Finite Group Databasebeta

← C2×#13079780 #15625799

Subgroups — C2×#13079780 #15625799

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
1C22×#66923C211yesmaximal, characteristic, complemented
2#13079780C2116yesmaximal, direct product factor
3C2×#10622677C212yesmaximal, complemented
4C2×#10622669C212yesmaximal, complemented
5C2×#10622657C211yesmaximal, characteristic, complemented
6C2×#10622647C211yesmaximal, characteristic
7C2×#10622656C211yesmaximal, characteristic, complemented
8C2×#10622646C211yesmaximal, characteristic
9C2×#10622635C212yesmaximal, complemented
10C2×#10622622C212yesmaximal, complemented
11C2×#10622538C211yesmaximal, characteristic, complemented
12C2×C11×#529C211yesmaximal, characteristic
13C11×#529—24no—
14C11×#529C2218yes—
15C2×C11×#126—21no—
16C2×C11×#125C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117—21no—
25C22×C42×C11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4—21no—
29C22×Dic11⋊C4—21no—
30C2×#66923—24no—
31C2×#66923—21no—
32C2×#66923—21no—
33C2×#66923C2212yes—
34C2×#66923C2212yes—
35C2×#66923C2218yescomplemented
36C2×#66899C2212yes—
37C2×#66899C2212yes—
38C2×#66896C2212yes—
39C2×#66896C2212yes—
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622677C22116yescomplemented
43#10622669C22116yescomplemented
44#10622657C2218yescomplemented
45#10622656C2218yescomplemented
46#10622647C2218yes—
47#10622646C2218yes—
48#10622635C22116yescomplemented
49#10622622C22116yescomplemented
50C2×#66872C2212yes—
51C2×#66872C2212yes—
52C2×#66871C2212yes—
53C2×#66871C2212yes—
54#10622538C2218yescomplemented
55C2×C4⋊(C11⋊C8)C2212yes—
56C2×C4×C11⋊C8C2212yes—
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C23×Dic11—21no—
66C11×#126—28no—
67C11×#125—22no—
68C11×#125C2314yes—
69C11×#124—22no—
70C11×#124C2314yes—
71C11×#123—28no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8C2314yes—
74C11×#121—22no—
75C11×#121C2314yes—
76C4×Q8×C11—22no—
77C4×Q8×C11C2314yes—
78C4×D4×C11—28no—
79C4×D4×C11—22no—
80C4×D4×C11C2314yes—
81C11×#117—28no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C42×C11—21no—
94C2×C42×C11D411yescharacteristic
95C2×C42×C11D411yescharacteristic
96C2×C42×C11D414yes—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2314yes—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11C2312yes—
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2314yes—
107C2×C4⋊Dic11C2314yes—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—28no—
113C2×Dic11⋊C4—28no—
114C22×C11⋊C8C2312yes—
115C22×C11⋊C8C2312yes—
116#66923—24no—
117#66923—24no—
118#66923—28no—
119#66923—28no—
120#66923C2318yes—
121#66923C2318yes—
122#66899C2318yes—
123#66899C2318yes—
124#66896C2318yes—
125#66896C2318yes—
126C22⋊(C11⋊C8)C2314yes—
127C22⋊(C11⋊C8)C2314yes—
128#66872C2318yes—
129#66872C2318yes—
130#66871C2318yes—
131#66871C2318yes—
132C4⋊(C11⋊C8)C2318yes—
133C4×C11⋊C8C2318yes—
134C2×#3232—111nomaximal, Sylow
135C24×C11—21no—
136C24×C11C2×D411yescharacteristic
137C2×Q8×C11—21no—
138C2×Q8×C11—24no—
139C2×Q8×C11C2412yes—
140C2×D4×C11—24no—
141C2×D4×C11—21no—
142C2×D4×C11—24no—
143C2×D4×C11—44no—
144C2×D4×C11C2412yes—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—24no—
151C22×C4×C11—42no—
152C22×C4×C11—44no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—44no—
168C22×Dic11—44no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C2412yes—
176C11×C4⋊C4C2412yes—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C42×C11—24no—
183C42×C11C2×D414yes—
184C42×C11C2×D412yes—
185C42×C11C2×D412yes—
186C42×C11C2×D414yes—
187C42×C11C2412yes—
188C42×C11C2412yes—
189C4⋊Dic11—24no—
190C4⋊Dic11—24no—
191C4⋊Dic11—22no—
192C4⋊Dic11—22no—
193C4⋊Dic11C2414yes—
194C4⋊Dic11C2414yes—
195Dic11⋊C4—28no—
196Dic11⋊C4—28no—
197Dic11⋊C4—28no—
198Dic11⋊C4—28no—
199C2×C11⋊C8—24no—
200C2×C11⋊C8—24no—
201C2×C11⋊C8C2414yes—
202C2×C11⋊C8C2414yes—
203C2×#529D1111yescharacteristic
204C22×#125—111no—
205#3232—1116no—
206C2×#499—112no—
207C2×#488—112no—
208C2×#484—111no—
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—22no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11#13514yes—
222C23×C11C22×D412yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—24no—
225Q8×C11—42no—
226D4×C11—24no—
227D4×C11—48no—
228D4×C11—42no—
229C2×C4×C11—22no—
230C2×C4×C11—28no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—44no—
241C2×C4×C11—48no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11C22×D412yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D412yes—
248C2×C4×C11C22×D412yes—
249C2×C4×C11C22×D412yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C112−1+414yes—
252C2×C4×C11C2511yescharacteristic
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—48no—
256C2×Dic11—48no—
257C2×Dic11—44no—
258C2×Dic11—44no—
259C11⋊C8—24no—
260C11⋊C8—24no—
261#529—24no—
262#529C2×D1118yes—
263C2×#126—21no—
264C2×#125—112no—
265C2×#125—112no—
266C2×#125—118no—
267C2×#125—221no—
268C2×#125—221no—
269C2×#125—224no—
270C2×#125C2×D1111yescharacteristic
271C2×#124C2×D1111yescharacteristic
272C2×#123—21no—
273C2×C22⋊Q8C2×D1111yescharacteristic
274C2×#121C2×D1111yescharacteristic
275C2×C4×Q8C2×D1111yescharacteristic
276C2×C4×D4—21no—
277C2×C4×D4C2×D1111yescharacteristic
278C2×#117—21no—
279C22×C4⋊C4—111no—
280C22×C4⋊C4—111no—
281C22×C4⋊C4—221no—
282C22×C4⋊C4—221no—
283C22×C42C2×D1111yescharacteristic
284#499—1116no—
285#488—1116no—
286#484—118no—
287#483—118no—
288#481—118no—
289#480—118no—
290#479—1116no—
291#478—1116no—
292#431—118no—
293C2×#107—112no—
294C2×#107—112no—
295C2×#106—112no—
296C2×#106—112no—
297C2×C4⋊C8—112no—
298C2×#103—112no—
299C2×#103—112no—
300C2×#102—112no—
301C2×#102—112no—
302C2×C22⋊C8—111no—
303C2×C22⋊C8—111no—
304C2×C4×C8—112no—
305C22×C11—22no—
306C22×C11—28no—
307C22×C11—22no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—84no—
312C22×C11#53612yes—
313C22×C11C2×#13514yes—
314C22×C11C2×#13512yes—
315C22×C11#57512yes—
316C22×C11C23×D411yescharacteristic
317C4×C11—22no—
318C4×C11—22no—
319C4×C11—22no—
320C4×C11—22no—
321C4×C11—22no—
322C4×C11—42no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11#53612yes—
326C4×C11C2×2−1+412yes—
327Dic11—44no—
328Dic11—44no—
329C22×Q8C22×D1111yescharacteristic
330C22×D4—21no—
331C22×D4C22×D1111yescharacteristic
332C23×C4—21no—
333C23×C4—221no—
334C23×C4—221no—
335C23×C4C22⋊D1111yescharacteristic
336C23×C4C22⋊D1111yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C22×C8—112no—
339C22×C8—112no—
340#126—28no—
341#125—22no—
342#125—118no—
343#125—118no—
344#125—228no—
345#125—224no—
346#125—224no—
347#125—228no—
348#125C22×D1114yes—
349#124—22no—
350#124C22×D1114yes—
351#123—28no—
352C22⋊Q8—22no—
353C22⋊Q8C22×D1114yes—
354#121—22no—
355#121C22×D1114yes—
356C4×Q8—22no—
357C4×Q8C22×D1114yes—
358C4×D4—28no—
359C4×D4—22no—
360C4×D4C22×D1114yes—
361#117—28no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—228no—
375C2×C4⋊C4—228no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C42—21no—
388C2×C42C22⋊D1111yescharacteristic
389C2×C42C22⋊D1111yescharacteristic
390C2×C42C22⋊D1114yes—
391C2×C42C22×D1111yescharacteristic
392C2×C42C22×D1111yescharacteristic
393C2×C42C22×D1114yes—
394#107—118no—
395#107—118no—
396#106—118no—
397#106—118no—
398C4⋊C8—118no—
399#103—118no—
400#103—118no—
401#102—118no—
402#102—118no—
403C22⋊C8—114no—
404C22⋊C8—114no—
405C4×C8—118no—
406C2×C11—24no—
407C2×C11—82no—
408C2×C11#323214yescomplemented
409C2×C11C2×#53611yescharacteristic
410C2×C11C22×#13511yescharacteristic
411C2×C11C2×#57511yescharacteristic
412C24—21no—
413C24C2×C22⋊D1111yescharacteristic
414C2×Q8—21no—
415C2×Q8—24no—
416C2×Q8C23×D1112yes—
417C2×D4—24no—
418C2×D4—24no—
419C2×D4—21no—
420C2×D4—44no—
421C2×D4C23×D1112yes—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—24no—
428C22×C4—42no—
429C22×C4—44no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—444no—
435C22×C4—444no—
436C22×C4C2×C22⋊D1114yes—
437C22×C4C2×C22⋊D1112yes—
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C2×C22⋊D1114yes—
444C22×C4C23×D1112yes—
445C22×C4C23×D1111yescharacteristic
446C2×C8—114no—
447C2×C8—114no—
448C2×C8—224no—
449C2×C8—224no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—114no—
457C4⋊C4—114no—
458C4⋊C4—224no—
459C4⋊C4—224no—
460C4⋊C4—222no—
461C4⋊C4—222no—
462C4⋊C4—228no—
463C4⋊C4—228no—
464C4⋊C4—228no—
465C4⋊C4—228no—
466C4⋊C4C23×D1112yes—
467C4⋊C4C23×D1112yes—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C42—24no—
474C42C2×C22⋊D1114yes—
475C42C2×C22⋊D1112yes—
476C42C2×C22⋊D1112yes—
477C42C2×C22⋊D1114yes—
478C42C23×D1112yes—
479C42C23×D1112yes—
480C11C2×#323211yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—22no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23#6700314yes—
488C23C22×C22⋊D1112yes—
489C23C22×C22⋊D1111yescharacteristic
490Q8—24no—
491Q8—42no—
492D4—24no—
493D4—48no—
494D4—42no—
495C2×C4—28no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—44no—
507C2×C4—48no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—448no—
514C2×C4—448no—
515C2×C4—444no—
516C2×C4—444no—
517C2×C4#6704314yes—
518C2×C4C22×C22⋊D1112yes—
519C2×C4C22×C22⋊D1112yes—
520C2×C4C22×C22⋊D1112yes—
521C2×C4C22×C22⋊D1112yes—
522C2×C4C22×C22⋊D1112yes—
523C2×C4C22×C22⋊D1111yescharacteristic
524C2×C4C24×D1111yescharacteristic
525C8—224no—
526C8—224no—
527C22—22no—
528C22—22no—
529C22—28no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—84no—
534C22C2×#6700314yes—
535C22C2×#6700312yes—
536C22#1062335312yes—
537C22#1062335612yes—
538C22C23×C22⋊D1111yescharacteristic
539C4—22no—
540C4—22no—
541C4—22no—
542C4—22no—
543C4—22no—
544C4—42no—
545C4—42no—
546C4—42no—
547C4—444no—
548C4—444no—
549C4#1062335612yes—
550C4C2×#6704312yes—
551C2—24no—
552C2—82no—
553C2#1307978014yesdirect product factor
554C2C2×#1062335611yescharacteristic
555C2C22×#6700311yescharacteristic
556C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#529C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#529D11
hypocenterC11C2×#3232
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C22×#66923C2semidirect
2. #13079780C2direct (N × H)
3. C2×#10622677C2semidirect
4. C2×#10622669C2semidirect
5. C2×#10622657C2semidirect
7. C2×#10622656C2semidirect
9. C2×#10622635C2semidirect
10. C2×#10622622C2semidirect
11. C2×#10622538C2semidirect
35. C2×#66923C22semidirect
42. #10622677C22semidirect
43. #10622669C22semidirect
44. #10622657C22semidirect
45. #10622656C22semidirect
48. #10622635C22semidirect
49. #10622622C22semidirect
54. #10622538C22semidirect
408. C2×C11#3232semidirect
480. C11C2×#3232semidirect
553. C2#13079780direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669232
#130797802
C2×#106226772
C2×#106226692
C2×#106226572
C2×#106226472
C2×#106226562
C2×#106226462
C2×#106226352
C2×#106226222
C2×#106225382
C2×C11×#5292
C2×#323211