Finite Group Databasebeta

← C2×C127×#1343 #44575362

Subgroups — C2×C127×#1343 #44575362

Order 32512.

1164 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#392×C127C211yesmaximal, characteristic
2C2×#342×C127C211yesmaximal, characteristic, complemented
3C2×#323×C127C211yesmaximal, characteristic, complemented
4C127×#1343C214yesmaximal, direct product factor
5C23×D4×C127—21no—
6C23×D4×C127C411yescharacteristic, complemented
7C22×C22⋊C4×C127—21no—
8C22×C22⋊C4×C127—21no—
9C22×C22⋊C4×C127C2211yescharacteristic
10C2×C22⋊C8×C127—21no—
11#392×C127—21no—
12#392×C127—21no—
13#392×C127C412yescomplemented
14#392×C127C2212yes—
15C2×#95×C127C411yescharacteristic, complemented
16#342×C127—21no—
17#342×C127C2212yescomplemented
18#323×C127—21no—
19#323×C127C2212yescomplemented
20C25×C127—21no—
21C25×C127D411yescharacteristic
22C22×D4×C127—22no—
23C22×D4×C127—22no—
24C22×D4×C127—21no—
25C22×D4×C127—44no—
26C22×D4×C127—41no—
27C22×D4×C127—41no—
28C22×D4×C127—44no—
29C22×D4×C127—42no—
30C22×D4×C127—42no—
31C22×D4×C127—44no—
32C22×D4×C127C2×C412yescomplemented
33C23×C4×C127—21no—
34C23×C4×C127—41no—
35C23×C4×C127C2×C411yescharacteristic
36C23×C4×C127D411yescharacteristic
37C22×C8×C127—41no—
38C2×C22⋊C4×C127—24no—
39C2×C22⋊C4×C127—22no—
40C2×C22⋊C4×C127—22no—
41C2×C22⋊C4×C127—22no—
42C2×C22⋊C4×C127—41no—
43C2×C22⋊C4×C127—41no—
44C2×C22⋊C4×C127—44no—
45C2×C22⋊C4×C127—41no—
46C2×C22⋊C4×C127—42no—
47C2×C22⋊C4×C127C2×C411yescharacteristic
48C2×C22⋊C4×C127D411yescharacteristic
49C2×C22⋊C4×C127D411yescharacteristic
50C2×C22⋊C4×C127C2311yescharacteristic
51C22⋊C8×C127—22no—
52C22⋊C8×C127—41no—
53#95×C127—21no—
54#95×C127C2×C412yescomplemented
55C24×C127—21no—
56C24×C127—21no—
57C24×C127—22no—
58C24×C127—24no—
59C24×C127—22no—
60C24×C127—42no—
61C24×C127—42no—
62C24×C127—42no—
63C24×C127—42no—
64C24×C127—42no—
65C24×C127—41no—
66C24×C127—41no—
67C24×C127—42no—
68C24×C127—42no—
69C24×C127C22⋊C411yescharacteristic
70C24×C127C22⋊C411yescharacteristic
71C24×C127D812yes—
72C24×C127SD1612yes—
73C24×C127C2×D411yescharacteristic
74C2×D4×C127—42no—
75C2×D4×C127—44no—
76C2×D4×C127—44no—
77C2×D4×C127—42no—
78C2×D4×C127—44no—
79C2×D4×C127—44no—
80C2×D4×C127—44no—
81C2×D4×C127—44no—
82C2×D4×C127—48no—
83C2×D4×C127—416no—
84C2×D4×C127—416no—
85C2×D4×C127—44no—
86C2×D4×C127—44no—
87C2×D4×C127—42no—
88C2×D4×C127—42no—
89C2×D4×C127—44no—
90C22×C4×C127—24no—
91C22×C4×C127—21no—
92C22×C4×C127—21no—
93C22×C4×C127—21no—
94C22×C4×C127—22no—
95C22×C4×C127—21no—
96C22×C4×C127—42no—
97C22×C4×C127—42no—
98C22×C4×C127—42no—
99C22×C4×C127—42no—
100C22×C4×C127—44no—
101C22×C4×C127—42no—
102C22×C4×C127—82no—
103C22×C4×C127—82no—
104C22×C4×C127C22⋊C411yescharacteristic
105C22×C4×C127C22⋊C411yescharacteristic
106C22×C4×C127C22×C411yescharacteristic
107C22×C4×C127C2×D411yescharacteristic
108C2×C8×C127—42no—
109C2×C8×C127—82no—
110C22⋊C4×C127—24no—
111C22⋊C4×C127—41no—
112C22⋊C4×C127—41no—
113C22⋊C4×C127—41no—
114C22⋊C4×C127—41no—
115C22⋊C4×C127—44no—
116C22⋊C4×C127—44no—
117C22⋊C4×C127—44no—
118C22⋊C4×C127—42no—
119C23×C127—22no—
120C23×C127—22no—
121C23×C127—22no—
122C23×C127—22no—
123C23×C127—21no—
124C23×C127—21no—
125C23×C127—22no—
126C23×C127—22no—
127C23×C127—21no—
128C23×C127—21no—
129C23×C127—24no—
130C23×C127—41no—
131C23×C127—41no—
132C23×C127—44no—
133C23×C127—44no—
134C23×C127—41no—
135C23×C127—41no—
136C23×C127—42no—
137C23×C127—48no—
138C23×C127—42no—
139C23×C127—44no—
140C23×C127—42no—
141C23×C127—48no—
142C23×C127—42no—
143C23×C127—42no—
144C23×C127—44no—
145C23×C127—42no—
146C23×C127—42no—
147C23×C127—42no—
148C23×C127—84no—
149C23×C127—81no—
150C23×C127—81no—
151C23×C127—84no—
152C23×C127—84no—
153C23×C127—82no—
154C23×C127—82no—
155C23×C127—82no—
156C23×C127—82no—
157C23×C127#9911yescharacteristic
158C23×C127#9911yescharacteristic
159C23×C127#10212yes—
160C23×C127#10212yes—
161C23×C127#10412yes—
162C23×C127C2×C22⋊C411yescharacteristic
163C23×C127C2×D811yescharacteristic
164C23×C127C2×SD1611yescharacteristic
165D4×C127—44no—
166D4×C127—416no—
167D4×C127—48no—
168D4×C127—48no—
169D4×C127—44no—
170D4×C127—48no—
171C2×C4×C127—24no—
172C2×C4×C127—21no—
173C2×C4×C127—21no—
174C2×C4×C127—21no—
175C2×C4×C127—21no—
176C2×C4×C127—48no—
177C2×C4×C127—42no—
178C2×C4×C127—42no—
179C2×C4×C127—42no—
180C2×C4×C127—42no—
181C2×C4×C127—42no—
182C2×C4×C127—41no—
183C2×C4×C127—41no—
184C2×C4×C127—41no—
185C2×C4×C127—41no—
186C2×C4×C127—44no—
187C2×C4×C127—81no—
188C2×C4×C127—88no—
189C2×C4×C127—82no—
190C2×C4×C127—82no—
191C8×C127—82no—
192C22×C127—24no—
193C22×C127—24no—
194C22×C127—21no—
195C22×C127—21no—
196C22×C127—21no—
197C22×C127—21no—
198C22×C127—21no—
199C22×C127—22no—
200C22×C127—21no—
201C22×C127—42no—
202C22×C127—41no—
203C22×C127—41no—
204C22×C127—44no—
205C22×C127—44no—
206C22×C127—44no—
207C22×C127—44no—
208C22×C127—41no—
209C22×C127—41no—
210C22×C127—41no—
211C22×C127—41no—
212C22×C127—44no—
213C22×C127—81no—
214C22×C127—81no—
215C22×C127—82no—
216C22×C127—82no—
217C22×C127—82no—
218C22×C127—82no—
219C22×C127—88no—
220C22×C127—88no—
221C22×C127—82no—
222C22×C127—82no—
223C22×C127#32712yes—
224C22×C127#32712yes—
225C22×C127AΣL(1,𝔽16)12yes—
226C22×C127#35312yes—
227C22×C127C2×#9911yescharacteristic
228C22×C127C2×#10211yescharacteristic
229C22×C127C2×#10411yescharacteristic
230C4×C127—44no—
231C4×C127—41no—
232C4×C127—41no—
233C4×C127—41no—
234C4×C127—41no—
235C4×C127—84no—
236C2×#1343C12711yesmaximal, characteristic, direct product factor, Sylow
237C2×C127—21no—
238C2×C127—21no—
239C2×C127—22no—
240C2×C127—41no—
241C2×C127—42no—
242C2×C127—41no—
243C2×C127—84no—
244C2×C127#134314yesdirect product factor
245C2×C127C2×#32711yescharacteristic
246C2×C127C2×AΣL(1,𝔽16)11yescharacteristic
247C2×C127C2×#35311yescharacteristic
248C2×#392C2×C12711yescharacteristic
249C2×#342C2×C12711yescharacteristic, complemented
250C2×#323C2×C12711yescharacteristic, complemented
251#1343C2×C12714yesdirect product factor
252C127C2×#134311yescharacteristic, direct product factor, Sylow
253C23×D4—21no—
254C23×D4C4×C12711yescharacteristic, complemented
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C22⋊C4C22×C12711yescharacteristic
258C2×C22⋊C8—21no—
259#392—21no—
260#392—21no—
261#392C4×C12712yescomplemented
262#392C22×C12712yes—
263C2×#95C4×C12711yescharacteristic, complemented
264#342—21no—
265#342C22×C12712yescomplemented
266#323—21no—
267#323C22×C12712yescomplemented
268C25—21no—
269C25D4×C12711yescharacteristic
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—21no—
273C22×D4—41no—
274C22×D4—41no—
275C22×D4—44no—
276C22×D4—44no—
277C22×D4—42no—
278C22×D4—42no—
279C22×D4—44no—
280C22×D4C2×C4×C12712yescomplemented
281C23×C4—21no—
282C23×C4—41no—
283C23×C4C2×C4×C12711yescharacteristic
284C23×C4D4×C12711yescharacteristic
285C22×C8—41no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—41no—
291C2×C22⋊C4—41no—
292C2×C22⋊C4—44no—
293C2×C22⋊C4—41no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4C2×C4×C12711yescharacteristic
296C2×C22⋊C4D4×C12711yescharacteristic
297C2×C22⋊C4D4×C12711yescharacteristic
298C2×C22⋊C4C23×C12711yescharacteristic
299C22⋊C8—22no—
300C22⋊C8—41no—
301#95—21no—
302#95C2×C4×C12712yescomplemented
303C24—21no—
304C24—21no—
305C24—22no—
306C24—24no—
307C24—22no—
308C24—42no—
309C24—42no—
310C24—42no—
311C24—42no—
312C24—42no—
313C24—41no—
314C24—41no—
315C24—42no—
316C24—42no—
317C24C22⋊C4×C12711yescharacteristic
318C24C22⋊C4×C12711yescharacteristic
319C24D8×C12712yes—
320C24SD16×C12712yes—
321C24C2×D4×C12711yescharacteristic
322C2×D4—42no—
323C2×D4—44no—
324C2×D4—44no—
325C2×D4—42no—
326C2×D4—44no—
327C2×D4—44no—
328C2×D4—44no—
329C2×D4—44no—
330C2×D4—48no—
331C2×D4—416no—
332C2×D4—416no—
333C2×D4—44no—
334C2×D4—44no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—44no—
338C22×C4—24no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—44no—
349C22×C4—42no—
350C22×C4—82no—
351C22×C4—82no—
352C22×C4C22⋊C4×C12711yescharacteristic
353C22×C4C22⋊C4×C12711yescharacteristic
354C22×C4C22×C4×C12711yescharacteristic
355C22×C4C2×D4×C12711yescharacteristic
356C2×C8—42no—
357C2×C8—82no—
358C22⋊C4—24no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—44no—
364C22⋊C4—44no—
365C22⋊C4—44no—
366C22⋊C4—42no—
367C23—22no—
368C23—22no—
369C23—22no—
370C23—22no—
371C23—21no—
372C23—21no—
373C23—22no—
374C23—22no—
375C23—21no—
376C23—21no—
377C23—24no—
378C23—41no—
379C23—41no—
380C23—44no—
381C23—44no—
382C23—41no—
383C23—41no—
384C23—42no—
385C23—48no—
386C23—42no—
387C23—44no—
388C23—42no—
389C23—48no—
390C23—42no—
391C23—42no—
392C23—44no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—84no—
397C23—81no—
398C23—81no—
399C23—84no—
400C23—84no—
401C23—82no—
402C23—82no—
403C23—82no—
404C23—82no—
405C23#99×C12711yescharacteristic
406C23#99×C12711yescharacteristic
407C23#102×C12712yes—
408C23#102×C12712yes—
409C23#104×C12712yes—
410C23C2×C22⋊C4×C12711yescharacteristic
411C23C2×D8×C12711yescharacteristic
412C23C2×SD16×C12711yescharacteristic
413D4—44no—
414D4—416no—
415D4—48no—
416D4—48no—
417D4—44no—
418D4—48no—
419C2×C4—24no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—48no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—44no—
435C2×C4—81no—
436C2×C4—88no—
437C2×C4—82no—
438C2×C4—82no—
439C8—82no—
440C22—24no—
441C22—24no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—21no—
449C22—42no—
450C22—41no—
451C22—41no—
452C22—44no—
453C22—44no—
454C22—44no—
455C22—44no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—44no—
461C22—81no—
462C22—81no—
463C22—82no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—88no—
468C22—88no—
469C22—82no—
470C22—82no—
471C22#327×C12712yes—
472C22#327×C12712yes—
473C22AΣL(1,𝔽16)×C12712yes—
474C22#353×C12712yes—
475C22C2×#99×C12711yescharacteristic
476C22C2×#102×C12711yescharacteristic
477C22C2×#104×C12711yescharacteristic
478C4—44no—
479C4—41no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—84no—
484C2—21no—
485C2—21no—
486C2—22no—
487C2—41no—
488C2—42no—
489C2—41no—
490C2—84no—
491C2C127×#134314yesdirect product factor
492C2C2×#327×C12711yescharacteristic
493C2C2×AΣL(1,𝔽16)×C12711yescharacteristic
494C2C2×#353×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC2×#392×C127C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C24×C127 ◁ C22×C22⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#342×C127C2semidirect
3. C2×#323×C127C2semidirect
4. C127×#1343C2direct (N × H)
6. C23×D4×C127C4semidirect
13. #392×C127C4semidirect
15. C2×#95×C127C4semidirect
17. #342×C127C22semidirect
19. #323×C127C22semidirect
32. C22×D4×C127C2×C4semidirect
54. #95×C127C2×C4semidirect
236. C2×#1343C127direct (N × H)
244. C2×C127#1343direct (N × H)
249. C2×#342C2×C127semidirect
250. C2×#323C2×C127semidirect
251. #1343C2×C127direct (N × H)
252. C127C2×#1343direct (N × H)
254. C23×D4C4×C127semidirect
261. #392C4×C127semidirect
263. C2×#95C4×C127semidirect
265. #342C22×C127semidirect
267. #323C22×C127semidirect
280. C22×D4C2×C4×C127semidirect
302. #95C2×C4×C127semidirect
491. C2C127×#1343direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#392×C1272
C2×#342×C1272
C2×#323×C1272
C127×#13432
C2×#1343127