Finite Group Databasebeta

← C2×#13073052 #14923012

Subgroups — C2×#13073052 #14923012

Order 2816.

2270 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073052C2116yesmaximal, direct product factor
2C2×#10622599C212yesmaximal, complemented
3C2×#10622607C212yesmaximal
4C2×#10622598C211yesmaximal, characteristic, complemented
5C2×#10622541C211yesmaximal, characteristic, complemented
6C2×#10622603C212yesmaximal
7C2×#10622591C212yesmaximal, complemented
8C2×#10622600C211yesmaximal, characteristic
9C2×#10622600C211yesmaximal, characteristic
10C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
12C2×C11×#384C211yesmaximal, characteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C4⋊C4C2212yes—
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2212yes—
29C11×#384C2218yescomplemented
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622607C22116yes—
38#10622603C22116yes—
39#10622600C2218yes—
40#10622600C2218yes—
41#10622599C22116yescomplemented
42#10622598C2218yescomplemented
43#10622591C22116yescomplemented
44C4⋊C4×Dic11C2218yescomplemented
45C4×(C2×D11)⋊C4C2218yes—
46#10622541C2218yescomplemented
47C24×D11C2311yescharacteristic
48C23×C4×C11C2312yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×Dic11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C22×C4×D11—24no—
59C22×C4×D11—24no—
60C22×C4×D11—24no—
61C22×C4×D11C2314yes—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4—44no—
65C2×C11×C4⋊C4—44no—
66C2×C11×C4⋊C4C2314yes—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2318yes—
69C2×C11×C4⋊C4C2318yes—
70C2×C42×C11—24no—
71C2×C42×C11C2314yes—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—44no—
74C2×(C2×D11)⋊C4—44no—
75C2×(C2×D11)⋊C4Q818yes—
76C2×(C2×D11)⋊C4C2314yes—
77C2×(C2×D11)⋊C4C2318yes—
78C2×(C2×D11)⋊C4C2318yes—
79C2×(C2×D11)⋊C4C2314yes—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—44no—
83C2×C4⋊Dic11C2314yes—
84C2×C4⋊Dic11C2314yes—
85C2×C4⋊Dic11C2318yes—
86C2×Dic11⋊C4—28no—
87C2×Dic11⋊C4C2318yes—
88C2×C4×Dic11—24no—
89C2×C4×Dic11—44no—
90C2×C4×Dic11C2314yes—
91C2×C4×Dic11C2318yes—
92C11⋊#95C2318yes—
93C11⋊#95C2314yes—
94C11⋊#95C2314yes—
95C11⋊#95C2318yes—
96C11⋊#95C2318yes—
97C11⋊#95C2318yes—
98C11⋊#95C2318yes—
99C2×#2497—111nomaximal, Sylow
100C24×C11C2411yescharacteristic
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11C2×Q814yes—
108C23×D11C2412yes—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11C2×Q814yes—
120C22×C4×C11#4114yes—
121C22×C4×C11#4114yes—
122C22×C4×C11#4114yes—
123C22×C4×C11#4114yes—
124C22×C4×C11C2414yes—
125C22×C4×C11C2414yes—
126C22×C4×C11C2412yes—
127C22×C4×C11C2412yes—
128C22×C4×C11C2412yes—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—24no—
141C22×Dic11—22no—
142C22×Dic11—24no—
143C22×Dic11C2×Q814yes—
144C22×Dic11C2412yes—
145C22×Dic11C2414yes—
146C22×Dic11C2412yes—
147C22×Dic11C2414yes—
148C22×Dic11C2412yes—
149C2×C4×D11—28no—
150C2×C4×D11—28no—
151C2×C4×D11—28no—
152C2×C4×D11—416no—
153C11×C4⋊C4—28no—
154C11×C4⋊C4—28no—
155C11×C4⋊C4—48no—
156C11×C4⋊C4—48no—
157C42×C11—28no—
158(C2×D11)⋊C4—28no—
159(C2×D11)⋊C4—48no—
160(C2×D11)⋊C4—48no—
161(C2×D11)⋊C4C2×Q8116yes—
162C4⋊Dic11—28no—
163C4⋊Dic11—28no—
164C4⋊Dic11—48no—
165Dic11⋊C4—216no—
166C4×Dic11—28no—
167C4×Dic11—48no—
168#2497—1116no—
169C2×#400—112no—
170C2×#396—112no—
171C2×#389—111no—
172C2×#389—111no—
173C2×#388—112no—
174C2×#387—112no—
175C2×#384D1111yescharacteristic, complemented
176C2×#380—111no—
177C2×#380—111no—
178C2×C4×C4⋊C4—111no—
179C2×C4×C22⋊C4—111no—
180C23×C11C22×Q812yes—
181C23×C11C2×#4112yes—
182C23×C11C2×#4112yes—
183C23×C11C2×#4112yes—
184C23×C11C2×#4112yes—
185C23×C11H(5,𝔽2)12yes—
186C23×C11H(5,𝔽2)12yes—
187C23×C11C2511yescharacteristic
188C22×D11—28no—
189C22×D11—28no—
190C22×D11—28no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—44no—
198C22×D11—44no—
199C22×D11—44no—
200C22×D11—44no—
201C22×D11C22×Q814yes—
202C2×C4×C11—28no—
203C2×C4×C11—28no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—48no—
215C2×C4×C11—48no—
216C2×C4×C11#126116yes—
217C2×C4×C11C22×Q814yes—
218C2×C4×C11C2×#4114yes—
219C2×C4×C11C2×#4114yes—
220C2×C4×C11C2×#4114yes—
221C2×C4×C11C2×#4114yes—
222C2×Dic11—28no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—44no—
238C2×Dic11—48no—
239C2×Dic11—44no—
240C2×Dic11—48no—
241C2×Dic11C22×Q814yes—
242C4×D11—416no—
243C24×C4—111no—
244C22×C4⋊C4—112no—
245C22×C4⋊C4—111no—
246C22×C4⋊C4—111no—
247C22×C4⋊C4—112no—
248C22×C4⋊C4C2×D1111yescharacteristic
249C22×C4⋊C4C2×D1111yescharacteristic
250C22×C4⋊C4C2×D1112yes—
251C22×C4⋊C4C2×D1112yes—
252C22×C22⋊C4—111no—
253C22×C22⋊C4—111no—
254C22×C22⋊C4—112no—
255C22×C22⋊C4—112no—
256C22×C42—111no—
257C22×C42—112no—
258C22×C42C2×D1111yescharacteristic
259#400—1116no—
260#396—1116no—
261#389—118no—
262#389—118no—
263#388—1116no—
264#387—1116no—
265#384C2×D1118yescomplemented
266#380—118no—
267#380—118no—
268C4×C4⋊C4—118no—
269C4×C22⋊C4—118no—
270C2×#95—112no—
271C2×#95—111no—
272C2×#95—112no—
273C2×#95—112no—
274C2×#95—112no—
275C2×#95—111no—
276C2×#95—112no—
277C22×C11C2×#12614yes—
278C22×C11#53314yes—
279C22×C11#54014yes—
280C22×C11#55314yes—
281C22×C11#55414yes—
282C22×C11#55414yes—
283C22×C11#55514yes—
284C22×C11C23×Q811yescharacteristic
285C22×C11C22×#4111yescharacteristic
286C22×C11C22×#4111yescharacteristic
287C22×C11C22×#4111yescharacteristic
288C22×C11C22×#4111yescharacteristic
289C22×C11C2×H(5,𝔽2)11yescharacteristic
290C22×C11C2×H(5,𝔽2)11yescharacteristic
291C2×D11—24no—
292C2×D11—24no—
293C2×D11—24no—
294C2×D11—42no—
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—416no—
299C4×C11—24no—
300C4×C11—24no—
301C4×C11—44no—
302C4×C11—44no—
303C4×C11C2×#12618yes—
304Dic11—24no—
305Dic11—42no—
306Dic11—44no—
307Dic11—42no—
308Dic11—44no—
309C25—111no—
310C23×C4—111no—
311C23×C4—112no—
312C23×C4—112no—
313C23×C4—111no—
314C23×C4—111no—
315C23×C4—114no—
316C23×C4—224no—
317C23×C4—224no—
318C23×C4—224no—
319C23×C4C22×D1112yes—
320C23×C4C22×D1112yes—
321C23×C4C22×D1111yescharacteristic
322C23×C4C22×D1111yescharacteristic
323C23×C4C22×D1111yescharacteristic
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—114no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—118no—
331C2×C4⋊C4—118no—
332C2×C4⋊C4—224no—
333C2×C4⋊C4—228no—
334C2×C4⋊C4—224no—
335C2×C4⋊C4—444no—
336C2×C4⋊C4C22×D1114yes—
337C2×C4⋊C4C22×D1114yes—
338C2×C4⋊C4C22×D1118yes—
339C2×C4⋊C4C22×D1118yes—
340C2×C22⋊C4—118no—
341C2×C22⋊C4—114no—
342C2×C22⋊C4—114no—
343C2×C22⋊C4—118no—
344C2×C22⋊C4—118no—
345C2×C22⋊C4—224no—
346C2×C22⋊C4—444no—
347C2×C22⋊C4—444no—
348C2×C42—24no—
349C2×C42—114no—
350C2×C42—118no—
351C2×C42—224no—
352C2×C42—444no—
353C2×C42C22×D1114yes—
354#95—114no—
355#95—114no—
356#95—118no—
357#95—118no—
358#95—118no—
359#95—118no—
360#95—118no—
361C2×C11#249718yescomplemented
362C2×C11C22×#12611yescharacteristic
363C2×C11C2×#53311yescharacteristic
364C2×C11C2×#54011yescharacteristic
365C2×C11C2×#55311yescharacteristic
366C2×C11C2×#55411yescharacteristic
367C2×C11C2×#55411yescharacteristic
368C2×C11C2×#55511yescharacteristic
369D11—44no—
370C24—114no—
371C24—112no—
372C24—222no—
373C24—222no—
374C24—222no—
375C24—222no—
376C24—222no—
377C24—222no—
378C24C23×D1111yescharacteristic
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—114no—
390C22×C4—112no—
391C22×C4—112no—
392C22×C4—114no—
393C22×C4—112no—
394C22×C4—114no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—224no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—224no—
401C22×C4—224no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—224no—
406C22×C4—224no—
407C22×C4—224no—
408C22×C4—222no—
409C22×C4—228no—
410C22×C4—228no—
411C22×C4—228no—
412C22×C4—4416no—
413C22×C4#433914yes—
414C22×C4#434114yes—
415C22×C4Q8×D1114yes—
416C22×C4#434314yes—
417C22×C4#434314yes—
418C22×C4C23×D1114yes—
419C22×C4C23×D1114yes—
420C22×C4C23×D1112yes—
421C22×C4C23×D1112yes—
422C22×C4C23×D1112yes—
423C4⋊C4—28no—
424C4⋊C4—28no—
425C4⋊C4—48no—
426C4⋊C4—48no—
427C4⋊C4—228no—
428C4⋊C4—2216no—
429C4⋊C4—228no—
430C4⋊C4—448no—
431C22⋊C4—1116no—
432C22⋊C4—228no—
433C22⋊C4—448no—
434C22⋊C4—448no—
435C42—28no—
436C42—228no—
437C42—448no—
438C11C2×#249711yescharacteristic, complemented, Sylow
439C23—114no—
440C23—228no—
441C23—228no—
442C23—228no—
443C23—222no—
444C23—222no—
445C23—222no—
446C23—222no—
447C23—222no—
448C23—222no—
449C23—444no—
450C23—444no—
451C23—444no—
452C23—444no—
453C23C2×#433912yes—
454C23C2×#434112yes—
455C23#6703712yes—
456C23#6703712yes—
457C23C2×Q8×D1112yes—
458C23C2×#434312yes—
459C23C2×#434312yes—
460C23C24×D1111yescharacteristic
461C2×C4—28no—
462C2×C4—28no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—48no—
474C2×C4—48no—
475C2×C4—114no—
476C2×C4—228no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—224no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—224no—
483C2×C4—224no—
484C2×C4—222no—
485C2×C4—222no—
486C2×C4—222no—
487C2×C4—224no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—222no—
491C2×C4—448no—
492C2×C4—444no—
493C2×C4—444no—
494C2×C4—448no—
495C2×C4—4416no—
496C2×C4#66951116yes—
497C2×C4C2×#433914yes—
498C2×C4C2×#434114yes—
499C2×C4C2×Q8×D1114yes—
500C2×C4C2×#434314yes—
501C2×C4C2×#434314yes—
502C22—224no—
503C22—224no—
504C22—224no—
505C22—442no—
506C22—442no—
507C22—442no—
508C22—442no—
509C22—4416no—
510C22#1062304214yes—
511C22C2×#6695114yes—
512C22#1062304514yes—
513C22#1062325014yes—
514C22#1062325914yes—
515C22#1062326114yes—
516C22#1062326514yes—
517C22C22×#433911yescharacteristic
518C22C22×#434111yescharacteristic
519C22C2×#6703711yescharacteristic
520C22C2×#6703711yescharacteristic
521C22C22×Q8×D1111yescharacteristic
522C22C22×#434311yescharacteristic
523C22C22×#434311yescharacteristic
524C4—24no—
525C4—24no—
526C4—44no—
527C4—44no—
528C4—224no—
529C4—442no—
530C4—444no—
531C4—444no—
532C4—442no—
533C4C2×#6695118yes—
534C2—444no—
535C2#1307305218yesdirect product factor
536C2C22×#6695111yescharacteristic
537C2C2×#1062325911yescharacteristic
538C2C2×#1062325011yescharacteristic
539C2C2×#1062304511yescharacteristic
540C2C2×#1062304211yescharacteristic
541C2C2×#1062326111yescharacteristic
542C2C2×#1062326511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#384C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#384D11
hypocenterC11C2×#2497
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
1. #13073052C2direct (N × H)
2. C2×#10622599C2semidirect
4. C2×#10622598C2semidirect
5. C2×#10622541C2semidirect
7. C2×#10622591C2semidirect
10. C2×C4⋊C4×Dic11C2semidirect
12. C2×C11×#384C2semidirect
29. C11×#384C22semidirect
41. #10622599C22semidirect
42. #10622598C22semidirect
43. #10622591C22semidirect
44. C4⋊C4×Dic11C22semidirect
46. #10622541C22semidirect
175. C2×#384D11semidirect
265. #384C2×D11semidirect
361. C2×C11#2497semidirect
438. C11C2×#2497semidirect
535. C2#13073052direct (N × H)

Maximal subgroups

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

subgroupindex
#130730522
C2×#106225992
C2×#106226072
C2×#106225982
C2×#106225412
C2×#106226032
C2×#106225912
C2×#106226002
C2×C4⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
C2×C11×#3842
C2×#249711