Finite Group Databasebeta

← C2×#13081636 #15634729

Subgroups — C2×#13081636 #15634729

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623108C211yesmaximal, characteristic, complemented
2#13081636C2116yesmaximal, direct product factor
3C2×#10622671C212yesmaximal, complemented
4C2×#10622698C211yesmaximal, characteristic, complemented
5C2×#10622640C212yesmaximal, complemented
6C2×#10622670C212yesmaximal, complemented
7C2×#10622696C211yesmaximal, characteristic, complemented
8C2×#10622628C211yesmaximal, characteristic, complemented
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622639C212yesmaximal, complemented
11C2×C4×#4323C211yesmaximal, characteristic, complemented
12C2×C11×#556C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C11×#556—24no—
15C11×#556C2218yescomplemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#126—22no—
18C2×C11×#124C2212yes—
19C2×C11×C22⋊Q8—21no—
20C2×C4×Q8×C11C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117—21no—
24C22×#4325C2212yes—
25C22×#4325C2212yes—
26C22×#4325C2212yes—
27C22×#4323C2211yescharacteristic
28C22×#4323C2212yes—
29#10623108—24no—
30#10623108C2218yescomplemented
31C2×#66948—21no—
32C2×#66948—22no—
33C2×#66927C2212yes—
34C2×#66927C2211yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×C4×D44C2212yes—
37C2×#66899C2212yes—
38C2×#66896C2211yescharacteristic
39#10622698C2218yescomplemented
40#10622696C2218yescomplemented
41#10622671C22116yescomplemented
42#10622670C22116yescomplemented
43#10622640C22116yescomplemented
44#10622639C22116yescomplemented
45#10622637C2218yescomplemented
46#10622628C2218yescomplemented
47C4×#4323C2218yescomplemented
48C2×#66873C2212yes—
49C2×#66873C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11D411yescharacteristic
56C22×Q8×C11C2312yes—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C2×#4343—28no—
60C2×#4343—48no—
61C22×D44—22no—
62C22×D44—21no—
63C22×D44—22no—
64C22×D44—21no—
65C22×D44C2311yescharacteristic
66C22×D44C2312yes—
67C22×C4×D11—22no—
68C22×C4×D11—21no—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8C2314yes—
71C11×#126—216no—
72C11×#124—24no—
73C11×#124C2318yes—
74C11×C22⋊Q8—28no—
75C4×Q8×C11—24no—
76C4×Q8×C11D414yes—
77C4×Q8×C11C2318yes—
78C4×Q8×C11C2314yes—
79C4×D4×C11—22no—
80C4×D4×C11C2314yes—
81C11×#117—28no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4D412yes—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—22no—
91C2×C42×C11—22no—
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2312yes—
94C2×#4325—28no—
95C2×#4325—44no—
96C2×#4325—44no—
97C2×#4325C2318yes—
98C2×#4325C2318yes—
99C2×#4325C2318yes—
100C2×#4323—24no—
101C2×#4323—44no—
102C2×#4323C2314yes—
103C2×#4323C2318yes—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—21no—
106C2×C4⋊Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2312yes—
109C22×C11⋊C8C2311yescharacteristic
110#66948—28no—
111#66948—216no—
112#66927—22no—
113#66927—24no—
114#66927C2314yes—
115#66927C2318yes—
116C4×D44—22no—
117C4×D44—24no—
118C4×D44C2314yes—
119C4×D44C2318yes—
120#66899C2318yes—
121#66896C2314yes—
122#66873C2314yes—
123#66873C2318yes—
124#66871C2314yes—
125C4⋊(C11⋊C8)C2314yes—
126C4⋊(C11⋊C8)C2318yes—
127#66867C2318yes—
128C4×C11⋊C8C2314yes—
129C2×#3397—111nomaximal, Sylow
130C24×C11—21no—
131C23×D11—21no—
132C23×D11—22no—
133C2×Q8×C11—24no—
134C2×Q8×C11—22no—
135C2×Q8×C11—24no—
136C2×Q8×C11—24no—
137C2×Q8×C11C2×D414yes—
138C2×Q8×C11C2414yes—
139C2×D4×C11—21no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11C2412yes—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—44no—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153#4343—432no—
154C2×D44—21no—
155C2×D44—22no—
156C2×D44—28no—
157C2×D44—24no—
158C2×D44—28no—
159C2×D44—24no—
160C2×D44—22no—
161C2×D44—24no—
162C2×D44—24no—
163C2×D44—22no—
164C2×D44—48no—
165C2×D44—44no—
166C2×D44—84no—
167C2×D44—82no—
168C2×D44C2412yes—
169C2×D44C2414yes—
170C2×C4×D11—28no—
171C2×C4×D11—24no—
172C2×C4×D11—48no—
173C2×C4×D11—44no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2×D414yes—
179C11×C4⋊C4C2×D418yes—
180C11×C4⋊C4C2412yes—
181C11×C22⋊C4—28no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—28no—
184C42×C11—28no—
185C42×C11C2×D412yes—
186C42×C11C2×D414yes—
187C42×C11C2412yes—
188C42×C11C2414yes—
189#4325—216no—
190#4325—48no—
191#4325—48no—
192#4323—28no—
193#4323—48no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4—24no—
196C4⋊Dic11—21no—
197C4⋊Dic11C2412yes—
198C2×C11⋊C8—24no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8#4114yescomplemented
201C2×C11⋊C8C2412yes—
202C2×C11⋊C8C2414yes—
203C2×C11⋊C8C2412yes—
204C2×#556D1111yescharacteristic, complemented
205C2×#550—111no—
206#3397—1116no—
207C2×#496—112no—
208C2×#492—111no—
209C2×#460—112no—
210C2×#463—112no—
211C2×#461—111no—
212C2×#459—111no—
213C2×#446—111no—
214C2×#440—112no—
215C2×C4×D8—111no—
216C23×C11—22no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11C22×D411yescharacteristic
221C22×D11—22no—
222C22×D11—24no—
223C22×D11—42no—
224C22×D11—44no—
225C22×D11—44no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—44no—
229Q8×C11—28no—
230Q8×C11—24no—
231Q8×C11—24no—
232Q8×C11—44no—
233D4×C11—22no—
234D4×C11—22no—
235D4×C11—42no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—44no—
242C2×C4×C11—42no—
243C2×C4×C11—48no—
244C2×C4×C11AGL(1,ℤ/8)14yes—
245C2×C4×C11C22×D414yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D414yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D412yes—
250C2×C4×C11C2×#4112yes—
251C2×C4×C11H(5,𝔽2)12yes—
252C2×C4×C11C2511yescharacteristic
253C2×Dic11—22no—
254C2×Dic11—42no—
255D44—22no—
256D44—24no—
257D44—24no—
258D44—22no—
259D44—416no—
260D44—42no—
261D44—44no—
262D44—48no—
263D44—88no—
264D44—84no—
265C4×D11—416no—
266C4×D11—48no—
267C11⋊C8—24no—
268C11⋊C8—22no—
269C11⋊C8C2×#4114yescomplemented
270C22×#41—221no—
271C22×SD16—112no—
272C22×SD16—112no—
273C22×SD16—112no—
274C22×D8—111no—
275C22×D8—112no—
276#556—24no—
277#556C2×D1118yescomplemented
278#550—118no—
279#550—224no—
280C2×C4⋊Q8C2×D1111yescharacteristic
281C2×#127—111no—
282C2×#127—112no—
283C2×#126—22no—
284C2×#124C2×D1112yes—
285C2×C22⋊Q8—21no—
286C2×#121—221no—
287C2×#121—222no—
288C2×C4×Q8C2×D1112yes—
289C2×C4×Q8C2×D1111yescharacteristic
290C2×C4×D4—111no—
291C2×C4×D4—112no—
292C2×C4×D4C2×D1111yescharacteristic
293C2×#117—21no—
294#496—1116no—
295#492—118no—
296#463—1116no—
297#461—118no—
298#460—1116no—
299#459—118no—
300#446—118no—
301#440—1116no—
302C4×D8—118no—
303C2×#107—111no—
304C2×C4⋊C8—111no—
305C2×C4⋊C8—112no—
306C2×#103—112no—
307C2×#102—111no—
308C2×#102—111no—
309C2×#102—112no—
310C2×#97—112no—
311C2×C4×C8—111no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—84no—
316C22×C11#55012yes—
317C22×C11C2×AGL(1,ℤ/8)12yes—
318C22×C11#57712yes—
319C22×C11C23×D411yescharacteristic
320C2×D11—42no—
321C2×D11—44no—
322C2×D11—44no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—44no—
326C2×D11—84no—
327C2×D11—88no—
328C4×C11—24no—
329C4×C11—24no—
330C4×C11—22no—
331C4×C11—44no—
332C4×C11—42no—
333C4×C11#55012yes—
334C4×C11C2×AGL(1,ℤ/8)14yes—
335C4×C11C22×#4111yescharacteristic
336C4×C11C2×H(5,𝔽2)11yescharacteristic
337Dic11—42no—
338C2×#41—228no—
339C2×#41—448no—
340C22×Q8C22⋊D1111yescharacteristic
341C22×Q8C22×D1112yes—
342C22×D4—111no—
343C22×D4—112no—
344C22×D4—222no—
345C22×D4—221no—
346C22×D4—222no—
347C22×D4—221no—
348C22×D4C22×D1111yescharacteristic
349C23×C4—21no—
350C23×C4—222no—
351C23×C4—221no—
352C2×SD16—118no—
353C2×SD16—118no—
354C2×SD16—118no—
355C2×SD16—228no—
356C2×SD16—444no—
357C2×SD16—444no—
358C2×D8—114no—
359C2×D8—118no—
360C2×D8—224no—
361C2×D8—444no—
362C22×C8—111no—
363C22×C8—112no—
364C22×C8—111no—
365C4⋊Q8—22no—
366C4⋊Q8C22×D1114yes—
367#127—114no—
368#127—118no—
369#127—222no—
370#127—224no—
371#126—216no—
372#124—24no—
373#124C22×D1118yes—
374C22⋊Q8—28no—
375#121—228no—
376#121—2216no—
377C4×Q8—24no—
378C4×Q8C22⋊D1114yes—
379C4×Q8C22×D1118yes—
380C4×Q8C22×D1114yes—
381C4×D4—22no—
382C4×D4—114no—
383C4×D4—118no—
384C4×D4—222no—
385C4×D4—224no—
386C4×D4C22×D1114yes—
387#117—28no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4C22⋊D1111yescharacteristic
393C2×C4⋊C4C22⋊D1112yes—
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—221no—
400C2×C42—22no—
401C2×C42C22×D1111yescharacteristic
402C2×C42C22×D1112yes—
403#107—114no—
404C4⋊C8—114no—
405C4⋊C8—118no—
406#103—118no—
407#102—114no—
408#102—114no—
409#102—118no—
410#97—118no—
411C4×C8—114no—
412C2×C11—82no—
413C2×C11#339714yescomplemented
414C2×C11C2×#55011yescharacteristic
415C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
416C2×C11C2×#57711yescharacteristic
417D11—82no—
418D11—84no—
419C24—21no—
420C24—222no—
421C24—221no—
422#41—4432no—
423C2×Q8—24no—
424C2×Q8—22no—
425C2×Q8—24no—
426C2×Q8—24no—
427C2×Q8C2×C22⋊D1114yes—
428C2×Q8C23×D1114yes—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—112no—
433C2×D4—114no—
434C2×D4—222no—
435C2×D4—224no—
436C2×D4—224no—
437C2×D4—222no—
438C2×D4—221no—
439C2×D4—222no—
440C2×D4—228no—
441C2×D4—224no—
442C2×D4—228no—
443C2×D4—224no—
444C2×D4—448no—
445C2×D4—444no—
446C2×D4—884no—
447C2×D4—882no—
448C2×D4C23×D1112yes—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—44no—
453C22×C4—221no—
454C22×C4—228no—
455C22×C4—224no—
456C22×C4—448no—
457C22×C4—444no—
458C22×C4C2×C22⋊D1112yes—
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1112yes—
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463SD16—2216no—
464SD16—448no—
465SD16—448no—
466D8—228no—
467D8—448no—
468C2×C8—114no—
469C2×C8—112no—
470C2×C8—112no—
471C2×C8—114no—
472C2×C8—224no—
473C2×C8—222no—
474C4⋊C4—24no—
475C4⋊C4—28no—
476C4⋊C4—24no—
477C4⋊C4—21no—
478C4⋊C4—112no—
479C4⋊C4—221no—
480C4⋊C4C2×C22⋊D1114yes—
481C4⋊C4C2×C22⋊D1118yes—
482C4⋊C4C23×D1112yes—
483C22⋊C4—28no—
484C22⋊C4—24no—
485C22⋊C4—28no—
486C22⋊C4—228no—
487C22⋊C4—224no—
488C42—28no—
489C42C2×C22⋊D1112yes—
490C42C2×C22⋊D1114yes—
491C42C23×D1112yes—
492C42C23×D1114yes—
493C11C2×#339711yescharacteristic, complemented, Sylow
494C23—22no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—224no—
499C23—222no—
500C23—444no—
501C23—442no—
502C23—442no—
503C23—444no—
504C23—444no—
505C23—442no—
506C23C22×C22⋊D1111yescharacteristic
507Q8—28no—
508Q8—24no—
509Q8—24no—
510Q8—44no—
511D4—22no—
512D4—22no—
513D4—42no—
514D4—222no—
515D4—224no—
516D4—224no—
517D4—222no—
518D4—4416no—
519D4—448no—
520D4—442no—
521D4—444no—
522D4—888no—
523D4—884no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—42no—
530C2×C4—44no—
531C2×C4—48no—
532C2×C4—222no—
533C2×C4—4416no—
534C2×C4—442no—
535C2×C4—448no—
536C2×C4#6700214yes—
537C2×C4#41×D1112yes—
538C2×C4#6704212yes—
539C2×C4C22×C22⋊D1114yes—
540C2×C4C22×C22⋊D1112yes—
541C2×C4C22×C22⋊D1114yes—
542C2×C4C22×C22⋊D1112yes—
543C2×C4C22×C22⋊D1111yescharacteristic
544C2×C4C24×D1111yescharacteristic
545C8—114no—
546C8—224no—
547C8—222no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—84no—
552C22—444no—
553C22—442no—
554C22—444no—
555C22—442no—
556C22—442no—
557C22—444no—
558C22—888no—
559C22—884no—
560C22C2×#6700212yes—
561C22#1062336512yes—
562C22#1062336812yes—
563C22C23×C22⋊D1111yescharacteristic
564C4—24no—
565C4—24no—
566C4—22no—
567C4—42no—
568C4—44no—
569C4—442no—
570C4C2×#6700214yes—
571C4#1062336512yes—
572C4C2×#41×D1111yescharacteristic
573C4C2×#6704211yescharacteristic
574C2—82no—
575C2—884no—
576C2—882no—
577C2#1308163614yesdirect product factor
578C2C2×#1062336511yescharacteristic
579C2C22×#6700211yescharacteristic
580C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
hypercenterC2×#556D11
hypocenterC11C2×#3397
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#10623108C2semidirect
2. #13081636C2direct (N × H)
3. C2×#10622671C2semidirect
4. C2×#10622698C2semidirect
5. C2×#10622640C2semidirect
6. C2×#10622670C2semidirect
7. C2×#10622696C2semidirect
8. C2×#10622628C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622639C2semidirect
11. C2×C4×#4323C2semidirect
12. C2×C11×#556C2semidirect
15. C11×#556C22semidirect
30. #10623108C22semidirect
39. #10622698C22semidirect
40. #10622696C22semidirect
41. #10622671C22semidirect
42. #10622670C22semidirect
43. #10622640C22semidirect
44. #10622639C22semidirect
45. #10622637C22semidirect
46. #10622628C22semidirect
47. C4×#4323C22semidirect
200. C2×C11⋊C8#41semidirect
204. C2×#556D11semidirect
269. C11⋊C8C2×#41semidirect
277. #556C2×D11semidirect
413. C2×C11#3397semidirect
493. C11C2×#3397semidirect
577. C2#13081636direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231082
#130816362
C2×#106226712
C2×#106226982
C2×#106226402
C2×#106226702
C2×#106226962
C2×#106226282
C2×#106226372
C2×#106226392
C2×C4×#43232
C2×C11×#5562
C2×#339711