Finite Group Databasebeta

← C2×#13079316 #15623686

Subgroups — C2×#13079316 #15623686

Order 2816.

2278 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic, complemented
2C2×#10623222C211yesmaximal, characteristic, complemented
3#13079316C2116yesmaximal, direct product factor
4C2×#10622325C211yesmaximal, characteristic, complemented
5C2×#10622680C211yesmaximal, characteristic, complemented
6C2×#10622702C211yesmaximal, characteristic, complemented
7C2×#10622496C212yesmaximal, complemented
8C2×#10622477C212yesmaximal, complemented
9C2×#10622482C212yesmaximal, complemented
10C2×#10622502C212yesmaximal, complemented
11C2×D11×#97C211yesmaximal, characteristic, complemented
12C2×C11×#501C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×#67000—21no—
17C22×D88C2212yes—
18C22×#4314C2212yes—
19C22×C8×D11C2212yes—
20#10623256—24no—
21#10623256C2218yescomplemented
22#10623222—24no—
23#10623222C2218yescomplemented
24C2×#66951—21no—
25C2×#66950C2211yescharacteristic
26C2×#66948—21no—
27C2×#66948C2211yescharacteristic
28C2×#66948C2212yes—
29C2×#66947—21no—
30C2×#66946—21no—
31C2×#66946—21no—
32C2×#66946C2211yescharacteristic
33C2×#66946C2212yes—
34C2×#66945—21no—
35C2×#66940C2211yescharacteristic
36C2×#66928C2211yescharacteristic
37C2×#66927C2211yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C11×#501C2218yescomplemented
40C2×C11×#107C2212yes—
41C2×C11×#106C2212yes—
42C2×C11×#97C2211yescharacteristic
43C2×#66879C2212yes—
44#10622702C2218yescomplemented
45#10622680C2218yescomplemented
46C2×#66874C2212yes—
47C2×#66873C2212yes—
48C2×#66873C2212yes—
49C2×#66873C2212yes—
50C2×#66867C2211yescharacteristic
51#10622502C22116yescomplemented
52#10622496C22116yescomplemented
53#10622482C22116yescomplemented
54#10622477C22116yescomplemented
55#10622325C2218yescomplemented
56D11×#97C2218yescomplemented
57C22×Q8×C11—21no—
58C2×#4343—28no—
59C2×#4343—48no—
60C22×D44—21no—
61C22×D44—22no—
62C22×D44—21no—
63C22×D44—21no—
64C22×D44C2312yes—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×C4×D11—22no—
68C22×C4×D11D411yescharacteristic
69C22×C4×D11D411yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×Dic22C2311yescharacteristic
72C22×C8×C11C2312yes—
73C11×C4⋊Q8—22no—
74C11×C4⋊Q8C2314yes—
75C11×#125—22no—
76C11×#125C2314yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84#67000—28no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—22no—
92C2×C4⋊Dic11—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11D411yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2312yes—
99C2×D88—28no—
100C2×D88C2318yes—
101C2×#4314—28no—
102C2×#4314C2318yes—
103C2×C8×D11—28no—
104C2×C8×D11C2318yes—
105#66951—28no—
106#66950—22no—
107#66950C2314yes—
108#66948—24no—
109#66948—28no—
110#66948—22no—
111#66948C2318yes—
112#66948C2314yes—
113#66947—28no—
114#66946—28no—
115#66946—24no—
116#66946—28no—
117#66946—22no—
118#66946C2314yes—
119#66946C2318yes—
120#66945—28no—
121#66940—22no—
122#66940C2314yes—
123#66928—22no—
124#66928C2314yes—
125#66927—22no—
126#66927C2314yes—
127C42×D11D414yes—
128C42×D11C2314yes—
129C11×#107C2318yes—
130C11×#106C2318yes—
131C11×#97C2314yes—
132#66879C2318yes—
133#66874C2318yes—
134#66873C2318yes—
135#66873C2318yes—
136#66873C2318yes—
137#66867C2314yes—
138C2×#3180—111nomaximal, Sylow
139C23×D11—21no—
140C23×D11—22no—
141C23×D11C2×D411yescharacteristic
142C2×Q8×C11—24no—
143C2×Q8×C11—44no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154#4343—432no—
155C2×D44—24no—
156C2×D44—28no—
157C2×D44—22no—
158C2×D44—24no—
159C2×D44—24no—
160C2×D44—21no—
161C2×D44—24no—
162C2×D44—24no—
163C2×D44—24no—
164C2×D44—44no—
165C2×D44—44no—
166C2×D44—44no—
167C2×D44—48no—
168C2×D44C2414yes—
169C2×D44C2412yes—
170C2×C4×D11—24no—
171C2×C4×D11—28no—
172C2×C4×D11—24no—
173C2×C4×D11—24no—
174C2×C4×D11—42no—
175C2×C4×D11—44no—
176C2×C4×D11—48no—
177C2×C4×D11C2×D412yes—
178C2×C4×D11C2×D414yes—
179C2×C4×D11C2×D414yes—
180C2×C4×D11C2412yes—
181C2×Dic22—21no—
182C2×Dic22—24no—
183C2×Dic22C2412yes—
184C2×C8×C11#4118yescomplemented
185C2×C8×C11C2414yes—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4C2412yes—
193C11×C4⋊C4C2412yes—
194C11×C4⋊C4C2414yes—
195C42×C11C2×D412yes—
196C42×C11C2412yes—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—28no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—24no—
203(C2×D11)⋊C4—24no—
204C4⋊Dic11—24no—
205Dic11⋊C4—24no—
206C4×Dic11—24no—
207C4×Dic11C2×D412yes—
208C4×Dic11C2×D414yes—
209C4×Dic11C2×D414yes—
210C4×Dic11C2412yes—
211C2×C11⋊C8—24no—
212C2×C11⋊C8C2414yes—
213D88—216no—
214#4314—216no—
215C8×D11—216no—
216C2×#532—111no—
217C2×#529—111no—
218#3180—1116no—
219C2×#501D1111yescharacteristic, complemented
220C2×#496—111no—
221C2×#490—111no—
222C2×#489—111no—
223C2×#466—112no—
224C2×#465—112no—
225C2×#442—112no—
226C2×#440—112no—
227C22×#97—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—24no—
233C22×D11—44no—
234C22×D11—42no—
235C22×D11—44no—
236C22×D11—42no—
237C22×D11—42no—
238C22×D11—44no—
239C22×D11AGL(1,ℤ/8)14yes—
240C22×D11C22×D412yes—
241Q8×C11—48no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—44no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11C22×D412yes—
251C2×C4×C11C22×D412yes—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4114yes—
254C2×C4×C11C2511yescharacteristic
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—42no—
260C2×Dic11C22×D412yes—
261C2×Dic11C22×D412yes—
262C2×Dic11C22×D412yes—
263D44—24no—
264D44—24no—
265D44—24no—
266D44—48no—
267D44—48no—
268D44—48no—
269D44—416no—
270D44—44no—
271D44—42no—
272C4×D11—28no—
273C4×D11—24no—
274C4×D11—24no—
275C4×D11—44no—
276C4×D11—48no—
277C4×D11—416no—
278Dic22—24no—
279Dic22—42no—
280C8×C11C2×#4118yescomplemented
281C11⋊C8—24no—
282C22×#41—221no—
283C22×SD16—112no—
284C22×D8—112no—
285C23×C8—112no—
286#532—118no—
287#532—224no—
288C2×C4⋊Q8C2×D1111yescharacteristic
289C2×#127—111no—
290#529—118no—
291#529—224no—
292C2×#126—221no—
293C2×#125C2×D1111yescharacteristic
294C2×#124—111no—
295C2×#124—221no—
296C2×#123—221no—
297C2×C22⋊Q8—111no—
298C2×#121—111no—
299C2×#121—112no—
300C2×#121—221no—
301C2×C4×Q8—111no—
302C2×C4×D4—111no—
303C2×C4×D4—112no—
304C2×C4×D4—221no—
305C2×C4×D4—221no—
306C2×#117—221no—
307C22×C42—111no—
308#501C2×D1118yescomplemented
309#496—118no—
310#490—118no—
311#489—118no—
312#466—1116no—
313#465—1116no—
314#442—1116no—
315#440—1116no—
316C2×#107C2×D1112yes—
317C2×#106C2×D1112yes—
318C2×#103—112no—
319C2×#102—112no—
320C2×#102—112no—
321C2×#102—112no—
322C2×#97—112no—
323C2×#97—111no—
324C2×#97—118no—
325C2×#97C2×D1111yescharacteristic
326C22×C11#53212yes—
327C22×C11C2×AGL(1,ℤ/8)12yes—
328C22×C11#57512yes—
329C22×C11C23×D411yescharacteristic
330C2×D11—28no—
331C2×D11—22no—
332C2×D11—22no—
333C2×D11—42no—
334C2×D11—44no—
335C2×D11—44no—
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—44no—
339C2×D11—88no—
340C2×D11—84no—
341C2×D11C2×AGL(1,ℤ/8)14yes—
342C4×C11—22no—
343C4×C11—22no—
344C4×C11—44no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11#53212yes—
348C4×C11C22×#4112yes—
349Dic11—22no—
350Dic11—22no—
351Dic11—22no—
352Dic11—42no—
353C2×#41—228no—
354C2×#41—448no—
355C22×Q8—21no—
356C22×Q8—111no—
357C22×D4—111no—
358C22×D4—112no—
359C22×D4—221no—
360C22×D4—222no—
361C22×D4—221no—
362C22×D4—221no—
363C23×C4—111no—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—221no—
367C23×C4—222no—
368C2×SD16—118no—
369C2×SD16—228no—
370C2×D8—118no—
371C2×D8—228no—
372C22×C8—112no—
373C22×C8—118no—
374C22×C8—228no—
375C22×C8C22×D1112yes—
376C4⋊Q8—22no—
377C4⋊Q8C22×D1114yes—
378#127—114no—
379#127—222no—
380#126—228no—
381#125—22no—
382#125C22×D1114yes—
383#124—114no—
384#124—228no—
385#124—222no—
386#123—228no—
387C22⋊Q8—114no—
388C22⋊Q8—222no—
389#121—114no—
390#121—118no—
391#121—222no—
392#121—224no—
393#121—228no—
394C4×Q8—114no—
395C4×Q8—222no—
396C4×D4—114no—
397C4×D4—118no—
398C4×D4—222no—
399C4×D4—224no—
400C4×D4—228no—
401C4×D4—228no—
402#117—228no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C22×D1112yes—
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C22⋊C4—221no—
412C2×C22⋊C4—222no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—114no—
422C2×C42—114no—
423C2×C42—221no—
424C2×C42C22×D1111yescharacteristic
425#107C22×D1118yes—
426#106C22×D1118yes—
427#103—118no—
428#102—118no—
429#102—118no—
430#102—118no—
431#97—118no—
432#97—114no—
433#97C22×D1114yes—
434C2×C11#318014yescomplemented
435C2×C11C2×#53211yescharacteristic
436C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
437C2×C11C2×#57511yescharacteristic
438D11—24no—
439D11—84no—
440D11—82no—
441C24—111no—
442C24—221no—
443C24—222no—
444#41—4432no—
445C2×Q8—24no—
446C2×Q8—44no—
447C2×Q8—112no—
448C2×Q8—221no—
449C2×Q8—224no—
450C2×D4—112no—
451C2×D4—114no—
452C2×D4—224no—
453C2×D4—228no—
454C2×D4—221no—
455C2×D4—224no—
456C2×D4—222no—
457C2×D4—224no—
458C2×D4—224no—
459C2×D4—224no—
460C2×D4—224no—
461C2×D4—444no—
462C2×D4—444no—
463C2×D4—448no—
464C2×D4—444no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—112no—
472C22×C4—114no—
473C22×C4—112no—
474C22×C4—114no—
475C22×C4—224no—
476C22×C4—228no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—221no—
480C22×C4—442no—
481C22×C4—448no—
482C22×C4—444no—
483C22×C4D4×D1111yescharacteristic
484C22×C4D4×D1111yescharacteristic
485C22×C4C23×D1111yescharacteristic
486SD16—2216no—
487D8—2216no—
488C2×C8—114no—
489C2×C8—224no—
490C2×C8—2216no—
491C2×C8#434318yescomplemented
492C2×C8C23×D1114yes—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—224no—
500C4⋊C4—224no—
501C4⋊C4C23×D1112yes—
502C4⋊C4C23×D1112yes—
503C4⋊C4C23×D1114yes—
504C22⋊C4—224no—
505C22⋊C4—228no—
506C22⋊C4—224no—
507C22⋊C4—228no—
508C22⋊C4—224no—
509C22⋊C4—224no—
510C22⋊C4—224no—
511C42—114no—
512C42—112no—
513C42—114no—
514C42—112no—
515C42—224no—
516C42D4×D1112yes—
517C42C23×D1112yes—
518C11C2×#318011yescharacteristic, complemented, Sylow
519C23—114no—
520C23—112no—
521C23—222no—
522C23—222no—
523C23—222no—
524C23—224no—
525C23—442no—
526C23—444no—
527C23—444no—
528C23—442no—
529C23—442no—
530C23—444no—
531C23C2×D4×D1111yescharacteristic
532Q8—48no—
533Q8—224no—
534Q8—442no—
535D4—224no—
536D4—224no—
537D4—224no—
538D4—448no—
539D4—448no—
540D4—4416no—
541D4—448no—
542D4—442no—
543D4—444no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—44no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—112no—
555C2×C4—228no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—222no—
562C2×C4—444no—
563C2×C4—4416no—
564C2×C4—448no—
565C2×C4—442no—
566C2×C4C2×D4×D1112yes—
567C2×C4C2×D4×D1112yes—
568C2×C4C2×D4×D1111yescharacteristic
569C2×C4C2×#434314yes—
570C2×C4C24×D1111yescharacteristic
571C8—224no—
572C8C2×#434318yescomplemented
573C22—114no—
574C22—228no—
575C22—222no—
576C22—222no—
577C22—442no—
578C22—444no—
579C22—444no—
580C22—442no—
581C22—442no—
582C22—444no—
583C22—888no—
584C22—884no—
585C22#1062325612yes—
586C22D11×AGL(1,ℤ/8)12yes—
587C22#1062330812yes—
588C22C22×D4×D1111yescharacteristic
589C4—22no—
590C4—22no—
591C4—44no—
592C4—42no—
593C4—42no—
594C4—222no—
595C4—222no—
596C4—222no—
597C4—442no—
598C4#1062325612yes—
599C4C22×#434312yes—
600C2—224no—
601C2—884no—
602C2—882no—
603C2#1307931614yesdirect product factor
604C2C2×#1062325611yescharacteristic
605C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
606C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#501C2
socleC23×C11C22×D4
hypercenterC2×#501D11
hypocenterC11C2×#3180
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#10623256C2semidirect
2. C2×#10623222C2semidirect
3. #13079316C2direct (N × H)
4. C2×#10622325C2semidirect
5. C2×#10622680C2semidirect
6. C2×#10622702C2semidirect
7. C2×#10622496C2semidirect
8. C2×#10622477C2semidirect
9. C2×#10622482C2semidirect
10. C2×#10622502C2semidirect
11. C2×D11×#97C2semidirect
12. C2×C11×#501C2semidirect
21. #10623256C22semidirect
23. #10623222C22semidirect
39. C11×#501C22semidirect
44. #10622702C22semidirect
45. #10622680C22semidirect
51. #10622502C22semidirect
52. #10622496C22semidirect
53. #10622482C22semidirect
54. #10622477C22semidirect
55. #10622325C22semidirect
56. D11×#97C22semidirect
184. C2×C8×C11#41semidirect
219. C2×#501D11semidirect
280. C8×C11C2×#41semidirect
308. #501C2×D11semidirect
434. C2×C11#3180semidirect
491. C2×C8#4343semidirect
518. C11C2×#3180semidirect
572. C8C2×#4343semidirect
603. C2#13079316direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×#106232222
#130793162
C2×#106223252
C2×#106226802
C2×#106227022
C2×#106224962
C2×#106224772
C2×#106224822
C2×#106225022
C2×D11×#972
C2×C11×#5012
C2×#318011