Finite Group Databasebeta

← C2×#13078576 #15621602

Subgroups — C2×#13078576 #15621602

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×#10623056C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic, complemented
3#13078576C2116yesmaximal, direct product factor
4C2×#10622476C212yesmaximal, complemented
5C2×#10622498C212yesmaximal, complemented
6C2×#10622479C212yesmaximal, complemented
7C2×#10622495C212yesmaximal, complemented
8C2×#10622611C211yesmaximal, characteristic, complemented
9C2×#10622744C211yesmaximal, characteristic, complemented
10C22×#66873C211yesmaximal, characteristic, complemented
11C2×#10622742C211yesmaximal, characteristic, complemented
12C2×C11×#428C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×C4×C22⋊D11—22no—
19C2×#66979C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21#10623056—24no—
22#10623056C2218yes—
23C2×#66948C2212yes—
24C2×#66948C2212yes—
25#10623035—24no—
26#10623035C2218yescomplemented
27C2×#66946—21no—
28C2×#66945C2212yescomplemented
29C2×C4⋊C4×D11C2212yescomplemented
30C2×#66940—21no—
31C2×#66935—22no—
32C2×#66928—21no—
33C2×#66927—21no—
34C11×#428C2218yescomplemented
35C2×C11×#107C2212yescomplemented
36C2×C11×#106C2212yescomplemented
37#10622744C2218yescomplemented
38#10622742C2218yescomplemented
39C2×#66885C2212yes—
40C2×#66885C2212yes—
41C2×(C2×D11)⋊C8C2212yescomplemented
42C2×(C2×D11)⋊C8C2212yescomplemented
43#10622611C2218yescomplemented
44C2×#66873C2212yes—
45C2×#66873C2212yes—
46C2×#66873C2218yescomplemented
47C2×#66872C2211yescharacteristic, complemented
48C2×#66872C2211yescharacteristic, complemented
49C2×#66871C2211yescharacteristic, complemented
50C2×#66871C2211yescharacteristic, complemented
51#10622498C22116yescomplemented
52#10622495C22116yescomplemented
53#10622479C22116yescomplemented
54#10622476C22116yescomplemented
55C24×D11—21no—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11D412yes—
59C2×#4339—24no—
60C2×#4339—24no—
61C2×#4339D414yes—
62C2×#4339C2314yes—
63C22×D44—24no—
64C22×D44—24no—
65C22×D44—21no—
66C22×D44—22no—
67C22×D44—22no—
68C22×D44—22no—
69C22×D44D411yescharacteristic
70C22×D44C2312yes—
71C22×D44C2314yes—
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⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C2×C22⋊Dic11—21no—
89C4×C22⋊D11—216no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93#66979—22no—
94#66979C2314yes—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—22no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—22no—
100C22×C11⋊C8—24no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2314yes—
104#66948—24no—
105#66948—24no—
106#66948C2318yes—
107#66948C2318yes—
108#66946—28no—
109#66945—24no—
110#66945C2318yescomplemented
111C4⋊C4×D11—24no—
112C4⋊C4×D11C2318yescomplemented
113#66940—28no—
114#66935—216no—
115#66928—28no—
116#66927—28no—
117C11×#107C2318yescomplemented
118C11×#106C2318yescomplemented
119#66885C2318yes—
120#66885C2318yes—
121(C2×D11)⋊C8C2318yescomplemented
122(C2×D11)⋊C8C2318yescomplemented
123#66873C2318yes—
124#66873C2318yes—
125#66872C2314yescomplemented
126#66872C2314yescomplemented
127#66871C2314yescomplemented
128#66871C2314yescomplemented
129C2×#3096—111nomaximal, Sylow
130C24×C11C2×D411yescharacteristic
131C23×D11—22no—
132C23×D11—24no—
133C23×D11—44no—
134C23×D11—82no—
135C23×D11—82no—
136C23×D11C2×D412yes—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—24no—
141C22×C4×C11—82no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11#4114yes—
145C22×C4×C11#4114yes—
146C22×C4×C11C2411yescharacteristic
147C22×C4×C11C2412yes—
148C2×C22⋊D11—28no—
149C2×C22⋊D11C2×D418yes—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C2×D412yes—
153#4339—216no—
154#4339—28no—
155#4339—28no—
156C2×D44—28no—
157C2×D44—28no—
158C2×D44—24no—
159C2×D44—24no—
160C2×D44—22no—
161C2×D44—24no—
162C2×D44—28no—
163C2×D44—24no—
164C2×D44—28no—
165C2×D44—44no—
166C2×D44—48no—
167C2×D44—84no—
168C2×D44—84no—
169C2×D44C2×D414yes—
170C2×D44C2414yes—
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—24no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4C2412yes—
187C11×C4⋊C4C2412yes—
188C11×C4⋊C4C2414yes—
189C11×C22⋊C4—24no—
190C42×C11—24no—
191C22⋊Dic11—24no—
192(C2×D11)⋊C4—28no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4—28no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11C2412yes—
198C4⋊Dic11C2412yes—
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×#428D1111yescharacteristic, complemented
215C2×#427—111no—
216C2×#418—111no—
217C22×#102—111no—
218C2×#408—111no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11#12314yes—
222C23×C11C22×D412yes—
223C23×C11C22×D411yescharacteristic
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—48no—
229C22×D11—44no—
230C22×D11—44no—
231C22×D11—44no—
232C22×D11—84no—
233C22×D11—84no—
234C22×D11—816no—
235C22×D11C22×D414yes—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—44no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—84no—
243C2×C4×C11#12314yes—
244C2×C4×C11#12318yes—
245C2×C4×C11C22×D412yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4112yes—
248C2×C4×C11C2×#4114yes—
249C2×C4×C11C2×#4112yes—
250C2×C4×C11C2×#4114yes—
251C2×C4×C11C2511yescharacteristic
252C22⋊D11—216no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11C22×D414yes—
259D44—28no—
260D44—24no—
261D44—24no—
262D44—48no—
263D44—44no—
264D44—88no—
265D44—88no—
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×D4—111no—
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—112no—
294C22×C4⋊C4C2×D1111yescharacteristic
295#482—1116no—
296#482—1116no—
297#481—1116no—
298#480—1116no—
299#428C2×D1118yescomplemented
300#427—118no—
301C2×#107—111no—
302C2×#107—111no—
303C2×#107C2×D1112yescomplemented
304C2×#106—111no—
305C2×#106—111no—
306C2×#106C2×D1112yescomplemented
307#418—118no—
308C2×#102—112no—
309C2×#102—112no—
310C2×#102—112no—
311C2×#102—112no—
312C2×#102—118no—
313#408—118no—
314C2×C22⋊C8—112no—
315C2×C22⋊C8—112no—
316C22×C11—28no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11C2×#12314yes—
320C22×C11C2×#12312yes—
321C22×C11#57612yes—
322C22×C11#57712yes—
323C22×C11C23×D411yescharacteristic
324C2×D11—24no—
325C2×D11—24no—
326C2×D11—24no—
327C2×D11—48no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—816no—
332C2×D11—88no—
333C4×C11—44no—
334C4×C11—42no—
335C4×C11—42no—
336C4×C11C2×#12314yes—
337C4×C11C2×#12312yes—
338C4×C11C22×#4111yescharacteristic
339C4×C11C22×#4111yescharacteristic
340Dic11—24no—
341Dic11—42no—
342Dic11—42no—
343C25—221no—
344C2×#41—114no—
345C2×#41—114no—
346C2×#41—224no—
347C2×#41—224no—
348C22×Q8—111no—
349C22×D4—112no—
350C22×D4—111no—
351C22×D4—112no—
352C22×D4—114no—
353C22×D4—222no—
354C22×D4—222no—
355C22×D4—224no—
356C22×D4—221no—
357C22×D4—222no—
358C22×D4—224no—
359C23×C4—21no—
360C23×C4—112no—
361C23×C4—222no—
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—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—118no—
391C2×C4⋊C4—224no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4C22×D1112yes—
394C2×C4⋊C4C22×D1114yes—
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—114no—
406#107—114no—
407#107C22×D1118yescomplemented
408#106—114no—
409#106—114no—
410#106C22×D1118yescomplemented
411#102—118no—
412#102—118no—
413#102—118no—
414#102—118no—
415C22⋊C8—118no—
416C22⋊C8—118no—
417C2×C11—24no—
418C2×C11#309614yescomplemented
419C2×C11C22×#12311yescharacteristic
420C2×C11C2×#57611yescharacteristic
421C2×C11C2×#57711yescharacteristic
422D11—44no—
423D11—84no—
424C24—112no—
425C24—222no—
426C24—224no—
427C24—444no—
428C24—882no—
429C24—882no—
430C24D4×D1111yescharacteristic
431#41—2216no—
432#41—228no—
433#41—228no—
434C2×Q8—114no—
435C2×Q8—224no—
436C2×D4—118no—
437C2×D4—114no—
438C2×D4—114no—
439C2×D4—228no—
440C2×D4—228no—
441C2×D4—228no—
442C2×D4—224no—
443C2×D4—224no—
444C2×D4—228no—
445C2×D4—222no—
446C2×D4—224no—
447C2×D4—224no—
448C2×D4—228no—
449C2×D4—444no—
450C2×D4—448no—
451C2×D4—884no—
452C2×D4—884no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—82no—
458C22×C4—112no—
459C22×C4—114no—
460C22×C4—114no—
461C22×C4—228no—
462C22×C4—224no—
463C22×C4—224no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—884no—
467C22×C4#433914yes—
468C22×C4D4×D1112yes—
469C22×C4D4×D1111yescharacteristic
470C22×C4#434314yes—
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—22no—
482C4⋊C4—24no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—112no—
486C4⋊C4—112no—
487C4⋊C4—228no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4C23×D1114yes—
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—114no—
505C23—224no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—448no—
510C23—444no—
511C23—444no—
512C23—444no—
513C23—884no—
514C23—884no—
515C23—8816no—
516C23#6694714yes—
517C23C2×D4×D1112yes—
518C23C2×D4×D1111yescharacteristic
519Q8—228no—
520D4—2216no—
521D4—228no—
522D4—224no—
523D4—224no—
524D4—444no—
525D4—448no—
526D4—888no—
527D4—888no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—44no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—84no—
535C2×C4—114no—
536C2×C4—224no—
537C2×C4—228no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—888no—
545C2×C4#6694714yes—
546C2×C4#6694718yes—
547C2×C4C2×#433912yes—
548C2×C4C2×#433914yes—
549C2×C4C2×D4×D1112yes—
550C2×C4C2×D4×D1111yescharacteristic
551C2×C4C2×#434312yes—
552C2×C4C2×#434314yes—
553C2×C4C24×D1111yescharacteristic
554C8—24no—
555C8—222no—
556C8—222no—
557C22—28no—
558C22—22no—
559C22—22no—
560C22—224no—
561C22—224no—
562C22—224no—
563C22—448no—
564C22—444no—
565C22—444no—
566C22—444no—
567C22—8816no—
568C22—888no—
569C22C2×#6694714yes—
570C22C2×#6694712yes—
571C22#1062330512yes—
572C22#1062330912yes—
573C22C22×D4×D1111yescharacteristic
574C4—44no—
575C4—42no—
576C4—42no—
577C4—224no—
578C4—442no—
579C4—442no—
580C4C2×#6694712yes—
581C4C2×#6694714yes—
582C4C22×#433911yescharacteristic
583C4C22×#434311yescharacteristic
584C2—24no—
585C2—444no—
586C2—884no—
587C2#1307857614yesdirect product factor
588C2C22×#6694711yescharacteristic
589C2C2×#1062330511yescharacteristic
590C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC2×#10623056C2
hypercenterC2×#428D11
hypocenterC11C2×#3096
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C2×#10623035C2semidirect
3. #13078576C2direct (N × H)
4. C2×#10622476C2semidirect
5. C2×#10622498C2semidirect
6. C2×#10622479C2semidirect
7. C2×#10622495C2semidirect
8. C2×#10622611C2semidirect
9. C2×#10622744C2semidirect
10. C22×#66873C2semidirect
11. C2×#10622742C2semidirect
12. C2×C11×#428C2semidirect
26. #10623035C22semidirect
28. C2×#66945C22semidirect
29. C2×C4⋊C4×D11C22semidirect
34. C11×#428C22semidirect
35. C2×C11×#107C22semidirect
36. C2×C11×#106C22semidirect
37. #10622744C22semidirect
38. #10622742C22semidirect
41. C2×(C2×D11)⋊C8C22semidirect
42. C2×(C2×D11)⋊C8C22semidirect
43. #10622611C22semidirect
46. C2×#66873C22semidirect
47. C2×#66872C22semidirect
48. C2×#66872C22semidirect
49. C2×#66871C22semidirect
50. C2×#66871C22semidirect
51. #10622498C22semidirect
52. #10622495C22semidirect
53. #10622479C22semidirect
54. #10622476C22semidirect
110. #66945C23semidirect
112. C4⋊C4×D11C23semidirect
117. C11×#107C23semidirect
118. C11×#106C23semidirect
121. (C2×D11)⋊C8C23semidirect
122. (C2×D11)⋊C8C23semidirect
125. #66872C23semidirect
126. #66872C23semidirect
127. #66871C23semidirect
128. #66871C23semidirect
214. C2×#428D11semidirect
299. #428C2×D11semidirect
303. C2×#107C2×D11semidirect
306. C2×#106C2×D11semidirect
407. #107C22×D11semidirect
410. #106C22×D11semidirect
418. C2×C11#3096semidirect
501. C11C2×#3096semidirect
587. C2#13078576direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230562
C2×#106230352
#130785762
C2×#106224762
C2×#106224982
C2×#106224792
C2×#106224952
C2×#106226112
C2×#106227442
C22×#668732
C2×#106227422
C2×C11×#4282
C2×#309611