Finite Group Databasebeta

← C2×#13080975 #15632198

Subgroups — C2×#13080975 #15632198

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic, complemented
2C2×#10623082C211yesmaximal, characteristic
3#13080975C2116yesmaximal, direct product factor
4C2×#10622293C211yesmaximal, characteristic, complemented
5C2×#10622390C212yesmaximal, complemented
6C2×#10622418C212yesmaximal, complemented
7C2×#10622633C211yesmaximal, characteristic, complemented
8C2×#10622621C211yesmaximal, characteristic, complemented
9C2×#10622784C212yesmaximal, complemented
10C2×C8×D44C211yesmaximal, characteristic, complemented
11C2×D11×#106C212yesmaximal, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C22×C11×SD16C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66999C2212yes—
18C2×#66991C2212yes—
19C2×#66977—21no—
20C22×C8×D11C2212yes—
21#10623110—24no—
22#10623110C2218yescomplemented
23#10623082—24no—
24#10623082C2218yes—
25C2×#66949—22no—
26C2×C4⋊C4×D11C2212yes—
27C2×C4⋊C4×D11C2212yes—
28C2×#66936—22no—
29C2×C4×D44—21no—
30C2×C4×D44C2211yescharacteristic
31C2×#66923—21no—
32C2×#66922C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C4×C11×SD16C2218yescomplemented
35C2×C11×#106C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66899C2212yes—
40C2×#66896C2212yes—
41#10622784C22116yescomplemented
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66881C2212yes—
44C2×#66881C2212yes—
45#10622633C2218yescomplemented
46#10622621C2218yescomplemented
47C2×#66872C2212yes—
48C2×#66872C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50D11×#106C22116yescomplemented
51#10622418C22116yescomplemented
52#10622390C22116yescomplemented
53C8×D44C2218yescomplemented
54#10622293C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C2×#4339—28no—
60C2×#4339—48no—
61C22×D44D411yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11C2312yes—
65C22×Dic22—21no—
66C22×Dic22—21no—
67C2×C11×SD16—24no—
68C2×C11×SD16C2314yes—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C4×Q8×C11—22no—
72C4×Q8×C11C2314yes—
73C4×D4×C11—22no—
74C4×D4×C11C2314yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—22no—
82#66999—24no—
83#66999C2318yes—
84#66991—24no—
85#66991C2318yes—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4D412yes—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2312yes—
93#66977—28no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—22no—
97C22×C11⋊C8C2312yes—
98C2×C8×D11—28no—
99C2×C8×D11C2318yes—
100#66949—216no—
101C4⋊C4×D11—24no—
102C4⋊C4×D11—24no—
103C4⋊C4×D11C2318yes—
104C4⋊C4×D11C2318yes—
105#66936—216no—
106C4×D44—28no—
107C4×D44D414yes—
108C4×D44C2314yes—
109#66923—28no—
110#66922—22no—
111#66922—22no—
112#66922C2314yes—
113#66922C2314yes—
114C11×#106C2314yes—
115C11×#103C2314yes—
116C11×#102C2314yes—
117C4×C8×C11C2314yes—
118#66899C2318yes—
119#66896C2318yes—
120(C2×D11)⋊C8C2318yes—
121#66881C2318yes—
122#66881C2318yes—
123#66872C2318yes—
124#66872C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126C2×#3335—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11C2×D412yes—
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—22no—
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
145C2×C22⋊D11—28no—
146C2×C22⋊D11—48no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11C2×D412yes—
150#4339—432no—
151C2×D44SD1618yescomplemented
152C2×D44C2×D414yes—
153C2×C4×D11—28no—
154C2×C4×D11—28no—
155C2×C4×D11—24no—
156C2×C4×D11—24no—
157C2×C4×D11—48no—
158C2×C4×D11—84no—
159C2×C4×D11C2×D414yes—
160C2×C4×D11C2414yes—
161C2×Dic22—24no—
162C2×Dic22—24no—
163C2×Dic22—44no—
164C2×Dic22—82no—
165C11×SD16—28no—
166C2×C8×C11—22no—
167C2×C8×C11#4114yescomplemented
168C2×C8×C11C2412yes—
169C2×C8×C11C2412yes—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4C2412yes—
174C11×C4⋊C4C2412yes—
175C11×C22⋊C4—24no—
176C42×C11—24no—
177C42×C11C2×D412yes—
178C42×C11C2412yes—
179C22⋊Dic11—28no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4C2×D418yes—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184C4⋊Dic11—24no—
185C4⋊Dic11—24no—
186C4⋊Dic11C2×D414yes—
187C4⋊Dic11C2414yes—
188C4⋊Dic11C2414yes—
189Dic11⋊C4—28no—
190Dic11⋊C4—28no—
191Dic11⋊C4—28no—
192C2×C11⋊C8—24no—
193C2×C11⋊C8C2414yes—
194C8×D11—216no—
195C2×#554—111no—
196C2×#547—111no—
197#3335—1116no—
198C2×#498—111no—
199C2×#481—112no—
200C2×#483—112no—
201C2×#475—111no—
202C2×#476—111no—
203C2×#465—112no—
204C2×C4×SD16D1111yescharacteristic, complemented
205C2×C8×D4—111no—
206C22×#106—112no—
207C23×C11—22no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11C22×D411yescharacteristic
212C22×D11—24no—
213C22×D11—24no—
214C22×D11C2×SD1618yes—
215C22×D11C22×D414yes—
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—42no—
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—42no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—48no—
230C2×C4×C11C2×SD1614yes—
231C2×C4×C11C22×D412yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D412yes—
234C2×C4×C11C2×#4112yes—
235C2×C4×C112−1+412yes—
236C2×C4×C11C2511yescharacteristic
237C22⋊D11—416no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—44no—
242C2×Dic11—44no—
243C2×Dic11C22×D414yes—
244D44C2×SD16116yescomplemented
245C4×D11—28no—
246C4×D11—24no—
247C4×D11—24no—
248C4×D11—416no—
249C4×D11—88no—
250Dic22—48no—
251Dic22—84no—
252C8×C11—22no—
253C8×C11C2×#4114yescomplemented
254C11⋊C8—24no—
255C22×#41—221no—
256C22×SD16C2×D1111yescharacteristic
257C23×C8—112no—
258#554—118no—
259#554—224no—
260#547—118no—
261#547—224no—
262C2×C4⋊Q8—111no—
263C2×C4⋊Q8—111no—
264C2×#125—221no—
265C2×#123—222no—
266C2×C22⋊Q8—112no—
267C2×C22⋊Q8—222no—
268C2×C22⋊Q8—221no—
269C2×#121—112no—
270C2×C4×Q8C2×D1111yescharacteristic
271C2×C4×D4—111no—
272C2×C4×D4—221no—
273C2×C4×D4C2×D1111yescharacteristic
274C22×C4⋊C4—112no—
275C22×C4⋊C4—112no—
276#498—118no—
277#483—1116no—
278#481—1116no—
279#476—118no—
280#475—118no—
281#465—1116no—
282C4×SD16C2×D1118yescomplemented
283C8×D4—118no—
284C2×#106—112no—
285C2×#106—112no—
286C2×#106—112no—
287C2×#106—112no—
288C2×#106—1116no—
289C2×#106C2×D1111yescharacteristic
290C2×C4⋊C8—111no—
291C2×#103—112no—
292C2×#103C2×D1111yescharacteristic
293C2×#102—112no—
294C2×#102C2×D1111yescharacteristic
295C2×C22⋊C8—112no—
296C2×C4×C8C2×D1111yescharacteristic
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—84no—
301C22×C11#54712yes—
302C22×C11C22×SD1612yes—
303C22×C11#57712yes—
304C22×C11C23×D411yescharacteristic
305C2×D11—216no—
306C2×D11—24no—
307C2×D11—24no—
308C2×D11C22×SD1618yes—
309C4×C11—22no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11#54712yes—
314C4×C11C22×SD1614yes—
315C4×C11C22×#4111yescharacteristic
316C4×C11C2×2−1+411yescharacteristic
317Dic11—24no—
318Dic11—44no—
319Dic11—44no—
320C2×#41—228no—
321C2×#41—448no—
322C22×Q8—221no—
323C22×Q8—221no—
324C22×Q8C22×D1111yescharacteristic
325C22×D4—111no—
326C22×D4—222no—
327C22×D4C22×D1111yescharacteristic
328C23×C4—21no—
329C23×C4—112no—
330C23×C4—222no—
331C23×C4—222no—
332C2×SD16—24no—
333C2×SD16C22×D1114yes—
334C22×C8—112no—
335C22×C8—118no—
336C22×C8—228no—
337C22×C8C22×D1111yescharacteristic
338C22×C8C22×D1111yescharacteristic
339C4⋊Q8—114no—
340C4⋊Q8—114no—
341C4⋊Q8—222no—
342C4⋊Q8—222no—
343#125—228no—
344#123—2216no—
345C22⋊Q8—118no—
346C22⋊Q8—2216no—
347C22⋊Q8—228no—
348C22⋊Q8—224no—
349#121—118no—
350#121—224no—
351C4×Q8—22no—
352C4×Q8C22×D1114yes—
353C4×D4—22no—
354C4×D4—114no—
355C4×D4—114no—
356C4×D4—228no—
357C4×D4C22×D1114yes—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—118no—
363C2×C4⋊C4—118no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—112no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C42—21no—
378C2×C42C22×D1111yescharacteristic
379#106—118no—
380#106—118no—
381#106—118no—
382#106—118no—
383#106C22×D1114yes—
384C4⋊C8—114no—
385#103—118no—
386#103C22×D1114yes—
387#102—118no—
388#102C22×D1114yes—
389C22⋊C8—118no—
390C4×C8C22×D1114yes—
391C2×C11—82no—
392C2×C11#333514yescomplemented
393C2×C11C2×#54711yescharacteristic
394C2×C11C23×SD1611yescharacteristic
395C2×C11C2×#57711yescharacteristic
396D11—28no—
397C24—21no—
398C24—112no—
399#41—4432no—
400C2×Q8—21no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—224no—
404C2×Q8—224no—
405C2×Q8—444no—
406C2×Q8—882no—
407C2×Q8C23×D1112yes—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—22no—
411C2×D4—118no—
412C2×D4—114no—
413C2×D4—228no—
414C2×D4—448no—
415C2×D4C23×D1112yes—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—44no—
421C22×C4—112no—
422C22×C4—114no—
423C22×C4—114no—
424C22×C4—228no—
425C22×C4—228no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—448no—
431C22×C4—884no—
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435SD16—28no—
436C2×C8—22no—
437C2×C8—114no—
438C2×C8—224no—
439C2×C8—2216no—
440C2×C8#433914yescomplemented
441C2×C8C23×D1112yes—
442C2×C8C23×D1112yes—
443C4⋊C4—24no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—114no—
447C4⋊C4—114no—
448C4⋊C4—114no—
449C4⋊C4—228no—
450C4⋊C4—228no—
451C4⋊C4—228no—
452C4⋊C4—222no—
453C4⋊C4—222no—
454C4⋊C4—224no—
455C4⋊C4—224no—
456C4⋊C4C23×D1112yes—
457C4⋊C4C23×D1112yes—
458C22⋊C4—24no—
459C22⋊C4—118no—
460C22⋊C4—228no—
461C22⋊C4—228no—
462C42—24no—
463C42D4×D1112yes—
464C42C23×D1112yes—
465C11C2×#333511yescharacteristic, complemented, Sylow
466C23—22no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—118no—
471C23—114no—
472C23—224no—
473C23—224no—
474C23C2×D4×D1111yescharacteristic
475Q8—22no—
476Q8—22no—
477Q8—42no—
478Q8—448no—
479Q8—884no—
480D4—22no—
481D4—22no—
482D4—42no—
483D4—1116no—
484D4—4416no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—48no—
493C2×C4—114no—
494C2×C4—224no—
495C2×C4—228no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—224no—
500C2×C4—4416no—
501C2×C4—444no—
502C2×C4—444no—
503C2×C4—888no—
504C2×C4SD16×D1114yes—
505C2×C4C2×#433912yes—
506C2×C4C2×D4×D1112yes—
507C2×C4C2×D4×D1112yes—
508C2×C4C2×D4×D1111yescharacteristic
509C2×C4#6704312yes—
510C2×C4C24×D1111yescharacteristic
511C8—22no—
512C8—224no—
513C8C2×#433914yescomplemented
514C22—42no—
515C22—42no—
516C22—42no—
517C22—84no—
518C22—118no—
519C22—2216no—
520C22—224no—
521C22—224no—
522C22#1062308212yes—
523C22C2×SD16×D1112yes—
524C22#1062330112yes—
525C22C22×D4×D1111yescharacteristic
526C4—22no—
527C4—42no—
528C4—42no—
529C4—42no—
530C4—224no—
531C4—444no—
532C4—444no—
533C4#1062308212yes—
534C4C2×SD16×D1114yes—
535C4C22×#433911yescharacteristic
536C4C2×#6704311yescharacteristic
537C2—82no—
538C2—228no—
539C2#1308097514yesdirect product factor
540C2C2×#1062308211yescharacteristic
541C2C22×SD16×D1111yescharacteristic
542C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10623082C2
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3335
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×#10623110C2semidirect
3. #13080975C2direct (N × H)
4. C2×#10622293C2semidirect
5. C2×#10622390C2semidirect
6. C2×#10622418C2semidirect
7. C2×#10622633C2semidirect
8. C2×#10622621C2semidirect
9. C2×#10622784C2semidirect
10. C2×C8×D44C2semidirect
11. C2×D11×#106C2semidirect
12. C2×C4×C11×SD16C2semidirect
22. #10623110C22semidirect
34. C4×C11×SD16C22semidirect
41. #10622784C22semidirect
45. #10622633C22semidirect
46. #10622621C22semidirect
50. D11×#106C22semidirect
51. #10622418C22semidirect
52. #10622390C22semidirect
53. C8×D44C22semidirect
54. #10622293C22semidirect
151. C2×D44SD16semidirect
167. C2×C8×C11#41semidirect
204. C2×C4×SD16D11semidirect
244. D44C2×SD16semidirect
253. C8×C11C2×#41semidirect
282. C4×SD16C2×D11semidirect
392. C2×C11#3335semidirect
440. C2×C8#4339semidirect
465. C11C2×#3335semidirect
513. C8C2×#4339semidirect
539. C2#13080975direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231102
C2×#106230822
#130809752
C2×#106222932
C2×#106223902
C2×#106224182
C2×#106226332
C2×#106226212
C2×#106227842
C2×C8×D442
C2×D11×#1062
C2×C4×C11×SD162
C2×#333511