Finite Group Databasebeta

← #14807088

Subgroups — #14807088

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 534 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#13069565C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068938C212yesmaximal, complemented
9#13068928C212yesmaximal, complemented
10#13068446C211yesmaximal, characteristic, complemented
11C2×C11×#556C211yesmaximal, characteristic, complemented
12C11×#556—24no—
13C11×#556—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#124—21no—
17C2×C11×C22⋊Q8C2212yes—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117C2212yes—
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×C11C2312yes—
49C22×C22⋊D11—22no—
50C22×D44C2311yescharacteristic
51C22×Dic22C2311yescharacteristic
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8D414yescomplemented
54C11×#126—216no—
55C11×#124—28no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—24no—
58C4×Q8×C11—28no—
59C4×Q8×C11—22no—
60C4×Q8×C11D414yescomplemented
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C11×#117—24no—
64C11×#117—24no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4D412yes—
74C2×C42×C11—22no—
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#25580—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—44no—
115C2×Q8×C11C2×D412yes—
116C2×D4×C11—22no—
117C2×D4×C11—42no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C2×C22⋊D11—44no—
132C2×C22⋊D11—44no—
133C2×C22⋊D11—82no—
134C22×Dic11—22no—
135C22×Dic11—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—22no—
139C2×D44—22no—
140C2×Dic22—21no—
141C2×Dic22—21no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4C2×D412yes—
151C11×C4⋊C4C2×D414yes—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—28no—
154C11×C22⋊C4—24no—
155C42×C11—28no—
156C42×C11—24no—
157C42×C11C2×D412yes—
158C42×C11C2×D412yes—
159C22⋊Dic11—44no—
160#4326—44no—
161#4325—44no—
162(C2×D11)⋊C4—44no—
163(C2×D11)⋊C4—42no—
164(C2×D11)⋊C4—42no—
165C4⋊Dic11—22no—
166C4⋊Dic11#4114yes—
167Dic11⋊C4—44no—
168C4×Dic11—81no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×#556D1111yescharacteristic, complemented
177C2×#489—111no—
178C2×#464—111no—
179#2540—111no—
180#2001—112no—
181#2000—112no—
182#1987—111no—
183#1955—111no—
184#1875—112no—
185#1873—112no—
186#1763—111no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11C22×D411yescharacteristic
195C22×D11—41no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—41no—
199C22×D11—41no—
200Q8×C11—22no—
201Q8×C11—22no—
202Q8×C11—48no—
203Q8×C11—42no—
204D4×C11—44no—
205C2×C4×C11—22no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11#12012yes—
223C2×C4×C11#12012yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C2×#4112yes—
227C2×C4×C11H(5,𝔽2)12yes—
228C22⋊D11—88no—
229C2×Dic11—24no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—41no—
233C2×Dic11—42no—
234D44—41no—
235D44—41no—
236D44—42no—
237Dic22—41no—
238Dic22—41no—
239Dic22—42no—
240C11⋊C8—41no—
241C11⋊C8—41no—
242C11⋊C8—42no—
243C22×Q16—111no—
244C22×SD16—111no—
245#556—24no—
246#556—24no—
247C2×C4⋊Q8C2×D1111yescharacteristic
248C2×#126—22no—
249C2×#124—21no—
250C2×#124—111no—
251C2×C22⋊Q8—112no—
252C2×C22⋊Q8C2×D1112yes—
253C2×#121—112no—
254C2×C4×Q8—21no—
255C2×C4×Q8C2×D1111yescharacteristic
256C2×C4×D4C2×D1111yescharacteristic
257C2×#117C2×D1112yes—
258#489—224no—
259#464—224no—
260C2×C4⋊C8—111no—
261C2×#103—112no—
262C2×#103—112no—
263C2×#103—111no—
264C2×#102—112no—
265C2×#102—111no—
266C2×C22⋊C8—112no—
267C2×C22⋊C8—112no—
268C2×#97—111no—
269#399—221no—
270#392—221no—
271#390—222no—
272C4×C4⋊C4—111no—
273#340—112no—
274#340—112no—
275#340—112no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11C2×#12011yescharacteristic
284C22×C11#54612yes—
285C22×C11#57512yes—
286C22×C11#57711yescharacteristic
287C22×C11#57811yescharacteristic
288C2×D11—81no—
289C2×D11—81no—
290C2×D11—81no—
291C2×D11—82no—
292C2×D11—82no—
293C4×C11—22no—
294C4×C11—22no—
295C4×C11—42no—
296C4×C11—42no—
297C4×C11—44no—
298C4×C11—42no—
299C4×C11#53211yescharacteristic
300C4×C11#53511yescharacteristic
301C4×C11#55012yes—
302Dic11—44no—
303Dic11—81no—
304C22×Q8—21no—
305C22×Q8—111no—
306C22×Q8C22×D1111yescharacteristic
307C22×D4—111no—
308C22×D4—222no—
309C22×D4C22⋊D1111yescharacteristic
310C23×C4C22×D1112yes—
311C2×Q16—222no—
312C2×Q16—442no—
313C2×SD16—222no—
314C2×SD16—442no—
315C22×C8—111no—
316C22×C8—111no—
317C22×C8—112no—
318C4⋊Q8—22no—
319C4⋊Q8C22⋊D1114yescomplemented
320#126—216no—
321#124—28no—
322#124—222no—
323#124—222no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326C22⋊Q8—224no—
327C22⋊Q8—442no—
328#121—224no—
329#121—442no—
330C4×Q8—28no—
331C4×Q8—22no—
332C4×Q8C22⋊D1114yescomplemented
333C4×D4—22no—
334C4×D4—22no—
335#117—24no—
336#117—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—112no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4C22⋊D1111yescharacteristic
343C2×C4⋊C4C22×D1111yescharacteristic
344C2×C4⋊C4C22×D1112yes—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—222no—
348C2×C22⋊C4—222no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4C22⋊D1112yes—
352C2×C42—22no—
353C2×C42—21no—
354C2×C42—221no—
355C2×C42C22×D1111yescharacteristic
356C4⋊C8—222no—
357#103—224no—
358#103—222no—
359#103—224no—
360#102—222no—
361#102—224no—
362C22⋊C8—442no—
363C22⋊C8—442no—
364#97—222no—
365#95—221no—
366C2×C11—82no—
367C2×C11#243111yescharacteristic
368C2×C11#300511yescharacteristic
369C2×C11#301311yescharacteristic
370C2×C11#331112yes—
371C2×C11#331312yes—
372D11—161no—
373C24—221no—
374C24C2×C22⋊D1112yes—
375C2×Q8—24no—
376C2×Q8—21no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—44no—
380C2×Q8—222no—
381C2×Q8—222no—
382C2×Q8—221no—
383C2×Q8—221no—
384C2×Q8C2×C22⋊D1112yes—
385C2×D4—22no—
386C2×D4—42no—
387C2×D4—222no—
388C2×D4—222no—
389C2×D4—221no—
390C2×D4—221no—
391C2×D4—444no—
392C2×D4—444no—
393C2×D4—882no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—222no—
404C22×C4—221no—
405C22×C4C2×C22⋊D1112yes—
406C22×C4C2×C22⋊D1111yescharacteristic
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409Q16—444no—
410SD16—444no—
411C2×C8—222no—
412C2×C8—222no—
413C2×C8—222no—
414C2×C8—222no—
415C2×C8—222no—
416C2×C8—221no—
417C2×C8—221no—
418C4⋊C4—28no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—114no—
425C4⋊C4—222no—
426C4⋊C4—444no—
427C4⋊C4C2×C22⋊D1112yes—
428C4⋊C4C2×C22⋊D1114yes—
429C22⋊C4—28no—
430C22⋊C4—28no—
431C22⋊C4—24no—
432C22⋊C4—444no—
433C22⋊C4—444no—
434C22⋊C4—442no—
435C22⋊C4—442no—
436C42—28no—
437C42—24no—
438C42—881no—
439C42C2×C22⋊D1112yes—
440C42C2×C22⋊D1112yes—
441C11#2558011yescharacteristic, complemented, Sylow
442C23—22no—
443C23—22no—
444C23—22no—
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—442no—
450C23—442no—
451C23—441no—
452C23—441no—
453C23—441no—
454C23C22×C22⋊D1111yescharacteristic
455Q8—22no—
456Q8—22no—
457Q8—48no—
458Q8—42no—
459Q8—441no—
460Q8—441no—
461Q8—442no—
462D4—44no—
463D4—441no—
464D4—441no—
465D4—442no—
466D4—888no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—44no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—224no—
485C2×C4—442no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—441no—
489C2×C4#6700612yes—
490C2×C4#6700612yes—
491C2×C4#41×D1112yes—
492C2×C4#6704212yes—
493C2×C4C22×C22⋊D1111yescharacteristic
494C2×C4C22×C22⋊D1111yescharacteristic
495C8—441no—
496C8—441no—
497C8—442no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—882no—
506C22—881no—
507C22—882no—
508C22—881no—
509C22—881no—
510C22#1062335312yes—
511C22#1062336012yes—
512C22#1062336811yescharacteristic
513C22#1062336911yescharacteristic
514C22C2×#6700611yescharacteristic
515C4—22no—
516C4—22no—
517C4—44no—
518C4—42no—
519C4—42no—
520C4—42no—
521C4—444no—
522C4—881no—
523C4#1062336111yescharacteristic
524C4#1062336311yescharacteristic
525C4#1062336512yes—
526C2—82no—
527C2—1761no—
528C2#1307223111yescharacteristic
529C2#1307785811yescharacteristic
530C2#1307793111yescharacteristic
531C2#1308064612yes—
532C2#1308067612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radical#13073555C2
hypercenterC2×#556D11
hypocenterC11#25580
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

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. #13069565C2semidirect
7. #13069415C2semidirect
8. #13068938C2semidirect
9. #13068928C2semidirect
10. #13068446C2semidirect
11. C2×C11×#556C2semidirect
53. C11×C4⋊Q8D4semidirect
60. C4×Q8×C11D4semidirect
176. C2×#556D11semidirect
319. C4⋊Q8C22⋊D11semidirect
332. C4×Q8C22⋊D11semidirect
441. C11#25580semidirect

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
#130695652
#130694152
#130689382
#130689282
#130684462
C2×C11×#5562
#2558011