Finite Group Databasebeta

← C2×#13068256 #14741514

Subgroups — C2×#13068256 #14741514

Order 2816.

966 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
1C2×#10622686C211yesmaximal, characteristic
2C2×#10622698C211yesmaximal, characteristic, complemented
3C2×#10622706C211yesmaximal, characteristic, complemented
4C2×#10622307C211yesmaximal, characteristic, complemented
5C2×#10622683C211yesmaximal, characteristic, complemented
6#13068256C218yesmaximal, direct product factor
7C2×#10622093C211yesmaximal, characteristic, complemented
8C2×C11×#486C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C22×#4325—22no—
12C22×#4323—22no—
13C2×#66927C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#486—22no—
16C11×#486C2214yescomplemented
17C2×C11×#102—22no—
18C2×C4×C8×C11C2211yescharacteristic
19C2×#66896—22no—
20C2×#66885—22no—
21#10622706—22no—
22#10622706C2214yescomplemented
23#10622698—22no—
24#10622698C2214yescomplemented
25#10622686—22no—
26#10622686C2214yes—
27#10622683—22no—
28#10622683C2214yescomplemented
29C2×#66874—22no—
30C2×C4×C11⋊C8C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622307—22no—
33#10622307C2214yescomplemented
34#10622093C2214yescomplemented
35C22×Q8×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44—21no—
42C22×Dic22—21no—
43C22×C8×C11D412yes—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8C2312yes—
48C11×#127—21no—
49C11×#127—21no—
50C11×#127—21no—
51C11×#127C2312yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C42×C11C2311yescharacteristic
55C2×#4325—28no—
56C2×#4325—48no—
57C2×#4323—28no—
58C2×#4323—48no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C22×C11⋊C8D412yes—
62C22×C11⋊C8D412yes—
63#66927—21no—
64#66927—21no—
65#66927—21no—
66#66927C2312yes—
67#66922—21no—
68#66922—21no—
69#66922—21no—
70#66922C2312yes—
71C11×#102—28no—
72C4×C8×C11D412yes—
73C4×C8×C11C2312yes—
74#66896—28no—
75#66885—28no—
76#66874—28no—
77C4×C11⋊C8D412yes—
78C4×C11⋊C8D412yes—
79C4×C11⋊C8C2312yes—
80C4×C11⋊C8C2312yes—
81C2×#1717—111nomaximal, Sylow
82C24×C11—41no—
83C23×D11—41no—
84C2×Q8×C11—22no—
85C2×Q8×C11—41no—
86C2×Q8×C11—44no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—44no—
94C2×D4×C11—44no—
95C2×D4×C11—44no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×Dic11—41no—
101C2×D44—22no—
102C2×D44—22no—
103C2×D44—22no—
104C2×D44—41no—
105C2×D44—41no—
106C2×D44—41no—
107C2×D44—44no—
108C2×D44—44no—
109C2×D44—44no—
110C2×Dic22—22no—
111C2×Dic22—41no—
112C2×Dic22—44no—
113C2×C8×C11—24no—
114C2×C8×C11C2×D414yes—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2411yescharacteristic
123#4325—416no—
124#4323—416no—
125C4⋊Dic11—22no—
126C4⋊Dic11—22no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C2×C11⋊C8—24no—
130C2×C11⋊C8—24no—
131C2×C11⋊C8C2×D414yes—
132C2×C11⋊C8C2×D414yes—
133C2×#493—111no—
134C2×#492—111no—
135C2×#487—111no—
136C2×#486—111no—
137C2×#486—111no—
138C2×#486D1111yescharacteristic, complemented
139#1717—118no—
140C2×#322—111no—
141C23×C11—42no—
142C23×C11—82no—
143C23×C11—82no—
144C23×C11—82no—
145C23×C11#12711yescharacteristic
146C22×D11—42no—
147C22×D11—82no—
148C22×D11—82no—
149C22×D11—82no—
150Q8×C11—44no—
151Q8×C11—82no—
152D4×C11—44no—
153D4×C11—44no—
154D4×C11—44no—
155D4×C11—82no—
156D4×C11—82no—
157D4×C11—82no—
158C2×C4×C11—42no—
159C2×C4×C11—82no—
160C2×C4×C11#12711yescharacteristic
161C2×C4×C11#12711yescharacteristic
162C2×C4×C11#12711yescharacteristic
163C2×C4×C11#13514yes—
164C2×C4×C11AGL(1,ℤ/8)14yes—
165C2×C4×C11AGL(1,ℤ/8)14yes—
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×Dic11—42no—
170C2×Dic11—82no—
171D44—44no—
172D44—44no—
173D44—44no—
174D44—82no—
175D44—82no—
176D44—82no—
177Dic22—44no—
178Dic22—82no—
179C8×C11—24no—
180C11⋊C8—24no—
181C11⋊C8—24no—
182C22×SD16—222no—
183C22×D8—222no—
184C2×C4⋊Q8—111no—
185C2×C4⋊Q8C2×D1111yescharacteristic
186C2×#127—111no—
187C2×#127C2×D1111yescharacteristic
188#493—114no—
189#493—222no—
190#492—114no—
191#492—222no—
192#487—114no—
193#487—222no—
194#486—22no—
195#486—114no—
196#486—114no—
197#486—222no—
198#486—222no—
199#486C2×D1114yescomplemented
200C2×#103—222no—
201C2×#102—22no—
202C2×#102—222no—
203C2×#102—222no—
204C2×C4×C8—111no—
205C2×C4×C8—111no—
206C2×C4×C8C2×D1111yescharacteristic
207#322—114no—
208C22×C11—82no—
209C22×C11—82no—
210C22×C11—82no—
211C22×C11—164no—
212C22×C11#49512yes—
213C22×C11#49612yes—
214C22×C11#49612yes—
215C22×C11C2×#12711yescharacteristic
216C2×D11—82no—
217C2×D11—82no—
218C2×D11—82no—
219C2×D11—164no—
220C4×C11—82no—
221C4×C11#49512yes—
222C4×C11#49612yes—
223C4×C11#49612yes—
224C4×C11C2×#13512yes—
225C4×C11C2×AGL(1,ℤ/8)12yes—
226C4×C11C2×AGL(1,ℤ/8)12yes—
227Dic11—82no—
228C22×Q8—21no—
229C22×Q8—221no—
230C22×D4—21no—
231C22×D4—21no—
232C22×D4—21no—
233C22×D4—221no—
234C22×D4—221no—
235C22×D4—221no—
236C2×SD16—228no—
237C2×SD16—448no—
238C2×D8—228no—
239C2×D8—448no—
240C22×C8—112no—
241C22×C8—112no—
242C22×C8C22⋊D1112yes—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—112no—
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250C4⋊Q8C22×D1112yes—
251#127—21no—
252#127—21no—
253#127—21no—
254#127—112no—
255#127—221no—
256#127—221no—
257#127—221no—
258#127C22×D1112yes—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—221no—
263C2×C42C22×D1111yescharacteristic
264#103—228no—
265#102—28no—
266#102—228no—
267#102—228no—
268C4×C8—112no—
269C4×C8—112no—
270C4×C8—112no—
271C4×C8—112no—
272C4×C8C22⋊D1112yes—
273C4×C8C22×D1112yes—
274C2×C11—162no—
275C2×C11#171714yescomplemented
276C2×C11C2×#49511yescharacteristic
277C2×C11C2×#49611yescharacteristic
278C2×C11C2×#49611yescharacteristic
279D11—162no—
280C24—41no—
281C24—441no—
282C2×Q8—22no—
283C2×Q8—41no—
284C2×Q8—44no—
285C2×Q8—222no—
286C2×Q8—441no—
287C2×Q8—444no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—44no—
292C2×D4—44no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—44no—
297C2×D4—222no—
298C2×D4—222no—
299C2×D4—222no—
300C2×D4—444no—
301C2×D4—444no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—444no—
306C22×C4—41no—
307C22×C4—441no—
308C22×C4D4×D1111yescharacteristic
309C22×C4D4×D1111yescharacteristic
310C22×C4C2×C22⋊D1111yescharacteristic
311SD16—4416no—
312D8—4416no—
313C2×C8—24no—
314C2×C8—114no—
315C2×C8—114no—
316C2×C8—224no—
317C2×C8—224no—
318C2×C8C2×C22⋊D1114yes—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—222no—
324C4⋊C4—222no—
325C4⋊C4—441no—
326C4⋊C4—441no—
327C42D4×D1111yescharacteristic
328C42D4×D1111yescharacteristic
329C42C2×C22⋊D1111yescharacteristic
330C42C23×D1111yescharacteristic
331C11C2×#171711yescharacteristic, complemented, Sylow
332C23—42no—
333C23—82no—
334C23—82no—
335C23—82no—
336C23—442no—
337C23—882no—
338C23—882no—
339C23—882no—
340C23#6699311yescharacteristic
341Q8—44no—
342Q8—82no—
343Q8—444no—
344Q8—882no—
345D4—44no—
346D4—44no—
347D4—44no—
348D4—82no—
349D4—82no—
350D4—82no—
351D4—444no—
352D4—444no—
353D4—444no—
354D4—882no—
355D4—882no—
356D4—882no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—442no—
360C2×C4—882no—
361C2×C4#6696414yes—
362C2×C4#6696714yes—
363C2×C4#6699311yescharacteristic
364C2×C4#6699311yescharacteristic
365C2×C4#6699311yescharacteristic
366C2×C4#6700314yes—
367C2×C4C2×D4×D1111yescharacteristic
368C2×C4C2×D4×D1111yescharacteristic
369C2×C4C22×C22⋊D1111yescharacteristic
370C8—24no—
371C8—224no—
372C8—224no—
373C22—82no—
374C22—82no—
375C22—82no—
376C22—164no—
377C22—882no—
378C22—882no—
379C22—882no—
380C22—1764no—
381C22#1062267212yes—
382C22#1062276712yes—
383C22#1062278912yes—
384C22C2×#6699311yescharacteristic
385C4—82no—
386C4—882no—
387C4#1062267212yes—
388C4#1062276712yes—
389C4#1062278912yes—
390C4C2×#6696412yes—
391C4C2×#6696712yes—
392C4C2×#6700312yes—
393C2—162no—
394C2—1762no—
395C2#1306825614yesdirect product factor
396C2C2×#1062267211yescharacteristic
397C2C2×#1062278911yescharacteristic
398C2C2×#1062276711yescharacteristic
subgroupG/H
centerC23#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#486C2
socleC23×C11#127
prime radicalC2×#10622686C2
hypercenterC2×#486D11
hypocenterC11C2×#1717
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
2. C2×#10622698C2semidirect
3. C2×#10622706C2semidirect
4. C2×#10622307C2semidirect
5. C2×#10622683C2semidirect
6. #13068256C2direct (N × H)
7. C2×#10622093C2semidirect
8. C2×C11×#486C2semidirect
16. C11×#486C22semidirect
22. #10622706C22semidirect
24. #10622698C22semidirect
28. #10622683C22semidirect
33. #10622307C22semidirect
34. #10622093C22semidirect
138. C2×#486D11semidirect
199. #486C2×D11semidirect
275. C2×C11#1717semidirect
331. C11C2×#1717semidirect
395. C2#13068256direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226862
C2×#106226982
C2×#106227062
C2×#106223072
C2×#106226832
#130682562
C2×#106220932
C2×C11×#4862
C2×#171711