Finite Group Databasebeta

← C2×#13067629 #14726014

Subgroups — C2×#13067629 #14726014

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×#10623175C211yesmaximal, characteristic
2C2×#10622580C211yesmaximal, characteristic, complemented
3C2×#10622606C211yesmaximal, characteristic, complemented
4#13067629C218yesmaximal, direct product factor
5C2×#10622176C211yesmaximal, characteristic, complemented
6C2×#10622108C211yesmaximal, characteristic, complemented
7C2×#10622106C211yesmaximal, characteristic, complemented
8C2×C11×#483C211yesmaximal, characteristic, complemented
9C2×C11×C22⋊Q8C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C2×#67000—21no—
12C2×#66983C2211yescharacteristic
13C22×(C2×D11)⋊C4—21no—
14C22×(C2×D11)⋊C4C2211yescharacteristic
15#10623175—22no—
16#10623175—22no—
17#10623175—22no—
18#10623175C2214yes—
19C2×#66951—21no—
20C2×#66948—21no—
21C2×#66947—21no—
22C2×#66935—21no—
23C2×(C22⋊D11)⋊C4—21no—
24C11×#483—22no—
25C11×#483C2214yescomplemented
26C2×C11×#106—21no—
27C2×C11×#103—21no—
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11⋊#95—21no—
30C2×C11⋊#95C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622606—22no—
33#10622606C2214yescomplemented
34#10622580—22no—
35#10622580C2214yescomplemented
36C2×#66873—21no—
37C2×#66871—21no—
38#10622176C2214yescomplemented
39#10622108C2214yescomplemented
40#10622106C2214yescomplemented
41C24×D11D411yescharacteristic
42C22×Q8×C11D411yescharacteristic
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C22×C22⋊D11—21no—
46C23×Dic11—21no—
47C23×Dic11D411yescharacteristic
48C22×D44—21no—
49C22×D44—21no—
50C22×D44D411yescharacteristic
51C22×C4×D11—21no—
52C22×C8×C11—21no—
53C11×C22⋊Q8—21no—
54C11×C22⋊Q8—21no—
55C11×C22⋊Q8D412yes—
56C11×C22⋊Q8C2312yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—21no—
66#67000—24no—
67#67000—24no—
68#66983—21no—
69#66983—21no—
70#66983D412yes—
71#66983C2312yes—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—44no—
82C2×(C2×D11)⋊C4D412yes—
83C2×(C2×D11)⋊C4C2312yes—
84C2×C4⋊Dic11D411yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C22×C11⋊C8—21no—
88#66951—24no—
89#66951—24no—
90#66948—24no—
91#66948—24no—
92#66947—24no—
93#66947—24no—
94#66935—24no—
95#66935—24no—
96(C22⋊D11)⋊C4—24no—
97(C22⋊D11)⋊C4—24no—
98C11×#106—24no—
99C11×#103—24no—
100C11×C22⋊C8—21no—
101C11×C22⋊C8C2312yes—
102C11⋊#95—21no—
103C11⋊#95—24no—
104C11⋊#95C2312yes—
105C22⋊(C11⋊C8)—21no—
106C22⋊(C11⋊C8)C2312yes—
107#66873—24no—
108#66871—24no—
109C2×#1612—111nomaximal, Sylow
110C24×C11C2×D411yescharacteristic
111C23×D11—21no—
112C23×D11—21no—
113C23×D11—22no—
114C23×D11—21no—
115C23×D11—22no—
116C23×D11—42no—
117C23×D11—42no—
118C23×D11C2×D412yes—
119C2×Q8×C11—21no—
120C2×Q8×C11—42no—
121C2×Q8×C11C2×D412yes—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—42no—
126C22×C4×C11—41no—
127C22×C4×C11—41no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—22no—
137C2×C22⋊D11—22no—
138C2×C22⋊D11—42no—
139C2×C22⋊D11—42no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—42no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11C2×D412yes—
149C2×D44—24no—
150C2×D44—24no—
151C2×D44—21no—
152C2×D44—42no—
153C2×D44—82no—
154C2×D44—82no—
155C2×D44C2×D412yes—
156C2×C4×D11—24no—
157C2×C4×D11—82no—
158C2×C8×C11—22no—
159C2×C8×C11—42no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—41no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4C2×D412yes—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—24no—
172(C2×D11)⋊C4—24no—
173(C2×D11)⋊C4—22no—
174(C2×D11)⋊C4—22no—
175(C2×D11)⋊C4—22no—
176(C2×D11)⋊C4—22no—
177(C2×D11)⋊C4—22no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4—48no—
180C4⋊Dic11—21no—
181C4⋊Dic11C2×D412yes—
182Dic11⋊C4—24no—
183C4×Dic11—24no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—42no—
186C2×#538—111no—
187C2×#483D1111yescharacteristic, complemented
188C2×#480—111no—
189C2×#397—111no—
190#1612—118no—
191C2×#328—111no—
192C2×#327—111no—
193C2×#323—111no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11#12011yescharacteristic
197C23×C11#12011yescharacteristic
198C23×C11#13512yes—
199C23×C11AGL(1,ℤ/8)12yes—
200C23×C11C22×D411yescharacteristic
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—48no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—81no—
216C22×D11—81no—
217C22×D11—84no—
218Q8×C11—42no—
219Q8×C11—81no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—82no—
234C2×C4×C11—82no—
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C22⋊D11—42no—
240C22⋊D11—42no—
241C22⋊D11—44no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—81no—
251C2×Dic11—84no—
252D44—42no—
253D44—81no—
254D44—84no—
255D44—84no—
256C4×D11—84no—
257C8×C11—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⋊Q8C2×D1111yescharacteristic
267C2×#121—111no—
268C2×#121—221no—
269C2×#120—221no—
270C2×C4×D4—221no—
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C22⋊C4—111no—
273C22×C22⋊C4—221no—
274#483—22no—
275#483C2×D1114yescomplemented
276#480—114no—
277#480—222no—
278C2×#107—221no—
279C2×#106—21no—
280C2×#103—21no—
281C2×#102—221no—
282C2×C22⋊C8—111no—
283C2×C22⋊C8C2×D1111yescharacteristic
284#397—114no—
285#397—222no—
286C2×#95—111no—
287C2×#95—221no—
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#44912yes—
298C22×C11#44912yes—
299C22×C11#45512yes—
300C22×C11#45812yes—
301C22×C11C2×#12011yescharacteristic
302C22×C11C2×#13511yescharacteristic
303C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
304C2×D11—44no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—84no—
312C2×D11—84no—
313C2×D11—84no—
314C2×D11—82no—
315C4×C11—21no—
316C4×C11—21no—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—42no—
320C4×C11—42no—
321C4×C11—82no—
322Dic11—42no—
323Dic11—42no—
324Dic11—82no—
325C25—111no—
326C22×Q8C22⋊D1111yescharacteristic
327C22×D4—111no—
328C22×D4—221no—
329C22×D4—221no—
330C22×D4—221no—
331C23×C4—21no—
332C23×C4—111no—
333C23×C4—221no—
334C23×C4—221no—
335C23×C4C22×D1111yescharacteristic
336C22×C8—21no—
337C22×C8—221no—
338#126—224no—
339#126—224no—
340#124—224no—
341#124—224no—
342#123—224no—
343#123—224no—
344C22⋊Q8—21no—
345C22⋊Q8—21no—
346C22⋊Q8C22⋊D1112yes—
347C22⋊Q8C22×D1112yes—
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—21no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4C22⋊D1111yescharacteristic
367C2×C4⋊C4C22×D1112yes—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—112no—
370C2×C22⋊C4—112no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4—444no—
381C2×C42—221no—
382#107—224no—
383#106—24no—
384#103—24no—
385#102—224no—
386C22⋊C8—21no—
387C22⋊C8—112no—
388C22⋊C8—221no—
389C22⋊C8C22×D1112yes—
390#95—112no—
391#95—224no—
392#95—221no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—22no—
396C2×C11#161214yescomplemented
397C2×C11C2×#44911yescharacteristic
398C2×C11C2×#45511yescharacteristic
399C2×C11C2×#45811yescharacteristic
400D11—82no—
401D11—82no—
402C24—112no—
403C24—222no—
404C24—221no—
405C24—221no—
406C24—222no—
407C24—221no—
408C24—442no—
409C24—442no—
410C24D4×D1111yescharacteristic
411C2×Q8—21no—
412C2×Q8—42no—
413C2×Q8C2×C22⋊D1112yes—
414C2×D4—112no—
415C2×D4—224no—
416C2×D4—224no—
417C2×D4—222no—
418C2×D4—222no—
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—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—112no—
434C22×C4—224no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—222no—
439C22×C4—442no—
440C22×C4—442no—
441C22×C4—442no—
442C22×C4—442no—
443C22×C4—882no—
444C22×C4D4×D1111yescharacteristic
445C22×C4D4×D1111yescharacteristic
446C22×C4D4×D1111yescharacteristic
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C23×D1111yescharacteristic
450C2×C8—22no—
451C2×C8—42no—
452C2×C8—222no—
453C2×C8—442no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—112no—
462C4⋊C4—224no—
463C4⋊C4—221no—
464C4⋊C4C2×C22⋊D1112yes—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—224no—
468C22⋊C4—224no—
469C22⋊C4—224no—
470C22⋊C4—222no—
471C22⋊C4—222no—
472C22⋊C4—222no—
473C22⋊C4—222no—
474C22⋊C4—222no—
475C22⋊C4—222no—
476C22⋊C4—448no—
477C42—224no—
478C11C2×#161211yescharacteristic, complemented, Sylow
479C23—22no—
480C23—22no—
481C23—222no—
482C23—222no—
483C23—222no—
484C23—222no—
485C23—442no—
486C23—442no—
487C23—448no—
488C23—442no—
489C23—442no—
490C23—442no—
491C23—442no—
492C23—442no—
493C23—442no—
494C23—442no—
495C23—881no—
496C23—881no—
497C23—884no—
498C23#6696712yes—
499C23#6696912yes—
500C23#6699011yescharacteristic
501C23#6699011yescharacteristic
502C23C2×D4×D1111yescharacteristic
503Q8—42no—
504Q8—81no—
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—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—884no—
536C2×C4—881no—
537C2×C4—884no—
538C2×C4#6699011yescharacteristic
539C2×C4#6699011yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4C22×C22⋊D1111yescharacteristic
542C8—42no—
543C8—442no—
544C22—24no—
545C22—24no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—444no—
551C22—442no—
552C22—442no—
553C22—442no—
554C22—442no—
555C22—442no—
556C22—442no—
557C22—882no—
558C22—884no—
559C22—884no—
560C22—884no—
561C22#1062266612yes—
562C22#1062278512yes—
563C22#1062278512yes—
564C22#1062281512yes—
565C22C2×#6696711yescharacteristic
566C22C2×#6696911yescharacteristic
567C22C2×#6699011yescharacteristic
568C4—21no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—42no—
573C4—42no—
574C4—82no—
575C4—442no—
576C4—442no—
577C4—882no—
578C2—21no—
579C2—21no—
580C2—22no—
581C2—882no—
582C2—882no—
583C2#1306762914yesdirect product factor
584C2C2×#1062278511yescharacteristic
585C2C2×#1062281511yescharacteristic
586C2C2×#1062266611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#483C2
socleC23×C11#120
prime radicalC2×#10623175C2
hypercenterC2×#483D11
hypocenterC11C2×#1612
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
2. C2×#10622580C2semidirect
3. C2×#10622606C2semidirect
4. #13067629C2direct (N × H)
5. C2×#10622176C2semidirect
6. C2×#10622108C2semidirect
7. C2×#10622106C2semidirect
8. C2×C11×#483C2semidirect
25. C11×#483C22semidirect
33. #10622606C22semidirect
35. #10622580C22semidirect
38. #10622176C22semidirect
39. #10622108C22semidirect
40. #10622106C22semidirect
187. C2×#483D11semidirect
275. #483C2×D11semidirect
396. C2×C11#1612semidirect
478. C11C2×#1612semidirect
583. C2#13067629direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231752
C2×#106225802
C2×#106226062
#130676292
C2×#106221762
C2×#106221082
C2×#106221062
C2×C11×#4832
C2×#161211