Finite Group Databasebeta

← C2×C127×#1393 #44576253

Subgroups — C2×C127×#1393 #44576253

Order 32512.

1154 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C127C212yesmaximal
2C2×#390×C127C211yesmaximal, characteristic
3C127×#1393C214yesmaximal, direct product factor
4C23×D4×C127C2211yescharacteristic
5C22×C4⋊C4×C127C411yescharacteristic, complemented
6C22×C22⋊C4×C127—22no—
7C22×C22⋊C4×C127—22no—
8C22×C42×C127C411yescharacteristic, complemented
9C2×#99×C127—22no—
10C2×#99×C127—24no—
11C2×#99×C127C418yescomplemented
12C2×#99×C127C2214yes—
13#390×C127—22no—
14#390×C127C412yescomplemented
15#390×C127C2212yes—
16C25×C127D412yes—
17C22×D4×C127—42no—
18C22×D4×C127—41no—
19C22×D4×C127—41no—
20C22×D4×C127C2×C414yes—
21C22×D4×C127C2×C411yescharacteristic
22C22×D4×C127D412yes—
23C22×D4×C127D412yes—
24C22×D4×C127Q812yes—
25C22×D4×C127C2311yescharacteristic
26C23×C4×C127—21no—
27C23×C4×C127—21no—
28C23×C4×C127—42no—
29C23×C4×C127C2×C411yescharacteristic
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127—41no—
32C2×C4⋊C4×C127—41no—
33C2×C4⋊C4×C127C2×C412yescomplemented
34C2×C22⋊C4×C127—28no—
35C2×C22⋊C4×C127—24no—
36C2×C22⋊C4×C127—24no—
37C2×C22⋊C4×C127—24no—
38C2×C22⋊C4×C127—48no—
39C2×C22⋊C4×C127—42no—
40C2×C22⋊C4×C127—44no—
41C2×C42×C127—21no—
42C2×C42×C127—42no—
43C2×C42×C127C2×C412yescomplemented
44#99×C127—28no—
45#99×C127—24no—
46#99×C127C2×C418yescomplemented
47C24×C127—22no—
48C24×C127—24no—
49C24×C127—22no—
50C24×C127—44no—
51C24×C127—44no—
52C24×C127C22⋊C414yes—
53C24×C127C22⋊C412yes—
54C24×C127C22⋊C411yescharacteristic
55C24×C127C4⋊C414yes—
56C24×C127C2×D412yes—
57C2×D4×C127—44no—
58C2×D4×C127—44no—
59C2×D4×C127—41no—
60C2×D4×C127—41no—
61C2×D4×C127—42no—
62C2×D4×C127—42no—
63C2×D4×C127—42no—
64C2×D4×C127—42no—
65C2×D4×C127—42no—
66C2×D4×C127—42no—
67C2×D4×C127—41no—
68C2×D4×C127—41no—
69C2×D4×C127C4212yes—
70C2×D4×C127C22⋊C414yes—
71C2×D4×C127C4⋊C414yes—
72C2×D4×C127C4⋊C412yes—
73C2×D4×C127C22×C412yes—
74C2×D4×C127C2×D411yescharacteristic
75C2×D4×C127C2×Q811yescharacteristic
76C22×C4×C127—22no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—24no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—42no—
83C22×C4×C127—42no—
84C22×C4×C127—48no—
85C22×C4×C127—44no—
86C22×C4×C127—44no—
87C22×C4×C127—41no—
88C22×C4×C127—41no—
89C22×C4×C127—84no—
90C22×C4×C127—84no—
91C22×C4×C127C4212yes—
92C22×C4×C127C22⋊C411yescharacteristic
93C22×C4×C127C4⋊C412yes—
94C22×C4×C127C22×C411yescharacteristic
95C4⋊C4×C127—42no—
96C4⋊C4×C127—42no—
97C22⋊C4×C127—28no—
98C22⋊C4×C127—48no—
99C22⋊C4×C127—48no—
100C22⋊C4×C127—48no—
101C22⋊C4×C127—44no—
102C42×C127—42no—
103C42×C127—42no—
104C23×C127—22no—
105C23×C127—22no—
106C23×C127—24no—
107C23×C127—24no—
108C23×C127—22no—
109C23×C127—22no—
110C23×C127—24no—
111C23×C127—24no—
112C23×C127—22no—
113C23×C127—22no—
114C23×C127—42no—
115C23×C127—42no—
116C23×C127—42no—
117C23×C127—48no—
118C23×C127—48no—
119C23×C127—42no—
120C23×C127—44no—
121C23×C127—44no—
122C23×C127—82no—
123C23×C127—82no—
124C23×C127—88no—
125C23×C127#9512yes—
126C23×C127#9514yes—
127C23×C127#9911yescharacteristic
128C23×C127#9912yes—
129C23×C127#9911yescharacteristic
130C23×C127C2×C22⋊C411yescharacteristic
131C23×C127C2×C22⋊C412yes—
132C23×C127C2×C4⋊C412yes—
133D4×C127—42no—
134D4×C127—44no—
135D4×C127—44no—
136D4×C127—42no—
137D4×C127—42no—
138D4×C127—41no—
139D4×C127—41no—
140C2×C4×C127—22no—
141C2×C4×C127—22no—
142C2×C4×C127—22no—
143C2×C4×C127—22no—
144C2×C4×C127—21no—
145C2×C4×C127—21no—
146C2×C4×C127—21no—
147C2×C4×C127—21no—
148C2×C4×C127—24no—
149C2×C4×C127—42no—
150C2×C4×C127—48no—
151C2×C4×C127—42no—
152C2×C4×C127—48no—
153C2×C4×C127—44no—
154C2×C4×C127—42no—
155C2×C4×C127—82no—
156C2×C4×C127—84no—
157C2×C4×C127—84no—
158C2×C4×C127—816no—
159C2×C4×C127—82no—
160C2×C4×C127#9512yes—
161C2×C4×C127C2×C4211yescharacteristic
162C2×C4×C127C2×C4⋊C411yescharacteristic
163C22×C127—21no—
164C22×C127—21no—
165C22×C127—21no—
166C22×C127—21no—
167C22×C127—24no—
168C22×C127—24no—
169C22×C127—22no—
170C22×C127—24no—
171C22×C127—22no—
172C22×C127—44no—
173C22×C127—42no—
174C22×C127—42no—
175C22×C127—42no—
176C22×C127—42no—
177C22×C127—42no—
178C22×C127—42no—
179C22×C127—48no—
180C22×C127—48no—
181C22×C127—82no—
182C22×C127—82no—
183C22×C127—84no—
184C22×C127—84no—
185C22×C127#34212yes—
186C22×C127#34212yes—
187C22×C127#35312yes—
188C22×C127#35412yes—
189C22×C127C2×#9511yescharacteristic
190C22×C127C2×#9911yescharacteristic
191C22×C127C2×#9911yescharacteristic
192C4×C127—22no—
193C4×C127—21no—
194C4×C127—21no—
195C4×C127—44no—
196C4×C127—88no—
197C4×C127—82no—
198C2×#1393C12711yesmaximal, characteristic, direct product factor, Sylow
199C2×C127—21no—
200C2×C127—21no—
201C2×C127—22no—
202C2×C127—42no—
203C2×C127—44no—
204C2×C127—42no—
205C2×C127#139314yesdirect product factor
206C2×C127C2×#34211yescharacteristic
207C2×C127C2×#35311yescharacteristic
208C2×C127C2×#35411yescharacteristic
209C22×#99C2×C12712yes—
210C2×#390C2×C12711yescharacteristic
211#1393C2×C12714yesdirect product factor
212C127C2×#139311yescharacteristic, direct product factor, Sylow
213C23×D4C22×C12711yescharacteristic
214C22×C4⋊C4C4×C12711yescharacteristic, complemented
215C22×C22⋊C4—22no—
216C22×C22⋊C4—22no—
217C22×C42C4×C12711yescharacteristic, complemented
218C2×#99—22no—
219C2×#99—24no—
220C2×#99C4×C12718yescomplemented
221C2×#99C22×C12714yes—
222#390—22no—
223#390C4×C12712yescomplemented
224#390C22×C12712yes—
225C25D4×C12712yes—
226C22×D4—42no—
227C22×D4—41no—
228C22×D4—41no—
229C22×D4C2×C4×C12714yes—
230C22×D4C2×C4×C12711yescharacteristic
231C22×D4D4×C12712yes—
232C22×D4D4×C12712yes—
233C22×D4Q8×C12712yes—
234C22×D4C23×C12711yescharacteristic
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—42no—
238C23×C4C2×C4×C12711yescharacteristic
239C2×C4⋊C4—21no—
240C2×C4⋊C4—41no—
241C2×C4⋊C4—41no—
242C2×C4⋊C4C2×C4×C12712yescomplemented
243C2×C22⋊C4—28no—
244C2×C22⋊C4—24no—
245C2×C22⋊C4—24no—
246C2×C22⋊C4—24no—
247C2×C22⋊C4—48no—
248C2×C22⋊C4—42no—
249C2×C22⋊C4—44no—
250C2×C42—21no—
251C2×C42—42no—
252C2×C42C2×C4×C12712yescomplemented
253#99—28no—
254#99—24no—
255#99C2×C4×C12718yescomplemented
256C24—22no—
257C24—24no—
258C24—22no—
259C24—44no—
260C24—44no—
261C24C22⋊C4×C12711yescharacteristic
262C24C22⋊C4×C12714yes—
263C24C22⋊C4×C12712yes—
264C24C4⋊C4×C12714yes—
265C24C2×D4×C12712yes—
266C2×D4—44no—
267C2×D4—44no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4C42×C12712yes—
279C2×D4C22⋊C4×C12714yes—
280C2×D4C4⋊C4×C12714yes—
281C2×D4C4⋊C4×C12712yes—
282C2×D4C22×C4×C12712yes—
283C2×D4C2×D4×C12711yescharacteristic
284C2×D4C2×Q8×C12711yescharacteristic
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—24no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—48no—
294C22×C4—44no—
295C22×C4—44no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—84no—
299C22×C4—84no—
300C22×C4C42×C12712yes—
301C22×C4C22⋊C4×C12711yescharacteristic
302C22×C4C4⋊C4×C12712yes—
303C22×C4C22×C4×C12711yescharacteristic
304C4⋊C4—42no—
305C4⋊C4—42no—
306C22⋊C4—28no—
307C22⋊C4—48no—
308C22⋊C4—48no—
309C22⋊C4—48no—
310C22⋊C4—44no—
311C42—42no—
312C42—42no—
313C23—22no—
314C23—22no—
315C23—24no—
316C23—24no—
317C23—22no—
318C23—22no—
319C23—24no—
320C23—24no—
321C23—22no—
322C23—22no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—48no—
327C23—48no—
328C23—42no—
329C23—44no—
330C23—44no—
331C23—82no—
332C23—82no—
333C23—88no—
334C23#95×C12712yes—
335C23#95×C12714yes—
336C23#99×C12711yescharacteristic
337C23#99×C12712yes—
338C23#99×C12711yescharacteristic
339C23C2×C22⋊C4×C12711yescharacteristic
340C23C2×C22⋊C4×C12712yes—
341C23C2×C4⋊C4×C12712yes—
342D4—42no—
343D4—44no—
344D4—44no—
345D4—42no—
346D4—42no—
347D4—41no—
348D4—41no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—24no—
358C2×C4—42no—
359C2×C4—48no—
360C2×C4—42no—
361C2×C4—48no—
362C2×C4—44no—
363C2×C4—42no—
364C2×C4—82no—
365C2×C4—84no—
366C2×C4—84no—
367C2×C4—816no—
368C2×C4—82no—
369C2×C4#95×C12712yes—
370C2×C4C2×C42×C12711yescharacteristic
371C2×C4C2×C4⋊C4×C12711yescharacteristic
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—24no—
377C22—24no—
378C22—22no—
379C22—24no—
380C22—22no—
381C22—44no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—48no—
389C22—48no—
390C22—82no—
391C22—82no—
392C22—84no—
393C22—84no—
394C22#342×C12712yes—
395C22#342×C12712yes—
396C22#353×C12712yes—
397C22#354×C12712yes—
398C22C2×#95×C12711yescharacteristic
399C22C2×#99×C12711yescharacteristic
400C22C2×#99×C12711yescharacteristic
401C4—22no—
402C4—21no—
403C4—21no—
404C4—44no—
405C4—88no—
406C4—82no—
407C2—21no—
408C2—21no—
409C2—22no—
410C2—42no—
411C2—44no—
412C2—42no—
413C2C127×#139314yesdirect product factor
414C2C2×#342×C12711yescharacteristic
415C2C2×#353×C12711yescharacteristic
416C2C2×#354×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#99
commutatorC2×C4C2×C42×C127
Frattini, cosocleC22×D4C23×C127
prime radicalC23×D4×C127C22
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C24×C127 ◁ C23×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1393C2direct (N × H)
5. C22×C4⋊C4×C127C4semidirect
8. C22×C42×C127C4semidirect
11. C2×#99×C127C4semidirect
14. #390×C127C4semidirect
33. C2×C4⋊C4×C127C2×C4semidirect
43. C2×C42×C127C2×C4semidirect
46. #99×C127C2×C4semidirect
198. C2×#1393C127direct (N × H)
205. C2×C127#1393direct (N × H)
211. #1393C2×C127direct (N × H)
212. C127C2×#1393direct (N × H)
214. C22×C4⋊C4C4×C127semidirect
217. C22×C42C4×C127semidirect
220. C2×#99C4×C127semidirect
223. #390C4×C127semidirect
242. C2×C4⋊C4C2×C4×C127semidirect
252. C2×C42C2×C4×C127semidirect
255. #99C2×C4×C127semidirect
413. C2C127×#1393direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#99×C1272
C2×#390×C1272
C127×#13932
C2×#1393127