Finite Group Databasebeta

← #14664420

Subgroups — #14664420

Order 2816.

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

normal subgroups only

This group has 378 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#13073828C211yesmaximal, characteristic
2#13066960C211yesmaximal, characteristic
3#13066642C214yesmaximal
4C4×C11×#101C211yesmaximal, characteristic
5C2×C4×Q8×C11C2211yescharacteristic
6C2×#66922C411yescharacteristic
7C2×C11×#101—21no—
8C4×C11×M16—21no—
9#10622843—21no—
10#10622599C412yes—
11#10622599C2212yes—
12#10622590—21no—
13C4×C4⋊Dic11C411yescharacteristic
14#10622542—21no—
15#10622542—21no—
16#10622539—21no—
17C11×#343C2212yes—
18#10622166—21no—
19#10622166C2212yes—
20C22×Q8×C11D411yescharacteristic
21C22×Dic22—21no—
22C2×C11×M16—22no—
23C4×Q8×C11—41no—
24C4×Q8×C11—41no—
25C2×C11×C4⋊C4C2×C411yescharacteristic
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C4⋊C4C2311yescharacteristic
28C2×C42×C11C2×C411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11C2×C412yes—
34C2×C4×Dic11—21no—
35#66922—41no—
36#66922—41no—
37C11×#101—24no—
38C11×#97—41no—
39C4×C8×C11—41no—
40C11⋊#95—22no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C11⋊#95C2×C412yes—
45C22⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—41no—
47#66867—41no—
48#11794—111nomaximal, Sylow
49C2×Q8×C11—22no—
50C2×Q8×C11—22no—
51C2×Q8×C11—41no—
52C22×C4×C11C22⋊C411yescharacteristic
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22×C411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×Dic11—22no—
60C22×Dic11—22no—
61C2×Dic22—44no—
62C2×Dic22—41no—
63C2×Dic22—41no—
64C11×M16—24no—
65C11×M16—42no—
66C2×C8×C11—42no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C42×C11—21no—
71C42×C11—21no—
72C42×C11—21no—
73C42×C11—21no—
74C42×C11—21no—
75C42×C11—21no—
76C4⋊Dic11—42no—
77C4⋊Dic11—42no—
78C4⋊Dic11—42no—
79C4×Dic11—42no—
80C2×C11⋊C8—42no—
81#2568—111no—
82C4×#101D1111yescharacteristic
83#1467—111no—
84#1353—114no—
85C23×C11C2×C22⋊C411yescharacteristic
86Q8×C11—44no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11#9911yescharacteristic
102C2×C4×C11#9911yescharacteristic
103C2×C4×C11#10412yes—
104C2×C4×C11#13712yes—
105C2×Dic11—42no—
106C2×Dic11—44no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110Dic22—82no—
111Dic22—82no—
112C8×C11—44no—
113C11⋊C8—82no—
114C2×C4⋊Q8—111no—
115C2×C4×Q8C2×D1111yescharacteristic
116#432—221no—
117C2×#101—21no—
118C4×M16—21no—
119#400—112no—
120#400—112no—
121#391—221no—
122#391—221no—
123#391—221no—
124#382—221no—
125C4×C4⋊C4—111no—
126#343C2×D1112yes—
127#324—112no—
128#324—221no—
129C22×C11—21no—
130C22×C11—21no—
131C22×C11C2×#9911yescharacteristic
132C22×C11#41911yescharacteristic
133C22×C11C2×#10411yescharacteristic
134C4×C11—21no—
135C4×C11—22no—
136C4×C11—22no—
137C4×C11—41no—
138C4×C11—41no—
139C4×C11—41no—
140C4×C11—41no—
141C4×C11#35512yes—
142Dic11—82no—
143Dic11—82no—
144C22×Q8—221no—
145C22×Q8C22⋊D1111yescharacteristic
146C2×M16—22no—
147C4⋊Q8—441no—
148C4⋊Q8—441no—
149C4×Q8—41no—
150C4×Q8—41no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—221no—
153C2×C4⋊C4—221no—
154C2×C4⋊C4C4×D1111yescharacteristic
155C2×C4⋊C4D4411yescharacteristic
156C2×C4⋊C4C22×D1111yescharacteristic
157C2×C42—221no—
158C2×C42C4×D1111yescharacteristic
159C2×C42D4411yescharacteristic
160C2×C42C22⋊D1111yescharacteristic
161C4⋊C8—441no—
162#101—24no—
163C22⋊C8—222no—
164#97—41no—
165#97—441no—
166C4×C8—41no—
167#95—112no—
168#95—222no—
169#95—222no—
170#95—222no—
171#95—222no—
172C2×C11—21no—
173C2×C11—21no—
174C2×C11#150811yescharacteristic
175C2×C11#212311yescharacteristic
176C2×C11C2×#35511yescharacteristic
177C2×Q8—22no—
178C2×Q8—22no—
179C2×Q8—41no—
180C2×Q8—444no—
181C2×Q8—441no—
182C2×Q8—441no—
183C22×C4—222no—
184C22×C4—222no—
185C22×C4(C2×D11)⋊C411yescharacteristic
186C22×C4(C2×D11)⋊C411yescharacteristic
187C22×C4(C2×D11)⋊C411yescharacteristic
188C22×C4(C2×D11)⋊C411yescharacteristic
189C22×C4C2×C4×D1111yescharacteristic
190C22×C4C2×D4411yescharacteristic
191C22×C4C2×C22⋊D1111yescharacteristic
192M16—24no—
193M16—42no—
194C2×C8—42no—
195C2×C8—442no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—442no—
200C4⋊C4—442no—
201C4⋊C4—442no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—442no—
209C11#1179411yescharacteristic, complemented, Sylow
210C23C2×(C2×D11)⋊C411yescharacteristic
211Q8—44no—
212Q8—882no—
213Q8—882no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—442no—
229C2×C4—444no—
230C2×C4—442no—
231C2×C4—442no—
232C2×C4—442no—
233C2×C4#6686912yes—
234C2×C4#6687011yescharacteristic
235C2×C4#6687011yescharacteristic
236C2×C4#6700412yes—
237C8—44no—
238C8—882no—
239C22—21no—
240C22—21no—
241C22C2×#6686911yescharacteristic
242C22C2×#6687011yescharacteristic
243C22#1062261711yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—41no—
251C4—882no—
252C4—882no—
253C4#1062211512yes—
254C2—21no—
255C2—21no—
256C2#1306713511yescharacteristic
257C2#1307027111yescharacteristic
258C2C2×#1062211511yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC4×C11×#101C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenterC4×#101D11
hypocenterC11#11794
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
209. C11#11794semidirect

Maximal subgroups

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

subgroupindex
#130738282
#130669602
#130666422
C4×C11×#1012
#1179411