Finite Group Databasebeta

← #14727819

Subgroups — #14727819

Order 2816.

1168 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079741C212yesmaximal, complemented
2#13074437C211yesmaximal, characteristic, complemented
3#13067653C214yesmaximal, complemented
4#13067636C214yesmaximal, complemented
5#13067176C212yesmaximal, complemented
6#13066930C211yesmaximal, characteristic, complemented
7C11×#3449C211yesmaximal, characteristic
8C22×C11×#41—21no—
9C11×#537—21no—
10C11×#537C2212yes—
11C11×#536—22no—
12C11×#535—22no—
13C11×#534—21no—
14C11×#534C2212yes—
15C11×#532—21no—
16C11×#532C2212yes—
17C11×#525—24no—
18C2×C11×#117C2211yescharacteristic
19C2×#66922C2211yescharacteristic, complemented
20#10622825—21no—
21#10622692—22no—
22#10622683—22no—
23#10622647C2218yescomplemented
24#10622621—24no—
25#10622599C2212yescomplemented
26#10622592—21no—
27#10622562C2212yes—
28#10622560—21no—
29#10622549C2211yescharacteristic, complemented
30#10622541—21no—
31#10622538C2212yescomplemented
32#10622175C2218yescomplemented
33#10622166C2212yescomplemented
34#10622163C2212yes—
35C2×C11×#41—22no—
36C2×C11×#41—22no—
37C2×C11×#41—22no—
38C2×C11×#41—22no—
39C2×C11×#41—44no—
40C2×C11×#41—44no—
41C22×Q8×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11D411yescharacteristic
46C22×Dic22—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8D412yes—
49C11×#127—21no—
50C11×#127D412yes—
51C11×#124—22no—
52C11×#124—22no—
53C11×#123—24no—
54C11×#123—24no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—24no—
57C11×#121—24no—
58C11×#121—24no—
59C11×#121—22no—
60C11×#121—22no—
61C11×#121—22no—
62C11×#121C2314yes—
63C11×#120—24no—
64C11×#120—24no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11D414yes—
69C11×#117—22no—
70C11×#117—22no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C11×C22⋊C4C2311yescharacteristic
75C2×C42×C11D411yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—22no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2312yes—
81C2×Dic11⋊C4—22no—
82#66922—22no—
83#66922—22no—
84#66896—28no—
85C11⋊#95—22no—
86C11⋊#95—21no—
87C11⋊#95—22no—
88C11⋊#95C2312yes—
89C22⋊(C11⋊C8)C2314yes—
90#66872—28no—
91C4⋊(C11⋊C8)—22no—
92C4×C11⋊C8—22no—
93#18309—111nomaximal, Sylow
94C24×C11—22no—
95C24×C11C2×D411yescharacteristic
96C11×#41—44no—
97C11×#41—48no—
98C11×#41—48no—
99C11×#41—44no—
100C11×#41—44no—
101C11×#41—44no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—44no—
105C2×D4×C11—24no—
106C2×D4×C11—22no—
107C2×D4×C11—24no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—44no—
113C2×D4×C11—44no—
114C2×D4×C11—44no—
115C2×D4×C11C2×D414yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—48no—
123C22×C4×C11SD1614yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C22×Dic11—22no—
131C22×Dic11—22no—
132C2×Dic22—42no—
133C2×Dic22—82no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4C2×D414yes—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—24no—
146C42×C11—21no—
147C42×C11—21no—
148C42×C11C2×D412yes—
149C42×C11C2×D412yes—
150C22⋊Dic11—82no—
151C4⋊Dic11—24no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154C4⋊Dic11—42no—
155Dic11⋊C4—82no—
156C2×C11⋊C8—24no—
157#3449D1111yescharacteristic
158#3227—112no—
159#2628—111no—
160#1616—114no—
161#1613—114no—
162#1517—112no—
163#1458—111no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—24no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—44no—
170C23×C11—82no—
171C23×C11—82no—
172C23×C11C2×SD1612yes—
173C23×C11C22×D411yescharacteristic
174Q8×C11—44no—
175Q8×C11—44no—
176D4×C11—44no—
177D4×C11—44no—
178D4×C11—48no—
179D4×C11—44no—
180D4×C11—44no—
181D4×C11—44no—
182D4×C11—82no—
183D4×C11—82no—
184D4×C11—82no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—24no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—48no—
195C2×C4×C11—44no—
196C2×C4×C11—48no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11#12012yes—
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11#12011yescharacteristic
202C2×C4×C11C2×SD1612yes—
203C2×C4×C11C2×SD1612yes—
204C2×C4×C11AGL(1,ℤ/8)12yes—
205C2×C4×C11C22×D412yes—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212Dic22—84no—
213C11⋊C8—44no—
214C22×#41—21no—
215#537—21no—
216#537C2×D1112yes—
217#536—22no—
218#535—22no—
219#534—21no—
220#534C2×D1112yes—
221#532—21no—
222#532C2×D1112yes—
223C2×C4⋊Q8—111no—
224#525—24no—
225C2×#117C2×D1111yescharacteristic
226#498—222no—
227#486—222no—
228#481—118no—
229#476—224no—
230#431—112no—
231#400—112no—
232#399—112no—
233#395—221no—
234#393—221no—
235#389—221no—
236#382—111no—
237#380—221no—
238#327—118no—
239#324—112no—
240#323—112no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—22no—
244C22×C11—42no—
245C22×C11—41no—
246C22×C11—41no—
247C22×C11—44no—
248C22×C11—44no—
249C22×C11—44no—
250C22×C11—81no—
251C22×C11—88no—
252C22×C11C2×#12011yescharacteristic
253C22×C11C22×SD1611yescharacteristic
254C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
255C4×C11—22no—
256C4×C11—22no—
257C4×C11—22no—
258C4×C11—44no—
259C4×C11—41no—
260C4×C11—41no—
261C4×C11#45012yes—
262C4×C11#45012yes—
263Dic11—82no—
264Dic11—82no—
265C2×#41—22no—
266C2×#41—22no—
267C2×#41—22no—
268C2×#41—22no—
269C2×#41—44no—
270C2×#41—44no—
271C22×Q8—21no—
272C22×Q8—221no—
273C22×D4—21no—
274C22×D4—22no—
275C23×C4—22no—
276C23×C4C22⋊D1111yescharacteristic
277C4⋊Q8—21no—
278C4⋊Q8—222no—
279C4⋊Q8—222no—
280C4⋊Q8C22⋊D1112yes—
281#127—21no—
282#127C22⋊D1112yes—
283#124—22no—
284#124—22no—
285#123—24no—
286#123—24no—
287C22⋊Q8—24no—
288C22⋊Q8—24no—
289#121—24no—
290#121—24no—
291#121—22no—
292#121—22no—
293#121—22no—
294#121C22×D1114yes—
295#120—24no—
296#120—24no—
297C4×D4—22no—
298C4×D4—22no—
299C4×D4—22no—
300C4×D4C22⋊D1114yes—
301#117—22no—
302#117—22no—
303C2×C4⋊C4—112no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4C22⋊D1111yescharacteristic
308C2×C4⋊C4C22×D1111yescharacteristic
309C2×C22⋊C4—222no—
310C2×C22⋊C4C22⋊D1111yescharacteristic
311C2×C22⋊C4C22×D1111yescharacteristic
312C2×C42C22⋊D1111yescharacteristic
313C2×C42C22×D1111yescharacteristic
314#106—228no—
315C4⋊C8—222no—
316#102—228no—
317C22⋊C8—114no—
318C4×C8—222no—
319#95—112no—
320#95—222no—
321#95—221no—
322#95—222no—
323C2×C11—21no—
324C2×C11—21no—
325C2×C11—42no—
326C2×C11—84no—
327C2×C11C2×#45011yescharacteristic
328C2×C11#302111yescharacteristic
329C2×C11#302811yescharacteristic
330C24—22no—
331C24C2×C22⋊D1111yescharacteristic
332#41—44no—
333#41—48no—
334#41—48no—
335#41—44no—
336#41—44no—
337#41—44no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—44no—
341C2×Q8—442no—
342C2×Q8—882no—
343C2×D4—24no—
344C2×D4—22no—
345C2×D4—24no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—44no—
351C2×D4—44no—
352C2×D4—44no—
353C2×D4C2×C22⋊D1114yes—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—24no—
358C22×C4—22no—
359C22×C4—24no—
360C22×C4—48no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4#432414yes—
364C22×C4C2×C22⋊D1111yescharacteristic
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367C22×C4C2×C22⋊D1111yescharacteristic
368C22×C4C2×C22⋊D1111yescharacteristic
369C22×C4C23×D1111yescharacteristic
370C2×C8—224no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—224no—
377C4⋊C4—442no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—882no—
381C4⋊C4C2×C22⋊D1114yes—
382C22⋊C4—24no—
383C22⋊C4—24no—
384C22⋊C4—22no—
385C22⋊C4—24no—
386C22⋊C4—22no—
387C22⋊C4—24no—
388C22⋊C4—882no—
389C42—21no—
390C42—21no—
391C42C2×C22⋊D1112yes—
392C42C2×C22⋊D1112yes—
393C11#1830911yescharacteristic, complemented, Sylow
394C23—21no—
395C23—21no—
396C23—24no—
397C23—41no—
398C23—41no—
399C23—44no—
400C23—82no—
401C23—82no—
402C23C2×#432412yes—
403C23C22×C22⋊D1111yescharacteristic
404Q8—44no—
405Q8—44no—
406Q8—884no—
407D4—44no—
408D4—44no—
409D4—48no—
410D4—44no—
411D4—44no—
412D4—44no—
413D4—82no—
414D4—82no—
415D4—82no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—48no—
426C2×C4—44no—
427C2×C4—48no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4#6698512yes—
437C2×C4C2×#432412yes—
438C2×C4C2×#432412yes—
439C2×C4#6700612yes—
440C2×C4#6700611yescharacteristic
441C2×C4#6700611yescharacteristic
442C2×C4C22×C22⋊D1112yes—
443C8—444no—
444C22—21no—
445C22—21no—
446C22—22no—
447C22—42no—
448C22—41no—
449C22—41no—
450C22—44no—
451C22—44no—
452C22—44no—
453C22—81no—
454C22—88no—
455C22C2×#6698511yescharacteristic
456C22C22×#432411yescharacteristic
457C22C2×#6700611yescharacteristic
458C4—22no—
459C4—22no—
460C4—22no—
461C4—41no—
462C4—44no—
463C4—41no—
464C4—882no—
465C4—882no—
466C4#1062283112yes—
467C4#1062283112yes—
468C2—21no—
469C2—21no—
470C2—42no—
471C2—84no—
472C2C2×#1062283111yescharacteristic
473C2#1307798811yescharacteristic
474C2#1307802211yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3449C2
socleC22×C11C2×#120
hypercenter#3449D11
hypocenterC11#18309
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #13079741C2semidirect
2. #13074437C2semidirect
3. #13067653C2semidirect
4. #13067636C2semidirect
5. #13067176C2semidirect
6. #13066930C2semidirect
19. C2×#66922C22semidirect
23. #10622647C22semidirect
25. #10622599C22semidirect
29. #10622549C22semidirect
31. #10622538C22semidirect
32. #10622175C22semidirect
33. #10622166C22semidirect
393. C11#18309semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130744372
#130676532
#130676362
#130671762
#130669302
C11×#34492
#1830911