Finite Group Databasebeta

← C127×#20732 #44584405

Subgroups — C127×#20732 #44584405

Order 32512.

1802 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic
2C2×#431×C127C211yesmaximal, characteristic, complemented
3C127×#2285C211yesmaximal, characteristic, complemented
4C127×#1823C212yesmaximal, complemented
5C127×#1802C214yesmaximal, complemented
6C127×#1786C212yesmaximal
7C4×#102×C127C214yesmaximal, complemented
8C23×D4×C127C2211yescharacteristic
9C24×C4×C127—21no—
10C2×C4×D4×C127—21no—
11C2×C4×D4×C127—21no—
12C2×C4×D4×C127—24no—
13C2×C4×D4×C127C418yescomplemented
14C2×C4×D4×C127C2212yes—
15C2×C4×D4×C127C2212yes—
16C2×#117×C127—21no—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C22⋊C4×C127—21no—
19C22×C42×C127C2211yescharacteristic
20#431×C127—24no—
21C2×C4⋊C8×C127C2212yescomplemented
22C2×#102×C127C2218yes—
23C2×C22⋊C8×C127C2212yes—
24C2×C4×C8×C127C2212yescomplemented
25#384×C127C2212yescomplemented
26#382×C127—21no—
27#380×C127—21no—
28#380×C127C2212yes—
29C4×C4⋊C4×C127—21no—
30C4×C4⋊C4×C127C2212yescomplemented
31#340×C127C2218yescomplemented
32C25×C127—21no—
33C22×D4×C127—28no—
34C22×D4×C127—21no—
35C22×D4×C127—22no—
36C22×D4×C127C2×C414yes—
37C22×D4×C127C2312yes—
38C23×C4×C127—21no—
39C23×C4×C127—28no—
40C23×C4×C127—22no—
41C23×C4×C127—22no—
42C23×C4×C127—44no—
43C23×C4×C127—44no—
44C23×C4×C127D411yescharacteristic
45C23×C4×C127D411yescharacteristic
46C23×C4×C127C2311yescharacteristic
47C22×C8×C127C2314yes—
48C4×D4×C127—28no—
49C4×D4×C127—28no—
50C4×D4×C127—24no—
51C4×D4×C127—24no—
52C4×D4×C127C2×C418yes—
53C4×D4×C127C2×C418yes—
54#117×C127—44no—
55C2×C4⋊C4×C127—21no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127C2×C414yes—
60C2×C4⋊C4×C127C2314yes—
61C2×C4⋊C4×C127C2312yes—
62C2×C22⋊C4×C127—28no—
63C2×C22⋊C4×C127—22no—
64C2×C22⋊C4×C127—22no—
65C2×C22⋊C4×C127—22no—
66C2×C42×C127—22no—
67C2×C42×C127C2×C414yes—
68C2×C42×C127D411yescharacteristic
69C2×C42×C127D411yescharacteristic
70C2×C42×C127D414yes—
71C2×C42×C127C2311yescharacteristic
72C2×C42×C127C2311yescharacteristic
73C4⋊C8×C127—24no—
74#102×C127—216no—
75C22⋊C8×C127—24no—
76C4×C8×C127—24no—
77#95×C127—22no—
78#95×C127—22no—
79C24×C127—28no—
80C24×C127—24no—
81C24×C127—22no—
82C24×C127—44no—
83C24×C127—42no—
84C24×C127—42no—
85C24×C127C2×D411yescharacteristic
86C2×D4×C127—28no—
87C2×D4×C127—216no—
88C2×D4×C127—216no—
89C2×D4×C127—24no—
90C2×D4×C127—22no—
91C2×D4×C127—24no—
92C2×D4×C127C22×C414yes—
93C2×D4×C127#4118yes—
94C22×C4×C127—24no—
95C22×C4×C127—24no—
96C22×C4×C127—22no—
97C22×C4×C127—28no—
98C22×C4×C127—28no—
99C22×C4×C127—24no—
100C22×C4×C127—42no—
101C22×C4×C127—42no—
102C22×C4×C127—42no—
103C22×C4×C127—432no—
104C22×C4×C127—44no—
105C22×C4×C127—44no—
106C22×C4×C127—44no—
107C22×C4×C127—44no—
108C22×C4×C127C22⋊C414yes—
109C22×C4×C127C22⋊C414yes—
110C22×C4×C127D814yes—
111C22×C4×C127SD1614yes—
112C22×C4×C127C22×C412yes—
113C22×C4×C127C2×D411yescharacteristic
114C22×C4×C127C2×D411yescharacteristic
115C22×C4×C127C2×D411yescharacteristic
116C22×C4×C127C2×D412yes—
117C22×C4×C127C2×D411yescharacteristic
118C22×C4×C127C2×D411yescharacteristic
119C22×C4×C127C2411yescharacteristic
120C2×C8×C127—24no—
121C2×C8×C127—28no—
122C4⋊C4×C127—24no—
123C4⋊C4×C127—22no—
124C4⋊C4×C127—28no—
125C4⋊C4×C127—44no—
126C4⋊C4×C127—44no—
127C4⋊C4×C127C22×C414yes—
128C22⋊C4×C127—28no—
129C22⋊C4×C127—28no—
130C22⋊C4×C127—44no—
131C42×C127—44no—
132C42×C127C22⋊C414yes—
133C42×C127C22⋊C414yes—
134C42×C127C22×C412yes—
135C42×C127C22×C412yes—
136C42×C127C2×D412yes—
137C42×C127C2×D412yes—
138C23×C127—22no—
139C23×C127—22no—
140C23×C127—216no—
141C23×C127—24no—
142C23×C127—28no—
143C23×C127—416no—
144C23×C127—416no—
145C23×C127—48no—
146C23×C127—42no—
147C23×C127—42no—
148C23×C127—44no—
149C23×C127—48no—
150C23×C127C2×C22⋊C412yes—
151C23×C127C2×D812yes—
152C23×C127C2×SD1612yes—
153C23×C127C22×D411yescharacteristic
154D4×C127—216no—
155D4×C127—24no—
156D4×C127—28no—
157D4×C127#11718yescomplemented
158C2×C4×C127—22no—
159C2×C4×C127—22no—
160C2×C4×C127—22no—
161C2×C4×C127—24no—
162C2×C4×C127—24no—
163C2×C4×C127—24no—
164C2×C4×C127—44no—
165C2×C4×C127—42no—
166C2×C4×C127—42no—
167C2×C4×C127—48no—
168C2×C4×C127—416no—
169C2×C4×C127—416no—
170C2×C4×C127—44no—
171C2×C4×C127—44no—
172C2×C4×C127—44no—
173C2×C4×C127#102116yescomplemented
174C2×C4×C127C2×C22⋊C412yes—
175C2×C4×C127C2×C22⋊C412yes—
176C2×C4×C127C2×C22⋊C412yes—
177C2×C4×C127C2×C22⋊C412yes—
178C2×C4×C127C2×C22⋊C412yes—
179C2×C4×C127C2×D812yes—
180C2×C4×C127C2×D812yes—
181C2×C4×C127C2×SD1612yes—
182C2×C4×C127C2×SD1612yes—
183C2×C4×C127C23×C411yescharacteristic
184C2×C4×C127C22×D411yescharacteristic
185C2×C4×C127C2×#4114yes—
186C8×C127—44no—
187C22×C127—24no—
188C22×C127—24no—
189C22×C127—22no—
190C22×C127—22no—
191C22×C127—28no—
192C22×C127—432no—
193C22×C127—48no—
194C22×C127—48no—
195C22×C127—44no—
196C22×C127—44no—
197C22×C127C2×#10214yes—
198C22×C127C22×C22⋊C411yescharacteristic
199C22×C127#52512yes—
200C22×C127C22×D811yescharacteristic
201C22×C127C22×SD1611yescharacteristic
202C22×C127#57512yes—
203C4×C127—22no—
204C4×C127—22no—
205C4×C127—22no—
206C4×C127—44no—
207C4×C127—84no—
208C4×C127C2×#10214yes—
209C4×C127C2×#10214yes—
210C4×C127C2×#11712yes—
211C4×C127#52512yes—
212#20732C12711yesmaximal, characteristic, direct product factor, Sylow
213C2×C127—24no—
214C2×C127—48no—
215C2×C127#228011yescharacteristic
216C2×C127C22×#10211yescharacteristic
217C2×C127#289611yescharacteristic
218C2×C127#310012yes—
219C2×C127#310112yes—
220C22×C4×D4C2×C12711yescharacteristic
221C2×#431C2×C12711yescharacteristic, complemented
222#2285C2×C12711yescharacteristic, complemented
223#1823C2×C12712yescomplemented
224#1802C2×C12714yescomplemented
225#1786C2×C12712yes—
226C4×#102C2×C12714yescomplemented
227C127#2073211yescharacteristic, direct product factor, Sylow
228C23×D4C22×C12711yescharacteristic
229C24×C4—21no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—24no—
233C2×C4×D4C4×C12718yescomplemented
234C2×C4×D4C22×C12712yes—
235C2×C4×D4C22×C12712yes—
236C2×#117—21no—
237C22×C4⋊C4C22×C12711yescharacteristic
238C22×C22⋊C4—21no—
239C22×C42C22×C12711yescharacteristic
240#431—24no—
241C2×C4⋊C8C22×C12712yescomplemented
242C2×#102C22×C12718yes—
243C2×C22⋊C8C22×C12712yes—
244C2×C4×C8C22×C12712yescomplemented
245#384C22×C12712yescomplemented
246#382—21no—
247#380—21no—
248#380C22×C12712yes—
249C4×C4⋊C4—21no—
250C4×C4⋊C4C22×C12712yescomplemented
251#340C22×C12718yescomplemented
252C25—21no—
253C22×D4—28no—
254C22×D4—21no—
255C22×D4—22no—
256C22×D4C2×C4×C12714yes—
257C22×D4C23×C12712yes—
258C23×C4—21no—
259C23×C4—28no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—44no—
263C23×C4—44no—
264C23×C4D4×C12711yescharacteristic
265C23×C4D4×C12711yescharacteristic
266C23×C4C23×C12711yescharacteristic
267C22×C8C23×C12714yes—
268C4×D4—28no—
269C4×D4—28no—
270C4×D4—24no—
271C4×D4—24no—
272C4×D4C2×C4×C12718yes—
273C4×D4C2×C4×C12718yes—
274#117—44no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4C2×C4×C12714yes—
280C2×C4⋊C4C23×C12714yes—
281C2×C4⋊C4C23×C12712yes—
282C2×C22⋊C4—28no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—22no—
286C2×C42—22no—
287C2×C42C2×C4×C12714yes—
288C2×C42D4×C12711yescharacteristic
289C2×C42D4×C12711yescharacteristic
290C2×C42D4×C12714yes—
291C2×C42C23×C12711yescharacteristic
292C2×C42C23×C12711yescharacteristic
293C4⋊C8—24no—
294#102—216no—
295C22⋊C8—24no—
296C4×C8—24no—
297#95—22no—
298#95—22no—
299C24—28no—
300C24—24no—
301C24—22no—
302C24—44no—
303C24—42no—
304C24—42no—
305C24C2×D4×C12711yescharacteristic
306C2×D4—28no—
307C2×D4—216no—
308C2×D4—216no—
309C2×D4—24no—
310C2×D4—22no—
311C2×D4—24no—
312C2×D4C22×C4×C12714yes—
313C2×D4#41×C12718yes—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—22no—
317C22×C4—28no—
318C22×C4—28no—
319C22×C4—24no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—432no—
324C22×C4—44no—
325C22×C4—44no—
326C22×C4—44no—
327C22×C4—44no—
328C22×C4C22⋊C4×C12714yes—
329C22×C4C22⋊C4×C12714yes—
330C22×C4D8×C12714yes—
331C22×C4SD16×C12714yes—
332C22×C4C22×C4×C12712yes—
333C22×C4C2×D4×C12711yescharacteristic
334C22×C4C2×D4×C12711yescharacteristic
335C22×C4C2×D4×C12711yescharacteristic
336C22×C4C2×D4×C12712yes—
337C22×C4C2×D4×C12711yescharacteristic
338C22×C4C2×D4×C12711yescharacteristic
339C22×C4C24×C12711yescharacteristic
340C2×C8—24no—
341C2×C8—28no—
342C4⋊C4—24no—
343C4⋊C4—22no—
344C4⋊C4—28no—
345C4⋊C4—44no—
346C4⋊C4—44no—
347C4⋊C4C22×C4×C12714yes—
348C22⋊C4—28no—
349C22⋊C4—28no—
350C22⋊C4—44no—
351C42—44no—
352C42C22⋊C4×C12714yes—
353C42C22⋊C4×C12714yes—
354C42C22×C4×C12712yes—
355C42C22×C4×C12712yes—
356C42C2×D4×C12712yes—
357C42C2×D4×C12712yes—
358C23—22no—
359C23—22no—
360C23—216no—
361C23—24no—
362C23—28no—
363C23—416no—
364C23—416no—
365C23—48no—
366C23—42no—
367C23—42no—
368C23—44no—
369C23—48no—
370C23C2×C22⋊C4×C12712yes—
371C23C2×D8×C12712yes—
372C23C2×SD16×C12712yes—
373C23C22×D4×C12711yescharacteristic
374D4—216no—
375D4—24no—
376D4—28no—
377D4#117×C12718yescomplemented
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—24no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—48no—
388C2×C4—416no—
389C2×C4—416no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4#102×C127116yescomplemented
394C2×C4C2×C22⋊C4×C12712yes—
395C2×C4C2×C22⋊C4×C12712yes—
396C2×C4C2×C22⋊C4×C12712yes—
397C2×C4C2×C22⋊C4×C12712yes—
398C2×C4C2×C22⋊C4×C12712yes—
399C2×C4C2×D8×C12712yes—
400C2×C4C2×D8×C12712yes—
401C2×C4C2×SD16×C12712yes—
402C2×C4C2×SD16×C12712yes—
403C2×C4C23×C4×C12711yescharacteristic
404C2×C4C22×D4×C12711yescharacteristic
405C2×C4C2×#41×C12714yes—
406C8—44no—
407C22—24no—
408C22—24no—
409C22—22no—
410C22—22no—
411C22—28no—
412C22—432no—
413C22—48no—
414C22—48no—
415C22—44no—
416C22—44no—
417C22C2×#102×C12714yes—
418C22C22×C22⋊C4×C12711yescharacteristic
419C22#525×C12712yes—
420C22C22×D8×C12711yescharacteristic
421C22C22×SD16×C12711yescharacteristic
422C22#575×C12712yes—
423C4—22no—
424C4—22no—
425C4—22no—
426C4—44no—
427C4—84no—
428C4C2×#102×C12714yes—
429C4C2×#102×C12714yes—
430C4C2×#117×C12712yes—
431C4#525×C12712yes—
432C2—24no—
433C2—48no—
434C2C127×#228011yescharacteristic
435C2C22×#102×C12711yescharacteristic
436C2C127×#289611yescharacteristic
437C2C127×#310012yes—
438C2C127×#310112yes—
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C22×D4
prime radicalC23×D4×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#431×C127C2semidirect
3. C127×#2285C2semidirect
4. C127×#1823C2semidirect
5. C127×#1802C2semidirect
7. C4×#102×C127C2semidirect
13. C2×C4×D4×C127C4semidirect
21. C2×C4⋊C8×C127C22semidirect
24. C2×C4×C8×C127C22semidirect
25. #384×C127C22semidirect
30. C4×C4⋊C4×C127C22semidirect
31. #340×C127C22semidirect
157. D4×C127#117semidirect
173. C2×C4×C127#102semidirect
212. #20732C127direct (N × H)
221. C2×#431C2×C127semidirect
222. #2285C2×C127semidirect
223. #1823C2×C127semidirect
224. #1802C2×C127semidirect
226. C4×#102C2×C127semidirect
227. C127#20732direct (N × H)
233. C2×C4×D4C4×C127semidirect
241. C2×C4⋊C8C22×C127semidirect
244. C2×C4×C8C22×C127semidirect
245. #384C22×C127semidirect
250. C4×C4⋊C4C22×C127semidirect
251. #340C22×C127semidirect
377. D4#117×C127semidirect
393. C2×C4#102×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1272
C2×#431×C1272
C127×#22852
C127×#18232
C127×#18022
C127×#17862
C4×#102×C1272
#20732127