Finite Group Databasebeta

← C2×#13081213 #15632491

Subgroups — C2×#13081213 #15632491

Order 2816.

2146 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic, complemented
2C2×#10623082C211yesmaximal, characteristic, complemented
3#13081213C2116yesmaximal, direct product factor
4C2×#10622293C211yesmaximal, characteristic, complemented
5C2×#10622390C212yesmaximal, complemented
6C2×#10622392C212yesmaximal, complemented
7C2×#10622621C211yesmaximal, characteristic, complemented
8C2×#10622620C211yesmaximal, characteristic, complemented
9C2×#10622772C212yesmaximal, complemented
10C2×#10622301C211yesmaximal, characteristic, complemented
11C2×#10622494C212yesmaximal, complemented
12C2×C4×C11×D8C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C22×C11×D8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66991C2212yes—
18C2×#66991C2212yes—
19C2×#66983—21no—
20C2×#66979—21no—
21C2×#66977—21no—
22C22×#4313C2212yes—
23#10623094—24no—
24#10623094C2218yescomplemented
25#10623082—24no—
26#10623082C2218yescomplemented
27C2×#66945C2212yes—
28C2×C4⋊C4×D11C2212yes—
29C2×#66938—22no—
30C2×#66936—22no—
31C2×C4×D44C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C4×C11×D8C2218yescomplemented
35C2×C11×#107C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66896C2212yes—
40C2×#66896C2212yes—
41#10622772C22116yescomplemented
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66881C2212yes—
44C2×#66881C2212yes—
45#10622621C2218yescomplemented
46#10622620C2218yescomplemented
47C2×#66872C2212yes—
48C2×#66871C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622494C22116yescomplemented
51#10622392C22116yescomplemented
52#10622390C22116yescomplemented
53#10622301C2218yescomplemented
54#10622293C2218yescomplemented
55C22×D4×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C22×C22⋊D11—22no—
60C22×C22⋊D11—22no—
61C2×#4339—28no—
62C2×#4339—48no—
63C22×D44D411yescharacteristic
64C22×C4×D11—22no—
65C22×C4×D11C2312yes—
66C22×Dic22—21no—
67C22×Dic22—21no—
68C2×C11×D8—24no—
69C2×C11×D8C2314yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11C2314yes—
75C4×D4×C11C2314yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83#66991—24no—
84#66991—24no—
85#66991C2318yes—
86#66991C2318yes—
87#66983—28no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4D412yes—
90#66979—28no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11D411yescharacteristic
94C2×C4⋊Dic11C2312yes—
95C2×C4⋊Dic11C2312yes—
96#66977—28no—
97C2×Dic11⋊C4—22no—
98C2×C4×Dic11—22no—
99C22×C11⋊C8C2312yes—
100C2×#4313—28no—
101C2×#4313C2318yes—
102#66945—24no—
103#66945C2318yes—
104C4⋊C4×D11—24no—
105C4⋊C4×D11C2318yes—
106#66938—216no—
107#66936—216no—
108C4×D44D414yes—
109C4×D44C2314yes—
110#66922—22no—
111#66922—22no—
112#66922C2314yes—
113#66922C2314yes—
114C11×#107C2314yes—
115C11×#102C2314yes—
116C11×#102C2314yes—
117C4×C8×C11C2314yes—
118#66896C2318yes—
119#66896C2318yes—
120(C2×D11)⋊C8C2318yes—
121#66881C2318yes—
122#66881C2318yes—
123#66872C2318yes—
124#66871C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126C2×#3354—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11—21no—
129C23×D11C2×D412yes—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
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—22no—
152C22×Dic11—22no—
153C22×Dic11C2×D412yes—
154#4339—432no—
155C2×D44—24no—
156C2×D44C2×D414yes—
157C2×C4×D11—28no—
158C2×C4×D11—24no—
159C2×C4×D11—24no—
160C2×C4×D11—48no—
161C2×C4×D11C2×D414yes—
162C2×C4×D11C2414yes—
163C2×Dic22—24no—
164C2×Dic22—24no—
165C2×Dic22—44no—
166C2×Dic22—82no—
167C11×D8—28no—
168C2×C8×C11—22no—
169C2×C8×C11#4114yescomplemented
170C2×C8×C11C2412yes—
171C2×C8×C11C2412yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4C2412yes—
175C11×C4⋊C4C2412yes—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—24no—
178C42×C11C2×D412yes—
179C42×C11C2412yes—
180C22⋊Dic11—28no—
181C22⋊Dic11—28no—
182(C2×D11)⋊C4—28no—
183(C2×D11)⋊C4C2×D418yes—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11—24no—
187C4⋊Dic11—24no—
188C4⋊Dic11C2×D414yes—
189C4⋊Dic11C2414yes—
190C4⋊Dic11C2414yes—
191Dic11⋊C4—28no—
192C4×Dic11—28no—
193C2×C11⋊C8—24no—
194C2×C11⋊C8C2414yes—
195#4313—216no—
196C2×#555—111no—
197C2×#547—111no—
198#3354—1116no—
199C2×#498—111no—
200C2×#481—112no—
201C2×#482—112no—
202C2×#476—111no—
203C2×#474—111no—
204C2×#469—112no—
205C2×C4×D8D1111yescharacteristic, complemented
206C2×#436—111no—
207C2×#428—112no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11C22×D411yescharacteristic
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11C22×D414yes—
221D4×C11—22no—
222D4×C11—22no—
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—42no—
226D4×C11—42no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—48no—
233C2×C4×C11—48no—
234C2×C4×C11AGL(1,ℤ/8)14yes—
235C2×C4×C11C22×D412yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D412yes—
238C2×C4×C11C2×#4112yes—
239C2×C4×C112−1+412yes—
240C2×C4×C11C2511yescharacteristic
241C22⋊D11—416no—
242C22⋊D11—88no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—44no—
247C2×Dic11—44no—
248C2×Dic11C22×D414yes—
249D44—28no—
250C4×D11—28no—
251C4×D11—24no—
252C4×D11—24no—
253C4×D11—416no—
254Dic22—48no—
255Dic22—84no—
256C8×C11—22no—
257C8×C11C2×#4114yescomplemented
258C11⋊C8—24no—
259C22×#41—221no—
260C22×D8C2×D1111yescharacteristic
261C22×M16—112no—
262#555—118no—
263#555—224no—
264#547—118no—
265#547—224no—
266C2×C4⋊Q8—111no—
267C2×C4⋊Q8—111no—
268C2×#124—222no—
269C2×#123—222no—
270C2×C22⋊Q8—221no—
271C2×#121—112no—
272C2×#121—112no—
273C2×#121—221no—
274C2×C4×D4—111no—
275C2×C4×D4C2×D1111yescharacteristic
276C2×C4×D4C2×D1111yescharacteristic
277C2×#117—112no—
278C2×#117—221no—
279C22×C4⋊C4—112no—
280#498—118no—
281#482—1116no—
282#481—1116no—
283#476—118no—
284#474—118no—
285#469—1116no—
286C4×D8C2×D1118yescomplemented
287#436—118no—
288#428—1116no—
289C2×#107—112no—
290C2×#107C2×D1111yescharacteristic
291C2×#106—112no—
292C2×#106—112no—
293C2×#106—112no—
294C2×C4⋊C8—111no—
295C2×#102—112no—
296C2×#102—112no—
297C2×#102C2×D1111yescharacteristic
298C2×#102C2×D1111yescharacteristic
299C2×C22⋊C8—112no—
300C2×C4×C8C2×D1111yescharacteristic
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—84no—
308C22×C11—84no—
309C22×C11#54712yes—
310C22×C11C2×AGL(1,ℤ/8)12yes—
311C22×C11#57712yes—
312C22×C11C23×D411yescharacteristic
313C2×D11—24no—
314C2×D11—24no—
315C2×D11—24no—
316C2×D11—48no—
317C4×C11—22no—
318C4×C11—42no—
319C4×C11—42no—
320C4×C11#54712yes—
321C4×C11C2×AGL(1,ℤ/8)14yes—
322C4×C11C22×#4111yescharacteristic
323C4×C11C2×2−1+411yescharacteristic
324Dic11—24no—
325Dic11—44no—
326Dic11—44no—
327C2×#41—228no—
328C2×#41—448no—
329C22×Q8—221no—
330C22×Q8—221no—
331C22×D4—111no—
332C22×D4—222no—
333C22×D4—222no—
334C22×D4C22×D1111yescharacteristic
335C22×D4C22×D1111yescharacteristic
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—112no—
339C23×C4—222no—
340C2×D8—24no—
341C2×D8C22×D1114yes—
342C2×M16—118no—
343C2×M16—228no—
344C22×C8—112no—
345C22×C8C22×D1111yescharacteristic
346C22×C8C22×D1111yescharacteristic
347C4⋊Q8—114no—
348C4⋊Q8—114no—
349C4⋊Q8—222no—
350C4⋊Q8—222no—
351#124—2216no—
352#123—2216no—
353C22⋊Q8—228no—
354#121—118no—
355#121—118no—
356#121—228no—
357#121—224no—
358#121—224no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—114no—
362C4×D4—114no—
363C4×D4C22×D1114yes—
364C4×D4C22×D1114yes—
365#117—118no—
366#117—224no—
367#117—228no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—118no—
372C2×C4⋊C4—224no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—112no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C42—222no—
385C2×C42C22×D1111yescharacteristic
386#107—118no—
387#107C22×D1114yes—
388#106—118no—
389#106—118no—
390#106—118no—
391C4⋊C8—114no—
392#102—118no—
393#102—118no—
394#102C22×D1114yes—
395#102C22×D1114yes—
396C22⋊C8—118no—
397C4×C8C22×D1114yes—
398C2×C11—82no—
399C2×C11—82no—
400C2×C11#335414yescomplemented
401C2×C11C2×#54711yescharacteristic
402C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
403C2×C11C2×#57711yescharacteristic
404D11—44no—
405C24—21no—
406C24—21no—
407C24—112no—
408#41—4432no—
409C2×Q8—224no—
410C2×Q8—224no—
411C2×Q8—444no—
412C2×Q8—882no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—114no—
420C2×D4—228no—
421C2×D4—228no—
422C2×D4—224no—
423C2×D4—448no—
424C2×D4—884no—
425C2×D4C23×D1112yes—
426C2×D4C23×D1112yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—228no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—448no—
442C22×C4D4×D1111yescharacteristic
443C22×C4D4×D1111yescharacteristic
444C22×C4C23×D1111yescharacteristic
445D8—28no—
446M16—2216no—
447C2×C8—22no—
448C2×C8—114no—
449C2×C8—224no—
450C2×C8#433914yescomplemented
451C2×C8C23×D1112yes—
452C2×C8C23×D1112yes—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—114no—
456C4⋊C4—114no—
457C4⋊C4—114no—
458C4⋊C4—228no—
459C4⋊C4—222no—
460C4⋊C4—222no—
461C4⋊C4—224no—
462C4⋊C4—224no—
463C4⋊C4C23×D1112yes—
464C4⋊C4C23×D1112yes—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—118no—
468C22⋊C4—228no—
469C22⋊C4—228no—
470C22⋊C4—228no—
471C42—228no—
472C42D4×D1112yes—
473C42C23×D1112yes—
474C11C2×#335411yescharacteristic, complemented, Sylow
475C23—22no—
476C23—22no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—114no—
484C23—224no—
485C23—224no—
486C23—224no—
487C23C2×D4×D1111yescharacteristic
488Q8—448no—
489Q8—884no—
490D4—22no—
491D4—22no—
492D4—22no—
493D4—22no—
494D4—42no—
495D4—42no—
496D4—228no—
497D4—4416no—
498D4—888no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—48no—
505C2×C4—48no—
506C2×C4—114no—
507C2×C4—224no—
508C2×C4—228no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—4416no—
514C2×C4—444no—
515C2×C4—444no—
516C2×C4#6696414yes—
517C2×C4C2×#433912yes—
518C2×C4C2×D4×D1112yes—
519C2×C4C2×D4×D1112yes—
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4#6704312yes—
522C2×C4C24×D1111yescharacteristic
523C8—22no—
524C8—224no—
525C8C2×#433914yescomplemented
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—84no—
533C22—84no—
534C22—224no—
535C22—224no—
536C22—224no—
537C22—448no—
538C22#1062308212yes—
539C22C2×#6696412yes—
540C22#1062330112yes—
541C22C22×D4×D1111yescharacteristic
542C4—22no—
543C4—42no—
544C4—42no—
545C4—224no—
546C4—444no—
547C4—444no—
548C4#1062308212yes—
549C4C2×#6696414yes—
550C4C22×#433911yescharacteristic
551C4C2×#6704311yescharacteristic
552C2—82no—
553C2—82no—
554C2—444no—
555C2#1308121314yesdirect product factor
556C2C2×#1062308211yescharacteristic
557C2C22×#6696411yescharacteristic
558C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
hypercenterC2×C4×D8D11
hypocenterC11C2×#3354
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×#10623094C2semidirect
2. C2×#10623082C2semidirect
3. #13081213C2direct (N × H)
4. C2×#10622293C2semidirect
5. C2×#10622390C2semidirect
6. C2×#10622392C2semidirect
7. C2×#10622621C2semidirect
8. C2×#10622620C2semidirect
9. C2×#10622772C2semidirect
10. C2×#10622301C2semidirect
11. C2×#10622494C2semidirect
12. C2×C4×C11×D8C2semidirect
24. #10623094C22semidirect
26. #10623082C22semidirect
34. C4×C11×D8C22semidirect
41. #10622772C22semidirect
45. #10622621C22semidirect
46. #10622620C22semidirect
50. #10622494C22semidirect
51. #10622392C22semidirect
52. #10622390C22semidirect
53. #10622301C22semidirect
54. #10622293C22semidirect
169. C2×C8×C11#41semidirect
205. C2×C4×D8D11semidirect
257. C8×C11C2×#41semidirect
286. C4×D8C2×D11semidirect
400. C2×C11#3354semidirect
450. C2×C8#4339semidirect
474. C11C2×#3354semidirect
525. C8C2×#4339semidirect
555. C2#13081213direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230942
C2×#106230822
#130812132
C2×#106222932
C2×#106223902
C2×#106223922
C2×#106226212
C2×#106226202
C2×#106227722
C2×#106223012
C2×#106224942
C2×C4×C11×D82
C2×#335411