Finite Group Databasebeta

← #14727826

Subgroups — #14727826

Order 2816.

908 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079757C212yesmaximal, complemented
2#13074382C211yesmaximal, characteristic
3#13067624C214yesmaximal, complemented
4#13067607C214yesmaximal
5#13067180C212yesmaximal, complemented
6#13066930C211yesmaximal, characteristic
7C11×#3458C211yesmaximal, characteristic
8C11×#544—22no—
9C11×#544—22no—
10C11×#544—21no—
11C11×#544C2212yes—
12C11×#543—21no—
13C11×#543C2212yes—
14C11×#533—24no—
15C11×#533—21no—
16C11×#533C2212yes—
17C2×C11×#117—21no—
18C2×C11×#117C2211yescharacteristic
19C2×#66977—21no—
20C2×#66922C2211yescharacteristic
21#10622694—22no—
22#10622692—22no—
23#10622656C2218yes—
24#10622633—24no—
25#10622596—21no—
26#10622596C2212yes—
27#10622566—21no—
28#10622566C2212yes—
29#10622549C2211yescharacteristic
30#10622542—21no—
31#10622538C2212yes—
32#10622176C2218yes—
33#10622166C2212yes—
34#10622163C2212yes—
35C23×C4×C11D411yescharacteristic
36C22×Dic22—21no—
37C11×C4⋊Q8—24no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—24no—
41C11×C4⋊Q8D412yes—
42C11×C4⋊Q8D412yes—
43C11×#125—24no—
44C11×#125—22no—
45C11×#125—24no—
46C11×#125—22no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—24no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8C2314yes—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×Q8×C11D414yes—
59C11×#117—22no—
60C11×#117—22no—
61C11×#117—22no—
62C11×#117—22no—
63C11×#117—22no—
64C11×#117—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C11×C22⋊C4C2311yescharacteristic
72C2×C42×C11—22no—
73C2×C42×C11D411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2312yes—
79#66977—44no—
80C2×Dic11⋊C4—22no—
81#66922—22no—
82#66922—22no—
83#66899—28no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—21no—
87C11⋊#95C2312yes—
88C22⋊(C11⋊C8)C2314yes—
89#66872—28no—
90C4⋊(C11⋊C8)—22no—
91C4×C11⋊C8—22no—
92#18310—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11C2×D414yes—
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
110C22×Dic11—22no—
111C22×Dic11—22no—
112C2×Dic22—41no—
113C2×Dic22—41no—
114C2×Dic22—42no—
115C2×Dic22—42no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4C2×D414yes—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—22no—
133C11×C22⋊C4—22no—
134C42×C11—24no—
135C42×C11—24no—
136C42×C11—21no—
137C42×C11—21no—
138C42×C11C2×D412yes—
139C42×C11C2×D412yes—
140C22⋊Dic11—44no—
141C4⋊Dic11—24no—
142C4⋊Dic11—42no—
143C4⋊Dic11—42no—
144Dic11⋊C4—44no—
145C2×C11⋊C8—24no—
146#3458D1111yescharacteristic
147#3229—112no—
148#2621—111no—
149#1611—114no—
150#1608—114no—
151#1518—112no—
152#1458—111no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11C2×SD1612yes—
158C23×C11C22×D411yescharacteristic
159Q8×C11—44no—
160Q8×C11—82no—
161Q8×C11—82no—
162Q8×C11—82no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—24no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—82no—
176C2×C4×C11—82no—
177C2×C4×C11#12012yes—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11C2×SD1612yes—
181C2×C4×C11C2×SD1612yes—
182C2×C4×C11#13712yes—
183C2×C4×C11C22×D412yes—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190Dic22—82no—
191Dic22—82no—
192C11⋊C8—44no—
193#544—22no—
194#544—22no—
195#544—21no—
196#544C2×D1112yes—
197#543—21no—
198#543C2×D1112yes—
199#533—24no—
200#533—21no—
201#533C2×D1112yes—
202C2×C4⋊Q8—111no—
203C2×C22⋊Q8—221no—
204C2×#117—21no—
205C2×#117C2×D1111yescharacteristic
206#498—222no—
207#487—222no—
208#483—118no—
209#475—224no—
210#431—112no—
211#398—112no—
212#398—221no—
213#397—112no—
214#397—221no—
215#391—221no—
216#382—111no—
217#328—118no—
218#324—112no—
219#323—112no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—22no—
223C22×C11—42no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—81no—
227C22×C11C2×#12011yescharacteristic
228C22×C11C22×SD1611yescharacteristic
229C22×C11C2×#13711yescharacteristic
230C4×C11—22no—
231C4×C11—22no—
232C4×C11—22no—
233C4×C11—41no—
234C4×C11—44no—
235C4×C11—41no—
236C4×C11—44no—
237C4×C11#44812yes—
238C4×C11#44812yes—
239Dic11—82no—
240Dic11—82no—
241C22×Q8—221no—
242C23×C4C22⋊D1111yescharacteristic
243C4⋊Q8—24no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—24no—
247C4⋊Q8—222no—
248C4⋊Q8—222no—
249C4⋊Q8C22⋊D1112yes—
250C4⋊Q8C22⋊D1112yes—
251#125—24no—
252#125—22no—
253#125—24no—
254#125—22no—
255C22⋊Q8—24no—
256C22⋊Q8—24no—
257C22⋊Q8—24no—
258C22⋊Q8—22no—
259C22⋊Q8—22no—
260C22⋊Q8—22no—
261C22⋊Q8—24no—
262C22⋊Q8—444no—
263C22⋊Q8C22×D1114yes—
264C4×Q8—22no—
265C4×Q8—22no—
266C4×Q8—22no—
267C4×Q8C22⋊D1114yes—
268#117—22no—
269#117—22no—
270#117—22no—
271#117—22no—
272#117—22no—
273#117—22no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—221no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4—221no—
280C2×C4⋊C4C22⋊D1111yescharacteristic
281C2×C4⋊C4C22×D1111yescharacteristic
282C2×C22⋊C4—22no—
283C2×C22⋊C4—222no—
284C2×C22⋊C4C22⋊D1111yescharacteristic
285C2×C22⋊C4C22×D1111yescharacteristic
286C2×C42—22no—
287C2×C42C22⋊D1111yescharacteristic
288C2×C42C22×D1111yescharacteristic
289#106—228no—
290C4⋊C8—222no—
291#103—228no—
292C22⋊C8—114no—
293C4×C8—222no—
294#95—112no—
295#95—221no—
296#95—222no—
297#95—222no—
298C2×C11—21no—
299C2×C11—21no—
300C2×C11—42no—
301C2×C11C2×#44811yescharacteristic
302C2×C11#302211yescharacteristic
303C2×C11#302811yescharacteristic
304C24C2×C22⋊D1111yescharacteristic
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—442no—
309C2×Q8—442no—
310C2×Q8—441no—
311C2×Q8—441no—
312C2×Q8C2×C22⋊D1114yes—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—222no—
319C22×C4—222no—
320C22×C4#432514yes—
321C22×C4C2×C22⋊D1111yescharacteristic
322C22×C4C2×C22⋊D1111yescharacteristic
323C22×C4C2×C22⋊D1111yescharacteristic
324C22×C4C2×C22⋊D1111yescharacteristic
325C22×C4C2×C22⋊D1111yescharacteristic
326C22×C4C23×D1111yescharacteristic
327C2×C8—224no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—24no—
339C4⋊C4—22no—
340C4⋊C4—24no—
341C4⋊C4—224no—
342C4⋊C4—444no—
343C4⋊C4—442no—
344C4⋊C4—442no—
345C4⋊C4C2×C22⋊D1114yes—
346C22⋊C4—24no—
347C22⋊C4—24no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—444no—
351C42—24no—
352C42—24no—
353C42—21no—
354C42—21no—
355C42C2×C22⋊D1112yes—
356C42C2×C22⋊D1112yes—
357C11#1831011yescharacteristic, complemented, Sylow
358C23—21no—
359C23—21no—
360C23—41no—
361C23—41no—
362C23C2×#432512yes—
363C23C22×C22⋊D1111yescharacteristic
364Q8—44no—
365Q8—82no—
366Q8—82no—
367Q8—82no—
368Q8—882no—
369Q8—882no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—24no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4C2×#432512yes—
391C2×C4C2×#432512yes—
392C2×C4#6699512yes—
393C2×C4#6700612yes—
394C2×C4#6700611yescharacteristic
395C2×C4#6700611yescharacteristic
396C2×C4C22×C22⋊D1112yes—
397C8—444no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—42no—
402C22—41no—
403C22—41no—
404C22—81no—
405C22C22×#432511yescharacteristic
406C22C2×#6699511yescharacteristic
407C22C2×#6700611yescharacteristic
408C4—22no—
409C4—22no—
410C4—22no—
411C4—41no—
412C4—44no—
413C4—41no—
414C4—44no—
415C4—882no—
416C4—882no—
417C4#1062284012yes—
418C4#1062284012yes—
419C2—21no—
420C2—21no—
421C2—42no—
422C2C2×#1062284011yescharacteristic
423C2#1307799511yescharacteristic
424C2#1307802211yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3458C2
socleC22×C11C2×#120
prime radicalC24×C11C2×D4
hypercenter#3458D11
hypocenterC11#18310
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3458

Complements

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

NH ≅ G/Ntype
1. #13079757C2semidirect
3. #13067624C2semidirect
5. #13067180C2semidirect
357. C11#18310semidirect

Maximal subgroups

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

subgroupindex
#130797572
#130743822
#130676242
#130676072
#130671802
#130669302
C11×#34582
#1831011