Finite Group Databasebeta

← C2×#13081202 #15632479

Subgroups — C2×#13081202 #15632479

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic, complemented
2C2×#10623082C211yesmaximal, characteristic
3#13081202C2116yesmaximal, direct product factor
4C2×#10622295C211yesmaximal, characteristic, complemented
5C2×#10622422C212yesmaximal, complemented
6C2×#10622397C212yesmaximal, complemented
7C2×#10622633C211yesmaximal, characteristic, complemented
8C2×#10622620C211yesmaximal, characteristic, complemented
9C2×#10622787C212yesmaximal, complemented
10C2×#10622301C211yesmaximal, characteristic, complemented
11C2×#10622474C212yesmaximal, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C22×C11×SD16C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66999C2212yes—
18C2×#66991C2212yes—
19C2×#66977—21no—
20C22×#4313C2212yes—
21#10623115—24no—
22#10623115C2218yescomplemented
23#10623082—24no—
24#10623082C2218yes—
25C2×#66951—22no—
26C2×#66945C2212yes—
27C2×C4⋊C4×D11C2212yes—
28C2×#66936—22no—
29C2×#66928—21no—
30C2×C4×D44C2211yescharacteristic
31C2×#66922C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22—21no—
34C4×C11×SD16C2218yescomplemented
35C2×C11×#106C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66899C2212yes—
40C2×#66896C2212yes—
41#10622787C22116yescomplemented
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66882C2212yes—
44C2×#66882C2212yes—
45#10622633C2218yescomplemented
46#10622620C2218yescomplemented
47C2×#66872C2212yes—
48C2×#66871C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622474C22116yescomplemented
51#10622422C22116yescomplemented
52#10622397C22116yescomplemented
53#10622301C2218yescomplemented
54#10622295C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C2×#4339—28no—
60C2×#4339—48no—
61C22×D44D411yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11C2312yes—
64C22×Dic22—21no—
65C22×Dic22—21no—
66C2×C11×SD16—24no—
67C2×C11×SD16C2314yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×Q8×C11—22no—
71C4×Q8×C11C2314yes—
72C4×D4×C11—22no—
73C4×D4×C11C2314yes—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—22no—
81#66999—24no—
82#66999C2318yes—
83#66991—24no—
84#66991C2318yes—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4D412yes—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2312yes—
93#66977—28no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×C4×Dic11—22no—
97C22×C11⋊C8C2312yes—
98C2×#4313—28no—
99C2×#4313C2318yes—
100#66951—216no—
101#66945—24no—
102#66945C2318yes—
103C4⋊C4×D11—24no—
104C4⋊C4×D11C2318yes—
105#66936—216no—
106#66928—28no—
107C4×D44D414yes—
108C4×D44C2314yes—
109#66922—22no—
110#66922—22no—
111#66922C2314yes—
112#66922C2314yes—
113C4×Dic22—28no—
114C11×#106C2314yes—
115C11×#103C2314yes—
116C11×#102C2314yes—
117C4×C8×C11C2314yes—
118#66899C2318yes—
119#66896C2318yes—
120(C2×D11)⋊C8C2318yes—
121#66882C2318yes—
122#66882C2318yes—
123#66872C2318yes—
124#66871C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126C2×#3353—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11C2×D412yes—
129C2×Q8×C11—21no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11C2412yes—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11C2412yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—24no—
141C22×C4×C11—44no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—28no—
146C2×C22⋊D11—48no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11C2×D412yes—
150#4339—432no—
151C2×D44—24no—
152C2×D44C2×D414yes—
153C2×C4×D11—28no—
154C2×C4×D11—24no—
155C2×C4×D11—24no—
156C2×C4×D11—48no—
157C2×C4×D11C2×D414yes—
158C2×C4×D11C2414yes—
159C2×Dic22—24no—
160C2×Dic22—24no—
161C2×Dic22—44no—
162C2×Dic22—44no—
163C11×SD16—28no—
164C2×C8×C11—22no—
165C2×C8×C11#4114yescomplemented
166C2×C8×C11C2412yes—
167C2×C8×C11C2412yes—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4C2412yes—
172C11×C4⋊C4C2412yes—
173C11×C22⋊C4—24no—
174C42×C11—24no—
175C42×C11C2×D412yes—
176C42×C11C2412yes—
177C22⋊Dic11—28no—
178(C2×D11)⋊C4—28no—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4C2×D418yes—
181C4⋊Dic11—22no—
182C4⋊Dic11—22no—
183C4⋊Dic11—24no—
184C4⋊Dic11—24no—
185C4⋊Dic11C2×D414yes—
186C4⋊Dic11C2414yes—
187C4⋊Dic11C2414yes—
188Dic11⋊C4—28no—
189Dic11⋊C4—28no—
190C4×Dic11—28no—
191C2×C11⋊C8—24no—
192C2×C11⋊C8C2414yes—
193#4313—216no—
194C2×#556—111no—
195C2×#547—111no—
196#3353—1116no—
197C2×#500—111no—
198C2×#484—112no—
199C2×#482—112no—
200C2×#475—111no—
201C2×#474—111no—
202C2×#468—112no—
203C2×C4×SD16D1111yescharacteristic, complemented
204C2×#436—111no—
205C2×#428—112no—
206C23×C11—22no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11C22×D411yescharacteristic
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11C22×D414yes—
215Q8×C11—22no—
216Q8×C11—22no—
217Q8×C11—42no—
218D4×C11—22no—
219D4×C11—22no—
220D4×C11—42no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—48no—
229C2×C4×C11AGL(1,ℤ/8)14yes—
230C2×C4×C11C22×D412yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D412yes—
233C2×C4×C11C2×#4112yes—
234C2×C4×C112−1+412yes—
235C2×C4×C11C2511yescharacteristic
236C22⋊D11—416no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—44no—
241C2×Dic11—44no—
242C2×Dic11C22×D414yes—
243D44—28no—
244C4×D11—28no—
245C4×D11—24no—
246C4×D11—24no—
247C4×D11—416no—
248Dic22—48no—
249Dic22—48no—
250C8×C11—22no—
251C8×C11C2×#4114yescomplemented
252C11⋊C8—24no—
253C22×#41—221no—
254C22×SD16C2×D1111yescharacteristic
255C22×M16—112no—
256#556—118no—
257#556—224no—
258#547—118no—
259#547—224no—
260C2×C4⋊Q8—111no—
261C2×C4⋊Q8—111no—
262C2×#126—222no—
263C2×#124—221no—
264C2×#123—222no—
265C2×C22⋊Q8—112no—
266C2×C22⋊Q8—221no—
267C2×#121—112no—
268C2×C4×Q8—221no—
269C2×C4×Q8C2×D1111yescharacteristic
270C2×C4×D4—111no—
271C2×C4×D4C2×D1111yescharacteristic
272C2×#117—112no—
273C22×C4⋊C4—112no—
274#500—118no—
275#484—1116no—
276#482—1116no—
277#475—118no—
278#474—118no—
279#468—1116no—
280C4×SD16C2×D1118yescomplemented
281#436—118no—
282#428—1116no—
283C2×#107—112no—
284C2×#107—112no—
285C2×#107—112no—
286C2×#106—112no—
287C2×#106C2×D1111yescharacteristic
288C2×C4⋊C8—111no—
289C2×#103—112no—
290C2×#103C2×D1111yescharacteristic
291C2×#102—112no—
292C2×#102C2×D1111yescharacteristic
293C2×C22⋊C8—112no—
294C2×C4×C8C2×D1111yescharacteristic
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—84no—
299C22×C11#54712yes—
300C22×C11C2×AGL(1,ℤ/8)12yes—
301C22×C11#57812yes—
302C22×C11C23×D411yescharacteristic
303C2×D11—24no—
304C2×D11—24no—
305C2×D11—24no—
306C2×D11—48no—
307C4×C11—22no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11#54712yes—
312C4×C11C2×AGL(1,ℤ/8)14yes—
313C4×C11C22×#4111yescharacteristic
314C4×C11C2×2−1+411yescharacteristic
315Dic11—24no—
316Dic11—44no—
317Dic11—44no—
318C2×#41—228no—
319C2×#41—448no—
320C22×Q8—221no—
321C22×Q8—221no—
322C22×Q8C22×D1111yescharacteristic
323C22×D4—111no—
324C22×D4—222no—
325C22×D4C22×D1111yescharacteristic
326C23×C4—21no—
327C23×C4—112no—
328C23×C4—222no—
329C2×SD16—24no—
330C2×SD16C22×D1114yes—
331C2×M16—118no—
332C2×M16—228no—
333C22×C8—112no—
334C22×C8C22×D1111yescharacteristic
335C22×C8C22×D1111yescharacteristic
336C4⋊Q8—114no—
337C4⋊Q8—114no—
338C4⋊Q8—222no—
339C4⋊Q8—222no—
340#126—2216no—
341#124—228no—
342#123—2216no—
343C22⋊Q8—118no—
344C22⋊Q8—228no—
345C22⋊Q8—224no—
346#121—118no—
347#121—224no—
348C4×Q8—22no—
349C4×Q8—228no—
350C4×Q8C22×D1114yes—
351C4×D4—22no—
352C4×D4—114no—
353C4×D4—114no—
354C4×D4C22×D1114yes—
355#117—118no—
356#117—224no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—118no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—112no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—222no—
374C2×C42—21no—
375C2×C42—222no—
376C2×C42C22×D1111yescharacteristic
377#107—118no—
378#107—118no—
379#107—118no—
380#106—118no—
381#106C22×D1114yes—
382C4⋊C8—114no—
383#103—118no—
384#103C22×D1114yes—
385#102—118no—
386#102C22×D1114yes—
387C22⋊C8—118no—
388C4×C8C22×D1114yes—
389C2×C11—82no—
390C2×C11#335314yescomplemented
391C2×C11C2×#54711yescharacteristic
392C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
393C2×C11C2×#57811yescharacteristic
394D11—44no—
395C24—21no—
396C24—112no—
397#41—4432no—
398C2×Q8—21no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—224no—
402C2×Q8—224no—
403C2×Q8—444no—
404C2×Q8—444no—
405C2×Q8C23×D1112yes—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4—22no—
409C2×D4—114no—
410C2×D4—228no—
411C2×D4—224no—
412C2×D4—448no—
413C2×D4C23×D1112yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—24no—
418C22×C4—44no—
419C22×C4—112no—
420C22×C4—114no—
421C22×C4—114no—
422C22×C4—228no—
423C22×C4—224no—
424C22×C4—224no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—448no—
428C22×C4D4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431SD16—28no—
432M16—2216no—
433C2×C8—22no—
434C2×C8—114no—
435C2×C8—224no—
436C2×C8#433914yescomplemented
437C2×C8C23×D1112yes—
438C2×C8C23×D1112yes—
439C4⋊C4—24no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—114no—
443C4⋊C4—114no—
444C4⋊C4—114no—
445C4⋊C4—228no—
446C4⋊C4—228no—
447C4⋊C4—222no—
448C4⋊C4—222no—
449C4⋊C4—224no—
450C4⋊C4—224no—
451C4⋊C4C23×D1112yes—
452C4⋊C4C23×D1112yes—
453C22⋊C4—24no—
454C22⋊C4—118no—
455C22⋊C4—228no—
456C22⋊C4—228no—
457C22⋊C4—228no—
458C42—24no—
459C42—228no—
460C42D4×D1112yes—
461C42C23×D1112yes—
462C11C2×#335311yescharacteristic, complemented, Sylow
463C23—22no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—114no—
468C23—224no—
469C23—224no—
470C23—224no—
471C23C2×D4×D1111yescharacteristic
472Q8—22no—
473Q8—22no—
474Q8—42no—
475Q8—448no—
476Q8—448no—
477D4—22no—
478D4—22no—
479D4—42no—
480D4—228no—
481D4—4416no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—48no—
490C2×C4—114no—
491C2×C4—224no—
492C2×C4—228no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—4416no—
498C2×C4—444no—
499C2×C4—444no—
500C2×C4#6696714yes—
501C2×C4C2×#433912yes—
502C2×C4C2×D4×D1112yes—
503C2×C4C2×D4×D1112yes—
504C2×C4C2×D4×D1111yescharacteristic
505C2×C4#6704312yes—
506C2×C4C24×D1111yescharacteristic
507C8—22no—
508C8—224no—
509C8C2×#433914yescomplemented
510C22—42no—
511C22—42no—
512C22—42no—
513C22—84no—
514C22—224no—
515C22—224no—
516C22—224no—
517C22—448no—
518C22#1062308212yes—
519C22C2×#6696712yes—
520C22#1062330212yes—
521C22C22×D4×D1111yescharacteristic
522C4—22no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—224no—
527C4—444no—
528C4—444no—
529C4#1062308212yes—
530C4C2×#6696714yes—
531C4C22×#433911yescharacteristic
532C4C2×#6704311yescharacteristic
533C2—82no—
534C2—444no—
535C2#1308120214yesdirect product factor
536C2C2×#1062308211yescharacteristic
537C2C22×#6696711yescharacteristic
538C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10623082C2
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3353
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×#10623115C2semidirect
3. #13081202C2direct (N × H)
4. C2×#10622295C2semidirect
5. C2×#10622422C2semidirect
6. C2×#10622397C2semidirect
7. C2×#10622633C2semidirect
8. C2×#10622620C2semidirect
9. C2×#10622787C2semidirect
10. C2×#10622301C2semidirect
11. C2×#10622474C2semidirect
12. C2×C4×C11×SD16C2semidirect
22. #10623115C22semidirect
34. C4×C11×SD16C22semidirect
41. #10622787C22semidirect
45. #10622633C22semidirect
46. #10622620C22semidirect
50. #10622474C22semidirect
51. #10622422C22semidirect
52. #10622397C22semidirect
53. #10622301C22semidirect
54. #10622295C22semidirect
165. C2×C8×C11#41semidirect
203. C2×C4×SD16D11semidirect
251. C8×C11C2×#41semidirect
280. C4×SD16C2×D11semidirect
390. C2×C11#3353semidirect
436. C2×C8#4339semidirect
462. C11C2×#3353semidirect
509. C8C2×#4339semidirect
535. C2#13081202direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×#106230822
#130812022
C2×#106222952
C2×#106224222
C2×#106223972
C2×#106226332
C2×#106226202
C2×#106227872
C2×#106223012
C2×#106224742
C2×C4×C11×SD162
C2×#335311