Finite Group Databasebeta

← #14727818

Subgroups — #14727818

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#13081949C211yesmaximal, characteristic
2#13079744C212yesmaximal, complemented
3#13067652C214yesmaximal, complemented
4#13067635C214yesmaximal, complemented
5#13067175C212yesmaximal, complemented
6#13066930C211yesmaximal, characteristic, complemented
7C11×#2628C211yesmaximal, characteristic, complemented
8C22×#4339—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic, complemented
10C2×C11×#117C2211yescharacteristic
11#10623057—22no—
12#10623056—22no—
13#10623055—24no—
14#10623041—21no—
15#10623041C2212yes—
16#10623024—21no—
17#10623024C2212yes—
18#10623008—21no—
19#10623008C2212yes—
20C11×#400C2212yescomplemented
21C11×#399C2212yes—
22C11×#395—21no—
23C11×#393—21no—
24C11×#389—21no—
25C11×#382C2211yescharacteristic, complemented
26C11×#380—21no—
27#10622701—22no—
28#10622697—24no—
29#10622692—22no—
30#10622581C2218yescomplemented
31#10622538C2212yescomplemented
32#10622166C2212yescomplemented
33#10622163C2212yes—
34#10622089C2218yescomplemented
35C22×Q8×C11—21no—
36C23×C4×C11D411yescharacteristic
37C22×C22⋊D11—22no—
38C2×#4339—22no—
39C2×#4339—22no—
40C2×#4339—22no—
41C2×#4339—22no—
42C2×#4339—44no—
43C2×#4339—44no—
44C22×D44—21no—
45C22×C4×D11—22no—
46C22×Dic22—21no—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C11×#117—22no—
50C11×#117—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4D411yescharacteristic
59C2×C11×C22⋊C4C2311yescharacteristic
60C2×C42×C11D411yescharacteristic
61C2×C42×C11C2311yescharacteristic
62#66983—22no—
63#66983—22no—
64#66983—22no—
65#66983C2314yes—
66#66950—24no—
67#66950—24no—
68#66948—24no—
69#66948—24no—
70#66939—24no—
71#66939—24no—
72#66935—24no—
73#66935—24no—
74#66928—22no—
75#66928—22no—
76#66927—21no—
77#66927D412yes—
78C4×D44—22no—
79C4×D44—22no—
80C4×D44—22no—
81C4×D44D414yes—
82#66922—21no—
83#66922D412yes—
84C11×#95—22no—
85C11×#95—21no—
86C11×#95—22no—
87C11×#95C2312yes—
88C22⋊(C11⋊C8)C2314yes—
89#66873—28no—
90#66872—28no—
91C4⋊(C11⋊C8)—22no—
92C4×C11⋊C8—22no—
93#18309—111nomaximal, Sylow
94C24×C11C2×D411yescharacteristic
95C23×D11—22no—
96C2×Q8×C11—42no—
97C2×Q8×C11—82no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11SD1614yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C2×C22⋊D11—24no—
111C2×C22⋊D11—24no—
112C2×C22⋊D11—44no—
113C2×C22⋊D11—44no—
114C22×Dic11—22no—
115#4339—44no—
116#4339—48no—
117#4339—48no—
118#4339—44no—
119#4339—44no—
120#4339—44no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—44no—
127C2×D44C2×D414yes—
128C2×C4×D11—24no—
129C2×C4×D11—24no—
130C2×C4×D11—48no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22—44no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—82no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—82no—
144C42×C11—21no—
145C42×C11—21no—
146C42×C11C2×D412yes—
147C42×C11C2×D412yes—
148(C2×D11)⋊C4—24no—
149(C2×D11)⋊C4—24no—
150(C2×D11)⋊C4—24no—
151(C2×D11)⋊C4—24no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11C2×D414yes—
156C2×C11⋊C8—24no—
157#3449—111no—
158#3227—112no—
159#2628D1111yescharacteristic, complemented
160#1616—114no—
161#1613—114no—
162#1517—112no—
163#1458—111no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11C2×SD1612yes—
169C23×C11C22×D411yescharacteristic
170C22×D11—24no—
171C22×D11—44no—
172C22×D11—82no—
173C22×D11—82no—
174Q8×C11—84no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11#12012yes—
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11#12011yescharacteristic
194C2×C4×C11C2×SD1612yes—
195C2×C4×C11C2×SD1612yes—
196C2×C4×C11AGL(1,ℤ/8)12yes—
197C2×C4×C11C22×D412yes—
198C22⋊D11—48no—
199C22⋊D11—44no—
200C22⋊D11—44no—
201C2×Dic11—24no—
202C2×Dic11—44no—
203D44—44no—
204D44—44no—
205D44—44no—
206D44—82no—
207D44—82no—
208D44—82no—
209C4×D11—48no—
210C4×D11—48no—
211Dic22—44no—
212Dic22—44no—
213C11⋊C8—44no—
214C22×#41—221no—
215#537—112no—
216#537—221no—
217#536—222no—
218#535—222no—
219#534—112no—
220#534—221no—
221#532—112no—
222#532—221no—
223C2×C4⋊Q8C2×D1111yescharacteristic, complemented
224#525—224no—
225C2×#117C2×D1111yescharacteristic
226#498—222no—
227#486—222no—
228#481—118no—
229#476—224no—
230#431—112no—
231#400C2×D1112yescomplemented
232#399C2×D1112yes—
233#395—21no—
234#393—21no—
235#389—21no—
236#382C2×D1111yescharacteristic, complemented
237#380—21no—
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—81no—
248C22×C11C2×#12011yescharacteristic
249C22×C11C22×SD1611yescharacteristic
250C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
251C2×D11—44no—
252C2×D11—44no—
253C2×D11—44no—
254C2×D11—88no—
255C4×C11—22no—
256C4×C11—22no—
257C4×C11—22no—
258C4×C11—41no—
259C4×C11—41no—
260C4×C11—82no—
261C4×C11—82no—
262C4×C11#45012yes—
263C4×C11#45012yes—
264Dic11—44no—
265C2×#41—222no—
266C2×#41—222no—
267C2×#41—222no—
268C2×#41—222no—
269C2×#41—444no—
270C2×#41—444no—
271C22×Q8—21no—
272C22×Q8—221no—
273C22×D4—221no—
274C22×D4—222no—
275C23×C4—222no—
276C23×C4C22⋊D1111yescharacteristic
277C4⋊Q8—22no—
278C4⋊Q8—22no—
279C4⋊Q8—112no—
280C4⋊Q8—221no—
281#127—112no—
282#127—221no—
283#124—222no—
284#124—222no—
285#123—224no—
286#123—224no—
287C22⋊Q8—224no—
288C22⋊Q8—224no—
289#121—114no—
290#121—224no—
291#121—224no—
292#121—222no—
293#121—222no—
294#121—222no—
295#120—224no—
296#120—224no—
297C4×D4—114no—
298C4×D4—222no—
299C4×D4—222no—
300C4×D4—222no—
301#117—22no—
302#117—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4C22⋊D1111yescharacteristic
307C2×C4⋊C4C22×D1112yes—
308C2×C4⋊C4C22×D1111yescharacteristic
309C2×C22⋊C4—22no—
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—22no—
320#95—21no—
321#95—22no—
322#95C22×D1112yes—
323C2×C11—21no—
324C2×C11—21no—
325C2×C11—42no—
326C2×C11C2×#45011yescharacteristic
327C2×C11#302111yescharacteristic
328C2×C11#302811yescharacteristic
329D11—84no—
330C24—222no—
331C24C2×C22⋊D1111yescharacteristic
332#41—444no—
333#41—448no—
334#41—448no—
335#41—444no—
336#41—444no—
337#41—444no—
338C2×Q8—42no—
339C2×Q8—82no—
340C2×Q8—222no—
341C2×Q8—222no—
342C2×Q8—444no—
343C2×D4—114no—
344C2×D4—222no—
345C2×D4—222no—
346C2×D4—222no—
347C2×D4—224no—
348C2×D4—224no—
349C2×D4—222no—
350C2×D4—222no—
351C2×D4—444no—
352C2×D4—444no—
353C2×D4—444no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—224no—
360C22×C4—222no—
361C22×C4—224no—
362C22×C4—448no—
363C22×C4#432514yes—
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—24no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—42no—
377C4⋊C4—82no—
378C4⋊C4—114no—
379C4⋊C4—222no—
380C4⋊C4—222no—
381C4⋊C4—222no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—82no—
385C22⋊C4—224no—
386C22⋊C4—224no—
387C22⋊C4—224no—
388C22⋊C4—224no—
389C42—21no—
390C42—21no—
391C42D4×D1112yes—
392C42D4×D1112yes—
393C11#1830911yescharacteristic, complemented, Sylow
394C23—21no—
395C23—21no—
396C23—41no—
397C23—41no—
398C23—224no—
399C23—444no—
400C23—882no—
401C23—882no—
402C23C2×#432512yes—
403C23C22×C22⋊D1111yescharacteristic
404Q8—84no—
405Q8—444no—
406Q8—444no—
407D4—444no—
408D4—444no—
409D4—448no—
410D4—444no—
411D4—444no—
412D4—444no—
413D4—882no—
414D4—882no—
415D4—882no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—224no—
433C2×C4—448no—
434C2×C4—444no—
435C2×C4—448no—
436C2×C4#6699012yes—
437C2×C4#6699011yescharacteristic
438C2×C4#6699011yescharacteristic
439C2×C4C2×#432512yes—
440C2×C4C2×#432512yes—
441C2×C4#6700212yes—
442C2×C4C2×D4×D1112yes—
443C8—444no—
444C22—21no—
445C22—21no—
446C22—22no—
447C22—42no—
448C22—41no—
449C22—41no—
450C22—81no—
451C22—444no—
452C22—444no—
453C22—444no—
454C22—888no—
455C22C2×#6699011yescharacteristic
456C22C22×#432511yescharacteristic
457C22C2×#6700211yescharacteristic
458C4—22no—
459C4—22no—
460C4—22no—
461C4—41no—
462C4—41no—
463C4—82no—
464C4—82no—
465C4—444no—
466C4#1062265912yes—
467C4#1062265912yes—
468C2—21no—
469C2—21no—
470C2—42no—
471C2—884no—
472C2C2×#1062265911yescharacteristic
473C2#1307798711yescharacteristic
474C2#1307802111yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2628C2
socleC22×C11C2×#120
prime radical#13081949C2
hypercenter#2628D11
hypocenterC11#18309
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2628

Complements

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

NH ≅ G/Ntype
2. #13079744C2semidirect
3. #13067652C2semidirect
4. #13067635C2semidirect
5. #13067175C2semidirect
6. #13066930C2semidirect
7. C11×#2628C2semidirect
9. C2×C11×C4⋊Q8C22semidirect
20. C11×#400C22semidirect
25. C11×#382C22semidirect
30. #10622581C22semidirect
31. #10622538C22semidirect
32. #10622166C22semidirect
34. #10622089C22semidirect
159. #2628D11semidirect
223. C2×C4⋊Q8C2×D11semidirect
231. #400C2×D11semidirect
236. #382C2×D11semidirect
393. C11#18309semidirect

Maximal subgroups

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

subgroupindex
#130819492
#130797442
#130676522
#130676352
#130671752
#130669302
C11×#26282
#1830911