Finite Group Databasebeta

← C2×#13081603 #15634681

Subgroups — C2×#13081603 #15634681

Order 2816.

1958 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623263C211yesmaximal, characteristic, complemented
2C2×#10623073C211yesmaximal, characteristic, complemented
3#13081603C2116yesmaximal, direct product factor
4C2×#10622781C212yesmaximal
5C2×#10622705C211yesmaximal, characteristic, complemented
6C2×#10622411C212yesmaximal, complemented
7C2×#10622779C212yesmaximal, complemented
8C2×#10622454C211yesmaximal, characteristic, complemented
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×#10622403C212yesmaximal, complemented
11C2×C4×#4323C211yesmaximal, characteristic
12C2×C11×#461C211yesmaximal, characteristic, complemented
13C22×C11×SD16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#67000C2212yes—
17C2×Q8×Dic11C2212yes—
18C22×#4326C2212yes—
19C22×#4326C2212yes—
20C2×#66989C2212yes—
21C22×#4323C2211yescharacteristic
22C2×#66979—21no—
23C2×#66977—21no—
24C22×#4314C2212yes—
25#10623263—24no—
26#10623263C2218yescomplemented
27#10623073—24no—
28#10623073C2218yescomplemented
29C2×#66951—22no—
30C2×#66950—21no—
31C2×#66945—21no—
32C2×#66940C2212yes—
33C2×#66932—22no—
34C2×C4×D44C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C11×#461C2218yescomplemented
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2212yes—
40C2×#66896C2211yescharacteristic
41#10622781C22116yes—
42#10622779C22116yescomplemented
43C2×#66880C2212yes—
44C2×Dic11⋊C8C2212yes—
45C2×C8×Dic11C2212yes—
46#10622705C2218yescomplemented
47C4×#4323C2218yes—
48C2×#66873C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622454C2218yescomplemented
52#10622443C2218yescomplemented
53#10622411C22116yescomplemented
54#10622403C22116yescomplemented
55C22×Q8×C11C2312yes—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×Dic22D411yescharacteristic
61C22×Dic22C2312yes—
62C2×C11×SD16—44no—
63C2×C11×SD16C2318yes—
64C22×C8×C11C2312yes—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8C2314yes—
67C4×D4×C11—22no—
68C4×D4×C11C2314yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76#67000—24no—
77#67000C2318yes—
78Q8×Dic11—24no—
79Q8×Dic11C2318yes—
80C2×#4326—28no—
81C2×#4326—44no—
82C2×#4326C2318yes—
83C2×#4326C2318yes—
84#66989—24no—
85#66989C2318yes—
86C2×#4323—24no—
87C2×#4323C2314yes—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91#66979—28no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97#66977—28no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4D412yes—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11C2312yes—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C2×#4314—44no—
106C2×#4314C2318yes—
107#66951—216no—
108#66950—28no—
109#66945—28no—
110#66940—24no—
111#66940C2318yes—
112#66932—216no—
113C4×D44—22no—
114C4×D44C2314yes—
115#66922—22no—
116#66922C2314yes—
117C4×Dic22D414yes—
118C4×Dic22C2314yes—
119C11×C4⋊C8C2314yes—
120C11×#103C2318yes—
121#66896C2314yes—
122#66880C2318yes—
123Dic11⋊C8C2318yes—
124C8×Dic11C2318yes—
125#66873C2314yes—
126#66871C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3393—111nomaximal, Sylow
129C24×C11—21no—
130C23×D11—21no—
131C2×Q8×C11—22no—
132C2×Q8×C11—24no—
133C2×Q8×C11—24no—
134C2×Q8×C11C2414yes—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11C2412yes—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—24no—
142C22×C4×C11—44no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—22no—
148C22×Dic11C2×D412yes—
149C22×Dic11C2×D412yes—
150C2×D44—21no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44C2412yes—
154C2×C4×D11—24no—
155C2×C4×D11—44no—
156C2×Dic22—24no—
157C2×Dic22—22no—
158C2×Dic22—24no—
159C2×Dic22—24no—
160C2×Dic22C2×D414yes—
161C2×Dic22C2414yes—
162C11×SD16—48no—
163C2×C8×C11—24no—
164C2×C8×C11C2414yes—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4C2412yes—
169C11×C22⋊C4—24no—
170C42×C11C2×D412yes—
171C42×C11C2412yes—
172C22⋊Dic11—28no—
173C22⋊Dic11—28no—
174#4326—216no—
175#4326—48no—
176#4323—28no—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4—28no—
179(C2×D11)⋊C4—24no—
180C4⋊Dic11—28no—
181C4⋊Dic11—24no—
182C4⋊Dic11—24no—
183C4⋊Dic11—21no—
184C4⋊Dic11C2×D414yes—
185C4⋊Dic11C2412yes—
186Dic11⋊C4—28no—
187Dic11⋊C4C2×D418yes—
188C4×Dic11—28no—
189C4×Dic11—28no—
190C4×Dic11C2×D414yes—
191C4×Dic11C2414yes—
192C2×C11⋊C8—22no—
193C2×C11⋊C8#4114yes—
194C2×C11⋊C8C2412yes—
195C2×C11⋊C8C2412yes—
196#4314—48no—
197C2×#556—111no—
198C2×#556—111no—
199#3393—1116no—
200C2×#495—112no—
201C2×#494—111no—
202C2×#464—112no—
203C2×#464—112no—
204C2×#461—111no—
205C2×#461D1111yescharacteristic, complemented
206C2×C8×Q8—111no—
207C2×C4×Q16—112no—
208C2×C4×D8—111no—
209C23×C11—22no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11C22×D411yescharacteristic
214C22×D11—22no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218Q8×C11—24no—
219Q8×C11—24no—
220Q8×C11—44no—
221D4×C11—22no—
222D4×C11—22no—
223D4×C11—42no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—44no—
228C2×C4×C11—42no—
229C2×C4×C11—48no—
230C2×C4×C11#13514yes—
231C2×C4×C11C22×D412yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D412yes—
234C2×C4×C11C2×#4112yes—
235C2×C4×C11H(5,𝔽2)12yes—
236C2×C4×C11C2511yescharacteristic
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—44no—
242C2×Dic11—42no—
243C2×Dic11C22×D414yes—
244C2×Dic11C22×D414yes—
245D44—22no—
246D44—22no—
247D44—42no—
248C4×D11—48no—
249Dic22—28no—
250Dic22—24no—
251Dic22—24no—
252Dic22—44no—
253C8×C11—24no—
254C11⋊C8—22no—
255C11⋊C8C2×#4114yes—
256C22×Q16—112no—
257C22×Q16—112no—
258C22×SD16—112no—
259C22×SD16C2×D1112yes—
260C22×D8—111no—
261#556—118no—
262#556—118no—
263#556—224no—
264#556—224no—
265C2×C4⋊Q8—111no—
266C2×C4⋊Q8C2×D1111yescharacteristic
267C2×#126—222no—
268C2×#126—222no—
269C2×#124—112no—
270C2×#124—112no—
271C2×C22⋊Q8—221no—
272C2×C22⋊Q8—221no—
273C2×C4×Q8—111no—
274C2×C4×Q8—112no—
275C2×C4×Q8—112no—
276C2×C4×D4—111no—
277C2×C4×D4C2×D1111yescharacteristic
278C2×#117—221no—
279C2×#117—221no—
280#495—1116no—
281#494—118no—
282#464—1116no—
283#464—1116no—
284#461—118no—
285#461C2×D1118yescomplemented
286C8×Q8—118no—
287C4×Q16—1116no—
288C4×D8—118no—
289C2×#107—111no—
290C2×C4⋊C8—112no—
291C2×C4⋊C8C2×D1111yescharacteristic
292C2×#103—112no—
293C2×#103C2×D1112yes—
294C2×#102—111no—
295C2×#102—111no—
296C2×C4×C8—112no—
297C2×C4×C8—111no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—84no—
302C22×C11#55012yes—
303C22×C11C2×#13512yes—
304C22×C11#57812yes—
305C22×C11C23×D411yescharacteristic
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—84no—
310C4×C11—22no—
311C4×C11—44no—
312C4×C11—42no—
313C4×C11#55012yes—
314C4×C11C2×#13514yes—
315C4×C11C22×#4111yescharacteristic
316C4×C11C2×H(5,𝔽2)11yescharacteristic
317Dic11—24no—
318Dic11—24no—
319Dic11—44no—
320Dic11—42no—
321C22×Q8—111no—
322C22×Q8—112no—
323C22×Q8C22×D1112yes—
324C22×D4—111no—
325C22×D4C22×D1111yescharacteristic
326C23×C4—21no—
327C23×C4—221no—
328C2×Q16—118no—
329C2×Q16—118no—
330C2×Q16—228no—
331C2×Q16—444no—
332C2×SD16—44no—
333C2×SD16—118no—
334C2×SD16—444no—
335C2×SD16C22×D1118yes—
336C2×D8—114no—
337C2×D8—224no—
338C22×C8—111no—
339C22×C8—111no—
340C22×C8C22×D1112yes—
341C4⋊Q8—22no—
342C4⋊Q8—114no—
343C4⋊Q8—222no—
344C4⋊Q8C22×D1114yes—
345#126—2216no—
346#126—2216no—
347#124—118no—
348#124—118no—
349#124—224no—
350#124—224no—
351C22⋊Q8—228no—
352C22⋊Q8—228no—
353C4×Q8—114no—
354C4×Q8—114no—
355C4×Q8—118no—
356C4×Q8—118no—
357C4×Q8—224no—
358C4×Q8—224no—
359C4×D4—22no—
360C4×D4—114no—
361C4×D4—222no—
362C4×D4C22×D1114yes—
363#117—228no—
364#117—228no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—222no—
378C2×C22⋊C4—222no—
379C2×C22⋊C4—222no—
380C2×C22⋊C4—221no—
381C2×C42—112no—
382C2×C42—222no—
383C2×C42—222no—
384C2×C42C22×D1111yescharacteristic
385#107—114no—
386C4⋊C8—118no—
387C4⋊C8C22×D1114yes—
388#103—118no—
389#103C22×D1118yes—
390#102—114no—
391#102—114no—
392C4×C8—118no—
393C4×C8—114no—
394C2×C11—82no—
395C2×C11#339314yescomplemented
396C2×C11C2×#55011yescharacteristic
397C2×C11C22×#13511yescharacteristic
398C2×C11C2×#57811yescharacteristic
399D11—82no—
400C24—21no—
401C24—221no—
402C2×Q8—22no—
403C2×Q8—24no—
404C2×Q8—24no—
405C2×Q8—114no—
406C2×Q8—114no—
407C2×Q8—224no—
408C2×Q8—222no—
409C2×Q8—224no—
410C2×Q8—224no—
411C2×Q8C23×D1114yes—
412C2×D4—21no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—112no—
416C2×D4—221no—
417C2×D4—222no—
418C2×D4—222no—
419C2×D4C23×D1112yes—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—44no—
424C22×C4—112no—
425C22×C4—112no—
426C22×C4—221no—
427C22×C4—222no—
428C22×C4—224no—
429C22×C4—444no—
430C22×C4D4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432C22×C4C23×D1111yescharacteristic
433Q16—2216no—
434Q16—448no—
435SD16—48no—
436SD16—448no—
437D8—228no—
438C2×C8—24no—
439C2×C8—114no—
440C2×C8—112no—
441C2×C8—112no—
442C2×C8—222no—
443C2×C8C23×D1114yes—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—21no—
447C4⋊C4—114no—
448C4⋊C4—118no—
449C4⋊C4—112no—
450C4⋊C4—228no—
451C4⋊C4—228no—
452C4⋊C4—221no—
453C4⋊C4—224no—
454C4⋊C4—224no—
455C4⋊C4C23×D1112yes—
456C22⋊C4—24no—
457C22⋊C4—228no—
458C22⋊C4—228no—
459C22⋊C4—228no—
460C22⋊C4—228no—
461C22⋊C4—224no—
462C42—114no—
463C42—114no—
464C42—228no—
465C42—228no—
466C42D4×D1112yes—
467C42C23×D1112yes—
468C11C2×#339311yescharacteristic, complemented, Sylow
469C23—22no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—222no—
474C23—442no—
475C23—442no—
476C23—442no—
477C23C2×D4×D1111yescharacteristic
478Q8—24no—
479Q8—24no—
480Q8—44no—
481Q8—228no—
482Q8—224no—
483Q8—224no—
484Q8—444no—
485D4—22no—
486D4—22no—
487D4—42no—
488D4—222no—
489D4—222no—
490D4—442no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—48no—
497C2×C4—114no—
498C2×C4—114no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—222no—
502C2×C4—224no—
503C2×C4—442no—
504C2×C4—444no—
505C2×C4—448no—
506C2×C4#6696914yes—
507C2×C4C2×D4×D1112yes—
508C2×C4C2×D4×D1112yes—
509C2×C4C2×D4×D1111yescharacteristic
510C2×C4#6703712yes—
511C2×C4#41×D1112yes—
512C2×C4C24×D1111yescharacteristic
513C8—24no—
514C8—114no—
515C8—222no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—84no—
520C22—442no—
521C22—442no—
522C22—442no—
523C22—884no—
524C22#1062313012yes—
525C22C2×#6696912yes—
526C22#1062331012yes—
527C22C22×D4×D1111yescharacteristic
528C4—22no—
529C4—42no—
530C4—44no—
531C4—224no—
532C4—224no—
533C4—442no—
534C4—444no—
535C4#1062313012yes—
536C4C2×#6696914yes—
537C4C2×#6703711yescharacteristic
538C4C2×#41×D1111yescharacteristic
539C2—82no—
540C2—882no—
541C2#1308160314yesdirect product factor
542C2C2×#1062313011yescharacteristic
543C2C22×#6696911yescharacteristic
544C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#461D11
hypocenterC11C2×#3393
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10623263C2semidirect
2. C2×#10623073C2semidirect
3. #13081603C2direct (N × H)
5. C2×#10622705C2semidirect
6. C2×#10622411C2semidirect
7. C2×#10622779C2semidirect
8. C2×#10622454C2semidirect
9. C2×#10622443C2semidirect
10. C2×#10622403C2semidirect
12. C2×C11×#461C2semidirect
26. #10623263C22semidirect
28. #10623073C22semidirect
37. C11×#461C22semidirect
42. #10622779C22semidirect
46. #10622705C22semidirect
51. #10622454C22semidirect
52. #10622443C22semidirect
53. #10622411C22semidirect
54. #10622403C22semidirect
205. C2×#461D11semidirect
285. #461C2×D11semidirect
395. C2×C11#3393semidirect
468. C11C2×#3393semidirect
541. C2#13081603direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106230732
#130816032
C2×#106227812
C2×#106227052
C2×#106224112
C2×#106227792
C2×#106224542
C2×#106224432
C2×#106224032
C2×C4×#43232
C2×C11×#4612
C2×#339311