Finite Group Databasebeta

← C2×#13081321 #15633422

Subgroups — C2×#13081321 #15633422

Order 2816.

2198 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic, complemented
2C2×#10623084C211yesmaximal, characteristic, complemented
3#13081321C2116yesmaximal, direct product factor
4C2×#10622377C212yesmaximal, complemented
5C2×#10622307C211yesmaximal, characteristic, complemented
6C2×#10622504C212yesmaximal, complemented
7C2×#10622621C211yesmaximal, characteristic, complemented
8C2×#10622628C211yesmaximal, characteristic, complemented
9C2×#10622763C212yesmaximal, complemented
10C2×#10622292C211yesmaximal, characteristic, complemented
11C2×#10622398C212yesmaximal, complemented
12C2×C4×C11×D8C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C22×C11×D8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66993C2212yes—
18C2×D4×Dic11C2212yes—
19C22×#4323C2212yes—
20C2×#66983—21no—
21C22×C4⋊Dic11—21no—
22C2×#66977—21no—
23#10623084—24no—
24#10623084C2218yescomplemented
25#10623074—24no—
26#10623074C2218yescomplemented
27C2×#66946C2212yes—
28C2×#66943C2212yes—
29C2×#66937—22no—
30C2×#66931—22no—
31C2×#66927C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C4×C11×D8C2218yescomplemented
35C2×C11×#107C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66896C2212yes—
40#10622763C22116yescomplemented
41C2×#66885C2212yes—
42C2×#66885C2212yes—
43C2×#66879C2212yes—
44C2×Dic11⋊C8C2212yes—
45#10622628C2218yescomplemented
46#10622621C2218yescomplemented
47C2×#66873C2212yes—
48C2×#66872C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622504C22116yescomplemented
51#10622398C22116yescomplemented
52#10622377C22116yescomplemented
53#10622307C2218yescomplemented
54#10622292C2218yescomplemented
55C22×D4×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C22×C22⋊D11—22no—
60C22×C22⋊D11—22no—
61C23×Dic11—22no—
62C2×#4339—28no—
63C2×#4339—48no—
64C22×D44—21no—
65C22×D44—21no—
66C22×D44C2312yes—
67C22×C4×D11—22no—
68C22×Dic22—21no—
69C22×Dic22D411yescharacteristic
70C2×C11×D8—24no—
71C2×C11×D8C2314yes—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11C2314yes—
77C4×D4×C11C2314yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—22no—
84#66993—24no—
85#66993C2318yes—
86D4×Dic11—24no—
87D4×Dic11C2318yes—
88C2×#4323—28no—
89C2×#4323C2318yes—
90#66983—28no—
91C2×(C2×D11)⋊C4—22no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—28no—
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11C2312yes—
97#66977—28no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4D412yes—
100C2×C4×Dic11C2312yes—
101C22×C11⋊C8C2312yes—
102#66946—24no—
103#66946C2318yes—
104#66943—24no—
105#66943C2318yes—
106#66937—216no—
107#66931—216no—
108#66927—22no—
109#66927C2314yes—
110#66922—22no—
111#66922C2314yes—
112C4×Dic22D414yes—
113C4×Dic22C2314yes—
114C11×#107C2314yes—
115C11×#102C2314yes—
116C11×#102C2314yes—
117C4×C8×C11C2314yes—
118#66896C2318yes—
119#66885C2318yes—
120#66885C2318yes—
121#66879C2318yes—
122Dic11⋊C8C2318yes—
123#66873C2318yes—
124#66872C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126C2×#3366—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11—21no—
129C23×D11—22no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11#4114yescomplemented
136C2×D4×C11C2412yes—
137C2×D4×C11C2412yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—44no—
143C22×C4×C11—44no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—28no—
148C2×C22⋊D11—28no—
149C2×C22⋊D11—48no—
150C2×C22⋊D11—84no—
151C22×Dic11—28no—
152C22×Dic11—22no—
153C22×Dic11—84no—
154C22×Dic11C2×D412yes—
155C22×Dic11C2×D412yes—
156#4339—432no—
157C2×D44—22no—
158C2×D44—24no—
159C2×D44—24no—
160C2×D44—24no—
161C2×D44—24no—
162C2×D44—44no—
163C2×D44—82no—
164C2×D44C2414yes—
165C2×C4×D11—28no—
166C2×C4×D11—48no—
167C2×Dic22—24no—
168C2×Dic22—24no—
169C2×Dic22—82no—
170C2×Dic22C2×D414yes—
171C11×D8—28no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11C2412yes—
175C2×C8×C11C2412yes—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2412yes—
179C11×C4⋊C4C2412yes—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C42×C11C2×D412yes—
183C42×C11C2412yes—
184C22⋊Dic11—28no—
185#4323—216no—
186(C2×D11)⋊C4—28no—
187C4⋊Dic11—28no—
188C4⋊Dic11—22no—
189C4⋊Dic11—24no—
190C4⋊Dic11C2×D414yes—
191C4⋊Dic11C2414yes—
192Dic11⋊C4—28no—
193Dic11⋊C4C2×D418yes—
194C4×Dic11C2×D414yes—
195C4×Dic11C2414yes—
196C2×C11⋊C8—24no—
197C2×C11⋊C8C2414yes—
198C2×#554—111no—
199C2×#550—111no—
200#3366—1116no—
201C2×#490—112no—
202C2×#486—111no—
203C2×#478—112no—
204C2×#476—111no—
205C2×#459—112no—
206C2×#459—111no—
207C2×#446—111no—
208C2×#442—112no—
209C2×C4×D8D1111yescharacteristic, complemented
210C23×C11—24no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11C22×D411yescharacteristic
219C22×D11—24no—
220C22×D11—44no—
221C22×D11—44no—
222C22×D11—44no—
223D4×C11—24no—
224D4×C11—22no—
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—42no—
228D4×C11C2×#4114yescomplemented
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—48no—
235C2×C4×C11—48no—
236C2×C4×C11AGL(1,ℤ/8)14yes—
237C2×C4×C11C22×D412yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D412yes—
240C2×C4×C11C2×#4112yes—
241C2×C4×C112−1+412yes—
242C2×C4×C11C2511yescharacteristic
243C22⋊D11—416no—
244C22⋊D11—88no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—44no—
249C2×Dic11—88no—
250C2×Dic11C22×D414yes—
251C2×Dic11C22×D414yes—
252D44—24no—
253D44—24no—
254D44—44no—
255D44—48no—
256D44—84no—
257C4×D11—416no—
258Dic22—28no—
259Dic22—84no—
260C8×C11—22no—
261C8×C11—22no—
262C11⋊C8—24no—
263C22×#41—221no—
264C22×D8—112no—
265C22×D8C2×D1111yescharacteristic
266#554—118no—
267#554—224no—
268#550—118no—
269#550—224no—
270C2×C4⋊Q8—111no—
271C2×#127—112no—
272C2×#127—111no—
273C2×#125—112no—
274C2×C22⋊Q8—222no—
275C2×C22⋊Q8—221no—
276C2×#121—222no—
277C2×#121—221no—
278C2×C4×Q8—111no—
279C2×C4×D4—112no—
280C2×C4×D4—112no—
281C2×C4×D4C2×D1111yescharacteristic
282C2×C4×D4C2×D1111yescharacteristic
283C22×C4⋊C4—221no—
284#490—1116no—
285#486—118no—
286#478—1116no—
287#476—118no—
288#459—1116no—
289#459—118no—
290#446—118no—
291#442—1116no—
292C4×D8C2×D1118yescomplemented
293C2×#107C2×D1111yescharacteristic
294C2×#106—112no—
295C2×C4⋊C8—112no—
296C2×C4⋊C8—111no—
297C2×#102—112no—
298C2×#102—112no—
299C2×#102—112no—
300C2×#102—112no—
301C2×#102C2×D1111yescharacteristic
302C2×#102C2×D1111yescharacteristic
303C2×#97—112no—
304C2×C4×C8C2×D1111yescharacteristic
305C22×C11—24no—
306C22×C11—48no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—84no—
313C22×C11#54812yes—
314C22×C11C2×AGL(1,ℤ/8)12yes—
315C22×C11#57612yes—
316C22×C11C23×D411yescharacteristic
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—88no—
321C4×C11—22no—
322C4×C11—42no—
323C4×C11—42no—
324C4×C11#54812yes—
325C4×C11C2×AGL(1,ℤ/8)14yes—
326C4×C11C22×#4111yescharacteristic
327C4×C11C2×2−1+411yescharacteristic
328Dic11—24no—
329Dic11—24no—
330Dic11—44no—
331C2×#41—228no—
332C2×#41—448no—
333C22×Q8—111no—
334C22×Q8—221no—
335C22×D4—112no—
336C22×D4—222no—
337C22×D4—222no—
338C22×D4—221no—
339C22×D4—221no—
340C22×D4C22×D1111yescharacteristic
341C22×D4C22×D1111yescharacteristic
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—222no—
345C23×C4—222no—
346C2×D8—24no—
347C2×D8—118no—
348C2×D8—228no—
349C2×D8C22×D1114yes—
350C22×C8—112no—
351C22×C8C22×D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353C4⋊Q8—114no—
354C4⋊Q8—222no—
355#127—118no—
356#127—114no—
357#127—224no—
358#127—222no—
359#125—118no—
360#125—224no—
361C22⋊Q8—2216no—
362C22⋊Q8—228no—
363#121—2216no—
364#121—228no—
365C4×Q8—114no—
366C4×Q8—114no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—118no—
370C4×D4—118no—
371C4×D4—224no—
372C4×D4—224no—
373C4×D4C22×D1114yes—
374C4×D4C22×D1114yes—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—228no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—222no—
388C2×C42—112no—
389C2×C42C22×D1111yescharacteristic
390#107C22×D1114yes—
391#106—118no—
392C4⋊C8—118no—
393C4⋊C8—114no—
394#102—118no—
395#102—118no—
396#102—118no—
397#102—118no—
398#102C22×D1114yes—
399#102C22×D1114yes—
400#97—118no—
401C4×C8C22×D1114yes—
402C2×C11—44no—
403C2×C11—82no—
404C2×C11#336614yescomplemented
405C2×C11C2×#54811yescharacteristic
406C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
407C2×C11C2×#57611yescharacteristic
408D11—84no—
409C24—21no—
410C24—21no—
411C24—222no—
412#41—4432no—
413C2×Q8—114no—
414C2×Q8—224no—
415C2×Q8—224no—
416C2×Q8—882no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—114no—
423C2×D4—228no—
424C2×D4—228no—
425C2×D4—224no—
426C2×D4—222no—
427C2×D4—224no—
428C2×D4—224no—
429C2×D4—224no—
430C2×D4—448no—
431C2×D4—444no—
432C2×D4—882no—
433C2×D4—884no—
434C2×D4#433914yescomplemented
435C2×D4C23×D1112yes—
436C2×D4C23×D1112yes—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4—112no—
444C22×C4—112no—
445C22×C4—228no—
446C22×C4—228no—
447C22×C4—222no—
448C22×C4—448no—
449C22×C4—884no—
450C22×C4D4×D1111yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453D8—28no—
454D8—2216no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—114no—
458C2×C8—224no—
459C2×C8C23×D1112yes—
460C2×C8C23×D1112yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—114no—
464C4⋊C4—118no—
465C4⋊C4—114no—
466C4⋊C4—228no—
467C4⋊C4—228no—
468C4⋊C4—222no—
469C4⋊C4—224no—
470C4⋊C4C23×D1112yes—
471C4⋊C4C23×D1112yes—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—228no—
475C22⋊C4—228no—
476C42—114no—
477C42—114no—
478C42D4×D1112yes—
479C42C23×D1112yes—
480C11C2×#336611yescharacteristic, complemented, Sylow
481C23—24no—
482C23—22no—
483C23—22no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—224no—
490C23—444no—
491C23—444no—
492C23—444no—
493C23C2×D4×D1111yescharacteristic
494Q8—228no—
495Q8—884no—
496D4—24no—
497D4—22no—
498D4—22no—
499D4—22no—
500D4—42no—
501D4—224no—
502D4—224no—
503D4—4416no—
504D4—448no—
505D4—444no—
506D4—884no—
507D4—888no—
508D4C2×#433914yescomplemented
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—48no—
515C2×C4—48no—
516C2×C4—114no—
517C2×C4—114no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—4416no—
522C2×C4—444no—
523C2×C4—888no—
524C2×C4#6696414yes—
525C2×C4C2×#433912yes—
526C2×C4C2×D4×D1112yes—
527C2×C4C2×D4×D1112yes—
528C2×C4C2×D4×D1111yescharacteristic
529C2×C4#6704312yes—
530C2×C4C24×D1111yescharacteristic
531C8—22no—
532C8—22no—
533C8—224no—
534C22—24no—
535C22—42no—
536C22—42no—
537C22—48no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—84no—
542C22—444no—
543C22—444no—
544C22—444no—
545C22—888no—
546C22#1062308312yes—
547C22C2×#6696412yes—
548C22#1062330012yes—
549C22C22×D4×D1111yescharacteristic
550C4—22no—
551C4—42no—
552C4—42no—
553C4—224no—
554C4—224no—
555C4—444no—
556C4#1062308312yes—
557C4C2×#6696414yes—
558C4C22×#433911yescharacteristic
559C4C2×#6704311yescharacteristic
560C2—44no—
561C2—82no—
562C2—884no—
563C2#1308132114yesdirect product factor
564C2C2×#1062308311yescharacteristic
565C2C22×#6696411yescharacteristic
566C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
hypercenterC2×C4×D8D11
hypocenterC11C2×#3366
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×#10623074C2semidirect
2. C2×#10623084C2semidirect
3. #13081321C2direct (N × H)
4. C2×#10622377C2semidirect
5. C2×#10622307C2semidirect
6. C2×#10622504C2semidirect
7. C2×#10622621C2semidirect
8. C2×#10622628C2semidirect
9. C2×#10622763C2semidirect
10. C2×#10622292C2semidirect
11. C2×#10622398C2semidirect
12. C2×C4×C11×D8C2semidirect
24. #10623084C22semidirect
26. #10623074C22semidirect
34. C4×C11×D8C22semidirect
40. #10622763C22semidirect
45. #10622628C22semidirect
46. #10622621C22semidirect
50. #10622504C22semidirect
51. #10622398C22semidirect
52. #10622377C22semidirect
53. #10622307C22semidirect
54. #10622292C22semidirect
135. C2×D4×C11#41semidirect
209. C2×C4×D8D11semidirect
228. D4×C11C2×#41semidirect
292. C4×D8C2×D11semidirect
404. C2×C11#3366semidirect
434. C2×D4#4339semidirect
480. C11C2×#3366semidirect
508. D4C2×#4339semidirect
563. C2#13081321direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106230842
#130813212
C2×#106223772
C2×#106223072
C2×#106225042
C2×#106226212
C2×#106226282
C2×#106227632
C2×#106222922
C2×#106223982
C2×C4×C11×D82
C2×#336611