Finite Group Databasebeta

← #14719841

Subgroups — #14719841

Order 2816.

1450 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic
2D11×#407C212yesmaximal, complemented
3#13066963C218yesmaximal, complemented
4#13066946C211yesmaximal, characteristic, complemented
5#13066942C212yesmaximal, complemented
6C11×#1463C211yesmaximal, characteristic, complemented
7C23×D44C411yescharacteristic
8C23×C4×D11C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×(C2×D11)⋊C4C411yescharacteristic
11C22×(C2×D11)⋊C4C411yescharacteristic
12C22×(C2×D11)⋊C4C2211yescharacteristic
13C22×Dic11⋊C4C411yescharacteristic
14C2×M16×D11—22no—
15C2×#66947—22no—
16C2×#66947—22no—
17C2×#66947—22no—
18C2×#66947—22no—
19C2×#66947C414yes—
20C2×#66947C2214yes—
21C11×#407C2212yes—
22#10622820C2212yes—
23#10622739—22no—
24#10622339—22no—
25#10622339C2214yescomplemented
26D11×C22⋊C8—22no—
27D11×C22⋊C8C2214yescomplemented
28C11×#324C2214yescomplemented
29#10622166C2214yescomplemented
30#10622106C2218yescomplemented
31C24×D11C2×C411yescharacteristic
32C24×D11C2×C411yescharacteristic
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×Dic11C2×C411yescharacteristic
37C23×Dic11C2×C411yescharacteristic
38C22×D44—22no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44—44no—
42C22×D44C2×C414yes—
43C22×C4×D11—44no—
44C22×C4×D11C2×C412yes—
45C22×C4×D11D412yes—
46C22×C4×D11D412yes—
47C22×C4×D11D412yes—
48C22×C4×D11D412yes—
49C22×C4×D11C2312yes—
50C2×C11×M16—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2×C412yes—
54C2×C11×C4⋊C4C2312yes—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4C2×C412yes—
64C2×(C2×D11)⋊C4C2×C414yes—
65C2×(C2×D11)⋊C4C2×C414yes—
66C2×(C2×D11)⋊C4C2312yes—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4C2×C414yes—
71C2×#4318—22no—
72M16×D11—48no—
73C2×#4313—24no—
74C2×C8×D11—24no—
75#66947—24no—
76#66947—24no—
77#66947—24no—
78#66947—24no—
79#66947—24no—
80#66947—24no—
81#66947—24no—
82#66947—24no—
83C11×C22⋊C8—22no—
84C11×C22⋊C8C2314yes—
85C22⋊(C11⋊C8)—22no—
86C22⋊(C11⋊C8)C2314yes—
87(C2×D11)⋊C8—24no—
88(C2×D11)⋊C8—24no—
89#17392—111nomaximal, Sylow
90C24×C11C22×C411yescharacteristic
91C23×D11—24no—
92C23×D11—21no—
93C23×D11—21no—
94C23×D11—42no—
95C23×D11—42no—
96C23×D11—42no—
97C23×D11—42no—
98C23×D11—42no—
99C23×D11C22⋊C412yes—
100C23×D11C22⋊C411yescharacteristic
101C23×D11C22⋊C411yescharacteristic
102C23×D11C22×C412yes—
103C23×D11C22×C412yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11—42no—
120C22×Dic11—42no—
121C22×Dic11C22⋊C412yes—
122C22×Dic11C22⋊C411yescharacteristic
123C22×Dic11C22⋊C411yescharacteristic
124C22×Dic11C22×C412yes—
125C22×Dic11C22×C412yes—
126C2×D44—24no—
127C2×D44—24no—
128C2×D44—48no—
129C2×D44—48no—
130C2×D44—44no—
131C2×D44—44no—
132C2×C4×D11—28no—
133C2×C4×D11—44no—
134C2×C4×D11—44no—
135C2×C4×D11—44no—
136C2×C4×D11—44no—
137C2×C4×D11—44no—
138C2×C4×D11C22⋊C412yes—
139C2×C4×D11C22⋊C412yes—
140C2×C4×D11C22⋊C412yes—
141C2×C4×D11C22⋊C412yes—
142C2×C4×D11C2×D412yes—
143C2×C4×D11C2×D412yes—
144C2×C4×D11C2×D412yes—
145C2×C4×D11C2×D412yes—
146C11×M16—44no—
147C2×C8×C11—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—24no—
150(C2×D11)⋊C4—24no—
151(C2×D11)⋊C4—24no—
152(C2×D11)⋊C4—24no—
153(C2×D11)⋊C4—24no—
154(C2×D11)⋊C4—24no—
155(C2×D11)⋊C4—24no—
156Dic11⋊C4—24no—
157Dic11⋊C4—24no—
158#4318—44no—
159C2×C11⋊C8—24no—
160#4313—48no—
161C8×D11—48no—
162C22×#123—111no—
163C2×#407—112no—
164#1468—118no—
165#1463—111no—
166#1463D1111yescharacteristic, complemented
167#1462—112no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11C2×C22⋊C411yescharacteristic
172C23×C11C2×C22⋊C411yescharacteristic
173C23×C11C23×C411yescharacteristic
174C22×D11—24no—
175C22×D11—22no—
176C22×D11—24no—
177C22×D11—24no—
178C22×D11—24no—
179C22×D11—22no—
180C22×D11—24no—
181C22×D11—41no—
182C22×D11—42no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—42no—
187C22×D11—416no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—88no—
197C22×D11#9914yes—
198C22×D11C2×C22⋊C412yes—
199C22×D11C2×C22⋊C412yes—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11C2×C22⋊C412yes—
213C2×C4×C11C22×D412yes—
214C2×Dic11—24no—
215C2×Dic11—22no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11C2×C22⋊C412yes—
223C2×Dic11C2×C22⋊C412yes—
224D44—48no—
225D44—48no—
226C4×D11—24no—
227C4×D11—24no—
228C4×D11—24no—
229C4×D11—24no—
230C4×D11—42no—
231C4×D11—42no—
232C4×D11—42no—
233C4×D11—42no—
234C8×C11—44no—
235C11⋊C8—44no—
236C23×D4—111no—
237C24×C4—111no—
238C22×M16—222no—
239C2×#123—114no—
240C2×#123—114no—
241C2×#123—222no—
242C2×#123—222no—
243C2×#123—222no—
244C2×#123—222no—
245C22×C4⋊C4—111no—
246C22×C4⋊C4C2×D1111yescharacteristic
247C22×C22⋊C4—111no—
248C22×C22⋊C4—111no—
249C22×C22⋊C4—111no—
250#407—112no—
251#407—114no—
252#407—222no—
253#407—222no—
254#407C2×D1112yes—
255C2×C22⋊C8—114no—
256C2×C22⋊C8—222no—
257#324—114no—
258#324C2×D1114yescomplemented
259#323—118no—
260C22×C11—28no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11C2×#9912yes—
268C22×C11#41312yes—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11#56812yes—
271C2×D11—22no—
272C2×D11—22no—
273C2×D11—22no—
274C2×D11—22no—
275C2×D11—22no—
276C2×D11—44no—
277C2×D11—48no—
278C2×D11—48no—
279C2×D11—44no—
280C2×D11—42no—
281C2×D11—42no—
282C2×D11—42no—
283C2×D11—84no—
284C2×D11—84no—
285C2×D11—84no—
286C2×D11C2×#9914yes—
287C4×C11—22no—
288C4×C11—22no—
289C4×C11—42no—
290C4×C11—42no—
291Dic11—22no—
292Dic11—22no—
293Dic11—42no—
294C25—111no—
295C25—111no—
296C22×D4—114no—
297C22×D4—221no—
298C22×D4—222no—
299C22×D4—221no—
300C22×D4—444no—
301C23×C4—111no—
302C23×C4—112no—
303C23×C4—112no—
304C23×C4—112no—
305C23×C4—112no—
306C23×C4—112no—
307C23×C4—112no—
308C23×C4—111no—
309C23×C4—444no—
310C23×C4C4×D1111yescharacteristic
311C23×C4C4×D1111yescharacteristic
312C23×C4C22×D1111yescharacteristic
313C2×M16—22no—
314C2×M16—224no—
315C2×M16—222no—
316C2×M16—448no—
317C22×C8—224no—
318#123—224no—
319#123—224no—
320#123—224no—
321#123—224no—
322#123—224no—
323#123—224no—
324#123—224no—
325#123—224no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—114no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4C4×D1112yes—
333C2×C4⋊C4C22×D1112yes—
334C2×C22⋊C4—114no—
335C2×C22⋊C4—114no—
336C2×C22⋊C4—112no—
337C2×C22⋊C4—112no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—221no—
340C2×C22⋊C4—221no—
341C2×C22⋊C4—221no—
342C2×C22⋊C4—222no—
343C2×C22⋊C4—221no—
344C2×C22⋊C4—222no—
345C2×C22⋊C4—222no—
346C22⋊C8—22no—
347C22⋊C8—114no—
348C22⋊C8—224no—
349C22⋊C8—224no—
350C22⋊C8—222no—
351C22⋊C8C22×D1114yes—
352C2×C11—22no—
353C2×C11—22no—
354C2×C11—22no—
355C2×C11#287911yescharacteristic
356C2×C11C22×#9911yescharacteristic
357C2×C11C2×#41311yescharacteristic
358D11—24no—
359D11—42no—
360D11—82no—
361C24—111no—
362C24—112no—
363C24—112no—
364C24—111no—
365C24—112no—
366C24—224no—
367C24—221no—
368C24—221no—
369C24—442no—
370C24—442no—
371C24—442no—
372C24—442no—
373C24—442no—
374C24C2×C4×D1111yescharacteristic
375C2×D4—224no—
376C2×D4—224no—
377C2×D4—444no—
378C2×D4—448no—
379C2×D4—444no—
380C2×D4—448no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—112no—
389C22×C4—111no—
390C22×C4—111no—
391C22×C4—112no—
392C22×C4—112no—
393C22×C4—112no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—112no—
397C22×C4—112no—
398C22×C4—112no—
399C22×C4—112no—
400C22×C4—112no—
401C22×C4—228no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—444no—
405C22×C4—444no—
406C22×C4—444no—
407C22×C4—444no—
408C22×C4—444no—
409C22×C4—442no—
410C22×C4—442no—
411C22×C4C2×C4×D1112yes—
412C22×C4C2×C4×D1112yes—
413C22×C4C2×C4×D1111yescharacteristic
414C22×C4D4×D1112yes—
415C22×C4D4×D1112yes—
416C22×C4C23×D1111yescharacteristic
417M16—44no—
418M16—448no—
419M16—444no—
420C2×C8—24no—
421C2×C8—224no—
422C2×C8—448no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—224no—
426C4⋊C4—224no—
427C22⋊C4—224no—
428C22⋊C4—224no—
429C22⋊C4—224no—
430C22⋊C4—224no—
431C22⋊C4—224no—
432C22⋊C4—224no—
433C11#1739211yescharacteristic, complemented, Sylow
434C23—22no—
435C23—22no—
436C23—22no—
437C23—112no—
438C23—114no—
439C23—112no—
440C23—224no—
441C23—224no—
442C23—224no—
443C23—222no—
444C23—224no—
445C23—222no—
446C23—224no—
447C23—441no—
448C23—442no—
449C23—441no—
450C23—441no—
451C23—441no—
452C23—442no—
453C23—4416no—
454C23—442no—
455C23—442no—
456C23—442no—
457C23—442no—
458C23—442no—
459C23—442no—
460C23—442no—
461C23—442no—
462C23—888no—
463C23C22⋊C4×D1111yescharacteristic
464C23C22⋊C4×D1111yescharacteristic
465C23C22×C4×D1111yescharacteristic
466D4—448no—
467D4—448no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—112no—
481C2×C4—112no—
482C2×C4—224no—
483C2×C4—224no—
484C2×C4—224no—
485C2×C4—224no—
486C2×C4—224no—
487C2×C4—222no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4C22⋊C4×D1112yes—
499C2×C4C2×D4×D1112yes—
500C8—44no—
501C8—444no—
502C22—28no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—114no—
510C22—222no—
511C22—222no—
512C22—222no—
513C22—222no—
514C22—222no—
515C22—444no—
516C22—448no—
517C22—448no—
518C22—444no—
519C22—442no—
520C22—442no—
521C22—442no—
522C22—884no—
523C22—884no—
524C22—884no—
525C22D11×#9912yes—
526C22#1062236412yes—
527C22C2×C22⋊C4×D1111yescharacteristic
528C22#1062327612yes—
529C4—22no—
530C4—22no—
531C4—42no—
532C4—42no—
533C4—222no—
534C4—222no—
535C4—442no—
536C2—22no—
537C2—22no—
538C2—22no—
539C2—224no—
540C2—442no—
541C2—882no—
542C2#1307705911yescharacteristic
543C2C2×D11×#9911yescharacteristic
544C2C2×#1062236411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1463C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D44C4
cosocleC22×C4×C11C24
hypercenter#1463D11
hypocenterC11#17392
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. D11×#407C2semidirect
3. #13066963C2semidirect
4. #13066946C2semidirect
5. #13066942C2semidirect
6. C11×#1463C2semidirect
25. #10622339C22semidirect
27. D11×C22⋊C8C22semidirect
28. C11×#324C22semidirect
29. #10622166C22semidirect
30. #10622106C22semidirect
166. #1463D11semidirect
258. #324C2×D11semidirect
433. C11#17392semidirect

Maximal subgroups

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

subgroupindex
C22×#669472
D11×#4072
#130669632
#130669462
#130669422
C11×#14632
#1739211