Finite Group Databasebeta

← C2×#13074490 #14920562

Subgroups — C2×#13074490 #14920562

Order 2816.

2894 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66943C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
3#13074490C2116yesmaximal, direct product factor
4C2×#10622605C211yesmaximal, characteristic, complemented
5C2×#10622597C212yesmaximal, complemented
6C2×#10622287C211yesmaximal, characteristic, complemented
7C2×#10622566C211yesmaximal, characteristic, complemented
8C2×#10622574C212yesmaximal
9C2×#10622559C212yesmaximal, complemented
10C2×#10622602C212yesmaximal, complemented
11C2×#10622264C211yesmaximal, characteristic, complemented
12C2×C11×#399C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2212yes—
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C22×C4⋊Dic11C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C2×#66943—28no—
31C2×#66943C2218yescomplemented
32C2×(C22⋊D11)⋊C4—28no—
33C2×(C22⋊D11)⋊C4C2218yes—
34C11×#399C2218yescomplemented
35C2×C11×#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622605C2218yescomplemented
42#10622602C22116yescomplemented
43#10622597C22116yescomplemented
44#10622574C22116yes—
45#10622566C2218yescomplemented
46#10622559C22116yescomplemented
47#10622287C2218yescomplemented
48#10622264C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11—24no—
56C22×C22⋊D11—24no—
57C22×C22⋊D11—24no—
58C22×C22⋊D11C2314yes—
59C23×Dic11—24no—
60C23×Dic11—44no—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2314yes—
67C22×C4×D11—24no—
68C22×C4×D11—44no—
69C22×C4×D11C2314yes—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—44no—
72C2×C11×C4⋊C4C2314yes—
73C2×C11×C4⋊C4C2318yes—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—44no—
76C2×C11×C22⋊C4C2314yes—
77C2×C11×C22⋊C4C2318yes—
78C2×C22⋊Dic11—28no—
79C2×C22⋊Dic11C2318yes—
80C2×(C2×D11)⋊C4—28no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—44no—
83C2×(C2×D11)⋊C4C2314yes—
84C2×(C2×D11)⋊C4C2318yes—
85C2×(C2×D11)⋊C4C2318yes—
86C2×C4⋊Dic11—24no—
87C2×C4⋊Dic11—28no—
88C2×C4⋊Dic11C2314yes—
89C2×C4⋊Dic11C2318yes—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—44no—
93C2×Dic11⋊C4C2314yes—
94C2×Dic11⋊C4C2318yes—
95C2×Dic11⋊C4C2318yes—
96C2×C4×Dic11D418yes—
97C2×C4×Dic11C2314yes—
98#66943—232no—
99(C22⋊D11)⋊C4—232no—
100C11×#95C2314yes—
101C11⋊#95C2318yes—
102C11⋊#95C2314yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C2×#2633—111nomaximal, Sylow
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—24no—
110C24×C11—24no—
111C24×C11#4114yes—
112C24×C11C2412yes—
113C24×C11C2411yescharacteristic
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—24no—
117C23×D11—24no—
118C23×D11#4114yes—
119C23×D11C2412yes—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11C2×D414yes—
130C22×C4×C11C2414yes—
131C22×C4×C11C2412yes—
132C22×C4×C11C2414yes—
133C22×C4×C11C2412yes—
134C2×C22⋊D11—232no—
135C2×C22⋊D11—28no—
136C2×C22⋊D11—28no—
137C2×C22⋊D11—28no—
138C22×Dic11—28no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—48no—
151C22×Dic11—416no—
152C22×Dic11C2×D414yes—
153C22×Dic11C2×D414yes—
154C22×Dic11C2414yes—
155C22×Dic11C2412yes—
156C22×Dic11C2414yes—
157C22×Dic11C2412yes—
158C22×Dic11C2412yes—
159C2×C4×D11—28no—
160C2×C4×D11—48no—
161C2×C4×D11—416no—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—48no—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—48no—
166C22⋊Dic11—216no—
167(C2×D11)⋊C4—216no—
168(C2×D11)⋊C4—28no—
169(C2×D11)⋊C4—48no—
170C4⋊Dic11—216no—
171C4⋊Dic11—28no—
172Dic11⋊C4—28no—
173Dic11⋊C4—216no—
174Dic11⋊C4—48no—
175C4×Dic11C2×D4116yes—
176C22×#125—111no—
177C22×C4×D4—111no—
178#2633—1116no—
179C2×#399—111no—
180C2×#399D1111yescharacteristic, complemented
181C2×#398—112no—
182C2×#397—111no—
183C2×#397—111no—
184C2×#394—112no—
185C2×#385—112no—
186C2×#385—112no—
187C2×#383—111no—
188C23×C11—28no—
189C23×C11—216no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—44no—
195C23×C11—44no—
196C23×C11—48no—
197C23×C11C22×D412yes—
198C23×C11C2×#4114yes—
199C23×C11C2×#4112yes—
200C23×C11C2×#4112yes—
201C23×C11H(5,𝔽2)14yes—
202C23×C112−1+414yes—
203C23×C11C2511yescharacteristic
204C22×D11—28no—
205C22×D11—216no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—44no—
211C22×D11—44no—
212C22×D11—48no—
213C22×D11C2×#4114yes—
214C2×C4×C11—28no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—44no—
225C2×C4×C11—48no—
226C2×C4×C11—48no—
227C2×C4×C11C22×D414yes—
228C22⋊D11—232no—
229C2×Dic11—28no—
230C2×Dic11—28no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—416no—
243C2×Dic11—48no—
244C2×Dic11—44no—
245C2×Dic11—48no—
246C2×Dic11C22×D414yes—
247C2×Dic11C22×D414yes—
248C4×D11—416no—
249C23×D4—111no—
250C24×C4—111no—
251C24×C4—111no—
252C2×#125—118no—
253C2×#125—228no—
254C2×C4×D4—118no—
255C2×C4×D4—228no—
256C22×C4⋊C4—112no—
257C22×C4⋊C4—111no—
258C22×C4⋊C4—112no—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—112no—
261C22×C4⋊C4C2×D1111yescharacteristic
262C22×C4⋊C4C2×D1112yes—
263C22×C22⋊C4—112no—
264C22×C22⋊C4—112no—
265C22×C22⋊C4—111no—
266C22×C22⋊C4—112no—
267C22×C22⋊C4C2×D1111yescharacteristic
268C22×C22⋊C4C2×D1112yes—
269C22×C42—111no—
270#399—118no—
271#399C2×D1118yescomplemented
272#398—1116no—
273#397—118no—
274#397—118no—
275#394—1116no—
276#385—1116no—
277#385—1116no—
278#383—118no—
279C2×#95—112no—
280C2×#95—112no—
281C2×#95—112no—
282C2×#95—111no—
283C2×#95—112no—
284C2×#95C2×D1111yescharacteristic
285C22×C11—24no—
286C22×C11—28no—
287C22×C11—416no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—44no—
291C22×C11#52514yes—
292C22×C11#53514yes—
293C22×C11#53614yes—
294C22×C11#53918yes—
295C22×C11#53918yes—
296C22×C11C23×D411yescharacteristic
297C22×C11C22×#4111yescharacteristic
298C22×C11C22×#4111yescharacteristic
299C22×C11C2×H(5,𝔽2)12yes—
300C22×C11C2×2−1+412yes—
301C2×D11—24no—
302C2×D11—28no—
303C2×D11—416no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—44no—
307C4×C11—24no—
308C4×C11—44no—
309C4×C11—42no—
310C4×C11—44no—
311Dic11—24no—
312Dic11—24no—
313Dic11—44no—
314Dic11—42no—
315Dic11—44no—
316C25—111no—
317C25C22×D1111yescharacteristic
318C22×D4—114no—
319C22×D4—224no—
320C22×D4—224no—
321C22×D4—224no—
322C23×C4—111no—
323C23×C4—111no—
324C23×C4—112no—
325C23×C4—112no—
326C23×C4—111no—
327C23×C4—114no—
328C23×C4—114no—
329C23×C4—224no—
330C23×C4—224no—
331C23×C4—444no—
332C23×C4—444no—
333C23×C4C22×D1112yes—
334C23×C4C22×D1112yes—
335C23×C4C22×D1111yescharacteristic
336C23×C4C22×D1111yescharacteristic
337#125—2232no—
338C4×D4—2232no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—114no—
342C2×C4⋊C4—118no—
343C2×C4⋊C4—118no—
344C2×C4⋊C4—114no—
345C2×C4⋊C4—118no—
346C2×C4⋊C4—224no—
347C2×C4⋊C4—228no—
348C2×C4⋊C4—228no—
349C2×C4⋊C4—224no—
350C2×C4⋊C4—444no—
351C2×C4⋊C4C22×D1114yes—
352C2×C4⋊C4C22×D1118yes—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—118no—
356C2×C22⋊C4—114no—
357C2×C22⋊C4—118no—
358C2×C22⋊C4—118no—
359C2×C22⋊C4—228no—
360C2×C22⋊C4—228no—
361C2×C22⋊C4—224no—
362C2×C22⋊C4—444no—
363C2×C22⋊C4C22×D1114yes—
364C2×C22⋊C4C22×D1118yes—
365C2×C42—118no—
366C2×C42—114no—
367#95—118no—
368#95—118no—
369#95—114no—
370#95—118no—
371#95—118no—
372#95C22×D1114yes—
373C2×C11—44no—
374C2×C11#263318yescomplemented
375C2×C11C2×#52511yescharacteristic
376C2×C11C2×#53511yescharacteristic
377C2×C11C2×#53611yescharacteristic
378C2×C11C2×#53912yes—
379C2×C11C2×#53912yes—
380D11—44no—
381C24—22no—
382C24—24no—
383C24—22no—
384C24—24no—
385C24—114no—
386C24—112no—
387C24—222no—
388C24—224no—
389C24—222no—
390C24—224no—
391C24#434314yes—
392C24C23×D1112yes—
393C24C23×D1111yescharacteristic
394C2×D4—228no—
395C2×D4—228no—
396C2×D4—2232no—
397C2×D4—228no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—114no—
408C22×C4—114no—
409C22×C4—112no—
410C22×C4—112no—
411C22×C4—114no—
412C22×C4—114no—
413C22×C4—112no—
414C22×C4—228no—
415C22×C4—228no—
416C22×C4—224no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—224no—
421C22×C4—224no—
422C22×C4—224no—
423C22×C4—224no—
424C22×C4—224no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—448no—
428C22×C4—4416no—
429C22×C4—448no—
430C22×C4—4416no—
431C22×C4D4×D1114yes—
432C22×C4C23×D1114yes—
433C22×C4C23×D1112yes—
434C22×C4C23×D1114yes—
435C22×C4C23×D1112yes—
436C4⋊C4—28no—
437C4⋊C4—48no—
438C4⋊C4—228no—
439C4⋊C4—2216no—
440C4⋊C4—2216no—
441C4⋊C4—228no—
442C4⋊C4—448no—
443C22⋊C4—28no—
444C22⋊C4—48no—
445C22⋊C4—2216no—
446C22⋊C4—2216no—
447C22⋊C4—228no—
448C22⋊C4—448no—
449C42—1116no—
450C11C2×#263311yescharacteristic, complemented, Sylow
451C23—28no—
452C23—216no—
453C23—22no—
454C23—24no—
455C23—22no—
456C23—24no—
457C23—44no—
458C23—44no—
459C23—48no—
460C23—114no—
461C23—228no—
462C23—222no—
463C23—224no—
464C23—2216no—
465C23—222no—
466C23—224no—
467C23—444no—
468C23—448no—
469C23—444no—
470C23C2×D4×D1112yes—
471C23#6703714yes—
472C23C2×#434314yes—
473C23C2×#434312yes—
474C23#41×D1112yes—
475C23#6704314yes—
476C23C24×D1111yescharacteristic
477D4—2232no—
478C2×C4—28no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—48no—
489C2×C4—44no—
490C2×C4—48no—
491C2×C4—114no—
492C2×C4—114no—
493C2×C4—228no—
494C2×C4—228no—
495C2×C4—224no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—4416no—
507C2×C4—4416no—
508C2×C4—444no—
509C2×C4—448no—
510C2×C4—448no—
511C2×C4C2×D4×D1114yes—
512C22—24no—
513C22—28no—
514C22—416no—
515C22—42no—
516C22—42no—
517C22—44no—
518C22—224no—
519C22—228no—
520C22—4416no—
521C22—442no—
522C22—442no—
523C22—444no—
524C22#1062315814yes—
525C22#1062317618yes—
526C22#1062317914yes—
527C22#1062319118yes—
528C22#1062324614yes—
529C22C22×D4×D1111yescharacteristic
530C22C2×#6703712yes—
531C22C22×#434311yescharacteristic
532C22C2×#41×D1111yescharacteristic
533C22C2×#6704312yes—
534C4—24no—
535C4—42no—
536C4—44no—
537C4—44no—
538C4—224no—
539C4—224no—
540C4—444no—
541C4—442no—
542C4—444no—
543C2—44no—
544C2—444no—
545C2#1307449018yesdirect product factor
546C2C2×#1062315811yescharacteristic
547C2C2×#1062324611yescharacteristic
548C2C2×#1062317911yescharacteristic
549C2C2×#1062319112yes—
550C2C2×#1062317612yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#399C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#399D11
hypocenterC11C2×#2633
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#66943C2semidirect
3. #13074490C2direct (N × H)
4. C2×#10622605C2semidirect
5. C2×#10622597C2semidirect
6. C2×#10622287C2semidirect
7. C2×#10622566C2semidirect
9. C2×#10622559C2semidirect
10. C2×#10622602C2semidirect
11. C2×#10622264C2semidirect
12. C2×C11×#399C2semidirect
31. C2×#66943C22semidirect
34. C11×#399C22semidirect
41. #10622605C22semidirect
42. #10622602C22semidirect
43. #10622597C22semidirect
45. #10622566C22semidirect
46. #10622559C22semidirect
47. #10622287C22semidirect
48. #10622264C22semidirect
180. C2×#399D11semidirect
271. #399C2×D11semidirect
374. C2×C11#2633semidirect
450. C11C2×#2633semidirect
545. C2#13074490direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669432
C22×(C22⋊D11)⋊C42
#130744902
C2×#106226052
C2×#106225972
C2×#106222872
C2×#106225662
C2×#106225742
C2×#106225592
C2×#106226022
C2×#106222642
C2×C11×#3992
C2×#263311