Finite Group Databasebeta

← C2×#13069719 #14780948

Subgroups — C2×#13069719 #14780948

Order 2816.

1938 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C212yesmaximal, complemented
2C2×#10622742C211yesmaximal, characteristic, complemented
3C2×#10622847C212yesmaximal, complemented
4#13069719C218yesmaximal, direct product factor
5C2×C11⋊#338C211yesmaximal, characteristic, complemented
6C2×C11×#575C211yesmaximal, characteristic, complemented
7C22×C11×#41C2212yes—
8C22×#4339C2211yescharacteristic
9C11×#575—24no—
10C11×#575—22no—
11C11×#575C2214yescomplemented
12C2×C11×#137—22no—
13C2×C11×AGL(1,ℤ/8)—22no—
14C2×C11×#135—22no—
15C22×C11×M16C2211yescharacteristic
16C2×#67004—22no—
17#10623353—24no—
18#10623353—24no—
19#10623353—24no—
20#10623353C2218yescomplemented
21C2×#67003—24no—
22C2×#67002—22no—
23C2×#66995—22no—
24C2×#66985—22no—
25C22×#4318C2212yes—
26C23×C11⋊C8C2211yescharacteristic
27#10622847—24no—
28#10622847C2218yescomplemented
29C2×C22⋊(C11⋊C8)—24no—
30#10622742—22no—
31#10622742C2214yescomplemented
32C2×(C2×D11)⋊C8—22no—
33C11⋊#338C2214yescomplemented
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—22no—
37C2×C11×#41—22no—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41D414yes—
45C2×C11×#41C2314yes—
46C22×Q8×C11D412yes—
47C22×D4×C11—22no—
48C22×D4×C11D412yes—
49C23×C4×C11—22no—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—21no—
52C2×#4339—21no—
53C2×#4339—21no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339—22no—
58C2×#4339D412yes—
59C2×#4339C2312yes—
60C22×D44D411yescharacteristic
61C22×C4×D11—21no—
62C22×Dic22D411yescharacteristic
63C11×#137—28no—
64C11×#137—28no—
65C11×AGL(1,ℤ/8)—28no—
66C11×AGL(1,ℤ/8)—28no—
67C11×#135—28no—
68C11×#135—28no—
69C2×C11×Q16—22no—
70C2×C11×SD16—24no—
71C2×C11×D8—22no—
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16D412yes—
75C2×C11×M16C2312yes—
76C22×C8×C11D412yes—
77#67004—28no—
78#67004—28no—
79#67003—216no—
80#67003—216no—
81#67002—28no—
82#67002—28no—
83C2×#4326—24no—
84#66995—28no—
85#66995—28no—
86C2×#4325—24no—
87C2×#4324—24no—
88#66985—28no—
89#66985—28no—
90C2×#4323—24no—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318—22no—
94C2×#4318—22no—
95C2×#4318D414yes—
96C2×#4318C2314yes—
97C22×C11⋊C8—21no—
98C22×C11⋊C8—21no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—22no—
101C22×C11⋊C8D414yes—
102C22×C11⋊C8C2312yes—
103C22⋊(C11⋊C8)—216no—
104(C2×D11)⋊C8—28no—
105C2×#2017—111nomaximal, Sylow
106C24×C11—22no—
107C24×C11#4111yescharacteristic
108C23×D11—21no—
109C11×#41—24no—
110C11×#41—24no—
111C11×#41—24no—
112C11×#41—24no—
113C11×#41—24no—
114C11×#41—24no—
115C11×#41—24no—
116C11×#41—24no—
117C11×#41—42no—
118C11×#41—42no—
119C11×#41—42no—
120C11×#41—42no—
121C11×#41—42no—
122C11×#41—42no—
123C11×#41—42no—
124C11×#41—42no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11C2×D414yes—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11C2×D414yes—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—22no—
161C2×C22⋊D11—22no—
162C2×C22⋊D11—42no—
163C2×C22⋊D11—42no—
164C22×Dic11—21no—
165#4339—24no—
166#4339—24no—
167#4339—24no—
168#4339—24no—
169#4339—42no—
170#4339—42no—
171#4339—42no—
172#4339—42no—
173C2×D44—22no—
174C2×D44—22no—
175C2×D44—21no—
176C2×D44C2×D412yes—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—41no—
180C2×C4×D11—41no—
181C2×C4×D11—41no—
182C2×C4×D11—41no—
183C2×Dic22—22no—
184C2×Dic22—22no—
185C2×Dic22—21no—
186C2×Dic22C2×D412yes—
187C11×Q16—28no—
188C11×SD16—216no—
189C11×D8—28no—
190C11×M16—24no—
191C11×M16—24no—
192C2×C8×C11—22no—
193C2×C8×C11—22no—
194C2×C8×C11C2×D414yes—
195#4326—216no—
196#4325—216no—
197#4324—216no—
198#4323—216no—
199#4318—24no—
200#4318—24no—
201#4318—24no—
202#4318—24no—
203C2×C11⋊C8—24no—
204C2×C11⋊C8—24no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—24no—
207C2×C11⋊C8—41no—
208C2×C11⋊C8—42no—
209C2×C11⋊C8—41no—
210C2×C11⋊C8C2×D418yes—
211C2×#575—112no—
212C2×#575D1111yescharacteristic, complemented
213C2×#408—112no—
214C2×#408—111no—
215#2017—118no—
216C2×#338—111no—
217C23×C11—24no—
218C23×C11—42no—
219C23×C11—48no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11#12111yescharacteristic
223C23×C11#12111yescharacteristic
224C23×C11#12112yes—
225C23×C11#12112yes—
226C23×C11C2×#4111yescharacteristic
227C22×D11—22no—
228C22×D11—44no—
229C22×D11—41no—
230C22×D11—41no—
231Q8×C11—24no—
232Q8×C11—24no—
233Q8×C11—42no—
234Q8×C11—42no—
235D4×C11—24no—
236D4×C11—24no—
237D4×C11—44no—
238D4×C11—44no—
239D4×C11—44no—
240D4×C11—44no—
241D4×C11—42no—
242D4×C11—42no—
243C2×C4×C11—24no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—44no—
247C2×C4×C11—44no—
248C2×C4×C11—44no—
249C2×C4×C11—44no—
250C2×C4×C11#12012yes—
251C2×C4×C11#12012yes—
252C2×C4×C11#12012yes—
253C2×C4×C11#12012yes—
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11#12012yes—
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12112yes—
260C2×C4×C11#12112yes—
261C2×C4×C11#12711yescharacteristic
262C2×C4×C11#12712yes—
263C2×C4×C11#12711yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D412yes—
266C2×C4×C11C22×D412yes—
267C2×C4×C11C22×D411yescharacteristic
268C22⋊D11—44no—
269C22⋊D11—44no—
270C2×Dic11—22no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273D44—24no—
274D44—42no—
275C4×D11—42no—
276C4×D11—42no—
277C4×D11—42no—
278C4×D11—42no—
279Dic22—24no—
280Dic22—42no—
281C8×C11—24no—
282C11⋊C8—28no—
283C11⋊C8—42no—
284C22×#41—111no—
285C22×#41C2×D1112yes—
286#575—24no—
287#575—22no—
288#575—118no—
289#575—224no—
290#575—224no—
291#575—224no—
292#575C2×D1114yescomplemented
293C2×#137—22no—
294C2×#137—222no—
295C2×#137—222no—
296C2×AGL(1,ℤ/8)—22no—
297C2×AGL(1,ℤ/8)—222no—
298C2×AGL(1,ℤ/8)—222no—
299C2×#135—22no—
300C2×#135—224no—
301C22×M16—112no—
302C22×M16C2×D1111yescharacteristic
303C23×C8—111no—
304#408—118no—
305#408—114no—
306#408—224no—
307#408—222no—
308C2×C22⋊C8—224no—
309C2×C22⋊C8—222no—
310#338—114no—
311C22×C11—22no—
312C22×C11—24no—
313C22×C11—41no—
314C22×C11—42no—
315C22×C11—41no—
316C22×C11—48no—
317C22×C11—44no—
318C22×C11—84no—
319C22×C11—84no—
320C22×C11#39212yes—
321C22×C11#39211yescharacteristic
322C22×C11#39211yescharacteristic
323C22×C11C2×#12111yescharacteristic
324C22×C11C2×#12112yes—
325C2×D11—44no—
326C2×D11—42no—
327C2×D11—82no—
328C2×D11—82no—
329C4×C11—44no—
330C4×C11#39211yescharacteristic
331C4×C11#39212yes—
332C4×C11#39211yescharacteristic
333C4×C11C2×#12012yes—
334C4×C11C2×#12011yescharacteristic
335C4×C11C2×#12711yescharacteristic
336Dic11—42no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—112no—
348C2×#41—112no—
349C2×#41—221no—
350C2×#41—221no—
351C2×#41—222no—
352C2×#41—222no—
353C2×#41—222no—
354C2×#41—222no—
355C2×#41C22⋊D1114yes—
356C2×#41C22×D1114yes—
357C22×Q8—111no—
358C22×Q8C22⋊D1112yes—
359C22×D4—22no—
360C22×D4—111no—
361C22×D4—221no—
362C22×D4C22⋊D1112yes—
363C23×C4—22no—
364C23×C4—221no—
365C23×C4C22×D1111yescharacteristic
366#137—28no—
367#137—28no—
368#137—228no—
369#137—228no—
370#137—228no—
371#137—228no—
372AGL(1,ℤ/8)—28no—
373AGL(1,ℤ/8)—28no—
374AGL(1,ℤ/8)—228no—
375AGL(1,ℤ/8)—228no—
376AGL(1,ℤ/8)—228no—
377AGL(1,ℤ/8)—228no—
378#135—28no—
379#135—28no—
380#135—2216no—
381#135—2216no—
382C2×Q16—22no—
383C2×Q16—224no—
384C2×SD16—24no—
385C2×SD16—224no—
386C2×SD16—224no—
387C2×D8—22no—
388C2×D8—224no—
389C2×M16—22no—
390C2×M16—22no—
391C2×M16—114no—
392C2×M16—114no—
393C2×M16—222no—
394C2×M16—222no—
395C2×M16—222no—
396C2×M16—222no—
397C2×M16C22⋊D1112yes—
398C2×M16C22×D1112yes—
399C22×C8—114no—
400C22×C8—112no—
401C22×C8—222no—
402C22×C8—222no—
403C22×C8—221no—
404C22×C8—221no—
405C22×C8C22⋊D1112yes—
406C22⋊C8—2216no—
407C22⋊C8—228no—
408C2×C11—21no—
409C2×C11—21no—
410C2×C11—22no—
411C2×C11—22no—
412C2×C11—84no—
413C2×C11#201712yescomplemented
414C2×C11C2×#39211yescharacteristic
415D11—82no—
416C24—22no—
417C24—221no—
418C24#434111yescharacteristic
419#41—24no—
420#41—24no—
421#41—24no—
422#41—24no—
423#41—24no—
424#41—24no—
425#41—24no—
426#41—24no—
427#41—42no—
428#41—42no—
429#41—42no—
430#41—42no—
431#41—42no—
432#41—42no—
433#41—42no—
434#41—42no—
435#41—224no—
436#41—224no—
437#41—224no—
438#41—224no—
439#41—442no—
440#41—442no—
441#41—442no—
442#41—442no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—112no—
449C2×Q8—221no—
450C2×Q8—222no—
451C2×Q8—222no—
452C2×Q8C2×C22⋊D1114yes—
453C2×D4—24no—
454C2×D4—24no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—112no—
465C2×D4—222no—
466C2×D4—222no—
467C2×D4—222no—
468C2×D4—222no—
469C2×D4—221no—
470C2×D4—442no—
471C2×D4—442no—
472C2×D4C2×C22⋊D1114yes—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—221no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—441no—
484C22×C4—441no—
485C22×C4—441no—
486C22×C4—441no—
487C22×C4D4×D1111yescharacteristic
488C22×C4D4×D1111yescharacteristic
489C22×C4D4×D1112yes—
490C22×C4D4×D1112yes—
491C22×C4#434111yescharacteristic
492C22×C4C2×C22⋊D1112yes—
493C22×C4C2×C22⋊D1112yes—
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497Q16—28no—
498Q16—2216no—
499SD16—216no—
500SD16—2216no—
501SD16—2216no—
502D8—28no—
503D8—2216no—
504M16—24no—
505M16—24no—
506M16—224no—
507M16—224no—
508M16—224no—
509M16—224no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—118no—
513C2×C8—224no—
514C2×C8—224no—
515C2×C8—224no—
516C2×C8—222no—
517C2×C8—442no—
518C2×C8—441no—
519C2×C8—441no—
520C2×C8C2×C22⋊D1114yes—
521C11C2×#201711yescharacteristic, complemented, Sylow
522C23—24no—
523C23—42no—
524C23—48no—
525C23—42no—
526C23—42no—
527C23—222no—
528C23—444no—
529C23—441no—
530C23—441no—
531C23#6699111yescharacteristic
532C23#6699111yescharacteristic
533C23#6699212yes—
534C23#6699212yes—
535C23C2×#434111yescharacteristic
536Q8—24no—
537Q8—24no—
538Q8—42no—
539Q8—42no—
540Q8—224no—
541Q8—442no—
542D4—24no—
543D4—24no—
544D4—44no—
545D4—44no—
546D4—44no—
547D4—44no—
548D4—42no—
549D4—42no—
550D4—224no—
551D4—444no—
552D4—444no—
553D4—442no—
554C2×C4—24no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—222no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4#6699012yes—
569C2×C4#6699012yes—
570C2×C4#6699012yes—
571C2×C4#6699012yes—
572C2×C4#6699111yescharacteristic
573C2×C4#6699111yescharacteristic
574C2×C4#6699212yes—
575C2×C4#6699212yes—
576C2×C4#6699312yes—
577C2×C4#6699311yescharacteristic
578C2×C4#6699311yescharacteristic
579C2×C4#6700611yescharacteristic
580C2×C4#6700611yescharacteristic
581C2×C4#6700612yes—
582C2×C4C2×D4×D1111yescharacteristic
583C2×C4C2×D4×D1112yes—
584C2×C4C22×C22⋊D1112yes—
585C2×C4C22×C22⋊D1111yescharacteristic
586C8—24no—
587C8—228no—
588C8—442no—
589C22—24no—
590C22—22no—
591C22—41no—
592C22—42no—
593C22—41no—
594C22—48no—
595C22—44no—
596C22—84no—
597C22—84no—
598C22—444no—
599C22—442no—
600C22—882no—
601C22—882no—
602C22#1062283612yes—
603C22#1062283611yescharacteristic
604C22#1062283611yescharacteristic
605C22C2×#6699111yescharacteristic
606C22C2×#6699212yes—
607C4—44no—
608C4—442no—
609C4#1062283611yescharacteristic
610C4#1062283612yes—
611C4#1062283611yescharacteristic
612C4C2×#6699012yes—
613C4C2×#6699311yescharacteristic
614C4C2×#6700611yescharacteristic
615C2—22no—
616C2—22no—
617C2—21no—
618C2—21no—
619C2—84no—
620C2—882no—
621C2#1306971912yesdirect product factor
622C2C2×#1062283611yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#575C2
socleC22×C11#392
hypercenterC2×#575D11
hypocenterC11C2×#2017
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#10623353C2semidirect
2. C2×#10622742C2semidirect
3. C2×#10622847C2semidirect
4. #13069719C2direct (N × H)
5. C2×C11⋊#338C2semidirect
6. C2×C11×#575C2semidirect
11. C11×#575C22semidirect
20. #10623353C22semidirect
28. #10622847C22semidirect
31. #10622742C22semidirect
33. C11⋊#338C22semidirect
212. C2×#575D11semidirect
292. #575C2×D11semidirect
413. C2×C11#2017semidirect
521. C11C2×#2017semidirect
621. C2#13069719direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233532
C2×#106227422
C2×#106228472
#130697192
C2×C11⋊#3382
C2×C11×#5752
C2×#201711