Finite Group Databasebeta

← C2×#13081263 #15633343

Subgroups — C2×#13081263 #15633343

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×#10623074C211yesmaximal, characteristic, complemented
3#13081263C2116yesmaximal, direct product factor
4C2×#10622381C212yesmaximal, complemented
5C2×#10622294C211yesmaximal, characteristic, complemented
6C2×#10622490C212yesmaximal, complemented
7C2×#10622621C211yesmaximal, characteristic, complemented
8C2×#10622766C212yesmaximal
9C2×#10622632C211yesmaximal, characteristic, complemented
10C2×C8×Dic22C211yesmaximal, characteristic, complemented
11C2×#10622371C212yesmaximal, complemented
12C2×C4×C11×D8C211yesmaximal, characteristic
13C22×C11×D8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66989C2212yes—
17C2×D4×Dic11C2212yes—
18C22×#4324C2212yes—
19C2×#66979—21no—
20C22×C4⋊Dic11—21no—
21C2×#66977—21no—
22C2×#66977—21no—
23#10623074—24no—
24#10623074C2218yescomplemented
25#10623073—24no—
26#10623073C2218yescomplemented
27C2×#66943C2212yes—
28C2×#66940C2212yes—
29C2×#66932—22no—
30C2×#66931—22no—
31C2×#66922C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C4×C11×D8C2218yes—
35C2×C11×#107C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66896C2212yes—
40#10622766C22116yes—
41C2×#66880C2212yes—
42C2×#66880C2212yes—
43C2×Dic11⋊C8C2212yes—
44C2×C8×Dic11C2212yes—
45#10622632C2218yescomplemented
46#10622621C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66872C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622490C22116yescomplemented
51#10622381C22116yescomplemented
52#10622371C22116yescomplemented
53#10622294C2218yescomplemented
54C8×Dic22C2218yescomplemented
55C22×D4×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×Dic11—22no—
60C22×Dic22—21no—
61C22×Dic22D411yescharacteristic
62C22×Dic22C2312yes—
63C2×C11×D8—24no—
64C2×C11×D8C2314yes—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11C2314yes—
70C4×D4×C11C2314yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—22no—
79#66989—24no—
80#66989C2318yes—
81D4×Dic11—24no—
82D4×Dic11C2318yes—
83C2×#4324—28no—
84C2×#4324C2318yes—
85#66979—28no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—28no—
91C2×C4⋊Dic11D411yescharacteristic
92C2×C4⋊Dic11C2312yes—
93#66977—28no—
94#66977—28no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4D412yes—
98C2×C4×Dic11—22no—
99C2×C4×Dic11C2312yes—
100C22×C11⋊C8C2312yes—
101#66943—24no—
102#66943C2318yes—
103#66940—24no—
104#66940C2318yes—
105#66932—216no—
106#66931—216no—
107#66922—22no—
108#66922—22no—
109#66922C2314yes—
110#66922C2314yes—
111C4×Dic22D414yes—
112C4×Dic22C2314yes—
113C11×#107C2314yes—
114C11×#102C2314yes—
115C11×#102C2314yes—
116C4×C8×C11C2314yes—
117#66896C2318yes—
118#66880C2318yes—
119#66880C2318yes—
120Dic11⋊C8C2318yes—
121C8×Dic11C2318yes—
122#66874C2318yes—
123#66872C2318yes—
124C4⋊(C11⋊C8)C2314yes—
125C2×#3360—111nomaximal, Sylow
126C24×C11—21no—
127C24×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11#4114yes—
134C2×D4×C11C2412yes—
135C2×D4×C11C2412yes—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—44no—
141C22×C4×C11—44no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—28no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—84no—
149C22×Dic11C2×D412yes—
150C22×Dic11C2×D412yes—
151C2×Dic22—24no—
152C2×Dic22—22no—
153C2×Dic22—24no—
154C2×Dic22—24no—
155C2×Dic22—24no—
156C2×Dic22—82no—
157C2×Dic22C2×D414yes—
158C2×Dic22C2414yes—
159C11×D8—28no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11C2412yes—
163C2×C8×C11C2412yes—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4C2412yes—
167C11×C4⋊C4C2412yes—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C42×C11C2×D412yes—
171C42×C11C2412yes—
172C22⋊Dic11—28no—
173C22⋊Dic11—28no—
174C22⋊Dic11—28no—
175#4324—216no—
176C4⋊Dic11—28no—
177C4⋊Dic11—22no—
178C4⋊Dic11—24no—
179C4⋊Dic11—24no—
180C4⋊Dic11—24no—
181C4⋊Dic11C2×D414yes—
182C4⋊Dic11C2414yes—
183Dic11⋊C4—28no—
184Dic11⋊C4—28no—
185Dic11⋊C4C2×D418yes—
186C4×Dic11—28no—
187C4×Dic11C2×D414yes—
188C4×Dic11C2414yes—
189C2×C11⋊C8—24no—
190C2×C11⋊C8C2414yes—
191C2×#556—111no—
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×D8D1111yescharacteristic
203C23×C11—24no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11C22×D411yescharacteristic
212D4×C11—24no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—42no—
217D4×C11C2×#4114yes—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—48no—
224C2×C4×C11—48no—
225C2×C4×C11#13514yes—
226C2×C4×C11C22×D412yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D412yes—
229C2×C4×C11C2×#4112yes—
230C2×C4×C112−1+412yes—
231C2×C4×C11C2511yescharacteristic
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—44no—
237C2×Dic11—44no—
238C2×Dic11—88no—
239C2×Dic11C22×D414yes—
240C2×Dic11C22×D414yes—
241Dic22—28no—
242Dic22—24no—
243Dic22—24no—
244Dic22—44no—
245Dic22—84no—
246C8×C11—22no—
247C8×C11—22no—
248C11⋊C8—24no—
249C22×SD16—112no—
250C22×D8C2×D1111yescharacteristic
251#556—118no—
252#556—224no—
253#554—118no—
254#554—224no—
255C2×C4⋊Q8—111no—
256C2×C4⋊Q8—111no—
257C2×#126—222no—
258C2×#125—112no—
259C2×#124—112no—
260C2×C22⋊Q8—222no—
261C2×C22⋊Q8—221no—
262C2×C22⋊Q8—221no—
263C2×C4×Q8—111no—
264C2×C4×Q8—112no—
265C2×C4×D4—112no—
266C2×C4×D4C2×D1111yescharacteristic
267C2×C4×D4C2×D1111yescharacteristic
268C2×#117—221no—
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×D8C2×D1118yes—
279C2×#107C2×D1111yescharacteristic
280C2×#106—112no—
281C2×C4⋊C8—112no—
282C2×C4⋊C8—111no—
283C2×#103—112no—
284C2×#103—112no—
285C2×#103—112no—
286C2×#102—112no—
287C2×#102C2×D1111yescharacteristic
288C2×#102C2×D1111yescharacteristic
289C2×C4×C8—112no—
290C2×C4×C8C2×D1111yescharacteristic
291C22×C11—24no—
292C22×C11—48no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—84no—
299C22×C11#54812yes—
300C22×C11C2×#13512yes—
301C22×C11#57712yes—
302C22×C11C23×D411yescharacteristic
303C4×C11—22no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11#54812yes—
307C4×C11C2×#13514yes—
308C4×C11C22×#4111yescharacteristic
309C4×C11C2×2−1+411yescharacteristic
310Dic11—24no—
311Dic11—24no—
312Dic11—44no—
313Dic11—44no—
314C22×Q8—111no—
315C22×Q8—112no—
316C22×Q8—221no—
317C22×D4C22×D1111yescharacteristic
318C22×D4C22×D1111yescharacteristic
319C23×C4—21no—
320C23×C4—21no—
321C23×C4—222no—
322C2×SD16—118no—
323C2×SD16—228no—
324C2×D8—24no—
325C2×D8C22×D1114yes—
326C22×C8—112no—
327C22×C8C22×D1111yescharacteristic
328C22×C8C22×D1111yescharacteristic
329C4⋊Q8—114no—
330C4⋊Q8—114no—
331C4⋊Q8—222no—
332C4⋊Q8—222no—
333#126—2216no—
334#125—118no—
335#125—224no—
336#124—118no—
337#124—224no—
338C22⋊Q8—2216no—
339C22⋊Q8—228no—
340C22⋊Q8—228no—
341C4×Q8—114no—
342C4×Q8—114no—
343C4×Q8—118no—
344C4×Q8—224no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—118no—
348C4×D4—224no—
349C4×D4C22×D1114yes—
350C4×D4C22×D1114yes—
351#117—228no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4—112no—
355C2×C4⋊C4—228no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C42—112no—
370C2×C42—222no—
371C2×C42C22×D1111yescharacteristic
372#107C22×D1114yes—
373#106—118no—
374C4⋊C8—118no—
375C4⋊C8—114no—
376#103—118no—
377#103—118no—
378#103—118no—
379#102—118no—
380#102C22×D1114yes—
381#102C22×D1114yes—
382C4×C8—118no—
383C4×C8C22×D1114yes—
384C2×C11—44no—
385C2×C11—82no—
386C2×C11#336014yescomplemented
387C2×C11C2×#54811yescharacteristic
388C2×C11C22×#13511yescharacteristic
389C2×C11C2×#57711yescharacteristic
390C24—21no—
391C24—21no—
392C2×Q8—114no—
393C2×Q8—114no—
394C2×Q8—224no—
395C2×Q8—222no—
396C2×Q8—224no—
397C2×Q8—224no—
398C2×Q8—224no—
399C2×Q8—882no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4#433914yes—
406C2×D4C23×D1112yes—
407C2×D4C23×D1112yes—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—228no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—884no—
420C22×C4D4×D1111yescharacteristic
421C22×C4D4×D1111yescharacteristic
422C22×C4C23×D1111yescharacteristic
423SD16—2216no—
424D8—28no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—114no—
428C2×C8—224no—
429C2×C8C23×D1112yes—
430C2×C8C23×D1112yes—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—114no—
434C4⋊C4—118no—
435C4⋊C4—114no—
436C4⋊C4—228no—
437C4⋊C4—228no—
438C4⋊C4—228no—
439C4⋊C4—222no—
440C4⋊C4—224no—
441C4⋊C4—224no—
442C4⋊C4—224no—
443C4⋊C4C23×D1112yes—
444C4⋊C4C23×D1112yes—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—228no—
448C22⋊C4—228no—
449C22⋊C4—228no—
450C42—114no—
451C42—114no—
452C42—228no—
453C42D4×D1112yes—
454C42C23×D1112yes—
455C11C2×#336011yescharacteristic, complemented, Sylow
456C23—24no—
457C23—22no—
458C23—22no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23C2×D4×D1111yescharacteristic
465Q8—228no—
466Q8—224no—
467Q8—224no—
468Q8—444no—
469Q8—884no—
470D4—24no—
471D4—22no—
472D4—22no—
473D4—22no—
474D4—42no—
475D4C2×#433914yes—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—48no—
482C2×C4—48no—
483C2×C4—114no—
484C2×C4—114no—
485C2×C4—224no—
486C2×C4—224no—
487C2×C4—224no—
488C2×C4—224no—
489C2×C4—444no—
490C2×C4—444no—
491C2×C4—888no—
492C2×C4#6696514yes—
493C2×C4C2×#433912yes—
494C2×C4C2×D4×D1112yes—
495C2×C4C2×D4×D1112yes—
496C2×C4C2×D4×D1111yescharacteristic
497C2×C4#6704312yes—
498C2×C4C24×D1111yescharacteristic
499C8—22no—
500C8—22no—
501C8—224no—
502C22—24no—
503C22—48no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—84no—
510C22#1062308312yes—
511C22C2×#6696512yes—
512C22#1062330112yes—
513C22C22×D4×D1111yescharacteristic
514C4—22no—
515C4—42no—
516C4—42no—
517C4—224no—
518C4—224no—
519C4—444no—
520C4—444no—
521C4#1062308312yes—
522C4C2×#6696514yes—
523C4C22×#433911yescharacteristic
524C4C2×#6704311yescharacteristic
525C2—44no—
526C2—82no—
527C2#1308126314yesdirect product factor
528C2C2×#1062308311yescharacteristic
529C2C22×#6696511yescharacteristic
530C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenterC2×C4×D8D11
hypocenterC11C2×#3360
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#10623073C2semidirect
2. C2×#10623074C2semidirect
3. #13081263C2direct (N × H)
4. C2×#10622381C2semidirect
5. C2×#10622294C2semidirect
6. C2×#10622490C2semidirect
7. C2×#10622621C2semidirect
9. C2×#10622632C2semidirect
10. C2×C8×Dic22C2semidirect
11. C2×#10622371C2semidirect
24. #10623074C22semidirect
26. #10623073C22semidirect
45. #10622632C22semidirect
46. #10622621C22semidirect
50. #10622490C22semidirect
51. #10622381C22semidirect
52. #10622371C22semidirect
53. #10622294C22semidirect
54. C8×Dic22C22semidirect
386. C2×C11#3360semidirect
455. C11C2×#3360semidirect
527. C2#13081263direct (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×#106230742
#130812632
C2×#106223812
C2×#106222942
C2×#106224902
C2×#106226212
C2×#106227662
C2×#106226322
C2×C8×Dic222
C2×#106223712
C2×C4×C11×D82
C2×#336011