Finite Group Databasebeta

← C2×#13079311 #15623681

Subgroups — C2×#13079311 #15623681

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×#10623211C211yesmaximal, characteristic, complemented
3#13079311C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622684C211yesmaximal, characteristic, complemented
6C2×#10622668C211yesmaximal, characteristic, complemented
7C2×#10622770C212yesmaximal, complemented
8C2×#10622784C212yesmaximal, complemented
9C2×#10622765C212yesmaximal, complemented
10C2×#10622777C212yesmaximal, complemented
11C2×D11×#97C211yesmaximal, characteristic, complemented
12C2×C11×#496C211yesmaximal, characteristic, complemented
13C22×#4341—21no—
14C22×C11×SD16C2212yes—
15C22×C11×D8C2212yes—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×#66991—21no—
21C2×#66991C2211yescharacteristic
22C2×#66991C2212yes—
23C2×#66989—21no—
24C2×D4×Dic11—21no—
25C2×D4×Dic11C2211yescharacteristic
26C2×D4×Dic11C2212yes—
27C22×C8×D11C2212yes—
28#10623247—24no—
29#10623247C2218yescomplemented
30#10623211—24no—
31#10623211C2218yescomplemented
32C2×#66936—21no—
33C2×(C22⋊D11)⋊C4—21no—
34C2×#66932—21no—
35C2×#66930—21no—
36C2×C42×D11C2211yescharacteristic
37C2×#66923C2211yescharacteristic
38C2×#66922C2211yescharacteristic
39C11×#496C2218yescomplemented
40C2×C11×#97C2211yescharacteristic
41C2×#66899C2212yes—
42C2×#66896C2212yes—
43C2×#66896C2212yes—
44C2×#66896C2212yes—
45#10622784C22116yescomplemented
46#10622777C22116yescomplemented
47#10622770C22116yescomplemented
48#10622765C22116yescomplemented
49C2×#66882C2212yes—
50C2×#66881C2212yes—
51C2×#66879C2212yes—
52#10622684C2218yescomplemented
53#10622668C2218yescomplemented
54C2×#66867C2211yescharacteristic
55D11×#97C2218yescomplemented
56#10622315C2218yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C22×D4×C11C2312yes—
62C22×C22⋊D11—21no—
63C22×C22⋊D11—22no—
64C23×Dic11—21no—
65C23×Dic11—22no—
66C2×#4341—28no—
67C2×#4341—48no—
68C22×C4×D11D411yescharacteristic
69C22×C4×D11D411yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×Dic22—21no—
72C2×C11×SD16—28no—
73C2×C11×SD16C2318yes—
74C2×C11×D8—28no—
75C2×C11×D8C2318yes—
76C22×C8×C11C2312yes—
77C11×#127—22no—
78C11×#127C2314yes—
79C11×#124—22no—
80C11×#124C2314yes—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88#66999—22no—
89#66999C2314yes—
90Q8×Dic11—22no—
91Q8×Dic11C2314yes—
92#66991—24no—
93#66991—28no—
94#66991—22no—
95#66991C2318yes—
96#66991C2314yes—
97#66989—28no—
98D4×Dic11—24no—
99D4×Dic11—28no—
100D4×Dic11—22no—
101D4×Dic11C2318yes—
102D4×Dic11C2314yes—
103C2×(C2×D11)⋊C4—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11C2312yes—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11D411yescharacteristic
114C2×C4×Dic11D411yescharacteristic
115C2×C4×Dic11C2311yescharacteristic
116C22×C11⋊C8C2312yes—
117C2×C8×D11—28no—
118C2×C8×D11C2318yes—
119#66936—28no—
120(C22⋊D11)⋊C4—28no—
121#66932—28no—
122#66930—28no—
123C42×D11D414yes—
124C42×D11C2314yes—
125#66923—22no—
126#66923C2314yes—
127#66922—22no—
128#66922C2314yes—
129C11×#97C2314yes—
130#66899C2318yes—
131#66896C2318yes—
132#66896C2318yes—
133#66896C2318yes—
134#66882C2318yes—
135#66881C2318yes—
136#66879C2318yes—
137#66867C2314yes—
138C2×#3180—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11—22no—
141C23×D11C2×D411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—24no—
144C2×Q8×C11C2412yes—
145C2×D4×C11—21no—
146C2×D4×C11—22no—
147C2×D4×C11—24no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—24no—
151C2×D4×C11—24no—
152C2×D4×C11—44no—
153C2×D4×C11—44no—
154C2×D4×C11C2412yes—
155C2×D4×C11C2414yes—
156C22×C4×C11—21no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—24no—
161C2×C22⋊D11—28no—
162C2×C22⋊D11—48no—
163C2×C22⋊D11—44no—
164C22×Dic11—24no—
165C22×Dic11—28no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—48no—
170C22×Dic11—44no—
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174#4341—432no—
175C2×C4×D11—24no—
176C2×C4×D11—24no—
177C2×C4×D11—42no—
178C2×C4×D11C2×D412yes—
179C2×C4×D11C2×D414yes—
180C2×C4×D11C2×D414yes—
181C2×C4×D11C2412yes—
182C2×Dic22—24no—
183C2×Dic22—44no—
184C11×SD16—216no—
185C11×D8—216no—
186C2×C8×C11#4118yescomplemented
187C2×C8×C11C2414yes—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—24no—
190C42×C11C2×D412yes—
191C42×C11C2412yes—
192C22⋊Dic11—24no—
193C22⋊Dic11—24no—
194C22⋊Dic11—28no—
195C22⋊Dic11—28no—
196(C2×D11)⋊C4—24no—
197C4⋊Dic11—24no—
198C4⋊Dic11—22no—
199C4⋊Dic11—24no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11C2412yes—
203C4⋊Dic11C2414yes—
204C4⋊Dic11C2412yes—
205Dic11⋊C4—24no—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208C4×Dic11—24no—
209C4×Dic11C2×D412yes—
210C4×Dic11C2×D414yes—
211C4×Dic11C2×D414yes—
212C4×Dic11C2412yes—
213C2×C11⋊C8—24no—
214C2×C11⋊C8C2414yes—
215C8×D11—216no—
216C2×#532—111no—
217C2×#529—111no—
218#3180—1116no—
219C2×#501—111no—
220C2×#496D1111yescharacteristic, complemented
221C2×#490—111no—
222C2×#489—111no—
223C2×#466—112no—
224C2×#465—112no—
225C2×#442—112no—
226C2×#440—112no—
227C22×#97—111no—
228C23×C11—22no—
229C23×C11—24no—
230C23×C11—42no—
231C23×C11—44no—
232C23×C11—44no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—44no—
236C23×C11C22×D411yescharacteristic
237C22×D11—22no—
238C22×D11—22no—
239C22×D11AGL(1,ℤ/8)14yes—
240C22×D11C22×D412yes—
241Q8×C11—24no—
242Q8×C11—42no—
243D4×C11—24no—
244D4×C11—24no—
245D4×C11—24no—
246D4×C11—48no—
247D4×C11—48no—
248D4×C11—42no—
249D4×C11—44no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—42no—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4114yes—
258C2×C4×C11C2511yescharacteristic
259C22⋊D11—416no—
260C22⋊D11—48no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—416no—
268C2×Dic11—48no—
269C2×Dic11—44no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11C22×D412yes—
273C2×Dic11C22×D412yes—
274C2×Dic11C22×D412yes—
275C4×D11—28no—
276C4×D11—24no—
277C4×D11—24no—
278C4×D11—44no—
279Dic22—48no—
280C8×C11C2×#4118yescomplemented
281C11⋊C8—24no—
282C22×#41—221no—
283C22×SD16C2×D1112yes—
284C22×D8C2×D1112yes—
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×#125—111no—
294C2×#124—221no—
295C2×#124C2×D1111yescharacteristic
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#501—118no—
309#496C2×D1118yescomplemented
310#490—118no—
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×#102—112no—
321C2×#102—112no—
322C2×#97—112no—
323C2×#97—111no—
324C2×#97—118no—
325C2×#97C2×D1111yescharacteristic
326C22×C11—42no—
327C22×C11—44no—
328C22×C11—44no—
329C22×C11—42no—
330C22×C11—44no—
331C22×C11—42no—
332C22×C11—88no—
333C22×C11—84no—
334C22×C11#53212yes—
335C22×C11C2×AGL(1,ℤ/8)12yes—
336C22×C11#57512yes—
337C22×C11C23×D411yescharacteristic
338C2×D11—28no—
339C2×D11—22no—
340C2×D11—22no—
341C2×D11C2×AGL(1,ℤ/8)14yes—
342C4×C11—22no—
343C4×C11—22no—
344C4×C11—42no—
345C4×C11#53212yes—
346C4×C11C22×#4112yes—
347Dic11—22no—
348Dic11—22no—
349Dic11—22no—
350Dic11—44no—
351Dic11—42no—
352Dic11—42no—
353C2×#41—228no—
354C2×#41—448no—
355C22×Q8—221no—
356C22×Q8C22×D1111yescharacteristic
357C22×D4—21no—
358C22×D4—21no—
359C22×D4—221no—
360C22×D4—222no—
361C22×D4C22×D1111yescharacteristic
362C22×D4C22×D1112yes—
363C23×C4—111no—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—221no—
367C23×C4—222no—
368C2×SD16—28no—
369C2×SD16C22×D1118yes—
370C2×D8—28no—
371C2×D8C22×D1118yes—
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—114no—
382#125—222no—
383#124—22no—
384#124—228no—
385#124C22×D1114yes—
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—112no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—222no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—222no—
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#102—118no—
430#102—118no—
431#97—118no—
432#97—114no—
433#97C22×D1114yes—
434C2×C11—84no—
435C2×C11—82no—
436C2×C11#318014yescomplemented
437C2×C11C2×#53211yescharacteristic
438C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
439C2×C11C2×#57511yescharacteristic
440D11—24no—
441C24—21no—
442C24—22no—
443C24—111no—
444#41—4432no—
445C2×Q8—21no—
446C2×Q8—24no—
447C2×Q8—224no—
448C2×Q8—444no—
449C2×Q8C23×D1112yes—
450C2×D4—21no—
451C2×D4—22no—
452C2×D4—24no—
453C2×D4—24no—
454C2×D4—24no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—224no—
460C2×D4—228no—
461C2×D4—448no—
462C2×D4—444no—
463C2×D4C23×D1112yes—
464C2×D4C23×D1114yes—
465C22×C4—21no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—112no—
470C22×C4—114no—
471C22×C4—112no—
472C22×C4—114no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—228no—
476C22×C4—224no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—222no—
480C22×C4—442no—
481C22×C4—448no—
482C22×C4—444no—
483C22×C4D4×D1111yescharacteristic
484C22×C4D4×D1111yescharacteristic
485C22×C4C23×D1111yescharacteristic
486SD16—216no—
487D8—216no—
488C2×C8—114no—
489C2×C8—224no—
490C2×C8—2216no—
491C2×C8#434118yescomplemented
492C2×C8C23×D1114yes—
493C4⋊C4—112no—
494C4⋊C4—112no—
495C4⋊C4—114no—
496C4⋊C4—224no—
497C4⋊C4—224no—
498C4⋊C4—222no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—224no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C22⋊C4—24no—
505C22⋊C4—24no—
506C22⋊C4—224no—
507C22⋊C4—224no—
508C22⋊C4—228no—
509C22⋊C4—224no—
510C22⋊C4—228no—
511C42—114no—
512C42—112no—
513C42—114no—
514C42—112no—
515C42—224no—
516C42D4×D1112yes—
517C42C23×D1112yes—
518C11C2×#318011yescharacteristic, complemented, Sylow
519C23—22no—
520C23—24no—
521C23—42no—
522C23—44no—
523C23—44no—
524C23—42no—
525C23—42no—
526C23—44no—
527C23—114no—
528C23—112no—
529C23—222no—
530C23—222no—
531C23C2×D4×D1111yescharacteristic
532Q8—24no—
533Q8—42no—
534Q8—448no—
535D4—24no—
536D4—24no—
537D4—24no—
538D4—48no—
539D4—48no—
540D4—42no—
541D4—44no—
542D4—4416no—
543D4—448no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—42no—
548C2×C4—112no—
549C2×C4—112no—
550C2×C4—112no—
551C2×C4—228no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—224no—
556C2×C4—224no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—224no—
560C2×C4—444no—
561C2×C4—4416no—
562C2×C4—448no—
563C2×C4—444no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4C2×D4×D1112yes—
567C2×C4C2×D4×D1112yes—
568C2×C4C2×D4×D1111yescharacteristic
569C2×C4C2×#434114yes—
570C2×C4C24×D1111yescharacteristic
571C8—224no—
572C8C2×#434118yescomplemented
573C22—42no—
574C22—44no—
575C22—44no—
576C22—42no—
577C22—42no—
578C22—44no—
579C22—88no—
580C22—84no—
581C22—114no—
582C22—228no—
583C22—222no—
584C22—222no—
585C22#1062324712yes—
586C22D11×AGL(1,ℤ/8)12yes—
587C22#1062330412yes—
588C22C22×D4×D1111yescharacteristic
589C4—22no—
590C4—22no—
591C4—42no—
592C4—222no—
593C4—222no—
594C4—222no—
595C4—444no—
596C4—442no—
597C4—442no—
598C4#1062324712yes—
599C4C22×#434112yes—
600C2—84no—
601C2—82no—
602C2—224no—
603C2#1307931114yesdirect product factor
604C2C2×#1062324711yescharacteristic
605C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
606C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#496C2
socleC23×C11C22×D4
hypercenterC2×#496D11
hypocenterC11C2×#3180
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. C2×#10623247C2semidirect
2. C2×#10623211C2semidirect
3. #13079311C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622684C2semidirect
6. C2×#10622668C2semidirect
7. C2×#10622770C2semidirect
8. C2×#10622784C2semidirect
9. C2×#10622765C2semidirect
10. C2×#10622777C2semidirect
11. C2×D11×#97C2semidirect
12. C2×C11×#496C2semidirect
29. #10623247C22semidirect
31. #10623211C22semidirect
39. C11×#496C22semidirect
45. #10622784C22semidirect
46. #10622777C22semidirect
47. #10622770C22semidirect
48. #10622765C22semidirect
52. #10622684C22semidirect
53. #10622668C22semidirect
55. D11×#97C22semidirect
56. #10622315C22semidirect
186. C2×C8×C11#41semidirect
220. C2×#496D11semidirect
280. C8×C11C2×#41semidirect
309. #496C2×D11semidirect
436. C2×C11#3180semidirect
491. C2×C8#4341semidirect
518. C11C2×#3180semidirect
572. C8C2×#4341semidirect
603. C2#13079311direct (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×#106232112
#130793112
C2×#106223152
C2×#106226842
C2×#106226682
C2×#106227702
C2×#106227842
C2×#106227652
C2×#106227772
C2×D11×#972
C2×C11×#4962
C2×#318011