Finite Group Databasebeta

← C2×#13081264 #15633344

Subgroups — C2×#13081264 #15633344

Order 2816.

1906 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×#10623073C211yesmaximal, characteristic, complemented
2C2×#10623261C211yesmaximal, characteristic, complemented
3#13081264C2116yesmaximal, direct product factor
4C2×#10622381C212yesmaximal, complemented
5C2×#10622706C211yesmaximal, characteristic, complemented
6C2×#10622470C212yesmaximal, complemented
7C2×#10622400C212yesmaximal
8C2×#10622454C211yesmaximal, characteristic, complemented
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×#10622465C212yesmaximal, complemented
11C2×C4×#4323C211yesmaximal, characteristic
12C2×C11×#476C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66999—22no—
16C2×#66989C2212yes—
17C22×#4323C2211yescharacteristic
18C2×#66979—21no—
19C2×#66977—21no—
20C22×#4314C2212yes—
21#10623261—24no—
22#10623261C2218yescomplemented
23#10623073—24no—
24#10623073C2218yescomplemented
25C2×#66950—21no—
26C2×#66946C2212yes—
27C2×C4⋊C4×D11—21no—
28C2×#66943C2212yes—
29C2×#66940C2212yes—
30C2×#66932—22no—
31C2×C4×D44C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#476C2218yescomplemented
35C2×C11×#106C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#102C2212yes—
38C2×#66896C2211yescharacteristic
39C2×#66880C2212yes—
40C2×Dic11⋊C8C2212yes—
41C2×C8×Dic11C2212yes—
42#10622706C2218yescomplemented
43C4×#4323C2218yes—
44C2×#66874C2212yes—
45C2×#66874C2212yes—
46C2×#66873C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622470C22116yescomplemented
50#10622465C22116yescomplemented
51#10622454C2218yescomplemented
52#10622443C2218yescomplemented
53#10622400C22116yes—
54#10622381C22116yescomplemented
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11—22no—
61C22×Dic22D411yescharacteristic
62C22×Dic22C2312yes—
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—
74C2×C22⋊Dic11—22no—
75#66999—216no—
76#66989—24no—
77#66989C2318yes—
78C2×#4323—24no—
79C2×#4323C2314yes—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—22no—
82#66979—28no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88#66977—28no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4D412yes—
92C2×C4×Dic11—22no—
93C2×C4×Dic11C2312yes—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×#4314—28no—
97C2×#4314C2318yes—
98#66950—28no—
99#66946—24no—
100#66946C2318yes—
101C4⋊C4×D11—28no—
102#66943—24no—
103#66943C2318yes—
104#66940—24no—
105#66940C2318yes—
106#66932—216no—
107C4×D44—22no—
108C4×D44C2314yes—
109#66922—22no—
110#66922C2314yes—
111C4×Dic22D414yes—
112C4×Dic22C2314yes—
113C11×#106C2318yes—
114C11×C4⋊C8C2314yes—
115C11×#102C2318yes—
116#66896C2314yes—
117#66880C2318yes—
118Dic11⋊C8C2318yes—
119C8×Dic11C2318yes—
120#66874C2318yes—
121#66874C2318yes—
122#66873C2314yes—
123#66871C2314yes—
124C4×C11⋊C8C2314yes—
125C2×#3360—111nomaximal, Sylow
126C24×C11—21no—
127C23×D11—21no—
128C2×Q8×C11—24no—
129C2×Q8×C11—82no—
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
141C22×Dic11—22no—
142C22×Dic11—21no—
143C22×Dic11C2×D412yes—
144C22×Dic11C2×D412yes—
145C2×D44—21no—
146C2×D44—22no—
147C2×D44#4114yes—
148C2×D44C2412yes—
149C2×C4×D11—28no—
150C2×C4×D11—24no—
151C2×C4×D11—44no—
152C2×C4×D11—84no—
153C2×Dic22—24no—
154C2×Dic22—22no—
155C2×Dic22—24no—
156C2×Dic22—24no—
157C2×Dic22C2×D414yes—
158C2×Dic22C2414yes—
159C2×C8×C11—24no—
160C2×C8×C11C2414yes—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4C2412yes—
165C11×C4⋊C4C2414yes—
166C11×C22⋊C4—24no—
167C42×C11C2×D412yes—
168C42×C11C2412yes—
169C22⋊Dic11—28no—
170C22⋊Dic11—28no—
171#4323—28no—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4—24no—
174C4⋊Dic11—28no—
175C4⋊Dic11—24no—
176C4⋊Dic11—24no—
177C4⋊Dic11—21no—
178C4⋊Dic11C2×D414yes—
179C4⋊Dic11C2412yes—
180Dic11⋊C4—28no—
181Dic11⋊C4—28no—
182Dic11⋊C4C2×D418yes—
183C4×Dic11—28no—
184C4×Dic11C2×D414yes—
185C4×Dic11C2414yes—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8C2412yes—
189C2×C11⋊C8C2412yes—
190#4314—216no—
191C2×#556—111no—
192C2×#554—111no—
193#3360—1116no—
194C2×#488—112no—
195C2×#487—111no—
196C2×#479—112no—
197C2×#476D1111yescharacteristic, complemented
198C2×#463—112no—
199C2×#461—111no—
200C2×C8×Q8—111no—
201C2×C4×SD16—112no—
202C2×C4×D8—111no—
203C23×C11—22no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11C22×D411yescharacteristic
208C22×D11—24no—
209C22×D11—22no—
210C22×D11—42no—
211C22×D11—42no—
212Q8×C11—84no—
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
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—22no—
233C2×Dic11—44no—
234C2×Dic11—42no—
235C2×Dic11C22×D414yes—
236C2×Dic11C22×D414yes—
237D44—24no—
238D44—22no—
239D44C2×#4114yes—
240C4×D11—48no—
241C4×D11—88no—
242Dic22—28no—
243Dic22—24no—
244Dic22—24no—
245Dic22—44no—
246C8×C11—24no—
247C11⋊C8—22no—
248C11⋊C8—22no—
249C22×SD16—112no—
250C22×D8—111no—
251#556—118no—
252#556—224no—
253#554—118no—
254#554—224no—
255C2×C4⋊Q8—111no—
256C2×C4⋊Q8C2×D1111yescharacteristic
257C2×#126—222no—
258C2×#125—112no—
259C2×#124—112no—
260C2×C22⋊Q8—221no—
261C2×C22⋊Q8—222no—
262C2×C22⋊Q8—221no—
263C2×C4×Q8—111no—
264C2×C4×Q8—112no—
265C2×C4×D4—112no—
266C2×C4×D4—111no—
267C2×C4×D4C2×D1111yescharacteristic
268C2×#117—221no—
269C22×C4⋊C4—221no—
270#488—1116no—
271#487—118no—
272#479—1116no—
273#476C2×D1118yescomplemented
274#463—1116no—
275#461—118no—
276C8×Q8—118no—
277C4×SD16—1116no—
278C4×D8—118no—
279C2×#107—111no—
280C2×#106C2×D1112yes—
281C2×C4⋊C8—112no—
282C2×C4⋊C8C2×D1111yescharacteristic
283C2×#103—112no—
284C2×#103—112no—
285C2×#103—112no—
286C2×#102—111no—
287C2×#102—111no—
288C2×#102C2×D1112yes—
289C2×C4×C8—112no—
290C2×C4×C8—111no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—84no—
295C22×C11#54812yes—
296C22×C11C2×#13512yes—
297C22×C11#57712yes—
298C22×C11C23×D411yescharacteristic
299C2×D11—24no—
300C2×D11—48no—
301C2×D11—42no—
302C2×D11—42no—
303C4×C11—22no—
304C4×C11—42no—
305C4×C11—44no—
306C4×C11#54812yes—
307C4×C11C2×#13514yes—
308C4×C11C22×#4111yescharacteristic
309C4×C11C2×2−1+411yescharacteristic
310Dic11—24no—
311Dic11—24no—
312Dic11—44no—
313Dic11—42no—
314C22×Q8—21no—
315C22×Q8—111no—
316C22×Q8—112no—
317C22×D4—111no—
318C22×D4C22×D1111yescharacteristic
319C23×C4—21no—
320C23×C4—222no—
321C23×C4—221no—
322C2×SD16—118no—
323C2×SD16—228no—
324C2×D8—114no—
325C2×D8—224no—
326C22×C8—111no—
327C22×C8—111no—
328C22×C8C22×D1112yes—
329C4⋊Q8—22no—
330C4⋊Q8—114no—
331C4⋊Q8—222no—
332C4⋊Q8C22×D1114yes—
333#126—2216no—
334#125—118no—
335#125—224no—
336#124—118no—
337#124—224no—
338C22⋊Q8—228no—
339C22⋊Q8—2216no—
340C22⋊Q8—228no—
341C4×Q8—114no—
342C4×Q8—114no—
343C4×Q8—118no—
344C4×Q8—224no—
345C4×D4—22no—
346C4×D4—118no—
347C4×D4—114no—
348C4×D4—224no—
349C4×D4—222no—
350C4×D4C22×D1114yes—
351#117—228no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—112no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—228no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4C22×D1112yes—
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—221no—
369C2×C42—112no—
370C2×C42—222no—
371C2×C42C22×D1111yescharacteristic
372#107—114no—
373#106C22×D1118yes—
374C4⋊C8—118no—
375C4⋊C8C22×D1114yes—
376#103—118no—
377#103—118no—
378#103—118no—
379#102—114no—
380#102—114no—
381#102C22×D1118yes—
382C4×C8—118no—
383C4×C8—114no—
384C2×C11—82no—
385C2×C11#336014yescomplemented
386C2×C11C2×#54811yescharacteristic
387C2×C11C22×#13511yescharacteristic
388C2×C11C2×#57711yescharacteristic
389D11—44no—
390C24—21no—
391C24—221no—
392C2×Q8—24no—
393C2×Q8—82no—
394C2×Q8—114no—
395C2×Q8—114no—
396C2×Q8—224no—
397C2×Q8—222no—
398C2×Q8—224no—
399C2×Q8—224no—
400C2×D4—21no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—114no—
404C2×D4—112no—
405C2×D4—221no—
406C2×D4—222no—
407C2×D4C23×D1112yes—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—44no—
412C22×C4—112no—
413C22×C4—112no—
414C22×C4—228no—
415C22×C4—222no—
416C22×C4—221no—
417C22×C4—224no—
418C22×C4—444no—
419C22×C4—884no—
420C22×C4D4×D1111yescharacteristic
421C22×C4D4×D1111yescharacteristic
422C22×C4C23×D1111yescharacteristic
423SD16—2216no—
424D8—228no—
425C2×C8—24no—
426C2×C8—112no—
427C2×C8—112no—
428C2×C8—222no—
429C2×C8—222no—
430C2×C8C23×D1114yes—
431C4⋊C4—24no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—114no—
435C4⋊C4—118no—
436C4⋊C4—112no—
437C4⋊C4—228no—
438C4⋊C4—228no—
439C4⋊C4—228no—
440C4⋊C4—221no—
441C4⋊C4—224no—
442C4⋊C4—224no—
443C4⋊C4C23×D1112yes—
444C4⋊C4C23×D1114yes—
445C22⋊C4—24no—
446C22⋊C4—228no—
447C22⋊C4—228no—
448C22⋊C4—228no—
449C22⋊C4—224no—
450C42—114no—
451C42—114no—
452C42—228no—
453C42D4×D1112yes—
454C42C23×D1112yes—
455C11C2×#336011yescharacteristic, complemented, Sylow
456C23—22no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—224no—
461C23—222no—
462C23—442no—
463C23—442no—
464C23C2×D4×D1111yescharacteristic
465Q8—84no—
466Q8—228no—
467Q8—224no—
468Q8—224no—
469Q8—444no—
470D4—22no—
471D4—22no—
472D4—42no—
473D4—114no—
474D4—224no—
475D4—222no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—48no—
482C2×C4—114no—
483C2×C4—114no—
484C2×C4—224no—
485C2×C4—224no—
486C2×C4—224no—
487C2×C4—222no—
488C2×C4—442no—
489C2×C4—444no—
490C2×C4—448no—
491C2×C4—888no—
492C2×C4#6696914yes—
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—222no—
501C8—222no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—84no—
506C22—224no—
507C22—448no—
508C22—442no—
509C22—442no—
510C22#1062316412yes—
511C22C2×#6696912yes—
512C22#1062330612yes—
513C22C22×D4×D1111yescharacteristic
514C4—22no—
515C4—42no—
516C4—44no—
517C4—224no—
518C4—224no—
519C4—442no—
520C4—444no—
521C4#1062316412yes—
522C4C2×#6696914yes—
523C4C2×#6704011yescharacteristic
524C4C2×#41×D1111yescharacteristic
525C2—82no—
526C2—444no—
527C2#1308126414yesdirect product factor
528C2C2×#1062316411yescharacteristic
529C2C22×#6696911yescharacteristic
530C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#476D11
hypocenterC11C2×#3360
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623073C2semidirect
2. C2×#10623261C2semidirect
3. #13081264C2direct (N × H)
4. C2×#10622381C2semidirect
5. C2×#10622706C2semidirect
6. C2×#10622470C2semidirect
8. C2×#10622454C2semidirect
9. C2×#10622443C2semidirect
10. C2×#10622465C2semidirect
12. C2×C11×#476C2semidirect
22. #10623261C22semidirect
24. #10623073C22semidirect
34. C11×#476C22semidirect
42. #10622706C22semidirect
49. #10622470C22semidirect
50. #10622465C22semidirect
51. #10622454C22semidirect
52. #10622443C22semidirect
54. #10622381C22semidirect
197. C2×#476D11semidirect
273. #476C2×D11semidirect
385. C2×C11#3360semidirect
455. C11C2×#3360semidirect
527. C2#13081264direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230732
C2×#106232612
#130812642
C2×#106223812
C2×#106227062
C2×#106224702
C2×#106224002
C2×#106224542
C2×#106224432
C2×#106224652
C2×C4×#43232
C2×C11×#4762
C2×#336011