Finite Group Databasebeta

← C2×#13079789 #15625808

Subgroups — C2×#13079789 #15625808

Order 2816.

1822 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623155C211yesmaximal, characteristic
2C22×#66943C211yesmaximal, characteristic, complemented
3#13079789C2116yesmaximal, direct product factor
4C2×#10622491C212yesmaximal, complemented
5C2×#10622413C212yesmaximal, complemented
6C2×#10622581C211yesmaximal, characteristic
7C2×#10622656C211yesmaximal, characteristic, complemented
8C2×#10622349C211yesmaximal, characteristic
9C2×#10622409C212yesmaximal, complemented
10C2×#10622504C212yesmaximal, complemented
11C2×#10622331C211yesmaximal, characteristic, complemented
12C2×C11×#484C211yesmaximal, characteristic, complemented
13C2×C11×C22⋊Q8C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#67000C2211yescharacteristic
16C2×Q8×Dic11C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C22×C4⋊Dic11—21no—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4—21no—
21C22×C4×Dic11C2211yescharacteristic
22#10623155—24no—
23#10623155C2218yes—
24C2×#66951—21no—
25C2×#66946C2211yescharacteristic
26C2×#66945—21no—
27C2×#66943—24no—
28C2×#66943—21no—
29C2×#66943—21no—
30C2×#66943C2212yes—
31C2×#66943C2212yes—
32C2×#66943C2211yescharacteristic
33C2×#66943C2218yescomplemented
34C2×#66939—21no—
35C2×(C22⋊D11)⋊C4—21no—
36C11×#484C2218yescomplemented
37C2×C11×#107C2212yes—
38C2×C11×#103C2212yes—
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×#66899C2212yes—
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×#66885C2212yes—
43C2×#66882C2212yes—
44C2×Dic11⋊C8C2212yes—
45C2×C8×Dic11C2212yes—
46#10622656C2218yescomplemented
47#10622581C2218yes—
48C2×#66873C2212yes—
49C2×#66872C2212yes—
50C2×#66872C2212yes—
51#10622504C22116yescomplemented
52#10622491C22116yescomplemented
53#10622413C22116yescomplemented
54#10622409C22116yescomplemented
55#10622349C2218yes—
56#10622331C2218yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C23×Dic11D411yescharacteristic
63C23×Dic11D411yescharacteristic
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×C8×C11C2312yes—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8C2314yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2314yes—
75C2×C11×C22⋊C4—21no—
76#67000—22no—
77#67000C2314yes—
78Q8×Dic11—22no—
79Q8×Dic11C2314yes—
80#66983—22no—
81#66983C2314yes—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—28no—
93C2×C4⋊Dic11C2312yes—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2314yes—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—28no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11D411yescharacteristic
102C2×C4×Dic11D411yescharacteristic
103C2×C4×Dic11D414yes—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2314yes—
107C22×C11⋊C8C2312yes—
108#66951—28no—
109#66946—22no—
110#66946C2314yes—
111#66945—28no—
112#66943—24no—
113#66943—24no—
114#66943—28no—
115#66943—28no—
116#66943—22no—
117#66943C2314yes—
118#66943C2318yes—
119#66943C2318yes—
120#66939—28no—
121(C22⋊D11)⋊C4—28no—
122C11×#107C2318yes—
123C11×#103C2318yes—
124C11×C22⋊C8C2314yes—
125#66899C2318yes—
126C22⋊(C11⋊C8)C2314yes—
127#66885C2318yes—
128#66882C2318yes—
129Dic11⋊C8C2318yes—
130C8×Dic11C2318yes—
131#66873C2318yes—
132#66872C2318yes—
133#66872C2318yes—
134C2×#3232—111nomaximal, Sylow
135C24×C11C2×D411yescharacteristic
136C23×D11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—24no—
139C2×Q8×C11C2412yes—
140C22×C4×C11—24no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—44no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—24no—
151C2×C22⋊D11—44no—
152C22×Dic11—24no—
153C22×Dic11—21no—
154C22×Dic11—24no—
155C22×Dic11—22no—
156C22×Dic11—42no—
157C22×Dic11—44no—
158C22×Dic11C2×D414yes—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D414yes—
164C2×D44—21no—
165C2×D44—24no—
166C2×D44C2412yes—
167C2×C4×D11—24no—
168C2×C4×D11—44no—
169C2×C8×C11—24no—
170C2×C8×C11C2414yes—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4C2412yes—
176C11×C4⋊C4C2414yes—
177C11×C22⋊C4—24no—
178(C2×D11)⋊C4—24no—
179(C2×D11)⋊C4—24no—
180(C2×D11)⋊C4—24no—
181(C2×D11)⋊C4—24no—
182C4⋊Dic11—24no—
183C4⋊Dic11—24no—
184C4⋊Dic11—28no—
185C4⋊Dic11—28no—
186C4⋊Dic11—24no—
187C4⋊Dic11—22no—
188C4⋊Dic11—21no—
189C4⋊Dic11C2412yes—
190C4⋊Dic11C2414yes—
191Dic11⋊C4—24no—
192Dic11⋊C4—28no—
193Dic11⋊C4—28no—
194C4×Dic11—24no—
195C4×Dic11C2×D412yes—
196C4×Dic11C2×D414yes—
197C4×Dic11C2×D412yes—
198C4×Dic11C2×D414yes—
199C4×Dic11C2412yes—
200C4×Dic11C2412yes—
201C2×C11⋊C8—24no—
202C2×C11⋊C8C2414yes—
203C2×#529—111no—
204C22×#125—111no—
205#3232—1116no—
206C2×#499—112no—
207C2×#488—112no—
208C2×#484D1111yescharacteristic, complemented
209C2×#481—111no—
210C2×#483—111no—
211C2×#480—111no—
212C2×#479—112no—
213C2×#478—112no—
214C2×#431—111no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11#13514yes—
218C23×C11C22×D412yes—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224Q8×C11—24no—
225Q8×C11—42no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—48no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—44no—
236C2×C4×C11C22×D412yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C112−1+414yes—
239C2×C4×C11C2511yescharacteristic
240C22⋊D11—48no—
241C2×Dic11—28no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—44no—
249C2×Dic11—48no—
250C2×Dic11—44no—
251C2×Dic11—42no—
252C2×Dic11C22×D412yes—
253C2×Dic11C22×D412yes—
254C2×Dic11C22×D412yes—
255C2×Dic11C22×D412yes—
256D44—24no—
257D44—42no—
258C4×D11—48no—
259C8×C11—24no—
260C11⋊C8—24no—
261#529—118no—
262#529—224no—
263C2×#126—221no—
264C2×#125—112no—
265C2×#125—112no—
266C2×#125—111no—
267C2×#125—118no—
268C2×#125—221no—
269C2×#125—221no—
270C2×#125—224no—
271C2×#124—111no—
272C2×#123—221no—
273C2×C22⋊Q8C2×D1111yescharacteristic
274C2×#121—111no—
275C2×C4×Q8—111no—
276C2×C4×D4—111no—
277C2×C4×D4—221no—
278C2×#117—221no—
279C22×C4⋊C4—111no—
280C22×C4⋊C4—221no—
281C22×C4⋊C4—221no—
282C22×C4⋊C4C2×D1111yescharacteristic
283C22×C42—111no—
284#499—1116no—
285#488—1116no—
286#484C2×D1118yescomplemented
287#483—118no—
288#481—118no—
289#480—118no—
290#479—1116no—
291#478—1116no—
292#431—118no—
293C2×#107—112no—
294C2×#107C2×D1112yes—
295C2×#106—112no—
296C2×#106—112no—
297C2×C4⋊C8—112no—
298C2×#103—112no—
299C2×#103C2×D1112yes—
300C2×#102—112no—
301C2×#102—112no—
302C2×C22⋊C8—111no—
303C2×C22⋊C8C2×D1111yescharacteristic
304C2×C4×C8—112no—
305C22×C11—22no—
306C22×C11—28no—
307C22×C11—22no—
308C22×C11#53612yes—
309C22×C11C2×#13514yes—
310C22×C11C2×#13512yes—
311C22×C11#57512yes—
312C22×C11C23×D411yescharacteristic
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—84no—
317C4×C11—22no—
318C4×C11—42no—
319C4×C11—44no—
320C4×C11—42no—
321C4×C11#53612yes—
322C4×C11C2×2−1+412yes—
323Dic11—22no—
324Dic11—22no—
325Dic11—22no—
326Dic11—22no—
327Dic11—44no—
328Dic11—42no—
329C22×Q8C22×D1111yescharacteristic
330C22×D4—111no—
331C22×D4—221no—
332C23×C4—21no—
333C23×C4—111no—
334C23×C4—111no—
335C23×C4—221no—
336C23×C4—221no—
337C23×C4C22×D1111yescharacteristic
338C22×C8—112no—
339C22×C8C22×D1112yes—
340#126—228no—
341#125—118no—
342#125—118no—
343#125—114no—
344#125—228no—
345#125—224no—
346#125—224no—
347#125—228no—
348#125—222no—
349#124—114no—
350#124—222no—
351#123—228no—
352C22⋊Q8—22no—
353C22⋊Q8C22×D1114yes—
354#121—114no—
355#121—222no—
356C4×Q8—114no—
357C4×Q8—222no—
358C4×D4—114no—
359C4×D4—222no—
360C4×D4—228no—
361#117—228no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—228no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—228no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4C22×D1112yes—
380C2×C4⋊C4C22×D1114yes—
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C22⋊C4—221no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—114no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—114no—
393C2×C42—221no—
394#107—118no—
395#107C22×D1118yes—
396#106—118no—
397#106—118no—
398C4⋊C8—118no—
399#103—118no—
400#103C22×D1118yes—
401#102—118no—
402#102—118no—
403C22⋊C8—114no—
404C22⋊C8C22×D1114yes—
405C4×C8—118no—
406C2×C11—24no—
407C2×C11#323214yescomplemented
408C2×C11C2×#53611yescharacteristic
409C2×C11C22×#13511yescharacteristic
410C2×C11C2×#57511yescharacteristic
411D11—82no—
412C24—221no—
413C24D4×D1111yescharacteristic
414C2×Q8—21no—
415C2×Q8—24no—
416C2×Q8C23×D1112yes—
417C2×D4—112no—
418C2×D4—224no—
419C2×D4—221no—
420C2×D4—224no—
421C2×D4—444no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—44no—
428C22×C4—114no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—114no—
434C22×C4—224no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—221no—
438C22×C4—222no—
439C22×C4—444no—
440C22×C4—442no—
441C22×C4—444no—
442C22×C4D4×D1112yes—
443C22×C4D4×D1111yescharacteristic
444C22×C4C23×D1112yes—
445C22×C4C23×D1111yescharacteristic
446C2×C8—24no—
447C2×C8—114no—
448C2×C8—224no—
449C2×C8C23×D1114yes—
450C4⋊C4—24no—
451C4⋊C4—22no—
452C4⋊C4—24no—
453C4⋊C4—21no—
454C4⋊C4—114no—
455C4⋊C4—112no—
456C4⋊C4—228no—
457C4⋊C4—228no—
458C4⋊C4—228no—
459C4⋊C4—228no—
460C4⋊C4—224no—
461C4⋊C4—224no—
462C4⋊C4—224no—
463C4⋊C4—224no—
464C4⋊C4—222no—
465C4⋊C4—221no—
466C4⋊C4C23×D1114yes—
467C4⋊C4C23×D1112yes—
468C22⋊C4—24no—
469C22⋊C4—224no—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C22⋊C4—224no—
473C42—114no—
474C42—112no—
475C42—112no—
476C42—114no—
477C42—112no—
478C42—112no—
479C42—224no—
480C11C2×#323211yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—222no—
484C23—442no—
485C23—442no—
486C23—442no—
487C23#6697214yes—
488C23C2×D4×D1112yes—
489C23C2×D4×D1111yescharacteristic
490Q8—24no—
491Q8—42no—
492D4—224no—
493D4—448no—
494D4—442no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—48no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—112no—
506C2×C4—112no—
507C2×C4—112no—
508C2×C4—112no—
509C2×C4—228no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—224no—
516C2×C4—448no—
517C2×C4—444no—
518C2×C4—448no—
519C2×C4—444no—
520C2×C4—442no—
521C2×C4C2×D4×D1112yes—
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4#6704314yes—
524C2×C4C24×D1111yescharacteristic
525C8—24no—
526C8—224no—
527C22—22no—
528C22—22no—
529C22—28no—
530C22—442no—
531C22—442no—
532C22—442no—
533C22—884no—
534C22#1062317912yes—
535C22C2×#6697214yes—
536C22C2×#6697212yes—
537C22#1062330412yes—
538C22C22×D4×D1111yescharacteristic
539C4—22no—
540C4—42no—
541C4—44no—
542C4—42no—
543C4—222no—
544C4—222no—
545C4—222no—
546C4—222no—
547C4—444no—
548C4—442no—
549C4#1062317912yes—
550C4C2×#6704312yes—
551C2—24no—
552C2—882no—
553C2#1307978914yesdirect product factor
554C2C2×#1062317911yescharacteristic
555C2C22×#6697211yescharacteristic
556C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#484C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#484D11
hypocenterC11C2×#3232
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
2. C22×#66943C2semidirect
3. #13079789C2direct (N × H)
4. C2×#10622491C2semidirect
5. C2×#10622413C2semidirect
7. C2×#10622656C2semidirect
9. C2×#10622409C2semidirect
10. C2×#10622504C2semidirect
11. C2×#10622331C2semidirect
12. C2×C11×#484C2semidirect
33. C2×#66943C22semidirect
36. C11×#484C22semidirect
46. #10622656C22semidirect
51. #10622504C22semidirect
52. #10622491C22semidirect
53. #10622413C22semidirect
54. #10622409C22semidirect
56. #10622331C22semidirect
208. C2×#484D11semidirect
286. #484C2×D11semidirect
407. C2×C11#3232semidirect
480. C11C2×#3232semidirect
553. C2#13079789direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231552
C22×#669432
#130797892
C2×#106224912
C2×#106224132
C2×#106225812
C2×#106226562
C2×#106223492
C2×#106224092
C2×#106225042
C2×#106223312
C2×C11×#4842
C2×#323211