Finite Group Databasebeta

← C2×#13081408 #15633460

Subgroups — C2×#13081408 #15633460

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic, complemented
2#13081408C2116yesmaximal, direct product factor
3C2×#10622702C212yesmaximal, complemented
4C2×#10622701C211yesmaximal, characteristic, complemented
5C2×#10622707C211yesmaximal, characteristic, complemented
6C2×#10622697C212yesmaximal, complemented
7C2×#10622629C212yesmaximal, complemented
8C2×#10622628C211yesmaximal, characteristic
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622627C212yesmaximal, complemented
11C2×C4×#4324C211yesmaximal, characteristic, complemented
12C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
13C23×Q8×C11—21no—
14D4×Q8×C11—24no—
15D4×Q8×C11C2218yescomplemented
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8—22no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2212yes—
23C2×#67000—21no—
24C22×#4324C2211yescharacteristic
25C22×#4323C2212yes—
26#10623116—24no—
27#10623116C2218yescomplemented
28C2×#66947—22no—
29C2×#66946—21no—
30C2×#66928C2212yes—
31C2×#66927C2211yescharacteristic
32C2×C4×D44C2212yes—
33C2×C4×Dic22C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622707C2218yescomplemented
36#10622702C22116yescomplemented
37#10622701C2218yescomplemented
38#10622697C22116yescomplemented
39#10622637C2218yescomplemented
40C4×#4324C2218yescomplemented
41#10622629C22116yescomplemented
42#10622628C2218yes—
43#10622627C22116yescomplemented
44C2×#66874C2212yes—
45C2×#66874C2211yescharacteristic
46C2×#66873C2212yes—
47C2×#66873C2212yes—
48C2×#66873C2212yes—
49C2×#66872C2211yescharacteristic
50C2×#66872C2212yes—
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—28no—
56C22×Q8×C11—22no—
57C22×Q8×C11—21no—
58C22×Q8×C11—48no—
59C22×Q8×C11D411yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—22no—
62C23×C4×C11—21no—
63C22×D44—21no—
64C22×D44—21no—
65C22×D44C2312yes—
66C22×C4×D11—22no—
67C22×Dic22C2311yescharacteristic
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—24no—
70C11×C4⋊Q8C2318yes—
71C11×C4⋊Q8C2314yes—
72C11×C22⋊Q8—28no—
73C11×C22⋊Q8—216no—
74C4×Q8×C11D414yes—
75C4×Q8×C11C2314yes—
76C4×D4×C11—22no—
77C4×D4×C11—24no—
78C4×D4×C11C2318yes—
79C4×D4×C11C2314yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D412yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2312yes—
90#67000—28no—
91C2×#4324—24no—
92C2×#4324C2314yes—
93C2×#4323—28no—
94C2×#4323C2318yes—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2312yes—
104#66947—216no—
105#66946—28no—
106#66928—24no—
107#66928C2318yes—
108#66927—22no—
109#66927C2314yes—
110C4×D44—24no—
111C4×D44C2318yes—
112C4×Dic22—22no—
113C4×Dic22C2314yes—
114#66896C2314yes—
115#66874C2318yes—
116#66874C2314yes—
117#66873C2318yes—
118#66873C2318yes—
119#66873C2318yes—
120#66872C2318yes—
121#66872C2314yes—
122C4⋊(C11⋊C8)C2314yes—
123C4⋊(C11⋊C8)C2318yes—
124#66867C2318yes—
125C4×C11⋊C8C2314yes—
126C2×#3373—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11—22no—
129C2×Q8×C11—24no—
130C2×Q8×C11—28no—
131C2×Q8×C11—24no—
132C2×Q8×C11—48no—
133C2×Q8×C11—432no—
134C2×Q8×C11—44no—
135C2×Q8×C11C2×D414yes—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11#4114yes—
139C2×D4×C11C2412yes—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—28no—
143C22×C4×C11—24no—
144C22×C4×C11—48no—
145C22×C4×C11—44no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C2×D44—22no—
154C2×D44—24no—
155C2×D44—24no—
156C2×D44—24no—
157C2×D44—24no—
158C2×D44—44no—
159C2×D44—82no—
160C2×D44C2414yes—
161C2×C4×D11—28no—
162C2×C4×D11—84no—
163C2×Dic22—21no—
164C2×Dic22—22no—
165C2×Dic22—22no—
166C2×Dic22C2412yes—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4C2×D414yes—
172C11×C4⋊C4C2×D418yes—
173C11×C4⋊C4C2414yes—
174C11×C4⋊C4C2412yes—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—28no—
177C42×C11C2×D412yes—
178C42×C11C2×D414yes—
179C42×C11C2412yes—
180C42×C11C2414yes—
181#4324—28no—
182#4323—216no—
183(C2×D11)⋊C4—28no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—28no—
186C4⋊Dic11—21no—
187C4⋊Dic11C2412yes—
188Dic11⋊C4—24no—
189C4×Dic11—24no—
190C2×C11⋊C8—24no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8C2412yes—
194C2×C11⋊C8C2412yes—
195C2×C11⋊C8C2414yes—
196C2×#559—111no—
197C2×D4×Q8D1111yescharacteristic, complemented
198#3373—1116no—
199C2×#489—112no—
200C2×#486—111no—
201C2×#475—111no—
202C2×#476—112no—
203C2×#463—112no—
204C2×#459—111no—
205C2×#446—111no—
206C2×#442—112no—
207C2×C4×SD16—111no—
208C23×C11—24no—
209C23×C11—22no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11C22×D411yescharacteristic
213C22×D11—24no—
214C22×D11—44no—
215C22×D11—44no—
216C22×D11—44no—
217Q8×C11—28no—
218Q8×C11—416no—
219Q8×C11—48no—
220D4×C11—24no—
221D4×C11—22no—
222D4×C11C2×#4114yes—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—416no—
229C2×C4×C11—44no—
230C2×C4×C11—42no—
231C2×C4×C11—48no—
232C2×C4×C11AGL(1,ℤ/8)14yes—
233C2×C4×C11C22×D412yes—
234C2×C4×C11C22×D414yes—
235C2×C4×C11C22×D414yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D412yes—
238C2×C4×C11C2×#4112yes—
239C2×C4×C112−1+412yes—
240C2×C4×C11C2511yescharacteristic
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245D44—24no—
246D44—24no—
247D44—44no—
248D44—48no—
249D44—84no—
250C4×D11—88no—
251Dic22—22no—
252Dic22—22no—
253Dic22—42no—
254C11⋊C8—24no—
255C11⋊C8—22no—
256C11⋊C8—22no—
257C23×Q8—21no—
258C22×SD16—111no—
259C22×D8—112no—
260#559—118no—
261#559—224no—
262D4×Q8—24no—
263D4×Q8C2×D1118yescomplemented
264C2×C4⋊Q8C2×D1111yescharacteristic
265C2×C4⋊Q8C2×D1112yes—
266C2×#127—111no—
267C2×#124—112no—
268C2×#124—221no—
269C2×#123—222no—
270C2×C22⋊Q8—21no—
271C2×C22⋊Q8—22no—
272C2×C4×Q8—111no—
273C2×C4×Q8C2×D1111yescharacteristic
274C2×C4×D4—112no—
275C2×C4×D4—221no—
276C2×C4×D4C2×D1111yescharacteristic
277C2×C4×D4C2×D1112yes—
278#489—1116no—
279#486—118no—
280#476—1116no—
281#475—118no—
282#463—1116no—
283#459—118no—
284#446—118no—
285#442—1116no—
286C4×SD16—118no—
287C2×#106—112no—
288C2×#106—111no—
289C2×C4⋊C8—111no—
290C2×C4⋊C8—112no—
291C2×#103—112no—
292C2×#103—111no—
293C2×#102—111no—
294C2×#102—112no—
295C2×#102—112no—
296C2×#102—112no—
297C2×#97—112no—
298C2×C4×C8—111no—
299C22×C11—24no—
300C22×C11—48no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11#54812yes—
304C22×C11C2×AGL(1,ℤ/8)12yes—
305C22×C11#57712yes—
306C22×C11C23×D411yescharacteristic
307C2×D11—44no—
308C2×D11—44no—
309C2×D11—44no—
310C2×D11—88no—
311C4×C11—24no—
312C4×C11—24no—
313C4×C11—22no—
314C4×C11—44no—
315C4×C11—42no—
316C4×C11#54812yes—
317C4×C11C2×AGL(1,ℤ/8)14yes—
318C4×C11C22×#4111yescharacteristic
319C4×C11C2×2−1+411yescharacteristic
320Dic11—42no—
321Dic11—42no—
322C22×Q8—28no—
323C22×Q8—22no—
324C22×Q8—21no—
325C22×Q8—48no—
326C22×Q8—111no—
327C22×Q8C22⋊D1111yescharacteristic
328C22×D4—112no—
329C22×D4—221no—
330C22×D4—221no—
331C22×D4C22×D1111yescharacteristic
332C23×C4—22no—
333C23×C4—21no—
334C23×C4—222no—
335C2×SD16—114no—
336C2×SD16—224no—
337C2×D8—118no—
338C2×D8—228no—
339C22×C8—112no—
340C22×C8—111no—
341C22×C8—111no—
342C4⋊Q8—24no—
343C4⋊Q8—22no—
344C4⋊Q8C22×D1114yes—
345C4⋊Q8C22×D1118yes—
346#127—114no—
347#127—222no—
348#124—118no—
349#124—228no—
350#124—224no—
351#123—2216no—
352C22⋊Q8—28no—
353C22⋊Q8—216no—
354C4×Q8—114no—
355C4×Q8—222no—
356C4×Q8C22⋊D1114yes—
357C4×Q8C22×D1114yes—
358C4×D4—24no—
359C4×D4—22no—
360C4×D4—118no—
361C4×D4—228no—
362C4×D4—224no—
363C4×D4C22×D1114yes—
364C4×D4C22×D1118yes—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4C22⋊D1111yescharacteristic
370C2×C4⋊C4C22⋊D1112yes—
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1112yes—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—222no—
378C2×C42—221no—
379C2×C42C22×D1112yes—
380C2×C42C22×D1111yescharacteristic
381#106—114no—
382#106—118no—
383C4⋊C8—114no—
384C4⋊C8—118no—
385#103—114no—
386#103—118no—
387#102—114no—
388#102—118no—
389#102—118no—
390#102—118no—
391#97—118no—
392C4×C8—114no—
393C2×C11—44no—
394C2×C11#337314yescomplemented
395C2×C11C2×#54811yescharacteristic
396C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
397C2×C11C2×#57711yescharacteristic
398D11—84no—
399C24—21no—
400C24—222no—
401C2×Q8—24no—
402C2×Q8—28no—
403C2×Q8—24no—
404C2×Q8—48no—
405C2×Q8—432no—
406C2×Q8—44no—
407C2×Q8—112no—
408C2×Q8—221no—
409C2×Q8—222no—
410C2×Q8—222no—
411C2×Q8C2×C22⋊D1114yes—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4—114no—
415C2×D4—224no—
416C2×D4—224no—
417C2×D4—224no—
418C2×D4—222no—
419C2×D4—224no—
420C2×D4—444no—
421C2×D4—882no—
422C2×D4#434314yes—
423C2×D4C23×D1112yes—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—28no—
427C22×C4—24no—
428C22×C4—48no—
429C22×C4—44no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—228no—
433C22×C4—884no—
434C22×C4C2×C22⋊D1112yes—
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1112yes—
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439SD16—228no—
440D8—2216no—
441C2×C8—112no—
442C2×C8—112no—
443C2×C8—114no—
444C2×C8—224no—
445C2×C8—222no—
446C2×C8—222no—
447C4⋊C4—28no—
448C4⋊C4—24no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—112no—
452C4⋊C4—221no—
453C4⋊C4—224no—
454C4⋊C4C2×C22⋊D1114yes—
455C4⋊C4C2×C22⋊D1118yes—
456C4⋊C4C23×D1114yes—
457C4⋊C4C23×D1112yes—
458C22⋊C4—28no—
459C22⋊C4—24no—
460C22⋊C4—228no—
461C22⋊C4—228no—
462C22⋊C4—228no—
463C42—224no—
464C42C2×C22⋊D1114yes—
465C42C2×C22⋊D1112yes—
466C42C23×D1112yes—
467C42C23×D1114yes—
468C11C2×#337311yescharacteristic, complemented, Sylow
469C23—24no—
470C23—22no—
471C23—42no—
472C23—42no—
473C23—224no—
474C23—444no—
475C23—444no—
476C23—444no—
477C23C22×C22⋊D1111yescharacteristic
478Q8—28no—
479Q8—416no—
480Q8—48no—
481Q8—222no—
482Q8—222no—
483Q8—442no—
484D4—24no—
485D4—22no—
486D4—224no—
487D4—224no—
488D4—448no—
489D4—444no—
490D4—884no—
491D4C2×#434314yes—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—416no—
498C2×C4—44no—
499C2×C4—42no—
500C2×C4—48no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—888no—
506C2×C4#6698514yes—
507C2×C4C2×#434312yes—
508C2×C4#6704012yes—
509C2×C4C22×C22⋊D1114yes—
510C2×C4C22×C22⋊D1112yes—
511C2×C4C22×C22⋊D1114yes—
512C2×C4C22×C22⋊D1112yes—
513C2×C4C22×C22⋊D1111yescharacteristic
514C2×C4C24×D1111yescharacteristic
515C8—224no—
516C8—222no—
517C8—222no—
518C22—24no—
519C22—48no—
520C22—42no—
521C22—42no—
522C22—444no—
523C22—444no—
524C22—444no—
525C22—888no—
526C22C2×#6698512yes—
527C22#1062334812yes—
528C22#1062336812yes—
529C22C23×C22⋊D1111yescharacteristic
530C4—24no—
531C4—24no—
532C4—22no—
533C4—44no—
534C4—42no—
535C4—442no—
536C4—442no—
537C4C2×#6698514yes—
538C4#1062334812yes—
539C4C22×#434311yescharacteristic
540C4C2×#6704011yescharacteristic
541C2—44no—
542C2—884no—
543C2#1308140814yesdirect product factor
544C2C2×#1062334811yescharacteristic
545C2C22×#6698511yescharacteristic
546C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×D4×Q8×C11C2
socleC23×C11C22×D4
prime radicalC2×#10622628C2
hypercenterC2×D4×Q8D11
hypocenterC11C2×#3373
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
2. #13081408C2direct (N × H)
3. C2×#10622702C2semidirect
4. C2×#10622701C2semidirect
5. C2×#10622707C2semidirect
6. C2×#10622697C2semidirect
7. C2×#10622629C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622627C2semidirect
11. C2×C4×#4324C2semidirect
12. C2×D4×Q8×C11C2semidirect
15. D4×Q8×C11C22semidirect
27. #10623116C22semidirect
35. #10622707C22semidirect
36. #10622702C22semidirect
37. #10622701C22semidirect
38. #10622697C22semidirect
39. #10622637C22semidirect
40. C4×#4324C22semidirect
41. #10622629C22semidirect
43. #10622627C22semidirect
197. C2×D4×Q8D11semidirect
263. D4×Q8C2×D11semidirect
394. C2×C11#3373semidirect
468. C11C2×#3373semidirect
543. C2#13081408direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
#130814082
C2×#106227022
C2×#106227012
C2×#106227072
C2×#106226972
C2×#106226292
C2×#106226282
C2×#106226372
C2×#106226272
C2×C4×#43242
C2×D4×Q8×C112
C2×#337311