Finite Group Databasebeta

← #14719710

Subgroups — #14719710

Order 2816.

1174 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
1C2×#10623077C211yesmaximal, characteristic
2#13077700C212yesmaximal, complemented
3#13066957C211yesmaximal, characteristic, complemented
4#13066955C212yesmaximal, complemented
5#13066948C212yesmaximal, complemented
6#13066947C212yesmaximal, complemented
7#13066935C212yesmaximal, complemented
8#13066927C212yesmaximal, complemented
9C11×#1466C211yesmaximal, characteristic, complemented
10C22×#4341C411yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×D4×Dic11C411yescharacteristic
13C2×C4×C22⋊D11C411yescharacteristic
14C2×C4×C22⋊D11C411yescharacteristic
15C22×Dic11⋊C4C411yescharacteristic
16C22×Dic11⋊C4C411yescharacteristic
17#10623077—24no—
18#10623077—24no—
19C2×C4⋊C4×D11C411yescharacteristic
20C2×#66940C411yescharacteristic
21C2×(C22⋊D11)⋊C4C2211yescharacteristic
22C2×(C22⋊D11)⋊C4C2211yescharacteristic
23C2×#66930C2211yescharacteristic
24C2×#66930C2211yescharacteristic
25C2×#66925C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C11×#432C2212yes—
28#10622539C2212yes—
29#10622441—24no—
30#10622332C2214yes—
31#10622331C2214yes—
32#10622314—24no—
33C11×#323C2212yes—
34C11×#323C2212yes—
35#10622163C2212yes—
36#10622163C2212yes—
37#10622107C2214yes—
38#10622106C2214yes—
39C22×D4×C11C2×C411yescharacteristic
40C23×C4×C11C2×C411yescharacteristic
41C23×C4×C11C2×C411yescharacteristic
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×D11C2×C411yescharacteristic
54C22×Dic22C2×C411yescharacteristic
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C2×C11×C4⋊C4C2×C411yescharacteristic
58C2×C11×C22⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4C2311yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11C2×C411yescharacteristic
62C2×C22⋊Dic11C2×C411yescharacteristic
63D4×Dic11—24no—
64C4×C22⋊D11—22no—
65C4×C22⋊D11—22no—
66C4×C22⋊D11—22no—
67C4×C22⋊D11—22no—
68C2×(C2×D11)⋊C4C2×C411yescharacteristic
69C2×(C2×D11)⋊C4C2311yescharacteristic
70C2×C4⋊Dic11C2×C411yescharacteristic
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4C2×C411yescharacteristic
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×C4×Dic11C2×C411yescharacteristic
84C2×C4×Dic11C2×C411yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C4⋊C4×D11—24no—
89#66940—24no—
90(C22⋊D11)⋊C4—24no—
91(C22⋊D11)⋊C4—24no—
92#66930—24no—
93#66930—24no—
94#66925—22no—
95#66925—22no—
96C4×Dic22D414yes—
97C4×Dic22D414yes—
98C11×C4⋊C8—22no—
99C11×C22⋊C8C2314yes—
100C11×#97—22no—
101C22⋊(C11⋊C8)C2314yes—
102#66879—24no—
103Dic11⋊C8—24no—
104Dic11⋊C8—24no—
105C8×Dic11—24no—
106C4⋊(C11⋊C8)—22no—
107#66867—22no—
108#17372—111nomaximal, Sylow
109C24×C11C22×C411yescharacteristic
110C24×C11C22×C411yescharacteristic
111C23×D11C22×C411yescharacteristic
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—81no—
120C22×C4×C11—81no—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C411yescharacteristic
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⋊D11M1614yes—
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×Dic11M1614yes—
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—22no—
155C2×C4×D11—81no—
156C2×C4×D11—81no—
157C2×Dic22—22no—
158C2×Dic22—22no—
159C2×Dic22C22⋊C414yes—
160C2×C8×C11—24no—
161C11×C4⋊C4—22no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C42×C11C2×D412yes—
165C42×C11C2×D412yes—
166C22⋊Dic11—22no—
167C22⋊Dic11—22no—
168(C2×D11)⋊C4—21no—
169(C2×D11)⋊C4—21no—
170(C2×D11)⋊C4—22no—
171C4⋊Dic11C22⋊C414yes—
172Dic11⋊C4—22no—
173Dic11⋊C4—22no—
174Dic11⋊C4—22no—
175Dic11⋊C4—22no—
176Dic11⋊C4—21no—
177Dic11⋊C4—21no—
178Dic11⋊C4—22no—
179Dic11⋊C4C22⋊C412yes—
180Dic11⋊C4C22⋊C412yes—
181Dic11⋊C4C22⋊C412yes—
182Dic11⋊C4C22⋊C412yes—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11C2×D414yes—
187C4×Dic11C2×D414yes—
188C2×C11⋊C8—24no—
189C2×#520—111no—
190#2983—112no—
191#1466—112no—
192#1466—111no—
193#1466D1111yescharacteristic, complemented
194#1464—112no—
195#1464—112no—
196#1460—112no—
197#1458—112no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11C2×M1612yes—
207C23×C11C2×M1612yes—
208C23×C11C23×C411yescharacteristic
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11C2×M1612yes—
214D4×C11—28no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—81no—
224C2×C4×C11—81no—
225C2×C4×C11—81no—
226C2×C4×C11—81no—
227C2×C4×C11C2×C22⋊C412yes—
228C2×C4×C11C2×C22⋊C411yescharacteristic
229C2×C4×C11C2×C22⋊C411yescharacteristic
230C2×C4×C11C22×D412yes—
231C22⋊D11—28no—
232C22⋊D11—28no—
233C2×Dic11—28no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—28no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—82no—
246C2×Dic11—82no—
247C2×Dic11C2×C22⋊C412yes—
248C2×Dic11C2×C22⋊C412yes—
249C2×Dic11C2×C22⋊C412yes—
250C2×Dic11C2×C22⋊C412yes—
251C2×Dic11C2×M1612yes—
252C2×Dic11C2×M1612yes—
253C2×Dic11C2×M1612yes—
254C4×D11—28no—
255C4×D11—82no—
256C4×D11—82no—
257Dic22—28no—
258C8×C11—44no—
259C11⋊C8—44no—
260C22×#41—111no—
261#520—224no—
262#520—224no—
263C2×C4×Q8—111no—
264C2×C4×Q8—111no—
265C2×C4×D4—111no—
266C2×C4×D4—111no—
267C2×C4×D4—111no—
268C2×C4×D4—111no—
269C2×C4×D4—111no—
270C2×C4×D4C2×D1111yescharacteristic
271C2×#117—111no—
272C2×#117—111no—
273C2×#117—111no—
274C22×C4⋊C4—111no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4—111no—
277#446—224no—
278#446—224no—
279#432—112no—
280#432—114no—
281#432C2×D1112yes—
282#431—114no—
283#324—114no—
284#323—112no—
285#323—112no—
286#323—114no—
287#323C2×D1112yes—
288#323C2×D1112yes—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11C22×C22⋊C411yescharacteristic
302C22×C11C22×M1611yescharacteristic
303C22×C11C22×M1611yescharacteristic
304C2×D11—22no—
305C2×D11—42no—
306C2×D11—41no—
307C2×D11—41no—
308C2×D11—42no—
309C4×C11—22no—
310C4×C11—22no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—41no—
314C4×C11—41no—
315Dic11—22no—
316Dic11—22no—
317Dic11—22no—
318Dic11—22no—
319Dic11—41no—
320Dic11—41no—
321Dic11#40714yes—
322C2×#41—224no—
323C2×#41—224no—
324C2×#41—224no—
325C22×Q8—111no—
326C22×D4—111no—
327C22×D4—111no—
328C22×D4C4×D1111yescharacteristic
329C23×C4—111no—
330C23×C4—111no—
331C23×C4—111no—
332C23×C4—111no—
333C23×C4—111no—
334C23×C4—111no—
335C23×C4—111no—
336C23×C4C4×D1111yescharacteristic
337C23×C4C4×D1111yescharacteristic
338C4×Q8—114no—
339C4×Q8—114no—
340C4×Q8—224no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—224no—
344C4×D4—224no—
345C4×D4—222no—
346C4×D4—222no—
347C4×D4—222no—
348C4×D4—222no—
349C4×D4—224no—
350#117—224no—
351#117—224no—
352#117—222no—
353#117—222no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—224no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4C4×D1111yescharacteristic
369C2×C22⋊C4—111no—
370C2×C22⋊C4—111no—
371C2×C22⋊C4—111no—
372C2×C22⋊C4—111no—
373C2×C22⋊C4C22×D1111yescharacteristic
374C2×C22⋊C4C22×D1111yescharacteristic
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42C22×D1111yescharacteristic
381C4⋊C8—22no—
382C4⋊C8—224no—
383C4⋊C8—224no—
384C4⋊C8—222no—
385C22⋊C8—114no—
386C22⋊C8C22×D1114yes—
387#97—22no—
388#97—224no—
389#97—222no—
390C4×C8—224no—
391C2×C11—21no—
392C2×C11—21no—
393C2×C11—42no—
394C2×C11—42no—
395C2×C11C2×#40711yescharacteristic
396C2×C11#288411yescharacteristic
397C2×C11#288811yescharacteristic
398D11—42no—
399C24—111no—
400C24C2×C4×D1111yescharacteristic
401C24C2×C4×D1111yescharacteristic
402#41—2232no—
403C2×Q8—114no—
404C2×Q8—222no—
405C2×Q8—222no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—114no—
410C2×D4—222no—
411C2×D4—222no—
412C2×D4—222no—
413C2×D4—222no—
414C2×D4—222no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—81no—
420C22×C4—81no—
421C22×C4—111no—
422C22×C4—114no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—222no—
430C22×C4—222no—
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—881no—
442C22×C4—881no—
443C22×C4—881no—
444C22×C4—881no—
445C22×C4C2×C4×D1111yescharacteristic
446C22×C4C2×C4×D1111yescharacteristic
447C22×C4C2×C4×D1111yescharacteristic
448C22×C4C2×C4×D1111yescharacteristic
449C22×C4C23×D1111yescharacteristic
450C2×C8—24no—
451C2×C8—224no—
452C4⋊C4—22no—
453C4⋊C4—112no—
454C4⋊C4—112no—
455C4⋊C4—112no—
456C4⋊C4—112no—
457C4⋊C4—114no—
458C4⋊C4—222no—
459C4⋊C4—222no—
460C4⋊C4—222no—
461C4⋊C4—222no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—222no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—222no—
468C22⋊C4—222no—
469C22⋊C4—221no—
470C22⋊C4—221no—
471C22⋊C4—222no—
472C42—114no—
473C42—114no—
474C42—222no—
475C42—222no—
476C42—222no—
477C42D4×D1112yes—
478C42D4×D1112yes—
479C11#1737211yescharacteristic, complemented, Sylow
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—112no—
489C23—221no—
490C23—221no—
491C23—441no—
492C23—441no—
493C23M16×D1112yes—
494C23M16×D1112yes—
495C23C22×C4×D1111yescharacteristic
496Q8—228no—
497D4—28no—
498D4—228no—
499D4—228no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—81no—
512C2×C4—112no—
513C2×C4—112no—
514C2×C4—112no—
515C2×C4—112no—
516C2×C4—112no—
517C2×C4—112no—
518C2×C4—112no—
519C2×C4—228no—
520C2×C4—228no—
521C2×C4—228no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—882no—
533C2×C4—882no—
534C2×C4—882no—
535C2×C4—882no—
536C2×C4C22⋊C4×D1112yes—
537C2×C4C22⋊C4×D1111yescharacteristic
538C2×C4C22⋊C4×D1111yescharacteristic
539C2×C4C2×D4×D1112yes—
540C8—44no—
541C8—444no—
542C22—21no—
543C22—21no—
544C22—22no—
545C22—22no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—222no—
555C22—442no—
556C22—442no—
557C22—441no—
558C22—441no—
559C22C2×C22⋊C4×D1111yescharacteristic
560C22C2×M16×D1111yescharacteristic
561C22C2×M16×D1111yescharacteristic
562C4—22no—
563C4—22no—
564C4—21no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—114no—
569C4—222no—
570C4—222no—
571C4—222no—
572C4—222no—
573C4—441no—
574C4—441no—
575C2—21no—
576C2—21no—
577C2—42no—
578C2—42no—
579C2—442no—
580C2D11×#40711yescharacteristic
581C2#1307707811yescharacteristic
582C2#1307709211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1466C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4341C4
cosocleC22×C4×C11C24
hypercenter#1466D11
hypocenterC11#17372
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. #13077700C2semidirect
3. #13066957C2semidirect
4. #13066955C2semidirect
5. #13066948C2semidirect
6. #13066947C2semidirect
7. #13066935C2semidirect
8. #13066927C2semidirect
9. C11×#1466C2semidirect
193. #1466D11semidirect
479. C11#17372semidirect

Maximal subgroups

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

subgroupindex
C2×#106230772
#130777002
#130669572
#130669552
#130669482
#130669472
#130669352
#130669272
C11×#14662
#1737211