Finite Group Databasebeta

← #14663443

Subgroups — #14663443

Order 2816.

374 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 87 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#13073821C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic
3#13066561C214yesmaximal
4C11×#1467C211yesmaximal, characteristic
5C2×C4×Q8×C11C2211yescharacteristic
6C2×#66922C411yescharacteristic
7C11×#432—21no—
8#10622843C412yes—
9#10622592—21no—
10#10622592—21no—
11#10622589C2212yes—
12C4×C4⋊Dic11C411yescharacteristic
13#10622541—21no—
14#10622541—21no—
15#10622538—21no—
16C11×#324—21no—
17C11×#324C2212yes—
18#10622166—21no—
19#10622166C2212yes—
20C22×Q8×C11C2×C411yescharacteristic
21C22×Dic22—21no—
22C4×Q8×C11—41no—
23C4×Q8×C11—41no—
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C11×C4⋊C4C2311yescharacteristic
27C2×C42×C11C2×C411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11C2×C412yes—
33C2×Dic11⋊C4—22no—
34C2×Dic11⋊C4—22no—
35C2×C4×Dic11C2×C412yes—
36#66922—41no—
37#66922—41no—
38C11×C4⋊C8—41no—
39C11×C22⋊C8—22no—
40C11×#97—41no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43C11⋊#95—21no—
44C22⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)—41no—
46C4×C11⋊C8—41no—
47#11574—111nomaximal, Sylow
48C2×Q8×C11—22no—
49C2×Q8×C11—22no—
50C2×Q8×C11—41no—
51C22×C4×C11C22⋊C411yescharacteristic
52C22×C4×C11C22⋊C411yescharacteristic
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22×C411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×Dic11—22no—
59C22×Dic11—22no—
60C2×Dic22—42no—
61C2×Dic22—82no—
62C2×C8×C11—42no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—41no—
66C42×C11—21no—
67C42×C11—21no—
68C42×C11—21no—
69C42×C11—21no—
70C42×C11—21no—
71C42×C11—21no—
72C4⋊Dic11—24no—
73C4⋊Dic11—42no—
74C4⋊Dic11—41no—
75C4⋊Dic11—41no—
76Dic11⋊C4—82no—
77Dic11⋊C4—82no—
78C4×Dic11—24no—
79C2×C11⋊C8—42no—
80#2567—111no—
81#1467D1111yescharacteristic
82#1461—111no—
83#1325—114no—
84C23×C11C2×C22⋊C411yescharacteristic
85Q8×C11—44no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—41no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11#9911yescharacteristic
101C2×C4×C11#9911yescharacteristic
102C2×C4×C11#10112yes—
103C2×C4×C11#13112yes—
104C2×Dic11—24no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110Dic22—84no—
111C8×C11—82no—
112C11⋊C8—82no—
113C2×C4⋊Q8—111no—
114C2×C4×Q8C2×D1111yescharacteristic
115#432—21no—
116#431—221no—
117#395—221no—
118#395—221no—
119#391—112no—
120#389—221no—
121#389—221no—
122#384—112no—
123C4×C4⋊C4—111no—
124#324—21no—
125#324—112no—
126#324—221no—
127#324C2×D1112yes—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11#40811yescharacteristic
131C22×C11C2×#9911yescharacteristic
132C22×C11C2×#10111yescharacteristic
133C4×C11—21no—
134C4×C11—22no—
135C4×C11—22no—
136C4×C11—41no—
137C4×C11—41no—
138C4×C11—41no—
139C4×C11—41no—
140C4×C11#35612yes—
141Dic11—44no—
142Dic11—82no—
143C22×Q8—221no—
144C22×Q8C4×D1111yescharacteristic
145C4⋊Q8—441no—
146C4⋊Q8—441no—
147C4×Q8—41no—
148C4×Q8—41no—
149C2×C4⋊C4—112no—
150C2×C4⋊C4—221no—
151C2×C4⋊C4—221no—
152C2×C4⋊C4—222no—
153C2×C4⋊C4—222no—
154C2×C4⋊C4D4411yescharacteristic
155C2×C4⋊C4C22⋊D1111yescharacteristic
156C2×C4⋊C4C22×D1111yescharacteristic
157C2×C42—112no—
158C2×C42C4×D1111yescharacteristic
159C2×C42D4411yescharacteristic
160C2×C42C22⋊D1111yescharacteristic
161C4⋊C8—41no—
162C4⋊C8—441no—
163C22⋊C8—22no—
164C22⋊C8—222no—
165#97—41no—
166C4×C8—441no—
167#95—221no—
168#95—222no—
169#95—222no—
170C2×C11—21no—
171C2×C11—21no—
172C2×C11#147211yescharacteristic
173C2×C11#212811yescharacteristic
174C2×C11C2×#35611yescharacteristic
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—41no—
178C2×Q8—442no—
179C2×Q8—882no—
180C22×C4—222no—
181C22×C4—222no—
182C22×C4(C2×D11)⋊C411yescharacteristic
183C22×C4(C2×D11)⋊C411yescharacteristic
184C22×C4(C2×D11)⋊C411yescharacteristic
185C22×C4(C2×D11)⋊C411yescharacteristic
186C22×C4C2×C4×D1111yescharacteristic
187C22×C4C2×D4411yescharacteristic
188C22×C4C2×C22⋊D1111yescharacteristic
189C2×C8—42no—
190C2×C8—442no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—224no—
195C4⋊C4—442no—
196C4⋊C4—441no—
197C4⋊C4—441no—
198C4⋊C4—882no—
199C4⋊C4—882no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—224no—
207C11#1157411yescharacteristic, complemented, Sylow
208C23C2×(C2×D11)⋊C411yescharacteristic
209Q8—44no—
210Q8—884no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—224no—
226C2×C4—442no—
227C2×C4—442no—
228C2×C4—442no—
229C2×C4—442no—
230C2×C4—442no—
231C2×C4#6687011yescharacteristic
232C2×C4#6687011yescharacteristic
233C2×C4#6688812yes—
234C2×C4#6696012yes—
235C8—82no—
236C8—882no—
237C22—21no—
238C22—21no—
239C22C2×#6687011yescharacteristic
240C22#1062274211yescharacteristic
241C22C2×#6688811yescharacteristic
242C4—21no—
243C4—22no—
244C4—22no—
245C4—41no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—444no—
250C4—882no—
251C4#1062211612yes—
252C2—21no—
253C2—21no—
254C2#1306698111yescharacteristic
255C2#1307028711yescharacteristic
256C2C2×#1062211611yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1467C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1467D11
hypocenterC11#11574
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
207. C11#11574semidirect

Maximal subgroups

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

subgroupindex
#130738212
#130669402
#130665612
C11×#14672
#1157411