Finite Group Databasebeta

← C2×#13073528 #14925509

Subgroups — C2×#13073528 #14925509

Order 2816.

4782 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C212yesmaximal, complemented
2C22×#66992C212yesmaximal, complemented
3C22×(C22⋊D11)⋊C4C212yesmaximal, complemented
4#13073528C2116yesmaximal, direct product factor
5C2×#10622604C211yesmaximal, characteristic, complemented
6C2×#10622574C212yesmaximal, complemented
7C2×#10622589C211yesmaximal, characteristic, complemented
8C2×#10622280C212yesmaximal, complemented
9C2×#10622555C212yesmaximal, complemented
10C2×C11×#394C211yesmaximal, characteristic, complemented
11C23×D4×C11C2211yescharacteristic
12C23×C22⋊D11C2212yes—
13C23×C22⋊D11C2212yes—
14C24×Dic11C2212yes—
15C23×D44C2211yescharacteristic
16C23×C4×D11C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2212yes—
21C2×#66992—216no—
22C2×#66992C22116yescomplemented
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C2×#66937—216no—
32C2×#66937C22116yescomplemented
33C2×(C22⋊D11)⋊C4—216no—
34C2×(C22⋊D11)⋊C4C22116yescomplemented
35C11×#394C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39#10622604C2218yescomplemented
40#10622589C2218yescomplemented
41#10622574C22116yescomplemented
42#10622555C22116yescomplemented
43#10622280C22116yescomplemented
44C25×C11C2312yes—
45C24×D11C2312yes—
46C22×D4×C11—28no—
47C22×D4×C11—42no—
48C22×D4×C11C2314yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—28no—
54C22×C22⋊D11—28no—
55C22×C22⋊D11—28no—
56C22×C22⋊D11—28no—
57C22×C22⋊D11—44no—
58C22×C22⋊D11D4116yescomplemented
59C22×C22⋊D11C2318yes—
60C22×C22⋊D11C2318yes—
61C23×Dic11—28no—
62C23×Dic11—28no—
63C23×Dic11—28no—
64C23×Dic11C2318yes—
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2312yes—
68C22×D44—28no—
69C22×D44—42no—
70C22×D44C2314yes—
71C22×C4×D11—28no—
72C22×C4×D11—28no—
73C22×C4×D11—28no—
74C22×C4×D11C2318yes—
75C2×C11×C4⋊C4—42no—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C22⋊C4—28no—
78C2×C11×C22⋊C4—28no—
79C2×C11×C22⋊C4C2318yes—
80C2×C11×C22⋊C4C2318yes—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11C2318yes—
83#66992—264no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4—28no—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×C4⋊Dic11—42no—
91C2×C4⋊Dic11C2314yes—
92C2×Dic11⋊C4—28no—
93C2×Dic11⋊C4—28no—
94C2×Dic11⋊C4—28no—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2318yes—
97C2×Dic11⋊C4C2318yes—
98C2×C4×Dic11D418yescomplemented
99C2×C4×Dic11C2314yes—
100#66937—264no—
101(C22⋊D11)⋊C4—264no—
102C11×#95C2314yes—
103C11⋊#95C2318yes—
104C11⋊#95C2314yes—
105C2×#2537—111nomaximal, Sylow
106C24×C11—24no—
107C24×C11—24no—
108C24×C11—24no—
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11C2×D418yes—
113C24×C11C2414yes—
114C24×C11C2411yescharacteristic
115C23×D11—24no—
116C23×D11—24no—
117C23×D11—24no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11—24no—
121C23×D11C2×D418yes—
122C23×D11C2414yes—
123C2×D4×C11—216no—
124C2×D4×C11—44no—
125C2×D4×C11—416no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11C2×D414yes—
136C22×C4×C11C2414yes—
137C22×C4×C11C2412yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C2×C22⋊D11—264no—
141C2×C22⋊D11—216no—
142C2×C22⋊D11—216no—
143C2×C22⋊D11—216no—
144C2×C22⋊D11—216no—
145C2×C22⋊D11—48no—
146C2×C22⋊D11—432no—
147C2×C22⋊D11C2×D4132yescomplemented
148C22×Dic11—216no—
149C22×Dic11—216no—
150C22×Dic11—216no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—432no—
158C22×Dic11C2×D418yes—
159C22×Dic11C2×D418yes—
160C22×Dic11#4118yes—
161C22×Dic11C2414yes—
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164C2×D44—216no—
165C2×D44—44no—
166C2×D44—416no—
167C2×C4×D11—216no—
168C2×C4×D11—216no—
169C2×C4×D11—216no—
170C2×C4×D11—432no—
171C11×C4⋊C4—44no—
172C11×C22⋊C4—216no—
173C11×C22⋊C4—216no—
174C22⋊Dic11—216no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—216no—
177(C2×D11)⋊C4—216no—
178C4⋊Dic11—44no—
179Dic11⋊C4—216no—
180Dic11⋊C4—216no—
181Dic11⋊C4—216no—
182C4×Dic11C2×D4116yescomplemented
183C22×#121—112no—
184C22×#121—112no—
185C22×C4×D4—112no—
186#2537—1116no—
187C2×#394—111no—
188C2×#394—112no—
189C2×#394D1111yescharacteristic, complemented
190C2×#384—111no—
191C2×#380—112no—
192C2×#380—112no—
193C23×C11—216no—
194C23×C11—216no—
195C23×C11—216no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—48no—
203C23×C11—48no—
204C23×C11—48no—
205C23×C11—48no—
206C23×C11C22×D418yes—
207C23×C11C22×D412yes—
208C23×C11C22×D414yes—
209C23×C11C2×#4114yes—
210C23×C11H(5,𝔽2)12yes—
211C23×C112−1+412yes—
212C23×C11C2511yescharacteristic
213C22×D11—216no—
214C22×D11—216no—
215C22×D11—216no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—48no—
223C22×D11—48no—
224C22×D11—48no—
225C22×D11—48no—
226C22×D11C22×D418yes—
227D4×C11—416no—
228C2×C4×C11—28no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—48no—
239C2×C4×C11—44no—
240C2×C4×C11—44no—
241C2×C4×C11C22×D414yes—
242C22⋊D11—264no—
243C22⋊D11—432no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—48no—
251C2×Dic11—48no—
252C2×Dic11—432no—
253C2×Dic11#121132yescomplemented
254C2×Dic11C22×D418yes—
255C2×Dic11C22×D418yes—
256C2×Dic11C2×#4118yes—
257D44—416no—
258C4×D11—432no—
259C23×D4—112no—
260C23×D4—112no—
261C23×D4—111no—
262C23×D4C2×D1111yescharacteristic
263C24×C4—112no—
264C24×C4—112no—
265C2×#121—1116no—
266C2×#121—1116no—
267C2×#121—2216no—
268C2×#121—2216no—
269C2×C4×D4—1116no—
270C2×C4×D4—2216no—
271C22×C4⋊C4—112no—
272C22×C4⋊C4—112no—
273C22×C4⋊C4—112no—
274C22×C4⋊C4—111no—
275C22×C4⋊C4C2×D1111yescharacteristic
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4—112no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4C2×D1112yes—
281C22×C22⋊C4C2×D1112yes—
282C22×C42—111no—
283#394—118no—
284#394—1116no—
285#394C2×D1118yescomplemented
286#384—118no—
287#380—1116no—
288#380—1116no—
289C2×#95—111no—
290C2×#95—112no—
291C2×#95C2×D1111yescharacteristic
292C22×C11—28no—
293C22×C11—28no—
294C22×C11—28no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—44no—
299C22×C11—432no—
300C22×C11C2×#12118yes—
301C22×C11#53714yes—
302C22×C11D4214yes—
303C22×C11#54718yes—
304C22×C11#55514yes—
305C22×C11C23×D411yescharacteristic
306C22×C11C23×D412yes—
307C22×C11C22×#4112yes—
308C22×C11C2×H(5,𝔽2)11yescharacteristic
309C22×C11C2×2−1+411yescharacteristic
310C2×D11—28no—
311C2×D11—28no—
312C2×D11—28no—
313C2×D11—44no—
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—432no—
318C4×C11—24no—
319C4×C11—44no—
320C4×C11—42no—
321C4×C11—42no—
322Dic11—44no—
323Dic11—44no—
324Dic11C2×#121116yescomplemented
325C25—112no—
326C25C22×D1112yes—
327C22×D4—28no—
328C22×D4—42no—
329C22×D4—1116no—
330C22×D4—118no—
331C22×D4—118no—
332C22×D4—114no—
333C22×D4—228no—
334C22×D4—228no—
335C22×D4—228no—
336C22×D4—228no—
337C22×D4—228no—
338C22×D4—442no—
339C22×D4—444no—
340C22×D4C22×D1114yes—
341C23×C4—112no—
342C23×C4—118no—
343C23×C4—112no—
344C23×C4—112no—
345C23×C4—118no—
346C23×C4—228no—
347C23×C4—228no—
348C23×C4—228no—
349C23×C4—228no—
350C23×C4—228no—
351C23×C4—228no—
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1112yes—
354C23×C4C22×D1111yescharacteristic
355C23×C4C22×D1111yescharacteristic
356#121—2264no—
357#121—2264no—
358C4×D4—2264no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—118no—
361C2×C4⋊C4—118no—
362C2×C4⋊C4—118no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—228no—
365C2×C4⋊C4—228no—
366C2×C4⋊C4—228no—
367C2×C4⋊C4—442no—
368C2×C4⋊C4C22×D1114yes—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—118no—
373C2×C22⋊C4—118no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—228no—
376C2×C22⋊C4—228no—
377C2×C22⋊C4—228no—
378C2×C22⋊C4—228no—
379C2×C22⋊C4C22×D1118yes—
380C2×C22⋊C4C22×D1118yes—
381C2×C42—118no—
382C2×C42—114no—
383#95—114no—
384#95—118no—
385#95C22×D1114yes—
386C2×C11—48no—
387C2×C11#253718yescomplemented
388C2×C11C22×#12112yes—
389C2×C11C2×#53711yescharacteristic
390C2×C11C2×D4211yescharacteristic
391C2×C11C2×#54712yes—
392C2×C11C2×#55511yescharacteristic
393D11—48no—
394C24—24no—
395C24—24no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24—118no—
401C24—114no—
402C24—224no—
403C24—224no—
404C24—224no—
405C24—224no—
406C24—224no—
407C24—224no—
408C24D4×D1118yes—
409C24C23×D1114yes—
410C24C23×D1111yescharacteristic
411C2×D4—216no—
412C2×D4—44no—
413C2×D4—416no—
414C2×D4—1132no—
415C2×D4—2216no—
416C2×D4—2216no—
417C2×D4—2264no—
418C2×D4—2216no—
419C2×D4—2216no—
420C2×D4—2216no—
421C2×D4—444no—
422C2×D4—4416no—
423C2×D4—448no—
424C2×D4—4432no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—118no—
435C22×C4—118no—
436C22×C4—118no—
437C22×C4—114no—
438C22×C4—114no—
439C22×C4—114no—
440C22×C4—2216no—
441C22×C4—2216no—
442C22×C4—2216no—
443C22×C4—2216no—
444C22×C4—2216no—
445C22×C4—2216no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—4432no—
453C22×C4—4432no—
454C22×C4D4×D1114yes—
455C22×C4C23×D1114yes—
456C22×C4C23×D1112yes—
457C22×C4C23×D1112yes—
458C22×C4C23×D1112yes—
459C4⋊C4—44no—
460C4⋊C4—2216no—
461C4⋊C4—2216no—
462C4⋊C4—2216no—
463C4⋊C4—444no—
464C22⋊C4—216no—
465C22⋊C4—216no—
466C22⋊C4—2216no—
467C22⋊C4—2216no—
468C22⋊C4—2216no—
469C22⋊C4—2216no—
470C42—1116no—
471C11C2×#253711yescharacteristic, complemented, Sylow
472C23—216no—
473C23—216no—
474C23—216no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—48no—
482C23—48no—
483C23—48no—
484C23—48no—
485C23—118no—
486C23—2216no—
487C23—2216no—
488C23—2216no—
489C23—224no—
490C23—224no—
491C23—224no—
492C23—224no—
493C23—224no—
494C23—224no—
495C23—448no—
496C23—448no—
497C23—448no—
498C23—448no—
499C23C2×D4×D1118yes—
500C23C2×D4×D1114yes—
501C23C2×D4×D1112yes—
502C23#6703712yes—
503C23#41×D1114yes—
504C23#6704312yes—
505C23C24×D1111yescharacteristic
506D4—416no—
507D4—2264no—
508D4—4416no—
509D4—4432no—
510C2×C4—28no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—44no—
521C2×C4—44no—
522C2×C4—48no—
523C2×C4—1132no—
524C2×C4—118no—
525C2×C4—118no—
526C2×C4—118no—
527C2×C4—224no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—4432no—
534C2×C4—4432no—
535C2×C4—448no—
536C2×C4—448no—
537C2×C4C2×D4×D1114yes—
538C22—28no—
539C22—28no—
540C22—28no—
541C22—44no—
542C22—44no—
543C22—432no—
544C22—44no—
545C22—44no—
546C22—228no—
547C22—228no—
548C22—228no—
549C22—444no—
550C22—444no—
551C22—4432no—
552C22—444no—
553C22—444no—
554C22#1062312114yes—
555C22#1062312814yes—
556C22D11×#12118yes—
557C22#1062318618yes—
558C22#1062320114yes—
559C22C22×D4×D1111yescharacteristic
560C22C22×D4×D1112yes—
561C22C2×#6703711yescharacteristic
562C22C2×#41×D1112yes—
563C22C2×#6704311yescharacteristic
564C4—24no—
565C4—42no—
566C4—42no—
567C4—44no—
568C4—1116no—
569C4—444no—
570C4—444no—
571C2—48no—
572C2—448no—
573C2#1307352818yesdirect product factor
574C2C2×D11×#12112yes—
575C2C2×#1062312811yescharacteristic
576C2C2×#1062312111yescharacteristic
577C2C2×#1062318612yes—
578C2C2×#1062320111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2537
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66937C2semidirect
2. C22×#66992C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. #13073528C2direct (N × H)
5. C2×#10622604C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622589C2semidirect
8. C2×#10622280C2semidirect
9. C2×#10622555C2semidirect
10. C2×C11×#394C2semidirect
22. C2×#66992C22semidirect
32. C2×#66937C22semidirect
34. C2×(C22⋊D11)⋊C4C22semidirect
35. C11×#394C22semidirect
39. #10622604C22semidirect
40. #10622589C22semidirect
41. #10622574C22semidirect
42. #10622555C22semidirect
43. #10622280C22semidirect
58. C22×C22⋊D11D4semidirect
98. C2×C4×Dic11D4semidirect
147. C2×C22⋊D11C2×D4semidirect
182. C4×Dic11C2×D4semidirect
189. C2×#394D11semidirect
253. C2×Dic11#121semidirect
285. #394C2×D11semidirect
324. Dic11C2×#121semidirect
387. C2×C11#2537semidirect
471. C11C2×#2537semidirect
573. C2#13073528direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669372
C22×#669922
C22×(C22⋊D11)⋊C42
#130735282
C2×#106226042
C2×#106225742
C2×#106225892
C2×#106222802
C2×#106225552
C2×C11×#3942
C2×#253711