Finite Group Databasebeta

← C2×#13081261 #15633341

Subgroups — C2×#13081261 #15633341

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×#10623110C211yesmaximal, characteristic, complemented
2#13081261C2116yesmaximal, direct product factor
3C2×#10622669C212yesmaximal, complemented
4C2×#10622694C211yesmaximal, characteristic, complemented
5C2×#10622635C212yesmaximal, complemented
6C2×#10622621C211yesmaximal, characteristic, complemented
7C2×#10622670C212yesmaximal
8C2×#10622696C211yesmaximal, characteristic, complemented
9C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
10C2×C4×#4325C212yesmaximal, complemented
11C2×C4×#4323C211yesmaximal, characteristic
12C2×C11×#556C211yesmaximal, characteristic, complemented
13C11×#556—24no—
14C11×#556C2218yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#126—22no—
17C2×C11×#124C2212yes—
18C2×C11×C22⋊Q8—21no—
19C2×C4×Q8×C11C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C2×#66999—21no—
24C22×#4325C2212yes—
25C22×#4323C2211yescharacteristic
26#10623110—24no—
27#10623110C2218yescomplemented
28C2×#66949—22no—
29C2×C4⋊C4×D11—21no—
30C2×C4×D44C2211yescharacteristic
31C2×C4×D44C2212yes—
32C2×#66923C2212yes—
33C2×#66922C2211yescharacteristic
34C2×#66899C2212yes—
35C2×#66899C2212yes—
36C2×#66899C2212yes—
37C2×#66896C2212yes—
38C2×#66896C2211yescharacteristic
39#10622696C2218yescomplemented
40#10622694C2218yescomplemented
41#10622670C22116yes—
42#10622669C22116yescomplemented
43C4×#4325C22116yescomplemented
44Q8×C11⋊C8C2218yescomplemented
45#10622635C22116yescomplemented
46C4×#4323C2218yes—
47#10622621C2218yescomplemented
48C2×#66873C2211yescharacteristic
49C2×#66872C2212yes—
50C2×#66871C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×C4×C11⋊C8C2211yescharacteristic
54C2×C4×C11⋊C8C2212yes—
55C22×Q8×C11D411yescharacteristic
56C22×Q8×C11C2312yes—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—22no—
62C22×Dic22—21no—
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8C2314yes—
65C11×#126—216no—
66C11×#124—24no—
67C11×#124C2318yes—
68C11×C22⋊Q8—28no—
69C4×Q8×C11—24no—
70C4×Q8×C11D414yes—
71C4×Q8×C11C2318yes—
72C4×Q8×C11C2314yes—
73C4×D4×C11—22no—
74C4×D4×C11C2314yes—
75C11×#117—28no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D412yes—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—22no—
85C2×C42×C11—22no—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2312yes—
88#66999—28no—
89C2×#4325—28no—
90C2×#4325C2318yes—
91C2×#4323—24no—
92C2×#4323C2314yes—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2312yes—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2312yes—
103#66949—216no—
104C4⋊C4×D11—28no—
105C4×D44—24no—
106C4×D44—22no—
107C4×D44C2314yes—
108C4×D44C2318yes—
109#66923—24no—
110#66923C2318yes—
111#66922—22no—
112#66922C2314yes—
113#66899C2318yes—
114#66899C2318yes—
115#66899C2318yes—
116#66896C2318yes—
117#66896C2314yes—
118#66873C2314yes—
119#66872C2318yes—
120#66871C2314yes—
121C4⋊(C11⋊C8)C2314yes—
122C4⋊(C11⋊C8)C2318yes—
123C4×C11⋊C8C2314yes—
124C4×C11⋊C8C2318yes—
125C2×#3360—111nomaximal, Sylow
126C24×C11—21no—
127C23×D11—21no—
128C2×Q8×C11—24no—
129C2×Q8×C11—22no—
130C2×Q8×C11—24no—
131C2×Q8×C11—24no—
132C2×Q8×C11C2×D414yes—
133C2×Q8×C11C2414yes—
134C2×D4×C11—21no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11C2412yes—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—44no—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—22no—
149C2×D44—21no—
150C2×D44—22no—
151C2×D44#4114yes—
152C2×D44C2412yes—
153C2×C4×D11—24no—
154C2×C4×D11—28no—
155C2×C4×D11—44no—
156C2×C4×D11—84no—
157C2×Dic22—24no—
158C2×Dic22—82no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4C2×D414yes—
164C11×C4⋊C4C2×D418yes—
165C11×C4⋊C4C2412yes—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—28no—
169C42×C11—28no—
170C42×C11C2×D412yes—
171C42×C11C2×D414yes—
172C42×C11C2412yes—
173C42×C11C2414yes—
174#4325—216no—
175#4323—28no—
176(C2×D11)⋊C4—24no—
177(C2×D11)⋊C4—28no—
178C4⋊Dic11—22no—
179C4⋊Dic11—24no—
180C4⋊Dic11—21no—
181C4⋊Dic11C2412yes—
182C4⋊Dic11C2414yes—
183Dic11⋊C4—28no—
184Dic11⋊C4—28no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—24no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8C2412yes—
189C2×C11⋊C8C2412yes—
190C2×C11⋊C8C2414yes—
191C2×#556D1111yescharacteristic, complemented
192C2×#554—111no—
193#3360—1116no—
194C2×#488—112no—
195C2×#487—111no—
196C2×#479—112no—
197C2×#476—111no—
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—28no—
213Q8×C11—24no—
214Q8×C11—24no—
215Q8×C11—44no—
216D4×C11—22no—
217D4×C11—22no—
218D4×C11—42no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—44no—
225C2×C4×C11—42no—
226C2×C4×C11—48no—
227C2×C4×C11#13514yes—
228C2×C4×C11C22×D414yes—
229C2×C4×C11C22×D414yes—
230C2×C4×C11C22×D412yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D412yes—
233C2×C4×C11C2×#4112yes—
234C2×C4×C112−1+412yes—
235C2×C4×C11C2511yescharacteristic
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—42no—
239C2×Dic11—44no—
240D44—24no—
241D44—22no—
242D44C2×#4114yes—
243C4×D11—48no—
244C4×D11—88no—
245Dic22—84no—
246C11⋊C8—22no—
247C11⋊C8—24no—
248C11⋊C8—22no—
249C22×SD16—112no—
250C22×D8—111no—
251#556—24no—
252#556C2×D1118yescomplemented
253#554—118no—
254#554—224no—
255C2×C4⋊Q8—111no—
256C2×C4⋊Q8C2×D1111yescharacteristic
257C2×#126—22no—
258C2×#125—112no—
259C2×#124C2×D1112yes—
260C2×C22⋊Q8—21no—
261C2×C22⋊Q8—221no—
262C2×C22⋊Q8—222no—
263C2×C4×Q8C2×D1112yes—
264C2×C4×Q8C2×D1111yescharacteristic
265C2×C4×D4—111no—
266C2×C4×D4—112no—
267C2×C4×D4C2×D1111yescharacteristic
268C2×#117—21no—
269C22×C4⋊C4—221no—
270#488—1116no—
271#487—118no—
272#479—1116no—
273#476—118no—
274#463—1116no—
275#461—118no—
276C8×Q8—118no—
277C4×SD16—1116no—
278C4×D8—118no—
279C2×#107—111no—
280C2×#106—112no—
281C2×C4⋊C8—112no—
282C2×C4⋊C8—111no—
283C2×#103—112no—
284C2×#103—112no—
285C2×#103—112no—
286C2×#102—111no—
287C2×#102—112no—
288C2×#102—111no—
289C2×C4×C8—111no—
290C2×C4×C8—112no—
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—24no—
304C4×C11—22no—
305C4×C11—24no—
306C4×C11—44no—
307C4×C11—42no—
308C4×C11#54812yes—
309C4×C11C2×#13514yes—
310C4×C11C22×#4111yescharacteristic
311C4×C11C2×2−1+411yescharacteristic
312Dic11—42no—
313Dic11—44no—
314C22×Q8—221no—
315C22×Q8C22⋊D1111yescharacteristic
316C22×Q8C22×D1112yes—
317C22×D4—111no—
318C22×D4C22×D1111yescharacteristic
319C23×C4—21no—
320C23×C4—221no—
321C23×C4—222no—
322C2×SD16—118no—
323C2×SD16—228no—
324C2×D8—114no—
325C2×D8—224no—
326C22×C8—111no—
327C22×C8—112no—
328C22×C8—111no—
329C4⋊Q8—22no—
330C4⋊Q8—114no—
331C4⋊Q8—222no—
332C4⋊Q8C22×D1114yes—
333#126—216no—
334#125—118no—
335#125—224no—
336#124—24no—
337#124C22×D1118yes—
338C22⋊Q8—28no—
339C22⋊Q8—228no—
340C22⋊Q8—2216no—
341C4×Q8—24no—
342C4×Q8C22⋊D1114yes—
343C4×Q8C22×D1118yes—
344C4×Q8C22×D1114yes—
345C4×D4—22no—
346C4×D4—114no—
347C4×D4—118no—
348C4×D4—222no—
349C4×D4—224no—
350C4×D4C22×D1114yes—
351#117—28no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—112no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—228no—
361C2×C4⋊C4C22⋊D1111yescharacteristic
362C2×C4⋊C4C22⋊D1112yes—
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C22⋊C4—22no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—222no—
369C2×C42—22no—
370C2×C42C22×D1111yescharacteristic
371C2×C42C22×D1112yes—
372#107—114no—
373#106—118no—
374C4⋊C8—114no—
375C4⋊C8—118no—
376#103—118no—
377#103—118no—
378#103—118no—
379#102—114no—
380#102—118no—
381#102—114no—
382C4×C8—114no—
383C4×C8—118no—
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—22no—
394C2×Q8—24no—
395C2×Q8—24no—
396C2×Q8—224no—
397C2×Q8—882no—
398C2×Q8C2×C22⋊D1114yes—
399C2×Q8C23×D1114yes—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—21no—
403C2×D4—114no—
404C2×D4—112no—
405C2×D4—222no—
406C2×D4—221no—
407C2×D4C23×D1112yes—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—44no—
412C22×C4—221no—
413C22×C4—222no—
414C22×C4—224no—
415C22×C4—228no—
416C22×C4—444no—
417C22×C4—884no—
418C22×C4C2×C22⋊D1112yes—
419C22×C4C2×C22⋊D1112yes—
420C22×C4C2×C22⋊D1111yescharacteristic
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C23×D1111yescharacteristic
423SD16—2216no—
424D8—228no—
425C2×C8—112no—
426C2×C8—114no—
427C2×C8—112no—
428C2×C8—222no—
429C2×C8—224no—
430C2×C8—222no—
431C4⋊C4—24no—
432C4⋊C4—28no—
433C4⋊C4—24no—
434C4⋊C4—21no—
435C4⋊C4—114no—
436C4⋊C4—112no—
437C4⋊C4—221no—
438C4⋊C4—222no—
439C4⋊C4—228no—
440C4⋊C4—224no—
441C4⋊C4—228no—
442C4⋊C4C2×C22⋊D1114yes—
443C4⋊C4C2×C22⋊D1118yes—
444C4⋊C4C23×D1112yes—
445C22⋊C4—28no—
446C22⋊C4—24no—
447C22⋊C4—28no—
448C22⋊C4—224no—
449C22⋊C4—228no—
450C42—28no—
451C42C2×C22⋊D1112yes—
452C42C2×C22⋊D1114yes—
453C42C23×D1112yes—
454C42C23×D1114yes—
455C11C2×#336011yescharacteristic, complemented, Sylow
456C23—22no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—224no—
461C23—222no—
462C23—442no—
463C23—442no—
464C23C22×C22⋊D1111yescharacteristic
465Q8—28no—
466Q8—24no—
467Q8—24no—
468Q8—44no—
469Q8—884no—
470D4—22no—
471D4—22no—
472D4—42no—
473D4—114no—
474D4—224no—
475D4—222no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—42no—
482C2×C4—44no—
483C2×C4—48no—
484C2×C4—222no—
485C2×C4—224no—
486C2×C4—442no—
487C2×C4—444no—
488C2×C4—448no—
489C2×C4—888no—
490C2×C4#6700314yes—
491C2×C4#41×D1112yes—
492C2×C4#6704312yes—
493C2×C4C22×C22⋊D1114yes—
494C2×C4C22×C22⋊D1114yes—
495C2×C4C22×C22⋊D1112yes—
496C2×C4C22×C22⋊D1112yes—
497C2×C4C22×C22⋊D1111yescharacteristic
498C2×C4C24×D1111yescharacteristic
499C8—222no—
500C8—224no—
501C8—222no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—84no—
506C22—224no—
507C22—448no—
508C22—442no—
509C22—442no—
510C22C2×#6700312yes—
511C22#1062336212yes—
512C22#1062336812yes—
513C22C23×C22⋊D1111yescharacteristic
514C4—24no—
515C4—24no—
516C4—22no—
517C4—42no—
518C4—44no—
519C4—442no—
520C4—444no—
521C4C2×#6700314yes—
522C4#1062336212yes—
523C4C2×#41×D1111yescharacteristic
524C4C2×#6704311yescharacteristic
525C2—82no—
526C2—444no—
527C2#1308126114yesdirect product factor
528C2C2×#1062336211yescharacteristic
529C2C22×#6700311yescharacteristic
530C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#556D11
hypocenterC11C2×#3360
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#10623110C2semidirect
2. #13081261C2direct (N × H)
3. C2×#10622669C2semidirect
4. C2×#10622694C2semidirect
5. C2×#10622635C2semidirect
6. C2×#10622621C2semidirect
8. C2×#10622696C2semidirect
9. C2×Q8×C11⋊C8C2semidirect
10. C2×C4×#4325C2semidirect
12. C2×C11×#556C2semidirect
14. C11×#556C22semidirect
27. #10623110C22semidirect
39. #10622696C22semidirect
40. #10622694C22semidirect
42. #10622669C22semidirect
43. C4×#4325C22semidirect
44. Q8×C11⋊C8C22semidirect
45. #10622635C22semidirect
47. #10622621C22semidirect
191. C2×#556D11semidirect
252. #556C2×D11semidirect
385. C2×C11#3360semidirect
455. C11C2×#3360semidirect
527. C2#13081261direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231102
#130812612
C2×#106226692
C2×#106226942
C2×#106226352
C2×#106226212
C2×#106226702
C2×#106226962
C2×Q8×C11⋊C82
C2×C4×#43252
C2×C4×#43232
C2×C11×#5562
C2×#336011