Finite Group Databasebeta

← C127×#10973 #44574646

Subgroups — C127×#10973 #44574646

Order 32512.

1450 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C127C211yesmaximal, characteristic
2C2×#413×C127C211yesmaximal, characteristic, complemented
3C22×#100×C127C212yesmaximal, complemented
4C127×#2879C211yesmaximal, characteristic, complemented
5C2×#344×C127C212yesmaximal, complemented
6C22×#41×C127C2211yescharacteristic
7C23×D4×C127C2211yescharacteristic
8C22×M16×C127C2212yes—
9C22×M16×C127C2212yes—
10#535×C127—24no—
11#535×C127—24no—
12C2×#127×C127—21no—
13C2×#124×C127—21no—
14C2×#121×C127—22no—
15C2×#120×C127C414yes—
16C2×#117×C127C2211yescharacteristic
17#413×C127—24no—
18C2×#101×C127—21no—
19C2×#100×C127—24no—
20C2×#100×C127—21no—
21C2×#100×C127—24no—
22C2×#100×C127—24no—
23#408×C127—24no—
24#407×C127—22no—
25#344×C127—24no—
26C25×C127C2×C412yes—
27C2×#41×C127—22no—
28C2×#41×C127—22no—
29C2×#41×C127—22no—
30C2×#41×C127—22no—
31C2×#41×C127—22no—
32C2×#41×C127—22no—
33C22×Q8×C127D411yescharacteristic
34C22×D4×C127—24no—
35C22×D4×C127—21no—
36C22×D4×C127—21no—
37C22×D4×C127—22no—
38C22×D4×C127—22no—
39C22×D4×C127—22no—
40C22×D4×C127—22no—
41C22×D4×C127—22no—
42C22×D4×C127C2×C412yes—
43C22×D4×C127D411yescharacteristic
44C22×D4×C127D414yes—
45C23×C4×C127D412yes—
46C23×C4×C127C2311yescharacteristic
47C2×M16×C127—22no—
48C2×M16×C127—22no—
49C2×M16×C127—22no—
50C2×M16×C127—22no—
51C2×M16×C127—22no—
52C2×M16×C127—22no—
53C2×M16×C127—22no—
54C2×M16×C127—22no—
55C2×M16×C127—22no—
56C2×M16×C127—22no—
57C2×M16×C127D414yescomplemented
58C2×M16×C127D414yescomplemented
59C22×C8×C127—22no—
60C22×C8×C127—22no—
61#127×C127—28no—
62#124×C127—28no—
63#121×C127—216no—
64#120×C127—28no—
65#120×C127—28no—
66#117×C127—22no—
67#117×C127D414yes—
68C2×C4⋊C4×C127—21no—
69C2×C22⋊C4×C127—24no—
70C2×C22⋊C4×C127C2×C412yes—
71C2×C42×C127—21no—
72#101×C127—24no—
73#100×C127—216no—
74#100×C127—24no—
75C22⋊C8×C127—28no—
76C24×C127—22no—
77C24×C127—22no—
78C24×C127—24no—
79C24×C127—24no—
80C24×C127—84no—
81C24×C127C22⋊C412yes—
82C24×C127C22⋊C414yes—
83C24×C127C22×C411yescharacteristic
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—
92C2×Q8×C127—21no—
93C2×Q8×C127—22no—
94C2×Q8×C127—22no—
95C2×Q8×C127—21no—
96C2×D4×C127—22no—
97C2×D4×C127—22no—
98C2×D4×C127—24no—
99C2×D4×C127—24no—
100C2×D4×C127—216no—
101C2×D4×C127—24no—
102C2×D4×C127—21no—
103C2×D4×C127—24no—
104C2×D4×C127—24no—
105C2×D4×C127—22no—
106C2×D4×C127—24no—
107C2×D4×C127—24no—
108C2×D4×C127—22no—
109C2×D4×C127—24no—
110C2×D4×C127—21no—
111C2×D4×C127—41no—
112C2×D4×C127—41no—
113C2×D4×C127—42no—
114C2×D4×C127—42no—
115C2×D4×C127—42no—
116C2×D4×C127—42no—
117C2×D4×C127—41no—
118C2×D4×C127—41no—
119C2×D4×C127—42no—
120C2×D4×C127—42no—
121C2×D4×C127—88no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—24no—
125C22×C4×C127—24no—
126C22×C4×C127—22no—
127C22×C4×C127C22⋊C412yes—
128C22×C4×C127C2×D411yescharacteristic
129C22×C4×C127C2×D411yescharacteristic
130C22×C4×C127C2×D412yes—
131C22×C4×C127C2×D412yes—
132C22×C4×C127C2×D412yes—
133C22×C4×C127C2×D412yes—
134C22×C4×C127#4112yes—
135C22×C4×C127#4112yes—
136M16×C127—24no—
137M16×C127—24no—
138M16×C127—24no—
139M16×C127—24no—
140M16×C127—42no—
141M16×C127—42no—
142M16×C127—42no—
143M16×C127—42no—
144C2×C8×C127—24no—
145C2×C8×C127—24no—
146C2×C8×C127—42no—
147C2×C8×C127—42no—
148C2×C8×C127—42no—
149C2×C8×C127—42no—
150C4⋊C4×C127—24no—
151C22⋊C4×C127—216no—
152C22⋊C4×C127—22no—
153C22⋊C4×C127C22⋊C414yes—
154C42×C127—24no—
155C23×C127—24no—
156C23×C127—22no—
157C23×C127—22no—
158C23×C127—22no—
159C23×C127—28no—
160C23×C127—42no—
161C23×C127—44no—
162C23×C127—48no—
163C23×C127—42no—
164C23×C127—42no—
165C23×C127—44no—
166C23×C127—88no—
167C23×C127—84no—
168C23×C127—84no—
169C23×C127—88no—
170C23×C127C2×C22⋊C411yescharacteristic
171C23×C127C2×C22⋊C411yescharacteristic
172C23×C127C2×C22⋊C411yescharacteristic
173C23×C127C4×D412yes—
174C23×C127C4×D412yes—
175Q8×C127—42no—
176Q8×C127—42no—
177D4×C127—44no—
178D4×C127—44no—
179D4×C127—44no—
180D4×C127—44no—
181D4×C127—42no—
182D4×C127—44no—
183D4×C127—44no—
184D4×C127—42no—
185D4×C127—816no—
186C2×C4×C127—24no—
187C2×C4×C127—22no—
188C2×C4×C127—22no—
189C2×C4×C127—22no—
190C2×C4×C127—44no—
191C2×C4×C127—44no—
192C2×C4×C127—44no—
193C2×C4×C127#12012yes—
194C2×C4×C127#12011yescharacteristic
195C2×C4×C127#12011yescharacteristic
196C2×C4×C127#12012yes—
197C2×C4×C127#12012yes—
198C2×C4×C127#12112yes—
199C2×C4×C127#12112yes—
200C2×C4×C127#12112yes—
201C2×C4×C127#12112yes—
202C2×C4×C127#12112yes—
203C2×C4×C127#12112yes—
204C2×C4×C127#12312yes—
205C2×C4×C127#12311yescharacteristic
206C2×C4×C127#12311yescharacteristic
207C2×C4×C127#12412yes—
208C2×C4×C127#12712yes—
209C8×C127—44no—
210C8×C127—44no—
211C22×C127—22no—
212C22×C127—24no—
213C22×C127—41no—
214C22×C127—41no—
215C22×C127—42no—
216C22×C127—44no—
217C22×C127—48no—
218C22×C127—44no—
219C22×C127—42no—
220C22×C127—44no—
221C22×C127—82no—
222C22×C127—88no—
223C22×C127—84no—
224C22×C127—88no—
225C22×C127—84no—
226C22×C127#37911yescharacteristic
227C22×C127#38611yescharacteristic
228C22×C127#38612yes—
229C22×C127#38611yescharacteristic
230C22×C127#39012yes—
231C4×C127—44no—
232C4×C127—42no—
233C4×C127#39212yes—
234C4×C127#39212yes—
235C4×C127#39412yes—
236C4×C127#39412yes—
237#10973C12711yesmaximal, characteristic, direct product factor, Sylow
238C2×C127—21no—
239C2×C127—21no—
240C2×C127—22no—
241C2×C127—22no—
242C2×C127—82no—
243C2×C127—84no—
244C2×C127#143811yescharacteristic
245C2×C127#191412yes—
246C2×#535C2×C12711yescharacteristic
247C2×#413C2×C12711yescharacteristic, complemented
248C22×#100C2×C12712yescomplemented
249#2879C2×C12711yescharacteristic, complemented
250C2×#344C2×C12712yescomplemented
251C127#1097311yescharacteristic, direct product factor, Sylow
252C22×#41C22×C12711yescharacteristic
253C23×D4C22×C12711yescharacteristic
254C22×M16C22×C12712yes—
255C22×M16C22×C12712yes—
256#535—24no—
257#535—24no—
258C2×#127—21no—
259C2×#124—21no—
260C2×#121—22no—
261C2×#120C4×C12714yes—
262C2×#117C22×C12711yescharacteristic
263#413—24no—
264C2×#101—21no—
265C2×#100—24no—
266C2×#100—21no—
267C2×#100—24no—
268C2×#100—24no—
269#408—24no—
270#407—22no—
271#344—24no—
272C25C2×C4×C12712yes—
273C2×#41—22no—
274C2×#41—22no—
275C2×#41—22no—
276C2×#41—22no—
277C2×#41—22no—
278C2×#41—22no—
279C22×Q8D4×C12711yescharacteristic
280C22×D4—24no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4C2×C4×C12712yes—
289C22×D4D4×C12711yescharacteristic
290C22×D4D4×C12714yes—
291C23×C4D4×C12712yes—
292C23×C4C23×C12711yescharacteristic
293C2×M16—22no—
294C2×M16—22no—
295C2×M16—22no—
296C2×M16—22no—
297C2×M16—22no—
298C2×M16—22no—
299C2×M16—22no—
300C2×M16—22no—
301C2×M16—22no—
302C2×M16—22no—
303C2×M16D4×C12714yescomplemented
304C2×M16D4×C12714yescomplemented
305C22×C8—22no—
306C22×C8—22no—
307#127—28no—
308#124—28no—
309#121—216no—
310#120—28no—
311#120—28no—
312#117—22no—
313#117D4×C12714yes—
314C2×C4⋊C4—21no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4C2×C4×C12712yes—
317C2×C42—21no—
318#101—24no—
319#100—216no—
320#100—24no—
321C22⋊C8—28no—
322C24—22no—
323C24—22no—
324C24—24no—
325C24—24no—
326C24—84no—
327C24C22⋊C4×C12712yes—
328C24C22⋊C4×C12714yes—
329C24C22×C4×C12711yescharacteristic
330#41—42no—
331#41—42no—
332#41—42no—
333#41—42no—
334#41—42no—
335#41—42no—
336#41—42no—
337#41—42no—
338C2×Q8—21no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—21no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—24no—
345C2×D4—24no—
346C2×D4—216no—
347C2×D4—24no—
348C2×D4—21no—
349C2×D4—24no—
350C2×D4—24no—
351C2×D4—22no—
352C2×D4—24no—
353C2×D4—24no—
354C2×D4—22no—
355C2×D4—24no—
356C2×D4—21no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—88no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—22no—
373C22×C4C22⋊C4×C12712yes—
374C22×C4C2×D4×C12711yescharacteristic
375C22×C4C2×D4×C12711yescharacteristic
376C22×C4C2×D4×C12712yes—
377C22×C4C2×D4×C12712yes—
378C22×C4C2×D4×C12712yes—
379C22×C4C2×D4×C12712yes—
380C22×C4#41×C12712yes—
381C22×C4#41×C12712yes—
382M16—24no—
383M16—24no—
384M16—24no—
385M16—24no—
386M16—42no—
387M16—42no—
388M16—42no—
389M16—42no—
390C2×C8—24no—
391C2×C8—24no—
392C2×C8—42no—
393C2×C8—42no—
394C2×C8—42no—
395C2×C8—42no—
396C4⋊C4—24no—
397C22⋊C4—216no—
398C22⋊C4—22no—
399C22⋊C4C22⋊C4×C12714yes—
400C42—24no—
401C23—24no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—28no—
406C23—42no—
407C23—44no—
408C23—48no—
409C23—42no—
410C23—42no—
411C23—44no—
412C23—88no—
413C23—84no—
414C23—84no—
415C23—88no—
416C23C2×C22⋊C4×C12711yescharacteristic
417C23C2×C22⋊C4×C12711yescharacteristic
418C23C2×C22⋊C4×C12711yescharacteristic
419C23C4×D4×C12712yes—
420C23C4×D4×C12712yes—
421Q8—42no—
422Q8—42no—
423D4—44no—
424D4—44no—
425D4—44no—
426D4—44no—
427D4—42no—
428D4—44no—
429D4—44no—
430D4—42no—
431D4—816no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4#120×C12711yescharacteristic
440C2×C4#120×C12712yes—
441C2×C4#120×C12711yescharacteristic
442C2×C4#120×C12712yes—
443C2×C4#120×C12712yes—
444C2×C4#121×C12712yes—
445C2×C4#121×C12712yes—
446C2×C4#121×C12712yes—
447C2×C4#121×C12712yes—
448C2×C4#121×C12712yes—
449C2×C4#121×C12712yes—
450C2×C4#123×C12711yescharacteristic
451C2×C4#123×C12712yes—
452C2×C4#123×C12711yescharacteristic
453C2×C4#124×C12712yes—
454C2×C4#127×C12712yes—
455C8—44no—
456C8—44no—
457C22—22no—
458C22—24no—
459C22—41no—
460C22—41no—
461C22—42no—
462C22—44no—
463C22—48no—
464C22—44no—
465C22—42no—
466C22—44no—
467C22—82no—
468C22—88no—
469C22—84no—
470C22—88no—
471C22—84no—
472C22#379×C12711yescharacteristic
473C22#386×C12711yescharacteristic
474C22#386×C12712yes—
475C22#386×C12711yescharacteristic
476C22#390×C12712yes—
477C4—44no—
478C4—42no—
479C4#392×C12712yes—
480C4#392×C12712yes—
481C4#394×C12712yes—
482C4#394×C12712yes—
483C2—21no—
484C2—21no—
485C2—22no—
486C2—22no—
487C2—82no—
488C2—84no—
489C2C127×#143811yescharacteristic
490C2C127×#191412yes—
subgroupG/H
center, socleC22×C127#386
commutatorC24C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC2×#535×C127C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#413×C127C2semidirect
3. C22×#100×C127C2semidirect
4. C127×#2879C2semidirect
5. C2×#344×C127C2semidirect
57. C2×M16×C127D4semidirect
58. C2×M16×C127D4semidirect
237. #10973C127direct (N × H)
247. C2×#413C2×C127semidirect
248. C22×#100C2×C127semidirect
249. #2879C2×C127semidirect
250. C2×#344C2×C127semidirect
251. C127#10973direct (N × H)
303. C2×M16D4×C127semidirect
304. C2×M16D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1272
C2×#413×C1272
C22×#100×C1272
C127×#28792
C2×#344×C1272
#10973127