Finite Group Databasebeta

← C2×#13081406 #15633458

Subgroups — C2×#13081406 #15633458

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×D4×Dic22C211yesmaximal, characteristic, complemented
3#13081406C2116yesmaximal, direct product factor
4C2×#10622408C212yesmaximal, complemented
5C2×#10622307C211yesmaximal, characteristic, complemented
6C2×#10622633C211yesmaximal, characteristic, complemented
7C2×#10622483C212yesmaximal, complemented
8C2×#10622778C212yesmaximal, complemented
9C2×#10622628C211yesmaximal, characteristic
10C2×#10622292C211yesmaximal, characteristic, complemented
11C2×#10622398C212yesmaximal, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
13C23×Dic22—21no—
14C22×C11×SD16C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#67000C2212yes—
18C2×D4×Dic11C2212yes—
19C22×#4323C2212yes—
20C2×#66977—21no—
21#10623116—24no—
22#10623116C2218yescomplemented
23D4×Dic22—24no—
24D4×Dic22C2218yescomplemented
25C2×#66947—22no—
26C2×#66946C2212yes—
27C2×#66941C2212yes—
28C2×#66931—22no—
29C2×#66928—21no—
30C2×#66927C2211yescharacteristic
31C2×C4×D44—21no—
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C4×C11×SD16C2218yescomplemented
35C2×C11×#106C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66899C2212yes—
40#10622778C22116yescomplemented
41C2×#66885C2212yes—
42C2×#66885C2212yes—
43C2×#66879C2212yes—
44C2×Dic11⋊C8C2212yes—
45#10622633C2218yescomplemented
46#10622628C2218yes—
47C2×#66873C2212yes—
48C2×#66872C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622483C22116yescomplemented
51#10622408C22116yescomplemented
52#10622398C22116yescomplemented
53#10622307C2218yescomplemented
54#10622292C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×Dic11—22no—
59C22×D44—21no—
60C22×D44—21no—
61C22×D44C2312yes—
62C22×C4×D11—22no—
63C22×Dic22—21no—
64C22×Dic22—22no—
65C22×Dic22—28no—
66C22×Dic22—48no—
67C22×Dic22D411yescharacteristic
68C2×C11×SD16—24no—
69C2×C11×SD16C2314yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×Q8×C11—22no—
73C4×Q8×C11C2314yes—
74C4×D4×C11—22no—
75C4×D4×C11C2314yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—22no—
83#67000—24no—
84#67000C2318yes—
85D4×Dic11—24no—
86D4×Dic11C2318yes—
87C2×#4323—28no—
88C2×#4323C2318yes—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11D411yescharacteristic
94C2×C4⋊Dic11C2312yes—
95#66977—28no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4D412yes—
98C2×C4×Dic11C2312yes—
99C22×C11⋊C8C2312yes—
100#66947—216no—
101#66946—24no—
102#66946C2318yes—
103#66941—24no—
104#66941C2318yes—
105#66931—216no—
106#66928—28no—
107#66927—22no—
108#66927C2314yes—
109C4×D44—28no—
110#66922—22no—
111#66922C2314yes—
112C4×Dic22D414yes—
113C4×Dic22C2314yes—
114C11×#106C2314yes—
115C11×#103C2314yes—
116C11×#102C2314yes—
117C4×C8×C11C2314yes—
118#66899C2318yes—
119#66885C2318yes—
120#66885C2318yes—
121#66879C2318yes—
122Dic11⋊C8C2318yes—
123#66873C2318yes—
124#66872C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126C2×#3373—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11—22no—
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#4114yes—
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
145C22×Dic11—28no—
146C22×Dic11—22no—
147C22×Dic11—48no—
148C22×Dic11C2×D412yes—
149C22×Dic11C2×D412yes—
150C2×D44—24no—
151C2×D44—22no—
152C2×D44—24no—
153C2×D44—24no—
154C2×D44—24no—
155C2×D44—44no—
156C2×D44—82no—
157C2×D44C2414yes—
158C2×C4×D11—28no—
159C2×C4×D11—84no—
160C2×Dic22—28no—
161C2×Dic22—24no—
162C2×Dic22—24no—
163C2×Dic22—432no—
164C2×Dic22—48no—
165C2×Dic22—44no—
166C2×Dic22C2×D414yes—
167C11×SD16—28no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11C2412yes—
171C2×C8×C11C2412yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4C2412yes—
176C11×C4⋊C4C2412yes—
177C11×C22⋊C4—24no—
178C42×C11—24no—
179C42×C11C2×D412yes—
180C42×C11C2412yes—
181C22⋊Dic11—28no—
182#4323—216no—
183(C2×D11)⋊C4—28no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—28no—
186C4⋊Dic11—22no—
187C4⋊Dic11—24no—
188C4⋊Dic11C2×D414yes—
189C4⋊Dic11C2414yes—
190Dic11⋊C4—28no—
191Dic11⋊C4C2×D418yes—
192C4×Dic11C2×D414yes—
193C4×Dic11C2414yes—
194C2×C11⋊C8—24no—
195C2×C11⋊C8C2414yes—
196C2×#559—111no—
197C2×D4×Q8—111no—
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×SD16D1111yescharacteristic, complemented
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—22no—
218Q8×C11—22no—
219Q8×C11—42no—
220D4×C11—24no—
221D4×C11—22no—
222D4×C11C2×#4114yes—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—48no—
231C2×C4×C11AGL(1,ℤ/8)14yes—
232C2×C4×C11C22×D412yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D412yes—
235C2×C4×C11C2×#4112yes—
236C2×C4×C112−1+412yes—
237C2×C4×C11C2511yescharacteristic
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—416no—
242C2×Dic11—44no—
243C2×Dic11C22×D414yes—
244C2×Dic11C22×D414yes—
245D44—24no—
246D44—24no—
247D44—44no—
248D44—48no—
249D44—84no—
250C4×D11—88no—
251Dic22—28no—
252Dic22—416no—
253Dic22—48no—
254C8×C11—22no—
255C8×C11—22no—
256C11⋊C8—24no—
257C23×Q8—221no—
258C22×SD16C2×D1111yescharacteristic
259C22×D8—112no—
260#559—118no—
261#559—224no—
262D4×Q8—118no—
263D4×Q8—224no—
264C2×C4⋊Q8—112no—
265C2×C4⋊Q8—111no—
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—221no—
277C2×C4×D4C2×D1111yescharacteristic
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×SD16C2×D1118yescomplemented
287C2×#106—112no—
288C2×#106C2×D1111yescharacteristic
289C2×C4⋊C8—112no—
290C2×C4⋊C8—111no—
291C2×#103—112no—
292C2×#103C2×D1111yescharacteristic
293C2×#102—112no—
294C2×#102—112no—
295C2×#102—112no—
296C2×#102C2×D1111yescharacteristic
297C2×#97—112no—
298C2×C4×C8C2×D1111yescharacteristic
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—22no—
312C4×C11—42no—
313C4×C11—42no—
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—44no—
322C22×Q8—111no—
323C22×Q8—222no—
324C22×Q8—228no—
325C22×Q8—221no—
326C22×Q8—448no—
327C22×Q8C22×D1111yescharacteristic
328C22×D4—112no—
329C22×D4—221no—
330C22×D4—221no—
331C22×D4C22×D1111yescharacteristic
332C23×C4—21no—
333C23×C4—222no—
334C23×C4—222no—
335C2×SD16—24no—
336C2×SD16C22×D1114yes—
337C2×D8—118no—
338C2×D8—228no—
339C22×C8—112no—
340C22×C8C22×D1111yescharacteristic
341C22×C8C22×D1111yescharacteristic
342C4⋊Q8—118no—
343C4⋊Q8—114no—
344C4⋊Q8—224no—
345C4⋊Q8—222no—
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—22no—
359C4×D4—118no—
360C4×D4—118no—
361C4×D4—228no—
362C4×D4—224no—
363C4×D4—224no—
364C4×D4C22×D1114yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—222no—
378C2×C42—21no—
379C2×C42—112no—
380C2×C42C22×D1111yescharacteristic
381#106—118no—
382#106C22×D1114yes—
383C4⋊C8—118no—
384C4⋊C8—114no—
385#103—118no—
386#103C22×D1114yes—
387#102—118no—
388#102—118no—
389#102—118no—
390#102C22×D1114yes—
391#97—118no—
392C4×C8C22×D1114yes—
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—21no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—114no—
405C2×Q8—228no—
406C2×Q8—224no—
407C2×Q8—224no—
408C2×Q8—448no—
409C2×Q8—4432no—
410C2×Q8—444no—
411C2×Q8C23×D1112yes—
412C2×D4—21no—
413C2×D4—22no—
414C2×D4—114no—
415C2×D4—224no—
416C2×D4—224no—
417C2×D4—222no—
418C2×D4—224no—
419C2×D4—224no—
420C2×D4—444no—
421C2×D4—882no—
422C2×D4#433914yes—
423C2×D4C23×D1112yes—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—24no—
428C22×C4—44no—
429C22×C4—112no—
430C22×C4—112no—
431C22×C4—228no—
432C22×C4—228no—
433C22×C4—222no—
434C22×C4—448no—
435C22×C4—884no—
436C22×C4D4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439SD16—28no—
440D8—2216no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—114no—
444C2×C8—224no—
445C2×C8C23×D1112yes—
446C2×C8C23×D1112yes—
447C4⋊C4—24no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—114no—
451C4⋊C4—118no—
452C4⋊C4—114no—
453C4⋊C4—228no—
454C4⋊C4—222no—
455C4⋊C4—224no—
456C4⋊C4C23×D1112yes—
457C4⋊C4C23×D1112yes—
458C22⋊C4—24no—
459C22⋊C4—228no—
460C22⋊C4—228no—
461C22⋊C4—228no—
462C22⋊C4—228no—
463C42—24no—
464C42—114no—
465C42—114no—
466C42D4×D1112yes—
467C42C23×D1112yes—
468C11C2×#337311yescharacteristic, complemented, Sylow
469C23—24no—
470C23—22no—
471C23—42no—
472C23—42no—
473C23—224no—
474C23—444no—
475C23—444no—
476C23—444no—
477C23C2×D4×D1111yescharacteristic
478Q8—22no—
479Q8—22no—
480Q8—42no—
481Q8—228no—
482Q8—4416no—
483Q8—448no—
484D4—24no—
485D4—22no—
486D4—224no—
487D4—224no—
488D4—448no—
489D4—444no—
490D4—884no—
491D4C2×#433914yes—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—48no—
500C2×C4—114no—
501C2×C4—114no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—4416no—
506C2×C4—444no—
507C2×C4—888no—
508C2×C4#6696714yes—
509C2×C4C2×#433912yes—
510C2×C4C2×D4×D1112yes—
511C2×C4C2×D4×D1112yes—
512C2×C4C2×D4×D1111yescharacteristic
513C2×C4#6704312yes—
514C2×C4C24×D1111yescharacteristic
515C8—22no—
516C8—22no—
517C8—224no—
518C22—24no—
519C22—48no—
520C22—42no—
521C22—42no—
522C22—444no—
523C22—444no—
524C22—444no—
525C22—888no—
526C22#1062308312yes—
527C22C2×#6696712yes—
528C22#1062330112yes—
529C22C22×D4×D1111yescharacteristic
530C4—22no—
531C4—42no—
532C4—42no—
533C4—42no—
534C4—224no—
535C4—224no—
536C4—444no—
537C4#1062308312yes—
538C4C2×#6696714yes—
539C4C22×#433911yescharacteristic
540C4C2×#6704311yescharacteristic
541C2—44no—
542C2—884no—
543C2#1308140614yesdirect product factor
544C2C2×#1062308311yescharacteristic
545C2C22×#6696711yescharacteristic
546C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10622628C2
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3373
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×#10623116C2semidirect
2. C2×D4×Dic22C2semidirect
3. #13081406C2direct (N × H)
4. C2×#10622408C2semidirect
5. C2×#10622307C2semidirect
6. C2×#10622633C2semidirect
7. C2×#10622483C2semidirect
8. C2×#10622778C2semidirect
10. C2×#10622292C2semidirect
11. C2×#10622398C2semidirect
12. C2×C4×C11×SD16C2semidirect
22. #10623116C22semidirect
24. D4×Dic22C22semidirect
34. C4×C11×SD16C22semidirect
40. #10622778C22semidirect
45. #10622633C22semidirect
50. #10622483C22semidirect
51. #10622408C22semidirect
52. #10622398C22semidirect
53. #10622307C22semidirect
54. #10622292C22semidirect
207. C2×C4×SD16D11semidirect
286. C4×SD16C2×D11semidirect
394. C2×C11#3373semidirect
468. C11C2×#3373semidirect
543. C2#13081406direct (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×D4×Dic222
#130814062
C2×#106224082
C2×#106223072
C2×#106226332
C2×#106224832
C2×#106227782
C2×#106226282
C2×#106222922
C2×#106223982
C2×C4×C11×SD162
C2×#337311