Finite Group Databasebeta

← C2×#13081026 #15632254

Subgroups — C2×#13081026 #15632254

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623263C211yesmaximal, characteristic, complemented
2C2×#10623094C211yesmaximal, characteristic
3#13081026C2116yesmaximal, direct product factor
4C2×#10622692C211yesmaximal, characteristic, complemented
5C2×#10622501C212yesmaximal, complemented
6C2×#10622397C212yesmaximal, complemented
7C2×#10622463C211yesmaximal, characteristic, complemented
8C2×#10622391C212yesmaximal, complemented
9C2×C4×#4324C211yesmaximal, characteristic, complemented
10C2×#10622447C211yesmaximal, characteristic, complemented
11C2×#10622493C212yesmaximal, complemented
12C2×C11×#474C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#67000—21no—
16C2×Q8×Dic11—21no—
17C2×#66991C2212yes—
18C22×#4324C2211yescharacteristic
19C2×#66983—21no—
20C2×#66979—21no—
21C22×C8×D11C2212yes—
22#10623263—24no—
23#10623263C2218yescomplemented
24#10623094—24no—
25#10623094C2218yes—
26C2×#66951—22no—
27C2×#66950C2212yes—
28C2×#66945C2212yes—
29C2×#66945C2212yes—
30C2×#66938—22no—
31C2×C4×D44C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#474C2218yescomplemented
35C2×C11×#107C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#102C2212yes—
38C2×#66896C2211yescharacteristic
39C2×(C2×D11)⋊C8C2212yes—
40C2×#66882C2212yes—
41C2×#66880C2212yes—
42#10622692C2218yescomplemented
43C4×#4324C2218yescomplemented
44C2×#66874C2211yescharacteristic
45C2×#66872C2212yes—
46C2×#66872C2212yes—
47C2×#66872C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622501C22116yescomplemented
50#10622493C22116yescomplemented
51#10622463C2218yescomplemented
52#10622447C2218yescomplemented
53#10622397C22116yescomplemented
54#10622391C22116yescomplemented
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C22×D44D411yescharacteristic
60C22×C4×D11C2312yes—
61C22×Dic22—21no—
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2312yes—
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8C2314yes—
66C4×D4×C11—22no—
67C4×D4×C11C2314yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C22⋊C4—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—22no—
74#67000—28no—
75Q8×Dic11—28no—
76#66991—24no—
77#66991C2318yes—
78C2×#4324—24no—
79C2×#4324C2314yes—
80#66983—28no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4D412yes—
85#66979—28no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11D411yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2312yes—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—22no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×C8×D11—28no—
98C2×C8×D11C2318yes—
99#66951—216no—
100#66950—24no—
101#66950C2318yes—
102#66945—24no—
103#66945—24no—
104#66945C2318yes—
105#66945C2318yes—
106#66938—216no—
107C4×D44D414yes—
108C4×D44C2314yes—
109#66922—22no—
110#66922C2314yes—
111C4×Dic22—22no—
112C4×Dic22C2314yes—
113C11×#107C2318yes—
114C11×C4⋊C8C2314yes—
115C11×#102C2318yes—
116#66896C2314yes—
117(C2×D11)⋊C8C2318yes—
118#66882C2318yes—
119#66880C2318yes—
120#66874C2314yes—
121#66872C2314yes—
122#66872C2318yes—
123#66872C2318yes—
124C4×C11⋊C8C2314yes—
125C2×#3340—111nomaximal, Sylow
126C24×C11—21no—
127C23×D11C2×D412yes—
128C2×Q8×C11—24no—
129C2×Q8×C11—44no—
130C2×D4×C11—21no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11C2412yes—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—44no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C2×C22⋊D11—28no—
142C2×C22⋊D11—84no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11C2×D412yes—
147C2×D44—24no—
148C2×D44C2×D414yes—
149C2×C4×D11—24no—
150C2×C4×D11—24no—
151C2×C4×D11C2×D414yes—
152C2×C4×D11C2414yes—
153C2×Dic22—21no—
154C2×Dic22—24no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—82no—
158C2×Dic22C2412yes—
159C2×C8×C11—24no—
160C2×C8×C11C2414yes—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4C2414yes—
165C11×C4⋊C4C2412yes—
166C11×C22⋊C4—24no—
167C42×C11C2×D412yes—
168C42×C11C2412yes—
169C22⋊Dic11—28no—
170#4324—28no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4C2×D418yes—
175C4⋊Dic11—28no—
176C4⋊Dic11—21no—
177C4⋊Dic11—22no—
178C4⋊Dic11—24no—
179C4⋊Dic11C2×D414yes—
180C4⋊Dic11C2414yes—
181C4⋊Dic11C2412yes—
182Dic11⋊C4—24no—
183C4×Dic11—28no—
184C4×Dic11—28no—
185C4×Dic11—24no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8#4114yes—
188C2×C11⋊C8C2412yes—
189C2×C11⋊C8C2412yes—
190C8×D11—216no—
191C2×#556—111no—
192C2×#555—111no—
193#3340—1116no—
194C2×#498—111no—
195C2×#485—112no—
196C2×#482—112no—
197C2×#477—111no—
198C2×#474D1111yescharacteristic, complemented
199C2×#465—112no—
200C2×C4×SD16—111no—
201C2×C8×D4—111no—
202C2×#427—112no—
203C23×C11—22no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11C22×D411yescharacteristic
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11C22×D414yes—
212Q8×C11—48no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—42no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—42no—
220C2×C4×C11—44no—
221C2×C4×C11—48no—
222C2×C4×C11#13514yes—
223C2×C4×C11C22×D412yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D412yes—
226C2×C4×C11C2×#4112yes—
227C2×C4×C112−1+412yes—
228C2×C4×C11C2511yescharacteristic
229C22⋊D11—88no—
230C2×Dic11—24no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—42no—
235C2×Dic11—44no—
236C2×Dic11—42no—
237C2×Dic11C22×D414yes—
238D44—28no—
239C4×D11—28no—
240C4×D11—24no—
241C4×D11—24no—
242Dic22—22no—
243Dic22—22no—
244Dic22—42no—
245Dic22—84no—
246C8×C11—24no—
247C11⋊C8—22no—
248C11⋊C8C2×#4114yes—
249C22×SD16—111no—
250C23×C8—112no—
251#556—118no—
252#556—224no—
253#555—118no—
254#555—224no—
255C2×C4⋊Q8—111no—
256C2×C4⋊Q8C2×D1111yescharacteristic
257C2×#126—222no—
258C2×#124—222no—
259C2×#124—221no—
260C2×C22⋊Q8—112no—
261C2×#121—112no—
262C2×#121—221no—
263C2×C4×Q8—111no—
264C2×C4×Q8—221no—
265C2×C4×D4—111no—
266C2×C4×D4C2×D1111yescharacteristic
267C2×#117—112no—
268C2×#117—112no—
269C2×#117—221no—
270#498—118no—
271#485—1116no—
272#482—1116no—
273#477—118no—
274#474C2×D1118yescomplemented
275#465—1116no—
276C4×SD16—118no—
277C8×D4—118no—
278#427—1116no—
279C2×#107—112no—
280C2×#107C2×D1112yes—
281C2×#106—112no—
282C2×#106—112no—
283C2×#106—111no—
284C2×C4⋊C8C2×D1111yescharacteristic
285C2×#103—112no—
286C2×#103—111no—
287C2×#102—111no—
288C2×#102C2×D1112yes—
289C2×C22⋊C8—112no—
290C2×C4×C8—111no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—84no—
295C22×C11#54712yes—
296C22×C11C2×#13512yes—
297C22×C11#57712yes—
298C22×C11C23×D411yescharacteristic
299C2×D11—24no—
300C2×D11—24no—
301C2×D11—24no—
302C2×D11—48no—
303C4×C11—22no—
304C4×C11—42no—
305C4×C11—44no—
306C4×C11#54712yes—
307C4×C11C2×#13514yes—
308C4×C11C22×#4111yescharacteristic
309C4×C11C2×2−1+411yescharacteristic
310Dic11—24no—
311Dic11—42no—
312Dic11—44no—
313Dic11—42no—
314C22×Q8—21no—
315C22×Q8—111no—
316C22×Q8—221no—
317C22×D4—111no—
318C22×D4—222no—
319C22×D4C22×D1111yescharacteristic
320C23×C4—21no—
321C23×C4—112no—
322C2×SD16—114no—
323C2×SD16—224no—
324C22×C8—111no—
325C22×C8—111no—
326C22×C8—118no—
327C22×C8—228no—
328C22×C8C22×D1112yes—
329C4⋊Q8—22no—
330C4⋊Q8—114no—
331C4⋊Q8—222no—
332C4⋊Q8C22×D1114yes—
333#126—2216no—
334#124—2216no—
335#124—228no—
336C22⋊Q8—118no—
337C22⋊Q8—224no—
338#121—118no—
339#121—228no—
340#121—224no—
341C4×Q8—114no—
342C4×Q8—228no—
343C4×Q8—222no—
344C4×D4—22no—
345C4×D4—114no—
346C4×D4—114no—
347C4×D4C22×D1114yes—
348#117—118no—
349#117—118no—
350#117—224no—
351#117—224no—
352#117—228no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—112no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4C22×D1111yescharacteristic
361C2×C4⋊C4C22×D1112yes—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—112no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—222no—
368C2×C42—222no—
369C2×C42—222no—
370C2×C42—221no—
371C2×C42C22×D1111yescharacteristic
372#107—118no—
373#107C22×D1118yes—
374#106—114no—
375#106—118no—
376#106—118no—
377C4⋊C8C22×D1114yes—
378#103—118no—
379#103—114no—
380#102—114no—
381#102C22×D1118yes—
382C22⋊C8—118no—
383C4×C8—114no—
384C2×C11—82no—
385C2×C11#334014yescomplemented
386C2×C11C2×#54711yescharacteristic
387C2×C11C22×#13511yescharacteristic
388C2×C11C2×#57711yescharacteristic
389D11—44no—
390C24—21no—
391C24—112no—
392C2×Q8—24no—
393C2×Q8—44no—
394C2×Q8—112no—
395C2×Q8—221no—
396C2×Q8—224no—
397C2×Q8—222no—
398C2×Q8—222no—
399C2×Q8—882no—
400C2×D4—21no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—114no—
404C2×D4—228no—
405C2×D4—224no—
406C2×D4—884no—
407C2×D4C23×D1112yes—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—44no—
412C22×C4—112no—
413C22×C4—114no—
414C22×C4—114no—
415C22×C4—224no—
416C22×C4—224no—
417C22×C4—221no—
418C22×C4—222no—
419C22×C4—221no—
420C22×C4D4×D1111yescharacteristic
421C22×C4D4×D1111yescharacteristic
422C22×C4C23×D1111yescharacteristic
423SD16—228no—
424C2×C8—24no—
425C2×C8—114no—
426C2×C8—112no—
427C2×C8—112no—
428C2×C8—2216no—
429C2×C8—222no—
430C2×C8C23×D1114yes—
431C4⋊C4—24no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—114no—
435C4⋊C4—112no—
436C4⋊C4—114no—
437C4⋊C4—228no—
438C4⋊C4—221no—
439C4⋊C4—222no—
440C4⋊C4—224no—
441C4⋊C4—224no—
442C4⋊C4C23×D1114yes—
443C4⋊C4C23×D1112yes—
444C22⋊C4—24no—
445C22⋊C4—118no—
446C22⋊C4—228no—
447C22⋊C4—228no—
448C22⋊C4—228no—
449C22⋊C4—228no—
450C42—228no—
451C42—228no—
452C42—224no—
453C42D4×D1112yes—
454C42C23×D1112yes—
455C11C2×#334011yescharacteristic, complemented, Sylow
456C23—22no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—114no—
461C23—224no—
462C23—224no—
463C23—224no—
464C23C2×D4×D1111yescharacteristic
465Q8—48no—
466Q8—222no—
467Q8—222no—
468Q8—442no—
469Q8—884no—
470D4—22no—
471D4—22no—
472D4—42no—
473D4—228no—
474D4—888no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—42no—
479C2×C4—44no—
480C2×C4—48no—
481C2×C4—114no—
482C2×C4—224no—
483C2×C4—228no—
484C2×C4—224no—
485C2×C4—224no—
486C2×C4—222no—
487C2×C4—224no—
488C2×C4—222no—
489C2×C4—444no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4#6696514yes—
493C2×C4C2×D4×D1112yes—
494C2×C4C2×D4×D1112yes—
495C2×C4C2×D4×D1111yescharacteristic
496C2×C4#6704012yes—
497C2×C4#41×D1112yes—
498C2×C4C24×D1111yescharacteristic
499C8—24no—
500C8—114no—
501C8—222no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—84no—
506C22—224no—
507C22—224no—
508C22—224no—
509C22—448no—
510C22#1062316212yes—
511C22C2×#6696512yes—
512C22#1062330912yes—
513C22C22×D4×D1111yescharacteristic
514C4—22no—
515C4—42no—
516C4—44no—
517C4—224no—
518C4—442no—
519C4—444no—
520C4—442no—
521C4#1062316212yes—
522C4C2×#6696514yes—
523C4C2×#6704011yescharacteristic
524C4C2×#41×D1111yescharacteristic
525C2—82no—
526C2—444no—
527C2#1308102614yesdirect product factor
528C2C2×#1062316211yescharacteristic
529C2C22×#6696511yescharacteristic
530C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC2×#10623094C2
hypercenterC2×#474D11
hypocenterC11C2×#3340
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623263C2semidirect
3. #13081026C2direct (N × H)
4. C2×#10622692C2semidirect
5. C2×#10622501C2semidirect
6. C2×#10622397C2semidirect
7. C2×#10622463C2semidirect
8. C2×#10622391C2semidirect
9. C2×C4×#4324C2semidirect
10. C2×#10622447C2semidirect
11. C2×#10622493C2semidirect
12. C2×C11×#474C2semidirect
23. #10623263C22semidirect
34. C11×#474C22semidirect
42. #10622692C22semidirect
43. C4×#4324C22semidirect
49. #10622501C22semidirect
50. #10622493C22semidirect
51. #10622463C22semidirect
52. #10622447C22semidirect
53. #10622397C22semidirect
54. #10622391C22semidirect
198. C2×#474D11semidirect
274. #474C2×D11semidirect
385. C2×C11#3340semidirect
455. C11C2×#3340semidirect
527. C2#13081026direct (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×#106230942
#130810262
C2×#106226922
C2×#106225012
C2×#106223972
C2×#106224632
C2×#106223912
C2×C4×#43242
C2×#106224472
C2×#106224932
C2×C11×#4742
C2×#334011