Finite Group Databasebeta

← C2×#13079313 #15623683

Subgroups — C2×#13079313 #15623683

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×#10623247C211yesmaximal, characteristic, complemented
2C2×#10623222C211yesmaximal, characteristic, complemented
3#13079313C2116yesmaximal, direct product factor
4C2×#10622678C211yesmaximal, characteristic, complemented
5C2×#10622687C211yesmaximal, characteristic, complemented
6C2×#10622327C211yesmaximal, characteristic, complemented
7C2×#10622388C212yesmaximal, complemented
8C2×#10622391C212yesmaximal, complemented
9C2×#10622398C212yesmaximal, complemented
10C2×#10622370C212yesmaximal, complemented
11C2×D11×#97C211yesmaximal, characteristic, complemented
12C2×C11×#490C211yesmaximal, characteristic, complemented
13C22×#4341—21no—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×#66991—21no—
17C2×#66991C2212yes—
18C2×#66989—21no—
19C2×D4×Dic11—21no—
20C2×D4×Dic11C2212yes—
21C22×#4324C2212yes—
22C22×#4323C2212yes—
23C22×C8×D11C2212yes—
24#10623247—24no—
25#10623247C2218yescomplemented
26#10623222—24no—
27#10623222C2218yescomplemented
28C2×#66951—21no—
29C2×#66950C2211yescharacteristic
30C2×#66948C2211yescharacteristic
31C2×#66947—21no—
32C2×#66946—21no—
33C2×#66946C2211yescharacteristic
34C2×#66945—21no—
35C2×#66940C2211yescharacteristic
36C2×#66928C2211yescharacteristic
37C2×C42×D11C2211yescharacteristic
38C2×#66922C2211yescharacteristic
39C11×#490C2218yescomplemented
40C2×C11×#102C2212yes—
41C2×C11×#102C2212yes—
42C2×C11×#97C2211yescharacteristic
43C2×#66885C2212yes—
44C2×#66880C2212yes—
45C2×#66879C2212yes—
46#10622687C2218yescomplemented
47#10622678C2218yescomplemented
48C2×#66872C2212yes—
49C2×#66871C2212yes—
50C2×#66867C2211yescharacteristic
51#10622398C22116yescomplemented
52#10622391C22116yescomplemented
53#10622388C22116yescomplemented
54#10622370C22116yescomplemented
55#10622327C2218yescomplemented
56D11×#97C2218yescomplemented
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11C2312yes—
60C22×C22⋊D11—22no—
61C23×Dic11—22no—
62C2×#4341—28no—
63C2×#4341—48no—
64C22×D44—21no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×C4×D11D411yescharacteristic
68C22×C4×D11D411yescharacteristic
69C22×C4×D11C2311yescharacteristic
70C22×Dic22—21no—
71C22×Dic22C2311yescharacteristic
72C22×C8×C11C2312yes—
73C11×#127—22no—
74C11×#127C2314yes—
75C11×#125—22no—
76C11×#125C2314yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84#66991—24no—
85#66991—28no—
86#66991C2318yes—
87#66989—28no—
88D4×Dic11—24no—
89D4×Dic11—28no—
90D4×Dic11C2318yes—
91C2×#4324—28no—
92C2×#4324C2318yes—
93C2×#4323—28no—
94C2×#4323C2318yes—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11C2312yes—
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11D411yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2312yes—
109C2×C8×D11—28no—
110C2×C8×D11C2318yes—
111#66951—28no—
112#66950—22no—
113#66950C2314yes—
114#66948—22no—
115#66948C2314yes—
116#66947—28no—
117#66946—28no—
118#66946—22no—
119#66946C2314yes—
120#66945—28no—
121#66940—22no—
122#66940C2314yes—
123#66928—22no—
124#66928C2314yes—
125C42×D11D414yes—
126C42×D11C2314yes—
127#66922—22no—
128#66922C2314yes—
129C11×#102C2318yes—
130C11×#102C2318yes—
131C11×#97C2314yes—
132#66885C2318yes—
133#66880C2318yes—
134#66879C2318yes—
135#66872C2318yes—
136#66871C2318yes—
137#66867C2314yes—
138C2×#3180—111nomaximal, Sylow
139C24×C11—22no—
140C23×D11—21no—
141C23×D11C2×D411yescharacteristic
142C2×D4×C11—22no—
143C2×D4×C11—24no—
144C2×D4×C11—24no—
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11—44no—
148C2×D4×C11—44no—
149C2×D4×C11C2414yes—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—28no—
156C2×C22⋊D11—48no—
157C22×Dic11—28no—
158C22×Dic11—21no—
159C22×Dic11—22no—
160C22×Dic11—48no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164#4341—432no—
165C2×D44—24no—
166C2×D44—21no—
167C2×D44—24no—
168C2×D44—44no—
169C2×D44C2412yes—
170C2×C4×D11—24no—
171C2×C4×D11—24no—
172C2×C4×D11—24no—
173C2×C4×D11—42no—
174C2×C4×D11—44no—
175C2×C4×D11C2×D412yes—
176C2×C4×D11C2×D414yes—
177C2×C4×D11C2×D414yes—
178C2×C4×D11C2412yes—
179C2×Dic22—24no—
180C2×Dic22—21no—
181C2×Dic22—24no—
182C2×Dic22—44no—
183C2×Dic22C2412yes—
184C2×C8×C11—24no—
185C2×C8×C11C2414yes—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4C2412yes—
191C11×C4⋊C4C2412yes—
192C42×C11C2×D412yes—
193C42×C11C2412yes—
194C22⋊Dic11—28no—
195C22⋊Dic11—28no—
196#4324—216no—
197#4323—216no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—24no—
203C4⋊Dic11—24no—
204C4⋊Dic11—22no—
205C4⋊Dic11—24no—
206C4⋊Dic11C2414yes—
207Dic11⋊C4—24no—
208C4×Dic11—24no—
209C4×Dic11C2×D412yes—
210C4×Dic11C2×D414yes—
211C4×Dic11C2×D414yes—
212C4×Dic11C2412yes—
213C2×C11⋊C8#4118yescomplemented
214C2×C11⋊C8C2414yes—
215C8×D11—216no—
216C2×#532—111no—
217C2×#529—111no—
218#3180—1116no—
219C2×#501—111no—
220C2×#496—111no—
221C2×#490D1111yescharacteristic, complemented
222C2×#489—111no—
223C2×#466—112no—
224C2×#465—112no—
225C2×#442—112no—
226C2×#440—112no—
227C22×#97—111no—
228C23×C11—24no—
229C23×C11—44no—
230C23×C11—44no—
231C23×C11—44no—
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—42no—
237C22×D11—42no—
238C22×D11—42no—
239C22×D11AGL(1,ℤ/8)14yes—
240C22×D11C22×D412yes—
241D4×C11—24no—
242D4×C11—24no—
243D4×C11—48no—
244D4×C11—48no—
245D4×C11—44no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4114yes—
256C2×C4×C11C2511yescharacteristic
257C22⋊D11—416no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—416no—
264C2×Dic11—42no—
265C2×Dic11—44no—
266C2×Dic11C22×D412yes—
267C2×Dic11C22×D412yes—
268C2×Dic11C22×D412yes—
269D44—24no—
270D44—48no—
271D44—42no—
272C4×D11—28no—
273C4×D11—24no—
274C4×D11—24no—
275C4×D11—44no—
276C4×D11—48no—
277Dic22—24no—
278Dic22—48no—
279Dic22—42no—
280C8×C11—24no—
281C11⋊C8C2×#4118yescomplemented
282C22×#41—221no—
283C22×SD16—112no—
284C22×D8—112no—
285C23×C8—112no—
286#532—118no—
287#532—224no—
288C2×C4⋊Q8—111no—
289C2×#127C2×D1111yescharacteristic
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—112no—
299C2×#121—111no—
300C2×#121—221no—
301C2×C4×Q8—111no—
302C2×C4×D4—112no—
303C2×C4×D4—111no—
304C2×C4×D4—221no—
305C2×C4×D4—221no—
306C2×#117—221no—
307C22×C42—111no—
308#501—118no—
309#496—118no—
310#490C2×D1118yescomplemented
311#489—118no—
312#466—1116no—
313#465—1116no—
314#442—1116no—
315#440—1116no—
316C2×#107—112no—
317C2×#106—112no—
318C2×#103—112no—
319C2×#102—112no—
320C2×#102C2×D1112yes—
321C2×#102C2×D1112yes—
322C2×#97—112no—
323C2×#97—111no—
324C2×#97—118no—
325C2×#97C2×D1111yescharacteristic
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—44no—
329C22×C11—88no—
330C22×C11#53212yes—
331C22×C11C2×AGL(1,ℤ/8)12yes—
332C22×C11#57512yes—
333C22×C11C23×D411yescharacteristic
334C2×D11—28no—
335C2×D11—22no—
336C2×D11—22no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—84no—
341C2×D11C2×AGL(1,ℤ/8)14yes—
342C4×C11—22no—
343C4×C11—22no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11#53212yes—
347C4×C11C22×#4112yes—
348Dic11—22no—
349Dic11—22no—
350Dic11—22no—
351Dic11—42no—
352Dic11—44no—
353C2×#41—228no—
354C2×#41—448no—
355C22×Q8—111no—
356C22×Q8—221no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4—111no—
360C22×D4—221no—
361C22×D4—222no—
362C22×D4C22×D1112yes—
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—114no—
377C4⋊Q8—222no—
378#127—22no—
379#127C22×D1114yes—
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—118no—
390#121—114no—
391#121—222no—
392#121—224no—
393#121—228no—
394C4×Q8—114no—
395C4×Q8—222no—
396C4×D4—118no—
397C4×D4—114no—
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—112no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4—222no—
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#107—118no—
426#106—118no—
427#103—118no—
428#102—118no—
429#102C22×D1118yes—
430#102C22×D1118yes—
431#97—118no—
432#97—114no—
433#97C22×D1114yes—
434C2×C11—84no—
435C2×C11#318014yescomplemented
436C2×C11C2×#53211yescharacteristic
437C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
438C2×C11C2×#57511yescharacteristic
439D11—24no—
440D11—82no—
441C24—22no—
442C24—111no—
443C24—221no—
444#41—4432no—
445C2×Q8—112no—
446C2×Q8—221no—
447C2×Q8—224no—
448C2×Q8—224no—
449C2×Q8—444no—
450C2×D4—22no—
451C2×D4—24no—
452C2×D4—24no—
453C2×D4—24no—
454C2×D4—24no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—112no—
458C2×D4—224no—
459C2×D4—228no—
460C2×D4—221no—
461C2×D4—224no—
462C2×D4—444no—
463C2×D4—448no—
464C2×D4C23×D1114yes—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—112no—
471C22×C4—114no—
472C22×C4—112no—
473C22×C4—114no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—228no—
477C22×C4—224no—
478C22×C4—221no—
479C22×C4—222no—
480C22×C4—442no—
481C22×C4—444no—
482C22×C4—448no—
483C22×C4D4×D1111yescharacteristic
484C22×C4D4×D1111yescharacteristic
485C22×C4C23×D1111yescharacteristic
486SD16—2216no—
487D8—2216no—
488C2×C8—24no—
489C2×C8—118no—
490C2×C8—114no—
491C2×C8—2216no—
492C2×C8C23×D1114yes—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—114no—
498C4⋊C4—224no—
499C4⋊C4—224no—
500C4⋊C4—222no—
501C4⋊C4—224no—
502C4⋊C4C23×D1112yes—
503C4⋊C4C23×D1112yes—
504C22⋊C4—224no—
505C22⋊C4—224no—
506C22⋊C4—224no—
507C22⋊C4—228no—
508C22⋊C4—228no—
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—24no—
520C23—44no—
521C23—44no—
522C23—44no—
523C23—114no—
524C23—112no—
525C23—222no—
526C23—222no—
527C23—222no—
528C23—442no—
529C23—442no—
530C23—442no—
531C23C2×D4×D1111yescharacteristic
532Q8—224no—
533Q8—448no—
534Q8—442no—
535D4—24no—
536D4—24no—
537D4—48no—
538D4—48no—
539D4—44no—
540D4—224no—
541D4—448no—
542D4—4416no—
543D4—442no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—112no—
551C2×C4—112no—
552C2×C4—112no—
553C2×C4—228no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—222no—
560C2×C4—224no—
561C2×C4—444no—
562C2×C4—448no—
563C2×C4—4416no—
564C2×C4—444no—
565C2×C4—442no—
566C2×C4C2×D4×D1112yes—
567C2×C4C2×D4×D1112yes—
568C2×C4C2×D4×D1111yescharacteristic
569C2×C4#41×D1114yes—
570C2×C4C24×D1111yescharacteristic
571C8—24no—
572C8—118no—
573C22—44no—
574C22—44no—
575C22—44no—
576C22—88no—
577C22—114no—
578C22—228no—
579C22—222no—
580C22—222no—
581C22—442no—
582C22—442no—
583C22—442no—
584C22—884no—
585C22#1062319912yes—
586C22D11×AGL(1,ℤ/8)12yes—
587C22#1062330412yes—
588C22C22×D4×D1111yescharacteristic
589C4—22no—
590C4—22no—
591C4—42no—
592C4—42no—
593C4—222no—
594C4—222no—
595C4—222no—
596C4—442no—
597C4—444no—
598C4#1062319912yes—
599C4C2×#41×D1112yes—
600C2—84no—
601C2—224no—
602C2—882no—
603C2#1307931314yesdirect product factor
604C2C2×#1062319911yescharacteristic
605C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
606C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#490C2
socleC23×C11C22×D4
hypercenterC2×#490D11
hypocenterC11C2×#3180
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#10623247C2semidirect
2. C2×#10623222C2semidirect
3. #13079313C2direct (N × H)
4. C2×#10622678C2semidirect
5. C2×#10622687C2semidirect
6. C2×#10622327C2semidirect
7. C2×#10622388C2semidirect
8. C2×#10622391C2semidirect
9. C2×#10622398C2semidirect
10. C2×#10622370C2semidirect
11. C2×D11×#97C2semidirect
12. C2×C11×#490C2semidirect
25. #10623247C22semidirect
27. #10623222C22semidirect
39. C11×#490C22semidirect
46. #10622687C22semidirect
47. #10622678C22semidirect
51. #10622398C22semidirect
52. #10622391C22semidirect
53. #10622388C22semidirect
54. #10622370C22semidirect
55. #10622327C22semidirect
56. D11×#97C22semidirect
213. C2×C11⋊C8#41semidirect
221. C2×#490D11semidirect
281. C11⋊C8C2×#41semidirect
310. #490C2×D11semidirect
435. C2×C11#3180semidirect
518. C11C2×#3180semidirect
603. C2#13079313direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232472
C2×#106232222
#130793132
C2×#106226782
C2×#106226872
C2×#106223272
C2×#106223882
C2×#106223912
C2×#106223982
C2×#106223702
C2×D11×#972
C2×C11×#4902
C2×#318011