Finite Group Databasebeta

← C127×#8366 #44572039

Subgroups — C127×#8366 #44572039

Order 32512.

1068 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C127C211yesmaximal, characteristic
2C127×#1789C212yesmaximal, complemented
3C4×#99×C127C211yesmaximal, characteristic, complemented
4C127×#1508C212yesmaximal, complemented
5C127×#1465C211yesmaximal, characteristic, complemented
6C22×#41×C127C2211yescharacteristic
7C23×Q8×C127C411yescharacteristic, complemented
8#548×C127—24no—
9#548×C127—24no—
10C2×#124×C127—21no—
11C2×#124×C127C411yescharacteristic, complemented
12C2×C22⋊Q8×C127—21no—
13C2×C22⋊Q8×C127C2211yescharacteristic
14C2×#121×C127—21no—
15C2×#121×C127C411yescharacteristic, complemented
16C2×C4×Q8×C127C411yescharacteristic, complemented
17C2×C4×D4×C127—21no—
18C2×C4×D4×C127C2211yescharacteristic
19C2×#104×C127—24no—
20C2×#99×C127—21no—
21#407×C127C2212yes—
22C4×C22⋊C4×C127C2212yes—
23#342×C127—21no—
24#328×C127—24no—
25#324×C127—21no—
26#323×C127—21no—
27C2×#41×C127—22no—
28C2×#41×C127—44no—
29C2×#41×C127D414yes—
30C22×Q8×C127—22no—
31C22×Q8×C127—22no—
32C22×Q8×C127—21no—
33C22×Q8×C127—44no—
34C22×Q8×C127C2×C411yescharacteristic
35C22×Q8×C127C2×C411yescharacteristic
36C22×D4×C127—21no—
37C22×D4×C127—21no—
38C22×D4×C127C2×C411yescharacteristic
39C22×D4×C127D411yescharacteristic
40C23×C4×C127—21no—
41C23×C4×C127—21no—
42C23×C4×C127C2×C411yescharacteristic
43C23×C4×C127C2311yescharacteristic
44C2×M16×C127—22no—
45#124×C127—28no—
46#124×C127—22no—
47#124×C127—22no—
48C22⋊Q8×C127—28no—
49C22⋊Q8×C127—22no—
50C22⋊Q8×C127D414yes—
51#121×C127—28no—
52#121×C127—22no—
53#121×C127—22no—
54C4×Q8×C127—22no—
55C4×Q8×C127—22no—
56C4×D4×C127—28no—
57C4×D4×C127—22no—
58C4×D4×C127—22no—
59C2×C4⋊C4×C127—21no—
60C2×C4⋊C4×C127—21no—
61C2×C4⋊C4×C127C2×C411yescharacteristic
62C2×C4⋊C4×C127D411yescharacteristic
63C2×C22⋊C4×C127—21no—
64C2×C22⋊C4×C127—21no—
65C2×C22⋊C4×C127—21no—
66C2×C22⋊C4×C127—21no—
67C2×C22⋊C4×C127—22no—
68C2×C22⋊C4×C127D411yescharacteristic
69C2×C22⋊C4×C127D411yescharacteristic
70C2×C42×C127—21no—
71C2×C42×C127—22no—
72C2×C42×C127C2×C411yescharacteristic
73#104×C127—48no—
74#99×C127—24no—
75C22⋊C8×C127—22no—
76C22⋊C8×C127—22no—
77#95×C127—22no—
78C24×C127—21no—
79C24×C127C22⋊C411yescharacteristic
80C24×C127C2×D411yescharacteristic
81#41×C127—28no—
82#41×C127—44no—
83#41×C127—48no—
84C2×Q8×C127—24no—
85C2×Q8×C127—24no—
86C2×Q8×C127—21no—
87C2×Q8×C127—21no—
88C2×Q8×C127—42no—
89C2×Q8×C127—44no—
90C2×Q8×C127—48no—
91C2×Q8×C127—44no—
92C2×Q8×C127—44no—
93C2×Q8×C127C22⋊C412yes—
94C2×Q8×C127C22⋊C412yes—
95C2×D4×C127—24no—
96C2×D4×C127—22no—
97C2×D4×C127—22no—
98C2×D4×C127—24no—
99C2×D4×C127—21no—
100C2×D4×C127—42no—
101C2×D4×C127—41no—
102C2×D4×C127—44no—
103C2×D4×C127—42no—
104C2×D4×C127—42no—
105C2×D4×C127C22⋊C412yes—
106C22×C4×C127—21no—
107C22×C4×C127—24no—
108C22×C4×C127—21no—
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—21no—
112C22×C4×C127—24no—
113C22×C4×C127—42no—
114C22×C4×C127—44no—
115C22×C4×C127—44no—
116C22×C4×C127—42no—
117C22×C4×C127—42no—
118C22×C4×C127C22⋊C411yescharacteristic
119C22×C4×C127C22⋊C411yescharacteristic
120C22×C4×C127C22⋊C411yescharacteristic
121C22×C4×C127C22×C411yescharacteristic
122C22×C4×C127C2×D412yes—
123C22×C4×C127C2×D412yes—
124C22×C4×C127C2×D411yescharacteristic
125M16×C127—44no—
126C2×C8×C127—42no—
127C4⋊C4×C127—24no—
128C4⋊C4×C127—21no—
129C4⋊C4×C127—24no—
130C4⋊C4×C127—22no—
131C4⋊C4×C127C22⋊C412yes—
132C22⋊C4×C127—24no—
133C22⋊C4×C127—24no—
134C22⋊C4×C127—24no—
135C22⋊C4×C127—24no—
136C22⋊C4×C127—22no—
137C22⋊C4×C127—22no—
138C22⋊C4×C127—24no—
139C22⋊C4×C127—42no—
140C42×C127—24no—
141C42×C127—21no—
142C42×C127—21no—
143C42×C127—44no—
144C23×C127—21no—
145C23×C127—21no—
146C23×C127—21no—
147C23×C127—21no—
148C23×C127—22no—
149C23×C127—41no—
150C23×C127—41no—
151C23×C127—41no—
152C23×C127—41no—
153C23×C127—42no—
154C23×C127—42no—
155C23×C127—41no—
156C23×C127—41no—
157C23×C127#10412yescomplemented
158C23×C127C2×C22⋊C411yescharacteristic
159C23×C127#12012yes—
160Q8×C127—24no—
161Q8×C127—22no—
162Q8×C127—42no—
163Q8×C127—48no—
164Q8×C127—42no—
165Q8×C127#9914yescomplemented
166D4×C127—24no—
167D4×C127—48no—
168D4×C127—42no—
169D4×C127—44no—
170D4×C127—48no—
171C2×C4×C127—24no—
172C2×C4×C127—22no—
173C2×C4×C127—24no—
174C2×C4×C127—22no—
175C2×C4×C127—21no—
176C2×C4×C127—21no—
177C2×C4×C127—22no—
178C2×C4×C127—22no—
179C2×C4×C127—21no—
180C2×C4×C127—21no—
181C2×C4×C127—21no—
182C2×C4×C127—41no—
183C2×C4×C127—42no—
184C2×C4×C127—48no—
185C2×C4×C127—48no—
186C2×C4×C127—42no—
187C2×C4×C127—42no—
188C2×C4×C127—41no—
189C2×C4×C127—41no—
190C2×C4×C127—42no—
191C2×C4×C127—41no—
192C2×C4×C127—41no—
193C2×C4×C127—44no—
194C2×C4×C127—82no—
195C2×C4×C127—82no—
196C2×C4×C127C2×C22⋊C411yescharacteristic
197C2×C4×C127C2×C22⋊C411yescharacteristic
198C2×C4×C127#12012yes—
199C8×C127—82no—
200C22×C127—21no—
201C22×C127—21no—
202C22×C127—22no—
203C22×C127—22no—
204C22×C127—22no—
205C22×C127—22no—
206C22×C127—42no—
207C22×C127—42no—
208C22×C127—41no—
209C22×C127—41no—
210C22×C127—42no—
211C22×C127—42no—
212C22×C127—42no—
213C22×C127—81no—
214C22×C127—81no—
215C22×C127—82no—
216C22×C127—82no—
217C22×C127#37911yescharacteristic
218C22×C127C2×#10411yescharacteristic
219C22×C127#42111yescharacteristic
220C4×C127—22no—
221C4×C127—24no—
222C4×C127—21no—
223C4×C127—41no—
224C4×C127—42no—
225C4×C127—41no—
226C4×C127—41no—
227C4×C127—42no—
228C4×C127—84no—
229C4×C127C2×#9912yes—
230#8366C12711yesmaximal, characteristic, direct product factor, Sylow
231C2×C127—21no—
232C2×C127—21no—
233C2×C127—42no—
234C2×C127—42no—
235C2×C127—82no—
236C2×C127#178111yescharacteristic
237C2×C127#178911yescharacteristic
238C2×C127#179611yescharacteristic
239C2×#548C2×C12711yescharacteristic
240#1789C2×C12712yescomplemented
241C4×#99C2×C12711yescharacteristic, complemented
242#1508C2×C12712yescomplemented
243#1465C2×C12711yescharacteristic, complemented
244C127#836611yescharacteristic, direct product factor, Sylow
245C22×#41C22×C12711yescharacteristic
246C23×Q8C4×C12711yescharacteristic, complemented
247#548—24no—
248#548—24no—
249C2×#124—21no—
250C2×#124C4×C12711yescharacteristic, complemented
251C2×C22⋊Q8—21no—
252C2×C22⋊Q8C22×C12711yescharacteristic
253C2×#121—21no—
254C2×#121C4×C12711yescharacteristic, complemented
255C2×C4×Q8C4×C12711yescharacteristic, complemented
256C2×C4×D4—21no—
257C2×C4×D4C22×C12711yescharacteristic
258C2×#104—24no—
259C2×#99—21no—
260#407C22×C12712yes—
261C4×C22⋊C4C22×C12712yes—
262#342—21no—
263#328—24no—
264#324—21no—
265#323—21no—
266C2×#41—22no—
267C2×#41—44no—
268C2×#41D4×C12714yes—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8—21no—
272C22×Q8—44no—
273C22×Q8C2×C4×C12711yescharacteristic
274C22×Q8C2×C4×C12711yescharacteristic
275C22×D4—21no—
276C22×D4—21no—
277C22×D4C2×C4×C12711yescharacteristic
278C22×D4D4×C12711yescharacteristic
279C23×C4—21no—
280C23×C4—21no—
281C23×C4C2×C4×C12711yescharacteristic
282C23×C4C23×C12711yescharacteristic
283C2×M16—22no—
284#124—28no—
285#124—22no—
286#124—22no—
287C22⋊Q8—28no—
288C22⋊Q8—22no—
289C22⋊Q8D4×C12714yes—
290#121—28no—
291#121—22no—
292#121—22no—
293C4×Q8—22no—
294C4×Q8—22no—
295C4×D4—28no—
296C4×D4—22no—
297C4×D4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4C2×C4×C12711yescharacteristic
301C2×C4⋊C4D4×C12711yescharacteristic
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4D4×C12711yescharacteristic
308C2×C22⋊C4D4×C12711yescharacteristic
309C2×C42—21no—
310C2×C42—22no—
311C2×C42C2×C4×C12711yescharacteristic
312#104—48no—
313#99—24no—
314C22⋊C8—22no—
315C22⋊C8—22no—
316#95—22no—
317C24—21no—
318C24C22⋊C4×C12711yescharacteristic
319C24C2×D4×C12711yescharacteristic
320#41—28no—
321#41—44no—
322#41—48no—
323C2×Q8—24no—
324C2×Q8—24no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—42no—
328C2×Q8—44no—
329C2×Q8—48no—
330C2×Q8—44no—
331C2×Q8—44no—
332C2×Q8C22⋊C4×C12712yes—
333C2×Q8C22⋊C4×C12712yes—
334C2×D4—24no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—24no—
338C2×D4—21no—
339C2×D4—42no—
340C2×D4—41no—
341C2×D4—44no—
342C2×D4—42no—
343C2×D4—42no—
344C2×D4C22⋊C4×C12712yes—
345C22×C4—21no—
346C22×C4—24no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—24no—
352C22×C4—42no—
353C22×C4—44no—
354C22×C4—44no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4C22⋊C4×C12711yescharacteristic
358C22×C4C22⋊C4×C12711yescharacteristic
359C22×C4C22⋊C4×C12711yescharacteristic
360C22×C4C22×C4×C12711yescharacteristic
361C22×C4C2×D4×C12712yes—
362C22×C4C2×D4×C12712yes—
363C22×C4C2×D4×C12711yescharacteristic
364M16—44no—
365C2×C8—42no—
366C4⋊C4—24no—
367C4⋊C4—21no—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4C22⋊C4×C12712yes—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—24no—
378C22⋊C4—42no—
379C42—24no—
380C42—21no—
381C42—21no—
382C42—44no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—22no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—42no—
393C23—42no—
394C23—41no—
395C23—41no—
396C23#104×C12712yescomplemented
397C23C2×C22⋊C4×C12711yescharacteristic
398C23#120×C12712yes—
399Q8—24no—
400Q8—22no—
401Q8—42no—
402Q8—48no—
403Q8—42no—
404Q8#99×C12714yescomplemented
405D4—24no—
406D4—48no—
407D4—42no—
408D4—44no—
409D4—48no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—48no—
424C2×C4—48no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—44no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4C2×C22⋊C4×C12711yescharacteristic
436C2×C4C2×C22⋊C4×C12711yescharacteristic
437C2×C4#120×C12712yes—
438C8—82no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—42no—
446C22—42no—
447C22—41no—
448C22—41no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—81no—
453C22—81no—
454C22—82no—
455C22—82no—
456C22#379×C12711yescharacteristic
457C22C2×#104×C12711yescharacteristic
458C22#421×C12711yescharacteristic
459C4—22no—
460C4—24no—
461C4—21no—
462C4—42no—
463C4—41no—
464C4—41no—
465C4—42no—
466C4—41no—
467C4—84no—
468C4C2×#99×C12712yes—
469C2—21no—
470C2—21no—
471C2—42no—
472C2—42no—
473C2—82no—
474C2C127×#178111yescharacteristic
475C2C127×#178911yescharacteristic
476C2C127×#179611yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC2×#548×C127C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1789C2semidirect
3. C4×#99×C127C2semidirect
4. C127×#1508C2semidirect
5. C127×#1465C2semidirect
7. C23×Q8×C127C4semidirect
11. C2×#124×C127C4semidirect
15. C2×#121×C127C4semidirect
16. C2×C4×Q8×C127C4semidirect
157. C23×C127#104semidirect
165. Q8×C127#99semidirect
230. #8366C127direct (N × H)
240. #1789C2×C127semidirect
241. C4×#99C2×C127semidirect
242. #1508C2×C127semidirect
243. #1465C2×C127semidirect
244. C127#8366direct (N × H)
246. C23×Q8C4×C127semidirect
250. C2×#124C4×C127semidirect
254. C2×#121C4×C127semidirect
255. C2×C4×Q8C4×C127semidirect
396. C23#104×C127semidirect
404. Q8#99×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C1272
C127×#17892
C4×#99×C1272
C127×#15082
C127×#14652
#8366127