Finite Group Databasebeta

← #14719984

Subgroups — #14719984

Order 2816.

1284 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623083C211yesmaximal, characteristic
2#13077066C212yesmaximal, complemented
3#13066981C212yesmaximal, complemented
4#13066978C214yesmaximal, complemented
5#13066951C212yesmaximal, complemented
6#13066934C211yesmaximal, characteristic, complemented
7#13066931C212yesmaximal, complemented
8C11×#1465C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C23×Dic22C411yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×#66992C412yes—
13C2×#66983C411yescharacteristic
14C2×#66977C2211yescharacteristic
15C2×#66960—22no—
16#10623083—22no—
17#10623083—22no—
18#10623083—24no—
19C2×#66949C2212yes—
20C2×#66938C412yes—
21C2×(C22⋊D11)⋊C4C2212yes—
22C2×#66928C411yescharacteristic
23C2×C4×Dic22C411yescharacteristic
24C11×#407C2212yes—
25C2×C22⋊(C11⋊C8)C2212yes—
26#10622742—22no—
27#10622340—24no—
28#10622339C2214yes—
29D11×C22⋊C8C2214yes—
30C11×#324C2212yes—
31C11×#323C2212yes—
32#10622166C2212yes—
33#10622163C2211yescharacteristic
34#10622163C2211yescharacteristic
35#10622107C2214yes—
36#10622107C2214yes—
37C22×D4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11C2×C412yes—
41C22×C22⋊D11C2×C412yes—
42C23×Dic11C2×C412yes—
43C2×#4339—44no—
44C2×#4339D412yes—
45C2×#4339D412yes—
46C2×#4339D414yes—
47C22×D44C2×C411yescharacteristic
48C22×C4×D11C2312yes—
49C22×Dic22—21no—
50C22×Dic22—22no—
51C22×Dic22—21no—
52C22×Dic22—44no—
53C22×Dic22C2×C411yescharacteristic
54C22×Dic22C2×C411yescharacteristic
55C22×Dic22C2×C412yes—
56C2×C11×M16—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4C2×C411yescharacteristic
61C2×C11×C22⋊C4C2311yescharacteristic
62C2×C42×C11C2×C411yescharacteristic
63C2×C22⋊Dic11C2×C412yes—
64#66992—24no—
65#66992—24no—
66#66983—22no—
67#66983—22no—
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×C4⋊Dic11C2×C411yescharacteristic
72#66977—22no—
73#66977—22no—
74C2×Dic11⋊C4C2×C412yes—
75C2×Dic11⋊C4C2312yes—
76C2×C4×Dic11C2×C412yes—
77C22×C11⋊C8—22no—
78#66960—48no—
79C2×#4313—24no—
80C2×C8×D11—24no—
81#66949—24no—
82#66949—24no—
83#66938—24no—
84#66938—24no—
85(C22⋊D11)⋊C4—24no—
86(C22⋊D11)⋊C4—24no—
87#66928—22no—
88#66928—22no—
89C4×Dic22—21no—
90C4×Dic22—22no—
91C4×Dic22—21no—
92C11×C22⋊C8—22no—
93C11×C22⋊C8C2314yes—
94C22⋊(C11⋊C8)—22no—
95C22⋊(C11⋊C8)C2312yes—
96C22⋊(C11⋊C8)C2312yes—
97(C2×D11)⋊C8—24no—
98(C2×D11)⋊C8—24no—
99#17414—111nomaximal, Sylow
100C24×C11C22×C411yescharacteristic
101C24×C11C22×C411yescharacteristic
102C23×D11C22×C412yes—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—41no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C22×C411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2411yescharacteristic
117C2×C22⋊D11—24no—
118C2×C22⋊D11—24no—
119C2×C22⋊D11—42no—
120C2×C22⋊D11—44no—
121C2×C22⋊D11C22⋊C414yes—
122C2×C22⋊D11C22⋊C414yes—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—44no—
126C22×Dic11C22×C412yes—
127C22×Dic11C22×C412yes—
128C22×Dic11C22×C412yes—
129#4339—28no—
130#4339—44no—
131#4339—48no—
132C2×D44—42no—
133C2×D44C22⋊C412yes—
134C2×D44C22⋊C412yes—
135C2×C4×D11—44no—
136C2×C4×D11C2×D414yes—
137C2×C4×D11C2×D414yes—
138C2×Dic22—24no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—42no—
144C2×Dic22—48no—
145C2×Dic22—44no—
146C2×Dic22—44no—
147C2×Dic22—44no—
148C2×Dic22C22⋊C412yes—
149C2×Dic22C22⋊C411yescharacteristic
150C2×Dic22C22⋊C411yescharacteristic
151C11×M16—44no—
152C2×C8×C11—24no—
153C11×C4⋊C4—22no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C42×C11—21no—
157C42×C11—21no—
158C22⋊Dic11—24no—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164Dic11⋊C4—22no—
165Dic11⋊C4—22no—
166Dic11⋊C4—24no—
167C4×Dic11—22no—
168C4×Dic11—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—44no—
172#4313—48no—
173C8×D11—48no—
174C2×#548—111no—
175#2880—112no—
176#1472—112no—
177#1472—114no—
178#1465—112no—
179#1465D1111yescharacteristic, complemented
180#1459—112no—
181#1459—111no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11C2×C22⋊C412yes—
191C23×C11#13112yescomplemented
192C23×C11C23×C411yescharacteristic
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11C2×C22⋊C414yes—
198D4×C11—44no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11C2×C22⋊C411yescharacteristic
213C2×C4×C11C2×C22⋊C411yescharacteristic
214C2×C4×C11C22×D412yes—
215C22⋊D11—28no—
216C22⋊D11—44no—
217C22⋊D11—48no—
218C2×Dic11—24no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—44no—
224C2×Dic11—44no—
225C2×Dic11—42no—
226C2×Dic11C2×C22⋊C412yes—
227C2×Dic11C2×C22⋊C412yes—
228D44—24no—
229D44—42no—
230C4×D11—28no—
231C4×D11—44no—
232Dic22—22no—
233Dic22—24no—
234Dic22—44no—
235Dic22—42no—
236Dic22—42no—
237Dic22—44no—
238Dic22#9914yes—
239C8×C11—44no—
240C11⋊C8—42no—
241C11⋊C8—42no—
242C22×#41—111no—
243C23×Q8—111no—
244C2×#131—222no—
245#548—222no—
246#548—222no—
247#548—224no—
248C2×#124—112no—
249C2×#124—111no—
250C2×C22⋊Q8—111no—
251C2×C22⋊Q8—112no—
252C2×#121—112no—
253C2×#121—111no—
254C2×C4×Q8—111no—
255C2×C4×D4—112no—
256C2×C4×D4C2×D1111yescharacteristic
257#408—224no—
258#408—222no—
259#407—114no—
260#407C2×D1112yes—
261C2×C22⋊C8—112no—
262C2×C22⋊C8—114no—
263#324—112no—
264#324—114no—
265#324—114no—
266#324C2×D1112yes—
267#323—111no—
268#323—111no—
269#323C2×D1112yes—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11C22×C22⋊C411yescharacteristic
283C22×C11C2×#13111yescharacteristic
284C22×C11#56811yescharacteristic
285C2×D11—24no—
286C2×D11—24no—
287C2×D11—24no—
288C2×D11—82no—
289C2×D11—82no—
290C4×C11—21no—
291C4×C11—22no—
292C4×C11—41no—
293C4×C11—41no—
294C4×C11—41no—
295C4×C11C2×#9912yes—
296Dic11—22no—
297Dic11—42no—
298Dic11—42no—
299Dic11C2×#9914yes—
300C2×#41—112no—
301C2×#41—114no—
302C2×#41—112no—
303C2×#41—444no—
304C22×Q8—111no—
305C22×Q8—112no—
306C22×Q8—111no—
307C22×Q8—221no—
308C22×Q8—222no—
309C22×Q8—221no—
310C22×Q8—444no—
311C22×D4—112no—
312C22×D4—112no—
313C22×D4—111no—
314C22×D4C4×D1111yescharacteristic
315C23×C4—112no—
316C23×C4—112no—
317C23×C4C4×D1111yescharacteristic
318C23×C4C22×D1111yescharacteristic
319#131—448no—
320C2×M16—22no—
321C2×M16—224no—
322C22×C8—224no—
323C22×C8—222no—
324#124—222no—
325#124—222no—
326#124—224no—
327#124—224no—
328C22⋊Q8—224no—
329C22⋊Q8—224no—
330C22⋊Q8—222no—
331C22⋊Q8—222no—
332#121—222no—
333#121—222no—
334#121—224no—
335#121—224no—
336C4×Q8—221no—
337C4×Q8—222no—
338C4×Q8—221no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—224no—
342C4×D4—224no—
343C2×C4⋊C4—112no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4C22×D1111yescharacteristic
347C2×C22⋊C4—112no—
348C2×C22⋊C4—112no—
349C2×C22⋊C4—112no—
350C2×C22⋊C4—112no—
351C2×C22⋊C4C4×D1111yescharacteristic
352C2×C22⋊C4C22×D1111yescharacteristic
353C2×C42—112no—
354C2×C42C4×D1111yescharacteristic
355C22⋊C8—22no—
356C22⋊C8—112no—
357C22⋊C8—112no—
358C22⋊C8—224no—
359C22⋊C8—224no—
360C22⋊C8—222no—
361C22⋊C8C22×D1114yes—
362C2×C11—21no—
363C2×C11—21no—
364C2×C11—42no—
365C2×C11—42no—
366C2×C11#288011yescharacteristic
367C2×C11C22×#9911yescharacteristic
368C2×C11#288911yescharacteristic
369D11—44no—
370C24—112no—
371C24C2×C4×D1111yescharacteristic
372C24C2×C4×D1111yescharacteristic
373#41—228no—
374#41—444no—
375#41—448no—
376C2×Q8—111no—
377C2×Q8—112no—
378C2×Q8—111no—
379C2×Q8—222no—
380C2×Q8—222no—
381C2×Q8—224no—
382C2×Q8—221no—
383C2×Q8—221no—
384C2×Q8—442no—
385C2×Q8—444no—
386C2×Q8—444no—
387C2×Q8—448no—
388C2×Q8—444no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—41no—
392C2×D4—114no—
393C2×D4—114no—
394C2×D4—112no—
395C2×D4—112no—
396C2×D4—224no—
397C2×D4—224no—
398C2×D4—442no—
399C2×D4—444no—
400C2×D4—442no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—112no—
406C22×C4—114no—
407C22×C4—114no—
408C22×C4—112no—
409C22×C4—112no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—444no—
413C22×C4—444no—
414C22×C4C2×C4×D1111yescharacteristic
415C22×C4C2×C4×D1111yescharacteristic
416C22×C4C2×C4×D1111yescharacteristic
417C22×C4C2×C4×D1111yescharacteristic
418C22×C4D4×D1112yes—
419C22×C4D4×D1112yes—
420C22×C4C23×D1111yescharacteristic
421M16—44no—
422M16—448no—
423C2×C8—24no—
424C2×C8—222no—
425C2×C8—222no—
426C2×C8—448no—
427C2×C8—444no—
428C4⋊C4—22no—
429C4⋊C4—222no—
430C4⋊C4—222no—
431C4⋊C4—221no—
432C4⋊C4—221no—
433C4⋊C4—224no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—224no—
437C22⋊C4—224no—
438C22⋊C4—224no—
439C22⋊C4—224no—
440C42—21no—
441C42—21no—
442C42—222no—
443C42—222no—
444C11#1741411yescharacteristic, complemented, Sylow
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—114no—
454C23—222no—
455C23—222no—
456C23—442no—
457C23—442no—
458C23C22⋊C4×D1112yes—
459C23#6696012yescomplemented
460C23C22×C4×D1111yescharacteristic
461Q8—114no—
462Q8—224no—
463Q8—222no—
464Q8—442no—
465Q8—444no—
466Q8—444no—
467Q8—442no—
468D4—44no—
469D4—228no—
470D4—224no—
471D4—442no—
472D4—444no—
473D4—448no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—112no—
488C2×C4—112no—
489C2×C4—228no—
490C2×C4—224no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—444no—
496C2×C4—444no—
497C2×C4—444no—
498C2×C4—442no—
499C2×C4C22⋊C4×D1111yescharacteristic
500C2×C4C22⋊C4×D1111yescharacteristic
501C2×C4C2×D4×D1112yes—
502C8—44no—
503C8—442no—
504C8—442no—
505C22—21no—
506C22—21no—
507C22—22no—
508C22—22no—
509C22—22no—
510C22—22no—
511C22—42no—
512C22—42no—
513C22—41no—
514C22—41no—
515C22—81no—
516C22—81no—
517C22—224no—
518C22—224no—
519C22—224no—
520C22—882no—
521C22—882no—
522C22C2×C22⋊C4×D1111yescharacteristic
523C22C2×#6696011yescharacteristic
524C22#1062327611yescharacteristic
525C4—22no—
526C4—21no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—114no—
531C4—222no—
532C4—442no—
533C4—442no—
534C4D11×#9912yes—
535C2—21no—
536C2—21no—
537C2—42no—
538C2—42no—
539C2—444no—
540C2#1307706611yescharacteristic
541C2C2×D11×#9911yescharacteristic
542C2#1307709711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1465C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623083C2
cosocleC22×C4×C11C24
hypercenter#1465D11
hypocenterC11#17414
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #13077066C2semidirect
3. #13066981C2semidirect
4. #13066978C2semidirect
5. #13066951C2semidirect
6. #13066934C2semidirect
7. #13066931C2semidirect
8. C11×#1465C2semidirect
179. #1465D11semidirect
191. C23×C11#131semidirect
444. C11#17414semidirect
459. C23#66960semidirect

Maximal subgroups

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

subgroupindex
C2×#106230832
#130770662
#130669812
#130669782
#130669512
#130669342
#130669312
C11×#14652
#1741411