Finite Group Databasebeta

← C2×#13074547 #14920208

Subgroups — C2×#13074547 #14920208

Order 2816.

3326 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic, complemented
2C22×#66991C211yesmaximal, characteristic
3#13074547C2116yesmaximal, direct product factor
4C2×#10622272C211yesmaximal, characteristic, complemented
5C2×#10622599C211yesmaximal, characteristic, complemented
6C2×#10622565C212yesmaximal, complemented
7C2×#10622835C211yesmaximal, characteristic, complemented
8C2×#10622560C212yesmaximal, complemented
9C2×#10622569C212yesmaximal, complemented
10C2×#10622569C212yesmaximal, complemented
11C2×D11×#95C211yesmaximal, characteristic, complemented
12C2×C11×#394C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×C4×D11C2212yes—
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C2×#66991—28no—
25C2×#66991C2218yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C2×#66949—28no—
32C2×#66949C2218yescomplemented
33C11×#394C2218yescomplemented
34C2×C11×#95C2211yescharacteristic
35#10622835C2218yescomplemented
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622599C2218yescomplemented
43#10622569C22116yescomplemented
44#10622569C22116yescomplemented
45#10622565C22116yescomplemented
46#10622560C22116yescomplemented
47D11×#95C2218yescomplemented
48#10622272C2218yescomplemented
49C25×C11C2312yes—
50C24×D11C2311yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—44no—
53C22×D4×C11C2314yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—28no—
59C22×C22⋊D11—28no—
60C22×C22⋊D11—28no—
61C22×C22⋊D11C2318yes—
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2312yes—
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C22×C4×D11—28no—
68C22×C4×D11—44no—
69C22×C4×D11—44no—
70C22×C4×D11—44no—
71C22×C4×D11D418yes—
72C22×C4×D11C2318yes—
73C22×C4×D11C2314yes—
74C22×Dic22—24no—
75C22×Dic22—44no—
76C22×Dic22C2314yes—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4—44no—
80C2×C11×C22⋊C4—44no—
81C2×C11×C22⋊C4C2318yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C22⋊Dic11—28no—
84C2×C22⋊Dic11—44no—
85C2×C22⋊Dic11—44no—
86C2×C22⋊Dic11C2318yes—
87C2×C22⋊Dic11C2318yes—
88C2×C22⋊Dic11C2318yes—
89#66991—232no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4C2314yes—
93C2×(C2×D11)⋊C4C2314yes—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11C2314yes—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2314yes—
100#66949—232no—
101C11×#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C2×#2639—111nomaximal, Sylow
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11C2414yes—
117C24×C11C2411yescharacteristic
118C23×D11—24no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11C2×D414yes—
122C23×D11#4118yes—
123C23×D11C2412yes—
124C2×D4×C11—28no—
125C2×D4×C11—48no—
126C2×D4×C11—416no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2414yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C2×C22⋊D11—216no—
142C2×C22⋊D11—216no—
143C2×C22⋊D11—216no—
144C2×C22⋊D11—432no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—22no—
157C22×Dic11C2×D414yes—
158C22×Dic11C2414yes—
159C22×Dic11C2414yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C2×C4×D11—216no—
164C2×C4×D11—416no—
165C2×C4×D11—48no—
166C2×C4×D11—48no—
167C2×C4×D11—48no—
168C2×C4×D11—432no—
169C2×C4×D11C2×D4116yes—
170C2×Dic22—28no—
171C2×Dic22—48no—
172C2×Dic22—416no—
173C11×C4⋊C4—28no—
174C11×C22⋊C4—48no—
175C11×C22⋊C4—48no—
176C22⋊Dic11—216no—
177C22⋊Dic11—48no—
178C22⋊Dic11—48no—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—28no—
181C4⋊Dic11—28no—
182Dic11⋊C4—28no—
183Dic11⋊C4—28no—
184C22×C22⋊Q8—111no—
185C22×#121—111no—
186#2639—1116no—
187C2×#400—111no—
188C2×#400—111no—
189C2×#397—112no—
190C2×#394—111no—
191C2×#394D1111yescharacteristic, complemented
192C2×#393—112no—
193C2×#386—112no—
194C2×#386—112no—
195C22×#95—111no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—48no—
204C23×C11—48no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11—48no—
209C23×C11—48no—
210C23×C11C22×D412yes—
211C23×C11C2×#4114yes—
212C23×C11H(5,𝔽2)14yes—
213C23×C11H(5,𝔽2)12yes—
214C23×C112−1+412yes—
215C23×C11C2511yescharacteristic
216C22×D11—28no—
217C22×D11—28no—
218C22×D11—216no—
219C22×D11—216no—
220C22×D11—24no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11#124116yes—
224C22×D11C22×D414yes—
225C22×D11C2×#4118yes—
226D4×C11—416no—
227C2×C4×C11—28no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—44no—
238C2×C4×C11—44no—
239C2×C4×C11—48no—
240C2×C4×C11C22×D414yes—
241C22⋊D11—432no—
242C2×Dic11—28no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—48no—
256C2×Dic11—44no—
257C2×Dic11—44no—
258C2×Dic11—48no—
259C2×Dic11C22×D414yes—
260C4×D11—416no—
261C4×D11—432no—
262Dic22—416no—
263C23×Q8—111no—
264C23×D4—112no—
265C23×D4C2×D1111yescharacteristic
266C24×C4—111no—
267C24×C4—112no—
268C2×C22⋊Q8—118no—
269C2×C22⋊Q8—228no—
270C2×#121—118no—
271C2×#121—228no—
272C22×C4⋊C4—111no—
273C22×C4⋊C4—111no—
274C22×C4⋊C4—111no—
275C22×C4⋊C4C2×D1111yescharacteristic
276C22×C22⋊C4—112no—
277C22×C22⋊C4—111no—
278C22×C22⋊C4—111no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4C2×D1112yes—
282C22×C22⋊C4C2×D1112yes—
283#400—118no—
284#400—118no—
285#397—1116no—
286#394—118no—
287#394C2×D1118yescomplemented
288#393—1116no—
289#386—1116no—
290#386—1116no—
291C2×#95—112no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95—111no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—118no—
298C2×#95C2×D1111yescharacteristic
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—816no—
307C22×C11C2×#12414yes—
308C22×C11#53414yes—
309C22×C11#53714yes—
310C22×C11#53818yes—
311C22×C11#53918yes—
312C22×C11C23×D411yescharacteristic
313C22×C11C22×#4112yes—
314C22×C11C2×H(5,𝔽2)12yes—
315C22×C11C2×H(5,𝔽2)11yescharacteristic
316C22×C11C2×2−1+411yescharacteristic
317C2×D11—232no—
318C2×D11—24no—
319C2×D11—24no—
320C2×D11—28no—
321C2×D11—28no—
322C2×D11C2×#12418yes—
323C4×C11—24no—
324C4×C11—42no—
325C4×C11—42no—
326C4×C11—44no—
327Dic11—24no—
328Dic11—44no—
329Dic11—42no—
330Dic11—42no—
331Dic11—44no—
332C25—111no—
333C25C22×D1112yes—
334C22×Q8—114no—
335C22×Q8—224no—
336C22×Q8—444no—
337C22×D4—24no—
338C22×D4—44no—
339C22×D4—118no—
340C22×D4—228no—
341C22×D4—228no—
342C22×D4—228no—
343C22×D4C22×D1114yes—
344C23×C4—111no—
345C23×C4—118no—
346C23×C4—114no—
347C23×C4—111no—
348C23×C4—111no—
349C23×C4—112no—
350C23×C4—112no—
351C23×C4—118no—
352C23×C4—228no—
353C23×C4—444no—
354C23×C4—444no—
355C23×C4—444no—
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1111yescharacteristic
358C23×C4C22×D1112yes—
359C23×C4C22×D1111yescharacteristic
360C22⋊Q8—2232no—
361#121—2232no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4—224no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4C22×D1114yes—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—118no—
373C2×C22⋊C4—114no—
374C2×C22⋊C4—114no—
375C2×C22⋊C4—118no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—224no—
379C2×C22⋊C4—228no—
380C2×C22⋊C4—444no—
381C2×C22⋊C4—444no—
382C2×C22⋊C4C22×D1118yes—
383C2×C22⋊C4C22×D1118yes—
384#95—118no—
385#95—114no—
386#95—118no—
387#95—118no—
388#95—118no—
389#95—118no—
390#95C22×D1114yes—
391C2×C11—84no—
392C2×C11#263918yescomplemented
393C2×C11C22×#12411yescharacteristic
394C2×C11C2×#53411yescharacteristic
395C2×C11C2×#53711yescharacteristic
396C2×C11C2×#53812yes—
397C2×C11C2×#53912yes—
398D11—28no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24—24no—
405C24—24no—
406C24—114no—
407C24—118no—
408C24—112no—
409C24—224no—
410C24—222no—
411C24—222no—
412C24C23×D1114yes—
413C24C23×D1111yescharacteristic
414C2×Q8—228no—
415C2×Q8—448no—
416C2×Q8—4416no—
417C2×D4—28no—
418C2×D4—48no—
419C2×D4—416no—
420C2×D4—2216no—
421C2×D4—2216no—
422C2×D4—2216no—
423C2×D4—4432no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—114no—
434C22×C4—112no—
435C22×C4—1116no—
436C22×C4—114no—
437C22×C4—114no—
438C22×C4—112no—
439C22×C4—112no—
440C22×C4—2216no—
441C22×C4—224no—
442C22×C4—222no—
443C22×C4—224no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4—4416no—
454C22×C4—448no—
455C22×C4—448no—
456C22×C4—448no—
457C22×C4—4432no—
458C22×C4D4×D1114yes—
459C22×C4C23×D1114yes—
460C22×C4C23×D1112yes—
461C22×C4C23×D1112yes—
462C22×C4C23×D1112yes—
463C4⋊C4—28no—
464C4⋊C4—228no—
465C4⋊C4—228no—
466C4⋊C4—228no—
467C22⋊C4—48no—
468C22⋊C4—48no—
469C22⋊C4—228no—
470C22⋊C4—228no—
471C22⋊C4—2216no—
472C22⋊C4—448no—
473C22⋊C4—448no—
474C11C2×#263911yescharacteristic, complemented, Sylow
475C23—24no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—24no—
482C23—48no—
483C23—48no—
484C23—48no—
485C23—48no—
486C23—48no—
487C23—48no—
488C23—48no—
489C23—114no—
490C23—118no—
491C23—1116no—
492C23—228no—
493C23—228no—
494C23—2216no—
495C23—224no—
496C23—222no—
497C23—2216no—
498C23—222no—
499C23C2×D4×D1112yes—
500C23#6703714yes—
501C23#6703712yes—
502C23#41×D1114yes—
503C23#6704312yes—
504C23C24×D1111yescharacteristic
505Q8—4416no—
506D4—416no—
507D4—4432no—
508C2×C4—28no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—44no—
519C2×C4—44no—
520C2×C4—48no—
521C2×C4—114no—
522C2×C4—228no—
523C2×C4—224no—
524C2×C4—222no—
525C2×C4—224no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—222no—
535C2×C4—4416no—
536C2×C4—4432no—
537C2×C4—444no—
538C2×C4—444no—
539C2×C4—448no—
540C2×C4—448no—
541C2×C4C2×D4×D1114yes—
542C22—44no—
543C22—44no—
544C22—44no—
545C22—44no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—816no—
550C22—118no—
551C22—224no—
552C22—224no—
553C22—228no—
554C22—228no—
555C22—2232no—
556C22#1062312014yes—
557C22#1062313914yes—
558C22#1062314418yes—
559C22#1062319118yes—
560C22D11×#12414yes—
561C22C22×D4×D1111yescharacteristic
562C22C2×#6703712yes—
563C22C2×#6703711yescharacteristic
564C22C2×#41×D1112yes—
565C22C2×#6704311yescharacteristic
566C4—24no—
567C4—42no—
568C4—42no—
569C4—44no—
570C4—224no—
571C4—444no—
572C4—442no—
573C4—442no—
574C4—444no—
575C2—84no—
576C2—228no—
577C2#1307454718yesdirect product factor
578C2C2×D11×#12411yescharacteristic
579C2C2×#1062312011yescharacteristic
580C2C2×#1062313911yescharacteristic
581C2C2×#1062314412yes—
582C2C2×#1062319112yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC22×#66991C2
hypercenterC2×#394D11
hypocenterC11C2×#2639
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66949C2semidirect
3. #13074547C2direct (N × H)
4. C2×#10622272C2semidirect
5. C2×#10622599C2semidirect
6. C2×#10622565C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622560C2semidirect
9. C2×#10622569C2semidirect
10. C2×#10622569C2semidirect
11. C2×D11×#95C2semidirect
12. C2×C11×#394C2semidirect
32. C2×#66949C22semidirect
33. C11×#394C22semidirect
35. #10622835C22semidirect
42. #10622599C22semidirect
43. #10622569C22semidirect
44. #10622569C22semidirect
45. #10622565C22semidirect
46. #10622560C22semidirect
47. D11×#95C22semidirect
48. #10622272C22semidirect
191. C2×#394D11semidirect
287. #394C2×D11semidirect
392. C2×C11#2639semidirect
474. C11C2×#2639semidirect
577. C2#13074547direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669492
C22×#669912
#130745472
C2×#106222722
C2×#106225992
C2×#106225652
C2×#106228352
C2×#106225602
C2×#106225692
C2×D11×#952
C2×C11×#3942
C2×#263911