Finite Group Databasebeta

← C2×#13079859 #15625937

Subgroups — C2×#13079859 #15625937

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×#10623259C211yesmaximal, characteristic, complemented
2C2×#10623222C211yesmaximal, characteristic
3#13079859C2116yesmaximal, direct product factor
4C2×#10622678C211yesmaximal, characteristic, complemented
5C2×#10622702C211yesmaximal, characteristic, complemented
6C2×#10622327C211yesmaximal, characteristic, complemented
7C2×#10622480C212yesmaximal, complemented
8C2×#10622498C212yesmaximal
9C2×#10622490C212yesmaximal, complemented
10C2×#10622484C212yesmaximal, complemented
11C2×#10622318C211yesmaximal, characteristic, complemented
12C2×C11×#501C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#125C2211yescharacteristic
15C2×#66999—21no—
16C2×Q8×Dic11—21no—
17#10623259—24no—
18#10623259C2218yescomplemented
19#10623222—24no—
20#10623222C2218yes—
21C2×#66951—21no—
22C2×#66950—21no—
23C2×#66950C2211yescharacteristic
24C2×#66948C2211yescharacteristic
25C2×#66947—21no—
26C2×#66946—21no—
27C2×#66946C2211yescharacteristic
28C2×#66945—21no—
29C2×#66945C2212yes—
30C2×#66943C2212yes—
31C2×#66940—21no—
32C2×#66940C2211yescharacteristic
33C2×#66928C2211yescharacteristic
34C2×C42×D11C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C11×#501C2218yescomplemented
37C2×C11×#107C2212yes—
38C2×C11×#106C2212yes—
39C2×C11×#97C2211yescharacteristic
40C2×#66885C2212yes—
41C2×(C2×D11)⋊C8C2212yes—
42C2×#66880C2212yes—
43C2×Dic11⋊C8C2212yes—
44#10622702C2218yescomplemented
45#10622678C2218yescomplemented
46C2×#66874C2212yes—
47C2×#66873C2212yes—
48C2×#66872C2212yes—
49C2×#66871C2212yes—
50C2×#66867C2211yescharacteristic
51#10622498C22116yes—
52#10622490C22116yescomplemented
53#10622484C22116yescomplemented
54#10622480C22116yescomplemented
55#10622327C2218yescomplemented
56#10622318C2218yescomplemented
57C22×Q8×C11—21no—
58C22×D44—21no—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11D411yescharacteristic
62C22×C4×D11D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×Dic22—21no—
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2312yes—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yes—
69C11×#125—22no—
70C11×#125C2314yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78#66999—28no—
79Q8×Dic11—28no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—21no—
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⋊Dic11C2312yes—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11D411yescharacteristic
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2312yes—
98#66951—28no—
99#66950—28no—
100#66950—22no—
101#66950C2314yes—
102#66948—22no—
103#66948C2314yes—
104#66947—28no—
105#66946—28no—
106#66946—22no—
107#66946C2314yes—
108#66945—24no—
109#66945—28no—
110#66945C2318yes—
111#66943—24no—
112#66943C2318yes—
113#66940—28no—
114#66940—22no—
115#66940C2314yes—
116#66928—22no—
117#66928C2314yes—
118C42×D11D414yes—
119C42×D11C2314yes—
120#66922—22no—
121#66922C2314yes—
122C11×#107C2318yes—
123C11×#106C2318yes—
124C11×#97C2314yes—
125#66885C2318yes—
126(C2×D11)⋊C8C2318yes—
127#66880C2318yes—
128Dic11⋊C8C2318yes—
129#66874C2318yes—
130#66873C2318yes—
131#66872C2318yes—
132#66871C2318yes—
133#66867C2314yes—
134C2×#3240—111nomaximal, Sylow
135C23×D11—21no—
136C23×D11C2×D411yescharacteristic
137C2×Q8×C11—24no—
138C2×Q8×C11—44no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—22no—
146C22×Dic11—21no—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C2×D44—24no—
151C2×D44—21no—
152C2×D44—24no—
153C2×D44—44no—
154C2×D44C2412yes—
155C2×C4×D11—24no—
156C2×C4×D11—24no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11—44no—
160C2×C4×D11C2×D412yes—
161C2×C4×D11C2×D414yes—
162C2×C4×D11C2×D414yes—
163C2×C4×D11C2412yes—
164C2×Dic22—24no—
165C2×Dic22—21no—
166C2×Dic22—24no—
167C2×Dic22—44no—
168C2×Dic22C2412yes—
169C2×C8×C11—24no—
170C2×C8×C11C2414yes—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4C2412yes—
178C11×C4⋊C4C2412yes—
179C11×C4⋊C4C2414yes—
180C42×C11C2×D412yes—
181C42×C11C2412yes—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—24no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—24no—
188C4⋊Dic11—28no—
189C4⋊Dic11—24no—
190C4⋊Dic11—22no—
191C4⋊Dic11—24no—
192C4⋊Dic11C2414yes—
193Dic11⋊C4—28no—
194Dic11⋊C4—24no—
195C4×Dic11—28no—
196C4×Dic11—24no—
197C4×Dic11C2×D412yes—
198C4×Dic11C2×D414yes—
199C4×Dic11C2×D414yes—
200C4×Dic11C2412yes—
201C2×C11⋊C8—24no—
202C2×C11⋊C8C2414yes—
203C2×#533—111no—
204C2×#529—111no—
205#3240—1116no—
206C2×#501—111no—
207C2×#501D1111yescharacteristic, complemented
208C2×#489—111no—
209C2×#489—111no—
210C2×#485—112no—
211C2×#482—112no—
212C2×#479—112no—
213C2×#478—112no—
214C2×#432—111no—
215C23×C11C22×D411yescharacteristic
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11C22×D412yes—
224Q8×C11—48no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—44no—
233C2×C4×C11C22×D412yes—
234C2×C4×C11C22×D412yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C112−1+414yes—
237C2×C4×C11C2511yescharacteristic
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—42no—
244C2×Dic11—44no—
245C2×Dic11C22×D412yes—
246C2×Dic11C22×D412yes—
247C2×Dic11C22×D412yes—
248D44—24no—
249D44—48no—
250D44—42no—
251C4×D11—24no—
252C4×D11—24no—
253C4×D11—44no—
254C4×D11—44no—
255C4×D11—48no—
256Dic22—24no—
257Dic22—48no—
258Dic22—42no—
259C8×C11—24no—
260C11⋊C8—24no—
261#533—118no—
262#533—224no—
263C2×C4⋊Q8—111no—
264C2×C4⋊Q8C2×D1111yescharacteristic
265#529—118no—
266#529—224no—
267C2×#126—221no—
268C2×#125—112no—
269C2×#125C2×D1111yescharacteristic
270C2×#124—111no—
271C2×#123—221no—
272C2×C22⋊Q8—111no—
273C2×C22⋊Q8—221no—
274C2×C22⋊Q8—221no—
275C2×#121—111no—
276C2×C4×Q8—111no—
277C2×C4×Q8—221no—
278C2×C4×Q8—221no—
279C2×C4×D4—111no—
280C2×C4×D4—221no—
281C2×#117—112no—
282C2×#117—221no—
283C22×C42—111no—
284#501—118no—
285#501C2×D1118yescomplemented
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×#107C2×D1112yes—
295C2×#106—112no—
296C2×#106C2×D1112yes—
297C2×C4⋊C8—112no—
298C2×#103—112no—
299C2×#103—112no—
300C2×#102—112no—
301C2×#102—112no—
302C2×C22⋊C8—112no—
303C2×#97—111no—
304C2×#97C2×D1111yescharacteristic
305C22×C11#53612yes—
306C22×C11#57512yes—
307C22×C11#57512yes—
308C22×C11C23×D411yescharacteristic
309C2×D11—22no—
310C2×D11—22no—
311C2×D11—22no—
312C2×D11—44no—
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—84no—
317C4×C11—22no—
318C4×C11—22no—
319C4×C11—44no—
320C4×C11—42no—
321C4×C11—42no—
322C4×C11#53612yes—
323C4×C11C2×2−1+412yes—
324Dic11—22no—
325Dic11—22no—
326Dic11—22no—
327Dic11—42no—
328Dic11—44no—
329C22×Q8—21no—
330C22×Q8—111no—
331C22×Q8—221no—
332C22×D4—111no—
333C22×D4—221no—
334C23×C4—111no—
335C23×C4—111no—
336C23×C4—111no—
337C23×C4—221no—
338C22×C8—112no—
339C22×C8C22×D1112yes—
340C4⋊Q8—22no—
341C4⋊Q8—114no—
342C4⋊Q8—222no—
343C4⋊Q8C22×D1114yes—
344#126—228no—
345#125—22no—
346#125—118no—
347#125—224no—
348#125C22×D1114yes—
349#124—114no—
350#124—222no—
351#123—228no—
352C22⋊Q8—114no—
353C22⋊Q8—222no—
354C22⋊Q8—228no—
355C22⋊Q8—228no—
356#121—114no—
357#121—222no—
358C4×Q8—114no—
359C4×Q8—222no—
360C4×Q8—228no—
361C4×Q8—228no—
362C4×D4—114no—
363C4×D4—222no—
364C4×D4—228no—
365#117—118no—
366#117—228no—
367#117—224no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—112no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4C22×D1112yes—
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—114no—
390C2×C42—114no—
391C2×C42—222no—
392C2×C42—221no—
393C2×C42C22×D1111yescharacteristic
394#107—118no—
395#107C22×D1118yes—
396#106—118no—
397#106C22×D1118yes—
398C4⋊C8—118no—
399#103—118no—
400#103—118no—
401#102—118no—
402#102—118no—
403C22⋊C8—118no—
404#97—114no—
405#97C22×D1114yes—
406C2×C11#324014yescomplemented
407C2×C11C2×#53611yescharacteristic
408C2×C11C2×#57511yescharacteristic
409C2×C11C2×#57511yescharacteristic
410D11—42no—
411D11—82no—
412C24—111no—
413C24—221no—
414C2×Q8—24no—
415C2×Q8—44no—
416C2×Q8—112no—
417C2×Q8—221no—
418C2×Q8—224no—
419C2×Q8—224no—
420C2×Q8—444no—
421C2×D4—112no—
422C2×D4—224no—
423C2×D4—221no—
424C2×D4—224no—
425C2×D4—444no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—224no—
437C22×C4—224no—
438C22×C4—221no—
439C22×C4—222no—
440C22×C4—442no—
441C22×C4—442no—
442C22×C4—444no—
443C22×C4D4×D1111yescharacteristic
444C22×C4D4×D1111yescharacteristic
445C22×C4C23×D1111yescharacteristic
446C2×C8—24no—
447C2×C8—114no—
448C2×C8—224no—
449C2×C8C23×D1114yes—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—114no—
457C4⋊C4—224no—
458C4⋊C4—224no—
459C4⋊C4—228no—
460C4⋊C4—228no—
461C4⋊C4—222no—
462C4⋊C4—224no—
463C4⋊C4C23×D1114yes—
464C4⋊C4C23×D1112yes—
465C4⋊C4C23×D1112yes—
466C22⋊C4—224no—
467C22⋊C4—224no—
468C22⋊C4—228no—
469C22⋊C4—224no—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C42—114no—
473C42—112no—
474C42—114no—
475C42—112no—
476C42—228no—
477C42—224no—
478C42D4×D1112yes—
479C42C23×D1112yes—
480C11C2×#324011yescharacteristic, complemented, Sylow
481C23—112no—
482C23—222no—
483C23—222no—
484C23—222no—
485C23—222no—
486C23—442no—
487C23—442no—
488C23—442no—
489C23C2×D4×D1111yescharacteristic
490Q8—48no—
491Q8—224no—
492Q8—448no—
493Q8—442no—
494D4—224no—
495D4—448no—
496D4—442no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—112no—
506C2×C4—112no—
507C2×C4—112no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—444no—
516C2×C4—444no—
517C2×C4—448no—
518C2×C4—442no—
519C2×C4—444no—
520C2×C4C2×D4×D1112yes—
521C2×C4C2×D4×D1112yes—
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4#6704014yes—
524C2×C4C24×D1111yescharacteristic
525C8—24no—
526C8—224no—
527C22—222no—
528C22—222no—
529C22—222no—
530C22—444no—
531C22—442no—
532C22—442no—
533C22—442no—
534C22—884no—
535C22#1062325512yes—
536C22#1062330412yes—
537C22#1062330812yes—
538C22C22×D4×D1111yescharacteristic
539C4—22no—
540C4—22no—
541C4—42no—
542C4—44no—
543C4—42no—
544C4—222no—
545C4—222no—
546C4—222no—
547C4—442no—
548C4—444no—
549C4#1062325512yes—
550C4C2×#6704012yes—
551C2—442no—
552C2—882no—
553C2#1307985914yesdirect product factor
554C2C2×#1062325511yescharacteristic
555C2C2×#1062330411yescharacteristic
556C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#501C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenterC2×#501D11
hypocenterC11C2×#3240
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13079859C2direct (N × H)
4. C2×#10622678C2semidirect
5. C2×#10622702C2semidirect
6. C2×#10622327C2semidirect
7. C2×#10622480C2semidirect
9. C2×#10622490C2semidirect
10. C2×#10622484C2semidirect
11. C2×#10622318C2semidirect
12. C2×C11×#501C2semidirect
18. #10623259C22semidirect
36. C11×#501C22semidirect
44. #10622702C22semidirect
45. #10622678C22semidirect
52. #10622490C22semidirect
53. #10622484C22semidirect
54. #10622480C22semidirect
55. #10622327C22semidirect
56. #10622318C22semidirect
207. C2×#501D11semidirect
285. #501C2×D11semidirect
406. C2×C11#3240semidirect
480. C11C2×#3240semidirect
553. C2#13079859direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106232222
#130798592
C2×#106226782
C2×#106227022
C2×#106223272
C2×#106224802
C2×#106224982
C2×#106224902
C2×#106224842
C2×#106223182
C2×C11×#5012
C2×#324011