Finite Group Databasebeta

← #14663415

Subgroups — #14663415

Order 2816.

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

normal subgroups only

This group has 394 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#13073601C211yesmaximal, characteristic
2#13066960C211yesmaximal, characteristic
3#13066549C214yesmaximal
4C11×#1461C211yesmaximal, characteristic
5C2×C4×Q8×C11C2211yescharacteristic
6C2×#66997C412yes—
7C2×#66922C411yescharacteristic
8C11×#431—21no—
9#10622596—21no—
10#10622596—21no—
11#10622587C2212yes—
12C4×C4⋊Dic11C411yescharacteristic
13#10622541—21no—
14#10622541—21no—
15#10622539—21no—
16C11×#324—21no—
17C11×#324C2212yes—
18#10622166—21no—
19#10622166C2212yes—
20C22×Q8×C11C2×C411yescharacteristic
21C22×Dic22C2×C412yes—
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
30#66997—44no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×Dic11⋊C4—22no—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11C2×C412yes—
37#66922—41no—
38#66922—41no—
39C11×C4⋊C8—41no—
40C11×C22⋊C8—22no—
41C4×C8×C11—41no—
42C11⋊#95—21no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45C22⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—41no—
47#66867—41no—
48#11568—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—24no—
62C2×Dic22—42no—
63C2×Dic22—42no—
64C2×C8×C11—42no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C42×C11—21no—
69C42×C11—21no—
70C42×C11—21no—
71C42×C11—21no—
72C42×C11—21no—
73C42×C11—21no—
74C4⋊Dic11—24no—
75C4⋊Dic11—42no—
76C4⋊Dic11—41no—
77C4⋊Dic11—41no—
78Dic11⋊C4—44no—
79Dic11⋊C4—44no—
80C4×Dic11—42no—
81C2×C11⋊C8—42no—
82#2546—111no—
83#1467—111no—
84#1461D1111yescharacteristic
85#1319—114no—
86C23×C11C2×C22⋊C411yescharacteristic
87Q8×C11—44no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11#9911yescharacteristic
103C2×C4×C11#9911yescharacteristic
104C2×C4×C11#10012yes—
105C2×C4×C11#13112yes—
106C2×Dic11—24no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112Dic22—84no—
113C8×C11—82no—
114C11⋊C8—82no—
115C2×C4⋊Q8—112no—
116C2×C4⋊Q8—111no—
117C2×C4×Q8C2×D1111yescharacteristic
118#432—221no—
119#431—21no—
120#398—221no—
121#398—221no—
122#391—112no—
123#389—221no—
124#389—221no—
125C4×C4⋊C4—111no—
126#324—21no—
127#324—112no—
128#324—221no—
129#324C2×D1112yes—
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—41no—
139C4×C11—41no—
140C4×C11—41no—
141C4×C11—41no—
142C4×C11#35612yes—
143Dic11—44no—
144Dic11—82no—
145C22×Q8—112no—
146C22×Q8C4×D1111yescharacteristic
147C4⋊Q8—441no—
148C4⋊Q8—441no—
149C4⋊Q8—444no—
150C4×Q8—41no—
151C4×Q8—41no—
152C2×C4⋊C4—221no—
153C2×C4⋊C4—222no—
154C2×C4⋊C4—222no—
155C2×C4⋊C4—221no—
156C2×C4⋊C4—221no—
157C2×C4⋊C4D4411yescharacteristic
158C2×C4⋊C4C22⋊D1111yescharacteristic
159C2×C4⋊C4C22×D1111yescharacteristic
160C2×C42—112no—
161C2×C42C4×D1111yescharacteristic
162C2×C42D4411yescharacteristic
163C2×C42C22⋊D1111yescharacteristic
164C4⋊C8—41no—
165C4⋊C8—441no—
166C22⋊C8—22no—
167C22⋊C8—222no—
168#97—441no—
169C4×C8—41no—
170#95—221no—
171#95—222no—
172#95—222no—
173C2×C11—21no—
174C2×C11—21no—
175C2×C11#147111yescharacteristic
176C2×C11#212911yescharacteristic
177C2×C11C2×#35611yescharacteristic
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—41no—
181C2×Q8—224no—
182C2×Q8—442no—
183C2×Q8—442no—
184C22×C4—222no—
185C22×C4—222no—
186C22×C4(C2×D11)⋊C411yescharacteristic
187C22×C4(C2×D11)⋊C411yescharacteristic
188C22×C4(C2×D11)⋊C411yescharacteristic
189C22×C4(C2×D11)⋊C411yescharacteristic
190C22×C4C2×C4×D1111yescharacteristic
191C22×C4C2×D4411yescharacteristic
192C22×C4C2×C22⋊D1111yescharacteristic
193C2×C8—42no—
194C2×C8—442no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—224no—
199C4⋊C4—444no—
200C4⋊C4—442no—
201C4⋊C4—441no—
202C4⋊C4—441no—
203C4⋊C4—444no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—442no—
211C11#1156811yescharacteristic, complemented, Sylow
212C23C2×(C2×D11)⋊C411yescharacteristic
213Q8—44no—
214Q8—884no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—224no—
230C2×C4—442no—
231C2×C4—442no—
232C2×C4—442no—
233C2×C4—442no—
234C2×C4—442no—
235C2×C4#6687011yescharacteristic
236C2×C4#6687011yescharacteristic
237C2×C4#6688712yes—
238C2×C4#6695412yes—
239C8—82no—
240C8—882no—
241C22—21no—
242C22—21no—
243C22C2×#6687011yescharacteristic
244C22#1062272311yescharacteristic
245C22C2×#6688711yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—41no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—444no—
254C4—882no—
255C4#1062211612yes—
256C2—21no—
257C2—21no—
258C2#1306697511yescharacteristic
259C2#1307029011yescharacteristic
260C2C2×#1062211611yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1461C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1461D11
hypocenterC11#11568
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

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
#130736012
#130669602
#130665492
C11×#14612
#1156811