Finite Group Databasebeta

← #14663416

Subgroups — #14663416

Order 2816.

394 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 95 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#13066960C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic
3#13066550C214yesmaximal
4C11×#2546C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C11×C4⋊Q8C412yes—
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#398—21no—
9C11×#398—21no—
10C11×#391C2212yes—
11C11×#389—21no—
12C11×#389—21no—
13C4×C11×C4⋊C4C411yescharacteristic
14#10622539—21no—
15#10622538—21no—
16#10622166—21no—
17#10622166—21no—
18#10622166C2212yes—
19#10622166C2212yes—
20C22×Q8×C11C2×C412yes—
21C22×Q8×C11C2×C411yescharacteristic
22C11×C4⋊Q8—41no—
23C11×C4⋊Q8—41no—
24C11×C4⋊Q8—44no—
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11C2×C412yes—
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C11×#95—21no—
40C11×#95—22no—
41C11×#95—22no—
42C22⋊(C11⋊C8)—22no—
43C22⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)—41no—
45C4⋊(C11⋊C8)—41no—
46#66867—41no—
47C4×C11⋊C8—41no—
48#11568—111nomaximal, Sylow
49C2×Q8×C11—22no—
50C2×Q8×C11—22no—
51C2×Q8×C11—24no—
52C2×Q8×C11—41no—
53C2×Q8×C11—42no—
54C2×Q8×C11—42no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22×C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C11×C4⋊C4—24no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—44no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—44no—
73C42×C11—21no—
74C42×C11—21no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—42no—
80C2×C11⋊C8—42no—
81C2×C11⋊C8—42no—
82#2546D1111yescharacteristic
83#1467—111no—
84#1461—111no—
85#1319—114no—
86C23×C11C2×C22⋊C411yescharacteristic
87Q8×C11—44no—
88Q8×C11—84no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—24no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11#9911yescharacteristic
110C2×C4×C11#9911yescharacteristic
111C2×C4×C11#10012yes—
112C2×C4×C11#13112yes—
113C11⋊C8—82no—
114C11⋊C8—82no—
115C2×C4⋊Q8Dic1111yescharacteristic
116C2×C4⋊Q8Dic1112yes—
117C2×C4×Q8C2×D1111yescharacteristic
118#432—221no—
119#431—221no—
120#398—21no—
121#398—21no—
122#391C2×D1112yes—
123#389—21no—
124#389—21no—
125C4×C4⋊C4Dic1111yescharacteristic
126#324—112no—
127#324—112no—
128#324—221no—
129#324—221no—
130C22×C11—21no—
131C22×C11—21no—
132C22×C11#40811yescharacteristic
133C22×C11C2×#9911yescharacteristic
134C22×C11C2×#10011yescharacteristic
135C4×C11—21no—
136C4×C11—22no—
137C4×C11—22no—
138C4×C11—44no—
139C4×C11—41no—
140C4×C11—41no—
141C4×C11—41no—
142C4×C11—41no—
143C4×C11—82no—
144C4×C11#35612yes—
145C22×Q8C2×Dic1112yes—
146C22×Q8C2×Dic1111yescharacteristic
147C4⋊Q8—41no—
148C4⋊Q8—41no—
149C4⋊Q8—44no—
150C4×Q8—41no—
151C4×Q8—41no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C22⋊D1111yescharacteristic
158C2×C4⋊C4C22⋊D1111yescharacteristic
159C2×C4⋊C4C22×D1111yescharacteristic
160C2×C42C2×Dic1111yescharacteristic
161C2×C42C2×Dic1112yes—
162C2×C42C22⋊D1111yescharacteristic
163C2×C42C22⋊D1111yescharacteristic
164C4⋊C8—441no—
165C4⋊C8—441no—
166C22⋊C8—222no—
167C22⋊C8—222no—
168#97—441no—
169C4×C8—441no—
170#95—21no—
171#95—22no—
172#95—22no—
173C2×C11—21no—
174C2×C11—21no—
175C2×C11#147111yescharacteristic
176C2×C11#212911yescharacteristic
177C2×C11C2×#35611yescharacteristic
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—24no—
181C2×Q8—41no—
182C2×Q8—42no—
183C2×Q8—42no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4C22⋊Dic1111yescharacteristic
187C22×C4C22⋊Dic1111yescharacteristic
188C22×C4C22⋊Dic1111yescharacteristic
189C22×C4C22⋊Dic1111yescharacteristic
190C22×C4C22×Dic1111yescharacteristic
191C22×C4C2×C22⋊D1111yescharacteristic
192C22×C4C2×C22⋊D1111yescharacteristic
193C2×C8—442no—
194C2×C8—442no—
195C4⋊C4—24no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—44no—
200C4⋊C4—42no—
201C4⋊C4—44no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—42no—
211C11#1156811yescharacteristic, complemented, Sylow
212C23C2×C22⋊Dic1111yescharacteristic
213Q8—44no—
214Q8—84no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—24no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4#6689712yes—
236C2×C4#6689811yescharacteristic
237C2×C4#6689811yescharacteristic
238C2×C4#6700112yes—
239C8—882no—
240C8—882no—
241C22—21no—
242C22—21no—
243C22C2×#6689711yescharacteristic
244C22C2×#6689811yescharacteristic
245C22#1062284711yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—44no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—82no—
255C4#1062218612yes—
256C2—21no—
257C2—21no—
258C2#1306697611yescharacteristic
259C2#1307029111yescharacteristic
260C2C2×#1062218611yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2546C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2546D11
hypocenterC11#11568
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
211. C11#11568semidirect

Maximal subgroups

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

subgroupindex
#130669602
#130669402
#130665502
C11×#25462
#1156811