Finite Group Databasebeta

← #14807077

Subgroups — #14807077

Order 2816.

1206 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×#10622702C211yesmaximal, characteristic, complemented
2C2×#10622641C211yesmaximal, characteristic, complemented
3#13073555C211yesmaximal, characteristic
4#13069624C212yesmaximal, complemented
5#13069617C212yesmaximal, complemented
6#13069569C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068933C212yesmaximal, complemented
9#13068923C212yesmaximal, complemented
10#13068446C211yesmaximal, characteristic, complemented
11C2×C11×#554C211yesmaximal, characteristic, complemented
12C11×#554—24no—
13C11×#554—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125—21no—
16C2×C11×C22⋊Q8—22no—
17C2×C11×C22⋊Q8C2212yes—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4C2212yes—
22C22×#4326C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C2×#66983C2212yes—
25C2×#66977C2212yes—
26C2×#66928C2211yescharacteristic
27C2×#66899C2212yes—
28#10622836—21no—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622702—24no—
32#10622641—24no—
33#10622605—21no—
34C2×#66874C2211yescharacteristic
35C2×#66874C2212yes—
36C2×#66873C2211yescharacteristic
37C2×#66873C2212yes—
38#10622570—22no—
39C4×C4⋊Dic11C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—22no—
49C23×C4×C11C2312yes—
50C22×C22⋊D11—22no—
51C22×D44C2311yescharacteristic
52C22×Dic22C2311yescharacteristic
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8D414yescomplemented
55C11×#125—28no—
56C11×C22⋊Q8—216no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8—24no—
59C4×Q8×C11—22no—
60C4×Q8×C11D414yescomplemented
61C4×D4×C11—28no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4D412yes—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—22no—
78C2×#4326—22no—
79C2×#4326—42no—
80C2×#4325—22no—
81C2×#4325—42no—
82#66983—24no—
83#66983—42no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—22no—
87C2×C4⋊Dic11C2312yes—
88#66977—24no—
89#66977—42no—
90C2×Dic11⋊C4—22no—
91C2×C4×Dic11—21no—
92C22×C11⋊C8C2312yes—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66928—22no—
96#66928—22no—
97#66899—24no—
98C11⋊#95—21no—
99C22⋊(C11⋊C8)—42no—
100C22⋊(C11⋊C8)—42no—
101#66874—22no—
102#66874—24no—
103#66873—22no—
104#66873—24no—
105C4⋊(C11⋊C8)—22no—
106#66867—22no—
107#25579—111nomaximal, Sylow
108C24×C11C2×D412yes—
109C23×D11—21no—
110C2×Q8×C11—24no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—81no—
115C2×Q8×C11—81no—
116C2×Q8×C11C2×D412yes—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—28no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—82no—
130C22×C4×C11—82no—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C2×C22⋊D11—44no—
136C2×C22⋊D11—44no—
137C2×C22⋊D11—82no—
138C22×Dic11—22no—
139C22×Dic11—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—22no—
143C2×D44—22no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4C2×D412yes—
156C11×C4⋊C4C2×D414yes—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—24no—
159C42×C11—24no—
160C42×C11C2×D412yes—
161C42×C11C2×D412yes—
162C22⋊Dic11—44no—
163#4326—44no—
164#4325—44no—
165(C2×D11)⋊C4—44no—
166(C2×D11)⋊C4—42no—
167(C2×D11)⋊C4—42no—
168C4⋊Dic11—22no—
169C4⋊Dic11#4114yes—
170Dic11⋊C4—44no—
171C4×Dic11—81no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×#554D1111yescharacteristic, complemented
180C2×#489—111no—
181C2×#464—111no—
182#2540—111no—
183#2001—112no—
184#2000—112no—
185#1988—111no—
186#1955—111no—
187#1874—112no—
188#1872—112no—
189#1763—111no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11#13714yes—
197C23×C11C22×D411yescharacteristic
198C22×D11—41no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—41no—
202C22×D11—41no—
203Q8×C11—22no—
204Q8×C11—22no—
205Q8×C11—42no—
206Q8×C11—84no—
207D4×C11—28no—
208C2×C4×C11—22no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—88no—
227C2×C4×C11#12012yes—
228C2×C4×C11#12012yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4112yes—
232C2×C4×C11H(5,𝔽2)12yes—
233C22⋊D11—88no—
234C2×Dic11—24no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—41no—
238C2×Dic11—42no—
239D44—41no—
240D44—41no—
241D44—42no—
242Dic22—41no—
243Dic22—41no—
244Dic22—42no—
245C11⋊C8—41no—
246C11⋊C8—41no—
247C11⋊C8—42no—
248C22×Q16—111no—
249C22×SD16—111no—
250#554—24no—
251#554—24no—
252C2×C4⋊Q8C2×D1111yescharacteristic
253C2×#125—21no—
254C2×#124—111no—
255C2×C22⋊Q8—22no—
256C2×C22⋊Q8—112no—
257C2×C22⋊Q8C2×D1112yes—
258C2×#121—112no—
259C2×C4×Q8C2×D1111yescharacteristic
260C2×C4×D4—21no—
261C2×C4×D4C2×D1111yescharacteristic
262C22×C4⋊C4C2×D1112yes—
263#489—224no—
264#464—224no—
265C2×C4⋊C8—111no—
266C2×#103—112no—
267C2×#103—112no—
268C2×#103—111no—
269C2×#102—112no—
270C2×#102—111no—
271C2×C22⋊C8—112no—
272C2×C22⋊C8—112no—
273C2×#97—111no—
274#399—221no—
275#392—221no—
276#390—222no—
277C4×C4⋊C4—111no—
278#340—112no—
279#340—112no—
280#340—112no—
281C22×C11—24no—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11C2×#12011yescharacteristic
289C22×C11#54612yes—
290C22×C11C2×#13712yes—
291C22×C11#57611yescharacteristic
292C22×C11#57711yescharacteristic
293C2×D11—81no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—82no—
297C2×D11—82no—
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—44no—
304C4×C11#53211yescharacteristic
305C4×C11#53511yescharacteristic
306C4×C11#55012yes—
307Dic11—44no—
308Dic11—81no—
309C22×Q8—21no—
310C22×Q8—111no—
311C22×Q8C22×D1111yescharacteristic
312C22×D4—111no—
313C22×D4—222no—
314C22×D4C22⋊D1111yescharacteristic
315C23×C4—22no—
316C23×C4C22×D1112yes—
317C2×Q16—222no—
318C2×Q16—442no—
319C2×SD16—222no—
320C2×SD16—442no—
321C22×C8—111no—
322C22×C8—111no—
323C22×C8—112no—
324C4⋊Q8—22no—
325C4⋊Q8C22⋊D1114yescomplemented
326#125—28no—
327#124—222no—
328#124—222no—
329C22⋊Q8—216no—
330C22⋊Q8—24no—
331C22⋊Q8—24no—
332C22⋊Q8—224no—
333C22⋊Q8—442no—
334#121—224no—
335#121—442no—
336C4×Q8—22no—
337C4×Q8C22⋊D1114yescomplemented
338C4×D4—28no—
339C4×D4—22no—
340C4×D4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4C22⋊D1111yescharacteristic
350C2×C4⋊C4C22×D1111yescharacteristic
351C2×C4⋊C4C22×D1112yes—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—222no—
355C2×C22⋊C4—221no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4C22⋊D1112yes—
358C2×C42—21no—
359C2×C42—221no—
360C2×C42C22×D1111yescharacteristic
361C4⋊C8—222no—
362#103—224no—
363#103—222no—
364#103—224no—
365#102—222no—
366#102—224no—
367C22⋊C8—442no—
368C22⋊C8—442no—
369#97—222no—
370#95—221no—
371C2×C11—44no—
372C2×C11#243111yescharacteristic
373C2×C11#300411yescharacteristic
374C2×C11#301211yescharacteristic
375C2×C11#331412yes—
376C2×C11#331612yes—
377D11—161no—
378C24—221no—
379C24C2×C22⋊D1112yes—
380C2×Q8—24no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—81no—
385C2×Q8—81no—
386C2×Q8—222no—
387C2×Q8—222no—
388C2×Q8—221no—
389C2×Q8—221no—
390C2×Q8C2×C22⋊D1112yes—
391C2×D4—24no—
392C2×D4—22no—
393C2×D4—222no—
394C2×D4—222no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4—444no—
398C2×D4—444no—
399C2×D4—882no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—28no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—82no—
411C22×C4—82no—
412C22×C4—222no—
413C22×C4—221no—
414C22×C4C2×C22⋊D1112yes—
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C2×C22⋊D1111yescharacteristic
417C22×C4C23×D1111yescharacteristic
418Q16—444no—
419SD16—444no—
420C2×C8—222no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8—222no—
425C2×C8—221no—
426C2×C8—221no—
427C4⋊C4—28no—
428C4⋊C4—28no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—114no—
435C4⋊C4—222no—
436C4⋊C4—444no—
437C4⋊C4C2×C22⋊D1112yes—
438C4⋊C4C2×C22⋊D1114yes—
439C22⋊C4—28no—
440C22⋊C4—24no—
441C22⋊C4—444no—
442C22⋊C4—444no—
443C22⋊C4—442no—
444C22⋊C4—442no—
445C42—24no—
446C42—881no—
447C42C2×C22⋊D1112yes—
448C42C2×C22⋊D1112yes—
449C11#2557911yescharacteristic, complemented, Sylow
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—442no—
457C23—442no—
458C23—441no—
459C23—441no—
460C23—441no—
461C23#6699514yes—
462C23C22×C22⋊D1111yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—42no—
466Q8—84no—
467Q8—441no—
468Q8—441no—
469Q8—442no—
470D4—28no—
471D4—441no—
472D4—441no—
473D4—442no—
474D4—888no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—88no—
494C2×C4—224no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4—441no—
499C2×C4#6700612yes—
500C2×C4#6700612yes—
501C2×C4#41×D1112yes—
502C2×C4#6704212yes—
503C2×C4C22×C22⋊D1111yescharacteristic
504C2×C4C22×C22⋊D1111yescharacteristic
505C8—441no—
506C8—441no—
507C8—442no—
508C22—24no—
509C22—24no—
510C22—24no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—881no—
516C22—881no—
517C22—882no—
518C22—882no—
519C22—881no—
520C22C2×#6699512yes—
521C22#1062336012yes—
522C22#1062336611yescharacteristic
523C22#1062336711yescharacteristic
524C22C2×#6700611yescharacteristic
525C4—22no—
526C4—22no—
527C4—42no—
528C4—42no—
529C4—42no—
530C4—44no—
531C4—444no—
532C4—881no—
533C4#1062336111yescharacteristic
534C4#1062336311yescharacteristic
535C4#1062336512yes—
536C2—44no—
537C2—1761no—
538C2#1307223111yescharacteristic
539C2#1307785011yescharacteristic
540C2#1307792011yescharacteristic
541C2#1308069112yes—
542C2#1308072112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radical#13073555C2
hypercenterC2×#554D11
hypocenterC11#25579
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#10622702C2semidirect
2. C2×#10622641C2semidirect
4. #13069624C2semidirect
5. #13069617C2semidirect
6. #13069569C2semidirect
7. #13069415C2semidirect
8. #13068933C2semidirect
9. #13068923C2semidirect
10. #13068446C2semidirect
11. C2×C11×#554C2semidirect
54. C11×C4⋊Q8D4semidirect
60. C4×Q8×C11D4semidirect
179. C2×#554D11semidirect
325. C4⋊Q8C22⋊D11semidirect
337. C4×Q8C22⋊D11semidirect
449. C11#25579semidirect

Maximal subgroups

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

subgroupindex
C2×#106227022
C2×#106226412
#130735552
#130696242
#130696172
#130695692
#130694152
#130689332
#130689232
#130684462
C2×C11×#5542
#2557911