Finite Group Databasebeta

← C2×D11×#398 #14919983

Subgroups — C2×D11×#398 #14919983

Order 2816.

4158 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D11C212yesmaximal
2C22×C4⋊C4×D11C211yesmaximal, characteristic
3C22×C4⋊C4×D11C211yesmaximal, characteristic
4C2×#10622270C212yesmaximal, complemented
5C2×#10622597C212yesmaximal, complemented
6C2×#10622274C211yesmaximal, characteristic, complemented
7C2×#10622593C211yesmaximal, characteristic, complemented
8C2×#10622596C211yesmaximal, characteristic, complemented
9D11×#398C2116yesmaximal, direct product factor
10C2×D11×#95C211yesmaximal, characteristic
11C2×D11×#95C212yesmaximal
12C2×C11×#398C211yesmaximal, characteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2211yescharacteristic
29C2×C4⋊C4×D11—216no—
30C2×C4⋊C4×D11—28no—
31C2×C4⋊C4×D11—28no—
32C2×C4⋊C4×D11C2218yes—
33C2×C4⋊C4×D11C22116yes—
34C2×C4⋊C4×D11C2218yes—
35C11×#398C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622597C22116yescomplemented
44#10622596C2218yescomplemented
45#10622593C2218yescomplemented
46D11×#95C22116yes—
47D11×#95C2218yes—
48#10622274C2218yescomplemented
49#10622270C22116yescomplemented
50C24×D11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×Dic11C2312yes—
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C22×C4×D11—24no—
62C22×C4×D11—28no—
63C22×C4×D11—24no—
64C22×C4×D11—28no—
65C22×C4×D11—28no—
66C22×C4×D11—28no—
67C22×C4×D11—28no—
68C22×C4×D11—24no—
69C22×C4×D11—28no—
70C22×C4×D11—28no—
71C22×C4×D11D418yes—
72C22×C4×D11D418yes—
73C22×C4×D11Q8116yes—
74C22×C4×D11C2318yes—
75C22×C4×D11C2314yes—
76C22×C4×D11C2314yes—
77C22×C4×D11C2314yes—
78C22×C4×D11C2318yes—
79C2×C11×C4⋊C4—28no—
80C2×C11×C4⋊C4—24no—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2318yes—
85C2×C4⋊Dic11—24no—
86C2×C4⋊Dic11—24no—
87C2×C4⋊Dic11—28no—
88C2×C4⋊Dic11C2318yes—
89C2×C4⋊Dic11C2314yes—
90C2×C4⋊Dic11C2314yes—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—28no—
95C2×Dic11⋊C4—28no—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2318yes—
98C2×Dic11⋊C4C2318yes—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2318yes—
101C4⋊C4×D11—232no—
102C4⋊C4×D11—232no—
103C4⋊C4×D11—264no—
104C11×#95C2318yes—
105C11×#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2318yes—
111C22×#398—111nomaximal, Sylow
112C24×C11C2411yescharacteristic
113C23×D11C2×D414yes—
114C23×D11C2×D414yes—
115C23×D11C2×Q818yes—
116C23×D11#4114yes—
117C23×D11#4118yes—
118C23×D11C2412yes—
119C22×C4×C11—22no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11C2×D414yes—
130C22×C4×C11C2×D414yes—
131C22×C4×C11C2×Q818yes—
132C22×C4×C11C2412yes—
133C22×C4×C11C2414yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2412yes—
136C22×C4×C11C2414yes—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11C2×D414yes—
148C22×Dic11C2×D414yes—
149C22×Dic11C2×Q818yes—
150C22×Dic11C2412yes—
151C22×Dic11C2414yes—
152C22×Dic11C2412yes—
153C22×Dic11C2412yes—
154C22×Dic11C2414yes—
155C2×C4×D11—232no—
156C2×C4×D11—264no—
157C2×C4×D11—232no—
158C2×C4×D11—216no—
159C2×C4×D11—28no—
160C2×C4×D11—216no—
161C2×C4×D11—216no—
162C2×C4×D11—28no—
163C2×C4×D11—28no—
164C2×C4×D11—216no—
165C2×C4×D11—216no—
166C2×C4×D11—216no—
167C2×C4×D11—216no—
168C2×C4×D11—432no—
169C2×C4×D11—416no—
170C2×C4×D11C2×D4116yes—
171C2×C4×D11C2×D4116yes—
172C2×C4×D11C2×Q8132yes—
173C11×C4⋊C4—216no—
174C11×C4⋊C4—28no—
175C11×C4⋊C4—28no—
176C4⋊Dic11—28no—
177C4⋊Dic11—216no—
178C4⋊Dic11—28no—
179Dic11⋊C4—28no—
180Dic11⋊C4—216no—
181Dic11⋊C4—216no—
182Dic11⋊C4—216no—
183Dic11⋊C4—28no—
184C23×C4⋊C4—111no—
185C23×C4⋊C4—112no—
186C23×C4⋊C4—111no—
187C2×#398—1116no—
188C2×#398—111no—
189C2×#398—112no—
190C2×#398—111no—
191C2×#398—111no—
192C2×#398—112no—
193C2×#398D1111yescharacteristic, direct product factor
194C22×#95—111no—
195C22×#95—112no—
196C23×C11C22×D412yes—
197C23×C11C22×D412yes—
198C23×C11C22×Q814yes—
199C23×C11C2×#4112yes—
200C23×C11C2×#4114yes—
201C23×C11C2511yescharacteristic
202C22×D11#121116yes—
203C22×D11C22⋊Q8132yes—
204C22×D11#123116yes—
205C22×D11#125132yes—
206C22×D11C4⋊Q8116yes—
207C22×D11C22×D414yes—
208C22×D11C22×D414yes—
209C22×D11C22×Q818yes—
210C22×D11C2×#4114yes—
211C22×D11C2×#4118yes—
212C2×C4×C11—28no—
213C2×C4×C11—216no—
214C2×C4×C11—28no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—48no—
226C2×C4×C11—44no—
227C2×C4×C11C22×D414yes—
228C2×C4×C11C22×D414yes—
229C2×C4×C11C22×Q818yes—
230C2×Dic11—28no—
231C2×Dic11—216no—
232C2×Dic11—28no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—48no—
244C2×Dic11—44no—
245C2×Dic11C22×D414yes—
246C2×Dic11C22×D414yes—
247C2×Dic11C22×Q818yes—
248C4×D11—232no—
249C4×D11—264no—
250C4×D11—232no—
251C4×D11—432no—
252C4×D11—416no—
253C24×C4—111no—
254C24×C4—111no—
255C24×C4—112no—
256C24×C4—112no—
257C24×C4—111no—
258C22×C4⋊C4—111no—
259C22×C4⋊C4—112no—
260C22×C4⋊C4—112no—
261C22×C4⋊C4—111no—
262C22×C4⋊C4—112no—
263C22×C4⋊C4—112no—
264C22×C4⋊C4—111no—
265C22×C4⋊C4—111no—
266C22×C4⋊C4—118no—
267C22×C4⋊C4—1116no—
268C22×C4⋊C4—118no—
269C22×C4⋊C4—228no—
270C22×C4⋊C4—2216no—
271C22×C4⋊C4—228no—
272C22×C4⋊C4C2×D1111yescharacteristic
273C22×C4⋊C4C2×D1112yes—
274C22×C4⋊C4C2×D1111yescharacteristic
275#398—118no—
276#398—118no—
277#398—1116no—
278#398—1116no—
279#398—118no—
280#398C2×D1118yesdirect product factor
281C2×#95—112no—
282C2×#95—111no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95—112no—
286C2×#95—118no—
287C2×#95—1116no—
288C2×#95C2×D1112yes—
289C2×#95C2×D1111yescharacteristic
290C22×C11C2×#12114yes—
291C22×C11C2×C22⋊Q818yes—
292C22×C11C2×#12314yes—
293C22×C11C2×#12518yes—
294C22×C11C2×C4⋊Q814yes—
295C22×C11C23×D411yescharacteristic
296C22×C11C23×D411yescharacteristic
297C22×C11C23×Q812yes—
298C22×C11C22×#4111yescharacteristic
299C22×C11C22×#4112yes—
300C2×D11#398164yesdirect product factor
301C2×D11C2×#12118yes—
302C2×D11C2×C22⋊Q8116yes—
303C2×D11C2×#12318yes—
304C2×D11C2×#125116yes—
305C2×D11C2×C4⋊Q818yes—
306C4×C11—24no—
307C4×C11—28no—
308C4×C11—24no—
309C4×C11—44no—
310C4×C11—42no—
311Dic11—24no—
312Dic11—28no—
313Dic11—24no—
314Dic11—44no—
315Dic11—42no—
316C25—111no—
317C23×C4—111no—
318C23×C4—111no—
319C23×C4—112no—
320C23×C4—118no—
321C23×C4—118no—
322C23×C4—1116no—
323C23×C4—114no—
324C23×C4—114no—
325C23×C4—118no—
326C23×C4—112no—
327C23×C4—111no—
328C23×C4—118no—
329C23×C4—114no—
330C23×C4—224no—
331C23×C4—228no—
332C23×C4—224no—
333C23×C4—228no—
334C23×C4—228no—
335C23×C4—228no—
336C23×C4—228no—
337C23×C4—224no—
338C23×C4—228no—
339C23×C4—228no—
340C23×C4C22×D1112yes—
341C23×C4C22×D1111yescharacteristic
342C23×C4C22×D1111yescharacteristic
343C23×C4C22×D1111yescharacteristic
344C23×C4C22×D1112yes—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—118no—
349C2×C4⋊C4—114no—
350C2×C4⋊C4—118no—
351C2×C4⋊C4—118no—
352C2×C4⋊C4—114no—
353C2×C4⋊C4—114no—
354C2×C4⋊C4—118no—
355C2×C4⋊C4—114no—
356C2×C4⋊C4—2232no—
357C2×C4⋊C4—2264no—
358C2×C4⋊C4—2232no—
359C2×C4⋊C4—228no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—228no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4—228no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—228no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4C22×D1114yes—
368C2×C4⋊C4C22×D1114yes—
369C2×C4⋊C4C22×D1118yes—
370#95—114no—
371#95—118no—
372#95—118no—
373#95—118no—
374#95—118no—
375#95C22×D1118yes—
376#95C22×D1114yes—
377C2×C11C2×#39818yescomplemented
378C2×C11C22×#12111yescharacteristic
379C2×C11C22×C22⋊Q812yes—
380C2×C11C22×#12311yescharacteristic
381C2×C11C22×#12512yes—
382C2×C11C22×C4⋊Q811yescharacteristic
383D11C2×#398116yesdirect product factor
384C24—114no—
385C24—114no—
386C24—118no—
387C24—114no—
388C24—118no—
389C24—112no—
390C24C23×D1111yescharacteristic
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—114no—
402C22×C4—114no—
403C22×C4—118no—
404C22×C4—114no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—1116no—
408C22×C4—1116no—
409C22×C4—1132no—
410C22×C4—112no—
411C22×C4—114no—
412C22×C4—228no—
413C22×C4—2216no—
414C22×C4—2232no—
415C22×C4—2264no—
416C22×C4—2232no—
417C22×C4—228no—
418C22×C4—2216no—
419C22×C4—2216no—
420C22×C4—2216no—
421C22×C4—2216no—
422C22×C4—228no—
423C22×C4—2216no—
424C22×C4—2216no—
425C22×C4—222no—
426C22×C4—224no—
427C22×C4—222no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4—222no—
433C22×C4—224no—
434C22×C4—224no—
435C22×C4—4432no—
436C22×C4—4416no—
437C22×C4D4×D1114yes—
438C22×C4D4×D1114yes—
439C22×C4Q8×D1118yes—
440C22×C4C23×D1112yes—
441C22×C4C23×D1114yes—
442C22×C4C23×D1112yes—
443C22×C4C23×D1112yes—
444C22×C4C23×D1114yes—
445C4⋊C4—28no—
446C4⋊C4—216no—
447C4⋊C4—28no—
448C4⋊C4—2216no—
449C4⋊C4—228no—
450C4⋊C4—2216no—
451C4⋊C4—228no—
452C4⋊C4—2216no—
453C4⋊C4—228no—
454C4⋊C4—2216no—
455C4⋊C4—228no—
456C11C22×#39811yescharacteristic, complemented, Sylow
457C23—1116no—
458C23—1116no—
459C23—1132no—
460C23—1116no—
461C23—114no—
462C23—114no—
463C23—118no—
464C23—114no—
465C23—118no—
466C23—1132no—
467C23C2×D4×D1112yes—
468C23C2×D4×D1112yes—
469C23C2×Q8×D1114yes—
470C23#41×D1112yes—
471C23#41×D1114yes—
472C23C24×D1111yescharacteristic
473C2×C4—28no—
474C2×C4—216no—
475C2×C4—28no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—48no—
487C2×C4—44no—
488C2×C4—114no—
489C2×C4—114no—
490C2×C4—118no—
491C2×C4—2232no—
492C2×C4—2264no—
493C2×C4—2232no—
494C2×C4—228no—
495C2×C4—2216no—
496C2×C4—228no—
497C2×C4—222no—
498C2×C4—224no—
499C2×C4—222no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—222no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—4432no—
508C2×C4—4416no—
509C2×C4—448no—
510C2×C4—444no—
511C2×C4C2×D4×D1114yes—
512C2×C4C2×D4×D1114yes—
513C2×C4C2×Q8×D1118yes—
514C22—1116no—
515C22—118no—
516C22—1164no—
517C22—118no—
518C22—1116no—
519C22—118no—
520C22D11×#12114yes—
521C22D11×C22⋊Q818yes—
522C22D11×#12314yes—
523C22D11×#12518yes—
524C22D11×C4⋊Q814yes—
525C22C22×D4×D1111yescharacteristic
526C22C22×D4×D1111yescharacteristic
527C22C22×Q8×D1112yes—
528C22C2×#41×D1111yescharacteristic
529C22C2×#41×D1112yes—
530C4—24no—
531C4—28no—
532C4—24no—
533C4—44no—
534C4—42no—
535C4—224no—
536C4—228no—
537C4—224no—
538C4—444no—
539C4—442no—
540C2—1116no—
541C2D11×#39818yesdirect product factor
542C2C2×D11×#12111yescharacteristic
543C2C2×D11×C22⋊Q812yes—
544C2C2×D11×#12311yescharacteristic
545C2C2×D11×#12512yes—
546C2C2×D11×C4⋊Q811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#398D11
hypocenterC11C22×#398
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
4. C2×#10622270C2semidirect
5. C2×#10622597C2semidirect
6. C2×#10622274C2semidirect
7. C2×#10622593C2semidirect
8. C2×#10622596C2semidirect
9. D11×#398C2direct (N × H)
12. C2×C11×#398C2semidirect
35. C11×#398C22semidirect
43. #10622597C22semidirect
44. #10622596C22semidirect
45. #10622593C22semidirect
48. #10622274C22semidirect
49. #10622270C22semidirect
193. C2×#398D11direct (N × H)
280. #398C2×D11direct (N × H)
300. C2×D11#398direct (N × H)
377. C2×C11C2×#398semidirect
383. D11C2×#398direct (N × H)
456. C11C22×#398semidirect
541. C2D11×#398direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D112
C2×#106222702
C2×#106225972
C2×#106222742
C2×#106225932
C2×#106225962
D11×#3982
C2×D11×#952
C2×C11×#3982
C22×#39811