Finite Group Databasebeta

← C2×#13069751 #14781042

Subgroups — C2×#13069751 #14781042

Order 2816.

1734 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic, complemented
2C22×#66885C211yesmaximal, characteristic
3C22×#66873C211yesmaximal, characteristic
4C2×#10622601C211yesmaximal, characteristic
5#13069751C218yesmaximal, direct product factor
6C2×#10622167C211yesmaximal, characteristic, complemented
7C2×#10622188C211yesmaximal, characteristic, complemented
8C2×C11×#340C211yesmaximal, characteristic, complemented
9C23×D44C2211yescharacteristic
10C23×Dic22—21no—
11C23×C8×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4—21no—
15C22×(C2×D11)⋊C4—21no—
16C22×C4⋊Dic11C2211yescharacteristic
17C22×Dic11⋊C4—21no—
18C22×C4×Dic11C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20C2×#66941—24no—
21C2×#66941—24no—
22C2×#66941—22no—
23C2×#66941C2214yescomplemented
24C2×#66885—24no—
25C2×#66885C2214yes—
26#10622601—22no—
27#10622601C2214yes—
28C2×#66873—24no—
29C2×#66873C2214yes—
30C11×#340C2214yescomplemented
31#10622188C2214yescomplemented
32#10622167C2214yescomplemented
33C24×D11—21no—
34C23×C4×C11—21no—
35C23×C4×C11—21no—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11—21no—
38C23×Dic11D411yescharacteristic
39C23×Dic11D411yescharacteristic
40C22×D44—22no—
41C22×D44—22no—
42C22×D44—22no—
43C22×D44—22no—
44C22×D44—21no—
45C22×D44—22no—
46C22×D44Q814yescomplemented
47C22×D44C2312yes—
48C22×Dic22—28no—
49C22×Dic22—24no—
50C22×Dic22—44no—
51C22×Dic22—44no—
52C22×C8×C11—22no—
53C22×C8×C11—22no—
54C22×C8×C11—22no—
55C22×C8×C11C2312yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D414yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—44no—
67C2×(C2×D11)⋊C4—44no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11D414yes—
71C2×C4⋊Dic11C2312yes—
72C2×Dic11⋊C4—28no—
73C2×Dic11⋊C4—24no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—22no—
76C2×C4×Dic11D412yes—
77C2×C4×Dic11C2312yes—
78C22×C11⋊C8—22no—
79C22×C11⋊C8—22no—
80C22×C11⋊C8—22no—
81C22×C11⋊C8C2312yes—
82#66941—216no—
83#66941—28no—
84#66941—28no—
85#66885—28no—
86#66873—28no—
87C2×#2023—111nomaximal, Sylow
88C24×C11C2×D411yescharacteristic
89C23×D11—24no—
90C23×D11—22no—
91C23×D11—42no—
92C23×D11—42no—
93C23×D11—42no—
94C23×D11—42no—
95C23×D11—42no—
96C23×D11—42no—
97C22×C4×C11—24no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×Q812yes—
109C22×C4×C11#4112yes—
110C22×C4×C11#4112yes—
111C22×C4×C11#4112yes—
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—24no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—42no—
120C22×Dic11—42no—
121C22×Dic11D814yes—
122C22×Dic11SD1614yes—
123C22×Dic11C2×D412yes—
124C22×Dic11C2×D412yes—
125C2×D44—24no—
126C2×D44—28no—
127C2×D44—28no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—42no—
134C2×D44—44no—
135C2×D44—44no—
136C2×D44—42no—
137C2×D44C2×Q814yescomplemented
138C2×Dic22—216no—
139C2×Dic22—48no—
140C2×Dic22—432no—
141C2×Dic22—48no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—44no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4C2×D414yes—
152(C2×D11)⋊C4—48no—
153(C2×D11)⋊C4—48no—
154C4⋊Dic11—24no—
155C4⋊Dic11—22no—
156C4⋊Dic11C2×D414yes—
157Dic11⋊C4—216no—
158C4×Dic11—24no—
159C4×Dic11—22no—
160C4×Dic11—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—44no—
165C22×C4⋊Q8—111no—
166C22×#102—111no—
167C22×#102—111no—
168C2×#390—111no—
169#2023—118no—
170C2×#340—111no—
171C2×#340D1111yescharacteristic, complemented
172C2×#336—111no—
173C23×C11#12012yes—
174C23×C11C22⋊Q812yes—
175C23×C11#12412yes—
176C23×C11C2×D812yes—
177C23×C11C2×SD1612yes—
178C23×C11AGL(1,ℤ/8)12yes—
179C23×C11#13712yes—
180C23×C11C22×D411yescharacteristic
181C22×D11—24no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—48no—
189C22×D11—48no—
190C22×D11—48no—
191C22×D11—84no—
192C22×D11—84no—
193C22×D11—84no—
194C22×D11—84no—
195C2×C4×C11—24no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—48no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—84no—
203C2×C4×C11#12012yes—
204C2×C4×C11C22⋊Q814yes—
205C2×C4×C11C22⋊Q812yes—
206C2×C4×C11C22⋊Q814yes—
207C2×C4×C11#12414yes—
208C2×C4×C11#12414yes—
209C2×C4×C11#12412yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×Q811yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—28no—
221C2×Dic11—28no—
222C2×Dic11—24no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—48no—
226C2×Dic11C2×D814yes—
227C2×Dic11C2×SD1614yes—
228D44—24no—
229D44—24no—
230D44—42no—
231D44—42no—
232D44—48no—
233Dic22—432no—
234C8×C11—42no—
235C11⋊C8—42no—
236C23×Q8—221no—
237C23×D4—111no—
238C23×C8—111no—
239C23×C8C2×D1111yescharacteristic
240C2×C4⋊Q8—114no—
241C2×C4⋊Q8—222no—
242C2×C4⋊Q8—224no—
243C2×C4⋊Q8—224no—
244C22×C4⋊C4—111no—
245C22×C4⋊C4—221no—
246C22×C4⋊C4C2×D1111yescharacteristic
247C22×C4⋊C4C2×D1111yescharacteristic
248C22×C22⋊C4—221no—
249C22×C22⋊C4—221no—
250C22×C42—111no—
251C2×#102—114no—
252C2×#102—114no—
253C2×#102—224no—
254C2×#102—224no—
255#390—114no—
256#390—222no—
257#340—114no—
258#340C2×D1114yescomplemented
259#336—114no—
260C22×C11#39314yes—
261C22×C11#44714yes—
262C22×C11#44814yes—
263C22×C11#47414yes—
264C22×C11#47614yes—
265C22×C11#48614yes—
266C22×C11#48914yes—
267C22×C11C2×#12011yescharacteristic
268C22×C11C2×C22⋊Q811yescharacteristic
269C22×C11C2×#12411yescharacteristic
270C22×C11C22×D811yescharacteristic
271C22×C11C22×SD1611yescharacteristic
272C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C11C2×#13711yescharacteristic
274C2×D11—44no—
275C2×D11—44no—
276C2×D11—44no—
277C2×D11—82no—
278C2×D11—82no—
279C2×D11—82no—
280C2×D11—82no—
281C2×D11—816no—
282C4×C11—44no—
283C4×C11—82no—
284C4×C11#39314yes—
285C4×C11C2×C22⋊Q811yescharacteristic
286C4×C11C2×C22⋊Q811yescharacteristic
287C4×C11C2×#12411yescharacteristic
288C4×C11C2×#12411yescharacteristic
289Dic11—24no—
290Dic11—24no—
291Dic11—44no—
292C25—221no—
293C22×Q8—224no—
294C22×Q8—228no—
295C22×Q8—444no—
296C22×Q8—444no—
297C22×D4—114no—
298C22×D4—112no—
299C22×D4—222no—
300C22×D4—222no—
301C22×D4—222no—
302C22×D4—222no—
303C22×D4—221no—
304C22×D4—222no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—111no—
308C23×C4—111no—
309C23×C4—221no—
310C23×C4C22×D1111yescharacteristic
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—112no—
315C22×C8—222no—
316C22×C8—222no—
317C22×C8—222no—
318C22×C8C22×D1112yes—
319C4⋊Q8—228no—
320C4⋊Q8—2216no—
321C4⋊Q8—228no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—114no—
328C2×C4⋊C4—112no—
329C2×C4⋊C4—224no—
330C2×C4⋊C4—228no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4D4414yes—
334C2×C4⋊C4C22×D1112yes—
335C2×C4⋊C4C22×D1112yes—
336C2×C22⋊C4—224no—
337C2×C22⋊C4—224no—
338C2×C22⋊C4—444no—
339C2×C22⋊C4—444no—
340C2×C42—112no—
341C2×C42—112no—
342C2×C42—222no—
343C2×C42—222no—
344#102—228no—
345#102—228no—
346C2×C11#202318yescomplemented
347C2×C11C2×#39311yescharacteristic
348C2×C11C2×#44711yescharacteristic
349C2×C11C2×#44811yescharacteristic
350C2×C11C2×#47411yescharacteristic
351C2×C11C2×#47611yescharacteristic
352C2×C11C2×#48611yescharacteristic
353C2×C11C2×#48911yescharacteristic
354D11—84no—
355C24—224no—
356C24—222no—
357C24—442no—
358C24—442no—
359C24—442no—
360C24—442no—
361C24—442no—
362C24—442no—
363C24D4×D1111yescharacteristic
364C2×Q8—2216no—
365C2×Q8—448no—
366C2×Q8—448no—
367C2×Q8—4432no—
368C2×D4—114no—
369C2×D4—228no—
370C2×D4—224no—
371C2×D4—228no—
372C2×D4—222no—
373C2×D4—222no—
374C2×D4—222no—
375C2×D4—222no—
376C2×D4—222no—
377C2×D4—444no—
378C2×D4—442no—
379C2×D4—444no—
380C2×D4—442no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—114no—
390C22×C4—114no—
391C22×C4—112no—
392C22×C4—112no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—224no—
398C22×C4—222no—
399C22×C4—442no—
400C22×C4—442no—
401C22×C4C2×D4412yes—
402C22×C4#433912yes—
403C22×C4#433912yes—
404C22×C4D4×D1111yescharacteristic
405C22×C4D4×D1112yes—
406C22×C4#434112yes—
407C22×C4Q8×D1112yes—
408C22×C4C23×D1111yescharacteristic
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—44no—
413C2×C8—222no—
414C2×C8—222no—
415C2×C8—222no—
416C2×C8—444no—
417C4⋊C4—24no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—42no—
422C4⋊C4—114no—
423C4⋊C4—2216no—
424C4⋊C4—224no—
425C4⋊C4—222no—
426C4⋊C4C2×D4414yes—
427C22⋊C4—448no—
428C22⋊C4—448no—
429C42—224no—
430C42—222no—
431C42—222no—
432C11C2×#202311yescharacteristic, complemented, Sylow
433C23—224no—
434C23—448no—
435C23—448no—
436C23—442no—
437C23—442no—
438C23—442no—
439C23—442no—
440C23—442no—
441C23—442no—
442C23—448no—
443C23—884no—
444C23—884no—
445C23—884no—
446C23—884no—
447C23#6693512yes—
448C23#6693812yes—
449C23#6694912yes—
450C23D8×D1112yes—
451C23SD16×D1112yes—
452C23#6696712yes—
453C23#6697112yes—
454C23C2×D4×D1111yescharacteristic
455Q8—4432no—
456D4—224no—
457D4—224no—
458D4—442no—
459D4—442no—
460D4—448no—
461C2×C4—24no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—48no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—84no—
469C2×C4—114no—
470C2×C4—114no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—228no—
476C2×C4—228no—
477C2×C4—224no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—448no—
481C2×C4#6692814yes—
482C2×C4#6693512yes—
483C2×C4#6693814yes—
484C2×C4#6693812yes—
485C2×C4#6694914yes—
486C2×C4#6694912yes—
487C2×C4#6695014yes—
488C2×C4C22×D4411yescharacteristic
489C2×C4C2×#433911yescharacteristic
490C2×C4C2×#433911yescharacteristic
491C2×C4C2×D4×D1111yescharacteristic
492C2×C4C2×#434111yescharacteristic
493C2×C4C2×Q8×D1111yescharacteristic
494C8—42no—
495C8—442no—
496C22—444no—
497C22—444no—
498C22—444no—
499C22—882no—
500C22—882no—
501C22—882no—
502C22—882no—
503C22—8816no—
504C22#1062228614yes—
505C22#1062237314yes—
506C22#1062238614yes—
507C22#1062240814yes—
508C22#1062241914yes—
509C22#1062248314yes—
510C22#1062250314yes—
511C22C2×#6693511yescharacteristic
512C22C2×#6693811yescharacteristic
513C22C2×#6694911yescharacteristic
514C22C2×D8×D1111yescharacteristic
515C22C2×SD16×D1111yescharacteristic
516C22C2×#6696711yescharacteristic
517C22C2×#6697111yescharacteristic
518C4—44no—
519C4—82no—
520C4—224no—
521C4—224no—
522C4—444no—
523C4#1062228614yes—
524C4C2×#6692811yescharacteristic
525C4C2×#6693811yescharacteristic
526C4C2×#6694911yescharacteristic
527C4C2×#6695011yescharacteristic
528C2—884no—
529C2#1306975118yesdirect product factor
530C2C2×#1062228611yescharacteristic
531C2C2×#1062238611yescharacteristic
532C2C2×#1062241911yescharacteristic
533C2C2×#1062250311yescharacteristic
534C2C2×#1062248311yescharacteristic
535C2C2×#1062237311yescharacteristic
536C2C2×#1062240811yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC24×C11C2×D4
prime radicalC23×D44C22
hypercenterC2×#340D11
hypocenterC11C2×#2023
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
5. #13069751C2direct (N × H)
6. C2×#10622167C2semidirect
7. C2×#10622188C2semidirect
8. C2×C11×#340C2semidirect
23. C2×#66941C22semidirect
30. C11×#340C22semidirect
31. #10622188C22semidirect
32. #10622167C22semidirect
46. C22×D44Q8semidirect
137. C2×D44C2×Q8semidirect
171. C2×#340D11semidirect
258. #340C2×D11semidirect
346. C2×C11#2023semidirect
432. C11C2×#2023semidirect
529. C2#13069751direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669412
C22×#668852
C22×#668732
C2×#106226012
#130697512
C2×#106221672
C2×#106221882
C2×C11×#3402
C2×#202311