Finite Group Databasebeta

← C2×#13081200 #15632477

Subgroups — C2×#13081200 #15632477

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×#10623073C211yesmaximal, characteristic, complemented
2#13081200C2116yesmaximal, direct product factor
3C2×#10622691C211yesmaximal, characteristic, complemented
4C2×#10622583C212yesmaximal, complemented
5C2×#10622648C212yesmaximal, complemented
6C2×#10622707C211yesmaximal, characteristic, complemented
7C2×#10622620C211yesmaximal, characteristic, complemented
8C2×#10622655C212yesmaximal, complemented
9C2×C4×#4324C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622577C212yesmaximal, complemented
12C2×C11×#547C211yesmaximal, characteristic
13C22×C11×#41—21no—
14C11×#547—24no—
15C11×#547C2218yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#123—22no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×#121C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C22×C11×C4⋊C4C2212yes—
23C2×#66989—21no—
24C22×#4324C2211yescharacteristic
25C2×#66979C2212yes—
26C2×#66977C2212yes—
27C22×#4318C2212yes—
28#10623073—24no—
29#10623073C2218yescomplemented
30C2×#66940—21no—
31C2×#66932—22no—
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C2×#66896C2212yes—
35C2×#66896C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622707C2218yescomplemented
38#10622691C2218yescomplemented
39#10622655C22116yescomplemented
40#10622648C22116yescomplemented
41C4×#4324C2218yescomplemented
42#10622625C2218yescomplemented
43#10622620C2218yescomplemented
44#10622583C22116yescomplemented
45C2×#66874C2212yes—
46C2×#66874C2211yescharacteristic
47#10622577C22116yescomplemented
48C2×#66872C2212yes—
49C2×#66872C2211yescharacteristic
50C2×#66871C2212yes—
51C2×#66871C2212yes—
52C2×#66871C2212yes—
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C11×#41—28no—
56C2×C11×#41—48no—
57C22×Q8×C11—21no—
58C22×D4×C11—22no—
59C22×D4×C11D411yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—22no—
62C23×C4×C11—21no—
63C23×C4×C11C2312yes—
64C22×Dic22—21no—
65C22×Dic22C2311yescharacteristic
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8C2314yes—
68C11×#123—216no—
69C11×C22⋊Q8—28no—
70C11×#121—24no—
71C11×#121C2318yes—
72C4×D4×C11—22no—
73C4×D4×C11D414yes—
74C4×D4×C11C2314yes—
75C4×D4×C11C2314yes—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2318yes—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4D412yes—
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89#66989—28no—
90C2×#4324—24no—
91C2×#4324C2314yes—
92#66979—24no—
93#66979C2318yes—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2312yes—
97#66977—24no—
98#66977C2318yes—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—22no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—22no—
103C2×#4318—28no—
104C2×#4318C2318yes—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2312yes—
107C22×C11⋊C8C2311yescharacteristic
108#66940—28no—
109#66932—216no—
110#66922—22no—
111#66922C2314yes—
112C4×Dic22—22no—
113C4×Dic22C2314yes—
114#66896C2318yes—
115#66896C2314yes—
116C22⋊(C11⋊C8)C2318yes—
117#66874C2314yes—
118#66874C2318yes—
119#66872C2314yes—
120#66872C2318yes—
121#66871C2318yes—
122#66871C2318yes—
123#66871C2318yes—
124C4⋊(C11⋊C8)C2314yes—
125C4×C11⋊C8C2314yes—
126C2×#3353—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D412yes—
129C11×#41—432no—
130C2×Q8×C11—24no—
131C2×Q8×C11—44no—
132C2×D4×C11—28no—
133C2×D4×C11—24no—
134C2×D4×C11—21no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—48no—
138C2×D4×C11C2×D414yes—
139C2×D4×C11C2412yes—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—28no—
145C22×C4×C11—24no—
146C22×C4×C11—48no—
147C22×C4×C11—44no—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2414yes—
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C2×Dic22—21no—
158C2×Dic22—24no—
159C2×Dic22—22no—
160C2×Dic22—22no—
161C2×Dic22—44no—
162C2×Dic22C2412yes—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—28no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4C2×D414yes—
168C11×C4⋊C4C2412yes—
169C11×C4⋊C4C2414yes—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—28no—
172C11×C22⋊C4C2×D418yes—
173C42×C11C2×D412yes—
174C42×C11C2412yes—
175C22⋊Dic11—28no—
176C22⋊Dic11—28no—
177#4324—28no—
178C4⋊Dic11—21no—
179C4⋊Dic11—22no—
180C4⋊Dic11—24no—
181C4⋊Dic11C2414yes—
182C4⋊Dic11C2412yes—
183Dic11⋊C4—24no—
184Dic11⋊C4—28no—
185C4×Dic11—24no—
186C4×Dic11—28no—
187#4318—216no—
188C2×C11⋊C8—24no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8#4114yescomplemented
191C2×C11⋊C8C2412yes—
192C2×C11⋊C8C2414yes—
193C2×C11⋊C8C2412yes—
194C2×#556—111no—
195C2×#547D1111yescharacteristic
196#3353—1116no—
197C2×#500—111no—
198C2×#484—112no—
199C2×#482—112no—
200C2×#475—111no—
201C2×#474—111no—
202C2×#468—112no—
203C2×C4×SD16—111no—
204C2×#436—111no—
205C2×#428—112no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—22no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11C22×D414yes—
214C23×C11C22×D411yescharacteristic
215Q8×C11—48no—
216D4×C11—28no—
217D4×C11—22no—
218D4×C11—22no—
219D4×C11—416no—
220D4×C11—42no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—28no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—416no—
229C2×C4×C11—42no—
230C2×C4×C11—44no—
231C2×C4×C11—48no—
232C2×C4×C11AGL(1,ℤ/8)14yes—
233C2×C4×C11C22×D414yes—
234C2×C4×C11C22×D412yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D412yes—
237C2×C4×C11C2×#4112yes—
238C2×C4×C112−1+412yes—
239C2×C4×C11C2511yescharacteristic
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—42no—
244C2×Dic11—44no—
245C2×Dic11—42no—
246Dic22—22no—
247Dic22—22no—
248Dic22—42no—
249Dic22—48no—
250C11⋊C8—24no—
251C11⋊C8—22no—
252C11⋊C8C2×#4114yescomplemented
253C22×#41—21no—
254C22×SD16—111no—
255C22×M16—112no—
256#556—118no—
257#556—224no—
258#547—24no—
259#547C2×D1118yes—
260C2×C4⋊Q8—111no—
261C2×C4⋊Q8C2×D1111yescharacteristic
262C2×#126—222no—
263C2×#124—221no—
264C2×#123—22no—
265C2×C22⋊Q8—21no—
266C2×C22⋊Q8—112no—
267C2×#121C2×D1112yes—
268C2×C4×Q8—111no—
269C2×C4×Q8—221no—
270C2×C4×D4C2×D1111yescharacteristic
271C2×C4×D4C2×D1111yescharacteristic
272C2×#117—112no—
273C22×C4⋊C4C2×D1112yes—
274#500—118no—
275#484—1116no—
276#482—1116no—
277#475—118no—
278#474—118no—
279#468—1116no—
280C4×SD16—118no—
281#436—118no—
282#428—1116no—
283C2×#107—112no—
284C2×#107—112no—
285C2×#107—112no—
286C2×#106—112no—
287C2×#106—111no—
288C2×C4⋊C8—111no—
289C2×#103—112no—
290C2×#103—111no—
291C2×#102—111no—
292C2×#102—112no—
293C2×C22⋊C8—112no—
294C2×C4×C8—111no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—48no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—84no—
303C22×C11#54712yes—
304C22×C11C2×AGL(1,ℤ/8)12yes—
305C22×C11#57812yes—
306C22×C11C23×D411yescharacteristic
307C4×C11—24no—
308C4×C11—22no—
309C4×C11—42no—
310C4×C11—44no—
311C4×C11#54712yes—
312C4×C11C2×AGL(1,ℤ/8)14yes—
313C4×C11C22×#4111yescharacteristic
314C4×C11C2×2−1+411yescharacteristic
315Dic11—42no—
316Dic11—44no—
317Dic11—42no—
318C2×#41—28no—
319C2×#41—48no—
320C22×Q8—21no—
321C22×Q8—111no—
322C22×Q8—221no—
323C22×D4—22no—
324C22×D4C22⋊D1111yescharacteristic
325C22×D4C22×D1111yescharacteristic
326C23×C4—22no—
327C23×C4—21no—
328C23×C4C22×D1112yes—
329C2×SD16—114no—
330C2×SD16—224no—
331C2×M16—118no—
332C2×M16—228no—
333C22×C8—111no—
334C22×C8—112no—
335C22×C8—111no—
336C4⋊Q8—22no—
337C4⋊Q8—114no—
338C4⋊Q8—222no—
339C4⋊Q8C22×D1114yes—
340#126—2216no—
341#124—228no—
342#123—216no—
343C22⋊Q8—28no—
344C22⋊Q8—118no—
345C22⋊Q8—224no—
346#121—24no—
347#121C22×D1118yes—
348C4×Q8—114no—
349C4×Q8—228no—
350C4×Q8—222no—
351C4×D4—22no—
352C4×D4C22⋊D1114yes—
353C4×D4C22×D1114yes—
354C4×D4C22×D1114yes—
355#117—118no—
356#117—224no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4C22⋊D1111yescharacteristic
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1112yes—
368C2×C4⋊C4C22×D1118yes—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4C22⋊D1112yes—
374C2×C42—222no—
375C2×C42—221no—
376C2×C42C22×D1111yescharacteristic
377#107—118no—
378#107—118no—
379#107—118no—
380#106—114no—
381#106—118no—
382C4⋊C8—114no—
383#103—114no—
384#103—118no—
385#102—114no—
386#102—118no—
387C22⋊C8—118no—
388C4×C8—114no—
389C2×C11—44no—
390C2×C11—82no—
391C2×C11#335314yescomplemented
392C2×C11C2×#54711yescharacteristic
393C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
394C2×C11C2×#57811yescharacteristic
395C24—21no—
396C24C2×C22⋊D1112yes—
397#41—432no—
398C2×Q8—24no—
399C2×Q8—44no—
400C2×Q8—112no—
401C2×Q8—221no—
402C2×Q8—224no—
403C2×Q8—222no—
404C2×Q8—222no—
405C2×Q8—444no—
406C2×D4—28no—
407C2×D4—24no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—21no—
411C2×D4—48no—
412C2×D4C2×C22⋊D1114yes—
413C2×D4C23×D1112yes—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—28no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—48no—
421C22×C4—44no—
422C22×C4—221no—
423C22×C4—222no—
424C22×C4—221no—
425C22×C4C2×C22⋊D1114yes—
426C22×C4C2×C22⋊D1112yes—
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C23×D1114yes—
430C22×C4C23×D1111yescharacteristic
431SD16—228no—
432M16—2216no—
433C2×C8—114no—
434C2×C8—112no—
435C2×C8—112no—
436C2×C8—114no—
437C2×C8—224no—
438C2×C8—222no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—28no—
442C4⋊C4—24no—
443C4⋊C4—112no—
444C4⋊C4—114no—
445C4⋊C4—221no—
446C4⋊C4—222no—
447C4⋊C4—224no—
448C4⋊C4—228no—
449C4⋊C4—224no—
450C4⋊C4C2×C22⋊D1114yes—
451C4⋊C4C23×D1112yes—
452C4⋊C4C23×D1114yes—
453C22⋊C4—24no—
454C22⋊C4—28no—
455C22⋊C4—228no—
456C22⋊C4—228no—
457C22⋊C4C2×C22⋊D1118yes—
458C42—228no—
459C42—224no—
460C42C2×C22⋊D1112yes—
461C42C23×D1112yes—
462C11C2×#335311yescharacteristic, complemented, Sylow
463C23—24no—
464C23—24no—
465C23—24no—
466C23—22no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23C22×C22⋊D1114yes—
471C23C22×C22⋊D1111yescharacteristic
472Q8—48no—
473Q8—222no—
474Q8—222no—
475Q8—448no—
476Q8—442no—
477D4—28no—
478D4—22no—
479D4—22no—
480D4—416no—
481D4—42no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—28no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—416no—
490C2×C4—42no—
491C2×C4—44no—
492C2×C4—48no—
493C2×C4—222no—
494C2×C4—224no—
495C2×C4—222no—
496C2×C4—444no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4#6698514yes—
500C2×C4#41×D1112yes—
501C2×C4#6704312yes—
502C2×C4C22×C22⋊D1114yes—
503C2×C4C22×C22⋊D1112yes—
504C2×C4C22×C22⋊D1112yes—
505C2×C4C22×C22⋊D1111yescharacteristic
506C2×C4C24×D1111yescharacteristic
507C8—114no—
508C8—224no—
509C8—222no—
510C22—24no—
511C22—24no—
512C22—24no—
513C22—48no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—84no—
518C22C2×#6698512yes—
519C22#1062335512yes—
520C22#1062336912yes—
521C22C23×C22⋊D1111yescharacteristic
522C4—24no—
523C4—22no—
524C4—42no—
525C4—44no—
526C4—444no—
527C4—442no—
528C4—442no—
529C4C2×#6698514yes—
530C4#1062335512yes—
531C4C2×#41×D1111yescharacteristic
532C4C2×#6704311yescharacteristic
533C2—44no—
534C2—82no—
535C2#1308120014yesdirect product factor
536C2C2×#1062335511yescharacteristic
537C2C22×#6698511yescharacteristic
538C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11C2×#3353
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10623073C2semidirect
2. #13081200C2direct (N × H)
3. C2×#10622691C2semidirect
4. C2×#10622583C2semidirect
5. C2×#10622648C2semidirect
6. C2×#10622707C2semidirect
7. C2×#10622620C2semidirect
8. C2×#10622655C2semidirect
9. C2×C4×#4324C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622577C2semidirect
29. #10623073C22semidirect
37. #10622707C22semidirect
38. #10622691C22semidirect
39. #10622655C22semidirect
40. #10622648C22semidirect
41. C4×#4324C22semidirect
42. #10622625C22semidirect
43. #10622620C22semidirect
44. #10622583C22semidirect
47. #10622577C22semidirect
190. C2×C11⋊C8#41semidirect
252. C11⋊C8C2×#41semidirect
391. C2×C11#3353semidirect
462. C11C2×#3353semidirect
535. C2#13081200direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230732
#130812002
C2×#106226912
C2×#106225832
C2×#106226482
C2×#106227072
C2×#106226202
C2×#106226552
C2×C4×#43242
C2×#106226252
C2×#106225772
C2×C11×#5472
C2×#335311