Finite Group Databasebeta

← C2×C127×#1345 #44575368

Subgroups — C2×C127×#1345 #44575368

Order 32512.

824 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#394×C127C211yesmaximal, characteristic
2C2×#343×C127C211yesmaximal, characteristic, complemented
3C2×#324×C127C211yesmaximal, characteristic, complemented
4C127×#1345C214yesmaximal, direct product factor
5C23×D4×C127C411yescharacteristic
6C22×M16×C127—21no—
7C22×C4⋊C4×C127C2211yescharacteristic
8C22×C22⋊C4×C127—21no—
9C22×C22⋊C4×C127—21no—
10C2×C22⋊C8×C127—21no—
11#394×C127—21no—
12#394×C127—21no—
13#394×C127C412yes—
14#394×C127C2212yes—
15C2×#95×C127C411yescharacteristic
16#343×C127—21no—
17#343×C127C2212yescomplemented
18#324×C127—21no—
19#324×C127C2212yescomplemented
20C25×C127—21no—
21C22×D4×C127—21no—
22C22×D4×C127—41no—
23C22×D4×C127—41no—
24C22×D4×C127—44no—
25C22×D4×C127C2×C412yes—
26C23×C4×C127—21no—
27C23×C4×C127C2×C411yescharacteristic
28C23×C4×C127D411yescharacteristic
29C23×C4×C127D411yescharacteristic
30C2×M16×C127—24no—
31C2×M16×C127—22no—
32C2×M16×C127—41no—
33C2×M16×C127—42no—
34C22×C8×C127—41no—
35C22×C8×C127—41no—
36C2×C4⋊C4×C127—41no—
37C2×C4⋊C4×C127—41no—
38C2×C4⋊C4×C127C2×C411yescharacteristic
39C2×C4⋊C4×C127D411yescharacteristic
40C2×C4⋊C4×C127D411yescharacteristic
41C2×C4⋊C4×C127C2311yescharacteristic
42C2×C22⋊C4×C127—22no—
43C2×C22⋊C4×C127—22no—
44C2×C22⋊C4×C127—22no—
45C2×C22⋊C4×C127—22no—
46C2×C22⋊C4×C127—44no—
47C2×C22⋊C4×C127—42no—
48C2×C22⋊C4×C127—42no—
49C22⋊C8×C127—22no—
50C22⋊C8×C127—41no—
51#95×C127—21no—
52#95×C127C2×C412yes—
53C24×C127—24no—
54C24×C127—22no—
55C24×C127—42no—
56C24×C127—42no—
57C24×C127—42no—
58C24×C127—41no—
59C24×C127—41no—
60C24×C127—42no—
61C24×C127—42no—
62C24×C127C22⋊C411yescharacteristic
63C2×D4×C127—42no—
64C2×D4×C127—42no—
65C2×D4×C127—44no—
66C2×D4×C127—44no—
67C2×D4×C127—48no—
68C2×D4×C127—44no—
69C2×D4×C127—44no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—22no—
73C22×C4×C127—21no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—22no—
78C22×C4×C127—42no—
79C22×C4×C127—42no—
80C22×C4×C127—42no—
81C22×C4×C127—42no—
82C22×C4×C127—42no—
83C22×C4×C127C22⋊C411yescharacteristic
84C22×C4×C127C22⋊C411yescharacteristic
85C22×C4×C127C22⋊C411yescharacteristic
86C22×C4×C127D812yes—
87C22×C4×C127SD1612yes—
88C22×C4×C127C22×C411yescharacteristic
89C22×C4×C127C2×D411yescharacteristic
90C22×C4×C127C2×D411yescharacteristic
91M16×C127—24no—
92M16×C127—44no—
93M16×C127—42no—
94C2×C8×C127—44no—
95C2×C8×C127—42no—
96C2×C8×C127—42no—
97C2×C8×C127—82no—
98C4⋊C4×C127—41no—
99C4⋊C4×C127—41no—
100C4⋊C4×C127—41no—
101C4⋊C4×C127—41no—
102C22⋊C4×C127—44no—
103C22⋊C4×C127—44no—
104C22⋊C4×C127—44no—
105C22⋊C4×C127—42no—
106C22⋊C4×C127—42no—
107C23×C127—22no—
108C23×C127—22no—
109C23×C127—24no—
110C23×C127—42no—
111C23×C127—44no—
112C23×C127—48no—
113C23×C127—48no—
114C23×C127—42no—
115C23×C127—42no—
116C23×C127—44no—
117C23×C127—42no—
118C23×C127—42no—
119C23×C127—42no—
120C23×C127—84no—
121C23×C127—84no—
122C23×C127—82no—
123C23×C127—82no—
124C23×C127—82no—
125C23×C127—82no—
126C23×C127#9911yescharacteristic
127C23×C127#9911yescharacteristic
128C23×C127#10212yes—
129C23×C127#10412yes—
130C23×C127C2×C22⋊C411yescharacteristic
131D4×C127—44no—
132D4×C127—44no—
133D4×C127—48no—
134C2×C4×C127—22no—
135C2×C4×C127—22no—
136C2×C4×C127—22no—
137C2×C4×C127—22no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—21no—
145C2×C4×C127—21no—
146C2×C4×C127—42no—
147C2×C4×C127—42no—
148C2×C4×C127—42no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—42no—
154C2×C4×C127—42no—
155C2×C4×C127—42no—
156C2×C4×C127—81no—
157C2×C4×C127—84no—
158C2×C4×C127#10212yes—
159C2×C4×C127C2×D811yescharacteristic
160C2×C4×C127C2×SD1611yescharacteristic
161C8×C127—44no—
162C8×C127—82no—
163C22×C127—24no—
164C22×C127—24no—
165C22×C127—21no—
166C22×C127—21no—
167C22×C127—21no—
168C22×C127—21no—
169C22×C127—44no—
170C22×C127—44no—
171C22×C127—44no—
172C22×C127—82no—
173C22×C127—82no—
174C22×C127—88no—
175C22×C127—88no—
176C22×C127—82no—
177C22×C127—82no—
178C22×C127#32712yes—
179C22×C127#32712yes—
180C22×C127AΣL(1,𝔽16)12yes—
181C22×C127#35512yes—
182C22×C127C2×#9911yescharacteristic
183C22×C127C2×#10211yescharacteristic
184C22×C127C2×#10411yescharacteristic
185C4×C127—21no—
186C4×C127—22no—
187C4×C127—21no—
188C4×C127—41no—
189C4×C127—41no—
190C4×C127—41no—
191C4×C127—41no—
192C4×C127—82no—
193C2×#1345C12711yesmaximal, characteristic, direct product factor, Sylow
194C2×C127—21no—
195C2×C127—21no—
196C2×C127—22no—
197C2×C127—84no—
198C2×C127#134514yesdirect product factor
199C2×C127C2×#32711yescharacteristic
200C2×C127C2×AΣL(1,𝔽16)11yescharacteristic
201C2×C127C2×#35511yescharacteristic
202C2×#394C2×C12711yescharacteristic
203C2×#343C2×C12711yescharacteristic, complemented
204C2×#324C2×C12711yescharacteristic, complemented
205#1345C2×C12714yesdirect product factor
206C127C2×#134511yescharacteristic, direct product factor, Sylow
207C23×D4C4×C12711yescharacteristic
208C22×M16—21no—
209C22×C4⋊C4C22×C12711yescharacteristic
210C22×C22⋊C4—21no—
211C22×C22⋊C4—21no—
212C2×C22⋊C8—21no—
213#394—21no—
214#394—21no—
215#394C4×C12712yes—
216#394C22×C12712yes—
217C2×#95C4×C12711yescharacteristic
218#343—21no—
219#343C22×C12712yescomplemented
220#324—21no—
221#324C22×C12712yescomplemented
222C25—21no—
223C22×D4—21no—
224C22×D4—41no—
225C22×D4—41no—
226C22×D4—44no—
227C22×D4C2×C4×C12712yes—
228C23×C4—21no—
229C23×C4C2×C4×C12711yescharacteristic
230C23×C4D4×C12711yescharacteristic
231C23×C4D4×C12711yescharacteristic
232C2×M16—24no—
233C2×M16—22no—
234C2×M16—41no—
235C2×M16—42no—
236C22×C8—41no—
237C22×C8—41no—
238C2×C4⋊C4—41no—
239C2×C4⋊C4—41no—
240C2×C4⋊C4C2×C4×C12711yescharacteristic
241C2×C4⋊C4D4×C12711yescharacteristic
242C2×C4⋊C4D4×C12711yescharacteristic
243C2×C4⋊C4C23×C12711yescharacteristic
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—44no—
249C2×C22⋊C4—42no—
250C2×C22⋊C4—42no—
251C22⋊C8—22no—
252C22⋊C8—41no—
253#95—21no—
254#95C2×C4×C12712yes—
255C24—24no—
256C24—22no—
257C24—42no—
258C24—42no—
259C24—42no—
260C24—41no—
261C24—41no—
262C24—42no—
263C24—42no—
264C24C22⋊C4×C12711yescharacteristic
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—44no—
268C2×D4—44no—
269C2×D4—48no—
270C2×D4—44no—
271C2×D4—44no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4C22⋊C4×C12711yescharacteristic
286C22×C4C22⋊C4×C12711yescharacteristic
287C22×C4C22⋊C4×C12711yescharacteristic
288C22×C4D8×C12712yes—
289C22×C4SD16×C12712yes—
290C22×C4C22×C4×C12711yescharacteristic
291C22×C4C2×D4×C12711yescharacteristic
292C22×C4C2×D4×C12711yescharacteristic
293M16—24no—
294M16—44no—
295M16—42no—
296C2×C8—44no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—82no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C22⋊C4—44no—
305C22⋊C4—44no—
306C22⋊C4—44no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C23—22no—
310C23—22no—
311C23—24no—
312C23—42no—
313C23—44no—
314C23—48no—
315C23—48no—
316C23—42no—
317C23—42no—
318C23—44no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—84no—
323C23—84no—
324C23—82no—
325C23—82no—
326C23—82no—
327C23—82no—
328C23#99×C12711yescharacteristic
329C23#99×C12711yescharacteristic
330C23#102×C12712yes—
331C23#104×C12712yes—
332C23C2×C22⋊C4×C12711yescharacteristic
333D4—44no—
334D4—44no—
335D4—48no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—81no—
359C2×C4—84no—
360C2×C4#102×C12712yes—
361C2×C4C2×D8×C12711yescharacteristic
362C2×C4C2×SD16×C12711yescharacteristic
363C8—44no—
364C8—82no—
365C22—24no—
366C22—24no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—44no—
372C22—44no—
373C22—44no—
374C22—82no—
375C22—82no—
376C22—88no—
377C22—88no—
378C22—82no—
379C22—82no—
380C22#327×C12712yes—
381C22#327×C12712yes—
382C22AΣL(1,𝔽16)×C12712yes—
383C22#355×C12712yes—
384C22C2×#99×C12711yescharacteristic
385C22C2×#102×C12711yescharacteristic
386C22C2×#104×C12711yescharacteristic
387C4—21no—
388C4—22no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—82no—
395C2—21no—
396C2—21no—
397C2—22no—
398C2—84no—
399C2C127×#134514yesdirect product factor
400C2C2×#327×C12711yescharacteristic
401C2C2×AΣL(1,𝔽16)×C12711yescharacteristic
402C2C2×#355×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC23×D4×C127C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C24×C127 ◁ C22×C4⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#343×C127C2semidirect
3. C2×#324×C127C2semidirect
4. C127×#1345C2direct (N × H)
17. #343×C127C22semidirect
19. #324×C127C22semidirect
193. C2×#1345C127direct (N × H)
198. C2×C127#1345direct (N × H)
203. C2×#343C2×C127semidirect
204. C2×#324C2×C127semidirect
205. #1345C2×C127direct (N × H)
206. C127C2×#1345direct (N × H)
219. #343C22×C127semidirect
221. #324C22×C127semidirect
399. C2C127×#1345direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#394×C1272
C2×#343×C1272
C2×#324×C1272
C127×#13452
C2×#1345127