Finite Group Databasebeta

← #14650450

Subgroups — #14650450

Order 2816.

426 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079762C211yesmaximal, characteristic
2#13077556C211yesmaximal, characteristic
3#13069436C211yesmaximal, characteristic
4#13067287C211yesmaximal, characteristic
5#13067181C211yesmaximal, characteristic
6#13066475C211yesmaximal, characteristic
7C11×#1275C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C2×C11×#97C2211yescharacteristic
13C2×#66880—21no—
14C2×#66880—21no—
15#10622715—21no—
16#10622714—21no—
17#10622549C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622464—22no—
20#10622334—22no—
21#10622314—22no—
22#10622314—22no—
23#10622294C412yescomplemented
24#10622293C412yescomplemented
25#10622124—22no—
26#10622105—22no—
27C22×Dic22—21no—
28C22×C8×C11D411yescharacteristic
29C22×C8×C11D411yescharacteristic
30C2×C42×C11C2311yescharacteristic
31#66979—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35#66977—21no—
36#66977D412yes—
37C2×#4318—21no—
38#66923—21no—
39#66922—21no—
40#66922—21no—
41#66922—21no—
42#66922C2×C412yes—
43#66922C2×C411yescharacteristic
44#66922C2×C411yescharacteristic
45C4×Dic22—21no—
46C4×Dic22D412yes—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C22⋊C8—21no—
50C11×C22⋊C8—21no—
51C11×#97—21no—
52C11×#97—21no—
53C4×C8×C11—21no—
54C4×C8×C11C2×C412yes—
55C11⋊#95—21no—
56C11⋊#95—21no—
57#66881—24no—
58#66880—24no—
59#66880—42no—
60#66880—42no—
61#66879—22no—
62Dic11⋊C8—24no—
63C8×Dic11—22no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D412yes—
66#9292—111nomaximal, Sylow
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C22×Dic11—41no—
71C22×Dic11—41no—
72C2×Dic22—22no—
73C2×Dic22—21no—
74C2×Dic22—41no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22C22⋊C412yes—
80C2×C8×C11—22no—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—41no—
87C2×C8×C11SD1612yes—
88C42×C11C22×C411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11#4111yescharacteristic
92C22⋊Dic11—22no—
93C4⋊Dic11—22no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—22no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11C22⋊C412yes—
103Dic11⋊C4—22no—
104Dic11⋊C4—22no—
105C4×Dic11—22no—
106#4318—41no—
107#4318—41no—
108C2×C11⋊C8—22no—
109#3229—111no—
110#2961—111no—
111#1960—111no—
112#1546—111no—
113#1518—111no—
114#1286—111no—
115#1275D1111yescharacteristic
116C23×C11#12111yescharacteristic
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11C2×C22⋊C411yescharacteristic
120C2×C4×C11C4×D411yescharacteristic
121C2×C4×C11C4×D411yescharacteristic
122C2×C4×C11#12011yescharacteristic
123C2×C4×C11#12111yescharacteristic
124C2×C4×C11#12311yescharacteristic
125C2×C4×C11C2×SD1611yescharacteristic
126C2×C4×C11#13511yescharacteristic
127C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—42no—
132C2×Dic11—81no—
133C2×Dic11—81no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137Dic22—42no—
138Dic22—42no—
139Dic22—42no—
140Dic22—81no—
141Dic22—81no—
142Dic22—81no—
143C8×C11—22no—
144C8×C11—42no—
145C8×C11—41no—
146C8×C11—81no—
147C11⋊C8—42no—
148#533—111no—
149C2×C4⋊Q8—111no—
150#498—112no—
151#487—112no—
152#483—222no—
153#475—222no—
154#446—222no—
155#446—222no—
156#431C2×D1111yescharacteristic
157#431C2×D1111yescharacteristic
158#424—221no—
159#423—111no—
160C2×#103—221no—
161C2×#103—221no—
162#405—221no—
163C2×#97C2×D1111yescharacteristic
164#382—111no—
165#332—222no—
166#328—222no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#38611yescharacteristic
170C22×C11#46011yescharacteristic
171C22×C11#46411yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11C4×SD1611yescharacteristic
177C4×C11#44011yescharacteristic
178C4×C11#44811yescharacteristic
179C4×C11#44911yescharacteristic
180Dic11—42no—
181Dic11—42no—
182Dic11—82no—
183Dic11—161no—
184C22×Q8—221no—
185C2×M16—221no—
186C22×C8D4411yescharacteristic
187C22×C8D4411yescharacteristic
188C4⋊Q8—111no—
189C4⋊Q8—111no—
190C4⋊Q8—112no—
191C4⋊Q8—221no—
192C4⋊Q8—221no—
193C4⋊Q8—221no—
194#125—221no—
195C22⋊Q8—112no—
196C22⋊Q8—221no—
197C4×Q8—112no—
198C4×Q8—221no—
199#117—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C42C22×D1111yescharacteristic
204#106—224no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—112no—
208C4⋊C8—224no—
209C4⋊C8—221no—
210#103—224no—
211#103—442no—
212#103—442no—
213C22⋊C8—21no—
214C22⋊C8—21no—
215#97—21no—
216#97—21no—
217#97—222no—
218C4×C8—21no—
219C4×C8—222no—
220C4×C8C4×D1112yes—
221#95—221no—
222#95—221no—
223C2×C11—21no—
224C2×C11—21no—
225C2×C11#188011yescharacteristic
226C2×C11#190211yescharacteristic
227C2×C11#190911yescharacteristic
228C2×Q8—112no—
229C2×Q8—221no—
230C2×Q8—222no—
231C2×Q8—441no—
232C2×Q8—441no—
233C2×Q8—441no—
234C2×Q8—441no—
235C2×Q8—441no—
236C22×C4—441no—
237C22×C4—441no—
238C22×C4C2×D4411yescharacteristic
239C22×C4D4×D1111yescharacteristic
240C22×C4#434311yescharacteristic
241M16—441no—
242M16—441no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—22no—
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—41no—
250C2×C8—222no—
251C2×C8#431412yes—
252C4⋊C4—112no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—222no—
256C4⋊C4—221no—
257C4⋊C4—222no—
258C4⋊C4—222no—
259C4⋊C4—222no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C22⋊C4—222no—
265C42—222no—
266C42C2×C4×D1111yescharacteristic
267C42#433911yescharacteristic
268C42D4×D1111yescharacteristic
269C42D4×D1111yescharacteristic
270C11#929211yescharacteristic, complemented, Sylow
271C23#6694811yescharacteristic
272Q8—442no—
273Q8—442no—
274Q8—442no—
275Q8—881no—
276Q8—881no—
277Q8—881no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—222no—
281C2×C4—222no—
282C2×C4—442no—
283C2×C4—881no—
284C2×C4—881no—
285C2×C4—881no—
286C2×C4—881no—
287C2×C4—881no—
288C2×C4C4×D4411yescharacteristic
289C2×C4C22⋊C4×D1111yescharacteristic
290C2×C4#6693511yescharacteristic
291C2×C4#6693711yescharacteristic
292C2×C4#6694611yescharacteristic
293C2×C4#6694711yescharacteristic
294C2×C4C2×#431411yescharacteristic
295C2×C4#6695711yescharacteristic
296C2×C4#6696111yescharacteristic
297C2×C4#6696211yescharacteristic
298C8—22no—
299C8—42no—
300C8—41no—
301C8—81no—
302C8—442no—
303C22—21no—
304C22—21no—
305C22#1062227811yescharacteristic
306C22#1062245811yescharacteristic
307C22#1062246111yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—442no—
313C4—442no—
314C4—882no—
315C4—1761no—
316C4C4×#431411yescharacteristic
317C4#1062232311yescharacteristic
318C4#1062234711yescharacteristic
319C4#1062235111yescharacteristic
320C2—21no—
321C2—21no—
322C2#1306897011yescharacteristic
323C2#1306909011yescharacteristic
324C2#1306913711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1275C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1275D11
hypocenterC11#9292
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
23. #10622294C4semidirect
24. #10622293C4semidirect
270. C11#9292semidirect

Maximal subgroups

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

subgroupindex
#130797622
#130775562
#130694362
#130672872
#130671812
#130664752
C11×#12752
#929211