Finite Group Databasebeta

← C2×#13081610 #15634689

Subgroups — C2×#13081610 #15634689

Order 2816.

2022 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic, complemented
2C2×#10623073C211yesmaximal, characteristic, complemented
3#13081610C2116yesmaximal, direct product factor
4C2×#10622781C212yesmaximal, complemented
5C2×#10622306C211yesmaximal, characteristic, complemented
6C2×#10622411C212yesmaximal, complemented
7C2×#10622644C211yesmaximal, characteristic, complemented
8C2×#10622400C212yesmaximal, complemented
9C2×#10622628C211yesmaximal, characteristic
10C2×C8×Dic22C211yesmaximal, characteristic, complemented
11C2×#10622465C212yesmaximal, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
13C22×C11×SD16C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#67000C2212yes—
17C22×#4326C2212yes—
18C2×#66989C2212yes—
19C22×#4323C2212yes—
20C2×#66979—21no—
21C2×#66977—21no—
22C22×#4314C2212yes—
23C22×#4314C2212yes—
24#10623116—24no—
25#10623116C2218yescomplemented
26#10623073—24no—
27#10623073C2218yescomplemented
28C2×#66947—22no—
29C2×#66946C2212yes—
30C2×#66940C2212yes—
31C2×#66932—22no—
32C2×#66928—21no—
33C2×#66927C2211yescharacteristic
34C2×C4×D44—21no—
35C2×#66922C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C4×C11×SD16C2218yescomplemented
38C2×C11×#106C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42#10622781C22116yescomplemented
43C2×Dic11⋊C8C2212yes—
44C2×C8×Dic11C2212yes—
45#10622644C2218yescomplemented
46#10622628C2218yes—
47C2×#66874C2212yes—
48C2×#66873C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622465C22116yescomplemented
51#10622411C22116yescomplemented
52#10622400C22116yescomplemented
53#10622306C2218yescomplemented
54C8×Dic22C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×D44—21no—
59C22×D44—21no—
60C22×D44C2312yes—
61C22×C4×D11—22no—
62C22×Dic22D411yescharacteristic
63C22×Dic22C2312yes—
64C2×C11×SD16—24no—
65C2×C11×SD16C2314yes—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×Q8×C11—22no—
69C4×Q8×C11C2314yes—
70C4×D4×C11—22no—
71C4×D4×C11C2314yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—22no—
80#67000—24no—
81#67000C2318yes—
82C2×#4326—44no—
83C2×#4326C2318yes—
84#66989—24no—
85#66989C2318yes—
86C2×#4323—44no—
87C2×#4323C2318yes—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91#66979—28no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11D411yescharacteristic
95#66977—28no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4D412yes—
98C2×C4×Dic11—22no—
99C2×C4×Dic11C2312yes—
100C22×C11⋊C8C2312yes—
101C2×#4314—28no—
102C2×#4314—44no—
103C2×#4314C2318yes—
104C2×#4314C2318yes—
105#66947—216no—
106#66946—24no—
107#66946C2318yes—
108#66940—24no—
109#66940C2318yes—
110#66932—216no—
111#66928—28no—
112#66927—22no—
113#66927C2314yes—
114C4×D44—28no—
115#66922—22no—
116#66922C2314yes—
117C4×Dic22D414yes—
118C4×Dic22C2314yes—
119C11×#106C2314yes—
120C11×#103C2314yes—
121C11×#102C2314yes—
122C4×C8×C11C2314yes—
123Dic11⋊C8C2318yes—
124C8×Dic11C2318yes—
125#66874C2318yes—
126#66873C2318yes—
127C4⋊(C11⋊C8)C2314yes—
128C2×#3394—111nomaximal, Sylow
129C24×C11—21no—
130C23×D11—22no—
131C2×Q8×C11—21no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11C2412yes—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11C2412yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—44no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—22no—
148C22×Dic11C2×D412yes—
149C22×Dic11C2×D412yes—
150C2×D44—24no—
151C2×D44—22no—
152C2×D44—24no—
153C2×D44—24no—
154C2×D44—24no—
155C2×D44—44no—
156C2×D44—82no—
157C2×D44C2414yes—
158C2×C4×D11—28no—
159C2×C4×D11—84no—
160C2×Dic22—24no—
161C2×Dic22—22no—
162C2×Dic22—24no—
163C2×Dic22—24no—
164C2×Dic22C2×D414yes—
165C2×Dic22C2414yes—
166C11×SD16—28no—
167C2×C8×C11—22no—
168C2×C8×C11#4114yes—
169C2×C8×C11C2412yes—
170C2×C8×C11C2412yes—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4C2412yes—
175C11×C4⋊C4C2412yes—
176C11×C22⋊C4—24no—
177C42×C11—24no—
178C42×C11C2×D412yes—
179C42×C11C2412yes—
180C22⋊Dic11—28no—
181C22⋊Dic11—28no—
182#4326—48no—
183#4323—48no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—28no—
187C4⋊Dic11—24no—
188C4⋊Dic11—24no—
189C4⋊Dic11C2×D414yes—
190Dic11⋊C4—28no—
191Dic11⋊C4C2×D418yes—
192C4×Dic11—28no—
193C4×Dic11C2×D414yes—
194C4×Dic11C2414yes—
195C2×C11⋊C8—24no—
196C2×C11⋊C8C2414yes—
197#4314—216no—
198#4314—48no—
199C2×#559—111no—
200C2×#556—111no—
201#3394—1116no—
202C2×#495—112no—
203C2×#492—111no—
204C2×#464—112no—
205C2×#462—111no—
206C2×#463—112no—
207C2×#459—111no—
208C2×C8×Q8—111no—
209C2×C4×SD16—112no—
210C2×C4×SD16D1111yescharacteristic, complemented
211C23×C11—22no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11C22×D411yescharacteristic
216C22×D11—24no—
217C22×D11—44no—
218C22×D11—44no—
219C22×D11—44no—
220Q8×C11—22no—
221Q8×C11—22no—
222Q8×C11—42no—
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—42no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—48no—
234C2×C4×C11#13514yes—
235C2×C4×C11C22×D412yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D412yes—
238C2×C4×C11C2×#4112yes—
239C2×C4×C11H(5,𝔽2)12yes—
240C2×C4×C11C2511yescharacteristic
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—44no—
245C2×Dic11C22×D414yes—
246C2×Dic11C22×D414yes—
247D44—24no—
248D44—24no—
249D44—44no—
250D44—48no—
251D44—84no—
252C4×D11—88no—
253Dic22—28no—
254Dic22—24no—
255Dic22—24no—
256Dic22—44no—
257C8×C11—22no—
258C8×C11C2×#4114yes—
259C11⋊C8—24no—
260C22×Q16—112no—
261C22×SD16—112no—
262C22×SD16—112no—
263C22×SD16C2×D1111yescharacteristic
264C22×D8—112no—
265#559—118no—
266#559—224no—
267#556—118no—
268#556—224no—
269C2×C4⋊Q8—111no—
270C2×#127—111no—
271C2×#126—222no—
272C2×#124—112no—
273C2×#124—112no—
274C2×#124—221no—
275C2×#123—222no—
276C2×C22⋊Q8—221no—
277C2×C4×Q8—111no—
278C2×C4×Q8—112no—
279C2×C4×Q8C2×D1111yescharacteristic
280C2×C4×D4—112no—
281C2×C4×D4—221no—
282C2×C4×D4C2×D1111yescharacteristic
283C2×#117—221no—
284#495—1116no—
285#492—118no—
286#464—1116no—
287#463—1116no—
288#462—118no—
289#459—118no—
290C8×Q8—118no—
291C4×SD16—1116no—
292C4×SD16C2×D1118yescomplemented
293C2×#106C2×D1111yescharacteristic
294C2×C4⋊C8—112no—
295C2×C4⋊C8—111no—
296C2×#103—112no—
297C2×#103C2×D1111yescharacteristic
298C2×#102—112no—
299C2×#102C2×D1111yescharacteristic
300C2×C4×C8—112no—
301C2×C4×C8C2×D1111yescharacteristic
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—84no—
306C22×C11#55012yes—
307C22×C11C2×#13512yes—
308C22×C11#57712yes—
309C22×C11C23×D411yescharacteristic
310C2×D11—44no—
311C2×D11—44no—
312C2×D11—44no—
313C2×D11—88no—
314C4×C11—22no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11#55012yes—
319C4×C11C2×#13514yes—
320C4×C11C22×#4111yescharacteristic
321C4×C11C2×H(5,𝔽2)11yescharacteristic
322Dic11—24no—
323Dic11—24no—
324Dic11—44no—
325C22×Q8—111no—
326C22×Q8—112no—
327C22×Q8C22×D1111yescharacteristic
328C22×D4—112no—
329C22×D4—221no—
330C22×D4—221no—
331C22×D4C22×D1111yescharacteristic
332C23×C4—21no—
333C23×C4—222no—
334C2×Q16—118no—
335C2×Q16—444no—
336C2×SD16—24no—
337C2×SD16—118no—
338C2×SD16—118no—
339C2×SD16—228no—
340C2×SD16—444no—
341C2×SD16C22×D1114yes—
342C2×D8—118no—
343C2×D8—444no—
344C22×C8—112no—
345C22×C8C22×D1111yescharacteristic
346C22×C8C22×D1111yescharacteristic
347C4⋊Q8—114no—
348C4⋊Q8—222no—
349#127—114no—
350#127—222no—
351#126—2216no—
352#124—118no—
353#124—118no—
354#124—228no—
355#124—224no—
356#124—224no—
357#123—2216no—
358C22⋊Q8—228no—
359C4×Q8—22no—
360C4×Q8—114no—
361C4×Q8—114no—
362C4×Q8—118no—
363C4×Q8—224no—
364C4×Q8C22×D1114yes—
365C4×D4—22no—
366C4×D4—118no—
367C4×D4—228no—
368C4×D4—224no—
369C4×D4C22×D1114yes—
370#117—228no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385C2×C42—21no—
386C2×C42—112no—
387C2×C42—222no—
388C2×C42C22×D1111yescharacteristic
389#106C22×D1114yes—
390C4⋊C8—118no—
391C4⋊C8—114no—
392#103—118no—
393#103C22×D1114yes—
394#102—118no—
395#102C22×D1114yes—
396C4×C8—118no—
397C4×C8C22×D1114yes—
398C2×C11—82no—
399C2×C11#339414yescomplemented
400C2×C11C2×#55011yescharacteristic
401C2×C11C22×#13511yescharacteristic
402C2×C11C2×#57711yescharacteristic
403D11—84no—
404C24—21no—
405C24—222no—
406C2×Q8—21no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—114no—
410C2×Q8—114no—
411C2×Q8—224no—
412C2×Q8—222no—
413C2×Q8—224no—
414C2×Q8—224no—
415C2×Q8C23×D1112yes—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—22no—
419C2×D4—114no—
420C2×D4—224no—
421C2×D4—224no—
422C2×D4—222no—
423C2×D4—224no—
424C2×D4—224no—
425C2×D4—444no—
426C2×D4—882no—
427C2×D4C23×D1112yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—44no—
433C22×C4—112no—
434C22×C4—112no—
435C22×C4—228no—
436C22×C4—222no—
437C22×C4—884no—
438C22×C4D4×D1111yescharacteristic
439C22×C4D4×D1111yescharacteristic
440C22×C4C23×D1111yescharacteristic
441Q16—448no—
442SD16—28no—
443SD16—2216no—
444SD16—448no—
445D8—448no—
446C2×C8—22no—
447C2×C8—114no—
448C2×C8—224no—
449C2×C8#433914yes—
450C2×C8C23×D1112yes—
451C2×C8C23×D1112yes—
452C4⋊C4—24no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—114no—
456C4⋊C4—118no—
457C4⋊C4—228no—
458C4⋊C4—224no—
459C4⋊C4—224no—
460C4⋊C4C23×D1112yes—
461C4⋊C4C23×D1112yes—
462C22⋊C4—24no—
463C22⋊C4—228no—
464C22⋊C4—228no—
465C22⋊C4—228no—
466C22⋊C4—228no—
467C22⋊C4—228no—
468C42—24no—
469C42—114no—
470C42—114no—
471C42—228no—
472C42D4×D1112yes—
473C42C23×D1112yes—
474C11C2×#339411yescharacteristic, complemented, Sylow
475C23—22no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—224no—
480C23—444no—
481C23—444no—
482C23—444no—
483C23C2×D4×D1111yescharacteristic
484Q8—22no—
485Q8—22no—
486Q8—42no—
487Q8—228no—
488Q8—224no—
489Q8—224no—
490Q8—444no—
491D4—22no—
492D4—22no—
493D4—42no—
494D4—224no—
495D4—224no—
496D4—448no—
497D4—444no—
498D4—884no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—48no—
507C2×C4—114no—
508C2×C4—114no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—444no—
513C2×C4—888no—
514C2×C4#6696914yes—
515C2×C4C2×#433912yes—
516C2×C4C2×D4×D1112yes—
517C2×C4C2×D4×D1112yes—
518C2×C4C2×D4×D1111yescharacteristic
519C2×C4#6704212yes—
520C2×C4C24×D1111yescharacteristic
521C8—22no—
522C8—224no—
523C8C2×#433914yes—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—84no—
528C22—444no—
529C22—444no—
530C22—444no—
531C22—888no—
532C22#1062308412yes—
533C22C2×#6696912yes—
534C22#1062330112yes—
535C22C22×D4×D1111yescharacteristic
536C4—22no—
537C4—42no—
538C4—42no—
539C4—42no—
540C4—224no—
541C4—224no—
542C4—444no—
543C4#1062308412yes—
544C4C2×#6696914yes—
545C4C22×#433911yescharacteristic
546C4C2×#6704211yescharacteristic
547C2—82no—
548C2—884no—
549C2#1308161014yesdirect product factor
550C2C2×#1062308411yescharacteristic
551C2C22×#6696911yescharacteristic
552C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10622628C2
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3394
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
2. C2×#10623073C2semidirect
3. #13081610C2direct (N × H)
4. C2×#10622781C2semidirect
5. C2×#10622306C2semidirect
6. C2×#10622411C2semidirect
7. C2×#10622644C2semidirect
8. C2×#10622400C2semidirect
10. C2×C8×Dic22C2semidirect
11. C2×#10622465C2semidirect
12. C2×C4×C11×SD16C2semidirect
25. #10623116C22semidirect
27. #10623073C22semidirect
37. C4×C11×SD16C22semidirect
42. #10622781C22semidirect
45. #10622644C22semidirect
50. #10622465C22semidirect
51. #10622411C22semidirect
52. #10622400C22semidirect
53. #10622306C22semidirect
54. C8×Dic22C22semidirect
210. C2×C4×SD16D11semidirect
292. C4×SD16C2×D11semidirect
399. C2×C11#3394semidirect
474. C11C2×#3394semidirect
549. C2#13081610direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106230732
#130816102
C2×#106227812
C2×#106223062
C2×#106224112
C2×#106226442
C2×#106224002
C2×#106226282
C2×C8×Dic222
C2×#106224652
C2×C4×C11×SD162
C2×#339411