Finite Group Databasebeta

← #14719683

Subgroups — #14719683

Order 2816.

1210 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623054C211yesmaximal, characteristic
2#13077644C212yesmaximal, complemented
3#13066959C212yesmaximal, complemented
4#13066951C212yesmaximal, complemented
5#13066950C211yesmaximal, characteristic, complemented
6#13066944C212yesmaximal, complemented
7#13066931C212yesmaximal, complemented
8D11×#324C212yesmaximal, complemented
9C11×#1464C211yesmaximal, characteristic, complemented
10C22×#4339C411yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C4⋊Dic11C411yescharacteristic
13#10623054—24no—
14#10623054—24no—
15C2×#66945C411yescharacteristic
16C2×#66945C411yescharacteristic
17C2×C4⋊C4×D11C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×(C22⋊D11)⋊C4C411yescharacteristic
20C2×(C22⋊D11)⋊C4C411yescharacteristic
21C2×(C22⋊D11)⋊C4C2211yescharacteristic
22C2×(C22⋊D11)⋊C4C2211yescharacteristic
23C2×C4×D44C411yescharacteristic
24C2×C4×D44C2211yescharacteristic
25C2×C4×Dic22C411yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C11×#432C2212yes—
28#10622539C2212yes—
29#10622449—24no—
30#10622339C2214yes—
31D11×C22⋊C8C2214yes—
32#10622319—24no—
33C11×#324C2212yes—
34C11×#323C2212yes—
35#10622166C2212yes—
36#10622163C2212yes—
37#10622107C2214yes—
38#10622107C2214yes—
39C23×C4×C11C2×C411yescharacteristic
40C22×C22⋊D11C2×C411yescharacteristic
41C22×C22⋊D11C2×C411yescharacteristic
42C23×Dic11C2×C411yescharacteristic
43C23×Dic11C2×C411yescharacteristic
44C2×#4339—24no—
45C2×#4339—22no—
46C2×#4339—22no—
47C2×#4339—24no—
48C22×D44C2×C411yescharacteristic
49C22×C4×D11C2×C411yescharacteristic
50C22×C4×D11C2×C411yescharacteristic
51C22×C4×D11C2×C411yescharacteristic
52C22×C4×D11C2×C411yescharacteristic
53C22×C4×D11C2311yescharacteristic
54C22×C4×D11C2311yescharacteristic
55C22×Dic22C2×C411yescharacteristic
56C11×#117—22no—
57C11×#117—22no—
58C2×C11×C4⋊C4C2×C411yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4C2×C411yescharacteristic
61C2×C11×C22⋊C4C2311yescharacteristic
62C2×C42×C11C2×C411yescharacteristic
63C2×C42×C11C2311yescharacteristic
64C2×(C2×D11)⋊C4C2×C411yescharacteristic
65C2×(C2×D11)⋊C4C2×C411yescharacteristic
66C2×(C2×D11)⋊C4C2×C411yescharacteristic
67C2×(C2×D11)⋊C4C2×C411yescharacteristic
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11C2×C411yescharacteristic
71C2×C4⋊Dic11C2×C411yescharacteristic
72C2×C4⋊Dic11C2×C411yescharacteristic
73C2×C4⋊Dic11C2×C411yescharacteristic
74C2×Dic11⋊C4C2×C411yescharacteristic
75C2×Dic11⋊C4C2×C411yescharacteristic
76C2×Dic11⋊C4C2311yescharacteristic
77C2×Dic11⋊C4C2311yescharacteristic
78C2×C4×Dic11C2×C411yescharacteristic
79C2×C4×Dic11C2×C411yescharacteristic
80C2×C4×Dic11C2×C411yescharacteristic
81C2×C4×Dic11C2×C411yescharacteristic
82C2×#4313—24no—
83C2×C8×D11—24no—
84#66945—24no—
85#66945—24no—
86C4⋊C4×D11—24no—
87C4⋊C4×D11—24no—
88(C22⋊D11)⋊C4—24no—
89(C22⋊D11)⋊C4—24no—
90(C22⋊D11)⋊C4—24no—
91(C22⋊D11)⋊C4—24no—
92C4×D44—22no—
93C4×D44—22no—
94C4×D44D414yes—
95C4×D44D414yes—
96C4×Dic22—22no—
97C4×Dic22—22no—
98C4×Dic22—22no—
99C4×Dic22—22no—
100C11×C4⋊C8—22no—
101C11×C22⋊C8C2314yes—
102C11×#97—22no—
103C22⋊(C11⋊C8)C2314yes—
104(C2×D11)⋊C8—24no—
105(C2×D11)⋊C8—24no—
106C4⋊(C11⋊C8)—22no—
107#66867—22no—
108#17368—111nomaximal, Sylow
109C24×C11C22×C411yescharacteristic
110C23×D11C22×C411yescharacteristic
111C23×D11C22×C411yescharacteristic
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C2×C22⋊D11—22no—
123C2×C22⋊D11—22no—
124C2×C22⋊D11—22no—
125C2×C22⋊D11—22no—
126C2×C22⋊D11—22no—
127C2×C22⋊D11M1614yescomplemented
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—81no—
131C22×Dic11—81no—
132C22×Dic11C22×C411yescharacteristic
133C22×Dic11C22×C411yescharacteristic
134C22×Dic11C22×C411yescharacteristic
135C22×Dic11C22×C411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C411yescharacteristic
138#4339—216no—
139#4339—216no—
140C2×D44—22no—
141C2×D44—22no—
142C2×D44C22⋊C412yes—
143C2×D44C22⋊C412yes—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—81no—
152C2×C4×D11—81no—
153C2×C4×D11—81no—
154C2×C4×D11—81no—
155C2×C4×D11M1614yescomplemented
156C2×C4×D11C2×D414yes—
157C2×C4×D11C2×D414yes—
158C2×Dic22—22no—
159C2×Dic22—22no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×C8×C11—24no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11C2×D412yes—
170C42×C11C2×D412yes—
171(C2×D11)⋊C4—22no—
172(C2×D11)⋊C4—22no—
173(C2×D11)⋊C4C22⋊C414yes—
174(C2×D11)⋊C4C22⋊C414yes—
175C4⋊Dic11—22no—
176C4⋊Dic11—22no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11C22⋊C412yes—
180C4⋊Dic11C22⋊C412yes—
181Dic11⋊C4—22no—
182Dic11⋊C4—22no—
183Dic11⋊C4—22no—
184Dic11⋊C4—22no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—22no—
189C2×C11⋊C8—24no—
190#4313—84no—
191C8×D11—84no—
192C2×#520—111no—
193#2973—112no—
194#1467—112no—
195#1465—112no—
196#1464—111no—
197#1464D1111yescharacteristic, complemented
198#1463—112no—
199#1459—112no—
200C2×#324—112no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11C2×M1612yes—
206C23×C11C23×C411yescharacteristic
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11C2×C22⋊C412yes—
214C22×D11C2×C22⋊C412yes—
215C22×D11C2×M1612yes—
216C22×D11C2×M1612yes—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11C2×C22⋊C412yes—
230C2×C4×C11C2×C22⋊C411yescharacteristic
231C2×C4×C11C2×C22⋊C411yescharacteristic
232C2×C4×C11C2×M1612yes—
233C2×C4×C11C22×D412yes—
234C22⋊D11—28no—
235C22⋊D11—28no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—82no—
247C2×Dic11—82no—
248C2×Dic11C2×C22⋊C412yes—
249C2×Dic11C2×C22⋊C412yes—
250C2×Dic11C2×M1612yes—
251C2×Dic11C2×M1612yes—
252D44—24no—
253D44—24no—
254C4×D11—28no—
255C4×D11—28no—
256C4×D11—44no—
257C4×D11—44no—
258C4×D11—82no—
259C4×D11—82no—
260Dic22—24no—
261Dic22—24no—
262C8×C11—44no—
263C11⋊C8—44no—
264C22×#41—111no—
265#520—224no—
266#520—224no—
267C2×C4×Q8—111no—
268C2×C4×Q8—111no—
269C2×C4×D4—111no—
270C2×C4×D4—111no—
271C2×C4×D4—111no—
272C2×C4×D4—111no—
273C2×C4×D4—111no—
274C2×C4×D4—111no—
275C2×#117—111no—
276C2×#117—111no—
277C2×#117C2×D1111yescharacteristic
278C22×C4⋊C4—111no—
279C22×C4⋊C4—111no—
280C22×C4⋊C4—111no—
281#435—224no—
282#435—224no—
283#432—112no—
284#432C2×D1112yes—
285#407—114no—
286C2×C22⋊C8—114no—
287#324—112no—
288#324—114no—
289#324—114no—
290#324C2×D1112yes—
291#323—112no—
292#323C2×D1112yes—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—22no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11C22×C22⋊C411yescharacteristic
301C22×C11C22×M1611yescharacteristic
302C22×C11C22×M1611yescharacteristic
303C2×D11—22no—
304C2×D11—22no—
305C2×D11—22no—
306C2×D11—22no—
307C2×D11—22no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11#40714yes—
313C4×C11—21no—
314C4×C11—21no—
315C4×C11—22no—
316C4×C11—22no—
317C4×C11—22no—
318C4×C11—41no—
319C4×C11—41no—
320Dic11—22no—
321Dic11—22no—
322Dic11—22no—
323Dic11—22no—
324Dic11—41no—
325Dic11—41no—
326C2×#41—224no—
327C2×#41—222no—
328C2×#41—222no—
329C2×#41—224no—
330C22×Q8—111no—
331C22×D4—111no—
332C22×D4—111no—
333C22×D4—111no—
334C23×C4—111no—
335C23×C4—111no—
336C23×C4—111no—
337C23×C4—111no—
338C23×C4—111no—
339C23×C4—111no—
340C23×C4—111no—
341C23×C4—111no—
342C23×C4C4×D1111yescharacteristic
343C2×M16—224no—
344C22×C8—224no—
345C4×Q8—222no—
346C4×Q8—222no—
347C4×Q8—222no—
348C4×Q8—222no—
349C4×D4—114no—
350C4×D4—114no—
351C4×D4—222no—
352C4×D4—222no—
353C4×D4—224no—
354C4×D4—224no—
355C4×D4—224no—
356C4×D4—224no—
357#117—22no—
358#117—22no—
359#117—224no—
360#117—224no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4C4×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—111no—
376C2×C22⋊C4—111no—
377C2×C22⋊C4—111no—
378C2×C22⋊C4—111no—
379C2×C22⋊C4C4×D1111yescharacteristic
380C2×C22⋊C4C22×D1111yescharacteristic
381C2×C42—111no—
382C2×C42—111no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42C4×D1111yescharacteristic
386C2×C42C22×D1111yescharacteristic
387C4⋊C8—22no—
388C4⋊C8—222no—
389C22⋊C8—114no—
390C22⋊C8—224no—
391C22⋊C8—224no—
392C22⋊C8C22×D1114yes—
393#97—22no—
394#97—222no—
395C2×C11—21no—
396C2×C11—21no—
397C2×C11—42no—
398C2×C11C2×#40711yescharacteristic
399C2×C11#288311yescharacteristic
400C2×C11#288911yescharacteristic
401D11—24no—
402D11—42no—
403C24—111no—
404C24—111no—
405C24C2×C4×D1111yescharacteristic
406#41—2216no—
407#41—2216no—
408C2×Q8—222no—
409C2×Q8—222no—
410C2×Q8—221no—
411C2×Q8—221no—
412C2×D4—114no—
413C2×D4—112no—
414C2×D4—112no—
415C2×D4—222no—
416C2×D4—222no—
417C2×D4—222no—
418C2×D4—222no—
419C2×D4—222no—
420C2×D4—222no—
421C2×D4—222no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—114no—
431C22×C4—114no—
432C22×C4—114no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—881no—
445C22×C4—881no—
446C22×C4—881no—
447C22×C4—881no—
448C22×C4—881no—
449C22×C4—881no—
450C22×C4C2×C4×D1111yescharacteristic
451C22×C4C2×C4×D1111yescharacteristic
452C22×C4C2×C4×D1111yescharacteristic
453C22×C4C2×C4×D1111yescharacteristic
454C22×C4C2×C4×D1111yescharacteristic
455C22×C4C23×D1111yescharacteristic
456M16—884no—
457C2×C8—24no—
458C2×C8—224no—
459C2×C8—884no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—112no—
463C4⋊C4—112no—
464C4⋊C4—222no—
465C4⋊C4—222no—
466C4⋊C4—222no—
467C4⋊C4—222no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—222no—
471C4⋊C4—222no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—114no—
475C22⋊C4—114no—
476C22⋊C4—222no—
477C22⋊C4—222no—
478C42—21no—
479C42—21no—
480C42—222no—
481C42—222no—
482C42—222no—
483C42—222no—
484C42D4×D1112yes—
485C42D4×D1112yes—
486C11#1736811yescharacteristic, complemented, Sylow
487C23—21no—
488C23—21no—
489C23—41no—
490C23—41no—
491C23—112no—
492C23—112no—
493C23—112no—
494C23—112no—
495C23—221no—
496C23—221no—
497C23—441no—
498C23—441no—
499C23—441no—
500C23—441no—
501C23M16×D1112yes—
502C23C22×C4×D1111yescharacteristic
503Q8—224no—
504Q8—224no—
505D4—224no—
506D4—224no—
507D4—228no—
508D4—228no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—112no—
522C2×C4—112no—
523C2×C4—112no—
524C2×C4—112no—
525C2×C4—228no—
526C2×C4—228no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—444no—
534C2×C4—444no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—882no—
540C2×C4—882no—
541C2×C4—882no—
542C2×C4—882no—
543C2×C4C22⋊C4×D1111yescharacteristic
544C2×C4C22⋊C4×D1111yescharacteristic
545C2×C4C22⋊C4×D1112yes—
546C2×C4M16×D1112yes—
547C2×C4C2×D4×D1112yes—
548C8—44no—
549C8—444no—
550C22—21no—
551C22—21no—
552C22—22no—
553C22—42no—
554C22—42no—
555C22—41no—
556C22—41no—
557C22—114no—
558C22—222no—
559C22—222no—
560C22—222no—
561C22—222no—
562C22—222no—
563C22—442no—
564C22—442no—
565C22—442no—
566C22—442no—
567C22C2×C22⋊C4×D1111yescharacteristic
568C22C2×M16×D1111yescharacteristic
569C22C2×M16×D1111yescharacteristic
570C4—22no—
571C4—21no—
572C4—21no—
573C4—22no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—222no—
578C4—222no—
579C4—222no—
580C4—222no—
581C4—441no—
582C4—441no—
583C2—21no—
584C2—21no—
585C2—42no—
586C2—224no—
587C2—442no—
588C2D11×#40711yescharacteristic
589C2#1307707511yescharacteristic
590C2#1307709711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1464C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4339C4
cosocleC22×C4×C11C24
hypercenter#1464D11
hypocenterC11#17368
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #13077644C2semidirect
3. #13066959C2semidirect
4. #13066951C2semidirect
5. #13066950C2semidirect
6. #13066944C2semidirect
7. #13066931C2semidirect
8. D11×#324C2semidirect
9. C11×#1464C2semidirect
127. C2×C22⋊D11M16semidirect
155. C2×C4×D11M16semidirect
197. #1464D11semidirect
486. C11#17368semidirect

Maximal subgroups

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

subgroupindex
C2×#106230542
#130776442
#130669592
#130669512
#130669502
#130669442
#130669312
D11×#3242
C11×#14642
#1736811