Finite Group Databasebeta

← #14719659

Subgroups — #14719659

Order 2816.

1646 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic
2#13077246C212yesmaximal, complemented
3#13066957C211yesmaximal, characteristic, complemented
4#13066956C212yesmaximal, complemented
5#13066941C214yesmaximal, complemented
6#13066935C214yesmaximal, complemented
7C11×#1466C211yesmaximal, 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×#432C2212yescomplemented
24#10622539C2212yescomplemented
25#10622450—22no—
26#10622446—22no—
27#10622339C2214yes—
28#10622331C2214yescomplemented
29#10622320—22no—
30#10622318—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—28no—
40C2×D4×D11—22no—
41C2×D4×D11—22no—
42C22×D44C2×C411yescharacteristic
43C22×C4×D11—22no—
44C22×C4×D11—22no—
45C22×C4×D11—22no—
46C22×C4×D11—22no—
47C22×C4×D11—48no—
48C22×C4×D11C2×C411yescharacteristic
49C22×C4×D11C2×C411yescharacteristic
50C22×C4×D11C2×C412yes—
51C22×C4×D11C2×C412yes—
52C22×C4×D11C2×C412yes—
53C22×C4×D11C2311yescharacteristic
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C2×C11×C4⋊C4C2×C411yescharacteristic
57C2×C11×C22⋊C4C2312yes—
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11C2×C412yes—
60D4×Dic11—22no—
61D4×Dic11—22no—
62C4×C22⋊D11—24no—
63C4×C22⋊D11—24no—
64C2×(C2×D11)⋊C4C2×C412yes—
65C2×(C2×D11)⋊C4C2312yes—
66C2×C4⋊Dic11C2×C411yescharacteristic
67C2×Dic11⋊C4C2×C412yes—
68C2×C4×Dic11C2×C411yescharacteristic
69C2×C4×Dic11C2×C411yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C2×#4313—24no—
72#66946—22no—
73#66946—22no—
74C4⋊C4×D11—22no—
75C4⋊C4×D11—22no—
76(C22⋊D11)⋊C4—24no—
77(C22⋊D11)⋊C4—24no—
78C22⋊C4×D11—24no—
79C22⋊C4×D11—24no—
80C4×D44—22no—
81C4×D44—22no—
82C42×D11D412yes—
83C42×D11D412yes—
84C42×D11D412yes—
85C42×D11D412yes—
86C11×C4⋊C8—22no—
87C11×C22⋊C8C2314yes—
88C11×#97—22no—
89C22⋊(C11⋊C8)C2314yes—
90(C2×D11)⋊C8—24no—
91Dic11⋊C8—24no—
92C8×Dic11—24no—
93C4⋊(C11⋊C8)—22no—
94#66867—22no—
95#17364—111nomaximal, Sylow
96C24×C11C22×C412yes—
97C23×D11—24no—
98C23×D11—22no—
99C23×D11—22no—
100C23×D11—24no—
101C23×D11—44no—
102C23×D11—44no—
103C23×D11C22×C411yescharacteristic
104C23×D11C22×C412yes—
105C2×D4×C11—24no—
106C2×D4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—44no—
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C22×C412yes—
113C22×C4×C11C2411yescharacteristic
114C2×C22⋊D11—24no—
115C2×C22⋊D11—24no—
116C2×C22⋊D11M1618yescomplemented
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—44no—
120C22×Dic11C22×C411yescharacteristic
121C22×Dic11C22×C412yes—
122C22×Dic11C22×C411yescharacteristic
123C22×Dic11C22×C411yescharacteristic
124D4×D11—216no—
125D4×D11—216no—
126C2×D44—24no—
127C2×D44—22no—
128C2×C4×D11—24no—
129C2×C4×D11—24no—
130C2×C4×D11—22no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—44no—
137C2×C4×D11—42no—
138C2×C4×D11—44no—
139C2×C4×D11—48no—
140C2×C4×D11—48no—
141C2×C4×D11—48no—
142C2×C4×D11—48no—
143C2×C4×D11—44no—
144C2×C4×D11C22⋊C412yes—
145C2×C4×D11C22⋊C412yes—
146C2×C4×D11C22⋊C411yescharacteristic
147C2×C4×D11C22⋊C411yescharacteristic
148C2×C4×D11C22⋊C411yescharacteristic
149C2×C4×D11C22⋊C411yescharacteristic
150C2×C4×D11C2×D412yes—
151C2×C4×D11C2×D412yes—
152C2×C8×C11—24no—
153C11×C4⋊C4—22no—
154C11×C22⋊C4—24no—
155C42×C11C2×D412yes—
156C42×C11C2×D412yes—
157C22⋊Dic11—24no—
158(C2×D11)⋊C4—24no—
159(C2×D11)⋊C4—24no—
160C4⋊Dic11—22no—
161Dic11⋊C4—24no—
162C4×Dic11C22⋊C412yes—
163C4×Dic11C22⋊C412yes—
164C4×Dic11C22⋊C412yes—
165C4×Dic11C22⋊C412yes—
166C4×Dic11C2×D412yes—
167C4×Dic11C2×D412yes—
168C2×C11⋊C8—24no—
169#4313—48no—
170C22×C4×D4—111no—
171#2920—112no—
172#1466—112no—
173#1466—111no—
174#1466D1111yescharacteristic, complemented
175#1462—114no—
176#1460—114no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11C2×M1614yes—
182C23×C11C23×C411yescharacteristic
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—22no—
186C22×D11—28no—
187C22×D11—28no—
188C22×D11—22no—
189C22×D11—22no—
190C22×D11—44no—
191C22×D11—416no—
192C22×D11—416no—
193C22×D11—44no—
194C22×D11—44no—
195C22×D11—44no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11C2×C22⋊C411yescharacteristic
199C22×D11C2×C22⋊C411yescharacteristic
200C22×D11C2×M1614yes—
201D4×C11—28no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—44no—
207C2×C4×C11—44no—
208C2×C4×C11—42no—
209C2×C4×C11C2×C22⋊C412yes—
210C2×C4×C11C2×C22⋊C411yescharacteristic
211C2×C4×C11C2×C22⋊C411yescharacteristic
212C2×C4×C11C22×D412yes—
213C22⋊D11—216no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—41no—
217C2×Dic11—44no—
218C2×Dic11—44no—
219C2×Dic11—42no—
220C2×Dic11C2×C22⋊C412yes—
221C2×Dic11C2×C22⋊C411yescharacteristic
222C2×Dic11C2×C22⋊C412yes—
223C2×Dic11C2×C22⋊C411yescharacteristic
224C2×Dic11C2×M1614yes—
225D44—28no—
226C4×D11—24no—
227C4×D11—22no—
228C4×D11—22no—
229C4×D11—24no—
230C4×D11—24no—
231C4×D11—22no—
232C4×D11—42no—
233C4×D11—44no—
234C4×D11—44no—
235C4×D11—44no—
236C4×D11—44no—
237C4×D11—44no—
238C4×D11—44no—
239C4×D11#10014yes—
240C8×C11—44no—
241C11⋊C8—44no—
242C23×D4—111no—
243C24×C4—112no—
244C2×C4×D4—111no—
245C2×C4×D4—112no—
246C2×C4×D4—111no—
247C2×C4×D4—112no—
248C2×C4×D4—111no—
249C2×C4×D4—222no—
250C2×C4×D4—222no—
251C2×C4×D4—222no—
252C2×C4×D4—222no—
253C2×C4×D4C2×D1111yescharacteristic
254C22×C4⋊C4—111no—
255C22×C22⋊C4—112no—
256C22×C42—111no—
257#432—112no—
258#432—222no—
259#432C2×D1112yescomplemented
260#431—114no—
261#431—222no—
262#423—222no—
263#407—114no—
264C4×M16—222no—
265#323—114no—
266#323—118no—
267#323C2×D1114yescomplemented
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—24no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11C22×C22⋊C411yescharacteristic
276C22×C11C22×M1612yes—
277C2×D11—28no—
278C2×D11—21no—
279C2×D11—21no—
280C2×D11—21no—
281C2×D11—21no—
282C2×D11—24no—
283C2×D11—416no—
284C2×D11—416no—
285C2×D11—44no—
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—44no—
289C2×D11#41012yes—
290C2×D11C2×#10012yes—
291C4×C11—22no—
292C4×C11—22no—
293C4×C11—21no—
294C4×C11—42no—
295C4×C11C2×#10012yes—
296Dic11—22no—
297Dic11—21no—
298Dic11—42no—
299Dic11#40714yes—
300Dic11C2×#10012yes—
301C25—112no—
302C22×D4—112no—
303C22×D4—111no—
304C22×D4—222no—
305C22×D4—222no—
306C22×D4—228no—
307C22×D4C4×D1111yescharacteristic
308C23×C4—111no—
309C23×C4—111no—
310C23×C4—111no—
311C23×C4—112no—
312C23×C4—112no—
313C23×C4—112no—
314C23×C4—112no—
315C23×C4—222no—
316C23×C4—222no—
317C23×C4—222no—
318C23×C4—222no—
319C23×C4—448no—
320C23×C4C4×D1112yes—
321C2×M16—224no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—224no—
325C4×D4—224no—
326C4×D4—222no—
327C4×D4—222no—
328C4×D4—224no—
329C4×D4—224no—
330C4×D4—222no—
331C4×D4—222no—
332C4×D4—222no—
333C4×D4—222no—
334C2×C4⋊C4—112no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—222no—
338C2×C4⋊C4C4×D1111yescharacteristic
339C2×C22⋊C4—112no—
340C2×C22⋊C4—112no—
341C2×C22⋊C4—112no—
342C2×C22⋊C4—224no—
343C2×C22⋊C4—224no—
344C2×C22⋊C4C22×D1112yes—
345C2×C42—111no—
346C2×C42—111no—
347C2×C42—111no—
348C2×C42—112no—
349C2×C42—112no—
350C2×C42—112no—
351C2×C42—112no—
352C2×C42C22×D1111yescharacteristic
353C4⋊C8—22no—
354C4⋊C8—224no—
355C4⋊C8—222no—
356C22⋊C8—114no—
357C22⋊C8—224no—
358C22⋊C8C22×D1114yes—
359#97—22no—
360#97—222no—
361C4×C8—224no—
362C2×C11—22no—
363C2×C11—44no—
364C2×C11C2×#40711yescharacteristic
365C2×C11C2×#41011yescharacteristic
366C2×C11C22×#10011yescharacteristic
367D11—22no—
368D11—22no—
369D11—44no—
370C24—111no—
371C24—112no—
372C24—222no—
373C24—222no—
374C24—224no—
375C24—224no—
376C24—444no—
377C24—444no—
378C24C2×C4×D1112yes—
379C2×D4—24no—
380C2×D4—22no—
381C2×D4—118no—
382C2×D4—224no—
383C2×D4—224no—
384C2×D4—224no—
385C2×D4—2216no—
386C2×D4—2216no—
387C2×D4—222no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—44no—
391C22×C4—111no—
392C22×C4—111no—
393C22×C4—111no—
394C22×C4—111no—
395C22×C4—112no—
396C22×C4—112no—
397C22×C4—111no—
398C22×C4—111no—
399C22×C4—111no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—112no—
403C22×C4—224no—
404C22×C4—224no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—444no—
414C22×C4—448no—
415C22×C4—442no—
416C22×C4—448no—
417C22×C4—448no—
418C22×C4—448no—
419C22×C4—444no—
420C22×C4—444no—
421C22×C4—444no—
422C22×C4C2×C4×D1111yescharacteristic
423C22×C4C2×C4×D1111yescharacteristic
424C22×C4C2×C4×D1112yes—
425C22×C4C23×D1111yescharacteristic
426M16—448no—
427C2×C8—24no—
428C2×C8—224no—
429C4⋊C4—22no—
430C4⋊C4—224no—
431C4⋊C4—222no—
432C22⋊C4—24no—
433C22⋊C4—224no—
434C22⋊C4—224no—
435C22⋊C4—224no—
436C42—112no—
437C42—112no—
438C42—112no—
439C42—112no—
440C42—112no—
441C42—112no—
442C42D4×D1112yes—
443C42D4×D1112yes—
444C11#1736411yescharacteristic, complemented, Sylow
445C23—22no—
446C23—22no—
447C23—42no—
448C23—42no—
449C23—111no—
450C23—111no—
451C23—114no—
452C23—222no—
453C23—222no—
454C23—228no—
455C23—228no—
456C23—222no—
457C23—222no—
458C23—222no—
459C23—442no—
460C23—442no—
461C23—444no—
462C23—444no—
463C23—444no—
464C23—4416no—
465C23—4416no—
466C23—444no—
467C23M16×D1114yes—
468C23C22×C4×D1111yescharacteristic
469D4—28no—
470D4—228no—
471D4—2216no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—41no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4—42no—
479C2×C4—112no—
480C2×C4—111no—
481C2×C4—114no—
482C2×C4—114no—
483C2×C4—112no—
484C2×C4—111no—
485C2×C4—222no—
486C2×C4—224no—
487C2×C4—224no—
488C2×C4—224no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—442no—
494C2×C4—444no—
495C2×C4—444no—
496C2×C4—444no—
497C2×C4—444no—
498C2×C4—444no—
499C2×C4—444no—
500C2×C4—441no—
501C2×C4—444no—
502C2×C4—444no—
503C2×C4—442no—
504C2×C4C22⋊C4×D1112yes—
505C2×C4C22⋊C4×D1111yescharacteristic
506C2×C4C22⋊C4×D1111yescharacteristic
507C2×C4C2×D4×D1112yes—
508C8—44no—
509C8—444no—
510C22—21no—
511C22—21no—
512C22—24no—
513C22—44no—
514C22—44no—
515C22—42no—
516C22—42no—
517C22—112no—
518C22—112no—
519C22—228no—
520C22—221no—
521C22—221no—
522C22—221no—
523C22—221no—
524C22—224no—
525C22—444no—
526C22—444no—
527C22—4416no—
528C22—4416no—
529C22—442no—
530C22—442no—
531C22C2×C22⋊C4×D1111yescharacteristic
532C22C2×M16×D1112yes—
533C4—22no—
534C4—22no—
535C4—21no—
536C4—42no—
537C4—114no—
538C4—112no—
539C4—222no—
540C4—221no—
541C4—442no—
542C4D11×#10012yes—
543C2—22no—
544C2—44no—
545C2—222no—
546C2—222no—
547C2—444no—
548C2D11×#40711yescharacteristic
549C2D11×#41011yescharacteristic
550C2C2×D11×#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1466C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×D11C4
cosocleC22×C4×C11C24
hypercenter#1466D11
hypocenterC11#17364
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. #13077246C2semidirect
3. #13066957C2semidirect
4. #13066956C2semidirect
5. #13066941C2semidirect
6. #13066935C2semidirect
7. C11×#1466C2semidirect
23. C11×#432C22semidirect
24. #10622539C22semidirect
28. #10622331C22semidirect
31. C11×#323C22semidirect
32. #10622163C22semidirect
33. #10622106C22semidirect
116. C2×C22⋊D11M16semidirect
174. #1466D11semidirect
259. #432C2×D11semidirect
267. #323C2×D11semidirect
444. 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
#130772462
#130669572
#130669562
#130669412
#130669352
C11×#14662
#1736411