Finite Group Databasebeta

← C2×#13079852 #15625930

Subgroups — C2×#13079852 #15625930

Order 2816.

1790 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×#10623001C211yesmaximal, characteristic, complemented
2#13079852C2116yesmaximal, direct product factor
3C2×#10622678C211yesmaximal, characteristic, complemented
4C2×#10622678C211yesmaximal, characteristic, complemented
5C2×#10622668C211yesmaximal, characteristic, complemented
6C2×#10622668C211yesmaximal, characteristic, complemented
7C2×#10622658C212yesmaximal, complemented
8C2×#10622648C212yesmaximal
9C2×#10622635C212yesmaximal, complemented
10C2×#10622622C212yesmaximal, complemented
11C2×#10622539C211yesmaximal, 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
26C2×#66979C2212yes—
27C2×#66977—21no—
28C2×#66977—21no—
29#10623001—24no—
30#10623001C2218yescomplemented
31C2×#66923C2212yes—
32C2×#66922C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22—21no—
35C2×C4×Dic22—21no—
36C2×#66899C2212yes—
37C2×#66899C2212yes—
38C2×#66896C2212yes—
39C2×#66896C2212yes—
40C2×C22⋊(C11⋊C8)C2212yes—
41#10622678C2218yescomplemented
42#10622678C2218yescomplemented
43#10622668C2218yescomplemented
44#10622668C2218yescomplemented
45#10622658C22116yescomplemented
46#10622648C22116yes—
47#10622635C22116yescomplemented
48#10622622C22116yescomplemented
49C2×#66872C2212yes—
50C2×#66872C2212yes—
51C2×#66871C2212yes—
52C2×#66871C2212yes—
53#10622539C2218yescomplemented
54C2×C4⋊(C11⋊C8)C2212yes—
55C2×#66867C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×Dic22—21no—
65C22×Dic22—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×C22⋊Dic11—22no—
101#66979—24no—
102#66979C2318yes—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2312yes—
107#66977—28no—
108#66977—28no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×C4×Dic11—22no—
112C22×C11⋊C8C2312yes—
113C22×C11⋊C8C2312yes—
114#66923—24no—
115#66923C2318yes—
116#66922—22no—
117#66922—22no—
118#66922C2314yes—
119#66922C2314yes—
120C4×Dic22—28no—
121C4×Dic22—28no—
122#66899C2318yes—
123#66899C2318yes—
124#66896C2318yes—
125#66896C2318yes—
126C22⋊(C11⋊C8)C2318yes—
127#66872C2318yes—
128#66872C2318yes—
129#66871C2318yes—
130#66871C2318yes—
131C4⋊(C11⋊C8)C2318yes—
132#66867C2314yes—
133#66867C2314yes—
134C2×#3240—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—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—24no—
150C22×C4×C11—42no—
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×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D414yes—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—22no—
164C22×Dic11—22no—
165C2×Dic22—24no—
166C2×Dic22—24no—
167C2×Dic22—44no—
168C2×Dic22—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×D414yes—
185C42×C11C2×D412yes—
186C42×C11C2×D412yes—
187C42×C11C2412yes—
188C42×C11C2412yes—
189C22⋊Dic11—28no—
190C4⋊Dic11—24no—
191C4⋊Dic11—24no—
192C4⋊Dic11—22no—
193C4⋊Dic11—22no—
194C4⋊Dic11C2414yes—
195C4⋊Dic11C2414yes—
196Dic11⋊C4—28no—
197Dic11⋊C4—28no—
198C4×Dic11—28no—
199C2×C11⋊C8—24no—
200C2×C11⋊C8—24no—
201C2×C11⋊C8C2414yes—
202C2×C11⋊C8C2414yes—
203C2×#533—111no—
204C2×#529D1111yescharacteristic
205#3240—1116no—
206C2×#501—111no—
207C2×#501—111no—
208C2×#489—111no—
209C2×#489—111no—
210C2×#485—112no—
211C2×#482—112no—
212C2×#479—112no—
213C2×#478—112no—
214C2×#432—111no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
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—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—44no—
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—44no—
256C2×Dic11—44no—
257Dic22—48no—
258Dic22—48no—
259C11⋊C8—24no—
260C11⋊C8—24no—
261#533—118no—
262#533—224no—
263C2×C4⋊Q8—111no—
264C2×C4⋊Q8—111no—
265#529—24no—
266#529C2×D1118yes—
267C2×#126—21no—
268C2×#125—112no—
269C2×#125C2×D1111yescharacteristic
270C2×#124C2×D1111yescharacteristic
271C2×#123—21no—
272C2×C22⋊Q8—221no—
273C2×C22⋊Q8—221no—
274C2×C22⋊Q8C2×D1111yescharacteristic
275C2×#121C2×D1111yescharacteristic
276C2×C4×Q8—221no—
277C2×C4×Q8—221no—
278C2×C4×Q8C2×D1111yescharacteristic
279C2×C4×D4—21no—
280C2×C4×D4C2×D1111yescharacteristic
281C2×#117—21no—
282C2×#117—112no—
283C22×C42C2×D1111yescharacteristic
284#501—118no—
285#501—118no—
286#489—118no—
287#489—118no—
288#485—1116no—
289#482—1116no—
290#479—1116no—
291#478—1116no—
292#432—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—112no—
303C2×#97—111no—
304C2×#97—111no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—44no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—84no—
313C22×C11#53612yes—
314C22×C11#57512yes—
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×Q8—221no—
330C22×Q8—221no—
331C22×Q8C22×D1111yescharacteristic
332C22×D4—21no—
333C22×D4C22×D1111yescharacteristic
334C23×C4—21no—
335C23×C4C22⋊D1111yescharacteristic
336C23×C4C22⋊D1111yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C22×C8—112no—
339C22×C8—112no—
340C4⋊Q8—114no—
341C4⋊Q8—114no—
342C4⋊Q8—222no—
343C4⋊Q8—222no—
344#126—28no—
345#125—22no—
346#125—118no—
347#125—224no—
348#125C22×D1114yes—
349#124—22no—
350#124C22×D1114yes—
351#123—28no—
352C22⋊Q8—22no—
353C22⋊Q8—228no—
354C22⋊Q8—228no—
355C22⋊Q8C22×D1114yes—
356#121—22no—
357#121C22×D1114yes—
358C4×Q8—22no—
359C4×Q8—228no—
360C4×Q8—228no—
361C4×Q8C22×D1114yes—
362C4×D4—28no—
363C4×D4—22no—
364C4×D4C22×D1114yes—
365#117—28no—
366#117—118no—
367#117—224no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—222no—
386C2×C42—21no—
387C2×C42—222no—
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—118no—
404#97—114no—
405#97—114no—
406C2×C11—42no—
407C2×C11—82no—
408C2×C11#324014yescomplemented
409C2×C11C2×#53611yescharacteristic
410C2×C11C2×#57511yescharacteristic
411C2×C11C2×#57511yescharacteristic
412C24—21no—
413C24C2×C22⋊D1111yescharacteristic
414C2×Q8—21no—
415C2×Q8—24no—
416C2×Q8—224no—
417C2×Q8—224no—
418C2×Q8—444no—
419C2×Q8—444no—
420C2×Q8C23×D1112yes—
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—21no—
424C2×D4—44no—
425C2×D4C23×D1112yes—
426C22×C4—24no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—44no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4C2×C22⋊D1112yes—
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1114yes—
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—222no—
459C4⋊C4—222no—
460C4⋊C4—228no—
461C4⋊C4—228no—
462C4⋊C4—224no—
463C4⋊C4—224no—
464C4⋊C4C23×D1112yes—
465C4⋊C4C23×D1112yes—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—228no—
472C42—24no—
473C42—228no—
474C42C2×C22⋊D1114yes—
475C42C2×C22⋊D1112yes—
476C42C2×C22⋊D1114yes—
477C42C2×C22⋊D1112yes—
478C42C23×D1112yes—
479C42C23×D1112yes—
480C11C2×#324011yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23C22×C22⋊D1112yes—
489C23C22×C22⋊D1111yescharacteristic
490Q8—24no—
491Q8—42no—
492Q8—448no—
493Q8—448no—
494D4—24no—
495D4—48no—
496D4—42no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—44no—
508C2×C4—44no—
509C2×C4—48no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—224no—
514C2×C4—224no—
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—22no—
530C22—44no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—84no—
535C22#1062335312yes—
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—42no—
552C2—82no—
553C2#1307985214yesdirect product factor
554C2C2×#1062335611yescharacteristic
555C2C2×#1062335311yescharacteristic
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×#3240
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. C2×#10623001C2semidirect
2. #13079852C2direct (N × H)
3. C2×#10622678C2semidirect
4. C2×#10622678C2semidirect
5. C2×#10622668C2semidirect
6. C2×#10622668C2semidirect
7. C2×#10622658C2semidirect
9. C2×#10622635C2semidirect
10. C2×#10622622C2semidirect
11. C2×#10622539C2semidirect
30. #10623001C22semidirect
41. #10622678C22semidirect
42. #10622678C22semidirect
43. #10622668C22semidirect
44. #10622668C22semidirect
45. #10622658C22semidirect
47. #10622635C22semidirect
48. #10622622C22semidirect
53. #10622539C22semidirect
408. C2×C11#3240semidirect
480. C11C2×#3240semidirect
553. C2#13079852direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230012
#130798522
C2×#106226782
C2×#106226682
C2×#106226582
C2×#106226482
C2×#106226352
C2×#106226222
C2×#106225392
C2×C11×#5292
C2×#324011