Finite Group Databasebeta

← #14735076

Subgroups — #14735076

Order 2816.

808 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 808 conjugacy classes of subgroups — too many to draw. Only its 171 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#13079806C212yesmaximal
2#13079019C211yesmaximal, characteristic
3#13067944C214yesmaximal, complemented
4#13067918C214yesmaximal, complemented
5#13067243C211yesmaximal, characteristic, complemented
6#13067218C212yesmaximal, complemented
7C2×C11×#564C211yesmaximal, characteristic, complemented
8C11×#564—24no—
9C11×#564—22no—
10C11×#564C2214yes—
11C2×C11×#125—22no—
12C2×C11×#125—22no—
13C2×C11×#125—22no—
14C2×C11×#125C2212yes—
15C2×C11×#125C2211yescharacteristic
16#10623008C2211yescharacteristic
17#10622682C2212yes—
18#10622681—22no—
19#10622680C2212yes—
20#10622680C2214yes—
21#10622679—24no—
22#10622678C2214yes—
23#10622581—22no—
24#10622580—22no—
25#10622579—22no—
26#10622539C2212yes—
27C4×#4318C2211yescharacteristic
28#10622181C2218yes—
29#10622181C2214yes—
30C2×#4339—21no—
31C11×#125—28no—
32C11×#125—28no—
33C11×#125—28no—
34C11×#125—28no—
35C11×#125—28no—
36C11×#125—28no—
37C11×#125—22no—
38C11×#125—22no—
39C11×#125—22no—
40C11×#125D414yes—
41C11×#125D412yes—
42C11×#125C2314yes—
43C11×#125C2312yes—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4D412yes—
51C2×C11×C4⋊C4D412yes—
52C2×C11×C4⋊C4D412yes—
53C2×C42×C11—22no—
54C2×C42×C11C2311yescharacteristic
55#66983—22no—
56C2×#4318—21no—
57#66928—21no—
58#66927C2311yescharacteristic
59C4×D44—22no—
60#66922C2311yescharacteristic
61C22⋊(C11⋊C8)—22no—
62#66874—24no—
63#66873—24no—
64#66873—24no—
65#66873—24no—
66#66872—24no—
67#66871—24no—
68C4⋊(C11⋊C8)—22no—
69#66867C2312yes—
70#66867C2314yes—
71C4×C11⋊C8—21no—
72#19003—111nomaximal, Sylow
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D412yes—
78C2×C22⋊D11—41no—
79#4339—44no—
80C2×D44—22no—
81C2×D44—21no—
82C2×C4×D11—41no—
83C2×Dic22—21no—
84C11×C4⋊C4—28no—
85C11×C4⋊C4—28no—
86C11×C4⋊C4—28no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4—24no—
89C11×C4⋊C4—24no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4C2×D414yes—
97C11×C4⋊C4C2×D414yes—
98C11×C4⋊C4C2×D414yes—
99C42×C11—28no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D412yes—
102C42×C11C2411yescharacteristic
103(C2×D11)⋊C4—42no—
104C4⋊Dic11—22no—
105#4318—42no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—24no—
108C2×#564D1111yescharacteristic, complemented
109#3234—112no—
110#3142—111no—
111#1663—114no—
112#1658—114no—
113#1534—111no—
114#1528—112no—
115C23×C11#12011yescharacteristic
116C22×D11—41no—
117C2×C4×C11—22no—
118C2×C4×C11—24no—
119C2×C4×C11—24no—
120C2×C4×C11—24no—
121C2×C4×C11—42no—
122C2×C4×C11—44no—
123C2×C4×C11—44no—
124C2×C4×C11—44no—
125C2×C4×C11#12012yes—
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11C22×D412yes—
128C2×C4×C11C22×D411yescharacteristic
129C22⋊D11—82no—
130C2×Dic11—41no—
131D44—44no—
132D44—42no—
133C4×D11—82no—
134Dic22—42no—
135C11⋊C8—44no—
136C11⋊C8—42no—
137#564—24no—
138#564—22no—
139#564C2×D1114yes—
140#532—111no—
141C2×#125—22no—
142C2×#125—22no—
143C2×#125—22no—
144C2×#125C2×D1111yescharacteristic
145C2×#125C2×D1112yes—
146#501—114no—
147#491—112no—
148#490—112no—
149#490—114no—
150#488—222no—
151#481—222no—
152#480—222no—
153#478—224no—
154#432—112no—
155#417—222no—
156C4×M16—111no—
157#330—118no—
158#330—114no—
159C22×C11—22no—
160C22×C11#45412yes—
161C22×C11C2×#12011yescharacteristic
162C2×D11—81no—
163C2×D11—82no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—22no—
167C4×C11—22no—
168C4×C11—44no—
169C4×C11—44no—
170C4×C11—44no—
171Dic11—81no—
172C2×#41—221no—
173C2×M16—221no—
174C4⋊Q8—111no—
175#127—111no—
176#125—28no—
177#125—28no—
178#125—28no—
179#125—28no—
180#125—28no—
181#125—28no—
182#125—22no—
183#125—22no—
184#125—22no—
185#125C22⋊D1114yes—
186#125C22⋊D1112yes—
187#125C22×D1112yes—
188#125C22×D1114yes—
189#124—221no—
190#121—222no—
191C4×D4—222no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4C22⋊D1112yes—
199C2×C4⋊C4C22⋊D1112yes—
200C2×C4⋊C4C22⋊D1112yes—
201C2×C42—22no—
202C2×C42C22×D1111yescharacteristic
203#107—224no—
204#106—224no—
205C4⋊C8—222no—
206#103—224no—
207#102—224no—
208#102—224no—
209#102—224no—
210C22⋊C8—222no—
211#97—112no—
212#97—114no—
213C4×C8—221no—
214C2×C11—22no—
215C2×C11C2×#45411yescharacteristic
216C2×C11#302012yes—
217D11—161no—
218#41—444no—
219C2×Q8—221no—
220C2×D4—222no—
221C2×D4—221no—
222C2×D4—441no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—441no—
227C22×C4C2×C22⋊D1111yescharacteristic
228C22×C4C2×C22⋊D1112yes—
229M16—442no—
230C2×C8—222no—
231C2×C8—224no—
232C4⋊C4—28no—
233C4⋊C4—28no—
234C4⋊C4—28no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—24no—
238C4⋊C4—22no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—24no—
242C4⋊C4—24no—
243C4⋊C4—24no—
244C4⋊C4—222no—
245C4⋊C4C2×C22⋊D1114yes—
246C4⋊C4C2×C22⋊D1114yes—
247C4⋊C4C2×C22⋊D1114yes—
248C22⋊C4—442no—
249C42—28no—
250C42C2×C22⋊D1111yescharacteristic
251C42C2×C22⋊D1112yes—
252C42C23×D1111yescharacteristic
253C11#1900311yescharacteristic, complemented, Sylow
254C23—441no—
255C23#6700611yescharacteristic
256Q8—442no—
257D4—442no—
258D4—444no—
259D4—882no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—42no—
265C2×C4—44no—
266C2×C4—44no—
267C2×C4—44no—
268C2×C4—441no—
269C2×C4—882no—
270C2×C4#6700612yes—
271C2×C4#6700611yescharacteristic
272C2×C4C22×C22⋊D1112yes—
273C2×C4C22×C22⋊D1111yescharacteristic
274C8—442no—
275C8—444no—
276C22—22no—
277C22—881no—
278C22—882no—
279C22#1062285812yes—
280C22C2×#6700611yescharacteristic
281C4—21no—
282C4—21no—
283C4—22no—
284C4—22no—
285C4—44no—
286C4—44no—
287C4—44no—
288C4—881no—
289C2—22no—
290C2—1761no—
291C2C2×#1062285811yescharacteristic
292C2#1307798012yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#564C2
socleC22×C11C2×#120
prime radical#10623008C22
hypercenterC2×#564D11
hypocenterC11#19003
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#564

Complements

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

NH ≅ G/Ntype
3. #13067944C2semidirect
4. #13067918C2semidirect
5. #13067243C2semidirect
6. #13067218C2semidirect
7. C2×C11×#564C2semidirect
108. C2×#564D11semidirect
253. C11#19003semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130790192
#130679442
#130679182
#130672432
#130672182
C2×C11×#5642
#1900311