Finite Group Databasebeta

← #14719686

Subgroups — #14719686

Order 2816.

1210 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623077C211yesmaximal, characteristic
2#13077642C212yesmaximal, complemented
3#13066958C212yesmaximal, complemented
4#13066951C212yesmaximal, complemented
5#13066947C212yesmaximal, complemented
6#13066944C212yesmaximal, complemented
7#13066934C211yesmaximal, characteristic, complemented
8C2×#10622107C212yesmaximal, complemented
9C11×#1459C211yesmaximal, characteristic, complemented
10C22×#4341C411yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×D4×Dic11C411yescharacteristic
13C2×C4×C22⋊D11C411yescharacteristic
14C2×C4×C22⋊D11C2211yescharacteristic
15C22×Dic11⋊C4C411yescharacteristic
16C22×Dic11⋊C4C2211yescharacteristic
17#10623077—24no—
18#10623077—24no—
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×(C22⋊D11)⋊C4C411yescharacteristic
22C2×(C22⋊D11)⋊C4C2211yescharacteristic
23C2×#66930C411yescharacteristic
24C2×#66930C2211yescharacteristic
25C2×#66925C411yescharacteristic
26C2×C4×Dic22C411yescharacteristic
27C2×C11×C22⋊C8C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622724—24no—
30#10622343—24no—
31#10622339C2214yes—
32#10622332C2214yes—
33C11×#324C2212yes—
34C11×#323C2212yes—
35#10622166C2212yes—
36#10622163C2212yes—
37#10622107C2214yes—
38#10622107C2214yes—
39C22×D4×C11C2×C411yescharacteristic
40C23×C4×C11C2×C411yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11C2×C411yescharacteristic
43C22×C22⋊D11C2×C411yescharacteristic
44C23×Dic11C2×C411yescharacteristic
45C23×Dic11C2×C411yescharacteristic
46C23×Dic11C2×C411yescharacteristic
47C23×Dic11C2×C411yescharacteristic
48C2×#4341—24no—
49C2×#4341—24no—
50C2×#4341—24no—
51C22×C4×D11C2×C411yescharacteristic
52C22×C4×D11C2×C411yescharacteristic
53C22×C4×D11C2311yescharacteristic
54C22×Dic22C2×C411yescharacteristic
55C22×C8×C11—22no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4C2×C411yescharacteristic
60C2×C11×C22⋊C4C2311yescharacteristic
61C2×C42×C11C2×C411yescharacteristic
62C2×C22⋊Dic11C2×C411yescharacteristic
63C2×C22⋊Dic11C2×C411yescharacteristic
64D4×Dic11—24no—
65C4×C22⋊D11—22no—
66C4×C22⋊D11—22no—
67C4×C22⋊D11D414yes—
68C4×C22⋊D11D414yes—
69C2×(C2×D11)⋊C4C2×C411yescharacteristic
70C2×(C2×D11)⋊C4C2×C411yescharacteristic
71C2×C4⋊Dic11C2×C411yescharacteristic
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4C2×C411yescharacteristic
77C2×Dic11⋊C4C2×C411yescharacteristic
78C2×Dic11⋊C4C2×C411yescharacteristic
79C2×Dic11⋊C4C2×C411yescharacteristic
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×Dic11⋊C4C2311yescharacteristic
83C2×Dic11⋊C4C2311yescharacteristic
84C2×C4×Dic11C2×C411yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8—22no—
90C2×#4313—24no—
91C4⋊C4×D11—24no—
92#66940—24no—
93(C22⋊D11)⋊C4—24no—
94(C22⋊D11)⋊C4—24no—
95#66930—24no—
96#66930—24no—
97#66925—22no—
98#66925—22no—
99C4×Dic22—22no—
100C4×Dic22—22no—
101C11×C22⋊C8—22no—
102C11×C22⋊C8C2314yes—
103C22⋊(C11⋊C8)—22no—
104C22⋊(C11⋊C8)C2314yes—
105(C2×D11)⋊C8—24no—
106#66879—24no—
107Dic11⋊C8—24no—
108#17368—111nomaximal, Sylow
109C24×C11C22×C411yescharacteristic
110C24×C11C22×C411yescharacteristic
111C23×D11C22×C411yescharacteristic
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11M1614yescomplemented
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—81no—
118C22×C4×C11—81no—
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2411yescharacteristic
126C2×C22⋊D11—22no—
127C2×C22⋊D11—22no—
128C2×C22⋊D11—22no—
129C2×C22⋊D11—22no—
130C2×C22⋊D11—22no—
131C2×C22⋊D11C22⋊C414yes—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—81no—
140C22×Dic11—81no—
141C22×Dic11M1614yescomplemented
142C22×Dic11C22×C411yescharacteristic
143C22×Dic11C22×C411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C22×Dic11C22×C411yescharacteristic
148C22×Dic11C22×C411yescharacteristic
149#4341—232no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—81no—
155C2×C4×D11—81no—
156C2×C4×D11C2×D414yes—
157C2×Dic22—22no—
158C2×Dic22—22no—
159C2×Dic22—22no—
160C2×C8×C11—24no—
161C2×C8×C11—82no—
162C11×C4⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C42×C11—21no—
166C42×C11—21no—
167C22⋊Dic11—22no—
168C22⋊Dic11C22⋊C414yes—
169(C2×D11)⋊C4—22no—
170(C2×D11)⋊C4C22⋊C412yes—
171(C2×D11)⋊C4C22⋊C412yes—
172C4⋊Dic11—22no—
173Dic11⋊C4—22no—
174Dic11⋊C4—22no—
175Dic11⋊C4—22no—
176Dic11⋊C4—21no—
177Dic11⋊C4—21no—
178Dic11⋊C4—21no—
179Dic11⋊C4—21no—
180Dic11⋊C4—22no—
181Dic11⋊C4—22no—
182Dic11⋊C4C22⋊C412yes—
183Dic11⋊C4C22⋊C412yes—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11C2×D414yes—
189C2×C11⋊C8—24no—
190C2×C11⋊C8—82no—
191#4313—84no—
192C2×#520—111no—
193#2973—112no—
194#1467—112no—
195#1465—112no—
196#1464—112no—
197#1463—112no—
198#1459—111no—
199#1459D1111yescharacteristic, complemented
200C2×#324—112no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11C2×C22⋊C412yes—
208C23×C11C2×M1612yes—
209C23×C11C2×M1612yes—
210C23×C11C2×M1612yes—
211C23×C11C23×C411yescharacteristic
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11C2×C22⋊C412yes—
217D4×C11—28no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—81no—
229C2×C4×C11—81no—
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—28no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—28no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—82no—
251C2×Dic11—82no—
252C2×Dic11C2×C22⋊C412yes—
253C2×Dic11C2×C22⋊C412yes—
254C2×Dic11C2×C22⋊C412yes—
255C2×Dic11C2×M1612yes—
256C2×Dic11C2×M1612yes—
257C4×D11—28no—
258C4×D11—44no—
259C4×D11—82no—
260Dic22—28no—
261C8×C11—44no—
262C11⋊C8—44no—
263C22×#41—111no—
264#520—224no—
265#520—224no—
266C2×C4×Q8—111no—
267C2×C4×Q8—111no—
268C2×C4×D4—111no—
269C2×C4×D4—111no—
270C2×C4×D4—111no—
271C2×C4×D4—111no—
272C2×C4×D4—111no—
273C2×C4×D4C2×D1111yescharacteristic
274C2×#117—111no—
275C2×#117—111no—
276C2×#117—111no—
277C22×C4⋊C4—111no—
278C22×C4⋊C4—111no—
279C22×C4⋊C4—111no—
280#435—224no—
281#435—224no—
282#432—114no—
283#407—114no—
284C2×C22⋊C8—112no—
285C2×C22⋊C8C2×D1112yes—
286#324—112no—
287#324—114no—
288#324—114no—
289#324C2×D1112yes—
290#323—112no—
291#323C2×D1112yes—
292C22×C11—21no—
293C22×C11—22no—
294C22×C11—21no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11#40714yes—
304C22×C11C22×C22⋊C411yescharacteristic
305C22×C11C22×M1611yescharacteristic
306C22×C11C22×M1611yescharacteristic
307C2×D11—22no—
308C2×D11—22no—
309C2×D11—22no—
310C2×D11—42no—
311C2×D11—42no—
312C4×C11—22no—
313C4×C11—21no—
314C4×C11—21no—
315C4×C11—22no—
316C4×C11—41no—
317C4×C11—41no—
318Dic11—22no—
319Dic11—22no—
320Dic11—22no—
321Dic11—22no—
322Dic11—22no—
323Dic11—41no—
324Dic11—41no—
325C2×#41—224no—
326C2×#41—224no—
327C2×#41—224no—
328C22×Q8—111no—
329C22×D4—111no—
330C22×D4—111no—
331C22×D4C4×D1111yescharacteristic
332C23×C4—111no—
333C23×C4—111no—
334C23×C4—111no—
335C23×C4—111no—
336C23×C4—111no—
337C23×C4—111no—
338C23×C4—111no—
339C23×C4C4×D1111yescharacteristic
340C23×C4C22×D1111yescharacteristic
341C2×M16—224no—
342C22×C8—22no—
343C22×C8—222no—
344C4×Q8—222no—
345C4×Q8—222no—
346C4×Q8—224no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—114no—
350C4×D4—114no—
351C4×D4—224no—
352C4×D4—224no—
353C4×D4—222no—
354C4×D4—222no—
355C4×D4—224no—
356#117—222no—
357#117—222no—
358#117—224no—
359#117—224no—
360C2×C4⋊C4—111no—
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—222no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—222no—
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×C42—111no—
386C2×C42C4×D1111yescharacteristic
387C4⋊C8—224no—
388C22⋊C8—22no—
389C22⋊C8—114no—
390C22⋊C8—224no—
391C22⋊C8—222no—
392C22⋊C8C22×D1114yes—
393#97—224no—
394C2×C11—21no—
395C2×C11—21no—
396C2×C11—24no—
397C2×C11—42no—
398C2×C11C2×#40711yescharacteristic
399C2×C11#288311yescharacteristic
400C2×C11#288911yescharacteristic
401D11—42no—
402C24—111no—
403C24C2×C4×D1111yescharacteristic
404C24C2×C4×D1111yescharacteristic
405#41—2232no—
406C2×Q8—222no—
407C2×Q8—222no—
408C2×Q8—222no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—114no—
412C2×D4—222no—
413C2×D4—222no—
414C2×D4—222no—
415C2×D4—222no—
416C2×D4—222no—
417C2×D4#431314yescomplemented
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—81no—
421C22×C4—81no—
422C22×C4—114no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—114no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—881no—
443C22×C4—881no—
444C22×C4—881no—
445C22×C4—881no—
446C22×C4C2×C4×D1111yescharacteristic
447C22×C4C2×C4×D1111yescharacteristic
448C22×C4C2×C4×D1111yescharacteristic
449C22×C4C2×C4×D1111yescharacteristic
450C22×C4D4×D1112yes—
451C22×C4D4×D1112yes—
452C22×C4C23×D1111yescharacteristic
453M16—884no—
454C2×C8—24no—
455C2×C8—82no—
456C2×C8—224no—
457C2×C8—882no—
458C4⋊C4—22no—
459C4⋊C4—112no—
460C4⋊C4—112no—
461C4⋊C4—222no—
462C4⋊C4—222no—
463C4⋊C4—222no—
464C4⋊C4—222no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—222no—
470C4⋊C4—222no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—114no—
474C22⋊C4—112no—
475C22⋊C4—112no—
476C22⋊C4—222no—
477C22⋊C4—222no—
478C42—21no—
479C42—21no—
480C42—114no—
481C42—222no—
482C42—222no—
483C42—222no—
484C42—222no—
485C11#1736811yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—112no—
493C23—221no—
494C23—221no—
495C23—441no—
496C23—441no—
497C23C22⋊C4×D1112yes—
498C23C2×#431312yes—
499C23C2×#431312yes—
500C23M16×D1112yes—
501C23C22×C4×D1111yescharacteristic
502Q8—228no—
503D4—28no—
504D4—228no—
505D4—228no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4—112no—
519C2×C4—112no—
520C2×C4—112no—
521C2×C4—112no—
522C2×C4—112no—
523C2×C4—228no—
524C2×C4—228no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—228no—
532C2×C4—221no—
533C2×C4—221no—
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×C4C22⋊C4×D1111yescharacteristic
543C2×C4C22⋊C4×D1111yescharacteristic
544C2×C4C2×#431312yes—
545C2×C4C2×D4×D1112yes—
546C8—44no—
547C8—444no—
548C22—21no—
549C22—22no—
550C22—21no—
551C22—22no—
552C22—22no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—41no—
558C22—41no—
559C22—222no—
560C22—222no—
561C22—222no—
562C22—442no—
563C22—442no—
564C22#1062233914yes—
565C22C2×C22⋊C4×D1111yescharacteristic
566C22C22×#431311yescharacteristic
567C22C2×M16×D1111yescharacteristic
568C4—22no—
569C4—22no—
570C4—21no—
571C4—21no—
572C4—41no—
573C4—41no—
574C4—222no—
575C4—222no—
576C4—222no—
577C4—222no—
578C4—222no—
579C4—441no—
580C4—441no—
581C2—21no—
582C2—21no—
583C2—24no—
584C2—42no—
585C2—442no—
586C2C2×#1062233911yescharacteristic
587C2#1307707411yescharacteristic
588C2#1307709711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1459C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4341C4
cosocleC22×C4×C11C24
hypercenter#1459D11
hypocenterC11#17368
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #13077642C2semidirect
3. #13066958C2semidirect
4. #13066951C2semidirect
5. #13066947C2semidirect
6. #13066944C2semidirect
7. #13066934C2semidirect
8. C2×#10622107C2semidirect
9. C11×#1459C2semidirect
114. C2×D4×C11M16semidirect
141. C22×Dic11M16semidirect
199. #1459D11semidirect
417. C2×D4#4313semidirect
485. C11#17368semidirect

Maximal subgroups

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

subgroupindex
C2×#106230772
#130776422
#130669582
#130669512
#130669472
#130669442
#130669342
C2×#106221072
C11×#14592
#1736811