomplemented
254D4×Q8—22no—
255D4×Q8—21no—
256#544—22no—
257#544—21no—
258#533—21no—
259#533C22×C12711yescharacteristic
260C2×C4⋊Q8—21no—
261C2×C4⋊Q8C22×C12711yescharacteristic
262#520—21no—
263C4×#41C22×C12711yescharacteristic
264#431C22×C12711yescharacteristic
265#423C22×C12711yescharacteristic
266C2×C4⋊C8C22×C12711yescharacteristic
267C2×#104—21no—
268C2×#103—22no—
269C4×C4⋊C4C22×C12711yescharacteristic
270#339—21no—
271#333—22no—
272#333—21no—
273#332—21no—
274#328—22no—
275Q8⋊C8—21no—
276D4⋊C8—21no—
277C2×#41D4×C12711yescharacteristic
278C22×Q8—22no—
279C22×Q8D4×C12712yes—
280C2×M16—21no—
281C22×C8—21no—
282C4⋊Q8—22no—
283C4⋊Q8—22no—
284C4⋊Q8—24no—
285C4⋊Q8—22no—
286C4⋊Q8—22no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8C2×C4×C12712yes—
290C4⋊Q8D4×C12712yes—
291C4⋊Q8D4×C12711yescharacteristic
292C4⋊Q8D4×C12711yescharacteristic
293#125—22no—
294#125—24no—
295#125—22no—
296#125—21no—
297C22⋊Q8—22no—
298C22⋊Q8—24no—
299C22⋊Q8—24no—
300C22⋊Q8—22no—
301C22⋊Q8—24no—
302C22⋊Q8—21no—
303C22⋊Q8D4×C12712yes—
304C4×Q8—22no—
305C4×Q8—22no—
306C4×Q8—22no—
307C4×Q8—21no—
308C4×Q8C2×C4×C12711yescharacteristic
309C4×Q8C2×C4×C12712yes—
310C4×Q8D4×C12711yescharacteristic
311C4×D4—24no—
312C4×D4—22no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4C2×C4×C12711yescharacteristic
316C4×D4D4×C12711yescharacteristic
317#117—22no—
318#117—21no—
319#117—21no—
320#117D4×C12711yescharacteristic
321C2×C4⋊C4—22no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42C23×C12711yescharacteristic
329C4⋊C8—21no—
330C4⋊C8—21no—
331C4⋊C8—21no—
332C4⋊C8—21no—
333C4⋊C8—21no—
334#104—42no—
335#103—44no—
336C22⋊C8—21no—
337C4×C8—21no—
338#95—21no—
339#41—21no—
340#41—21no—
341#41SD16×C12712yes—
342#41Q16×C12712yes—
343C2×Q8—24no—
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8—42no—
347C2×Q8—42no—
348C2×Q8—82no—
349C2×Q8—82no—
350C2×Q8C22⋊C4×C12711yescharacteristic
351C2×Q8C22⋊C4×C12712yes—
352C2×Q8C22⋊C4×C12714yes—
353C2×D4—21no—
354C2×D4C22⋊C4×C12711yescharacteristic
355C22×C4—21no—
356C22×C4—24no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4C2×D4×C12711yescharacteristic
362C22×C4C2×D4×C12711yescharacteristic
363C22×C4C2×D4×C12711yescharacteristic
364M16—41no—
365M16—41no—
366C2×C8—42no—
367C2×C8—41no—
368C2×C8—41no—
369C2×C8—41no—
370C4⋊C4—24no—
371C4⋊C4—24no—
372C4⋊C4—24no—
373C4⋊C4—24no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—41no—
387C4⋊C4C22⋊C4×C12712yes—
388C4⋊C4C22⋊C4×C12711yescharacteristic
389C4⋊C4C22⋊C4×C12711yescharacteristic
390C22⋊C4—24no—
391C22⋊C4—22no—
392C22⋊C4—21no—
393C22⋊C4—21no—
394C22⋊C4—21no—
395C42—24no—
396C42—21no—
397C42—22no—
398C42—21no—
399C42—21no—
400C42—41no—
401C42—41no—
402C42C22×C4×C12711yescharacteristic
403C42C2×D4×C12711yescharacteristic
404C42C2×D4×C12711yescharacteristic
405C42C2×D4×C12711yescharacteristic
406C23—21no—
407C23#120×C12711yescharacteristic
408Q8—21no—
409Q8—44no—
410Q8—42no—
411Q8—42no—
412Q8—41no—
413Q8—42no—
414Q8—41no—
415Q8—84no—
416Q8#103×C12712yescomplemented
417D4—22no—
418D4—22no—
419D4—21no—
420D4#103×C12712yescomplemented
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—82no—
437C2×C4—84no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4C2×C22⋊C4×C12711yescharacteristic
441C2×C4C2×C22⋊C4×C12711yescharacteristic
442C2×C4C2×C22⋊C4×C12711yescharacteristic
443C2×C4#120×C12711yescharacteristic
444C2×C4#120×C12711yescharacteristic
445C2×C4#120×C12711yescharacteristic
446C2×C4C2×SD16×C12711yescharacteristic
447C2×C4C2×Q16×C12711yescharacteristic
448C2×C4#137×C12711yescharacteristic
449C2×C4#137×C12711yescharacteristic
450C8—81no—
451C8—81no—
452C8—81no—
453C22—21no—
454C22—21no—
455C22—22no—
456C22—41no—
457C22—41no—
458C22#379×C12711yescharacteristic
459C22#448×C12711yescharacteristic
460C22#451×C12711yescharacteristic
461C4—22no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—41no—
466C4—44no—
467C4—42no—
468C4—41no—
469C4—42no—
470C4—82no—
471C4C2×#103×C12711yescharacteristic
472C4#419×C12711yescharacteristic
473C4#448×C12711yescharacteristic
474C4#451×C12711yescharacteristic
475C4#453×C12711yescharacteristic
476C4#455×C12711yescharacteristic
477C2—21no—
478C2—21no—
479C2—42no—
480C2C127×#178711yescharacteristic
481C2C127×#179211yescharacteristic
482C2C127×#179611yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×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
2. C127×#1981C2semidirect
4. C127×#1550C2semidirect
5. C127×#1548C2semidirect
6. C127×#1503C2semidirect
8. Q82×C127C4semidirect
11. #554×C127C4semidirect
174. Q8×C127#103semidirect
178. D4×C127#103semidirect
235. #8425C127direct (N × H)
243. #1981C2×C127semidirect
245. #1550C2×C127semidirect
246. #1548C2×C127semidirect
247. #1503C2×C127semidirect
249. C127#8425direct (N × H)
250. Q82C4×C127semidirect
253. #554C4×C127semidirect
416. Q8#103×C127semidirect
420. D4#103×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35032
C127×#19812
C127×#18062
C127×#15502
C127×#15482
C127×#15032
C127×#14772
#8425127