Finite Group Databasebeta

← C127×#10975 #44574648

Subgroups — C127×#10975 #44574648

Order 32512.

2054 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
1C22×#127×C127C211yesmaximal, characteristic
2C2×#418×C127C212yesmaximal, complemented
3C22×#100×C127C211yesmaximal, characteristic, complemented
4C127×#2309C211yesmaximal, characteristic, complemented
5C2×#339×C127C212yesmaximal, complemented
6C23×D4×C127—22no—
7C23×D4×C127C2211yescharacteristic
8C23×D4×C127C2211yescharacteristic
9C22×M16×C127C2212yes—
10C2×#127×C127—22no—
11C2×#127×C127—24no—
12C2×#127×C127—24no—
13C2×#127×C127C414yescomplemented
14C2×#117×C127C2212yes—
15C22×C42×C127C2211yescharacteristic
16#418×C127—24no—
17#418×C127—24no—
18C2×#102×C127—24no—
19C2×#100×C127—22no—
20C2×#100×C127—24no—
21#390×C127—24no—
22#379×C127—22no—
23#339×C127—24no—
24C25×C127—21no—
25C25×C127D412yes—
26C22×D4×C127—216no—
27C22×D4×C127—28no—
28C22×D4×C127—22no—
29C22×D4×C127—22no—
30C22×D4×C127—22no—
31C22×D4×C127—22no—
32C22×D4×C127—22no—
33C22×D4×C127—21no—
34C22×D4×C127—22no—
35C22×D4×C127—22no—
36C22×D4×C127—22no—
37C22×D4×C127—22no—
38C22×D4×C127—22no—
39C22×D4×C127—22no—
40C22×D4×C127—416no—
41C22×D4×C127C2×C412yes—
42C22×D4×C127C2×C412yes—
43C22×D4×C127D412yes—
44C22×D4×C127D414yes—
45C23×C4×C127—21no—
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×C127D414yescomplemented
53C22×C8×C127—22no—
54#127×C127—216no—
55#127×C127—28no—
56#127×C127—28no—
57#117×C127—22no—
58#117×C127—22no—
59#117×C127—22no—
60#117×C127—22no—
61C2×C4⋊C4×C127D414yescomplemented
62C2×C22⋊C4×C127—22no—
63C2×C22⋊C4×C127—28no—
64C2×C42×C127—22no—
65C2×C42×C127—21no—
66C2×C42×C127—22no—
67C2×C42×C127C2×C412yes—
68C2×C42×C127D414yes—
69#102×C127—216no—
70#100×C127—28no—
71C24×C127—22no—
72C24×C127—24no—
73C24×C127—24no—
74C24×C127—22no—
75C24×C127—24no—
76C24×C127—22no—
77C24×C127—48no—
78C24×C127—48no—
79C24×C127—41no—
80C24×C127—42no—
81C24×C127—41no—
82C24×C127C22⋊C414yes—
83C24×C127C2×D411yescharacteristic
84C2×D4×C127—232no—
85C2×D4×C127—22no—
86C2×D4×C127—22no—
87C2×D4×C127—22no—
88C2×D4×C127—24no—
89C2×D4×C127—24no—
90C2×D4×C127—24no—
91C2×D4×C127—24no—
92C2×D4×C127—24no—
93C2×D4×C127—22no—
94C2×D4×C127—24no—
95C2×D4×C127—24no—
96C2×D4×C127—24no—
97C2×D4×C127—24no—
98C2×D4×C127—24no—
99C2×D4×C127—24no—
100C2×D4×C127—22no—
101C2×D4×C127—432no—
102C2×D4×C127—464no—
103C2×D4×C127—42no—
104C2×D4×C127—41no—
105C2×D4×C127—42no—
106C2×D4×C127—42no—
107C2×D4×C127—42no—
108C2×D4×C127—42no—
109C2×D4×C127—42no—
110C2×D4×C127—42no—
111C2×D4×C127—42no—
112C2×D4×C127—42no—
113C2×D4×C127—41no—
114C2×D4×C127—42no—
115C2×D4×C127—42no—
116C2×D4×C127—42no—
117C2×D4×C127—42no—
118C2×D4×C127C22⋊C414yescomplemented
119C22×C4×C127—28no—
120C22×C4×C127—22no—
121C22×C4×C127—24no—
122C22×C4×C127—24no—
123C22×C4×C127C22×C411yescharacteristic
124C22×C4×C127C2×D412yes—
125C22×C4×C127C2×D412yes—
126C22×C4×C127C2×D412yes—
127C22×C4×C127C2×D412yes—
128C22×C4×C127C2×D411yescharacteristic
129C22×C4×C127#4112yes—
130C22×C4×C127#4112yes—
131M16×C127—24no—
132M16×C127—24no—
133M16×C127—42no—
134M16×C127—42no—
135C2×C8×C127—24no—
136C2×C8×C127—42no—
137C2×C8×C127—42no—
138C4⋊C4×C127—24no—
139C4⋊C4×C127—24no—
140C22⋊C4×C127—42no—
141C22⋊C4×C127—42no—
142C22⋊C4×C127—88no—
143C42×C127—22no—
144C42×C127—24no—
145C42×C127—42no—
146C42×C127—42no—
147C42×C127C22⋊C414yescomplemented
148C23×C127—24no—
149C23×C127—24no—
150C23×C127—24no—
151C23×C127—24no—
152C23×C127—24no—
153C23×C127—48no—
154C23×C127—48no—
155C23×C127—416no—
156C23×C127—416no—
157C23×C127—42no—
158C23×C127—42no—
159C23×C127—44no—
160C23×C127—44no—
161C23×C127—44no—
162C23×C127—44no—
163C23×C127—48no—
164C23×C127—84no—
165C23×C127—88no—
166C23×C127—84no—
167C23×C127—88no—
168C23×C127—84no—
169C23×C127C2×C22⋊C411yescharacteristic
170C23×C127#12012yes—
171C23×C127#12011yescharacteristic
172C23×C127#12112yes—
173C23×C127#12311yescharacteristic
174D4×C127—28no—
175D4×C127—464no—
176D4×C127—44no—
177D4×C127—44no—
178D4×C127—44no—
179D4×C127—44no—
180D4×C127—44no—
181D4×C127—44no—
182D4×C127—44no—
183C2×C4×C127—28no—
184C2×C4×C127—216no—
185C2×C4×C127—24no—
186C2×C4×C127—44no—
187C2×C4×C127—48no—
188C2×C4×C127C2×C22⋊C411yescharacteristic
189C2×C4×C127C2×C22⋊C411yescharacteristic
190C2×C4×C127C4×D412yes—
191C2×C4×C127C4×D412yes—
192C2×C4×C127#12012yes—
193C2×C4×C127#12011yescharacteristic
194C2×C4×C127#12012yes—
195C2×C4×C127#12112yes—
196C2×C4×C127#12112yes—
197C2×C4×C127#12112yes—
198C2×C4×C127#12112yes—
199C2×C4×C127#12112yes—
200C2×C4×C127#12312yes—
201C2×C4×C127#12311yescharacteristic
202C2×C4×C127#12412yes—
203C2×C4×C127#12712yes—
204C8×C127—44no—
205C22×C127—22no—
206C22×C127—22no—
207C22×C127—24no—
208C22×C127—24no—
209C22×C127—48no—
210C22×C127—48no—
211C22×C127—48no—
212C22×C127—44no—
213C22×C127—44no—
214C22×C127—84no—
215C22×C127—84no—
216C22×C127—88no—
217C22×C127—88no—
218C22×C127—84no—
219C22×C127—88no—
220C22×C127—88no—
221C22×C127#37911yescharacteristic
222C22×C127#38611yescharacteristic
223C22×C127#38611yescharacteristic
224C22×C127#39212yes—
225C22×C127#39412yes—
226C22×C127#45314yes—
227C4×C127—28no—
228C4×C127—84no—
229C4×C127#38612yes—
230C4×C127#39012yes—
231C4×C127#39212yes—
232C4×C127#39412yes—
233#10975C12711yesmaximal, characteristic, direct product factor, Sylow
234C2×C127—21no—
235C2×C127—21no—
236C2×C127—22no—
237C2×C127—84no—
238C2×C127—84no—
239C2×C127#143811yescharacteristic
240C2×C127#188712yes—
241C2×C127#200214yes—
242C22×#127C2×C12711yescharacteristic
243C2×#418C2×C12712yescomplemented
244C22×#100C2×C12711yescharacteristic, complemented
245#2309C2×C12711yescharacteristic, complemented
246C2×#339C2×C12712yescomplemented
247C127#1097511yescharacteristic, direct product factor, Sylow
248C23×D4—22no—
249C23×D4C22×C12711yescharacteristic
250C23×D4C22×C12711yescharacteristic
251C22×M16C22×C12712yes—
252C2×#127—22no—
253C2×#127—24no—
254C2×#127—24no—
255C2×#127C4×C12714yescomplemented
256C2×#117C22×C12712yes—
257C22×C42C22×C12711yescharacteristic
258#418—24no—
259#418—24no—
260C2×#102—24no—
261C2×#100—22no—
262C2×#100—24no—
263#390—24no—
264#379—22no—
265#339—24no—
266C25—21no—
267C25D4×C12712yes—
268C22×D4—216no—
269C22×D4—28no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—21no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—416no—
283C22×D4C2×C4×C12712yes—
284C22×D4C2×C4×C12712yes—
285C22×D4D4×C12712yes—
286C22×D4D4×C12714yes—
287C23×C4—21no—
288C23×C4C23×C12711yescharacteristic
289C2×M16—22no—
290C2×M16—22no—
291C2×M16—22no—
292C2×M16—22no—
293C2×M16—22no—
294C2×M16D4×C12714yescomplemented
295C22×C8—22no—
296#127—216no—
297#127—28no—
298#127—28no—
299#117—22no—
300#117—22no—
301#117—22no—
302#117—22no—
303C2×C4⋊C4D4×C12714yescomplemented
304C2×C22⋊C4—22no—
305C2×C22⋊C4—28no—
306C2×C42—22no—
307C2×C42—21no—
308C2×C42—22no—
309C2×C42C2×C4×C12712yes—
310C2×C42D4×C12714yes—
311#102—216no—
312#100—28no—
313C24—22no—
314C24—22no—
315C24—24no—
316C24—24no—
317C24—24no—
318C24—22no—
319C24—48no—
320C24—48no—
321C24—41no—
322C24—42no—
323C24—41no—
324C24C22⋊C4×C12714yes—
325C24C2×D4×C12711yescharacteristic
326C2×D4—232no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—24no—
331C2×D4—24no—
332C2×D4—24no—
333C2×D4—24no—
334C2×D4—24no—
335C2×D4—22no—
336C2×D4—24no—
337C2×D4—24no—
338C2×D4—24no—
339C2×D4—24no—
340C2×D4—24no—
341C2×D4—24no—
342C2×D4—22no—
343C2×D4—432no—
344C2×D4—464no—
345C2×D4—42no—
346C2×D4—41no—
347C2×D4—42no—
348C2×D4—42no—
349C2×D4—42no—
350C2×D4—42no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4—42no—
354C2×D4—42no—
355C2×D4—41no—
356C2×D4—42no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4C22⋊C4×C12714yescomplemented
361C22×C4—28no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4C22×C4×C12711yescharacteristic
366C22×C4C2×D4×C12712yes—
367C22×C4C2×D4×C12712yes—
368C22×C4C2×D4×C12712yes—
369C22×C4C2×D4×C12712yes—
370C22×C4C2×D4×C12711yescharacteristic
371C22×C4#41×C12712yes—
372C22×C4#41×C12712yes—
373M16—24no—
374M16—24no—
375M16—42no—
376M16—42no—
377C2×C8—24no—
378C2×C8—42no—
379C2×C8—42no—
380C4⋊C4—24no—
381C4⋊C4—24no—
382C22⋊C4—42no—
383C22⋊C4—42no—
384C22⋊C4—88no—
385C42—22no—
386C42—24no—
387C42—42no—
388C42—42no—
389C42C22⋊C4×C12714yescomplemented
390C23—24no—
391C23—24no—
392C23—24no—
393C23—24no—
394C23—24no—
395C23—48no—
396C23—48no—
397C23—416no—
398C23—416no—
399C23—42no—
400C23—42no—
401C23—44no—
402C23—44no—
403C23—44no—
404C23—44no—
405C23—48no—
406C23—84no—
407C23—88no—
408C23—84no—
409C23—88no—
410C23—84no—
411C23C2×C22⋊C4×C12711yescharacteristic
412C23#120×C12712yes—
413C23#120×C12711yescharacteristic
414C23#121×C12712yes—
415C23#123×C12711yescharacteristic
416D4—28no—
417D4—464no—
418D4—44no—
419D4—44no—
420D4—44no—
421D4—44no—
422D4—44no—
423D4—44no—
424D4—44no—
425C2×C4—28no—
426C2×C4—216no—
427C2×C4—24no—
428C2×C4—44no—
429C2×C4—48no—
430C2×C4C2×C22⋊C4×C12711yescharacteristic
431C2×C4C2×C22⋊C4×C12711yescharacteristic
432C2×C4C4×D4×C12712yes—
433C2×C4C4×D4×C12712yes—
434C2×C4#120×C12712yes—
435C2×C4#120×C12711yescharacteristic
436C2×C4#120×C12712yes—
437C2×C4#121×C12712yes—
438C2×C4#121×C12712yes—
439C2×C4#121×C12712yes—
440C2×C4#121×C12712yes—
441C2×C4#121×C12712yes—
442C2×C4#123×C12712yes—
443C2×C4#123×C12711yescharacteristic
444C2×C4#124×C12712yes—
445C2×C4#127×C12712yes—
446C8—44no—
447C22—22no—
448C22—22no—
449C22—24no—
450C22—24no—
451C22—48no—
452C22—48no—
453C22—48no—
454C22—44no—
455C22—44no—
456C22—84no—
457C22—84no—
458C22—88no—
459C22—88no—
460C22—84no—
461C22—88no—
462C22—88no—
463C22#379×C12711yescharacteristic
464C22#386×C12711yescharacteristic
465C22#386×C12711yescharacteristic
466C22#392×C12712yes—
467C22#394×C12712yes—
468C22#453×C12714yes—
469C4—28no—
470C4—84no—
471C4#386×C12712yes—
472C4#390×C12712yes—
473C4#392×C12712yes—
474C4#394×C12712yes—
475C2—21no—
476C2—21no—
477C2—22no—
478C2—84no—
479C2—84no—
480C2C127×#143811yescharacteristic
481C2C127×#188712yes—
482C2C127×#200214yes—
subgroupG/H
center, socleC23×C127#120
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC22×#127×C127C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#418×C127C2semidirect
3. C22×#100×C127C2semidirect
4. C127×#2309C2semidirect
5. C2×#339×C127C2semidirect
13. C2×#127×C127C4semidirect
52. C2×M16×C127D4semidirect
61. C2×C4⋊C4×C127D4semidirect
118. C2×D4×C127C22⋊C4semidirect
147. C42×C127C22⋊C4semidirect
233. #10975C127direct (N × H)
243. C2×#418C2×C127semidirect
244. C22×#100C2×C127semidirect
245. #2309C2×C127semidirect
246. C2×#339C2×C127semidirect
247. C127#10975direct (N × H)
255. C2×#127C4×C127semidirect
294. C2×M16D4×C127semidirect
303. C2×C4⋊C4D4×C127semidirect
360. C2×D4C22⋊C4×C127semidirect
389. C42C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#127×C1272
C2×#418×C1272
C22×#100×C1272
C127×#23092
C2×#339×C1272
#10975127