Finite Group Databasebeta

← C2×#13081407 #15633459

Subgroups — C2×#13081407 #15633459

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
2C2×#10623258C211yesmaximal, characteristic, complemented
3#13081407C2116yesmaximal, direct product factor
4C2×#10622408C212yesmaximal, complemented
5C2×#10622701C211yesmaximal, characteristic, complemented
6C2×#10622483C212yesmaximal, complemented
7C2×#10622432C212yesmaximal, complemented
8C2×#10622456C211yesmaximal, characteristic
9C2×#10622444C211yesmaximal, characteristic, complemented
10C2×#10622482C212yesmaximal, complemented
11C2×C4×#4325C211yesmaximal, characteristic, complemented
12C2×C11×#475C211yesmaximal, characteristic, complemented
13C22×Q8×D11—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×#67000C2212yes—
17C2×#66999—21no—
18C22×#4325C2211yescharacteristic
19C22×D88C2212yes—
20#10623258—24no—
21#10623258C2218yescomplemented
22#10623116—24no—
23#10623116C2218yescomplemented
24C2×#66949—22no—
25C2×#66947—22no—
26C2×#66946C2212yes—
27C2×#66946C2212yes—
28C2×#66941C2212yes—
29C2×#66928—21no—
30C2×#66927C2211yescharacteristic
31C2×C4×D44—21no—
32C2×C4×D44C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#475C2218yescomplemented
35C2×C11×#106C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#103C2212yes—
38C2×#66899C2211yescharacteristic
39C2×#66885C2212yes—
40C2×#66879C2212yes—
41C2×Dic11⋊C8C2212yes—
42#10622701C2218yescomplemented
43C4×#4325C2218yescomplemented
44C2×#66873C2212yes—
45C2×#66873C2211yescharacteristic
46C2×#66873C2212yes—
47C2×#66872C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622483C22116yescomplemented
50#10622482C22116yescomplemented
51#10622456C2218yes—
52#10622444C2218yescomplemented
53#10622432C22116yescomplemented
54#10622408C22116yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11C2311yescharacteristic
57C2×Q8×D11—28no—
58C2×Q8×D11—48no—
59C22×D44—21no—
60C22×D44—21no—
61C22×D44C2312yes—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×Dic22—22no—
67C22×Dic22D411yescharacteristic
68C22×C8×C11C2312yes—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8C2314yes—
71C4×Q8×C11—22no—
72C4×Q8×C11C2314yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79#67000—24no—
80#67000C2318yes—
81#66999—28no—
82C2×#4325—24no—
83C2×#4325C2314yes—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×C4⋊Dic11D411yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4D412yes—
93C2×C4×Dic11C2312yes—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×D88—28no—
97C2×D88C2318yes—
98#66949—216no—
99#66947—216no—
100#66946—24no—
101#66946—24no—
102#66946C2318yes—
103#66946C2318yes—
104#66941—24no—
105#66941C2318yes—
106#66928—28no—
107#66927—22no—
108#66927C2314yes—
109C4×D44—22no—
110C4×D44—28no—
111C4×D44C2314yes—
112C4×Dic22D414yes—
113C4×Dic22C2314yes—
114C11×#106C2318yes—
115C11×C4⋊C8C2314yes—
116C11×#103C2318yes—
117#66899C2314yes—
118#66885C2318yes—
119#66879C2318yes—
120Dic11⋊C8C2318yes—
121#66873C2314yes—
122#66873C2318yes—
123#66873C2318yes—
124#66872C2314yes—
125C4×C11⋊C8C2314yes—
126C2×#3373—111nomaximal, Sylow
127C23×D11—21no—
128C23×D11—22no—
129C2×Q8×C11—24no—
130C2×Q8×C11—21no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—44no—
134C2×Q8×C11C2412yes—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11C2×D412yes—
143C22×Dic11C2×D412yes—
144Q8×D11—432no—
145C2×D44—21no—
146C2×D44—24no—
147C2×D44—22no—
148C2×D44—24no—
149C2×D44—24no—
150C2×D44—22no—
151C2×D44—24no—
152C2×D44—44no—
153C2×D44—82no—
154C2×D44#4114yes—
155C2×D44C2414yes—
156C2×D44C2412yes—
157C2×C4×D11—28no—
158C2×C4×D11—28no—
159C2×C4×D11—24no—
160C2×C4×D11—48no—
161C2×C4×D11—44no—
162C2×C4×D11—84no—
163C2×Dic22—28no—
164C2×Dic22—24no—
165C2×Dic22—48no—
166C2×Dic22C2×D414yes—
167C2×C8×C11—24no—
168C2×C8×C11C2414yes—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4C2412yes—
174C11×C4⋊C4C2414yes—
175C42×C11—24no—
176C42×C11C2×D412yes—
177C42×C11C2412yes—
178#4325—28no—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4—28no—
183(C2×D11)⋊C4—24no—
184C4⋊Dic11—21no—
185C4⋊Dic11C2×D414yes—
186C4⋊Dic11C2412yes—
187Dic11⋊C4—28no—
188Dic11⋊C4C2×D418yes—
189C4×Dic11C2×D414yes—
190C4×Dic11C2414yes—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8C2412yes—
194C2×C11⋊C8C2412yes—
195D88—216no—
196C2×#559—111no—
197C2×D4×Q8—111no—
198#3373—1116no—
199C2×#489—112no—
200C2×#486—111no—
201C2×#475D1111yescharacteristic, complemented
202C2×#476—112no—
203C2×#463—112no—
204C2×#459—111no—
205C2×#446—111no—
206C2×#442—112no—
207C2×C4×SD16—111no—
208C23×C11C22×D411yescharacteristic
209C22×D11—24no—
210C22×D11—22no—
211C22×D11—24no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—44no—
215C22×D11—44no—
216C22×D11—44no—
217Q8×C11—22no—
218Q8×C11—22no—
219Q8×C11—42no—
220Q8×C11—48no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—42no—
226C2×C4×C11—44no—
227C2×C4×C11—42no—
228C2×C4×C11AGL(1,ℤ/8)14yes—
229C2×C4×C11C22×D412yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D412yes—
232C2×C4×C11C2×#4112yes—
233C2×C4×C112−1+412yes—
234C2×C4×C11C2511yescharacteristic
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—22no—
238C2×Dic11—42no—
239C2×Dic11C22×D414yes—
240C2×Dic11C22×D414yes—
241D44—24no—
242D44—24no—
243D44—22no—
244D44—24no—
245D44—44no—
246D44—48no—
247D44—84no—
248D44C2×#4114yes—
249C4×D11—416no—
250C4×D11—48no—
251C4×D11—88no—
252Dic22—28no—
253Dic22—416no—
254C8×C11—24no—
255C11⋊C8—22no—
256C11⋊C8—22no—
257C23×Q8—221no—
258C22×SD16—111no—
259C22×D8—112no—
260#559—118no—
261#559—224no—
262D4×Q8—118no—
263D4×Q8—224no—
264C2×C4⋊Q8—112no—
265C2×C4⋊Q8C2×D1111yescharacteristic
266C2×#127—111no—
267C2×#124—112no—
268C2×#124—221no—
269C2×#123—222no—
270C2×C22⋊Q8—222no—
271C2×C22⋊Q8—221no—
272C2×C4×Q8—111no—
273C2×C4×Q8C2×D1111yescharacteristic
274C2×C4×D4—112no—
275C2×C4×D4—112no—
276C2×C4×D4—111no—
277C2×C4×D4—221no—
278#489—1116no—
279#486—118no—
280#476—1116no—
281#475C2×D1118yescomplemented
282#463—1116no—
283#459—118no—
284#446—118no—
285#442—1116no—
286C4×SD16—118no—
287C2×#106—111no—
288C2×#106C2×D1112yes—
289C2×C4⋊C8—112no—
290C2×C4⋊C8C2×D1111yescharacteristic
291C2×#103—111no—
292C2×#103C2×D1112yes—
293C2×#102—112no—
294C2×#102—112no—
295C2×#102—112no—
296C2×#102—111no—
297C2×#97—112no—
298C2×C4×C8—111no—
299C22×C11#54812yes—
300C22×C11C2×AGL(1,ℤ/8)12yes—
301C22×C11#57712yes—
302C22×C11C23×D411yescharacteristic
303C2×D11—24no—
304C2×D11—48no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—44no—
308C2×D11—44no—
309C2×D11—44no—
310C2×D11—88no—
311C4×C11—22no—
312C4×C11—42no—
313C4×C11—44no—
314C4×C11—42no—
315C4×C11#54812yes—
316C4×C11C2×AGL(1,ℤ/8)14yes—
317C4×C11C22×#4111yescharacteristic
318C4×C11C2×2−1+411yescharacteristic
319Dic11—24no—
320Dic11—24no—
321Dic11—42no—
322C22×Q8—21no—
323C22×Q8—111no—
324C22×Q8—222no—
325C22×Q8—228no—
326C22×Q8—448no—
327C22×Q8C22×D1111yescharacteristic
328C22×D4—111no—
329C22×D4—112no—
330C22×D4—221no—
331C22×D4—221no—
332C23×C4—222no—
333C23×C4—222no—
334C23×C4—221no—
335C2×SD16—114no—
336C2×SD16—224no—
337C2×D8—118no—
338C2×D8—228no—
339C22×C8—111no—
340C22×C8—111no—
341C22×C8C22×D1112yes—
342C4⋊Q8—22no—
343C4⋊Q8—118no—
344C4⋊Q8—224no—
345C4⋊Q8C22×D1114yes—
346#127—114no—
347#127—222no—
348#124—118no—
349#124—228no—
350#124—224no—
351#123—2216no—
352C22⋊Q8—2216no—
353C22⋊Q8—228no—
354C4×Q8—22no—
355C4×Q8—114no—
356C4×Q8—114no—
357C4×Q8C22×D1114yes—
358C4×D4—118no—
359C4×D4—118no—
360C4×D4—114no—
361C4×D4—228no—
362C4×D4—224no—
363C4×D4—224no—
364C4×D4—222no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1112yes—
373C2×C22⋊C4—222no—
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—221no—
378C2×C42—21no—
379C2×C42—112no—
380C2×C42C22×D1111yescharacteristic
381#106—114no—
382#106C22×D1118yes—
383C4⋊C8—118no—
384C4⋊C8C22×D1114yes—
385#103—114no—
386#103C22×D1118yes—
387#102—118no—
388#102—114no—
389#102—118no—
390#102—118no—
391#97—118no—
392C4×C8—114no—
393C2×C11#337314yescomplemented
394C2×C11C2×#54811yescharacteristic
395C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
396C2×C11C2×#57711yescharacteristic
397D11—44no—
398D11—84no—
399C24—221no—
400C24—222no—
401C2×Q8—21no—
402C2×Q8—24no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—44no—
406C2×Q8—114no—
407C2×Q8—228no—
408C2×Q8—224no—
409C2×Q8—448no—
410C2×Q8—4432no—
411C2×Q8C23×D1112yes—
412C2×D4—114no—
413C2×D4—112no—
414C2×D4—114no—
415C2×D4—221no—
416C2×D4—224no—
417C2×D4—222no—
418C2×D4—224no—
419C2×D4—222no—
420C2×D4—224no—
421C2×D4—224no—
422C2×D4—444no—
423C2×D4—882no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—112no—
428C22×C4—112no—
429C22×C4—228no—
430C22×C4—228no—
431C22×C4—221no—
432C22×C4—224no—
433C22×C4—448no—
434C22×C4—444no—
435C22×C4—884no—
436C22×C4D4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439SD16—228no—
440D8—2216no—
441C2×C8—24no—
442C2×C8—112no—
443C2×C8—112no—
444C2×C8—222no—
445C2×C8—222no—
446C2×C8C23×D1114yes—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—114no—
452C4⋊C4—118no—
453C4⋊C4—112no—
454C4⋊C4—228no—
455C4⋊C4—221no—
456C4⋊C4C23×D1114yes—
457C4⋊C4C23×D1112yes—
458C22⋊C4—228no—
459C22⋊C4—228no—
460C22⋊C4—228no—
461C22⋊C4—228no—
462C22⋊C4—224no—
463C42—24no—
464C42—114no—
465C42—114no—
466C42D4×D1112yes—
467C42C23×D1112yes—
468C11C2×#337311yescharacteristic, complemented, Sylow
469C23—224no—
470C23—222no—
471C23—224no—
472C23—442no—
473C23—442no—
474C23—444no—
475C23—444no—
476C23—444no—
477C23C2×D4×D1111yescharacteristic
478Q8—22no—
479Q8—22no—
480Q8—48no—
481Q8—42no—
482Q8—228no—
483Q8—4416no—
484D4—114no—
485D4—224no—
486D4—222no—
487D4—224no—
488D4—224no—
489D4—448no—
490D4—444no—
491D4—884no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—114no—
500C2×C4—114no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—222no—
504C2×C4—4416no—
505C2×C4—442no—
506C2×C4—448no—
507C2×C4—888no—
508C2×C4#6696714yes—
509C2×C4C2×D4×D1112yes—
510C2×C4C2×D4×D1112yes—
511C2×C4C2×D4×D1111yescharacteristic
512C2×C4#6704012yes—
513C2×C4#41×D1112yes—
514C2×C4C24×D1111yescharacteristic
515C8—24no—
516C8—222no—
517C8—222no—
518C22—224no—
519C22—448no—
520C22—442no—
521C22—442no—
522C22—444no—
523C22—444no—
524C22—444no—
525C22—888no—
526C22#1062316412yes—
527C22C2×#6696712yes—
528C22#1062330912yes—
529C22C22×D4×D1111yescharacteristic
530C4—22no—
531C4—44no—
532C4—42no—
533C4—42no—
534C4—224no—
535C4—224no—
536C4—442no—
537C4#1062316412yes—
538C4C2×#6696714yes—
539C4C2×#6704011yescharacteristic
540C4C2×#41×D1111yescharacteristic
541C2—444no—
542C2—884no—
543C2#1308140714yesdirect product factor
544C2C2×#1062316411yescharacteristic
545C2C22×#6696711yescharacteristic
546C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC2×#10622456C2
hypercenterC2×#475D11
hypocenterC11C2×#3373
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
2. C2×#10623258C2semidirect
3. #13081407C2direct (N × H)
4. C2×#10622408C2semidirect
5. C2×#10622701C2semidirect
6. C2×#10622483C2semidirect
7. C2×#10622432C2semidirect
9. C2×#10622444C2semidirect
10. C2×#10622482C2semidirect
11. C2×C4×#4325C2semidirect
12. C2×C11×#475C2semidirect
21. #10623258C22semidirect
23. #10623116C22semidirect
34. C11×#475C22semidirect
42. #10622701C22semidirect
43. C4×#4325C22semidirect
49. #10622483C22semidirect
50. #10622482C22semidirect
52. #10622444C22semidirect
53. #10622432C22semidirect
54. #10622408C22semidirect
201. C2×#475D11semidirect
281. #475C2×D11semidirect
393. C2×C11#3373semidirect
468. C11C2×#3373semidirect
543. C2#13081407direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106232582
#130814072
C2×#106224082
C2×#106227012
C2×#106224832
C2×#106224322
C2×#106224562
C2×#106224442
C2×#106224822
C2×C4×#43252
C2×C11×#4752
C2×#337311