Finite Group Databasebeta

← #14647185

Subgroups — #14647185

Order 2816.

526 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 107 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#13071022C211yesmaximal, characteristic
2#13068379C212yesmaximal
3#13066498C212yesmaximal, complemented
4#13066497C211yesmaximal, characteristic, complemented
5C11×#1295C211yesmaximal, characteristic, complemented
6C2×#66945C412yes—
7C2×C42×D11C2211yescharacteristic
8C2×C11×#97C2212yes—
9C11×#382C2211yescharacteristic
10C2×(C2×D11)⋊C8—22no—
11#10622589C412yes—
12#10622549C2211yescharacteristic
13C2×#66867C2212yes—
14#10622280—22no—
15#10622262—22no—
16#10622188—22no—
17C22×C4×D11C2×C411yescharacteristic
18C22×C4×D11D412yes—
19C22×C8×C11—22no—
20C2×C11×C4⋊C4C2×C412yes—
21C2×C42×C11C2311yescharacteristic
22C2×(C2×D11)⋊C4—22no—
23C2×C4⋊Dic11C2×C412yes—
24C2×Dic11⋊C4—22no—
25C2×Dic11⋊C4—22no—
26C2×C4×Dic11—22no—
27C2×C4×Dic11C2×C411yescharacteristic
28C2×C4×Dic11D412yes—
29C22×C11⋊C8—22no—
30#66945—44no—
31C42×D11—22no—
32C42×D11—21no—
33C42×D11—21no—
34C11×#97—22no—
35C11×#97—22no—
36C11×#95—22no—
37C11⋊#95—22no—
38(C2×D11)⋊C8—28no—
39#66867—22no—
40#66867—22no—
41#8722—111nomaximal, Sylow
42C23×D11C22⋊C411yescharacteristic
43C22×C4×C11—22no—
44C22×C4×C11C22×C411yescharacteristic
45C22×C4×C11C2×D412yes—
46C22×Dic11—22no—
47C22×Dic11C22⋊C411yescharacteristic
48C22×Dic11C22⋊C412yes—
49C2×C4×D11—22no—
50C2×C4×D11—24no—
51C2×C4×D11—22no—
52C2×C4×D11—21no—
53C2×C4×D11—21no—
54C2×C4×D11—22no—
55C2×C4×D11—22no—
56C2×C4×D11—42no—
57C2×C8×C11—24no—
58C2×C8×C11—42no—
59C2×C8×C11—42no—
60C11×C4⋊C4—42no—
61C42×C11#4112yes—
62C42×C11#4111yescharacteristic
63C42×C11#4111yescharacteristic
64(C2×D11)⋊C4—44no—
65C4⋊Dic11—42no—
66Dic11⋊C4—44no—
67Dic11⋊C4—44no—
68C4×Dic11—21no—
69C4×Dic11—21no—
70C4×Dic11—22no—
71C4×Dic11—22no—
72C4×Dic11—44no—
73C2×C11⋊C8—24no—
74C2×C11⋊C8—42no—
75C2×C11⋊C8—42no—
76#2285—111no—
77#1749—112no—
78#1295—112no—
79#1295—111no—
80#1295D1111yescharacteristic, complemented
81C23×C11C2×C22⋊C411yescharacteristic
82C22×D11—21no—
83C22×D11—21no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11#10012yes—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11—42no—
94C2×C4×C11#11711yescharacteristic
95C2×C4×C11#11711yescharacteristic
96C2×C4×C11#12312yes—
97C2×C4×C11#12312yes—
98C2×Dic11—21no—
99C2×Dic11—22no—
100C2×Dic11—21no—
101C2×Dic11—22no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11#10112yes—
106C2×Dic11#10414yes—
107C4×D11—24no—
108C4×D11—24no—
109C4×D11—44no—
110C4×D11—44no—
111C8×C11—44no—
112C11⋊C8—44no—
113C2×#117—112no—
114C22×C42—111no—
115C2×C22⋊C8—222no—
116C2×#97—112no—
117C2×#97C2×D1112yes—
118#384—112no—
119#382—111no—
120#382C2×D1111yescharacteristic
121#380—222no—
122C4×C4⋊C4—222no—
123#336—222no—
124C22×C11#38111yescharacteristic
125C22×C11C2×#10011yescharacteristic
126C22×C11C2×#10111yescharacteristic
127C22×C11C2×#10412yes—
128C22×C11#42112yes—
129C2×D11—22no—
130C2×D11—24no—
131C2×D11—41no—
132C2×D11—42no—
133C2×D11—41no—
134C4×C11—21no—
135C4×C11—21no—
136C4×C11—22no—
137C4×C11—22no—
138C4×C11—82no—
139Dic11—22no—
140Dic11—24no—
141Dic11—82no—
142C23×C4—111no—
143C23×C4—112no—
144C22×C8—22no—
145C22×C8—222no—
146#117—444no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4—222no—
149C2×C4⋊C4—222no—
150C2×C4⋊C4C4×D1112yes—
151C2×C22⋊C4—222no—
152C2×C42—111no—
153C2×C42—112no—
154C2×C42—222no—
155C2×C42—221no—
156C2×C42—221no—
157C2×C42—222no—
158C2×C42C22×D1111yescharacteristic
159C22⋊C8—228no—
160#97—22no—
161#97—22no—
162#97—222no—
163#97—222no—
164#95—22no—
165#95—222no—
166C2×C11#152611yescharacteristic
167C2×C11#153012yes—
168C2×C11#153711yescharacteristic
169C2×C11#182111yescharacteristic
170C2×C11#182612yes—
171D11—42no—
172C24—111no—
173C22×C4—22no—
174C22×C4—111no—
175C22×C4—112no—
176C22×C4—222no—
177C22×C4—224no—
178C22×C4—222no—
179C22×C4—221no—
180C22×C4—221no—
181C22×C4—222no—
182C22×C4—222no—
183C22×C4—222no—
184C22×C4—442no—
185C22×C4C2×C4×D1111yescharacteristic
186C22×C4D4×D1112yes—
187C2×C8—24no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—224no—
191C2×C8—442no—
192C2×C8—442no—
193C4⋊C4—42no—
194C4⋊C4—442no—
195C4⋊C4—444no—
196C4⋊C4—444no—
197C22⋊C4—444no—
198C42—221no—
199C42—222no—
200C42—221no—
201C42—222no—
202C42—444no—
203C42#433912yes—
204C42#434111yescharacteristic
205C42#434311yescharacteristic
206C11#872211yescharacteristic, complemented, Sylow
207C23—112no—
208C23—221no—
209C23—221no—
210C23—222no—
211C23—222no—
212C23C22⋊C4×D1111yescharacteristic
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—112no—
221C2×C4—114no—
222C2×C4—224no—
223C2×C4—224no—
224C2×C4—221no—
225C2×C4—222no—
226C2×C4—221no—
227C2×C4—222no—
228C2×C4—444no—
229C2×C4—444no—
230C2×C4—442no—
231C2×C4—442no—
232C2×C4—442no—
233C2×C4#6692511yescharacteristic
234C2×C4#6693612yes—
235C2×C4#6694511yescharacteristic
236C2×C4#6694712yes—
237C8—44no—
238C8—444no—
239C22—222no—
240C22—224no—
241C22—442no—
242C22—441no—
243C22—441no—
244C22#1062227711yescharacteristic
245C22D11×#10011yescharacteristic
246C22D11×#10111yescharacteristic
247C22D11×#10412yes—
248C22#1062243412yes—
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—222no—
255C4—224no—
256C4—882no—
257C2—442no—
258C2#1306720911yescharacteristic
259C2#1306722512yes—
260C2#1306725211yescharacteristic
261C2#1306869511yescharacteristic
262C2#1306871412yes—
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1295D11
hypocenterC11#8722
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
3. #13066498C2semidirect
4. #13066497C2semidirect
5. C11×#1295C2semidirect
80. #1295D11semidirect
206. C11#8722semidirect

Maximal subgroups

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

subgroupindex
#130710222
#130683792
#130664982
#130664972
C11×#12952
#872211