Finite Group Databasebeta

← #14645933

Subgroups — #14645933

Order 2816.

922 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 922 conjugacy classes of subgroups — too many to draw. Only its 119 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#13082387C211yesmaximal, characteristic
2#13069557C211yesmaximal, characteristic, complemented
3#13067312C212yesmaximal, complemented
4#13067228C212yesmaximal, complemented
5C11×#1467C211yesmaximal, characteristic, complemented
6C2×#67040C412yes—
7C2×C4×Q8×C11C2211yescharacteristic
8#10623108—22no—
9#10623107—24no—
10Q8×D44—22no—
11#10623041—22no—
12#10623041C412yes—
13#10623008—22no—
14#10623008C2212yes—
15C11×#432C2212yes—
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C2×#66867C2211yescharacteristic
18C11×#324—22no—
19#10622162—22no—
20#10622123—22no—
21#10622119—22no—
22#10622102—24no—
23C22×Q8×C11C2×C411yescharacteristic
24#67040—48no—
25C2×#4343—24no—
26C2×Q8×D11—24no—
27C2×#4339—24no—
28C2×#4339C2×C414yes—
29C4×Q8×C11—22no—
30C4×Q8×C11—22no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4D412yes—
33C2×C42×C11D412yes—
34C2×C42×C11C2311yescharacteristic
35#66983—24no—
36#66983—22no—
37#66983—22no—
38C22×C11⋊C8—21no—
39C22×C11⋊C8—21no—
40#66950—28no—
41#66950—24no—
42#66948—28no—
43#66948—24no—
44#66928—24no—
45#66928D414yes—
46#66927—22no—
47#66927D412yes—
48C4×D44—24no—
49C4×D44—24no—
50C4×D44—22no—
51C4×D44—22no—
52#66922—22no—
53#66922D412yes—
54C11×C4⋊C8—22no—
55C11×C22⋊C8—22no—
56C11×#97—22no—
57C4⋊(C11⋊C8)—22no—
58#66867—22no—
59#8459—111nomaximal, Sylow
60C2×Q8×C11—24no—
61C2×Q8×C11—22no—
62C22×C4×C11C22⋊C412yes—
63C22×C4×C11C22⋊C412yes—
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C2×C22⋊D11—24no—
68#4343—416no—
69Q8×D11—416no—
70#4339—48no—
71#4339—48no—
72#4339—48no—
73C2×D44—24no—
74C2×D44—24no—
75C2×D44—22no—
76C2×D44—22no—
77C2×D44C22⋊C414yes—
78C2×C4×D11—28no—
79C2×C4×D11—24no—
80C2×Dic22—24no—
81C2×Dic22C22⋊C414yes—
82C2×C8×C11—42no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—24no—
85C42×C11—22no—
86C42×C11—22no—
87C42×C11C2×D412yes—
88C42×C11C2×D412yes—
89(C2×D11)⋊C4—28no—
90(C2×D11)⋊C4—24no—
91(C2×D11)⋊C4—24no—
92C4⋊Dic11—24no—
93C4⋊Dic11—22no—
94C4⋊Dic11—22no—
95C2×C11⋊C8—22no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100#3497—111no—
101#1985—111no—
102#1551—112no—
103#1530—112no—
104#1467D1111yescharacteristic, complemented
105C23×C11C2×C22⋊C411yescharacteristic
106C22×D11—24no—
107Q8×C11—28no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—41no—
115C2×C4×C11—42no—
116C2×C4×C11#10014yes—
117C2×C4×C11C2×C22⋊C412yes—
118C2×C4×C11#12011yescharacteristic
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11#12012yes—
121C22⋊D11—48no—
122C2×Dic11—24no—
123D44—44no—
124D44—48no—
125D44—42no—
126D44—42no—
127D44—82no—
128D44—84no—
129C4×D11—416no—
130C4×D11—48no—
131Dic22—48no—
132Dic22—44no—
133C8×C11—82no—
134C11⋊C8—42no—
135C11⋊C8—81no—
136C2×2−1+4—112no—
137#550—222no—
138D4×Q8—222no—
139#548—224no—
140#537—112no—
141#537—222no—
142#532—112no—
143#532—222no—
144C2×C4×Q8C2×D1111yescharacteristic
145#432C2×D1112yes—
146C2×C4⋊C8—111no—
147C2×#97—111no—
148#336—222no—
149#333—222no—
150#331—222no—
151#329—224no—
152#324—22no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11#37911yescharacteristic
156C22×C11C2×#10012yes—
157C2×D11—44no—
158C2×D11—44no—
159C2×D11—44no—
160C4×C11—21no—
161C4×C11—22no—
162C4×C11—24no—
163C4×C11—22no—
164C4×C11—42no—
165C4×C11#45411yescharacteristic
166C4×C11#45611yescharacteristic
167Dic11—44no—
1682−1+4—448no—
169C2×#41—114no—
170C2×#41—224no—
171C2×#41—224no—
172C22×Q8—224no—
173C22×Q8C4×D1111yescharacteristic
174C22×C8—221no—
175C22×C8—221no—
176C4⋊Q8—112no—
177C4⋊Q8—222no—
178#127—112no—
179#127—222no—
180#124—114no—
181#124—224no—
182C22⋊Q8—224no—
183C22⋊Q8—228no—
184#121—224no—
185#121—228no—
186#121—224no—
187#121—222no—
188#121—222no—
189C4×Q8—22no—
190C4×Q8—22no—
191C4×D4—224no—
192C4×D4—224no—
193C4×D4—222no—
194C4×D4—222no—
195C2×C4⋊C4C4×D1111yescharacteristic
196C2×C4⋊C4C22⋊D1112yes—
197C2×C42D4412yes—
198C2×C42C22×D1111yescharacteristic
199C4⋊C8—22no—
200C4⋊C8—222no—
201C22⋊C8—22no—
202#97—22no—
203#97—222no—
204C2×C11—22no—
205C2×C11#178311yescharacteristic
206C2×C11#179311yescharacteristic
207C2×C11#179411yescharacteristic
208D11—84no—
209#41—448no—
210#41—448no—
211#41—4416no—
212#41—448no—
213C2×Q8—24no—
214C2×Q8—22no—
215C2×Q8—114no—
216C2×Q8—224no—
217C2×Q8—4416no—
218C2×D4—114no—
219C2×D4—224no—
220C2×D4—224no—
221C2×D4—224no—
222C2×D4—222no—
223C2×D4—222no—
224C22×C4—228no—
225C22×C4—224no—
226C22×C4(C2×D11)⋊C412yes—
227C22×C4(C2×D11)⋊C412yes—
228C22×C4C2×C4×D1111yescharacteristic
229C22×C4C2×D4411yescharacteristic
230C22×C4C2×C22⋊D1111yescharacteristic
231C2×C8—42no—
232C2×C8—222no—
233C2×C8—441no—
234C2×C8—441no—
235C2×C8—442no—
236C2×C8—441no—
237C4⋊C4—22no—
238C4⋊C4—24no—
239C4⋊C4—224no—
240C4⋊C4—222no—
241C4⋊C4—222no—
242C22⋊C4—228no—
243C22⋊C4—224no—
244C22⋊C4—224no—
245C42—22no—
246C42—22no—
247C42D4×D1112yes—
248C42D4×D1112yes—
249C11#845911yescharacteristic, complemented, Sylow
250C23—224no—
251C23C2×(C2×D11)⋊C411yescharacteristic
252Q8—28no—
253Q8—444no—
254Q8—448no—
255D4—444no—
256D4—448no—
257D4—448no—
258D4—442no—
259D4—442no—
260D4—882no—
261D4—884no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—224no—
271C2×C4—4416no—
272C2×C4—448no—
273C2×C4#6688714yes—
274C2×C4C22⋊C4×D1112yes—
275C2×C4#6693511yescharacteristic
276C2×C4#6693511yescharacteristic
277C2×C4#6699012yes—
278C8—82no—
279C8—442no—
280C8—881no—
281C22—21no—
282C22—21no—
283C22—444no—
284C22—444no—
285C22—444no—
286C22#1062256811yescharacteristic
287C22C2×#6688712yes—
288C4—21no—
289C4—22no—
290C4—24no—
291C4—22no—
292C4—42no—
293C4—444no—
294C4#1062236511yescharacteristic
295C4#1062236611yescharacteristic
296C2—22no—
297C2—884no—
298C2#1306853611yescharacteristic
299C2#1306857711yescharacteristic
300C2#1306858211yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1467C2
socleC22×C11#379
prime radical#13082387C2
cosocleC2×C42×C11C23
hypercenter#1467D11
hypocenterC11#8459
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. #13069557C2semidirect
3. #13067312C2semidirect
4. #13067228C2semidirect
5. C11×#1467C2semidirect
104. #1467D11semidirect
249. C11#8459semidirect

Maximal subgroups

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

subgroupindex
#130823872
#130695572
#130673122
#130672282
C11×#14672
#845911