Finite Group Databasebeta

← C2×#13081301 #15633385

Subgroups — C2×#13081301 #15633385

Order 2816.

1830 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic
2#13081301C2116yesmaximal, direct product factor
3C2×#10622681C212yesmaximal
4C2×#10622706C211yesmaximal, characteristic, complemented
5C2×#10622676C212yesmaximal, complemented
6C2×#10622700C211yesmaximal, characteristic
7C2×#10622641C212yesmaximal
8C2×#10622644C211yesmaximal, characteristic, complemented
9C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
10C2×C4×#4326C212yesmaximal, complemented
11C2×C4×#4325C211yesmaximal, characteristic
12C2×C11×#557C211yesmaximal, characteristic, complemented
13C11×#557—24no—
14C11×#557C2218yescomplemented
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125—22no—
18C2×C11×#125C2212yes—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×#66999—21no—
24C22×#4326C2212yes—
25C22×#4325C2211yescharacteristic
26#10623115—24no—
27#10623115C2218yes—
28C2×#66951—22no—
29C2×#66945—21no—
30C2×#66928C2212yes—
31C2×C4×D44C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2212yes—
34C2×#66899C2211yescharacteristic
35#10622706C2218yescomplemented
36#10622700C2218yes—
37#10622681C22116yes—
38#10622676C22116yescomplemented
39#10622644C2218yescomplemented
40C4×#4326C22116yescomplemented
41#10622641C22116yes—
42C4×#4325C2218yes—
43Q8×C11⋊C8C2218yescomplemented
44C2×#66874C2212yes—
45C2×#66874C2212yes—
46C2×#66874C2212yes—
47C2×#66873C2212yes—
48C2×#66873C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66871C2212yes—
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×C4×C11⋊C8C2211yescharacteristic
54C2×C4×C11⋊C8C2212yes—
55C22×Q8×C11—21no—
56C22×Q8×C11D411yescharacteristic
57C22×Q8×C11C2311yescharacteristic
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×Dic22C2312yes—
61C11×C4⋊Q8—28no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8C2314yes—
64C11×#125—216no—
65C11×#125—24no—
66C11×#125C2318yes—
67C4×Q8×C11—28no—
68C4×Q8×C11—24no—
69C4×Q8×C11—22no—
70C4×Q8×C11D414yes—
71C4×Q8×C11C2314yes—
72C4×Q8×C11C2318yes—
73C4×Q8×C11C2314yes—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D412yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C42×C11—22no—
84C2×C42×C11—21no—
85C2×C42×C11C2312yes—
86C2×C42×C11C2311yescharacteristic
87#66999—28no—
88C2×#4326—28no—
89C2×#4326C2318yes—
90C2×#4325—24no—
91C2×#4325C2314yes—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—22no—
99C2×C4×Dic11—22no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2312yes—
103#66951—216no—
104#66945—28no—
105#66928—24no—
106#66928C2318yes—
107C4×D44—22no—
108C4×D44C2314yes—
109#66922—22no—
110#66922C2314yes—
111C4×Dic22—24no—
112C4×Dic22C2318yes—
113#66899C2314yes—
114#66874C2318yes—
115#66874C2318yes—
116#66874C2318yes—
117#66873C2314yes—
118#66873C2318yes—
119#66872C2314yes—
120#66871C2318yes—
121C4⋊(C11⋊C8)C2318yes—
122C4⋊(C11⋊C8)C2314yes—
123C4×C11⋊C8C2314yes—
124C4×C11⋊C8C2318yes—
125C2×#3364—111nomaximal, Sylow
126C23×D11—21no—
127C2×Q8×C11—24no—
128C2×Q8×C11—21no—
129C2×Q8×C11—24no—
130C2×Q8×C11—22no—
131C2×Q8×C11—44no—
132C2×Q8×C11C2×D414yes—
133C2×Q8×C11#4114yes—
134C2×Q8×C11C2412yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—22no—
145C2×D44—21no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44C2412yes—
149C2×C4×D11—24no—
150C2×C4×D11—44no—
151C2×Dic22—22no—
152C2×Dic22—24no—
153C2×Dic22—24no—
154C2×Dic22C2414yes—
155C11×C4⋊C4—28no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—28no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—28no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4C2×D414yes—
163C11×C4⋊C4C2×D418yes—
164C11×C4⋊C4C2414yes—
165C11×C4⋊C4C2412yes—
166C42×C11—28no—
167C42×C11—24no—
168C42×C11C2×D414yes—
169C42×C11C2×D412yes—
170C42×C11C2414yes—
171C42×C11C2412yes—
172#4326—216no—
173#4325—28no—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—28no—
176(C2×D11)⋊C4—28no—
177C4⋊Dic11—21no—
178C4⋊Dic11—24no—
179C4⋊Dic11—24no—
180C4⋊Dic11C2412yes—
181Dic11⋊C4—28no—
182C4×Dic11—28no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—24no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8C2412yes—
187C2×C11⋊C8C2414yes—
188C2×C11⋊C8C2412yes—
189C2×#557D1111yescharacteristic, complemented
190C2×#556—111no—
191#3364—1116no—
192C2×#488—112no—
193C2×#487—111no—
194C2×#479—112no—
195C2×#474—111no—
196C2×#464—112no—
197C2×#462—111no—
198C2×C8×Q8—111no—
199C2×C4×Q16—112no—
200C2×C4×SD16—111no—
201C23×C11C22×D411yescharacteristic
202C22×D11—22no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206Q8×C11—24no—
207Q8×C11—28no—
208Q8×C11—22no—
209Q8×C11—48no—
210Q8×C11C2×#4114yes—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—44no—
219C2×C4×C11—42no—
220C2×C4×C11#13514yes—
221C2×C4×C11C22×D414yes—
222C2×C4×C11C22×D414yes—
223C2×C4×C11C22×D412yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D412yes—
226C2×C4×C11C2×#4112yes—
227C2×C4×C112−1+412yes—
228C2×C4×C11C2511yescharacteristic
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—44no—
232C2×Dic11—42no—
233D44—22no—
234D44—22no—
235D44—42no—
236C4×D11—48no—
237Dic22—24no—
238Dic22—24no—
239Dic22—44no—
240C11⋊C8—22no—
241C11⋊C8—24no—
242C11⋊C8—22no—
243C22×Q16—112no—
244C22×SD16—111no—
245#557—24no—
246#557C2×D1118yescomplemented
247#556—118no—
248#556—224no—
249C2×C4⋊Q8—21no—
250C2×C4⋊Q8—111no—
251C2×C4⋊Q8C2×D1111yescharacteristic
252C2×#126—222no—
253C2×#125—22no—
254C2×#125C2×D1112yes—
255C2×#124—112no—
256C2×C22⋊Q8—221no—
257C2×C4×Q8—21no—
258C2×C4×Q8—112no—
259C2×C4×Q8C2×D1111yescharacteristic
260C2×C4×Q8C2×D1112yes—
261C2×C4×Q8C2×D1111yescharacteristic
262C2×C4×D4—111no—
263C2×#117—221no—
264#488—1116no—
265#487—118no—
266#479—1116no—
267#474—118no—
268#464—1116no—
269#462—118no—
270C8×Q8—118no—
271C4×Q16—1116no—
272C4×SD16—118no—
273C2×#107—112no—
274C2×#106—111no—
275C2×C4⋊C8—112no—
276C2×C4⋊C8—111no—
277C2×#103—111no—
278C2×#103—112no—
279C2×#103—112no—
280C2×#103—112no—
281C2×#102—111no—
282C2×#102—112no—
283C2×C4×C8—111no—
284C2×C4×C8—112no—
285C22×C11#54812yes—
286C22×C11C2×#13512yes—
287C22×C11#57812yes—
288C22×C11C23×D411yescharacteristic
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—42no—
292C2×D11—84no—
293C4×C11—24no—
294C4×C11—24no—
295C4×C11—24no—
296C4×C11—22no—
297C4×C11—44no—
298C4×C11—42no—
299C4×C11#54812yes—
300C4×C11C2×#13514yes—
301C4×C11C22×#4111yescharacteristic
302C4×C11C2×2−1+411yescharacteristic
303Dic11—44no—
304Dic11—42no—
305C22×Q8—21no—
306C22×Q8—112no—
307C22×Q8C22⋊D1111yescharacteristic
308C22×Q8C22×D1111yescharacteristic
309C22×D4—111no—
310C23×C4—221no—
311C2×Q16—118no—
312C2×Q16—228no—
313C2×SD16—114no—
314C2×SD16—224no—
315C22×C8—111no—
316C22×C8—112no—
317C22×C8—111no—
318C4⋊Q8—28no—
319C4⋊Q8—22no—
320C4⋊Q8—114no—
321C4⋊Q8—222no—
322C4⋊Q8C22×D1114yes—
323#126—2216no—
324#125—216no—
325#125—24no—
326#125C22×D1118yes—
327#124—118no—
328#124—224no—
329C22⋊Q8—228no—
330C4×Q8—28no—
331C4×Q8—24no—
332C4×Q8—22no—
333C4×Q8—118no—
334C4×Q8—224no—
335C4×Q8C22⋊D1114yes—
336C4×Q8C22×D1114yes—
337C4×Q8C22×D1118yes—
338C4×Q8C22×D1114yes—
339C4×D4—114no—
340C4×D4—222no—
341#117—228no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4C22⋊D1111yescharacteristic
352C2×C4⋊C4C22⋊D1112yes—
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C4⋊C4C22×D1112yes—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—222no—
358C2×C42—22no—
359C2×C42—21no—
360C2×C42—222no—
361C2×C42C22×D1111yescharacteristic
362C2×C42C22×D1112yes—
363#107—118no—
364#106—114no—
365C4⋊C8—114no—
366C4⋊C8—118no—
367#103—114no—
368#103—118no—
369#103—118no—
370#103—118no—
371#102—114no—
372#102—118no—
373C4×C8—114no—
374C4×C8—118no—
375C2×C11#336414yescomplemented
376C2×C11C2×#54811yescharacteristic
377C2×C11C22×#13511yescharacteristic
378C2×C11C2×#57811yescharacteristic
379D11—82no—
380C24—221no—
381C2×Q8—24no—
382C2×Q8—22no—
383C2×Q8—21no—
384C2×Q8—24no—
385C2×Q8—44no—
386C2×Q8—114no—
387C2×Q8—222no—
388C2×Q8—224no—
389C2×Q8—224no—
390C2×Q8#434314yes—
391C2×Q8C2×C22⋊D1114yes—
392C2×Q8C23×D1112yes—
393C2×D4—112no—
394C2×D4—222no—
395C2×D4—222no—
396C2×D4—221no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—221no—
401C22×C4—222no—
402C22×C4—224no—
403C22×C4—444no—
404C22×C4C2×C22⋊D1112yes—
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C2×C22⋊D1112yes—
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409Q16—2216no—
410SD16—228no—
411C2×C8—112no—
412C2×C8—114no—
413C2×C8—112no—
414C2×C8—222no—
415C2×C8—224no—
416C2×C8—222no—
417C4⋊C4—28no—
418C4⋊C4—24no—
419C4⋊C4—28no—
420C4⋊C4—24no—
421C4⋊C4—28no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—112no—
425C4⋊C4—221no—
426C4⋊C4—224no—
427C4⋊C4—228no—
428C4⋊C4—224no—
429C4⋊C4C2×C22⋊D1114yes—
430C4⋊C4C2×C22⋊D1118yes—
431C4⋊C4C23×D1112yes—
432C4⋊C4C23×D1114yes—
433C22⋊C4—228no—
434C22⋊C4—224no—
435C22⋊C4—228no—
436C42—28no—
437C42—24no—
438C42—228no—
439C42C2×C22⋊D1112yes—
440C42C2×C22⋊D1114yes—
441C42C23×D1112yes—
442C42C23×D1114yes—
443C11C2×#336411yescharacteristic, complemented, Sylow
444C23—222no—
445C23—442no—
446C23—442no—
447C23—442no—
448C23C22×C22⋊D1111yescharacteristic
449Q8—24no—
450Q8—28no—
451Q8—22no—
452Q8—48no—
453Q8—224no—
454Q8—224no—
455Q8—444no—
456Q8C2×#434314yes—
457D4—222no—
458D4—222no—
459D4—442no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—44no—
468C2×C4—42no—
469C2×C4—222no—
470C2×C4—224no—
471C2×C4—444no—
472C2×C4—442no—
473C2×C4—448no—
474C2×C4#6700314yes—
475C2×C4C2×#434312yes—
476C2×C4#6704012yes—
477C2×C4C22×C22⋊D1114yes—
478C2×C4C22×C22⋊D1112yes—
479C2×C4C22×C22⋊D1114yes—
480C2×C4C22×C22⋊D1111yescharacteristic
481C2×C4C22×C22⋊D1112yes—
482C2×C4C24×D1111yescharacteristic
483C8—222no—
484C8—224no—
485C8—222no—
486C22—442no—
487C22—442no—
488C22—442no—
489C22—884no—
490C22#1062334812yes—
491C22C2×#6700312yes—
492C22#1062336912yes—
493C22C23×C22⋊D1111yescharacteristic
494C4—24no—
495C4—24no—
496C4—24no—
497C4—22no—
498C4—44no—
499C4—42no—
500C4—442no—
501C4—444no—
502C4#1062334812yes—
503C4C2×#6700314yes—
504C4C22×#434311yescharacteristic
505C4C2×#6704011yescharacteristic
506C2—882no—
507C2#1308130114yesdirect product factor
508C2C2×#1062334811yescharacteristic
509C2C22×#6700311yescharacteristic
510C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#557C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#557D11
hypocenterC11C2×#3364
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #13081301C2direct (N × H)
4. C2×#10622706C2semidirect
5. C2×#10622676C2semidirect
8. C2×#10622644C2semidirect
9. C2×Q8×C11⋊C8C2semidirect
10. C2×C4×#4326C2semidirect
12. C2×C11×#557C2semidirect
14. C11×#557C22semidirect
35. #10622706C22semidirect
38. #10622676C22semidirect
39. #10622644C22semidirect
40. C4×#4326C22semidirect
43. Q8×C11⋊C8C22semidirect
189. C2×#557D11semidirect
246. #557C2×D11semidirect
375. C2×C11#3364semidirect
443. C11C2×#3364semidirect
507. C2#13081301direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
#130813012
C2×#106226812
C2×#106227062
C2×#106226762
C2×#106227002
C2×#106226412
C2×#106226442
C2×Q8×C11⋊C82
C2×C4×#43262
C2×C4×#43252
C2×C11×#5572
C2×#336411