Finite Group Databasebeta

← C127×#10725 #44574398

Subgroups — C127×#10725 #44574398

Order 32512.

3062 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C127C211yesmaximal, characteristic
2C2×#379×C127C212yesmaximal
3C2×#342×C127C214yesmaximal, complemented
4C26×C127C2211yescharacteristic
5C24×C4×C127C412yescomplemented
6C22×C22⋊C4×C127—24no—
7C22×C22⋊C4×C127—28no—
8C22×C22⋊C4×C127—24no—
9C22×C22⋊C4×C127C412yescomplemented
10C22×C22⋊C4×C127C2214yes—
11C22×C22⋊C4×C127C2212yes—
12#379×C127—24no—
13#379×C127C418yescomplemented
14#342×C127—28no—
15C25×C127—24no—
16C25×C127—24no—
17C25×C127—48no—
18C25×C127C2×C411yescharacteristic
19C25×C127C2×C411yescharacteristic
20C25×C127C2×C414yes—
21C25×C127D414yes—
22C25×C127D412yes—
23C25×C127Q812yes—
24C25×C127C2311yescharacteristic
25C23×C4×C127—24no—
26C23×C4×C127—28no—
27C23×C4×C127—24no—
28C23×C4×C127—48no—
29C23×C4×C127C2×C414yes—
30C2×C22⋊C4×C127—232no—
31C2×C22⋊C4×C127—24no—
32C2×C22⋊C4×C127—24no—
33C2×C22⋊C4×C127—24no—
34C2×C22⋊C4×C127—28no—
35C2×C22⋊C4×C127—28no—
36C2×C22⋊C4×C127—28no—
37C2×C22⋊C4×C127—216no—
38C2×C22⋊C4×C127—24no—
39C2×C22⋊C4×C127—416no—
40C2×C22⋊C4×C127C2×C418yescomplemented
41C2×C22⋊C4×C127D418yes—
42C24×C127—28no—
43C24×C127—22no—
44C24×C127—22no—
45C24×C127—216no—
46C24×C127—22no—
47C24×C127—22no—
48C24×C127—216no—
49C24×C127—28no—
50C24×C127—28no—
51C24×C127—28no—
52C24×C127—28no—
53C24×C127—416no—
54C24×C127—44no—
55C24×C127—48no—
56C24×C127—48no—
57C24×C127—48no—
58C24×C127—44no—
59C24×C127—432no—
60C24×C127—432no—
61C24×C127C4212yes—
62C24×C127C4212yes—
63C24×C127C22⋊C412yes—
64C24×C127C22⋊C418yes—
65C24×C127C22⋊C412yes—
66C24×C127C4⋊C412yes—
67C24×C127C4⋊C418yes—
68C24×C127C4⋊C412yes—
69C24×C127C22×C411yescharacteristic
70C24×C127C22×C412yes—
71C24×C127C2×D412yes—
72C24×C127C2×D411yescharacteristic
73C24×C127C2×D414yes—
74C24×C127C2×Q811yescharacteristic
75C24×C127#4114yes—
76C22×C4×C127—216no—
77C22×C4×C127—24no—
78C22×C4×C127—24no—
79C22×C4×C127—28no—
80C22×C4×C127—432no—
81C22×C4×C127—48no—
82C22×C4×C127—48no—
83C22×C4×C127—48no—
84C22×C4×C127—416no—
85C22×C4×C127—44no—
86C22×C4×C127—44no—
87C22×C4×C127C22⋊C418yescomplemented
88C22⋊C4×C127—216no—
89C22⋊C4×C127—216no—
90C22⋊C4×C127—216no—
91C22⋊C4×C127—432no—
92C22⋊C4×C127—48no—
93C23×C127—216no—
94C23×C127—216no—
95C23×C127—28no—
96C23×C127—28no—
97C23×C127—24no—
98C23×C127—22no—
99C23×C127—24no—
100C23×C127—22no—
101C23×C127—24no—
102C23×C127—24no—
103C23×C127—28no—
104C23×C127—216no—
105C23×C127—216no—
106C23×C127—24no—
107C23×C127—22no—
108C23×C127—24no—
109C23×C127—22no—
110C23×C127—216no—
111C23×C127—216no—
112C23×C127—28no—
113C23×C127—44no—
114C23×C127—48no—
115C23×C127—48no—
116C23×C127—44no—
117C23×C127—44no—
118C23×C127—42no—
119C23×C127—48no—
120C23×C127—42no—
121C23×C127—48no—
122C23×C127—432no—
123C23×C127—432no—
124C23×C127—464no—
125C23×C127—432no—
126C23×C127—432no—
127C23×C127—48no—
128C23×C127—48no—
129C23×C127#9514yes—
130C23×C127#9514yes—
131C23×C127#9918yes—
132C23×C127C2×C4211yescharacteristic
133C23×C127C2×C22⋊C412yes—
134C23×C127C2×C22⋊C412yes—
135C23×C127C2×C22⋊C411yescharacteristic
136C23×C127C2×C4⋊C411yescharacteristic
137C23×C127C2×C4⋊C412yes—
138C23×C127#11712yes—
139C23×C127C4×D418yes—
140C23×C127#12014yes—
141C23×C127#12114yes—
142C23×C127C22⋊Q814yes—
143C23×C127#12314yes—
144C2×C4×C127—28no—
145C2×C4×C127—432no—
146C2×C4×C127—48no—
147C2×C4×C127—48no—
148C2×C4×C127—48no—
149C2×C4×C127—416no—
150C2×C4×C127—48no—
151C2×C4×C127—88no—
152C2×C4×C127—88no—
153C22×C127—216no—
154C22×C127—216no—
155C22×C127—28no—
156C22×C127—28no—
157C22×C127—24no—
158C22×C127—24no—
159C22×C127—24no—
160C22×C127—24no—
161C22×C127—22no—
162C22×C127—22no—
163C22×C127—24no—
164C22×C127—28no—
165C22×C127—24no—
166C22×C127—28no—
167C22×C127—24no—
168C22×C127—28no—
169C22×C127—48no—
170C22×C127—44no—
171C22×C127—44no—
172C22×C127—432no—
173C22×C127—432no—
174C22×C127—48no—
175C22×C127—48no—
176C22×C127—44no—
177C22×C127—44no—
178C22×C127#34218yescomplemented
179C22×C127C2×#9511yescharacteristic
180C22×C127C4×C22⋊C412yes—
181C22×C127#37911yescharacteristic
182C22×C127#38012yes—
183C22×C127#38111yescharacteristic
184C22×C127#38514yes—
185C22×C127#38614yes—
186C22×C127C2×#9914yes—
187C4×C127—48no—
188C4×C127—88no—
189#10725C12711yesmaximal, characteristic, direct product factor, Sylow
190C2×C127—24no—
191C2×C127—28no—
192C2×C127—22no—
193C2×C127—22no—
194C2×C127—24no—
195C2×C127—44no—
196C2×C127C22⋊#9511yescharacteristic
197C2×C127C2×#34212yes—
198C2×C127#178112yes—
199C2×C127#181912yes—
200C23×C22⋊C4C2×C12711yescharacteristic
201C2×#379C2×C12712yes—
202C2×#342C2×C12714yescomplemented
203C127#1072511yescharacteristic, direct product factor, Sylow
204C26C22×C12711yescharacteristic
205C24×C4C4×C12712yescomplemented
206C22×C22⋊C4—24no—
207C22×C22⋊C4—28no—
208C22×C22⋊C4—24no—
209C22×C22⋊C4C4×C12712yescomplemented
210C22×C22⋊C4C22×C12714yes—
211C22×C22⋊C4C22×C12712yes—
212#379—24no—
213#379C4×C12718yescomplemented
214#342—28no—
215C25—24no—
216C25—24no—
217C25—48no—
218C25C2×C4×C12711yescharacteristic
219C25C2×C4×C12711yescharacteristic
220C25C2×C4×C12714yes—
221C25D4×C12714yes—
222C25D4×C12712yes—
223C25Q8×C12712yes—
224C25C23×C12711yescharacteristic
225C23×C4—24no—
226C23×C4—28no—
227C23×C4—24no—
228C23×C4—48no—
229C23×C4C2×C4×C12714yes—
230C2×C22⋊C4—232no—
231C2×C22⋊C4—24no—
232C2×C22⋊C4—24no—
233C2×C22⋊C4—24no—
234C2×C22⋊C4—28no—
235C2×C22⋊C4—28no—
236C2×C22⋊C4—28no—
237C2×C22⋊C4—216no—
238C2×C22⋊C4—24no—
239C2×C22⋊C4—416no—
240C2×C22⋊C4C2×C4×C12718yescomplemented
241C2×C22⋊C4D4×C12718yes—
242C24—28no—
243C24—22no—
244C24—22no—
245C24—216no—
246C24—22no—
247C24—22no—
248C24—216no—
249C24—28no—
250C24—28no—
251C24—28no—
252C24—28no—
253C24—416no—
254C24—44no—
255C24—48no—
256C24—48no—
257C24—48no—
258C24—44no—
259C24—432no—
260C24—432no—
261C24C42×C12712yes—
262C24C42×C12712yes—
263C24C22⋊C4×C12712yes—
264C24C22⋊C4×C12718yes—
265C24C22⋊C4×C12712yes—
266C24C4⋊C4×C12712yes—
267C24C4⋊C4×C12718yes—
268C24C4⋊C4×C12712yes—
269C24C22×C4×C12711yescharacteristic
270C24C22×C4×C12712yes—
271C24C2×D4×C12712yes—
272C24C2×D4×C12711yescharacteristic
273C24C2×D4×C12714yes—
274C24C2×Q8×C12711yescharacteristic
275C24#41×C12714yes—
276C22×C4—216no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—28no—
280C22×C4—432no—
281C22×C4—48no—
282C22×C4—48no—
283C22×C4—48no—
284C22×C4—416no—
285C22×C4—44no—
286C22×C4—44no—
287C22×C4C22⋊C4×C12718yescomplemented
288C22⋊C4—216no—
289C22⋊C4—216no—
290C22⋊C4—216no—
291C22⋊C4—432no—
292C22⋊C4—48no—
293C23—216no—
294C23—216no—
295C23—28no—
296C23—28no—
297C23—24no—
298C23—22no—
299C23—24no—
300C23—22no—
301C23—24no—
302C23—24no—
303C23—28no—
304C23—216no—
305C23—216no—
306C23—24no—
307C23—22no—
308C23—24no—
309C23—22no—
310C23—216no—
311C23—216no—
312C23—28no—
313C23—44no—
314C23—48no—
315C23—48no—
316C23—44no—
317C23—44no—
318C23—42no—
319C23—48no—
320C23—42no—
321C23—48no—
322C23—432no—
323C23—432no—
324C23—464no—
325C23—432no—
326C23—432no—
327C23—48no—
328C23—48no—
329C23#95×C12714yes—
330C23#95×C12714yes—
331C23#99×C12718yes—
332C23C2×C42×C12711yescharacteristic
333C23C2×C22⋊C4×C12712yes—
334C23C2×C22⋊C4×C12712yes—
335C23C2×C22⋊C4×C12711yescharacteristic
336C23C2×C4⋊C4×C12711yescharacteristic
337C23C2×C4⋊C4×C12712yes—
338C23#117×C12712yes—
339C23C4×D4×C12718yes—
340C23#120×C12714yes—
341C23#121×C12714yes—
342C23C22⋊Q8×C12714yes—
343C23#123×C12714yes—
344C2×C4—28no—
345C2×C4—432no—
346C2×C4—48no—
347C2×C4—48no—
348C2×C4—48no—
349C2×C4—416no—
350C2×C4—48no—
351C2×C4—88no—
352C2×C4—88no—
353C22—216no—
354C22—216no—
355C22—28no—
356C22—28no—
357C22—24no—
358C22—24no—
359C22—24no—
360C22—24no—
361C22—22no—
362C22—22no—
363C22—24no—
364C22—28no—
365C22—24no—
366C22—28no—
367C22—24no—
368C22—28no—
369C22—48no—
370C22—44no—
371C22—44no—
372C22—432no—
373C22—432no—
374C22—48no—
375C22—48no—
376C22—44no—
377C22—44no—
378C22#342×C12718yescomplemented
379C22C2×#95×C12711yescharacteristic
380C22C4×C22⋊C4×C12712yes—
381C22#379×C12711yescharacteristic
382C22#380×C12712yes—
383C22#381×C12711yescharacteristic
384C22#385×C12714yes—
385C22#386×C12714yes—
386C22C2×#99×C12714yes—
387C4—48no—
388C4—88no—
389C2—24no—
390C2—28no—
391C2—22no—
392C2—22no—
393C2—24no—
394C2—44no—
395C2C127×C22⋊#9511yescharacteristic
396C2C2×#342×C12712yes—
397C2C127×#178112yes—
398C2C127×#181912yes—
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC23C2×C42×C127
Frattini, cosocleC25C23×C127
prime radicalC26×C127C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C26×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#342×C127C2semidirect
5. C24×C4×C127C4semidirect
9. C22×C22⋊C4×C127C4semidirect
13. #379×C127C4semidirect
40. C2×C22⋊C4×C127C2×C4semidirect
87. C22×C4×C127C22⋊C4semidirect
178. C22×C127#342semidirect
189. #10725C127direct (N × H)
202. C2×#342C2×C127semidirect
203. C127#10725direct (N × H)
205. C24×C4C4×C127semidirect
209. C22×C22⋊C4C4×C127semidirect
213. #379C4×C127semidirect
240. C2×C22⋊C4C2×C4×C127semidirect
287. C22×C4C22⋊C4×C127semidirect
378. C22#342×C127semidirect

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×#379×C1272
C2×#342×C1272
#10725127