Finite Group Databasebeta

← C2×#13081199 #15632476

Subgroups — C2×#13081199 #15632476

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×#10623263C211yesmaximal, characteristic, complemented
2C2×#10623257C211yesmaximal, characteristic
3#13081199C2116yesmaximal, direct product factor
4C2×#10622497C212yesmaximal, complemented
5C2×#10622498C212yesmaximal, complemented
6C2×#10622707C211yesmaximal, characteristic, complemented
7C2×#10622700C211yesmaximal, characteristic, complemented
8C2×#10622499C212yesmaximal, complemented
9C2×C4×#4314C211yesmaximal, characteristic, complemented
10C2×#10622301C211yesmaximal, characteristic, complemented
11C2×#10622494C212yesmaximal, complemented
12C2×C11×#500C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×#67000—21no—
17C2×#66999—21no—
18C2×Q8×Dic11—21no—
19C22×#4314C2211yescharacteristic
20C22×#4313C2212yes—
21#10623263—24no—
22#10623263C2218yescomplemented
23#10623257—24no—
24#10623257C2218yes—
25C2×#66951—22no—
26C2×#66950C2212yes—
27C2×#66948C2212yes—
28C2×#66947—22no—
29C2×#66945C2212yes—
30C2×C4⋊C4×D11C2212yes—
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#10622707C2218yescomplemented
43#10622700C2218yescomplemented
44C2×#66874C2212yes—
45C2×#66873C2212yes—
46C2×#66872C2212yes—
47C2×#66871C2212yes—
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622499C22116yescomplemented
50#10622498C22116yescomplemented
51#10622497C22116yescomplemented
52#10622494C22116yescomplemented
53C4×#4314C2218yescomplemented
54#10622301C2218yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11—21no—
57C2×#4343—28no—
58C2×#4343—48no—
59C22×D44—22no—
60C22×D44D411yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11—21no—
64C22×C4×D11C2312yes—
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8C2314yes—
71C11×C4⋊Q8C2314yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2312yes—
76C2×C42×C11C2311yescharacteristic
77#67000—28no—
78#66999—28no—
79Q8×Dic11—28no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4D412yes—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—22no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—22no—
93C22×C11⋊C8C2312yes—
94C2×#4314—24no—
95C2×#4314C2314yes—
96C2×#4313—28no—
97C2×#4313C2318yes—
98#66951—216no—
99#66950—24no—
100#66950C2318yes—
101#66948—24no—
102#66948C2318yes—
103#66947—216no—
104#66945—24no—
105#66945C2318yes—
106C4⋊C4×D11—24no—
107C4⋊C4×D11C2318yes—
108C4×D44—22no—
109C4×D44D414yes—
110C4×D44C2314yes—
111C4×D44C2314yes—
112C4×Dic22—22no—
113C4×Dic22C2314yes—
114C11×#107C2318yes—
115C11×#107C2318yes—
116C4×C8×C11C2314yes—
117#66885C2314yes—
118(C2×D11)⋊C8C2318yes—
119#66881C2314yes—
120#66880C2314yes—
121#66874C2318yes—
122#66873C2318yes—
123#66872C2318yes—
124#66871C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126C2×#3353—111nomaximal, Sylow
127C23×D11—21no—
128C23×D11C2×D412yes—
129C2×Q8×C11—24no—
130C2×Q8×C11—24no—
131C2×Q8×C11—44no—
132C2×Q8×C11—44no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C2×D412yes—
142#4343—432no—
143C2×D44—28no—
144C2×D44—24no—
145C2×D44—21no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—48no—
149C2×D44C2×D414yes—
150C2×D44C2412yes—
151C2×C4×D11—28no—
152C2×C4×D11—24no—
153C2×C4×D11—24no—
154C2×C4×D11—24no—
155C2×C4×D11—48no—
156C2×C4×D11—44no—
157C2×C4×D11C2×D414yes—
158C2×C4×D11C2414yes—
159C2×Dic22—21no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22C2412yes—
163C2×C8×C11—22no—
164C2×C8×C11#4114yescomplemented
165C2×C8×C11C2412yes—
166C2×C8×C11C2412yes—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4C2414yes—
172C11×C4⋊C4C2414yes—
173C42×C11C2×D412yes—
174C42×C11C2412yes—
175(C2×D11)⋊C4—28no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4—24no—
179(C2×D11)⋊C4C2×D418yes—
180C4⋊Dic11—28no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11C2×D414yes—
184C4⋊Dic11C2412yes—
185C4⋊Dic11C2412yes—
186Dic11⋊C4—28no—
187Dic11⋊C4—24no—
188C4×Dic11—28no—
189C4×Dic11—24no—
190C2×C11⋊C8—24no—
191C2×C11⋊C8C2414yes—
192#4314—28no—
193#4313—216no—
194C2×#556—111no—
195C2×#547—111no—
196#3353—1116no—
197C2×#500D1111yescharacteristic, complemented
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×C11C22×D411yescharacteristic
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—22no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11C22×D414yes—
215Q8×C11—48no—
216Q8×C11—48no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—44no—
221C2×C4×C11—44no—
222C2×C4×C11AGL(1,ℤ/8)14yes—
223C2×C4×C11C22×D412yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D412yes—
226C2×C4×C11C2×#4112yes—
227C2×C4×C112−1+412yes—
228C2×C4×C11C2511yescharacteristic
229C2×Dic11—24no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11C22×D414yes—
237D44—28no—
238D44—22no—
239D44—22no—
240D44—416no—
241D44—42no—
242C4×D11—28no—
243C4×D11—24no—
244C4×D11—24no—
245C4×D11—416no—
246C4×D11—48no—
247Dic22—22no—
248Dic22—22no—
249Dic22—42no—
250C8×C11—22no—
251C8×C11C2×#4114yescomplemented
252C11⋊C8—24no—
253C22×#41—221no—
254C22×SD16—111no—
255C22×M16—112no—
256#556—118no—
257#556—224no—
258#547—118no—
259#547—224no—
260C2×C4⋊Q8C2×D1111yescharacteristic
261C2×C4⋊Q8C2×D1111yescharacteristic
262C2×#126—222no—
263C2×#124—221no—
264C2×#123—222no—
265C2×C22⋊Q8—112no—
266C2×C22⋊Q8—221no—
267C2×#121—112no—
268C2×C4×Q8—111no—
269C2×C4×Q8—221no—
270C2×C4×D4—111no—
271C2×C4×D4—111no—
272C2×#117—112no—
273C22×C4⋊C4—112no—
274#500C2×D1118yescomplemented
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×#107C2×D1112yes—
285C2×#107C2×D1112yes—
286C2×#106—111no—
287C2×#106—112no—
288C2×C4⋊C8—111no—
289C2×#103—111no—
290C2×#103—112no—
291C2×#102—111no—
292C2×#102—112no—
293C2×C22⋊C8—112no—
294C2×C4×C8C2×D1111yescharacteristic
295C22×C11#54712yes—
296C22×C11C2×AGL(1,ℤ/8)12yes—
297C22×C11#57812yes—
298C22×C11C23×D411yescharacteristic
299C2×D11—24no—
300C2×D11—24no—
301C2×D11—24no—
302C2×D11—48no—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—84no—
307C4×C11—22no—
308C4×C11—44no—
309C4×C11—44no—
310C4×C11#54712yes—
311C4×C11C2×AGL(1,ℤ/8)14yes—
312C4×C11C22×#4111yescharacteristic
313C4×C11C2×2−1+411yescharacteristic
314Dic11—24no—
315Dic11—42no—
316Dic11—42no—
317Dic11—42no—
318C2×#41—228no—
319C2×#41—448no—
320C22×Q8—21no—
321C22×Q8—21no—
322C22×Q8—111no—
323C22×D4—111no—
324C22×D4—111no—
325C22×D4—222no—
326C23×C4—112no—
327C23×C4—222no—
328C23×C4—221no—
329C2×SD16—114no—
330C2×SD16—224no—
331C2×M16—118no—
332C2×M16—228no—
333C22×C8—112no—
334C22×C8C22×D1111yescharacteristic
335C22×C8C22×D1111yescharacteristic
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8C22×D1114yes—
339C4⋊Q8C22×D1114yes—
340#126—2216no—
341#124—228no—
342#123—2216no—
343C22⋊Q8—118no—
344C22⋊Q8—224no—
345C22⋊Q8—228no—
346#121—118no—
347#121—224no—
348C4×Q8—114no—
349C4×Q8—228no—
350C4×Q8—222no—
351C4×D4—114no—
352C4×D4—114no—
353C4×D4—114no—
354C4×D4—222no—
355#117—118no—
356#117—224no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—118no—
363C2×C4⋊C4—224no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22×D1112yes—
368C2×C4⋊C4C22×D1112yes—
369C2×C22⋊C4—112no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—221no—
374C2×C42—222no—
375C2×C42—221no—
376C2×C42C22×D1111yescharacteristic
377#107—118no—
378#107C22×D1118yes—
379#107C22×D1118yes—
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×C8C22×D1114yes—
389C2×C11#335314yescomplemented
390C2×C11C2×#54711yescharacteristic
391C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
392C2×C11C2×#57811yescharacteristic
393D11—44no—
394D11—82no—
395C24—112no—
396C24—221no—
397#41—4432no—
398C2×Q8—24no—
399C2×Q8—24no—
400C2×Q8—44no—
401C2×Q8—44no—
402C2×Q8—112no—
403C2×Q8—221no—
404C2×Q8—222no—
405C2×Q8—222no—
406C2×D4—114no—
407C2×D4—112no—
408C2×D4—228no—
409C2×D4—224no—
410C2×D4—221no—
411C2×D4—222no—
412C2×D4—222no—
413C2×D4—448no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—112no—
417C22×C4—114no—
418C22×C4—114no—
419C22×C4—228no—
420C22×C4—224no—
421C22×C4—224no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—224no—
426C22×C4—448no—
427C22×C4—444no—
428C22×C4D4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431SD16—228no—
432M16—2216no—
433C2×C8—22no—
434C2×C8—114no—
435C2×C8—224no—
436C2×C8#434314yescomplemented
437C2×C8C23×D1112yes—
438C2×C8C23×D1112yes—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—114no—
444C4⋊C4—112no—
445C4⋊C4—112no—
446C4⋊C4—228no—
447C4⋊C4—228no—
448C4⋊C4—221no—
449C4⋊C4—221no—
450C4⋊C4—224no—
451C4⋊C4C23×D1114yes—
452C4⋊C4C23×D1114yes—
453C22⋊C4—118no—
454C22⋊C4—228no—
455C22⋊C4—228no—
456C22⋊C4—228no—
457C22⋊C4—224no—
458C42—228no—
459C42—224no—
460C42D4×D1112yes—
461C42C23×D1112yes—
462C11C2×#335311yescharacteristic, complemented, Sylow
463C23—114no—
464C23—224no—
465C23—224no—
466C23—224no—
467C23—222no—
468C23—442no—
469C23—442no—
470C23—442no—
471C23C2×D4×D1111yescharacteristic
472Q8—48no—
473Q8—48no—
474Q8—222no—
475Q8—222no—
476Q8—442no—
477D4—228no—
478D4—222no—
479D4—222no—
480D4—4416no—
481D4—442no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—114no—
488C2×C4—224no—
489C2×C4—228no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—4416no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—448no—
500C2×C4#6696414yes—
501C2×C4C2×D4×D1112yes—
502C2×C4C2×D4×D1111yescharacteristic
503C2×C4C2×D4×D1112yes—
504C2×C4C2×#434312yes—
505C2×C4#6704012yes—
506C2×C4C24×D1111yescharacteristic
507C8—22no—
508C8—224no—
509C8C2×#434314yescomplemented
510C22—224no—
511C22—224no—
512C22—224no—
513C22—448no—
514C22—442no—
515C22—442no—
516C22—442no—
517C22—884no—
518C22#1062325712yes—
519C22C2×#6696412yes—
520C22#1062329712yes—
521C22C22×D4×D1111yescharacteristic
522C4—22no—
523C4—44no—
524C4—44no—
525C4—224no—
526C4—442no—
527C4—442no—
528C4—442no—
529C4#1062325712yes—
530C4C2×#6696414yes—
531C4C22×#434311yescharacteristic
532C4C2×#6704011yescharacteristic
533C2—444no—
534C2—882no—
535C2#1308119914yesdirect product factor
536C2C2×#1062325711yescharacteristic
537C2C22×#6696411yescharacteristic
538C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#500C2
socleC23×C11C22×D4
prime radicalC2×#10623257C2
hypercenterC2×#500D11
hypocenterC11C2×#3353
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
1. C2×#10623263C2semidirect
3. #13081199C2direct (N × H)
4. C2×#10622497C2semidirect
5. C2×#10622498C2semidirect
6. C2×#10622707C2semidirect
7. C2×#10622700C2semidirect
8. C2×#10622499C2semidirect
9. C2×C4×#4314C2semidirect
10. C2×#10622301C2semidirect
11. C2×#10622494C2semidirect
12. C2×C11×#500C2semidirect
22. #10623263C22semidirect
34. C11×#500C22semidirect
42. #10622707C22semidirect
43. #10622700C22semidirect
49. #10622499C22semidirect
50. #10622498C22semidirect
51. #10622497C22semidirect
52. #10622494C22semidirect
53. C4×#4314C22semidirect
54. #10622301C22semidirect
164. C2×C8×C11#41semidirect
197. C2×#500D11semidirect
251. C8×C11C2×#41semidirect
274. #500C2×D11semidirect
389. C2×C11#3353semidirect
436. C2×C8#4343semidirect
462. C11C2×#3353semidirect
509. C8C2×#4343semidirect
535. C2#13081199direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106232572
#130811992
C2×#106224972
C2×#106224982
C2×#106227072
C2×#106227002
C2×#106224992
C2×C4×#43142
C2×#106223012
C2×#106224942
C2×C11×#5002
C2×#335311