Finite Group Databasebeta

← C127×#10996 #44574669

Subgroups — C127×#10996 #44574669

Order 32512.

1306 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3449C211yesmaximal, characteristic
2C2×#413×C127C212yesmaximal, complemented
3C2×#408×C127C212yesmaximal, complemented
4C127×#1742C211yesmaximal, characteristic, complemented
5C127×#1729C211yesmaximal, characteristic, complemented
6C22×#41×C127C2212yes—
7C22×M16×C127C2212yes—
8C22×M16×C127C2211yescharacteristic
9C23×C8×C127C2211yescharacteristic
10#537×C127—22no—
11#536×C127—22no—
12#535×C127—22no—
13#534×C127C414yes—
14#532×C127—22no—
15#525×C127—24no—
16C2×#117×C127C2211yescharacteristic
17#413×C127—24no—
18#413×C127—24no—
19C2×#101×C127—22no—
20C2×#100×C127—22no—
21#408×C127—24no—
22#408×C127—24no—
23C2×C22⋊C8×C127—24no—
24#343×C127—22no—
25#336×C127—22no—
26C2×#41×C127—22no—
27C2×#41×C127—22no—
28C2×#41×C127—22no—
29C2×#41×C127—22no—
30C2×#41×C127—22no—
31C2×#41×C127—22no—
32C2×#41×C127—22no—
33C2×#41×C127—22no—
34C2×#41×C127—22no—
35C2×#41×C127—22no—
36C2×#41×C127—22no—
37C2×#41×C127—22no—
38C22×Q8×C127D412yes—
39C22×D4×C127C2×C414yes—
40C22×D4×C127D412yes—
41C23×C4×C127D414yes—
42C23×C4×C127C2311yescharacteristic
43C2×M16×C127—22no—
44C2×M16×C127—21no—
45C2×M16×C127—22no—
46C2×M16×C127—22no—
47C2×M16×C127—22no—
48C2×M16×C127—22no—
49C2×M16×C127—22no—
50C2×M16×C127—22no—
51C2×M16×C127D414yescomplemented
52C2×M16×C127D412yescomplemented
53C22×C8×C127—21no—
54C22×C8×C127—22no—
55C22×C8×C127—22no—
56C22×C8×C127—21no—
57C22×C8×C127—22no—
58C22×C8×C127—21no—
59C22×C8×C127D412yescomplemented
60C4⋊Q8×C127—22no—
61#127×C127—22no—
62#124×C127—24no—
63#123×C127—28no—
64C22⋊Q8×C127—28no—
65#121×C127—28no—
66#121×C127—28no—
67#120×C127—28no—
68C4×D4×C127—28no—
69#117×C127—22no—
70#117×C127—22no—
71C2×C4⋊C4×C127D412yes—
72C2×C22⋊C4×C127C2×C412yes—
73C2×C42×C127D412yes—
74#101×C127—28no—
75#100×C127—28no—
76C22⋊C8×C127—216no—
77C24×C127C22⋊C414yes—
78C24×C127C22×C411yescharacteristic
79#41×C127—42no—
80#41×C127—42no—
81#41×C127—42no—
82#41×C127—42no—
83#41×C127—42no—
84#41×C127—42no—
85#41×C127—42no—
86#41×C127—42no—
87#41×C127—42no—
88#41×C127—42no—
89#41×C127—42no—
90#41×C127—42no—
91#41×C127—42no—
92#41×C127—42no—
93#41×C127—42no—
94#41×C127—42no—
95C2×Q8×C127—22no—
96C2×Q8×C127—22no—
97C2×Q8×C127—22no—
98C2×Q8×C127—22no—
99C2×Q8×C127—22no—
100C2×Q8×C127—22no—
101C2×D4×C127—24no—
102C2×D4×C127—24no—
103C2×D4×C127—24no—
104C2×D4×C127—24no—
105C2×D4×C127—24no—
106C2×D4×C127—24no—
107C2×D4×C127—28no—
108C2×D4×C127—22no—
109C2×D4×C127—22no—
110C2×D4×C127—22no—
111C2×D4×C127—22no—
112C2×D4×C127—22no—
113C2×D4×C127—22no—
114C22×C4×C127—24no—
115C22×C4×C127—24no—
116C22×C4×C127—24no—
117C22×C4×C127—24no—
118C22×C4×C127—24no—
119C22×C4×C127—24no—
120C22×C4×C127C22⋊C414yes—
121C22×C4×C127C22⋊C414yes—
122C22×C4×C127C2×D412yes—
123C22×C4×C127C2×D412yes—
124C22×C4×C127C2×D412yes—
125C22×C4×C127C2×D411yescharacteristic
126C22×C4×C127C2×D411yescharacteristic
127C22×C4×C127C2×D411yescharacteristic
128C22×C4×C127C2×D411yescharacteristic
129C22×C4×C127#4111yescharacteristic
130C22×C4×C127#4112yes—
131C22×C4×C127#4111yescharacteristic
132M16×C127—24no—
133M16×C127—24no—
134M16×C127—24no—
135M16×C127—42no—
136M16×C127—42no—
137M16×C127—42no—
138C2×C8×C127—24no—
139C2×C8×C127—24no—
140C2×C8×C127—22no—
141C2×C8×C127—22no—
142C2×C8×C127—41no—
143C2×C8×C127—42no—
144C2×C8×C127—41no—
145C2×C8×C127—42no—
146C2×C8×C127—42no—
147C2×C8×C127—41no—
148C2×C8×C127—41no—
149C4⋊C4×C127—28no—
150C4⋊C4×C127—24no—
151C22⋊C4×C127—216no—
152C22⋊C4×C127—24no—
153C42×C127—22no—
154C42×C127—22no—
155C23×C127—24no—
156C23×C127—24no—
157C23×C127—24no—
158C23×C127—42no—
159C23×C127—48no—
160C23×C127C2×C22⋊C412yes—
161C23×C127C2×C22⋊C411yescharacteristic
162C23×C127C4×D412yes—
163C23×C127C4×D411yescharacteristic
164C23×C127C4×D411yescharacteristic
165Q8×C127—42no—
166Q8×C127—42no—
167Q8×C127—42no—
168Q8×C127—42no—
169D4×C127—44no—
170D4×C127—44no—
171D4×C127—44no—
172D4×C127—44no—
173D4×C127—42no—
174D4×C127—42no—
175D4×C127—42no—
176D4×C127—42no—
177D4×C127—88no—
178C2×C4×C127—24no—
179C2×C4×C127—24no—
180C2×C4×C127—24no—
181C2×C4×C127—24no—
182C2×C4×C127—44no—
183C2×C4×C127—44no—
184C2×C4×C127—44no—
185C2×C4×C127—44no—
186C2×C4×C127—44no—
187C2×C4×C127#12012yes—
188C2×C4×C127#12012yes—
189C2×C4×C127#12011yescharacteristic
190C2×C4×C127#12012yes—
191C2×C4×C127#12011yescharacteristic
192C2×C4×C127#12112yes—
193C2×C4×C127#12112yes—
194C2×C4×C127#12112yes—
195C2×C4×C127#12112yes—
196C2×C4×C127#12111yescharacteristic
197C2×C4×C127#12111yescharacteristic
198C2×C4×C127#12112yes—
199C2×C4×C127#12312yes—
200C2×C4×C127#12312yes—
201C2×C4×C127#12411yescharacteristic
202C2×C4×C127#12411yescharacteristic
203C2×C4×C127#12711yescharacteristic
204C2×C4×C127#12711yescharacteristic
205C8×C127—42no—
206C8×C127—44no—
207C8×C127—42no—
208C22×C127—22no—
209C22×C127—24no—
210C22×C127—41no—
211C22×C127—42no—
212C22×C127—41no—
213C22×C127—48no—
214C22×C127—44no—
215C22×C127—48no—
216C22×C127—84no—
217C22×C127#37911yescharacteristic
218C22×C127#38612yes—
219C22×C127#38612yes—
220C22×C127#39011yescharacteristic
221C22×C127#39011yescharacteristic
222C4×C127—44no—
223C4×C127—44no—
224C4×C127#39211yescharacteristic
225C4×C127#39212yes—
226C4×C127#39211yescharacteristic
227C4×C127#39411yescharacteristic
228C4×C127#39412yes—
229C4×C127#39411yescharacteristic
230#10996C12711yesmaximal, characteristic, direct product factor, Sylow
231C2×C127—22no—
232C2×C127—22no—
233C2×C127—21no—
234C2×C127—21no—
235C2×C127—84no—
236C2×C127#143811yescharacteristic
237C2×C127#179112yes—
238#3449C2×C12711yescharacteristic
239C2×#413C2×C12712yescomplemented
240C2×#408C2×C12712yescomplemented
241#1742C2×C12711yescharacteristic, complemented
242#1729C2×C12711yescharacteristic, complemented
243C127#1099611yescharacteristic, direct product factor, Sylow
244C22×#41C22×C12712yes—
245C22×M16C22×C12712yes—
246C22×M16C22×C12711yescharacteristic
247C23×C8C22×C12711yescharacteristic
248#537—22no—
249#536—22no—
250#535—22no—
251#534C4×C12714yes—
252#532—22no—
253#525—24no—
254C2×#117C22×C12711yescharacteristic
255#413—24no—
256#413—24no—
257C2×#101—22no—
258C2×#100—22no—
259#408—24no—
260#408—24no—
261C2×C22⋊C8—24no—
262#343—22no—
263#336—22no—
264C2×#41—22no—
265C2×#41—22no—
266C2×#41—22no—
267C2×#41—22no—
268C2×#41—22no—
269C2×#41—22no—
270C2×#41—22no—
271C2×#41—22no—
272C2×#41—22no—
273C2×#41—22no—
274C2×#41—22no—
275C2×#41—22no—
276C22×Q8D4×C12712yes—
277C22×D4C2×C4×C12714yes—
278C22×D4D4×C12712yes—
279C23×C4D4×C12714yes—
280C23×C4C23×C12711yescharacteristic
281C2×M16—22no—
282C2×M16—21no—
283C2×M16—22no—
284C2×M16—22no—
285C2×M16—22no—
286C2×M16—22no—
287C2×M16—22no—
288C2×M16—22no—
289C2×M16D4×C12714yescomplemented
290C2×M16D4×C12712yescomplemented
291C22×C8—21no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—21no—
295C22×C8—22no—
296C22×C8—21no—
297C22×C8D4×C12712yescomplemented
298C4⋊Q8—22no—
299#127—22no—
300#124—24no—
301#123—28no—
302C22⋊Q8—28no—
303#121—28no—
304#121—28no—
305#120—28no—
306C4×D4—28no—
307#117—22no—
308#117—22no—
309C2×C4⋊C4D4×C12712yes—
310C2×C22⋊C4C2×C4×C12712yes—
311C2×C42D4×C12712yes—
312#101—28no—
313#100—28no—
314C22⋊C8—216no—
315C24C22⋊C4×C12714yes—
316C24C22×C4×C12711yescharacteristic
317#41—42no—
318#41—42no—
319#41—42no—
320#41—42no—
321#41—42no—
322#41—42no—
323#41—42no—
324#41—42no—
325#41—42no—
326#41—42no—
327#41—42no—
328#41—42no—
329#41—42no—
330#41—42no—
331#41—42no—
332#41—42no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×D4—24no—
340C2×D4—24no—
341C2×D4—24no—
342C2×D4—24no—
343C2×D4—24no—
344C2×D4—24no—
345C2×D4—28no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4C22⋊C4×C12714yes—
359C22×C4C22⋊C4×C12714yes—
360C22×C4C2×D4×C12712yes—
361C22×C4C2×D4×C12712yes—
362C22×C4C2×D4×C12712yes—
363C22×C4C2×D4×C12711yescharacteristic
364C22×C4C2×D4×C12711yescharacteristic
365C22×C4C2×D4×C12711yescharacteristic
366C22×C4C2×D4×C12711yescharacteristic
367C22×C4#41×C12711yescharacteristic
368C22×C4#41×C12712yes—
369C22×C4#41×C12711yescharacteristic
370M16—24no—
371M16—24no—
372M16—24no—
373M16—42no—
374M16—42no—
375M16—42no—
376C2×C8—24no—
377C2×C8—24no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—41no—
381C2×C8—41no—
382C2×C8—42no—
383C2×C8—42no—
384C2×C8—42no—
385C2×C8—41no—
386C2×C8—41no—
387C4⋊C4—28no—
388C4⋊C4—24no—
389C22⋊C4—216no—
390C22⋊C4—24no—
391C42—22no—
392C42—22no—
393C23—24no—
394C23—24no—
395C23—24no—
396C23—42no—
397C23—48no—
398C23C2×C22⋊C4×C12712yes—
399C23C2×C22⋊C4×C12711yescharacteristic
400C23C4×D4×C12712yes—
401C23C4×D4×C12711yescharacteristic
402C23C4×D4×C12711yescharacteristic
403Q8—42no—
404Q8—42no—
405Q8—42no—
406Q8—42no—
407D4—44no—
408D4—44no—
409D4—44no—
410D4—44no—
411D4—42no—
412D4—42no—
413D4—42no—
414D4—42no—
415D4—88no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4#120×C12712yes—
426C2×C4#120×C12712yes—
427C2×C4#120×C12711yescharacteristic
428C2×C4#120×C12711yescharacteristic
429C2×C4#120×C12712yes—
430C2×C4#121×C12712yes—
431C2×C4#121×C12712yes—
432C2×C4#121×C12712yes—
433C2×C4#121×C12712yes—
434C2×C4#121×C12711yescharacteristic
435C2×C4#121×C12711yescharacteristic
436C2×C4#121×C12712yes—
437C2×C4#123×C12712yes—
438C2×C4#123×C12712yes—
439C2×C4#124×C12711yescharacteristic
440C2×C4#124×C12711yescharacteristic
441C2×C4#127×C12711yescharacteristic
442C2×C4#127×C12711yescharacteristic
443C8—42no—
444C8—44no—
445C8—42no—
446C22—22no—
447C22—24no—
448C22—41no—
449C22—42no—
450C22—41no—
451C22—48no—
452C22—44no—
453C22—48no—
454C22—84no—
455C22#379×C12711yescharacteristic
456C22#386×C12712yes—
457C22#386×C12712yes—
458C22#390×C12711yescharacteristic
459C22#390×C12711yescharacteristic
460C4—44no—
461C4—44no—
462C4#392×C12711yescharacteristic
463C4#392×C12712yes—
464C4#392×C12711yescharacteristic
465C4#394×C12711yescharacteristic
466C4#394×C12712yes—
467C4#394×C12711yescharacteristic
468C2—22no—
469C2—22no—
470C2—21no—
471C2—21no—
472C2—84no—
473C2C127×#143811yescharacteristic
474C2C127×#179112yes—
subgroupG/H
centerC2×C4×C127#120
commutatorC24C22×C4×C127
Frattini, cosocleC23×C4C23×C127
socleC22×C127#379
prime radicalC127×#3449C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#413×C127C2semidirect
3. C2×#408×C127C2semidirect
4. C127×#1742C2semidirect
5. C127×#1729C2semidirect
51. C2×M16×C127D4semidirect
52. C2×M16×C127D4semidirect
59. C22×C8×C127D4semidirect
230. #10996C127direct (N × H)
239. C2×#413C2×C127semidirect
240. C2×#408C2×C127semidirect
241. #1742C2×C127semidirect
242. #1729C2×C127semidirect
243. C127#10996direct (N × H)
289. C2×M16D4×C127semidirect
290. C2×M16D4×C127semidirect
297. C22×C8D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34492
C2×#413×C1272
C2×#408×C1272
C127×#17422
C127×#17292
#10996127