Finite Group Databasebeta

← C2×#13069750 #14781041

Subgroups — C2×#13069750 #14781041

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×#66896C211yesmaximal, characteristic
3C2×#10622834C211yesmaximal, characteristic
4#13069750C218yesmaximal, direct product factor
5C2×#10622189C211yesmaximal, characteristic, complemented
6C2×#10622167C211yesmaximal, characteristic, complemented
7C2×#10622188C211yesmaximal, characteristic, complemented
8C22×C11×#102C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C23×Dic22—21no—
11C23×C8×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C22⋊Dic11—21no—
14C22×C22⋊Dic11—21no—
15C22×C4⋊Dic11C2211yescharacteristic
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×C11×#102—24no—
25C2×C11×#102C2214yes—
26#10622834—22no—
27#10622834C2214yes—
28C2×#66896—24no—
29C2×#66896C2214yes—
30#10622189C2214yescomplemented
31#10622188C2214yescomplemented
32#10622167C2214yescomplemented
33C25×C11—21no—
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—21no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11Q814yescomplemented
41C22×D4×C11C2312yes—
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—21no—
45C23×Dic11—21no—
46C23×Dic11D411yescharacteristic
47C23×Dic11D411yescharacteristic
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⋊C4D414yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—44no—
63C2×C22⋊Dic11—44no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11D414yes—
70C2×C4⋊Dic11C2312yes—
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—
85C11×#102—28no—
86#66896—28no—
87C2×#2023—111nomaximal, Sylow
88C24×C11—24no—
89C24×C11—22no—
90C24×C11—42no—
91C24×C11—42no—
92C24×C11—42no—
93C24×C11—42no—
94C24×C11—42no—
95C24×C11—42no—
96C24×C11C2×D411yescharacteristic
97C2×D4×C11—28no—
98C2×D4×C11—28no—
99C2×D4×C11—24no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—42no—
106C2×D4×C11—44no—
107C2×D4×C11—42no—
108C2×D4×C11—44no—
109C2×D4×C11C2×Q814yescomplemented
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×Q812yes—
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×C4×C11#4112yes—
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—24no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—42no—
130C22×Dic11—42no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C22×Dic11D814yes—
135C22×Dic11SD1614yes—
136C22×Dic11C2×D412yes—
137C22×Dic11C2×D412yes—
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⋊C4C2×D414yes—
149C22⋊Dic11—48no—
150C22⋊Dic11—48no—
151C4⋊Dic11—24no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11—42no—
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×#102D1111yescharacteristic
168C2×#390—111no—
169#2023—118no—
170C2×#340—111no—
171C2×#340—111no—
172C2×#336—111no—
173C23×C11—24no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—48no—
181C23×C11—48no—
182C23×C11—48no—
183C23×C11—84no—
184C23×C11—84no—
185C23×C11—84no—
186C23×C11—84no—
187C23×C11#12012yes—
188C23×C11C22⋊Q812yes—
189C23×C11#12412yes—
190C23×C11C2×D812yes—
191C23×C11C2×SD1612yes—
192C23×C11AGL(1,ℤ/8)12yes—
193C23×C11#13712yes—
194C23×C11C22×D411yescharacteristic
195D4×C11—24no—
196D4×C11—24no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—48no—
200C2×C4×C11—24no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—48no—
204C2×C4×C11#12012yes—
205C2×C4×C11C22⋊Q814yes—
206C2×C4×C11C22⋊Q812yes—
207C2×C4×C11C22⋊Q814yes—
208C2×C4×C11#12414yes—
209C2×C4×C11#12412yes—
210C2×C4×C11#12414yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×Q811yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—28no—
222C2×Dic11—28no—
223C2×Dic11—24no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—48no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—84no—
231C2×Dic11C2×D814yes—
232C2×Dic11C2×SD1614yes—
233Dic22—432no—
234C8×C11—42no—
235C11⋊C8—42no—
236C23×Q8—221no—
237C23×D4C2×D1111yescharacteristic
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—111no—
246C22×C4⋊C4—221no—
247C22×C4⋊C4C2×D1111yescharacteristic
248C22×C22⋊C4—221no—
249C22×C22⋊C4—221no—
250C22×C42—111no—
251C2×#102—24no—
252C2×#102—114no—
253C2×#102—224no—
254C2×#102C2×D1114yes—
255#390—114no—
256#390—222no—
257#340—114no—
258#340—114no—
259#336—114no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11—44no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11—82no—
266C22×C11—82no—
267C22×C11—816no—
268C22×C11#39314yes—
269C22×C11#44714yes—
270C22×C11#44814yes—
271C22×C11#47414yes—
272C22×C11#47614yes—
273C22×C11#48614yes—
274C22×C11#48914yes—
275C22×C11C2×#12011yescharacteristic
276C22×C11C2×C22⋊Q811yescharacteristic
277C22×C11C2×#12411yescharacteristic
278C22×C11C22×D811yescharacteristic
279C22×C11C22×SD1611yescharacteristic
280C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C11C2×#13711yescharacteristic
282C4×C11—44no—
283C4×C11#39314yes—
284C4×C11C2×C22⋊Q811yescharacteristic
285C4×C11C2×C22⋊Q811yescharacteristic
286C4×C11C2×#12411yescharacteristic
287C4×C11C2×#12411yescharacteristic
288Dic11—24no—
289Dic11—24no—
290Dic11—44no—
291Dic11—82no—
292C25—21no—
293C22×Q8—224no—
294C22×Q8—228no—
295C22×Q8—444no—
296C22×Q8—444no—
297C22×D4—22no—
298C22×D4—22no—
299C22×D4—21no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4Dic2214yescomplemented
304C22×D4C22×D1112yes—
305C23×C4—21no—
306C23×C4—111no—
307C23×C4—111no—
308C23×C4—221no—
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—114no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—224no—
328C2×C4⋊C4—228no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4C22⋊D1114yes—
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—28no—
345#102—228no—
346C2×C11—84no—
347C2×C11#202318yescomplemented
348C2×C11C2×#39311yescharacteristic
349C2×C11C2×#44711yescharacteristic
350C2×C11C2×#44811yescharacteristic
351C2×C11C2×#47411yescharacteristic
352C2×C11C2×#47611yescharacteristic
353C2×C11C2×#48611yescharacteristic
354C2×C11C2×#48911yescharacteristic
355C24—24no—
356C24—22no—
357C24—42no—
358C24—42no—
359C24—42no—
360C24—42no—
361C24—42no—
362C24—42no—
363C24D4×D1111yescharacteristic
364C2×Q8—2216no—
365C2×Q8—448no—
366C2×Q8—4432no—
367C2×Q8—448no—
368C2×D4—28no—
369C2×D4—24no—
370C2×D4—28no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—44no—
377C2×D4—42no—
378C2×D4—44no—
379C2×D4—42no—
380C2×D4C2×Dic2214yescomplemented
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—114no—
386C22×C4—114no—
387C22×C4—112no—
388C22×C4—112no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—224no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4—442no—
399C22×C4—442no—
400C22×C4—442no—
401C22×C4C2×Dic2212yes—
402C22×C4#433912yes—
403C22×C4D4×D1111yescharacteristic
404C22×C4D4×D1112yes—
405C22×C4#434112yes—
406C22×C4#434112yes—
407C22×C4C2×C22⋊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—114no—
420C4⋊C4—2216no—
421C4⋊C4—224no—
422C4⋊C4—222no—
423C4⋊C4—222no—
424C4⋊C4—222no—
425C4⋊C4—442no—
426C4⋊C4C2×C22⋊D1114yes—
427C22⋊C4—448no—
428C22⋊C4—448no—
429C42—224no—
430C42—222no—
431C42—222no—
432C11C2×#202311yescharacteristic, complemented, Sylow
433C23—24no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23—48no—
440C23—42no—
441C23—48no—
442C23—48no—
443C23—84no—
444C23—84no—
445C23—84no—
446C23—84no—
447C23#6693112yes—
448C23#6693812yes—
449C23D8×D1112yes—
450C23#6696412yes—
451C23SD16×D1112yes—
452C23#6696812yes—
453C23#6699012yes—
454C23C2×D4×D1111yescharacteristic
455Q8—4432no—
456D4—24no—
457D4—24no—
458D4—42no—
459D4—48no—
460D4—42no—
461C2×C4—24no—
462C2×C4—48no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—114no—
466C2×C4—114no—
467C2×C4—228no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—228no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—224no—
474C2×C4—448no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—884no—
481C2×C4#6693114yes—
482C2×C4#6693112yes—
483C2×C4#6693814yes—
484C2×C4#6693812yes—
485C2×C4#6697714yes—
486C2×C4#6698914yes—
487C2×C4#6699012yes—
488C2×C4C22×Dic2211yescharacteristic
489C2×C4C2×#433911yescharacteristic
490C2×C4C2×D4×D1111yescharacteristic
491C2×C4C2×#434111yescharacteristic
492C2×C4C2×#434111yescharacteristic
493C2×C4C22×C22⋊D1111yescharacteristic
494C8—42no—
495C8—442no—
496C22—44no—
497C22—44no—
498C22—44no—
499C22—82no—
500C22—82no—
501C22—82no—
502C22—82no—
503C22—816no—
504C22#1062237214yes—
505C22#1062237314yes—
506C22#1062237414yes—
507C22#1062237814yes—
508C22#1062256014yes—
509C22#1062276914yes—
510C22#1062278314yes—
511C22C2×#6693111yescharacteristic
512C22C2×#6693811yescharacteristic
513C22C2×D8×D1111yescharacteristic
514C22C2×#6696411yescharacteristic
515C22C2×SD16×D1111yescharacteristic
516C22C2×#6696811yescharacteristic
517C22C2×#6699011yescharacteristic
518C4—44no—
519C4—224no—
520C4—224no—
521C4—444no—
522C4—882no—
523C4#1062256014yes—
524C4C2×#6693111yescharacteristic
525C4C2×#6693811yescharacteristic
526C4C2×#6697711yescharacteristic
527C4C2×#6698911yescharacteristic
528C2—84no—
529C2#1306975018yesdirect product factor
530C2C2×#1062256011yescharacteristic
531C2C2×#1062276911yescharacteristic
532C2C2×#1062278311yescharacteristic
533C2C2×#1062237211yescharacteristic
534C2C2×#1062237411yescharacteristic
535C2C2×#1062237311yescharacteristic
536C2C2×#1062237811yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
prime radicalC23×D4×C11C22
hypercenterC22×#102D11
hypocenterC11C2×#2023
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
4. #13069750C2direct (N × H)
5. C2×#10622189C2semidirect
6. C2×#10622167C2semidirect
7. C2×#10622188C2semidirect
23. C2×#66941C22semidirect
30. #10622189C22semidirect
31. #10622188C22semidirect
32. #10622167C22semidirect
40. C22×D4×C11Q8semidirect
109. C2×D4×C11C2×Q8semidirect
303. C22×D4Dic22semidirect
347. C2×C11#2023semidirect
380. C2×D4C2×Dic22semidirect
432. C11C2×#2023semidirect
529. C2#13069750direct (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×#668962
C2×#106228342
#130697502
C2×#106221892
C2×#106221672
C2×#106221882
C22×C11×#1022
C2×#202311