Finite Group Databasebeta

← C2×#13072917 #14922819

Subgroups — C2×#13072917 #14922819

Order 2816.

3678 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C212yesmaximal
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
3C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4#13072917C2116yesmaximal, direct product factor
5C2×#10622274C211yesmaximal, characteristic, complemented
6C2×#10622593C211yesmaximal, characteristic, complemented
7C2×#10622566C211yesmaximal, characteristic, complemented
8C2×#10622260C212yesmaximal, complemented
9C2×#10622277C212yesmaximal, complemented
10C2×#10622280C211yesmaximal, characteristic, complemented
11C2×#10622555C212yesmaximal, complemented
12C2×C11×#397C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C23×C4×D11C2212yes—
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C2×C4⋊C4×D11—28no—
31C2×C4⋊C4×D11C2218yescomplemented
32C2×#66936—216no—
33C2×#66936C22116yes—
34C2×(C22⋊D11)⋊C4—28no—
35C2×(C22⋊D11)⋊C4C2218yes—
36C11×#397C2218yescomplemented
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43#10622593C2218yescomplemented
44#10622566C2218yescomplemented
45#10622555C22116yescomplemented
46#10622280C2218yescomplemented
47#10622277C22116yescomplemented
48#10622274C2218yescomplemented
49#10622260C22116yescomplemented
50C25×C11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—24no—
57C22×C22⋊D11—24no—
58C22×C22⋊D11D418yes—
59C22×C22⋊D11C2314yes—
60C23×Dic11—24no—
61C23×Dic11—28no—
62C23×Dic11C2314yes—
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C22×C4×D11—28no—
69C22×C4×D11—28no—
70C22×C4×D11—28no—
71C22×C4×D11—28no—
72C22×C4×D11D418yes—
73C22×C4×D11C2318yes—
74C22×C4×D11C2314yes—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C22⋊C4—28no—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2318yes—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11C2318yes—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4C2314yes—
86C2×(C2×D11)⋊C4C2318yes—
87C2×C4⋊Dic11—24no—
88C2×C4⋊Dic11—28no—
89C2×C4⋊Dic11C2318yes—
90C2×C4⋊Dic11C2314yes—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—28no—
93C2×Dic11⋊C4—28no—
94C2×Dic11⋊C4—28no—
95C2×Dic11⋊C4C2314yes—
96C2×Dic11⋊C4C2318yes—
97C2×Dic11⋊C4C2318yes—
98C2×Dic11⋊C4C2318yes—
99C2×C4×Dic11—24no—
100C2×C4×Dic11C2314yes—
101C4⋊C4×D11—232no—
102#66936—264no—
103(C22⋊D11)⋊C4—232no—
104C11×#95C2318yes—
105C11×#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C2×#2486—111nomaximal, Sylow
111C24×C11—22no—
112C24×C11—24no—
113C24×C11—22no—
114C24×C11—24no—
115C24×C11C2×D414yes—
116C24×C11C2412yes—
117C24×C11C2411yescharacteristic
118C23×D11—24no—
119C23×D11—24no—
120C23×D11C2×D414yes—
121C23×D11C2×D414yes—
122C23×D11#4114yes—
123C23×D11C2412yes—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2414yes—
136C22×C4×C11C2414yes—
137C22×C4×C11C2412yes—
138C2×C22⋊D11—232no—
139C2×C22⋊D11—28no—
140C2×C22⋊D11—28no—
141C2×C22⋊D11C2×D4116yes—
142C22×Dic11—28no—
143C22×Dic11—216no—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—416no—
155C22×Dic11C2×D414yes—
156C22×Dic11C2×D414yes—
157C22×Dic11#4118yes—
158C22×Dic11C2412yes—
159C22×Dic11C2414yes—
160C22×Dic11C2414yes—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C2×C4×D11—232no—
164C2×C4×D11—216no—
165C2×C4×D11—216no—
166C2×C4×D11—216no—
167C2×C4×D11—216no—
168C2×C4×D11—432no—
169C2×C4×D11C2×D4116yes—
170C11×C4⋊C4—28no—
171C11×C22⋊C4—216no—
172C11×C22⋊C4—28no—
173C22⋊Dic11—216no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—216no—
176C4⋊Dic11—216no—
177C4⋊Dic11—28no—
178Dic11⋊C4—216no—
179Dic11⋊C4—216no—
180Dic11⋊C4—216no—
181Dic11⋊C4—28no—
182C4×Dic11—28no—
183C22×#123—112no—
184C22×C4×D4—111no—
185C23×C4⋊C4—111no—
186#2486—1116no—
187C2×#398—111no—
188C2×#398—111no—
189C2×#397—111no—
190C2×#397D1111yescharacteristic, complemented
191C2×#389—112no—
192C2×#381—112no—
193C2×#380—111no—
194C2×#380—112no—
195C23×C11—28no—
196C23×C11—216no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—22no—
200C23×C11—24no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11—48no—
204C23×C11C22×D414yes—
205C23×C11C22×D412yes—
206C23×C11C22×D412yes—
207C23×C11C2×#4112yes—
208C23×C11C2×#4114yes—
209C23×C112−1+414yes—
210C23×C11C2511yescharacteristic
211C22×D11—28no—
212C22×D11—28no—
213C22×D11—216no—
214C22×D11—216no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11#121116yes—
218C22×D11C22×D414yes—
219C22×D11C22×D414yes—
220C22×D11C2×#4114yes—
221C2×C4×C11—28no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—48no—
232C2×C4×C11—44no—
233C2×C4×C11—48no—
234C2×C4×C11C22×D414yes—
235C22⋊D11—232no—
236C2×Dic11—28no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—48no—
248C2×Dic11—44no—
249C2×Dic11—48no—
250C2×Dic11—416no—
251C2×Dic11#123116yescomplemented
252C2×Dic11C22×D414yes—
253C2×Dic11C22×D414yes—
254C2×Dic11C2×#4118yes—
255C4×D11—232no—
256C4×D11—432no—
257C23×D4—111no—
258C24×C4—111no—
259C24×C4—111no—
260C24×C4—112no—
261C2×#123—1116no—
262C2×#123—2216no—
263C2×C4×D4—118no—
264C2×C4×D4—228no—
265C22×C4⋊C4—111no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4—112no—
268C22×C4⋊C4—112no—
269C22×C4⋊C4—111no—
270C22×C4⋊C4—112no—
271C22×C4⋊C4—118no—
272C22×C4⋊C4—228no—
273C22×C4⋊C4C2×D1111yescharacteristic
274C22×C22⋊C4—112no—
275C22×C22⋊C4—111no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4C2×D1111yescharacteristic
278C22×C22⋊C4C2×D1112yes—
279C22×C42—111no—
280#398—118no—
281#398—118no—
282#397—118no—
283#397C2×D1118yescomplemented
284#389—1116no—
285#381—1116no—
286#380—1116no—
287#380—118no—
288C2×#95—111no—
289C2×#95—112no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95C2×D1111yescharacteristic
293C2×#95C2×D1112yes—
294C22×C11—24no—
295C22×C11—28no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—44no—
299C22×C11—416no—
300C22×C11C2×#12114yes—
301C22×C11C2×#12314yes—
302C22×C11#53614yes—
303C22×C11#54718yes—
304C22×C11#55218yes—
305C22×C11C23×D411yescharacteristic
306C22×C11C23×D411yescharacteristic
307C22×C11C22×#4111yescharacteristic
308C22×C11C22×#4112yes—
309C22×C11C2×2−1+412yes—
310C2×D11—24no—
311C2×D11—24no—
312C2×D11—28no—
313C2×D11—28no—
314C2×D11—232no—
315C2×D11C2×#12118yes—
316C4×C11—24no—
317C4×C11—44no—
318C4×C11—42no—
319C4×C11—44no—
320Dic11—24no—
321Dic11—44no—
322Dic11—42no—
323Dic11—44no—
324Dic11C2×#12318yescomplemented
325C25—111no—
326C25C22×D1111yescharacteristic
327C22×D4—118no—
328C22×D4—114no—
329C22×D4—224no—
330C22×D4—224no—
331C23×C4—111no—
332C23×C4—111no—
333C23×C4—118no—
334C23×C4—114no—
335C23×C4—114no—
336C23×C4—112no—
337C23×C4—112no—
338C23×C4—111no—
339C23×C4—118no—
340C23×C4—228no—
341C23×C4—228no—
342C23×C4—228no—
343C23×C4—228no—
344C23×C4—224no—
345C23×C4—228no—
346C23×C4C22×D1112yes—
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1112yes—
349C23×C4C22×D1111yescharacteristic
350#123—2264no—
351C4×D4—2232no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—118no—
354C2×C4⋊C4—114no—
355C2×C4⋊C4—114no—
356C2×C4⋊C4—118no—
357C2×C4⋊C4—118no—
358C2×C4⋊C4—118no—
359C2×C4⋊C4—2232no—
360C2×C4⋊C4—228no—
361C2×C4⋊C4—228no—
362C2×C4⋊C4—228no—
363C2×C4⋊C4—228no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4C22×D1114yes—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—114no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4—228no—
374C2×C22⋊C4—228no—
375C2×C22⋊C4C22×D1114yes—
376C2×C22⋊C4C22×D1118yes—
377C2×C42—114no—
378C2×C42—224no—
379#95—118no—
380#95—118no—
381#95—114no—
382#95—118no—
383#95C22×D1114yes—
384#95C22×D1118yes—
385C2×C11—44no—
386C2×C11#248618yescomplemented
387C2×C11C22×#12111yescharacteristic
388C2×C11C22×#12311yescharacteristic
389C2×C11C2×#53611yescharacteristic
390C2×C11C2×#54712yes—
391C2×C11C2×#55212yes—
392D11—28no—
393C24—22no—
394C24—24no—
395C24—22no—
396C24—24no—
397C24—114no—
398C24—114no—
399C24—114no—
400C24—112no—
401C24—224no—
402C24—224no—
403C24D4×D1114yes—
404C24C23×D1112yes—
405C24C23×D1111yescharacteristic
406C2×D4—1116no—
407C2×D4—228no—
408C2×D4—2232no—
409C2×D4—228no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—114no—
420C22×C4—118no—
421C22×C4—112no—
422C22×C4—114no—
423C22×C4—112no—
424C22×C4—1116no—
425C22×C4—112no—
426C22×C4—114no—
427C22×C4—114no—
428C22×C4—2232no—
429C22×C4—2216no—
430C22×C4—2216no—
431C22×C4—2216no—
432C22×C4—2216no—
433C22×C4—228no—
434C22×C4—2216no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—222no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—224no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—4432no—
446C22×C4—4416no—
447C22×C4D4×D1114yes—
448C22×C4C23×D1112yes—
449C22×C4C23×D1114yes—
450C22×C4C23×D1114yes—
451C22×C4C23×D1112yes—
452C4⋊C4—28no—
453C4⋊C4—2216no—
454C4⋊C4—2216no—
455C4⋊C4—2216no—
456C4⋊C4—2216no—
457C4⋊C4—228no—
458C4⋊C4—228no—
459C22⋊C4—216no—
460C22⋊C4—28no—
461C22⋊C4—228no—
462C22⋊C4—2216no—
463C22⋊C4—2216no—
464C42—228no—
465C11C2×#248611yescharacteristic, complemented, Sylow
466C23—28no—
467C23—216no—
468C23—22no—
469C23—24no—
470C23—22no—
471C23—24no—
472C23—48no—
473C23—44no—
474C23—44no—
475C23—1116no—
476C23—114no—
477C23—114no—
478C23—114no—
479C23—2216no—
480C23—228no—
481C23—2216no—
482C23—224no—
483C23—224no—
484C23—228no—
485C23C2×D4×D1114yes—
486C23C2×D4×D1112yes—
487C23C2×D4×D1112yes—
488C23#41×D1112yes—
489C23#41×D1114yes—
490C23#6704314yes—
491C23C24×D1111yescharacteristic
492D4—2232no—
493C2×C4—28no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—48no—
504C2×C4—48no—
505C2×C4—44no—
506C2×C4—1116no—
507C2×C4—114no—
508C2×C4—118no—
509C2×C4—114no—
510C2×C4—2232no—
511C2×C4—228no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—222no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—4432no—
523C2×C4—4416no—
524C2×C4—448no—
525C2×C4—444no—
526C2×C4—448no—
527C2×C4C2×D4×D1114yes—
528C22—28no—
529C22—24no—
530C22—44no—
531C22—416no—
532C22—42no—
533C22—42no—
534C22—118no—
535C22—228no—
536C22—2232no—
537C22—224no—
538C22—228no—
539C22—224no—
540C22D11×#12114yes—
541C22D11×#12314yes—
542C22#1062318618yes—
543C22#1062320614yes—
544C22#1062323918yes—
545C22C22×D4×D1111yescharacteristic
546C22C22×D4×D1111yescharacteristic
547C22C2×#41×D1111yescharacteristic
548C22C2×#41×D1112yes—
549C22C2×#6704312yes—
550C4—24no—
551C4—42no—
552C4—44no—
553C4—44no—
554C4—118no—
555C4—224no—
556C4—444no—
557C4—444no—
558C4—442no—
559C2—44no—
560C2—228no—
561C2#1307291718yesdirect product factor
562C2C2×D11×#12111yescharacteristic
563C2C2×D11×#12311yescharacteristic
564C2C2×#1062320611yescharacteristic
565C2C2×#1062318612yes—
566C2C2×#1062323912yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#397D11
hypocenterC11C2×#2486
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D11C2semidirect
4. #13072917C2direct (N × H)
5. C2×#10622274C2semidirect
6. C2×#10622593C2semidirect
7. C2×#10622566C2semidirect
8. C2×#10622260C2semidirect
9. C2×#10622277C2semidirect
10. C2×#10622280C2semidirect
11. C2×#10622555C2semidirect
12. C2×C11×#397C2semidirect
31. C2×C4⋊C4×D11C22semidirect
36. C11×#397C22semidirect
43. #10622593C22semidirect
44. #10622566C22semidirect
45. #10622555C22semidirect
46. #10622280C22semidirect
47. #10622277C22semidirect
48. #10622274C22semidirect
49. #10622260C22semidirect
190. C2×#397D11semidirect
251. C2×Dic11#123semidirect
283. #397C2×D11semidirect
324. Dic11C2×#123semidirect
386. C2×C11#2486semidirect
465. C11C2×#2486semidirect
561. C2#13072917direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669362
C22×(C22⋊D11)⋊C42
C22×C4⋊C4×D112
#130729172
C2×#106222742
C2×#106225932
C2×#106225662
C2×#106222602
C2×#106222772
C2×#106222802
C2×#106225552
C2×C11×#3972
C2×#248611