Finite Group Databasebeta

← C2×#13081319 #15633420

Subgroups — C2×#13081319 #15633420

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×#10623110C211yesmaximal, characteristic, complemented
2#13081319C2116yesmaximal, direct product factor
3C2×#10622684C212yesmaximal, complemented
4C2×#10622683C211yesmaximal, characteristic, complemented
5C2×#10622622C212yesmaximal, complemented
6C2×#10622621C211yesmaximal, characteristic, complemented
7C2×#10622685C211yesmaximal, characteristic, complemented
8C2×#10622685C212yesmaximal, complemented
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622627C212yesmaximal, complemented
11C2×C4×#4323C211yesmaximal, characteristic, complemented
12C2×C11×#550C211yesmaximal, characteristic, complemented
13C22×C11×#41—21no—
14C11×#550—24no—
15C11×#550C2218yescomplemented
16C2×C11×#127C2211yescharacteristic
17C2×C11×#127C2212yes—
18C2×C11×#121—21no—
19C2×C11×#121—22no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2212yes—
23C2×#66999—21no—
24C22×#4323C2211yescharacteristic
25C22×#4323C2212yes—
26#10623110—24no—
27#10623110C2218yescomplemented
28C2×#66949—22no—
29C2×C4⋊C4×D11—21no—
30C2×C4×D44C2211yescharacteristic
31C2×C4×D44C2212yes—
32C2×#66923C2212yes—
33C2×#66922C2211yescharacteristic
34C2×#66896C2212yes—
35C2×#66896C2212yes—
36C2×#66896C2212yes—
37C2×#66896C2211yescharacteristic
38C2×#66896C2212yes—
39#10622685C2218yescomplemented
40#10622685C22116yescomplemented
41#10622684C22116yescomplemented
42#10622683C2218yescomplemented
43#10622637C2218yescomplemented
44#10622627C22116yescomplemented
45C4×#4323C2218yescomplemented
46#10622622C22116yescomplemented
47#10622621C2218yescomplemented
48C2×#66873C2211yescharacteristic
49C2×#66872C2212yes—
50C2×#66871C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C11×#41—28no—
56C2×C11×#41—48no—
57C22×Q8×C11D411yescharacteristic
58C22×D4×C11—22no—
59C22×D4×C11—21no—
60C22×D4×C11—22no—
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2312yes—
64C23×C4×C11—22no—
65C23×C4×C11—21no—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×C4×D11—22no—
69C22×Dic22—21no—
70C11×#127—22no—
71C11×#127—24no—
72C11×#127C2314yes—
73C11×#127C2318yes—
74C11×#121—28no—
75C11×#121—216no—
76C4×Q8×C11D414yes—
77C4×Q8×C11C2314yes—
78C4×D4×C11—22no—
79C4×D4×C11—24no—
80C4×D4×C11C2314yes—
81C4×D4×C11C2318yes—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D412yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2312yes—
89#66999—28no—
90C2×#4323—24no—
91C2×#4323—28no—
92C2×#4323C2314yes—
93C2×#4323C2318yes—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—22no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2312yes—
104#66949—216no—
105C4⋊C4×D11—28no—
106C4×D44—24no—
107C4×D44—22no—
108C4×D44C2314yes—
109C4×D44C2318yes—
110#66923—24no—
111#66923C2318yes—
112#66922—22no—
113#66922C2314yes—
114#66896C2318yes—
115#66896C2318yes—
116#66896C2318yes—
117#66896C2314yes—
118#66896C2318yes—
119#66873C2314yes—
120#66872C2318yes—
121#66871C2314yes—
122C4⋊(C11⋊C8)C2314yes—
123C4⋊(C11⋊C8)C2318yes—
124#66867C2318yes—
125C4×C11⋊C8C2314yes—
126C2×#3366—111nomaximal, Sylow
127C24×C11—22no—
128C24×C11—21no—
129C23×D11—21no—
130C11×#41—432no—
131C2×Q8×C11—24no—
132C2×Q8×C11C2×D414yes—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—28no—
136C2×D4×C11—24no—
137C2×D4×C11—28no—
138C2×D4×C11—24no—
139C2×D4×C11—22no—
140C2×D4×C11—24no—
141C2×D4×C11—22no—
142C2×D4×C11—24no—
143C2×D4×C11—48no—
144C2×D4×C11—44no—
145C2×D4×C11—82no—
146C2×D4×C11—84no—
147C2×D4×C11C2412yes—
148C2×D4×C11C2414yes—
149C22×C4×C11—21no—
150C22×C4×C11—28no—
151C22×C4×C11—24no—
152C22×C4×C11—48no—
153C22×C4×C11—44no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C22×Dic11—21no—
160C22×Dic11—22no—
161C2×D44—21no—
162C2×D44—22no—
163C2×D44#4114yescomplemented
164C2×D44C2412yes—
165C2×C4×D11—24no—
166C2×C4×D11—28no—
167C2×C4×D11—44no—
168C2×C4×D11—84no—
169C2×Dic22—24no—
170C2×Dic22—82no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C2×D414yes—
173C11×C4⋊C4C2×D418yes—
174C11×C4⋊C4C2412yes—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—24no—
177C42×C11C2×D412yes—
178C42×C11C2×D414yes—
179C42×C11C2412yes—
180C42×C11C2414yes—
181#4323—28no—
182#4323—216no—
183(C2×D11)⋊C4—24no—
184(C2×D11)⋊C4—28no—
185C4⋊Dic11—22no—
186C4⋊Dic11—24no—
187C4⋊Dic11—21no—
188C4⋊Dic11C2412yes—
189C4⋊Dic11C2414yes—
190Dic11⋊C4—28no—
191Dic11⋊C4—28no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—24no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8C2412yes—
196C2×C11⋊C8C2412yes—
197C2×C11⋊C8C2414yes—
198C2×#554—111no—
199C2×#550D1111yescharacteristic, complemented
200#3366—1116no—
201C2×#490—112no—
202C2×#486—111no—
203C2×#478—112no—
204C2×#476—111no—
205C2×#459—111no—
206C2×#459—112no—
207C2×#446—111no—
208C2×#442—112no—
209C2×C4×D8—111no—
210C23×C11—24no—
211C23×C11—22no—
212C23×C11—44no—
213C23×C11—42no—
214C23×C11—44no—
215C23×C11—42no—
216C23×C11—44no—
217C23×C11—42no—
218C23×C11C22×D411yescharacteristic
219C22×D11—24no—
220C22×D11—22no—
221C22×D11—42no—
222C22×D11—42no—
223Q8×C11—28no—
224D4×C11—22no—
225D4×C11—24no—
226D4×C11—22no—
227D4×C11—24no—
228D4×C11—416no—
229D4×C11—42no—
230D4×C11—44no—
231D4×C11—48no—
232D4×C11—84no—
233D4×C11—88no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—416no—
239C2×C4×C11—42no—
240C2×C4×C11—48no—
241C2×C4×C11AGL(1,ℤ/8)14yes—
242C2×C4×C11C22×D414yes—
243C2×C4×C11C22×D414yes—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D412yes—
247C2×C4×C11C2×#4112yes—
248C2×C4×C112−1+412yes—
249C2×C4×C11C2511yescharacteristic
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11—42no—
253C2×Dic11—44no—
254D44—24no—
255D44—22no—
256D44C2×#4114yescomplemented
257C4×D11—48no—
258C4×D11—88no—
259Dic22—84no—
260C11⋊C8—22no—
261C11⋊C8—24no—
262C11⋊C8—22no—
263C22×#41—21no—
264C22×D8—111no—
265C22×D8—112no—
266#554—118no—
267#554—224no—
268#550—24no—
269#550C2×D1118yescomplemented
270C2×C4⋊Q8—111no—
271C2×#127C2×D1111yescharacteristic
272C2×#127C2×D1112yes—
273C2×#125—112no—
274C2×C22⋊Q8—221no—
275C2×C22⋊Q8—222no—
276C2×#121—21no—
277C2×#121—22no—
278C2×C4×Q8C2×D1111yescharacteristic
279C2×C4×D4—111no—
280C2×C4×D4—112no—
281C2×C4×D4C2×D1112yes—
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×D8—118no—
293C2×#107—111no—
294C2×#106—112no—
295C2×C4⋊C8—112no—
296C2×C4⋊C8—111no—
297C2×#102—112no—
298C2×#102—112no—
299C2×#102—112no—
300C2×#102—111no—
301C2×#102—112no—
302C2×#102—111no—
303C2×#97—112no—
304C2×C4×C8—111no—
305C22×C11—44no—
306C22×C11—42no—
307C22×C11—44no—
308C22×C11—42no—
309C22×C11—44no—
310C22×C11—42no—
311C22×C11—88no—
312C22×C11—84no—
313C22×C11#54812yes—
314C22×C11C2×AGL(1,ℤ/8)12yes—
315C22×C11#57612yes—
316C22×C11C23×D411yescharacteristic
317C2×D11—24no—
318C2×D11—48no—
319C2×D11—42no—
320C2×D11—42no—
321C4×C11—24no—
322C4×C11—22no—
323C4×C11—24no—
324C4×C11—42no—
325C4×C11#54812yes—
326C4×C11C2×AGL(1,ℤ/8)14yes—
327C4×C11C22×#4111yescharacteristic
328C4×C11C2×2−1+411yescharacteristic
329Dic11—42no—
330Dic11—44no—
331C2×#41—28no—
332C2×#41—48no—
333C22×Q8—221no—
334C22×Q8C22⋊D1111yescharacteristic
335C22×D4—22no—
336C22×D4—21no—
337C22×D4—21no—
338C22×D4—22no—
339C22×D4—111no—
340C22×D4C22×D1112yes—
341C22×D4C22×D1111yescharacteristic
342C23×C4—22no—
343C23×C4—21no—
344C23×C4—221no—
345C23×C4—222no—
346C2×D8—114no—
347C2×D8—118no—
348C2×D8—224no—
349C2×D8—228no—
350C22×C8—111no—
351C22×C8—112no—
352C22×C8—111no—
353C4⋊Q8—114no—
354C4⋊Q8—222no—
355#127—24no—
356#127—22no—
357#127C22×D1114yes—
358#127C22×D1118yes—
359#125—118no—
360#125—224no—
361C22⋊Q8—228no—
362C22⋊Q8—2216no—
363#121—28no—
364#121—216no—
365C4×Q8C22⋊D1114yes—
366C4×Q8C22×D1114yes—
367C4×D4—24no—
368C4×D4—22no—
369C4×D4—114no—
370C4×D4—118no—
371C4×D4—224no—
372C4×D4—222no—
373C4×D4C22×D1114yes—
374C4×D4C22×D1118yes—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—228no—
381C2×C4⋊C4C22⋊D1111yescharacteristic
382C2×C4⋊C4C22⋊D1112yes—
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—221no—
387C2×C22⋊C4—222no—
388C2×C42C22×D1112yes—
389C2×C42C22×D1111yescharacteristic
390#107—114no—
391#106—118no—
392C4⋊C8—114no—
393C4⋊C8—118no—
394#102—114no—
395#102—118no—
396#102—118no—
397#102—118no—
398#102—118no—
399#102—114no—
400#97—118no—
401C4×C8—114no—
402C2×C11—84no—
403C2×C11—82no—
404C2×C11#336614yescomplemented
405C2×C11C2×#54811yescharacteristic
406C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
407C2×C11C2×#57611yescharacteristic
408D11—44no—
409C24—22no—
410C24—21no—
411C24—221no—
412#41—432no—
413C2×Q8—24no—
414C2×Q8—224no—
415C2×Q8—882no—
416C2×Q8C2×C22⋊D1114yes—
417C2×D4—22no—
418C2×D4—24no—
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—28no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—28no—
427C2×D4—48no—
428C2×D4—44no—
429C2×D4—84no—
430C2×D4—82no—
431C2×D4—114no—
432C2×D4—112no—
433C2×D4—222no—
434C2×D4—221no—
435C2×D4C23×D1112yes—
436C2×D4C23×D1114yes—
437C22×C4—21no—
438C22×C4—28no—
439C22×C4—24no—
440C22×C4—48no—
441C22×C4—44no—
442C22×C4—221no—
443C22×C4—222no—
444C22×C4—224no—
445C22×C4—228no—
446C22×C4—444no—
447C22×C4—884no—
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1112yes—
450C22×C4C2×C22⋊D1112yes—
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453D8—228no—
454D8—2216no—
455C2×C8—112no—
456C2×C8—112no—
457C2×C8—114no—
458C2×C8—222no—
459C2×C8—224no—
460C2×C8—222no—
461C4⋊C4—21no—
462C4⋊C4—114no—
463C4⋊C4—112no—
464C4⋊C4—221no—
465C4⋊C4—222no—
466C4⋊C4—228no—
467C4⋊C4—224no—
468C4⋊C4—228no—
469C4⋊C4C2×C22⋊D1114yes—
470C4⋊C4C2×C22⋊D1118yes—
471C4⋊C4C23×D1112yes—
472C22⋊C4—24no—
473C22⋊C4—28no—
474C22⋊C4—224no—
475C22⋊C4—228no—
476C42C2×C22⋊D1114yes—
477C42C2×C22⋊D1112yes—
478C42C23×D1112yes—
479C42C23×D1114yes—
480C11C2×#336611yescharacteristic, complemented, Sylow
481C23—24no—
482C23—22no—
483C23—44no—
484C23—42no—
485C23—44no—
486C23—42no—
487C23—42no—
488C23—44no—
489C23—224no—
490C23—222no—
491C23—442no—
492C23—442no—
493C23C22×C22⋊D1111yescharacteristic
494Q8—28no—
495Q8—884no—
496D4—22no—
497D4—24no—
498D4—22no—
499D4—24no—
500D4—416no—
501D4—48no—
502D4—42no—
503D4—44no—
504D4—88no—
505D4—84no—
506D4—114no—
507D4—224no—
508D4—222no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—416no—
514C2×C4—42no—
515C2×C4—48no—
516C2×C4—222no—
517C2×C4—224no—
518C2×C4—442no—
519C2×C4—444no—
520C2×C4—448no—
521C2×C4—888no—
522C2×C4#6698514yes—
523C2×C4#41×D1112yes—
524C2×C4#6704312yes—
525C2×C4C22×C22⋊D1112yes—
526C2×C4C22×C22⋊D1114yes—
527C2×C4C22×C22⋊D1114yes—
528C2×C4C22×C22⋊D1112yes—
529C2×C4C22×C22⋊D1111yescharacteristic
530C2×C4C24×D1111yescharacteristic
531C8—222no—
532C8—224no—
533C8—222no—
534C22—44no—
535C22—42no—
536C22—44no—
537C22—42no—
538C22—42no—
539C22—44no—
540C22—88no—
541C22—84no—
542C22—224no—
543C22—442no—
544C22—448no—
545C22—442no—
546C22C2×#6698512yes—
547C22#1062336212yes—
548C22#1062336612yes—
549C22C23×C22⋊D1111yescharacteristic
550C4—24no—
551C4—24no—
552C4—22no—
553C4—42no—
554C4—442no—
555C4—444no—
556C4C2×#6698514yes—
557C4#1062336212yes—
558C4C2×#41×D1111yescharacteristic
559C4C2×#6704311yescharacteristic
560C2—84no—
561C2—82no—
562C2—444no—
563C2#1308131914yesdirect product factor
564C2C2×#1062336211yescharacteristic
565C2C22×#6698511yescharacteristic
566C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11C2×#3366
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10623110C2semidirect
2. #13081319C2direct (N × H)
3. C2×#10622684C2semidirect
4. C2×#10622683C2semidirect
5. C2×#10622622C2semidirect
6. C2×#10622621C2semidirect
7. C2×#10622685C2semidirect
8. C2×#10622685C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622627C2semidirect
11. C2×C4×#4323C2semidirect
12. C2×C11×#550C2semidirect
15. C11×#550C22semidirect
27. #10623110C22semidirect
39. #10622685C22semidirect
40. #10622685C22semidirect
41. #10622684C22semidirect
42. #10622683C22semidirect
43. #10622637C22semidirect
44. #10622627C22semidirect
45. C4×#4323C22semidirect
46. #10622622C22semidirect
47. #10622621C22semidirect
163. C2×D44#41semidirect
199. C2×#550D11semidirect
256. D44C2×#41semidirect
269. #550C2×D11semidirect
404. C2×C11#3366semidirect
480. C11C2×#3366semidirect
563. C2#13081319direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231102
#130813192
C2×#106226842
C2×#106226832
C2×#106226222
C2×#106226212
C2×#106226852
C2×#106226372
C2×#106226272
C2×C4×#43232
C2×C11×#5502
C2×#336611