Finite Group Databasebeta

← #14650452

Subgroups — #14650452

Order 2816.

426 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 107 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#13077553C211yesmaximal, characteristic
3#13069435C211yesmaximal, characteristic
4#13067289C211yesmaximal, characteristic
5#13067179C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic
7C11×#1286C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#382C2211yescharacteristic
13#10622735—21no—
14#10622732—21no—
15C2×#66874—21no—
16C2×#66874—21no—
17#10622538C2211yescharacteristic
18C2×#66867C2211yescharacteristic
19#10622464—22no—
20#10622441—22no—
21#10622441—22no—
22#10622334—22no—
23#10622294C412yescomplemented
24#10622293C412yescomplemented
25#10622120—22no—
26#10622090—22no—
27C22×Dic22—21no—
28C2×C11×M16—21no—
29C2×C11×C4⋊C4—21no—
30C2×C42×C11C2311yescharacteristic
31#66979—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34#66977—21no—
35#66977D412yes—
36C22×C11⋊C8D411yescharacteristic
37C22×C11⋊C8D411yescharacteristic
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×C4⋊C8D412yes—
50C11×C22⋊C8—21no—
51C4×C8×C11C2×C412yes—
52C11×#95—21no—
53C11×#95—21no—
54C22⋊(C11⋊C8)—21no—
55#66881—24no—
56#66880—24no—
57#66879—22no—
58Dic11⋊C8—24no—
59C8×Dic11—22no—
60#66874—42no—
61#66874—42no—
62C4⋊(C11⋊C8)—21no—
63#66867—21no—
64#66867—21no—
65C4×C11⋊C8—21no—
66#9292—111nomaximal, Sylow
67C22×C4×C11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
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—
80C11×M16—41no—
81C11×M16—41no—
82C2×C8×C11—22no—
83C2×C8×C11—22no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C42×C11C22×C411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11#4111yescharacteristic
90C22⋊Dic11—22no—
91C4⋊Dic11—22no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—22no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11C22⋊C412yes—
99Dic11⋊C4—22no—
100Dic11⋊C4—22no—
101C4×Dic11—22no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8SD1612yes—
109#3229—111no—
110#2961—111no—
111#1960—111no—
112#1546—111no—
113#1518—111no—
114#1286D1111yescharacteristic
115#1275—111no—
116C23×C11#12111yescharacteristic
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11C2×C22⋊C411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12311yescharacteristic
128C2×C4×C11C2×SD1611yescharacteristic
129C2×C4×C11#13511yescharacteristic
130C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×Dic11—22no—
133C2×Dic11—22no—
134C2×Dic11—42no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137Dic22—42no—
138Dic22—42no—
139Dic22—42no—
140Dic22—81no—
141Dic22—81no—
142Dic22—81no—
143C8×C11—42no—
144C8×C11—42no—
145C11⋊C8—22no—
146C11⋊C8—41no—
147C11⋊C8—81no—
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#431—111no—
157#431C2×D1111yescharacteristic
158#424—221no—
159#423C2×D1111yescharacteristic
160C2×#103—221no—
161C2×#103—221no—
162#405—221no—
163C2×#97—111no—
164#382C2×D1111yescharacteristic
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×C11—161no—
177C4×C11C4×SD1611yescharacteristic
178C4×C11#44011yescharacteristic
179C4×C11#44811yescharacteristic
180C4×C11#44911yescharacteristic
181Dic11—42no—
182Dic11—42no—
183Dic11—82no—
184C22×Q8—221no—
185C2×M16—21no—
186C22×C8—111no—
187C22×C8—111no—
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—21no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C42C22×D1111yescharacteristic
204#106—224no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—224no—
208C4⋊C8—221no—
209C4⋊C8D4412yes—
210#103—224no—
211#103—442no—
212#103—442no—
213C22⋊C8—21no—
214C22⋊C8—221no—
215#97—222no—
216#97—221no—
217#97—221no—
218C4×C8—222no—
219C4×C8—221no—
220C4×C8C4×D1112yes—
221#95—21no—
222#95—21no—
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—41no—
237C22×C4—441no—
238C22×C4#433911yescharacteristic
239C22×C4D4×D1111yescharacteristic
240C22×C4D4×D1111yescharacteristic
241M16—41no—
242M16—41no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—112no—
246C2×C8—221no—
247C2×C8—221no—
248C2×C8—221no—
249C2×C8—221no—
250C2×C8—221no—
251C2×C8—441no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—112no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—222no—
259C4⋊C4—222no—
260C4⋊C4—222no—
261C4⋊C4—222no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C22⋊C4—222no—
265C42—222no—
266C42C2×C4×D1111yescharacteristic
267C42C2×D4411yescharacteristic
268C42D4×D1111yescharacteristic
269C42#434311yescharacteristic
270C11#929211yescharacteristic, complemented, Sylow
271C23#6693711yescharacteristic
272Q8—442no—
273Q8—442no—
274Q8—442no—
275Q8—881no—
276Q8—881no—
277Q8—881no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—222no—
284C2×C4—222no—
285C2×C4—442no—
286C2×C4—881no—
287C2×C4—881no—
288C2×C4C4×D4411yescharacteristic
289C2×C4C22⋊C4×D1111yescharacteristic
290C2×C4#6693511yescharacteristic
291C2×C4#6694611yescharacteristic
292C2×C4#6694711yescharacteristic
293C2×C4#6694811yescharacteristic
294C2×C4#6696411yescharacteristic
295C2×C4SD16×D1111yescharacteristic
296C2×C4#6696911yescharacteristic
297C2×C4#6697111yescharacteristic
298C8—42no—
299C8—42no—
300C8—222no—
301C8—441no—
302C8—881no—
303C22—21no—
304C22—21no—
305C22#1062227811yescharacteristic
306C22#1062237511yescharacteristic
307C22#1062241111yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—161no—
313C4—442no—
314C4—442no—
315C4—882no—
316C4#1062239411yescharacteristic
317C4#1062241911yescharacteristic
318C4#1062246511yescharacteristic
319C4#1062250211yescharacteristic
320C2—21no—
321C2—21no—
322C2#1306897211yescharacteristic
323C2#1306908811yescharacteristic
324C2#1306913711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#9292
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

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
#130775532
#130694352
#130672892
#130671792
#130664462
C11×#12862
#929211