Finite Group Databasebeta

← C2×#13081338 #15633452

Subgroups — C2×#13081338 #15633452

Order 2816.

2070 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×D4×Dic22C211yesmaximal, characteristic, complemented
3#13081338C2116yesmaximal, direct product factor
4C2×#10622408C212yesmaximal, complemented
5C2×#10622694C211yesmaximal, characteristic, complemented
6C2×#10622407C212yesmaximal, complemented
7C2×#10622459C211yesmaximal, characteristic, complemented
8C2×#10622778C212yesmaximal
9C2×#10622444C211yesmaximal, characteristic, complemented
10C2×#10622777C212yesmaximal, complemented
11C2×C4×#4323C211yesmaximal, characteristic
12C2×C11×#461C211yesmaximal, characteristic, complemented
13C23×Dic22—21no—
14C22×C11×SD16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#67000C2212yes—
18C2×Q8×Dic11C2212yes—
19C2×D4×Dic11C2212yes—
20C22×#4323C2211yescharacteristic
21C2×#66977—21no—
22#10623263—24no—
23#10623263C2218yescomplemented
24D4×Dic22—24no—
25D4×Dic22C2218yescomplemented
26C2×#66951—22no—
27C2×#66950—21no—
28C2×#66945—21no—
29C2×#66941C2212yes—
30C2×#66931—22no—
31C2×C4×D44C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#461C2218yescomplemented
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×#103C2212yes—
37C2×#66899C2212yes—
38C2×#66899C2212yes—
39C2×#66896C2211yescharacteristic
40#10622778C22116yes—
41#10622777C22116yescomplemented
42C2×#66885C2212yes—
43C2×#66882C2212yes—
44C2×#66879C2212yes—
45C2×Dic11⋊C8C2212yes—
46#10622694C2218yescomplemented
47C4×#4323C2218yes—
48C2×#66873C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622459C2218yescomplemented
52#10622444C2218yescomplemented
53#10622408C22116yescomplemented
54#10622407C22116yescomplemented
55C22×Q8×C11C2312yes—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×Dic11—22no—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22—21no—
62C22×Dic22—22no—
63C22×Dic22—28no—
64C22×Dic22—48no—
65C22×Dic22D411yescharacteristic
66C2×C11×SD16—28no—
67C2×C11×SD16C2318yes—
68C22×C8×C11C2312yes—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8C2314yes—
71C4×D4×C11—22no—
72C4×D4×C11C2314yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—22no—
79#67000—24no—
80#67000C2318yes—
81Q8×Dic11—24no—
82Q8×Dic11C2318yes—
83D4×Dic11—24no—
84D4×Dic11C2318yes—
85C2×#4323—24no—
86C2×#4323C2314yes—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11D411yescharacteristic
93C2×C4⋊Dic11C2312yes—
94C2×C4⋊Dic11C2311yescharacteristic
95#66977—28no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4D412yes—
98C2×C4×Dic11—22no—
99C2×C4×Dic11C2312yes—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102#66951—216no—
103#66950—28no—
104#66945—28no—
105#66941—24no—
106#66941C2318yes—
107#66931—216no—
108C4×D44—22no—
109C4×D44C2314yes—
110#66922—22no—
111#66922C2314yes—
112C4×Dic22D414yes—
113C4×Dic22C2314yes—
114C11×C4⋊C8C2314yes—
115C11×#103C2318yes—
116#66899C2318yes—
117#66899C2318yes—
118#66896C2314yes—
119#66885C2318yes—
120#66882C2318yes—
121#66879C2318yes—
122Dic11⋊C8C2318yes—
123#66873C2314yes—
124#66871C2314yes—
125C4×C11⋊C8C2314yes—
126C2×#3367—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—24no—
131C2×Q8×C11—24no—
132C2×Q8×C11C2414yes—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11#4114yes—
136C2×D4×C11C2412yes—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—24no—
140C22×C4×C11—44no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—28no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—48no—
148C22×Dic11C2×D412yes—
149C22×Dic11C2×D412yes—
150C2×D44—21no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44C2412yes—
154C2×C4×D11—24no—
155C2×C4×D11—44no—
156C2×Dic22—28no—
157C2×Dic22—24no—
158C2×Dic22—24no—
159C2×Dic22—432no—
160C2×Dic22—48no—
161C2×Dic22—44no—
162C2×Dic22C2×D414yes—
163C11×SD16—216no—
164C2×C8×C11—24no—
165C2×C8×C11C2414yes—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4C2412yes—
170C11×C22⋊C4—24no—
171C42×C11C2×D412yes—
172C42×C11C2412yes—
173C22⋊Dic11—28no—
174#4323—28no—
175(C2×D11)⋊C4—28no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—24no—
178C4⋊Dic11—28no—
179C4⋊Dic11—22no—
180C4⋊Dic11—24no—
181C4⋊Dic11—21no—
182C4⋊Dic11C2×D414yes—
183C4⋊Dic11C2412yes—
184C4⋊Dic11C2414yes—
185Dic11⋊C4—28no—
186Dic11⋊C4C2×D418yes—
187C4×Dic11—28no—
188C4×Dic11C2×D414yes—
189C4×Dic11C2414yes—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8C2412yes—
193C2×C11⋊C8C2412yes—
194C2×#556—111no—
195C2×D4×Q8—111no—
196#3367—1116no—
197C2×#489—112no—
198C2×#487—111no—
199C2×#477—112no—
200C2×#474—111no—
201C2×#463—112no—
202C2×#461D1111yescharacteristic, complemented
203C2×#446—111no—
204C2×#440—112no—
205C2×C4×D8—111no—
206C23×C11—24no—
207C23×C11—22no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11C22×D411yescharacteristic
211C22×D11—22no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215Q8×C11—24no—
216Q8×C11—24no—
217Q8×C11—44no—
218D4×C11—24no—
219D4×C11—22no—
220D4×C11C2×#4114yes—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—44no—
225C2×C4×C11—42no—
226C2×C4×C11—48no—
227C2×C4×C11AGL(1,ℤ/8)14yes—
228C2×C4×C11C22×D412yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D412yes—
231C2×C4×C11C2×#4112yes—
232C2×C4×C112−1+412yes—
233C2×C4×C11C2511yescharacteristic
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—416no—
239C2×Dic11—44no—
240C2×Dic11—42no—
241C2×Dic11C22×D414yes—
242C2×Dic11C22×D414yes—
243D44—22no—
244D44—22no—
245D44—42no—
246C4×D11—48no—
247Dic22—28no—
248Dic22—416no—
249Dic22—48no—
250C8×C11—24no—
251C11⋊C8—22no—
252C11⋊C8—22no—
253C23×Q8—221no—
254C22×SD16C2×D1112yes—
255C22×D8—111no—
256#556—118no—
257#556—224no—
258D4×Q8—118no—
259D4×Q8—224no—
260C2×C4⋊Q8—112no—
261C2×C4⋊Q8—111no—
262C2×C4⋊Q8C2×D1111yescharacteristic
263C2×#126—222no—
264C2×#124—112no—
265C2×C22⋊Q8—222no—
266C2×C22⋊Q8—221no—
267C2×C22⋊Q8—221no—
268C2×C4×Q8—111no—
269C2×C4×Q8—112no—
270C2×C4×D4—112no—
271C2×C4×D4—111no—
272C2×C4×D4C2×D1111yescharacteristic
273C2×#117—221no—
274#489—1116no—
275#487—118no—
276#477—1116no—
277#474—118no—
278#463—1116no—
279#461C2×D1118yescomplemented
280#446—118no—
281#440—1116no—
282C4×D8—118no—
283C2×#107—112no—
284C2×#107—111no—
285C2×C4⋊C8—112no—
286C2×C4⋊C8C2×D1111yescharacteristic
287C2×#103—112no—
288C2×#103—112no—
289C2×#103C2×D1112yes—
290C2×#102—111no—
291C2×#102—112no—
292C2×#102—111no—
293C2×#97—112no—
294C2×C4×C8—111no—
295C22×C11—24no—
296C22×C11—48no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11#54812yes—
300C22×C11C2×AGL(1,ℤ/8)12yes—
301C22×C11#57812yes—
302C22×C11C23×D411yescharacteristic
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—84no—
307C4×C11—22no—
308C4×C11—44no—
309C4×C11—42no—
310C4×C11#54812yes—
311C4×C11C2×AGL(1,ℤ/8)14yes—
312C4×C11C22×#4111yescharacteristic
313C4×C11C2×2−1+411yescharacteristic
314Dic11—24no—
315Dic11—24no—
316Dic11—44no—
317Dic11—42no—
318C22×Q8—111no—
319C22×Q8—222no—
320C22×Q8—228no—
321C22×Q8—221no—
322C22×Q8—448no—
323C22×Q8C22×D1112yes—
324C22×D4—111no—
325C22×D4C22×D1111yescharacteristic
326C23×C4—21no—
327C23×C4—222no—
328C23×C4—221no—
329C2×SD16—28no—
330C2×SD16C22×D1118yes—
331C2×D8—114no—
332C2×D8—224no—
333C22×C8—111no—
334C22×C8—111no—
335C22×C8C22×D1112yes—
336C4⋊Q8—22no—
337C4⋊Q8—118no—
338C4⋊Q8—114no—
339C4⋊Q8—224no—
340C4⋊Q8—222no—
341C4⋊Q8C22×D1114yes—
342#126—2216no—
343#124—118no—
344#124—224no—
345C22⋊Q8—2216no—
346C22⋊Q8—228no—
347C22⋊Q8—228no—
348C4×Q8—114no—
349C4×Q8—114no—
350C4×Q8—118no—
351C4×Q8—224no—
352C4×D4—22no—
353C4×D4—118no—
354C4×D4—114no—
355C4×D4—224no—
356C4×D4—222no—
357C4×D4C22×D1114yes—
358#117—228no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—221no—
374C2×C42—112no—
375C2×C42—222no—
376C2×C42C22×D1111yescharacteristic
377#107—118no—
378#107—114no—
379C4⋊C8—118no—
380C4⋊C8C22×D1114yes—
381#103—118no—
382#103—118no—
383#103C22×D1118yes—
384#102—114no—
385#102—118no—
386#102—114no—
387#97—118no—
388C4×C8—114no—
389C2×C11—44no—
390C2×C11#336714yescomplemented
391C2×C11C2×#54811yescharacteristic
392C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
393C2×C11C2×#57811yescharacteristic
394D11—82no—
395C24—21no—
396C24—221no—
397C2×Q8—22no—
398C2×Q8—24no—
399C2×Q8—24no—
400C2×Q8—114no—
401C2×Q8—228no—
402C2×Q8—224no—
403C2×Q8—224no—
404C2×Q8—448no—
405C2×Q8—4432no—
406C2×Q8—444no—
407C2×Q8C23×D1114yes—
408C2×D4—21no—
409C2×D4—22no—
410C2×D4—112no—
411C2×D4—221no—
412C2×D4—222no—
413C2×D4—222no—
414C2×D4#434114yes—
415C2×D4C23×D1112yes—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—24no—
419C22×C4—44no—
420C22×C4—112no—
421C22×C4—112no—
422C22×C4—228no—
423C22×C4—221no—
424C22×C4—222no—
425C22×C4—224no—
426C22×C4—448no—
427C22×C4—444no—
428C22×C4D4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431SD16—216no—
432D8—228no—
433C2×C8—24no—
434C2×C8—112no—
435C2×C8—112no—
436C2×C8—222no—
437C2×C8—222no—
438C2×C8C23×D1114yes—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—21no—
442C4⋊C4—114no—
443C4⋊C4—118no—
444C4⋊C4—114no—
445C4⋊C4—112no—
446C4⋊C4—228no—
447C4⋊C4—228no—
448C4⋊C4—221no—
449C4⋊C4—222no—
450C4⋊C4—224no—
451C4⋊C4C23×D1112yes—
452C22⋊C4—24no—
453C22⋊C4—228no—
454C22⋊C4—228no—
455C22⋊C4—228no—
456C22⋊C4—224no—
457C42—114no—
458C42—114no—
459C42—228no—
460C42D4×D1112yes—
461C42C23×D1112yes—
462C11C2×#336711yescharacteristic, complemented, Sylow
463C23—24no—
464C23—22no—
465C23—42no—
466C23—42no—
467C23—222no—
468C23—442no—
469C23—442no—
470C23—442no—
471C23C2×D4×D1111yescharacteristic
472Q8—24no—
473Q8—24no—
474Q8—44no—
475Q8—228no—
476Q8—4416no—
477Q8—448no—
478D4—24no—
479D4—22no—
480D4—222no—
481D4—222no—
482D4—442no—
483D4C2×#434114yes—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—42no—
488C2×C4—44no—
489C2×C4—48no—
490C2×C4—114no—
491C2×C4—114no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—222no—
495C2×C4—224no—
496C2×C4—4416no—
497C2×C4—444no—
498C2×C4—442no—
499C2×C4—448no—
500C2×C4#6696714yes—
501C2×C4C2×D4×D1112yes—
502C2×C4C2×D4×D1112yes—
503C2×C4C2×D4×D1111yescharacteristic
504C2×C4C2×#434112yes—
505C2×C4#6704312yes—
506C2×C4C24×D1111yescharacteristic
507C8—24no—
508C8—222no—
509C8—222no—
510C22—24no—
511C22—42no—
512C22—42no—
513C22—48no—
514C22—442no—
515C22—442no—
516C22—442no—
517C22—884no—
518C22#1062312912yes—
519C22C2×#6696712yes—
520C22#1062331012yes—
521C22C22×D4×D1111yescharacteristic
522C4—22no—
523C4—42no—
524C4—44no—
525C4—224no—
526C4—224no—
527C4—444no—
528C4—442no—
529C4#1062312912yes—
530C4C2×#6696714yes—
531C4C22×#434111yescharacteristic
532C4C2×#6704311yescharacteristic
533C2—44no—
534C2—882no—
535C2#1308133814yesdirect product factor
536C2C2×#1062312911yescharacteristic
537C2C22×#6696711yescharacteristic
538C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#461D11
hypocenterC11C2×#3367
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10623263C2semidirect
2. C2×D4×Dic22C2semidirect
3. #13081338C2direct (N × H)
4. C2×#10622408C2semidirect
5. C2×#10622694C2semidirect
6. C2×#10622407C2semidirect
7. C2×#10622459C2semidirect
9. C2×#10622444C2semidirect
10. C2×#10622777C2semidirect
12. C2×C11×#461C2semidirect
23. #10623263C22semidirect
25. D4×Dic22C22semidirect
34. C11×#461C22semidirect
41. #10622777C22semidirect
46. #10622694C22semidirect
51. #10622459C22semidirect
52. #10622444C22semidirect
53. #10622408C22semidirect
54. #10622407C22semidirect
202. C2×#461D11semidirect
279. #461C2×D11semidirect
390. C2×C11#3367semidirect
462. C11C2×#3367semidirect
535. C2#13081338direct (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×D4×Dic222
#130813382
C2×#106224082
C2×#106226942
C2×#106224072
C2×#106224592
C2×#106227782
C2×#106224442
C2×#106227772
C2×C4×#43232
C2×C11×#4612
C2×#336711