Finite Group Databasebeta

← C2×#13081241 #15632522

Subgroups — C2×#13081241 #15632522

Order 2816.

1930 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623265C211yesmaximal, characteristic
2C2×#10623261C211yesmaximal, characteristic, complemented
3#13081241C2116yesmaximal, direct product factor
4C2×#10622501C212yesmaximal, complemented
5C2×#10622495C212yesmaximal, complemented
6C2×#10622704C211yesmaximal, characteristic, complemented
7C2×#10622697C211yesmaximal, characteristic, complemented
8C2×#10622499C212yesmaximal, complemented
9C2×C4×#4314C211yesmaximal, characteristic, complemented
10C2×#10622301C211yesmaximal, characteristic, complemented
11C2×#10622494C212yesmaximal, complemented
12C2×C11×#500C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×#67000—22no—
16C2×#66999—22no—
17C22×#4314C2211yescharacteristic
18C22×#4313C2212yes—
19#10623265—24no—
20#10623265C2218yes—
21#10623261—24no—
22#10623261C2218yescomplemented
23C2×#66950C2212yes—
24C2×#66948—21no—
25C2×#66948C2212yes—
26C2×#66946—21no—
27C2×#66945—21no—
28C2×#66945C2212yes—
29C2×C4⋊C4×D11C2212yes—
30C2×#66943—21no—
31C2×C4×D44C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#500C2218yescomplemented
35C2×C11×#107C2212yes—
36C2×C11×#107C2212yes—
37C2×C4×C8×C11C2211yescharacteristic
38C2×#66885C2211yescharacteristic
39C2×(C2×D11)⋊C8C2212yes—
40C2×#66881C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42#10622704C2218yescomplemented
43#10622697C2218yescomplemented
44C2×#66874C2212yes—
45C2×#66873C2212yes—
46C2×#66872C2212yes—
47C2×#66871C2212yes—
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622501C22116yescomplemented
50#10622499C22116yescomplemented
51#10622495C22116yescomplemented
52#10622494C22116yescomplemented
53C4×#4314C2218yescomplemented
54#10622301C2218yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11—21no—
57C22×D44—22no—
58C22×D44D411yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—22no—
62C22×C4×D11C2312yes—
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yes—
69C11×C4⋊Q8C2314yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C42×C11C2311yescharacteristic
75#67000—216no—
76#66999—216no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4D412yes—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11D411yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—22no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—22no—
90C22×C11⋊C8C2312yes—
91C2×#4314—24no—
92C2×#4314C2314yes—
93C2×#4313—28no—
94C2×#4313C2318yes—
95#66950—24no—
96#66950C2318yes—
97#66948—28no—
98#66948—24no—
99#66948C2318yes—
100#66946—28no—
101#66945—24no—
102#66945—28no—
103#66945C2318yes—
104C4⋊C4×D11—24no—
105C4⋊C4×D11C2318yes—
106#66943—28no—
107C4×D44—22no—
108C4×D44D414yes—
109C4×D44C2314yes—
110C4×D44C2314yes—
111C4×Dic22—22no—
112C4×Dic22C2314yes—
113C11×#107C2318yes—
114C11×#107C2318yes—
115C4×C8×C11C2314yes—
116#66885C2314yes—
117(C2×D11)⋊C8C2318yes—
118#66881C2314yes—
119#66880C2314yes—
120#66874C2318yes—
121#66873C2318yes—
122#66872C2318yes—
123#66871C2318yes—
124C4⋊(C11⋊C8)C2314yes—
125C2×#3357—111nomaximal, Sylow
126C23×D11—21no—
127C23×D11C2×D412yes—
128C2×Q8×C11—24no—
129C2×Q8×C11—24no—
130C2×Q8×C11—82no—
131C2×Q8×C11—82no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11C2×D412yes—
141C2×D44—28no—
142C2×D44—24no—
143C2×D44—21no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—84no—
147C2×D44C2×D414yes—
148C2×D44C2412yes—
149C2×C4×D11—28no—
150C2×C4×D11—24no—
151C2×C4×D11—24no—
152C2×C4×D11—24no—
153C2×C4×D11—44no—
154C2×C4×D11—84no—
155C2×C4×D11C2×D414yes—
156C2×C4×D11C2414yes—
157C2×Dic22—21no—
158C2×Dic22—22no—
159C2×Dic22—22no—
160C2×Dic22C2412yes—
161C2×C8×C11—22no—
162C2×C8×C11#4114yes—
163C2×C8×C11C2412yes—
164C2×C8×C11C2412yes—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4C2414yes—
170C11×C4⋊C4C2414yes—
171C42×C11C2×D412yes—
172C42×C11C2412yes—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—28no—
176(C2×D11)⋊C4—24no—
177(C2×D11)⋊C4C2×D418yes—
178C4⋊Dic11—28no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11C2×D414yes—
182C4⋊Dic11C2412yes—
183C4⋊Dic11C2412yes—
184Dic11⋊C4—28no—
185Dic11⋊C4—24no—
186C4×Dic11—28no—
187C4×Dic11—24no—
188C2×C11⋊C8—24no—
189C2×C11⋊C8C2414yes—
190#4314—28no—
191#4313—216no—
192C2×#555—111no—
193C2×#554—111no—
194#3357—1116no—
195C2×#500D1111yescharacteristic, complemented
196C2×#485—112no—
197C2×#480—112no—
198C2×#477—111no—
199C2×#476—111no—
200C2×#468—112no—
201C2×C4×SD16—111no—
202C2×#436—111no—
203C2×#428—112no—
204C23×C11C22×D411yescharacteristic
205C22×D11—24no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—22no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11C22×D414yes—
213Q8×C11—84no—
214Q8×C11—84no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11#13714yes—
221C2×C4×C11C22×D412yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D412yes—
224C2×C4×C11C2×#4112yes—
225C2×C4×C112−1+412yes—
226C2×C4×C11C2511yescharacteristic
227C2×Dic11—24no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11C22×D414yes—
235D44—28no—
236D44—22no—
237D44—22no—
238D44—42no—
239D44—88no—
240C4×D11—28no—
241C4×D11—24no—
242C4×D11—24no—
243C4×D11—48no—
244C4×D11—88no—
245Dic22—22no—
246Dic22—22no—
247Dic22—42no—
248C8×C11—22no—
249C8×C11C2×#4114yes—
250C11⋊C8—24no—
251C22×SD16—111no—
252C22×M16—112no—
253#555—118no—
254#555—224no—
255#554—118no—
256#554—224no—
257C2×C4⋊Q8C2×D1111yescharacteristic
258C2×C4⋊Q8C2×D1111yescharacteristic
259C2×#125—221no—
260C2×#124—222no—
261C2×C22⋊Q8—112no—
262C2×C22⋊Q8—222no—
263C2×#121—112no—
264C2×#121—221no—
265C2×C4×Q8—111no—
266C2×C4×D4—111no—
267C2×C4×D4—111no—
268C2×C4×D4—221no—
269C2×#117—112no—
270C2×#117—221no—
271C22×C4⋊C4—112no—
272#500C2×D1118yescomplemented
273#485—1116no—
274#480—1116no—
275#477—118no—
276#476—118no—
277#468—1116no—
278C4×SD16—118no—
279#436—118no—
280#428—1116no—
281C2×#107—112no—
282C2×#107C2×D1112yes—
283C2×#107C2×D1112yes—
284C2×#106—111no—
285C2×#106—112no—
286C2×C4⋊C8—111no—
287C2×#103—111no—
288C2×#103—112no—
289C2×#102—111no—
290C2×#102—112no—
291C2×C22⋊C8—112no—
292C2×C4×C8C2×D1111yescharacteristic
293C22×C11#54712yes—
294C22×C11C2×#13712yes—
295C22×C11#57612yes—
296C22×C11C23×D411yescharacteristic
297C2×D11—24no—
298C2×D11—24no—
299C2×D11—24no—
300C2×D11—48no—
301C2×D11—42no—
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—84no—
305C4×C11—22no—
306C4×C11—44no—
307C4×C11—44no—
308C4×C11#54712yes—
309C4×C11C2×#13714yes—
310C4×C11C22×#4111yescharacteristic
311C4×C11C2×2−1+411yescharacteristic
312Dic11—24no—
313Dic11—42no—
314Dic11—42no—
315Dic11—42no—
316C22×Q8—21no—
317C22×Q8—21no—
318C22×Q8—111no—
319C22×D4—111no—
320C22×D4—111no—
321C22×D4—222no—
322C23×C4—112no—
323C23×C4—222no—
324C23×C4—221no—
325C2×SD16—114no—
326C2×SD16—224no—
327C2×M16—118no—
328C2×M16—228no—
329C22×C8—112no—
330C22×C8C22×D1111yescharacteristic
331C22×C8C22×D1111yescharacteristic
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8C22×D1114yes—
335C4⋊Q8C22×D1114yes—
336#125—228no—
337#124—2216no—
338C22⋊Q8—118no—
339C22⋊Q8—2216no—
340C22⋊Q8—224no—
341#121—118no—
342#121—224no—
343#121—228no—
344C4×Q8—114no—
345C4×Q8—222no—
346C4×D4—114no—
347C4×D4—114no—
348C4×D4—114no—
349C4×D4—228no—
350C4×D4—222no—
351#117—118no—
352#117—228no—
353#117—224no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—118no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4C22×D1112yes—
365C2×C4⋊C4C22×D1112yes—
366C2×C22⋊C4—112no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—222no—
370C2×C22⋊C4—221no—
371C2×C42—222no—
372C2×C42—221no—
373C2×C42C22×D1111yescharacteristic
374#107—118no—
375#107C22×D1118yes—
376#107C22×D1118yes—
377#106—114no—
378#106—118no—
379C4⋊C8—114no—
380#103—114no—
381#103—118no—
382#102—114no—
383#102—118no—
384C22⋊C8—118no—
385C4×C8C22×D1114yes—
386C2×C11#335714yescomplemented
387C2×C11C2×#54711yescharacteristic
388C2×C11C22×#13711yescharacteristic
389C2×C11C2×#57611yescharacteristic
390D11—44no—
391D11—82no—
392C24—112no—
393C24—221no—
394C2×Q8—24no—
395C2×Q8—24no—
396C2×Q8—82no—
397C2×Q8—82no—
398C2×Q8—112no—
399C2×Q8—221no—
400C2×Q8—222no—
401C2×Q8—222no—
402C2×D4—114no—
403C2×D4—112no—
404C2×D4—228no—
405C2×D4—224no—
406C2×D4—221no—
407C2×D4—222no—
408C2×D4—222no—
409C2×D4—884no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—112no—
413C22×C4—114no—
414C22×C4—114no—
415C22×C4—228no—
416C22×C4—224no—
417C22×C4—224no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—224no—
422C22×C4—444no—
423C22×C4—884no—
424C22×C4D4×D1111yescharacteristic
425C22×C4D4×D1111yescharacteristic
426C22×C4C23×D1111yescharacteristic
427SD16—228no—
428M16—2216no—
429C2×C8—22no—
430C2×C8—114no—
431C2×C8—224no—
432C2×C8#434314yes—
433C2×C8C23×D1112yes—
434C2×C8C23×D1112yes—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—114no—
440C4⋊C4—112no—
441C4⋊C4—112no—
442C4⋊C4—228no—
443C4⋊C4—228no—
444C4⋊C4—221no—
445C4⋊C4—221no—
446C4⋊C4—224no—
447C4⋊C4C23×D1114yes—
448C4⋊C4C23×D1114yes—
449C22⋊C4—118no—
450C22⋊C4—228no—
451C22⋊C4—228no—
452C22⋊C4—228no—
453C22⋊C4—224no—
454C42—228no—
455C42—224no—
456C42D4×D1112yes—
457C42C23×D1112yes—
458C11C2×#335711yescharacteristic, complemented, Sylow
459C23—114no—
460C23—224no—
461C23—224no—
462C23—224no—
463C23—222no—
464C23—442no—
465C23—442no—
466C23—442no—
467C23C2×D4×D1111yescharacteristic
468Q8—84no—
469Q8—84no—
470Q8—222no—
471Q8—222no—
472Q8—442no—
473D4—228no—
474D4—222no—
475D4—222no—
476D4—442no—
477D4—888no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4—114no—
484C2×C4—224no—
485C2×C4—228no—
486C2×C4—224no—
487C2×C4—224no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4—448no—
495C2×C4—888no—
496C2×C4#6697114yes—
497C2×C4C2×D4×D1112yes—
498C2×C4C2×D4×D1111yescharacteristic
499C2×C4C2×D4×D1112yes—
500C2×C4C2×#434312yes—
501C2×C4#6704012yes—
502C2×C4C24×D1111yescharacteristic
503C8—22no—
504C8—224no—
505C8C2×#434314yes—
506C22—224no—
507C22—224no—
508C22—224no—
509C22—448no—
510C22—442no—
511C22—442no—
512C22—442no—
513C22—884no—
514C22#1062325712yes—
515C22#1062328812yes—
516C22C2×#6697112yes—
517C22C22×D4×D1111yescharacteristic
518C4—22no—
519C4—44no—
520C4—44no—
521C4—224no—
522C4—442no—
523C4—442no—
524C4—442no—
525C4#1062325712yes—
526C4C2×#6697114yes—
527C4C22×#434311yescharacteristic
528C4C2×#6704011yescharacteristic
529C2—444no—
530C2—882no—
531C2#1308124114yesdirect product factor
532C2C2×#1062325711yescharacteristic
533C2C22×#6697111yescharacteristic
534C2C2×#1062328811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#500C2
socleC23×C11C22×D4
prime radicalC2×#10623265C2
hypercenterC2×#500D11
hypocenterC11C2×#3357
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
2. C2×#10623261C2semidirect
3. #13081241C2direct (N × H)
4. C2×#10622501C2semidirect
5. C2×#10622495C2semidirect
6. C2×#10622704C2semidirect
7. C2×#10622697C2semidirect
8. C2×#10622499C2semidirect
9. C2×C4×#4314C2semidirect
10. C2×#10622301C2semidirect
11. C2×#10622494C2semidirect
12. C2×C11×#500C2semidirect
22. #10623261C22semidirect
34. C11×#500C22semidirect
42. #10622704C22semidirect
43. #10622697C22semidirect
49. #10622501C22semidirect
50. #10622499C22semidirect
51. #10622495C22semidirect
52. #10622494C22semidirect
53. C4×#4314C22semidirect
54. #10622301C22semidirect
195. C2×#500D11semidirect
272. #500C2×D11semidirect
386. C2×C11#3357semidirect
458. C11C2×#3357semidirect
531. C2#13081241direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232652
C2×#106232612
#130812412
C2×#106225012
C2×#106224952
C2×#106227042
C2×#106226972
C2×#106224992
C2×C4×#43142
C2×#106223012
C2×#106224942
C2×C11×#5002
C2×#335711