Finite Group Databasebeta

← C2×#13067628 #14726013

Subgroups — C2×#13067628 #14726013

Order 2816.

1156 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623025C211yesmaximal, characteristic
2C2×#10622584C211yesmaximal, characteristic, complemented
3C2×#10622580C211yesmaximal, characteristic, complemented
4#13067628C218yesmaximal, direct product factor
5C2×#10622090C211yesmaximal, characteristic, complemented
6C2×#10622089C211yesmaximal, characteristic, complemented
7C2×#10622163C211yesmaximal, characteristic, complemented
8C2×C11×#397C211yesmaximal, characteristic, complemented
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×C11×C22⋊C4—21no—
11C22×C11×C22⋊C4C2211yescharacteristic
12C2×#67006—21no—
13C2×#66983C2211yescharacteristic
14C2×C4×C22⋊D11—21no—
15C2×#66977C2211yescharacteristic
16#10623025—22no—
17#10623025—22no—
18#10623025—22no—
19#10623025C2214yes—
20C2×#66938—21no—
21C2×#66937—21no—
22C2×#66936—21no—
23C2×#66932—21no—
24C11×#397—22no—
25C11×#397C2214yescomplemented
26C2×C11×#95—21no—
27C2×C11×#95C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30#10622584—22no—
31#10622584C2214yescomplemented
32C2×#66874—21no—
33#10622580—22no—
34#10622580C2214yescomplemented
35C2×#66873—21no—
36C2×#66872—21no—
37C2×#66871—21no—
38#10622163C2214yescomplemented
39#10622090C2214yescomplemented
40#10622089C2214yescomplemented
41C25×C11D411yescharacteristic
42C23×C4×C11—21no—
43C23×C4×C11—21no—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—21no—
47C22×C22⋊D11—21no—
48C22×C22⋊D11—21no—
49C22×D44D411yescharacteristic
50C22×C4×D11—21no—
51C22×Dic22D411yescharacteristic
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—44no—
64C2×C11×C22⋊C4D412yes—
65C2×C11×C22⋊C4C2312yes—
66#67006—24no—
67#67006—24no—
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
71#66983—21no—
72#66983—21no—
73#66983D412yes—
74#66983C2312yes—
75C4×C22⋊D11—24no—
76C4×C22⋊D11—24no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11D411yescharacteristic
80C2×C4⋊Dic11D411yescharacteristic
81#66977—21no—
82#66977—21no—
83#66977D412yes—
84#66977C2312yes—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C22×C11⋊C8—21no—
89C22×C11⋊C8—21no—
90#66938—24no—
91#66938—24no—
92#66937—24no—
93#66937—24no—
94#66936—24no—
95#66936—24no—
96#66932—24no—
97#66932—24no—
98C11×#95—24no—
99C11×#95—21no—
100C11×#95C2312yes—
101C22⋊(C11⋊C8)—21no—
102C22⋊(C11⋊C8)—21no—
103C22⋊(C11⋊C8)C2312yes—
104C22⋊(C11⋊C8)C2312yes—
105#66874—24no—
106#66873—24no—
107#66872—24no—
108#66871—24no—
109C2×#1612—111nomaximal, Sylow
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11—22no—
114C24×C11—42no—
115C24×C11—42no—
116C24×C11C2×D411yescharacteristic
117C24×C11C2×D412yes—
118C23×D11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—24no—
140C2×C22⋊D11—24no—
141C2×C22⋊D11—22no—
142C2×C22⋊D11—22no—
143C2×C22⋊D11—42no—
144C2×C22⋊D11—42no—
145C2×C22⋊D11—82no—
146C2×C22⋊D11—82no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C2×D44—21no—
151C2×D44—42no—
152C2×D44C2×D412yes—
153C2×C4×D11—24no—
154C2×C4×D11—82no—
155C2×Dic22—21no—
156C2×Dic22—42no—
157C2×Dic22C2×D412yes—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4—41no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—48no—
167C22⋊Dic11—24no—
168C22⋊Dic11—24no—
169C22⋊Dic11—22no—
170C22⋊Dic11—22no—
171(C2×D11)⋊C4—24no—
172(C2×D11)⋊C4—22no—
173(C2×D11)⋊C4—22no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11C2×D412yes—
177C4⋊Dic11C2×D412yes—
178Dic11⋊C4—24no—
179Dic11⋊C4—22no—
180Dic11⋊C4—22no—
181C4×Dic11—24no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—42no—
185C2×C11⋊C8—42no—
186C2×#538—111no—
187C2×#483—111no—
188C2×#480—111no—
189C2×#397D1111yescharacteristic, complemented
190#1612—118no—
191C2×#328—111no—
192C2×#327—111no—
193C2×#323—111no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—48no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—81no—
207C23×C11—81no—
208C23×C11—84no—
209C23×C11#12011yescharacteristic
210C23×C11#12011yescharacteristic
211C23×C11#13512yes—
212C23×C11AGL(1,ℤ/8)12yes—
213C23×C11C22×D411yescharacteristic
214C22×D11—22no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—81no—
234C2×C4×C11—84no—
235C2×C4×C11—82no—
236C2×C4×C11—82no—
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C22⋊D11—42no—
242C22⋊D11—42no—
243C22⋊D11—44no—
244C22⋊D11—84no—
245C22⋊D11—84no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252D44—42no—
253D44—81no—
254C4×D11—84no—
255Dic22—42no—
256Dic22—81no—
257C11⋊C8—42no—
258C11⋊C8—42no—
259#538—114no—
260#538—222no—
261#538—222no—
262#538—222no—
263C2×#126—221no—
264C2×#124—221no—
265C2×#123—221no—
266C2×C22⋊Q8—111no—
267C2×#121—111no—
268C2×#121—221no—
269C2×#120—221no—
270C2×C4×D4—221no—
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C22⋊C4—21no—
273C22×C22⋊C4C2×D1111yescharacteristic
274#483—114no—
275#483—222no—
276#480—114no—
277#480—222no—
278C2×#107—221no—
279C2×#106—221no—
280C2×#103—221no—
281C2×#102—221no—
282C2×C22⋊C8—111no—
283C2×C22⋊C8—111no—
284#397—22no—
285#397C2×D1114yescomplemented
286C2×#95—21no—
287C2×#95C2×D1111yescharacteristic
288#328—114no—
289#327—114no—
290#323—114no—
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—44no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—82no—
302C22×C11—84no—
303C22×C11—84no—
304C22×C11#44912yes—
305C22×C11#44912yes—
306C22×C11#45512yes—
307C22×C11#45812yes—
308C22×C11C2×#12011yescharacteristic
309C22×C11C2×#13511yescharacteristic
310C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—42no—
314C2×D11—84no—
315C4×C11—21no—
316C4×C11—21no—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—42no—
320C4×C11—82no—
321C4×C11—82no—
322Dic11—42no—
323Dic11—42no—
324Dic11—42no—
325C25C22⋊D1111yescharacteristic
326C22×Q8—111no—
327C22×D4—111no—
328C22×D4—221no—
329C22×D4—221no—
330C22×D4—221no—
331C23×C4—21no—
332C23×C4—21no—
333C23×C4—221no—
334C23×C4C22⋊D1111yescharacteristic
335C23×C4C22×D1111yescharacteristic
336C22×C8—221no—
337C22×C8—221no—
338#126—224no—
339#126—224no—
340#124—224no—
341#124—224no—
342#123—224no—
343#123—224no—
344C22⋊Q8—112no—
345C22⋊Q8—112no—
346C22⋊Q8—221no—
347C22⋊Q8—221no—
348#121—112no—
349#121—112no—
350#121—224no—
351#121—224no—
352#121—221no—
353#121—221no—
354#120—224no—
355#120—224no—
356C4×D4—224no—
357C4×D4—224no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22×D1112yes—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4C22⋊D1112yes—
380C2×C22⋊C4C22×D1112yes—
381C2×C42—221no—
382#107—224no—
383#106—224no—
384#103—224no—
385#102—224no—
386C22⋊C8—112no—
387C22⋊C8—112no—
388C22⋊C8—221no—
389C22⋊C8—221no—
390#95—24no—
391#95—21no—
392#95C22×D1112yes—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—22no—
396C2×C11—82no—
397C2×C11#161214yescomplemented
398C2×C11C2×#44911yescharacteristic
399C2×C11C2×#45511yescharacteristic
400C2×C11C2×#45811yescharacteristic
401D11—82no—
402C24—22no—
403C24—21no—
404C24—21no—
405C24—22no—
406C24—42no—
407C24—42no—
408C24—221no—
409C24C2×C22⋊D1111yescharacteristic
410C24C2×C22⋊D1112yes—
411C2×Q8—112no—
412C2×Q8—221no—
413C2×Q8—442no—
414C2×D4—112no—
415C2×D4—222no—
416C2×D4—222no—
417C2×D4—224no—
418C2×D4—224no—
419C2×D4—221no—
420C2×D4—442no—
421C2×D4—442no—
422C2×D4—442no—
423C2×D4—882no—
424C2×D4—882no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—42no—
438C22×C4—224no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—882no—
443C22×C4D4×D1111yescharacteristic
444C22×C4D4×D1111yescharacteristic
445C22×C4D4×D1111yescharacteristic
446C22×C4D4×D1111yescharacteristic
447C22×C4C2×C22⋊D1112yes—
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C23×D1111yescharacteristic
450C2×C8—222no—
451C2×C8—222no—
452C2×C8—442no—
453C2×C8—442no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—112no—
459C4⋊C4—112no—
460C4⋊C4—224no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—222no—
464C4⋊C4—222no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—48no—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C22⋊C4—224no—
473C22⋊C4—222no—
474C22⋊C4—222no—
475C22⋊C4—222no—
476C22⋊C4—222no—
477C42—224no—
478C11C2×#161211yescharacteristic, complemented, Sylow
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—42no—
485C23—42no—
486C23—48no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—81no—
492C23—81no—
493C23—84no—
494C23—222no—
495C23—442no—
496C23—442no—
497C23—442no—
498C23#6698512yes—
499C23#6699011yescharacteristic
500C23#6699011yescharacteristic
501C23#6700312yes—
502C23C22×C22⋊D1111yescharacteristic
503Q8—442no—
504Q8—881no—
505D4—442no—
506D4—442no—
507D4—442no—
508D4—444no—
509D4—881no—
510D4—884no—
511D4—884no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—81no—
528C2×C4—84no—
529C2×C4—82no—
530C2×C4—82no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—442no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4—884no—
538C2×C4#6699011yescharacteristic
539C2×C4#6699011yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4C2×D4×D1111yescharacteristic
542C8—442no—
543C8—442no—
544C22—24no—
545C22—24no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—44no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—82no—
555C22—84no—
556C22—84no—
557C22—442no—
558C22—442no—
559C22—442no—
560C22—884no—
561C22#1062265012yes—
562C22#1062265012yes—
563C22#1062266612yes—
564C22#1062267412yes—
565C22C2×#6698511yescharacteristic
566C22C2×#6699011yescharacteristic
567C22C2×#6700311yescharacteristic
568C4—21no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—42no—
573C4—82no—
574C4—82no—
575C4—442no—
576C4—442no—
577C4—442no—
578C2—21no—
579C2—21no—
580C2—22no—
581C2—82no—
582C2—882no—
583C2#1306762814yesdirect product factor
584C2C2×#1062265011yescharacteristic
585C2C2×#1062267411yescharacteristic
586C2C2×#1062266611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#397C2
socleC23×C11#120
prime radicalC2×#10623025C2
hypercenterC2×#397D11
hypocenterC11C2×#1612
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. C2×#10622584C2semidirect
3. C2×#10622580C2semidirect
4. #13067628C2direct (N × H)
5. C2×#10622090C2semidirect
6. C2×#10622089C2semidirect
7. C2×#10622163C2semidirect
8. C2×C11×#397C2semidirect
25. C11×#397C22semidirect
31. #10622584C22semidirect
34. #10622580C22semidirect
38. #10622163C22semidirect
39. #10622090C22semidirect
40. #10622089C22semidirect
189. C2×#397D11semidirect
285. #397C2×D11semidirect
397. C2×C11#1612semidirect
478. C11C2×#1612semidirect
583. C2#13067628direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230252
C2×#106225842
C2×#106225802
#130676282
C2×#106220902
C2×#106220892
C2×#106221632
C2×C11×#3972
C2×#161211