Finite Group Databasebeta

← #14719658

Subgroups — #14719658

Order 2816.

1646 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic
2#13077244C212yesmaximal, complemented
3#13066955C214yesmaximal, complemented
4#13066941C214yesmaximal, complemented
5#13066937C211yesmaximal, characteristic, complemented
6#13066936C212yesmaximal, complemented
7C11×#1460C211yesmaximal, characteristic, complemented
8C22×D4×D11C411yescharacteristic
9C23×C4×D11C412yes—
10C2×C4×D4×C11C2211yescharacteristic
11C2×D4×Dic11C411yescharacteristic
12C2×C4×C22⋊D11C412yes—
13C4×D4×D11—22no—
14C4×D4×D11—22no—
15C4×D4×D11—22no—
16C4×D4×D11—22no—
17C2×#66946C411yescharacteristic
18C2×C4⋊C4×D11C411yescharacteristic
19C2×(C22⋊D11)⋊C4C2212yes—
20C2×C22⋊C4×D11C2212yes—
21C2×C4×D44C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C11×#431C2212yescomplemented
24#10622538C2212yescomplemented
25#10622450—22no—
26#10622448—22no—
27#10622339C2214yes—
28#10622332C2214yescomplemented
29C4×#4313—22no—
30#10622298—22no—
31C11×#323C2214yescomplemented
32#10622163C2214yescomplemented
33#10622106C2218yescomplemented
34C24×D11C2×C412yes—
35C22×D4×C11C2×C411yescharacteristic
36C23×C4×C11C2×C412yes—
37C22×C22⋊D11C2×C412yes—
38C23×Dic11C2×C412yes—
39C2×D4×D11—24no—
40C2×D4×D11—24no—
41C2×D4×D11—22no—
42C2×D4×D11—22no—
43C22×D44C2×C411yescharacteristic
44C22×C4×D11—22no—
45C22×C4×D11—22no—
46C22×C4×D11—22no—
47C22×C4×D11—22no—
48C22×C4×D11—48no—
49C22×C4×D11C2×C411yescharacteristic
50C22×C4×D11C2×C411yescharacteristic
51C22×C4×D11C2×C412yes—
52C22×C4×D11C2×C412yes—
53C22×C4×D11C2×C412yes—
54C22×C4×D11C2311yescharacteristic
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C2×C11×C4⋊C4C2×C411yescharacteristic
58C2×C11×C22⋊C4C2312yes—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11C2×C412yes—
61D4×Dic11—22no—
62D4×Dic11—22no—
63C4×C22⋊D11—24no—
64C4×C22⋊D11—24no—
65C2×(C2×D11)⋊C4C2×C412yes—
66C2×(C2×D11)⋊C4C2312yes—
67C2×C4⋊Dic11C2×C411yescharacteristic
68C2×Dic11⋊C4C2×C412yes—
69C2×C4×Dic11C2×C411yescharacteristic
70C2×C4×Dic11C2×C411yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C2×#4313—24no—
73#66946—22no—
74#66946—22no—
75C4⋊C4×D11—22no—
76C4⋊C4×D11—22no—
77(C22⋊D11)⋊C4—24no—
78(C22⋊D11)⋊C4—24no—
79C22⋊C4×D11—24no—
80C22⋊C4×D11—24no—
81C4×D44—22no—
82C4×D44—22no—
83C42×D11D412yes—
84C42×D11D412yes—
85C42×D11D412yes—
86C42×D11D412yes—
87C11×C4⋊C8—22no—
88C11×C22⋊C8C2314yes—
89C4×C8×C11—22no—
90C22⋊(C11⋊C8)C2314yes—
91(C2×D11)⋊C8—24no—
92#66879—24no—
93Dic11⋊C8—24no—
94C4⋊(C11⋊C8)—22no—
95C4×C11⋊C8—22no—
96#17364—111nomaximal, Sylow
97C24×C11C22×C412yes—
98C23×D11—24no—
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—24no—
102C23×D11—44no—
103C23×D11—44no—
104C23×D11C22×C411yescharacteristic
105C23×D11C22×C412yes—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11M1614yescomplemented
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—44no—
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C22×C412yes—
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C2×C22⋊D11—24no—
117C2×C22⋊D11—24no—
118C2×C22⋊D11—24no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—44no—
122C22×Dic11C22×C411yescharacteristic
123C22×Dic11C22×C411yescharacteristic
124C22×Dic11C22×C412yes—
125C22×Dic11C22×C411yescharacteristic
126D4×D11—216no—
127D4×D11—216no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44M1614yescomplemented
131C2×C4×D11—24no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—44no—
141C2×C4×D11—42no—
142C2×C4×D11—44no—
143C2×C4×D11—48no—
144C2×C4×D11—48no—
145C2×C4×D11—48no—
146C2×C4×D11—48no—
147C2×C4×D11—44no—
148C2×C4×D11C22⋊C412yes—
149C2×C4×D11C22⋊C412yes—
150C2×C4×D11C22⋊C411yescharacteristic
151C2×C4×D11C22⋊C411yescharacteristic
152C2×C4×D11C22⋊C411yescharacteristic
153C2×C4×D11C22⋊C411yescharacteristic
154C2×C4×D11C2×D412yes—
155C2×C4×D11C2×D412yes—
156C2×C8×C11—24no—
157C11×C4⋊C4—22no—
158C11×C22⋊C4—24no—
159C42×C11C2×D412yes—
160C42×C11C2×D412yes—
161C22⋊Dic11—24no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—24no—
164C4⋊Dic11—22no—
165Dic11⋊C4—24no—
166C4×Dic11C22⋊C412yes—
167C4×Dic11C22⋊C412yes—
168C4×Dic11C22⋊C412yes—
169C4×Dic11C22⋊C412yes—
170C4×Dic11C2×D412yes—
171C4×Dic11C2×D412yes—
172C2×C11⋊C8—24no—
173#4313—48no—
174C22×C4×D4—111no—
175#2920—112no—
176#1466—114no—
177#1462—114no—
178#1460—112no—
179#1460—111no—
180#1460D1111yescharacteristic, complemented
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11C2×M1614yes—
186C23×C11C23×C411yescharacteristic
187C22×D11—21no—
188C22×D11—21no—
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—28no—
192C22×D11—28no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—44no—
196C22×D11—416no—
197C22×D11—416no—
198C22×D11—44no—
199C22×D11—44no—
200C22×D11—44no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11C2×C22⋊C411yescharacteristic
204C22×D11C2×C22⋊C411yescharacteristic
205C22×D11C2×M1614yes—
206D4×C11—28no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—41no—
210C2×C4×C11—44no—
211C2×C4×C11—44no—
212C2×C4×C11—42no—
213C2×C4×C11C2×C22⋊C411yescharacteristic
214C2×C4×C11C2×C22⋊C412yes—
215C2×C4×C11C2×C22⋊C411yescharacteristic
216C2×C4×C11C2×M1612yes—
217C2×C4×C11C2×M1612yes—
218C2×C4×C11C22×D412yes—
219C22⋊D11—216no—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—41no—
225C2×Dic11—44no—
226C2×Dic11—44no—
227C2×Dic11—42no—
228C2×Dic11C2×C22⋊C412yes—
229C2×Dic11C2×C22⋊C412yes—
230C2×Dic11C2×C22⋊C411yescharacteristic
231C2×Dic11C2×C22⋊C411yescharacteristic
232D44—28no—
233C4×D11—24no—
234C4×D11—22no—
235C4×D11—24no—
236C4×D11—24no—
237C4×D11—22no—
238C4×D11—22no—
239C4×D11—42no—
240C4×D11—44no—
241C4×D11—44no—
242C4×D11—44no—
243C4×D11—44no—
244C4×D11—44no—
245C4×D11—44no—
246C4×D11#10014yes—
247C8×C11—44no—
248C11⋊C8—44no—
249C23×D4—111no—
250C24×C4—112no—
251C2×C4×D4—111no—
252C2×C4×D4—112no—
253C2×C4×D4—111no—
254C2×C4×D4—112no—
255C2×C4×D4—111no—
256C2×C4×D4—222no—
257C2×C4×D4—222no—
258C2×C4×D4—222no—
259C2×C4×D4—222no—
260C2×C4×D4C2×D1111yescharacteristic
261C22×C4⋊C4—111no—
262C22×C22⋊C4—112no—
263C22×C42—111no—
264#432—114no—
265#432—222no—
266#431—112no—
267#431—222no—
268#431C2×D1112yescomplemented
269#423—222no—
270#407—114no—
271C4×M16—222no—
272#323—114no—
273#323—118no—
274#323C2×D1114yescomplemented
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—24no—
278C22×C11—44no—
279C22×C11—44no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11C22×C22⋊C411yescharacteristic
283C22×C11C22×M1611yescharacteristic
284C22×C11C22×M1611yescharacteristic
285C2×D11—24no—
286C2×D11—24no—
287C2×D11—21no—
288C2×D11—21no—
289C2×D11—21no—
290C2×D11—21no—
291C2×D11—24no—
292C2×D11—416no—
293C2×D11—416no—
294C2×D11—44no—
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—44no—
298C2×D11#41012yes—
299C2×D11C2×#10012yes—
300C4×C11—22no—
301C4×C11—21no—
302C4×C11—42no—
303C4×C11#40714yes—
304C4×C11C2×#10012yes—
305Dic11—22no—
306Dic11—22no—
307Dic11—21no—
308Dic11—42no—
309Dic11C2×#10012yes—
310C25—112no—
311C22×D4—112no—
312C22×D4—111no—
313C22×D4—222no—
314C22×D4—222no—
315C22×D4—224no—
316C22×D4—224no—
317C22×D4C4×D1111yescharacteristic
318C23×C4—111no—
319C23×C4—111no—
320C23×C4—111no—
321C23×C4—112no—
322C23×C4—112no—
323C23×C4—112no—
324C23×C4—112no—
325C23×C4—222no—
326C23×C4—222no—
327C23×C4—222no—
328C23×C4—222no—
329C23×C4—448no—
330C23×C4C4×D1112yes—
331C2×M16—224no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—224no—
335C4×D4—224no—
336C4×D4—222no—
337C4×D4—222no—
338C4×D4—224no—
339C4×D4—224no—
340C4×D4—222no—
341C4×D4—222no—
342C4×D4—222no—
343C4×D4—222no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4C4×D1111yescharacteristic
349C2×C22⋊C4—112no—
350C2×C22⋊C4—112no—
351C2×C22⋊C4—112no—
352C2×C22⋊C4—224no—
353C2×C22⋊C4—224no—
354C2×C22⋊C4C22×D1112yes—
355C2×C42—111no—
356C2×C42—111no—
357C2×C42—111no—
358C2×C42—112no—
359C2×C42—112no—
360C2×C42—112no—
361C2×C42—112no—
362C2×C42C22×D1111yescharacteristic
363C4⋊C8—22no—
364C4⋊C8—224no—
365C4⋊C8—222no—
366C22⋊C8—114no—
367C22⋊C8—224no—
368C22⋊C8C22×D1114yes—
369#97—224no—
370C4×C8—22no—
371C4×C8—222no—
372C2×C11—21no—
373C2×C11—21no—
374C2×C11—44no—
375C2×C11C2×#40711yescharacteristic
376C2×C11C2×#41011yescharacteristic
377C2×C11C22×#10011yescharacteristic
378D11—22no—
379D11—22no—
380D11—44no—
381C24—111no—
382C24—112no—
383C24—222no—
384C24—222no—
385C24—224no—
386C24—224no—
387C24—444no—
388C24—444no—
389C24C2×C4×D1112yes—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—114no—
393C2×D4—224no—
394C2×D4—2216no—
395C2×D4—2216no—
396C2×D4—224no—
397C2×D4—224no—
398C2×D4—222no—
399C2×D4—222no—
400C2×D4#431314yescomplemented
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—44no—
404C22×C4—111no—
405C22×C4—111no—
406C22×C4—111no—
407C22×C4—111no—
408C22×C4—112no—
409C22×C4—112no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—111no—
413C22×C4—112no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—224no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—444no—
428C22×C4—448no—
429C22×C4—442no—
430C22×C4—448no—
431C22×C4—448no—
432C22×C4—448no—
433C22×C4—444no—
434C22×C4—444no—
435C22×C4—444no—
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4C2×C4×D1112yes—
438C22×C4C2×C4×D1111yescharacteristic
439C22×C4C23×D1111yescharacteristic
440M16—448no—
441C2×C8—24no—
442C2×C8—224no—
443C4⋊C4—22no—
444C4⋊C4—224no—
445C4⋊C4—222no—
446C22⋊C4—24no—
447C22⋊C4—224no—
448C22⋊C4—224no—
449C22⋊C4—224no—
450C42—112no—
451C42—112no—
452C42—112no—
453C42—112no—
454C42—112no—
455C42—112no—
456C42D4×D1112yes—
457C42D4×D1112yes—
458C11#1736411yescharacteristic, complemented, Sylow
459C23—22no—
460C23—22no—
461C23—42no—
462C23—42no—
463C23—111no—
464C23—111no—
465C23—114no—
466C23—222no—
467C23—222no—
468C23—228no—
469C23—228no—
470C23—221no—
471C23—221no—
472C23—222no—
473C23—222no—
474C23—442no—
475C23—442no—
476C23—444no—
477C23—444no—
478C23—444no—
479C23—4416no—
480C23—4416no—
481C23—444no—
482C23C2×#431314yes—
483C23C22×C4×D1111yescharacteristic
484D4—28no—
485D4—2216no—
486D4—228no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—41no—
490C2×C4—44no—
491C2×C4—44no—
492C2×C4—42no—
493C2×C4—111no—
494C2×C4—114no—
495C2×C4—112no—
496C2×C4—112no—
497C2×C4—111no—
498C2×C4—222no—
499C2×C4—224no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—442no—
509C2×C4—444no—
510C2×C4—444no—
511C2×C4—444no—
512C2×C4—444no—
513C2×C4—444no—
514C2×C4—444no—
515C2×C4—441no—
516C2×C4—444no—
517C2×C4—444no—
518C2×C4—442no—
519C2×C4C22⋊C4×D1111yescharacteristic
520C2×C4C22⋊C4×D1112yes—
521C2×C4C22⋊C4×D1111yescharacteristic
522C2×C4C2×#431312yes—
523C2×C4M16×D1112yes—
524C2×C4C2×D4×D1112yes—
525C8—44no—
526C8—444no—
527C22—21no—
528C22—21no—
529C22—24no—
530C22—44no—
531C22—44no—
532C22—42no—
533C22—42no—
534C22—112no—
535C22—112no—
536C22—224no—
537C22—224no—
538C22—221no—
539C22—221no—
540C22—221no—
541C22—221no—
542C22—224no—
543C22—444no—
544C22—444no—
545C22—4416no—
546C22—4416no—
547C22—442no—
548C22—442no—
549C22C2×C22⋊C4×D1111yescharacteristic
550C22C22×#431311yescharacteristic
551C22C2×M16×D1111yescharacteristic
552C4—22no—
553C4—21no—
554C4—42no—
555C4—112no—
556C4—222no—
557C4—222no—
558C4—221no—
559C4—442no—
560C4#1062233914yes—
561C4D11×#10012yes—
562C2—21no—
563C2—21no—
564C2—44no—
565C2—222no—
566C2—222no—
567C2—444no—
568C2C2×#1062233911yescharacteristic
569C2D11×#41011yescharacteristic
570C2C2×D11×#10011yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1460C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×D11C4
cosocleC22×C4×C11C24
hypercenter#1460D11
hypocenterC11#17364
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #13077244C2semidirect
3. #13066955C2semidirect
4. #13066941C2semidirect
5. #13066937C2semidirect
6. #13066936C2semidirect
7. C11×#1460C2semidirect
23. C11×#431C22semidirect
24. #10622538C22semidirect
28. #10622332C22semidirect
31. C11×#323C22semidirect
32. #10622163C22semidirect
33. #10622106C22semidirect
108. C2×D4×C11M16semidirect
130. C2×D44M16semidirect
180. #1460D11semidirect
268. #431C2×D11semidirect
274. #323C2×D11semidirect
400. C2×D4#4313semidirect
458. C11#17364semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
#130772442
#130669552
#130669412
#130669372
#130669362
C11×#14602
#1736411