Finite Group Databasebeta

← C2×C127×#1462 #44581027

Subgroups — C2×C127×#1462 #44581027

Order 32512.

2790 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C127C211yesmaximal, characteristic
2C2×#407×C127C212yesmaximal, complemented
3C127×#1462C218yesmaximal, direct product factor
4C2×#323×C127C214yesmaximal, complemented
5C26×C127C411yescharacteristic
6C24×C4×C127C411yescharacteristic
7C24×C4×C127C2211yescharacteristic
8C22×M16×C127—22no—
9C22×C22⋊C4×C127—22no—
10C22×C22⋊C4×C127—22no—
11C22×C22⋊C4×C127—24no—
12C22×C22⋊C4×C127C414yes—
13C22×C22⋊C4×C127C412yes—
14C22×C22⋊C4×C127C2212yes—
15C22×C22⋊C4×C127C2214yes—
16#407×C127—24no—
17#407×C127C2218yescomplemented
18C2×C22⋊C8×C127—22no—
19C2×C22⋊C8×C127C2214yescomplemented
20#323×C127C22116yescomplemented
21C25×C127—22no—
22C25×C127—21no—
23C25×C127—21no—
24C25×C127—28no—
25C25×C127—44no—
26C25×C127—44no—
27C25×C127C2×C411yescharacteristic
28C25×C127C2×C414yes—
29C25×C127C2×C412yes—
30C23×C4×C127—22no—
31C23×C4×C127—21no—
32C23×C4×C127—21no—
33C23×C4×C127—44no—
34C23×C4×C127—44no—
35C23×C4×C127C2×C414yes—
36C23×C4×C127C2×C412yes—
37C23×C4×C127C2×C412yes—
38C23×C4×C127C2×C411yescharacteristic
39C23×C4×C127D412yes—
40C23×C4×C127D412yes—
41C23×C4×C127D414yes—
42C23×C4×C127C2311yescharacteristic
43C23×C4×C127C2312yes—
44C2×M16×C127—28no—
45C2×M16×C127—48no—
46C22×C8×C127—24no—
47C2×C22⋊C4×C127—28no—
48C2×C22⋊C4×C127—24no—
49C2×C22⋊C4×C127—28no—
50C2×C22⋊C4×C127—24no—
51C2×C22⋊C4×C127—28no—
52C2×C22⋊C4×C127—24no—
53C2×C22⋊C4×C127—28no—
54C2×C22⋊C4×C127—24no—
55C2×C22⋊C4×C127C2×C414yes—
56C2×C22⋊C4×C127C2×C418yes—
57C2×C22⋊C4×C127C2314yes—
58C22⋊C8×C127—28no—
59C22⋊C8×C127—24no—
60C22⋊C8×C127C2318yescomplemented
61C24×C127—24no—
62C24×C127—24no—
63C24×C127—24no—
64C24×C127—216no—
65C24×C127—28no—
66C24×C127—28no—
67C24×C127—24no—
68C24×C127—24no—
69C24×C127—22no—
70C24×C127—22no—
71C24×C127—24no—
72C24×C127—216no—
73C24×C127—44no—
74C24×C127—48no—
75C24×C127—44no—
76C24×C127—48no—
77C24×C127—464no—
78C24×C127—48no—
79C24×C127—44no—
80C24×C127—48no—
81C24×C127—44no—
82C24×C127—44no—
83C24×C127—44no—
84C24×C127C22⋊C412yes—
85C24×C127C22⋊C411yescharacteristic
86C24×C127C22⋊C411yescharacteristic
87C24×C127M1618yescomplemented
88C24×C127C22×C412yes—
89C24×C127C22×C411yescharacteristic
90C24×C127C22×C414yes—
91C22×C4×C127—28no—
92C22×C4×C127—22no—
93C22×C4×C127—24no—
94C22×C4×C127—24no—
95C22×C4×C127—22no—
96C22×C4×C127—44no—
97C22×C4×C127—42no—
98C22×C4×C127—44no—
99C22×C4×C127—48no—
100C22×C4×C127—42no—
101C22×C4×C127—44no—
102C22×C4×C127—48no—
103C22×C4×C127—44no—
104C22×C4×C127—44no—
105C22×C4×C127—48no—
106C22×C4×C127—44no—
107C22×C4×C127C22⋊C414yes—
108C22×C4×C127C22⋊C412yes—
109C22×C4×C127C22⋊C412yes—
110C22×C4×C127C22⋊C414yes—
111C22×C4×C127C22×C414yes—
112C22×C4×C127C22×C411yescharacteristic
113C22×C4×C127C22×C412yes—
114C22×C4×C127C2×D414yes—
115C22×C4×C127C2×D412yes—
116C22×C4×C127C2×D412yes—
117C22×C4×C127C2×D414yes—
118C22×C4×C127C2411yescharacteristic
119M16×C127—416no—
120C2×C8×C127—28no—
121C2×C8×C127—48no—
122C22⋊C4×C127—28no—
123C22⋊C4×C127—216no—
124C22⋊C4×C127—28no—
125C23×C127—232no—
126C23×C127—24no—
127C23×C127—24no—
128C23×C127—22no—
129C23×C127—22no—
130C23×C127—24no—
131C23×C127—22no—
132C23×C127—24no—
133C23×C127—22no—
134C23×C127—24no—
135C23×C127—22no—
136C23×C127—24no—
137C23×C127—22no—
138C23×C127—216no—
139C23×C127—216no—
140C23×C127—24no—
141C23×C127—24no—
142C23×C127—28no—
143C23×C127—28no—
144C23×C127—416no—
145C23×C127—44no—
146C23×C127—44no—
147C23×C127—464no—
148C23×C127—464no—
149C23×C127—44no—
150C23×C127—48no—
151C23×C127—44no—
152C23×C127—48no—
153C23×C127—432no—
154C23×C127—432no—
155C23×C127—416no—
156C23×C127—48no—
157C23×C127—44no—
158C23×C127—48no—
159C23×C127—44no—
160C23×C127#9914yes—
161C23×C127#10014yes—
162C23×C127C2×C22⋊C411yescharacteristic
163C23×C127C2×C22⋊C412yes—
164C23×C127C2×C22⋊C412yes—
165C23×C127C2×C22⋊C411yescharacteristic
166C23×C127C2×M1614yes—
167C23×C127C2×M1618yescomplemented
168C23×C127C23×C411yescharacteristic
169C2×C4×C127—24no—
170C2×C4×C127—28no—
171C2×C4×C127—28no—
172C2×C4×C127—24no—
173C2×C4×C127—24no—
174C2×C4×C127—44no—
175C2×C4×C127—42no—
176C2×C4×C127—41no—
177C2×C4×C127—42no—
178C2×C4×C127—42no—
179C2×C4×C127—44no—
180C2×C4×C127—41no—
181C2×C4×C127—44no—
182C2×C4×C127—48no—
183C2×C4×C127—48no—
184C2×C4×C127—44no—
185C2×C4×C127—44no—
186C2×C4×C127C2×C22⋊C412yes—
187C2×C4×C127C2×C22⋊C414yes—
188C2×C4×C127C22×D412yes—
189C8×C127—48no—
190C22×C127—216no—
191C22×C127—216no—
192C22×C127—22no—
193C22×C127—22no—
194C22×C127—21no—
195C22×C127—22no—
196C22×C127—21no—
197C22×C127—21no—
198C22×C127—22no—
199C22×C127—21no—
200C22×C127—28no—
201C22×C127—28no—
202C22×C127—28no—
203C22×C127—28no—
204C22×C127—48no—
205C22×C127—48no—
206C22×C127—416no—
207C22×C127—432no—
208C22×C127—432no—
209C22×C127—44no—
210C22×C127—44no—
211C22×C127—416no—
212C22×C127#40712yes—
213C22×C127#40712yes—
214C22×C127C2×#9914yes—
215C22×C127C2×#9912yes—
216C22×C127C2×#10014yes—
217C22×C127C2×#10012yes—
218C22×C127C22×C22⋊C411yescharacteristic
219C22×C127C22×M1612yes—
220C4×C127—22no—
221C4×C127—22no—
222C4×C127—24no—
223C4×C127—44no—
224C2×#1462C12711yesmaximal, characteristic, direct product factor, Sylow
225C2×C127—22no—
226C2×C127—22no—
227C2×C127—24no—
228C2×C127—24no—
229C2×C127—48no—
230C2×C127#146214yesdirect product factor
231C2×C127C2×#40711yescharacteristic
232C2×C127C22×#9911yescharacteristic
233C2×C127C22×#10011yescharacteristic
234C23×C22⋊C4C2×C12711yescharacteristic
235C2×#407C2×C12712yescomplemented
236#1462C2×C12718yesdirect product factor
237C2×#323C2×C12714yescomplemented
238C127C2×#146211yescharacteristic, direct product factor, Sylow
239C26C4×C12711yescharacteristic
240C24×C4C4×C12711yescharacteristic
241C24×C4C22×C12711yescharacteristic
242C22×M16—22no—
243C22×C22⋊C4—22no—
244C22×C22⋊C4—22no—
245C22×C22⋊C4—24no—
246C22×C22⋊C4C4×C12714yes—
247C22×C22⋊C4C4×C12712yes—
248C22×C22⋊C4C22×C12712yes—
249C22×C22⋊C4C22×C12714yes—
250#407—24no—
251#407C22×C12718yescomplemented
252C2×C22⋊C8—22no—
253C2×C22⋊C8C22×C12714yescomplemented
254#323C22×C127116yescomplemented
255C25—22no—
256C25—21no—
257C25—21no—
258C25—28no—
259C25—44no—
260C25—44no—
261C25C2×C4×C12711yescharacteristic
262C25C2×C4×C12714yes—
263C25C2×C4×C12712yes—
264C23×C4—22no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4C2×C4×C12714yes—
270C23×C4C2×C4×C12712yes—
271C23×C4C2×C4×C12712yes—
272C23×C4C2×C4×C12711yescharacteristic
273C23×C4D4×C12712yes—
274C23×C4D4×C12712yes—
275C23×C4D4×C12714yes—
276C23×C4C23×C12711yescharacteristic
277C23×C4C23×C12712yes—
278C2×M16—28no—
279C2×M16—48no—
280C22×C8—24no—
281C2×C22⋊C4—28no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—28no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—28no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—28no—
289C2×C22⋊C4C2×C4×C12714yes—
290C2×C22⋊C4C2×C4×C12718yes—
291C2×C22⋊C4C23×C12714yes—
292C22⋊C8—28no—
293C22⋊C8—24no—
294C22⋊C8C23×C12718yescomplemented
295C24—24no—
296C24—24no—
297C24—24no—
298C24—216no—
299C24—28no—
300C24—28no—
301C24—24no—
302C24—24no—
303C24—22no—
304C24—22no—
305C24—24no—
306C24—216no—
307C24—44no—
308C24—48no—
309C24—44no—
310C24—48no—
311C24—464no—
312C24—48no—
313C24—44no—
314C24—48no—
315C24—44no—
316C24—44no—
317C24—44no—
318C24C22⋊C4×C12712yes—
319C24C22⋊C4×C12711yescharacteristic
320C24C22⋊C4×C12711yescharacteristic
321C24M16×C12718yescomplemented
322C24C22×C4×C12712yes—
323C24C22×C4×C12711yescharacteristic
324C24C22×C4×C12714yes—
325C22×C4—28no—
326C22×C4—22no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—22no—
330C22×C4—44no—
331C22×C4—42no—
332C22×C4—44no—
333C22×C4—48no—
334C22×C4—42no—
335C22×C4—44no—
336C22×C4—48no—
337C22×C4—44no—
338C22×C4—44no—
339C22×C4—48no—
340C22×C4—44no—
341C22×C4C22⋊C4×C12714yes—
342C22×C4C22⋊C4×C12712yes—
343C22×C4C22⋊C4×C12712yes—
344C22×C4C22⋊C4×C12714yes—
345C22×C4C22×C4×C12714yes—
346C22×C4C22×C4×C12711yescharacteristic
347C22×C4C22×C4×C12712yes—
348C22×C4C2×D4×C12712yes—
349C22×C4C2×D4×C12714yes—
350C22×C4C2×D4×C12712yes—
351C22×C4C2×D4×C12714yes—
352C22×C4C24×C12711yescharacteristic
353M16—416no—
354C2×C8—28no—
355C2×C8—48no—
356C22⋊C4—28no—
357C22⋊C4—216no—
358C22⋊C4—28no—
359C23—232no—
360C23—24no—
361C23—24no—
362C23—22no—
363C23—22no—
364C23—24no—
365C23—22no—
366C23—24no—
367C23—22no—
368C23—24no—
369C23—22no—
370C23—24no—
371C23—22no—
372C23—216no—
373C23—216no—
374C23—24no—
375C23—24no—
376C23—28no—
377C23—28no—
378C23—416no—
379C23—44no—
380C23—44no—
381C23—464no—
382C23—464no—
383C23—44no—
384C23—48no—
385C23—44no—
386C23—48no—
387C23—432no—
388C23—432no—
389C23—416no—
390C23—48no—
391C23—44no—
392C23—48no—
393C23—44no—
394C23#99×C12714yes—
395C23#100×C12714yes—
396C23C2×C22⋊C4×C12711yescharacteristic
397C23C2×C22⋊C4×C12712yes—
398C23C2×C22⋊C4×C12712yes—
399C23C2×C22⋊C4×C12711yescharacteristic
400C23C2×M16×C12714yes—
401C23C2×M16×C12718yescomplemented
402C23C23×C4×C12711yescharacteristic
403C2×C4—24no—
404C2×C4—28no—
405C2×C4—28no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—41no—
415C2×C4—44no—
416C2×C4—48no—
417C2×C4—48no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4C2×C22⋊C4×C12712yes—
421C2×C4C2×C22⋊C4×C12714yes—
422C2×C4C22×D4×C12712yes—
423C8—48no—
424C22—216no—
425C22—216no—
426C22—22no—
427C22—22no—
428C22—21no—
429C22—22no—
430C22—21no—
431C22—21no—
432C22—22no—
433C22—21no—
434C22—28no—
435C22—28no—
436C22—28no—
437C22—28no—
438C22—48no—
439C22—48no—
440C22—416no—
441C22—432no—
442C22—432no—
443C22—44no—
444C22—44no—
445C22—416no—
446C22#407×C12712yes—
447C22#407×C12712yes—
448C22C2×#99×C12714yes—
449C22C2×#99×C12712yes—
450C22C2×#100×C12714yes—
451C22C2×#100×C12712yes—
452C22C22×C22⋊C4×C12711yescharacteristic
453C22C22×M16×C12712yes—
454C4—22no—
455C4—22no—
456C4—24no—
457C4—44no—
458C2—22no—
459C2—22no—
460C2—24no—
461C2—24no—
462C2—48no—
463C2C127×#146214yesdirect product factor
464C2C2×#407×C12711yescharacteristic
465C2C22×#99×C12711yescharacteristic
466C2C22×#100×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC26×C127C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#407×C127C2semidirect
3. C127×#1462C2direct (N × H)
4. C2×#323×C127C2semidirect
17. #407×C127C22semidirect
19. C2×C22⋊C8×C127C22semidirect
20. #323×C127C22semidirect
60. C22⋊C8×C127C23semidirect
87. C24×C127M16semidirect
167. C23×C127C2×M16semidirect
224. C2×#1462C127direct (N × H)
230. C2×C127#1462direct (N × H)
235. C2×#407C2×C127semidirect
236. #1462C2×C127direct (N × H)
237. C2×#323C2×C127semidirect
238. C127C2×#1462direct (N × H)
251. #407C22×C127semidirect
253. C2×C22⋊C8C22×C127semidirect
254. #323C22×C127semidirect
294. C22⋊C8C23×C127semidirect
321. C24M16×C127semidirect
401. C23C2×M16×C127semidirect
463. C2C127×#1462direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1272
C2×#407×C1272
C127×#14622
C2×#323×C1272
C2×#1462127