Finite Group Databasebeta

← C2×#13078598 #15621626

Subgroups — C2×#13078598 #15621626

Order 2816.

2234 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623041C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic, complemented
3#13078598C2116yesmaximal, direct product factor
4C2×#10622497C212yesmaximal, complemented
5C2×#10622480C212yesmaximal, complemented
6C2×#10622479C212yesmaximal, complemented
7C2×#10622495C212yesmaximal, complemented
8C22×#66871C211yesmaximal, characteristic, complemented
9C2×#10622746C211yesmaximal, characteristic, complemented
10C2×#10622615C211yesmaximal, characteristic, complemented
11C2×#10622742C211yesmaximal, characteristic, complemented
12C2×C11×#428C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66983—22no—
19C22×C4⋊Dic11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21#10623054—24no—
22#10623054C2218yescomplemented
23#10623041—24no—
24#10623041C2218yes—
25C2×#66950—21no—
26C2×#66950C2212yes—
27C2×#66948—21no—
28C2×#66948C2212yes—
29C2×#66945C2212yes—
30C2×C4⋊C4×D11C2212yes—
31C2×(C22⋊D11)⋊C4—22no—
32C2×C4×D44—21no—
33C2×C4×Dic22—21no—
34C11×#428C2218yescomplemented
35C2×C11×#107C2212yes—
36C2×C11×#106C2212yes—
37#10622746C2218yescomplemented
38#10622742C2218yescomplemented
39C2×#66885C2212yes—
40C2×(C2×D11)⋊C8C2212yes—
41C2×(C2×D11)⋊C8C2212yes—
42C2×#66880C2212yes—
43#10622615C2218yescomplemented
44C2×#66874C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66871C2212yes—
49C2×#66871C2212yes—
50C2×#66871C2218yescomplemented
51#10622497C22116yescomplemented
52#10622495C22116yescomplemented
53#10622480C22116yescomplemented
54#10622479C22116yescomplemented
55C23×C4×C11—21no—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—21no—
58C22×C22⋊D11D412yes—
59C23×Dic11—21no—
60C2×#4339—24no—
61C2×#4339—24no—
62C2×#4339—22no—
63C2×#4339—24no—
64C2×#4339—24no—
65C2×#4339D414yes—
66C2×#4339C2314yes—
67C2×#4339C2314yes—
68C22×D44—22no—
69C22×D44D411yescharacteristic
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×C4×D11—22no—
73C22×C4×D11C2312yes—
74C22×Dic22D411yescharacteristic
75C22×Dic22C2311yescharacteristic
76C2×C11×M16—24no—
77C2×C11×M16C2314yes—
78C22×C8×C11C2312yes—
79C11×#117—22no—
80C11×#117C2314yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2314yes—
87C2×C11×C22⋊C4—21no—
88C2×C42×C11—21no—
89#66983—216no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11C2312yes—
97C2×C4⋊Dic11C2314yes—
98C2×Dic11⋊C4—22no—
99C2×C4×Dic11—22no—
100C22×C11⋊C8—24no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2314yes—
104#66950—24no—
105#66950—28no—
106#66950C2318yes—
107#66948—28no—
108#66948—24no—
109#66948C2318yes—
110#66945—24no—
111#66945C2318yes—
112C4⋊C4×D11—24no—
113C4⋊C4×D11C2318yes—
114(C22⋊D11)⋊C4—216no—
115C4×D44—28no—
116C4×Dic22—28no—
117C11×#107C2318yes—
118C11×#106C2318yes—
119#66885C2318yes—
120(C2×D11)⋊C8C2318yes—
121(C2×D11)⋊C8C2318yes—
122#66880C2318yes—
123#66874C2314yes—
124#66874C2314yes—
125#66873C2314yes—
126#66873C2314yes—
127#66871C2318yes—
128#66871C2318yes—
129C2×#3098—111nomaximal, Sylow
130C24×C11C2×D411yescharacteristic
131C23×D11—21no—
132C23×D11C2×D412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—82no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11#4114yes—
141C22×C4×C11#4114yes—
142C22×C4×C11C2411yescharacteristic
143C22×C4×C11C2412yes—
144C2×C22⋊D11—28no—
145C2×C22⋊D11—24no—
146C2×C22⋊D11—44no—
147C2×C22⋊D11C2×D418yes—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11—24no—
151C22×Dic11—82no—
152C22×Dic11C2×D412yes—
153#4339—216no—
154#4339—28no—
155#4339—28no—
156#4339—28no—
157#4339—28no—
158#4339—48no—
159C2×D44—28no—
160C2×D44—24no—
161C2×D44—21no—
162C2×D44—22no—
163C2×D44—22no—
164C2×D44—84no—
165C2×D44C2×D414yes—
166C2×D44C2412yes—
167C2×C4×D11—28no—
168C2×C4×D11—24no—
169C2×C4×D11—24no—
170C2×C4×D11—24no—
171C2×C4×D11—44no—
172C2×C4×D11—84no—
173C2×C4×D11C2×D414yes—
174C2×C4×D11C2414yes—
175C2×Dic22—24no—
176C2×Dic22—21no—
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22C2×D414yes—
180C2×Dic22C2412yes—
181C11×M16—28no—
182C2×C8×C11—24no—
183C2×C8×C11C2414yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4C2414yes—
189C11×C4⋊C4C2412yes—
190C11×C4⋊C4C2412yes—
191C11×C22⋊C4—24no—
192C42×C11—24no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4—28no—
196C4⋊Dic11—28no—
197C4⋊Dic11—24no—
198C4⋊Dic11—22no—
199C4⋊Dic11C2414yes—
200Dic11⋊C4—28no—
201C4×Dic11—28no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—28no—
205C2×C11⋊C8C2412yes—
206C2×C11⋊C8C2412yes—
207C2×#537—111no—
208C2×#520—111no—
209#3098—1116no—
210C2×#484—112no—
211C2×#485—112no—
212C2×#482—112no—
213C2×#480—112no—
214C2×#428D1111yescharacteristic, complemented
215C22×#107—111no—
216C2×#417—111no—
217C2×#416—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—22no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11C22×D414yes—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—42no—
236C2×C4×C11—44no—
237C2×C4×C11—42no—
238C2×C4×C11—84no—
239C2×C4×C11#12314yes—
240C2×C4×C11#12318yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4112yes—
244C2×C4×C11C2×#4114yes—
245C2×C4×C11C2×#4112yes—
246C2×C4×C11C2×#4114yes—
247C2×C4×C11C2511yescharacteristic
248C22⋊D11—216no—
249C22⋊D11—48no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—42no—
254C2×Dic11—44no—
255C2×Dic11—84no—
256C2×Dic11C22×D414yes—
257D44—28no—
258D44—22no—
259D44—22no—
260D44—42no—
261D44—88no—
262C4×D11—28no—
263C4×D11—24no—
264C4×D11—24no—
265C4×D11—48no—
266C4×D11—88no—
267Dic22—28no—
268Dic22—22no—
269Dic22—22no—
270Dic22—42no—
271C8×C11—24no—
272C11⋊C8—22no—
273C11⋊C8—22no—
274C22×#41—111no—
275C22×#41—111no—
276C22×M16C2×D1111yescharacteristic
277C23×C8—111no—
278#537—118no—
279#537—224no—
280C2×C22⋊Q8—112no—
281C2×C22⋊Q8—221no—
282C2×#121—112no—
283C2×#121—221no—
284C2×#121—222no—
285#520—118no—
286#520—224no—
287C2×C4×Q8—221no—
288C2×C4×D4—221no—
289C2×C4×D4—222no—
290C2×#117—112no—
291C2×#117C2×D1111yescharacteristic
292C22×C4⋊C4—111no—
293C22×C4⋊C4—112no—
294C22×C4⋊C4C2×D1111yescharacteristic
295#485—1116no—
296#484—1116no—
297#482—1116no—
298#480—1116no—
299#428C2×D1118yescomplemented
300C2×#107—112no—
301C2×#107—112no—
302C2×#107—118no—
303C2×#107C2×D1112yes—
304C2×#106C2×D1112yes—
305#417—118no—
306#416—118no—
307C2×#103—112no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#102—112no—
311C2×#102—111no—
312C2×#102—111no—
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#57812yes—
323C22×C11C23×D411yescharacteristic
324C2×D11—24no—
325C2×D11—24no—
326C2×D11—24no—
327C2×D11—48no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—84no—
332C4×C11—44no—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11C2×#12314yes—
336C4×C11C2×#12312yes—
337C4×C11C22×#4111yescharacteristic
338C4×C11C22×#4111yescharacteristic
339Dic11—24no—
340Dic11—42no—
341Dic11—44no—
342C2×#41—114no—
343C2×#41—114no—
344C2×#41—114no—
345C2×#41—224no—
346C2×#41—222no—
347C2×#41—224no—
348C2×#41—224no—
349C2×#41—224no—
350C22×Q8—111no—
351C22×Q8—111no—
352C22×D4—112no—
353C22×D4—111no—
354C22×D4—111no—
355C22×D4—222no—
356C22×D4—221no—
357C23×C4—21no—
358C23×C4—112no—
359C23×C4—222no—
360C23×C4—221no—
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—
370C22⋊Q8—118no—
371C22⋊Q8—224no—
372C22⋊Q8—228no—
373#121—118no—
374#121—224no—
375#121—228no—
376#121—2216no—
377C4×Q8—228no—
378C4×D4—228no—
379C4×D4—2216no—
380#117—22no—
381#117—118no—
382#117—224no—
383#117C22×D1114yes—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—112no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—118no—
389C2×C4⋊C4—224no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1112yes—
396C2×C4⋊C4C22×D1114yes—
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—222no—
400C2×C22⋊C4—222no—
401C2×C22⋊C4—222no—
402C2×C42—21no—
403C2×C42—222no—
404#107—118no—
405#107—118no—
406#107C22×D1118yes—
407#106C22×D1118yes—
408#103—118no—
409#103—114no—
410#103—114no—
411#102—118no—
412#102—114no—
413#102—114no—
414C22⋊C8—118no—
415C22⋊C8—118no—
416C2×C11—24no—
417C2×C11#309814yescomplemented
418C2×C11C22×#12311yescharacteristic
419C2×C11C2×#57611yescharacteristic
420C2×C11C2×#57811yescharacteristic
421D11—44no—
422D11—82no—
423C24—112no—
424C24—221no—
425C24D4×D1111yescharacteristic
426#41—2216no—
427#41—228no—
428#41—228no—
429#41—228no—
430#41—228no—
431#41—448no—
432C2×Q8—114no—
433C2×Q8—112no—
434C2×Q8—224no—
435C2×Q8—221no—
436C2×Q8—222no—
437C2×Q8—222no—
438C2×D4—118no—
439C2×D4—114no—
440C2×D4—112no—
441C2×D4—228no—
442C2×D4—228no—
443C2×D4—224no—
444C2×D4—224no—
445C2×D4—222no—
446C2×D4—221no—
447C2×D4—222no—
448C2×D4—444no—
449C2×D4—884no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—82no—
455C22×C4—112no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—228no—
459C22×C4—224no—
460C22×C4—224no—
461C22×C4—222no—
462C22×C4—221no—
463C22×C4—224no—
464C22×C4—224no—
465C22×C4—444no—
466C22×C4—884no—
467C22×C4—882no—
468C22×C4#433914yes—
469C22×C4D4×D1112yes—
470C22×C4D4×D1111yescharacteristic
471C22×C4#434314yes—
472C22×C4C23×D1112yes—
473C22×C4C23×D1111yescharacteristic
474M16—28no—
475C2×C8—24no—
476C2×C8—112no—
477C2×C8—112no—
478C2×C8—222no—
479C2×C8—222no—
480C2×C8—228no—
481C2×C8C23×D1114yes—
482C4⋊C4—24no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—114no—
487C4⋊C4—228no—
488C4⋊C4—228no—
489C4⋊C4—222no—
490C4⋊C4—224no—
491C4⋊C4C23×D1112yes—
492C4⋊C4C23×D1112yes—
493C4⋊C4C23×D1114yes—
494C22⋊C4—24no—
495C22⋊C4—228no—
496C22⋊C4—228no—
497C22⋊C4—228no—
498C42—24no—
499C42—228no—
500C11C2×#309811yescharacteristic, complemented, Sylow
501C23—22no—
502C23—22no—
503C23—114no—
504C23—224no—
505C23—224no—
506C23—224no—
507C23—222no—
508C23—442no—
509C23—442no—
510C23—442no—
511C23#6694714yes—
512C23C2×D4×D1112yes—
513C23C2×D4×D1111yescharacteristic
514Q8—228no—
515Q8—222no—
516Q8—222no—
517Q8—442no—
518D4—2216no—
519D4—228no—
520D4—222no—
521D4—222no—
522D4—448no—
523D4—442no—
524D4—888no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—84no—
532C2×C4—114no—
533C2×C4—224no—
534C2×C4—228no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—222no—
539C2×C4—442no—
540C2×C4—444no—
541C2×C4—448no—
542C2×C4—888no—
543C2×C4—884no—
544C2×C4#6694714yes—
545C2×C4#6694718yes—
546C2×C4C2×#433912yes—
547C2×C4C2×#433914yes—
548C2×C4C2×D4×D1112yes—
549C2×C4C2×D4×D1111yescharacteristic
550C2×C4C2×#434312yes—
551C2×C4C2×#434314yes—
552C2×C4C24×D1111yescharacteristic
553C8—24no—
554C8—222no—
555C8—222no—
556C22—28no—
557C22—22no—
558C22—22no—
559C22—224no—
560C22—224no—
561C22—224no—
562C22—448no—
563C22—442no—
564C22—442no—
565C22—442no—
566C22—884no—
567C22C2×#6694714yes—
568C22C2×#6694712yes—
569C22#1062330512yes—
570C22#1062331012yes—
571C22C22×D4×D1111yescharacteristic
572C4—44no—
573C4—42no—
574C4—42no—
575C4—224no—
576C4—444no—
577C4—442no—
578C4C2×#6694712yes—
579C4C2×#6694714yes—
580C4C22×#433911yescharacteristic
581C4C22×#434311yescharacteristic
582C2—24no—
583C2—444no—
584C2—882no—
585C2#1307859814yesdirect product factor
586C2C22×#6694711yescharacteristic
587C2C2×#1062330511yescharacteristic
588C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC2×#10623041C2
hypercenterC2×#428D11
hypocenterC11C2×#3098
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×#10623054C2semidirect
3. #13078598C2direct (N × H)
4. C2×#10622497C2semidirect
5. C2×#10622480C2semidirect
6. C2×#10622479C2semidirect
7. C2×#10622495C2semidirect
8. C22×#66871C2semidirect
9. C2×#10622746C2semidirect
10. C2×#10622615C2semidirect
11. C2×#10622742C2semidirect
12. C2×C11×#428C2semidirect
22. #10623054C22semidirect
34. C11×#428C22semidirect
37. #10622746C22semidirect
38. #10622742C22semidirect
43. #10622615C22semidirect
50. C2×#66871C22semidirect
51. #10622497C22semidirect
52. #10622495C22semidirect
53. #10622480C22semidirect
54. #10622479C22semidirect
214. C2×#428D11semidirect
299. #428C2×D11semidirect
417. C2×C11#3098semidirect
500. C11C2×#3098semidirect
585. C2#13078598direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230412
C2×#106230542
#130785982
C2×#106224972
C2×#106224802
C2×#106224792
C2×#106224952
C22×#668712
C2×#106227462
C2×#106226152
C2×#106227422
C2×C11×#4282
C2×#309811