Finite Group Databasebeta

← C2×#13078572 #15621598

Subgroups — C2×#13078572 #15621598

Order 2816.

2362 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623336C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic, complemented
3#13078572C2116yesmaximal, direct product factor
4C2×#10622390C212yesmaximal, complemented
5C2×#10622392C212yesmaximal, complemented
6C2×#10622397C212yesmaximal, complemented
7C2×#10622387C212yesmaximal, complemented
8C2×#10622734C211yesmaximal, characteristic, complemented
9C2×#10622611C211yesmaximal, characteristic, complemented
10C22×#66896C211yesmaximal, characteristic, complemented
11C2×#10622742C211yesmaximal, characteristic, complemented
12C2×C11×#418C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C2×#67006—22no—
18#10623336—24no—
19#10623336C2218yes—
20C2×#66993—21no—
21C2×#66991C2212yes—
22C2×#66991C2212yes—
23C2×#66989—21no—
24C2×#66979C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27#10623054—24no—
28#10623054C2218yescomplemented
29C2×#66945C2212yescomplemented
30C2×C4⋊C4×D11C2212yescomplemented
31C2×(C22⋊D11)⋊C4—22no—
32C2×C4×D44—21no—
33C2×C4×Dic22—21no—
34C11×#418C2218yescomplemented
35C2×C11×#102C2212yes—
36C2×C11×#102C2212yes—
37C2×#66896C2212yes—
38C2×#66896C2212yes—
39C2×#66896C2218yescomplemented
40#10622742C2218yescomplemented
41#10622734C2218yescomplemented
42C2×(C2×D11)⋊C8C2212yescomplemented
43C2×(C2×D11)⋊C8C2212yescomplemented
44C2×#66882C2212yescomplemented
45C2×#66881C2212yescomplemented
46#10622611C2218yescomplemented
47C2×#66872C2211yescharacteristic, complemented
48C2×#66872C2211yescharacteristic, complemented
49C2×#66871C2211yescharacteristic, complemented
50C2×#66871C2211yescharacteristic, complemented
51#10622397C22116yescomplemented
52#10622392C22116yescomplemented
53#10622390C22116yescomplemented
54#10622387C22116yescomplemented
55C25×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—22no—
58C22×D4×C11—24no—
59C22×D4×C11—24no—
60C22×D4×C11C2312yes—
61C22×D4×C11C2314yes—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—22no—
64C22×C22⋊D11—22no—
65C22×C22⋊D11D412yes—
66C23×Dic11—21no—
67C2×#4339—24no—
68C2×#4339—24no—
69C2×#4339D414yes—
70C2×#4339C2314yes—
71C22×D44D411yescharacteristic
72C22×C4×D11—22no—
73C22×C4×D11C2312yes—
74C22×Dic22D411yescharacteristic
75C2×C11×M16—24no—
76C2×C11×M16C2314yes—
77C22×C8×C11C2312yes—
78C11×#117—22no—
79C11×#117C2314yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84#67006—216no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88#66993—28no—
89#66991—24no—
90#66991—24no—
91#66991C2318yes—
92#66991C2318yes—
93#66989—28no—
94C2×(C2×D11)⋊C4—22no—
95#66979—22no—
96#66979C2314yes—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11C2314yes—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—22no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—22no—
106C22×C11⋊C8—24no—
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2314yes—
110#66945—24no—
111#66945C2318yescomplemented
112C4⋊C4×D11—24no—
113C4⋊C4×D11C2318yescomplemented
114(C22⋊D11)⋊C4—216no—
115C4×D44—28no—
116C4×Dic22—28no—
117C11×#102C2318yes—
118C11×#102C2318yes—
119#66896C2318yes—
120#66896C2318yes—
121(C2×D11)⋊C8C2318yescomplemented
122(C2×D11)⋊C8C2318yescomplemented
123#66882C2318yescomplemented
124#66881C2318yescomplemented
125#66872C2314yescomplemented
126#66872C2314yescomplemented
127#66871C2314yescomplemented
128#66871C2314yescomplemented
129C2×#3096—111nomaximal, Sylow
130C24×C11—22no—
131C24×C11—24no—
132C24×C11—44no—
133C24×C11—82no—
134C24×C11—82no—
135C24×C11C2×D411yescharacteristic
136C23×D11C2×D412yes—
137C2×D4×C11—24no—
138C2×D4×C11—22no—
139C2×D4×C11—24no—
140C2×D4×C11—28no—
141C2×D4×C11—24no—
142C2×D4×C11—28no—
143C2×D4×C11—44no—
144C2×D4×C11—48no—
145C2×D4×C11C2414yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11#4114yes—
151C22×C4×C11#4114yes—
152C22×C4×C11C2411yescharacteristic
153C22×C4×C11C2412yes—
154C2×C22⋊D11—28no—
155C2×C22⋊D11—28no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—84no—
158C2×C22⋊D11—84no—
159C2×C22⋊D11C2×D418yes—
160C22×Dic11—22no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—24no—
164C22×Dic11—82no—
165C22×Dic11C2×D412yes—
166#4339—216no—
167#4339—28no—
168#4339—28no—
169C2×D44—24no—
170C2×D44C2×D414yes—
171C2×C4×D11—28no—
172C2×C4×D11—24no—
173C2×C4×D11—24no—
174C2×C4×D11—84no—
175C2×C4×D11C2×D414yes—
176C2×C4×D11C2414yes—
177C2×Dic22—24no—
178C2×Dic22C2×D414yes—
179C11×M16—28no—
180C2×C8×C11—24no—
181C2×C8×C11C2414yes—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4C2412yes—
185C11×C4⋊C4C2412yes—
186C11×C22⋊C4—24no—
187C42×C11—24no—
188C22⋊Dic11—28no—
189C22⋊Dic11—28no—
190C22⋊Dic11—24no—
191(C2×D11)⋊C4—28no—
192C4⋊Dic11—24no—
193C4⋊Dic11—22no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C2412yes—
197C4⋊Dic11C2412yes—
198C4⋊Dic11C2414yes—
199Dic11⋊C4—28no—
200C4×Dic11—28no—
201C4×Dic11—24no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—28no—
205C2×C11⋊C8C2412yes—
206C2×C11⋊C8C2412yes—
207C2×#535—111no—
208C2×#520—111no—
209#3096—1116no—
210C2×#481—112no—
211C2×#482—112no—
212C2×#482—112no—
213C2×#480—112no—
214C2×#428—111no—
215C2×#427—111no—
216C2×#418D1111yescharacteristic, complemented
217C22×#102—111no—
218C2×#408—111no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—24no—
222C23×C11—48no—
223C23×C11—44no—
224C23×C11—44no—
225C23×C11—44no—
226C23×C11—84no—
227C23×C11—84no—
228C23×C11—816no—
229C23×C11#12314yes—
230C23×C11C22×D412yes—
231C23×C11C22×D411yescharacteristic
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11C22×D414yes—
236D4×C11—24no—
237D4×C11—24no—
238D4×C11—48no—
239D4×C11—44no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11#12314yes—
245C2×C4×C11#12318yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4112yes—
249C2×C4×C11C2×#4114yes—
250C2×C4×C11C2×#4112yes—
251C2×C4×C11C2×#4114yes—
252C2×C4×C11C2511yescharacteristic
253C22⋊D11—216no—
254C22⋊D11—88no—
255C22⋊D11—88no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—44no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—84no—
264C2×Dic11C22×D414yes—
265D44—28no—
266C4×D11—28no—
267C4×D11—24no—
268C4×D11—24no—
269C4×D11—88no—
270Dic22—28no—
271C8×C11—24no—
272C11⋊C8—22no—
273C11⋊C8—22no—
274C22×#41—111no—
275C23×D4C2×D1111yescharacteristic
276C22×M16C2×D1111yescharacteristic
277C23×C8—111no—
278#535—118no—
279#535—224no—
280C2×#127—221no—
281C2×#124—221no—
282C2×#121—112no—
283C2×#121—112no—
284C2×#120—222no—
285#520—118no—
286#520—224no—
287C2×C4×Q8—221no—
288C2×C4×D4—221no—
289C2×C4×D4—222no—
290C2×#117—111no—
291C2×#117—112no—
292C2×#117C2×D1111yescharacteristic
293C22×C4⋊C4—111no—
294C22×C4⋊C4—112no—
295#482—1116no—
296#482—1116no—
297#481—1116no—
298#480—1116no—
299#428—118no—
300#427—118no—
301C2×#107—112no—
302C2×#107—111no—
303C2×#107—111no—
304C2×#106—112no—
305C2×#106—111no—
306C2×#106—111no—
307#418C2×D1118yescomplemented
308C2×#102—112no—
309C2×#102—112no—
310C2×#102—118no—
311C2×#102C2×D1112yes—
312C2×#102C2×D1112yes—
313#408—118no—
314C2×C22⋊C8—112no—
315C2×C22⋊C8—112no—
316C22×C11—28no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—816no—
323C22×C11—88no—
324C22×C11C2×#12314yes—
325C22×C11C2×#12312yes—
326C22×C11#57612yes—
327C22×C11#57712yes—
328C22×C11C23×D411yescharacteristic
329C2×D11—24no—
330C2×D11—24no—
331C2×D11—24no—
332C2×D11—48no—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11C2×#12314yes—
336C4×C11C2×#12312yes—
337C4×C11C22×#4111yescharacteristic
338C4×C11C22×#4111yescharacteristic
339Dic11—24no—
340Dic11—44no—
341Dic11—42no—
342Dic11—42no—
343C25—21no—
344C2×#41—114no—
345C2×#41—114no—
346C2×#41—224no—
347C2×#41—224no—
348C22×Q8—111no—
349C22×D4—24no—
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—24no—
353C22×D4—112no—
354C22×D4—111no—
355C22×D4—222no—
356C22×D4—222no—
357C22×D4C22×D1112yes—
358C22×D4C22×D1114yes—
359C23×C4—112no—
360C23×C4—222no—
361C23×C4—221no—
362C23×C4C22×D1111yescharacteristic
363C2×M16—24no—
364C2×M16C22×D1114yes—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8—114no—
368C22×C8—224no—
369C22×C8C22×D1112yes—
370#127—228no—
371#124—228no—
372#121—118no—
373#121—118no—
374#121—224no—
375#121—224no—
376#120—2216no—
377C4×Q8—228no—
378C4×D4—228no—
379C4×D4—2216no—
380#117—22no—
381#117—114no—
382#117—118no—
383#117—224no—
384#117—222no—
385#117C22×D1114yes—
386C2×C4⋊C4—112no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—118no—
391C2×C4⋊C4—224no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—222no—
400C2×C22⋊C4—222no—
401C2×C22⋊C4—221no—
402C2×C42—21no—
403C2×C42—222no—
404C2×C42—221no—
405#107—118no—
406#107—114no—
407#107—114no—
408#106—118no—
409#106—114no—
410#106—114no—
411#102—118no—
412#102—118no—
413#102C22×D1118yes—
414#102C22×D1118yes—
415C22⋊C8—118no—
416C22⋊C8—118no—
417C2×C11—24no—
418C2×C11—84no—
419C2×C11#309614yescomplemented
420C2×C11C22×#12311yescharacteristic
421C2×C11C2×#57611yescharacteristic
422C2×C11C2×#57711yescharacteristic
423D11—44no—
424C24—22no—
425C24—24no—
426C24—44no—
427C24—82no—
428C24—82no—
429C24—112no—
430C24D4×D1111yescharacteristic
431#41—2216no—
432#41—228no—
433#41—228no—
434C2×Q8—114no—
435C2×Q8—224no—
436C2×D4—24no—
437C2×D4—28no—
438C2×D4—22no—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—28no—
442C2×D4—44no—
443C2×D4—48no—
444C2×D4—118no—
445C2×D4—114no—
446C2×D4—228no—
447C2×D4—228no—
448C2×D4—228no—
449C2×D4—224no—
450C2×D4—884no—
451C2×D4—884no—
452C2×D4C23×D1114yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—112no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—228no—
459C22×C4—224no—
460C22×C4—224no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—222no—
464C22×C4—224no—
465C22×C4—884no—
466C22×C4—882no—
467C22×C4#433914yes—
468C22×C4D4×D1112yes—
469C22×C4D4×D1111yescharacteristic
470C22×C4#434114yes—
471C22×C4C23×D1112yes—
472C22×C4C23×D1111yescharacteristic
473M16—28no—
474C2×C8—24no—
475C2×C8—112no—
476C2×C8—112no—
477C2×C8—222no—
478C2×C8—222no—
479C2×C8—228no—
480C2×C8C23×D1114yes—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—114no—
484C4⋊C4—112no—
485C4⋊C4—112no—
486C4⋊C4—228no—
487C4⋊C4—222no—
488C4⋊C4—224no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4C23×D1112yes—
492C4⋊C4C23×D1112yes—
493C22⋊C4—24no—
494C22⋊C4—228no—
495C22⋊C4—228no—
496C22⋊C4—228no—
497C22⋊C4—224no—
498C42—24no—
499C42—228no—
500C42—224no—
501C11C2×#309611yescharacteristic, complemented, Sylow
502C23—22no—
503C23—22no—
504C23—24no—
505C23—48no—
506C23—44no—
507C23—44no—
508C23—44no—
509C23—84no—
510C23—84no—
511C23—816no—
512C23—114no—
513C23—224no—
514C23—224no—
515C23—224no—
516C23#6693614yes—
517C23C2×D4×D1112yes—
518C23C2×D4×D1111yescharacteristic
519Q8—228no—
520D4—24no—
521D4—24no—
522D4—44no—
523D4—48no—
524D4—2216no—
525D4—228no—
526D4—888no—
527D4—888no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—114no—
533C2×C4—224no—
534C2×C4—228no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—224no—
540C2×C4—444no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—888no—
544C2×C4—884no—
545C2×C4#6693614yes—
546C2×C4#6693618yes—
547C2×C4C2×#433912yes—
548C2×C4C2×#433914yes—
549C2×C4C2×D4×D1112yes—
550C2×C4C2×D4×D1111yescharacteristic
551C2×C4C2×#434112yes—
552C2×C4C2×#434114yes—
553C2×C4C24×D1111yescharacteristic
554C8—24no—
555C8—222no—
556C8—222no—
557C22—28no—
558C22—22no—
559C22—22no—
560C22—44no—
561C22—44no—
562C22—44no—
563C22—816no—
564C22—88no—
565C22—224no—
566C22—224no—
567C22—224no—
568C22—448no—
569C22C2×#6693614yes—
570C22C2×#6693612yes—
571C22#1062330512yes—
572C22#1062330612yes—
573C22C22×D4×D1111yescharacteristic
574C4—42no—
575C4—42no—
576C4—224no—
577C4—444no—
578C4—442no—
579C4—442no—
580C4C2×#6693612yes—
581C4C2×#6693614yes—
582C4C22×#433911yescharacteristic
583C4C22×#434111yescharacteristic
584C2—24no—
585C2—84no—
586C2—444no—
587C2#1307857214yesdirect product factor
588C2C22×#6693611yescharacteristic
589C2C2×#1062330511yescharacteristic
590C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#418C2
socleC23×C11C22×D4
prime radicalC2×#10623336C2
hypercenterC2×#418D11
hypocenterC11C2×#3096
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#10623054C2semidirect
3. #13078572C2direct (N × H)
4. C2×#10622390C2semidirect
5. C2×#10622392C2semidirect
6. C2×#10622397C2semidirect
7. C2×#10622387C2semidirect
8. C2×#10622734C2semidirect
9. C2×#10622611C2semidirect
10. C22×#66896C2semidirect
11. C2×#10622742C2semidirect
12. C2×C11×#418C2semidirect
28. #10623054C22semidirect
29. C2×#66945C22semidirect
30. C2×C4⋊C4×D11C22semidirect
34. C11×#418C22semidirect
39. C2×#66896C22semidirect
40. #10622742C22semidirect
41. #10622734C22semidirect
42. C2×(C2×D11)⋊C8C22semidirect
43. C2×(C2×D11)⋊C8C22semidirect
44. C2×#66882C22semidirect
45. C2×#66881C22semidirect
46. #10622611C22semidirect
47. C2×#66872C22semidirect
48. C2×#66872C22semidirect
49. C2×#66871C22semidirect
50. C2×#66871C22semidirect
51. #10622397C22semidirect
52. #10622392C22semidirect
53. #10622390C22semidirect
54. #10622387C22semidirect
111. #66945C23semidirect
113. C4⋊C4×D11C23semidirect
121. (C2×D11)⋊C8C23semidirect
122. (C2×D11)⋊C8C23semidirect
123. #66882C23semidirect
124. #66881C23semidirect
125. #66872C23semidirect
126. #66872C23semidirect
127. #66871C23semidirect
128. #66871C23semidirect
216. C2×#418D11semidirect
307. #418C2×D11semidirect
419. C2×C11#3096semidirect
501. C11C2×#3096semidirect
587. C2#13078572direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233362
C2×#106230542
#130785722
C2×#106223902
C2×#106223922
C2×#106223972
C2×#106223872
C2×#106227342
C2×#106226112
C22×#668962
C2×#106227422
C2×C11×#4182
C2×#309611