Finite Group Databasebeta

← C2×#13071251 #14912413

Subgroups — C2×#13071251 #14912413

Order 2816.

3262 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
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2#13071251C2116yesmaximal, direct product factor
3C2×#10622558C212yesmaximal, complemented
4C2×#10622591C212yesmaximal, complemented
5C2×#10622569C212yesmaximal
6C2×#10622602C212yesmaximal, complemented
7C2×#10622264C211yesmaximal, characteristic, complemented
8C2×#10622263C211yesmaximal, characteristic, complemented
9C2×#10622824C211yesmaximal, characteristic, complemented
10C2×#10622279C211yesmaximal, characteristic, complemented
11C2×D11×#95C211yesmaximal, characteristic, complemented
12C2×C11×#380C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C4×D11C2212yes—
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C2×C4×C22⋊D11C4116yescomplemented
22C2×C4×C22⋊D11C2218yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C11×#380C2218yescomplemented
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32#10622824C2218yescomplemented
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622602C22116yescomplemented
41#10622591C22116yescomplemented
42#10622569C22116yes—
43#10622558C22116yescomplemented
44#10622279C2218yescomplemented
45D11×#95C2218yescomplemented
46#10622264C2218yescomplemented
47#10622263C2218yescomplemented
48C25×C11C2311yescharacteristic
49C24×D11C2311yescharacteristic
50C23×C4×C11—44no—
51C23×C4×C11C2×C418yescomplemented
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2314yes—
57C22×C22⋊D11—28no—
58C22×C22⋊D11C2×C418yes—
59C22×C22⋊D11C2314yes—
60C23×Dic11C2312yes—
61C23×Dic11C2312yes—
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C22×C4×D11—28no—
66C22×C4×D11—44no—
67C22×C4×D11—44no—
68C22×C4×D11—44no—
69C22×C4×D11C2×C418yes—
70C22×C4×D11C2318yes—
71C22×C4×D11C2314yes—
72C2×C11×C4⋊C4—44no—
73C2×C11×C4⋊C4C2318yes—
74C2×C11×C22⋊C4—44no—
75C2×C11×C22⋊C4C2318yes—
76C2×C22⋊Dic11—44no—
77C2×C22⋊Dic11C2×C418yescomplemented
78C2×C22⋊Dic11C2318yes—
79C2×C22⋊Dic11C2314yes—
80C4×C22⋊D11C2×C4164yescomplemented
81C2×(C2×D11)⋊C4—28no—
82C2×(C2×D11)⋊C4C2×C418yes—
83C2×(C2×D11)⋊C4C2318yes—
84C2×(C2×D11)⋊C4C2314yes—
85C2×Dic11⋊C4—44no—
86C2×Dic11⋊C4C2×C418yescomplemented
87C2×Dic11⋊C4C2318yes—
88C2×Dic11⋊C4C2314yes—
89C2×C4×Dic11—44no—
90C2×C4×Dic11C2×C418yescomplemented
91C2×C4×Dic11C2318yes—
92C2×C4×Dic11C2314yes—
93C11×#95C2314yes—
94C11×#95C2314yes—
95C11⋊#95C2314yes—
96C11⋊#95C2318yes—
97C11⋊#95C2314yes—
98C11⋊#95C2318yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C2×#2318—111nomaximal, Sylow
103C24×C11—24no—
104C24×C11—24no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11C22×C414yes—
108C24×C11C2412yes—
109C24×C11C2411yescharacteristic
110C23×D11—24no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11C22×C414yes—
114C23×D11#4118yes—
115C23×D11C2412yes—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—416no—
125C22×C4×C11—48no—
126C22×C4×C11C22×C414yes—
127C22×C4×C11C22×C414yes—
128C22×C4×C11C22×C4116yescomplemented
129C22×C4×C11C2414yes—
130C22×C4×C11C2414yes—
131C22×C4×C11C2412yes—
132C22×C4×C11C2412yes—
133C2×C22⋊D11—232no—
134C2×C22⋊D11—216no—
135C2×C22⋊D11C22×C4116yes—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11C22×C414yes—
147C22×Dic11C22×C414yes—
148C22×Dic11C22×C414yes—
149C22×Dic11C2414yes—
150C22×Dic11C2414yes—
151C22×Dic11C2412yes—
152C22×Dic11C2412yes—
153C22×Dic11C2412yes—
154C2×C4×D11—216no—
155C2×C4×D11—416no—
156C2×C4×D11—48no—
157C2×C4×D11—48no—
158C2×C4×D11—48no—
159C2×C4×D11—432no—
160C2×C4×D11C22×C4116yes—
161C11×C4⋊C4—48no—
162C11×C22⋊C4—48no—
163C22⋊Dic11—48no—
164C22⋊Dic11C22×C4116yescomplemented
165(C2×D11)⋊C4—216no—
166(C2×D11)⋊C4C22×C4116yes—
167Dic11⋊C4—48no—
168Dic11⋊C4C22×C4116yescomplemented
169C4×Dic11—48no—
170C4×Dic11C22×C4116yescomplemented
171C22×C4×D4—111no—
172#2318—1116no—
173C2×#388—112no—
174C2×#387—112no—
175C2×#386—112no—
176C2×#385—112no—
177C2×#383—111no—
178C2×#382—111no—
179C2×#381—111no—
180C2×#380D1111yescharacteristic, complemented
181C2×C4×C22⋊C4—111no—
182C22×#95—111no—
183C23×C11—28no—
184C23×C11—28no—
185C23×C11—28no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—48no—
191C23×C11—48no—
192C23×C11C23×C414yes—
193C23×C11C23×C412yes—
194C23×C11C2×#4114yes—
195C23×C11H(5,𝔽2)14yes—
196C23×C11H(5,𝔽2)12yes—
197C23×C112−1+412yes—
198C23×C11C2511yescharacteristic
199C22×D11—28no—
200C22×D11—28no—
201C22×D11—216no—
202C22×D11—216no—
203C22×D11—24no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11#117116yes—
207C22×D11C23×C414yes—
208C22×D11C2×#4118yes—
209C2×C4×C11—28no—
210C2×C4×C11—28no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—416no—
220C2×C4×C11—48no—
221C2×C4×C11—48no—
222C2×C4×C11C23×C414yes—
223C2×C4×C11C23×C414yes—
224C22⋊D11—232no—
225C2×Dic11—28no—
226C2×Dic11—28no—
227C2×Dic11—28no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—48no—
239C2×Dic11—48no—
240C2×Dic11C23×C414yes—
241C2×Dic11C23×C414yes—
242C2×Dic11C23×C414yes—
243C4×D11—416no—
244C4×D11—432no—
245C23×D4—111no—
246C24×C4—111no—
247C24×C4—112no—
248C24×C4C2×D1111yescharacteristic
249C2×C4×D4—118no—
250C2×C4×D4—1116no—
251C22×C4⋊C4—111no—
252C22×C4⋊C4—112no—
253C22×C4⋊C4C2×D1112yes—
254C22×C22⋊C4—111no—
255C22×C22⋊C4—111no—
256C22×C22⋊C4—112no—
257C22×C22⋊C4—112no—
258C22×C22⋊C4C2×D1112yes—
259C22×C42—111no—
260C22×C42—112no—
261#388—1116no—
262#387—1116no—
263#386—1116no—
264#385—1116no—
265#383—118no—
266#382—118no—
267#381—118no—
268#380C2×D1118yescomplemented
269C4×C22⋊C4—118no—
270C2×#95—111no—
271C2×#95—112no—
272C2×#95—111no—
273C2×#95—112no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95—112no—
277C2×#95—118no—
278C2×#95C2×D1111yescharacteristic
279C2×#95C2×D1111yescharacteristic
280C22×C11—24no—
281C22×C11—24no—
282C22×C11—24no—
283C22×C11—416no—
284C22×C11—44no—
285C22×C11—44no—
286C22×C11C2×#11714yes—
287C22×C11#51814yes—
288C22×C11#52014yes—
289C22×C11#53818yes—
290C22×C11#53918yes—
291C22×C11C24×C411yescharacteristic
292C22×C11C22×#4112yes—
293C22×C11C2×H(5,𝔽2)12yes—
294C22×C11C2×H(5,𝔽2)11yescharacteristic
295C22×C11C2×2−1+411yescharacteristic
296C2×D11—232no—
297C2×D11—24no—
298C2×D11—24no—
299C2×D11—28no—
300C2×D11—28no—
301C2×D11C2×#11718yes—
302C4×C11—24no—
303C4×C11—24no—
304C4×C11—44no—
305C4×C11—44no—
306Dic11—24no—
307Dic11—24no—
308Dic11—24no—
309Dic11—44no—
310Dic11—44no—
311C25—111no—
312C25C22×D1111yescharacteristic
313C22×D4—118no—
314C22×D4—114no—
315C22×D4—228no—
316C23×C4—44no—
317C23×C4—111no—
318C23×C4—111no—
319C23×C4—111no—
320C23×C4—118no—
321C23×C4—114no—
322C23×C4—112no—
323C23×C4—112no—
324C23×C4—118no—
325C23×C4—228no—
326C23×C4—444no—
327C23×C4—444no—
328C23×C4—444no—
329C23×C4C4×D1118yescomplemented
330C23×C4C22×D1112yes—
331C23×C4C22×D1112yes—
332C23×C4C22×D1111yescharacteristic
333C23×C4C22×D1111yescharacteristic
334C23×C4C22×D1114yes—
335C4×D4—1164no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—118no—
338C2×C4⋊C4—114no—
339C2×C4⋊C4—118no—
340C2×C4⋊C4—444no—
341C2×C4⋊C4C22×D1118yes—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—118no—
344C2×C22⋊C4—114no—
345C2×C22⋊C4—118no—
346C2×C22⋊C4—114no—
347C2×C22⋊C4—118no—
348C2×C22⋊C4—118no—
349C2×C22⋊C4—228no—
350C2×C22⋊C4—444no—
351C2×C22⋊C4C22×D1118yes—
352C2×C42—118no—
353C2×C42—114no—
354C2×C42—118no—
355C2×C42—444no—
356#95—114no—
357#95—118no—
358#95—114no—
359#95—118no—
360#95—118no—
361#95—118no—
362#95—118no—
363#95C22×D1114yes—
364#95C22×D1114yes—
365C2×C11—44no—
366C2×C11#231818yescomplemented
367C2×C11C22×#11711yescharacteristic
368C2×C11C2×#51811yescharacteristic
369C2×C11C2×#52011yescharacteristic
370C2×C11C2×#53812yes—
371C2×C11C2×#53912yes—
372D11—28no—
373C24—22no—
374C24—24no—
375C24—22no—
376C24—24no—
377C24—114no—
378C24—118no—
379C24—112no—
380C24—224no—
381C24—222no—
382C24—222no—
383C24C2×C4×D1114yes—
384C24C23×D1112yes—
385C24C23×D1111yescharacteristic
386C2×D4—1116no—
387C2×D4—2232no—
388C2×D4—2216no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—48no—
398C22×C4—416no—
399C22×C4—114no—
400C22×C4—114no—
401C22×C4—114no—
402C22×C4—112no—
403C22×C4—112no—
404C22×C4—112no—
405C22×C4—1116no—
406C22×C4—114no—
407C22×C4—114no—
408C22×C4—2216no—
409C22×C4—224no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4—224no—
416C22×C4—224no—
417C22×C4—224no—
418C22×C4—224no—
419C22×C4—4416no—
420C22×C4—448no—
421C22×C4—448no—
422C22×C4—448no—
423C22×C4—4432no—
424C22×C4C2×C4×D1114yes—
425C22×C4C2×C4×D1114yes—
426C22×C4C2×C4×D11116yescomplemented
427C22×C4C23×D1114yes—
428C22×C4C23×D1114yes—
429C22×C4C23×D1112yes—
430C22×C4C23×D1112yes—
431C4⋊C4—48no—
432C4⋊C4—1116no—
433C4⋊C4—448no—
434C22⋊C4—48no—
435C22⋊C4—1116no—
436C22⋊C4—1116no—
437C22⋊C4—2216no—
438C22⋊C4—448no—
439C42—1116no—
440C42—448no—
441C11C2×#231811yescharacteristic, complemented, Sylow
442C23—28no—
443C23—28no—
444C23—28no—
445C23—22no—
446C23—24no—
447C23—22no—
448C23—24no—
449C23—48no—
450C23—48no—
451C23—1116no—
452C23—114no—
453C23—118no—
454C23—228no—
455C23—228no—
456C23—2216no—
457C23—2216no—
458C23—222no—
459C23—224no—
460C23—222no—
461C23C22×C4×D1114yes—
462C23C22×C4×D1112yes—
463C23#6703714yes—
464C23#6703712yes—
465C23#6704012yes—
466C23#41×D1114yes—
467C23C24×D1111yescharacteristic
468D4—2232no—
469C2×C4—28no—
470C2×C4—28no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—416no—
480C2×C4—48no—
481C2×C4—48no—
482C2×C4—114no—
483C2×C4—114no—
484C2×C4—114no—
485C2×C4—228no—
486C2×C4—228no—
487C2×C4—228no—
488C2×C4—224no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—4416no—
499C2×C4—4432no—
500C2×C4—448no—
501C2×C4—448no—
502C2×C4C22×C4×D1114yes—
503C2×C4C22×C4×D1114yes—
504C22—24no—
505C22—24no—
506C22—24no—
507C22—44no—
508C22—44no—
509C22—416no—
510C22—118no—
511C22—228no—
512C22—228no—
513C22—2232no—
514C22—224no—
515C22—224no—
516C22#1062301714yes—
517C22#1062303514yes—
518C22D11×#11714yes—
519C22#1062314418yes—
520C22#1062316918yes—
521C22C23×C4×D1111yescharacteristic
522C22C2×#6703711yescharacteristic
523C22C2×#6703712yes—
524C22C2×#6704011yescharacteristic
525C22C2×#41×D1112yes—
526C4—24no—
527C4—24no—
528C4—44no—
529C4—44no—
530C4—224no—
531C4—224no—
532C4—224no—
533C4—444no—
534C4—444no—
535C2—44no—
536C2—228no—
537C2#1307125118yesdirect product factor
538C2C2×D11×#11711yescharacteristic
539C2C2×#1062301711yescharacteristic
540C2C2×#1062303511yescharacteristic
541C2C2×#1062314412yes—
542C2C2×#1062316912yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
cosocleC23×C11C25
hypercenterC2×#380D11
hypocenterC11C2×#2318
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #13071251C2direct (N × H)
3. C2×#10622558C2semidirect
4. C2×#10622591C2semidirect
6. C2×#10622602C2semidirect
7. C2×#10622264C2semidirect
8. C2×#10622263C2semidirect
9. C2×#10622824C2semidirect
10. C2×#10622279C2semidirect
11. C2×D11×#95C2semidirect
12. C2×C11×#380C2semidirect
21. C2×C4×C22⋊D11C4semidirect
29. C11×#380C22semidirect
32. #10622824C22semidirect
40. #10622602C22semidirect
41. #10622591C22semidirect
43. #10622558C22semidirect
44. #10622279C22semidirect
45. D11×#95C22semidirect
46. #10622264C22semidirect
47. #10622263C22semidirect
51. C23×C4×C11C2×C4semidirect
77. C2×C22⋊Dic11C2×C4semidirect
80. C4×C22⋊D11C2×C4semidirect
86. C2×Dic11⋊C4C2×C4semidirect
90. C2×C4×Dic11C2×C4semidirect
128. C22×C4×C11C22×C4semidirect
164. C22⋊Dic11C22×C4semidirect
168. Dic11⋊C4C22×C4semidirect
170. C4×Dic11C22×C4semidirect
180. C2×#380D11semidirect
268. #380C2×D11semidirect
329. C23×C4C4×D11semidirect
366. C2×C11#2318semidirect
426. C22×C4C2×C4×D11semidirect
441. C11C2×#2318semidirect
537. C2#13071251direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
#130712512
C2×#106225582
C2×#106225912
C2×#106225692
C2×#106226022
C2×#106222642
C2×#106222632
C2×#106228242
C2×#106222792
C2×D11×#952
C2×C11×#3802
C2×#231811