Finite Group Databasebeta

← #14664317

Subgroups — #14664317

Order 2816.

316 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 75 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#13079266C211yesmaximal, characteristic
2#13068371C211yesmaximal, characteristic, complemented
3#13066608C212yesmaximal, complemented
4#13066602C212yesmaximal, complemented
5C11×#2166C211yesmaximal, characteristic, complemented
6#10623066—21no—
7C11×#405C2211yescharacteristic
8#10622748C2212yes—
9#10622728—21no—
10#10622714—21no—
11#10622326—21no—
12#10622324C412yescomplemented
13#10622308C411yescharacteristic, complemented
14C4×D88—21no—
15#10622296C411yescharacteristic, complemented
16C11×#364—21no—
17C11×#349C2212yes—
18C11×#347—21no—
19C11⋊#338C2211yescharacteristic
20#10622195C2211yescharacteristic
21#10622169—21no—
22C2×C11×M16C2311yescharacteristic
23C22×C8×C11D411yescharacteristic
24C11×#117D411yescharacteristic
25#66983—22no—
26#66979—21no—
27C2×#4318—21no—
28C2×D88—21no—
29C2×D88C2×C412yes—
30#66947—42no—
31#66937—42no—
32#66927—21no—
33C4×D44—22no—
34#66923—21no—
35C11×M32—22no—
36C11×#97C2×C411yescharacteristic
37C11×#97D411yescharacteristic
38C4×C8×C11C2×C411yescharacteristic
39C4×C8×C11D411yescharacteristic
40#66885—22no—
41#66885—22no—
42#66882—21no—
43#66881C2×C412yes—
44#66879—22no—
45C8×Dic11—22no—
46#11770—111nomaximal, Sylow
47C22×C4×C11C2×D411yescharacteristic
48C2×C22⋊D11—42no—
49C2×D44—22no—
50C2×D44—42no—
51C2×C4×D11—42no—
52C11×M16—41no—
53C2×C8×C11—21no—
54C2×C8×C11—21no—
55C2×C8×C11C22⋊C411yescharacteristic
56C2×C8×C11C22⋊C411yescharacteristic
57C2×C8×C11C22×C411yescharacteristic
58C2×C8×C11C2×D411yescharacteristic
59C11×C4⋊C4—21no—
60C11×C22⋊C4—21no—
61C42×C11C22⋊C411yescharacteristic
62C42×C11C22⋊C411yescharacteristic
63C22⋊Dic11—41no—
64(C2×D11)⋊C4—42no—
65(C2×D11)⋊C4—42no—
66C4⋊Dic11—22no—
67C4⋊Dic11—41no—
68Dic11⋊C4—42no—
69C4×Dic11—22no—
70#4318—41no—
71#4318—41no—
72C2×C11⋊C8—22no—
73D88—42no—
74D88—41no—
75D88—41no—
76C11×C16—42no—
77#3176—111no—
78#2166D1111yescharacteristic, complemented
79#1747—111no—
80#1341—112no—
81#1339—112no—
82C23×C11AGL(1,ℤ/8)11yescharacteristic
83C22×D11—42no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11C2×C22⋊C411yescharacteristic
89C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
90C22⋊D11—162no—
91C2×Dic11—42no—
92C2×Dic11—42no—
93D44—42no—
94D44—42no—
95D44—162no—
96C4×D11—162no—
97C8×C11—21no—
98C8×C11—21no—
99C8×C11—21no—
100C8×C11#10411yescharacteristic
101C8×C11#10411yescharacteristic
102C11⋊C8—42no—
103#540—221no—
104#499—111no—
105#493—111no—
106#490—221no—
107#469—112no—
108#466—221no—
109#442—112no—
110C4×D8—221no—
111#405—221no—
112#405C2×D1111yescharacteristic
113#364—21no—
114#349C2×D1112yes—
115#347—21no—
116#338—111no—
117H(3,ℤ/4)—111no—
118H(3,ℤ/4)—221no—
119C22×C11—21no—
120C22×C11—41no—
121C22×C11#41811yescharacteristic
122C2×D11—82no—
123C2×D11—82no—
124C2×D11—82no—
125C4×C11—21no—
126C4×C11—41no—
127C4×C11—41no—
128C4×C11#41011yescharacteristic
129C4×C11C2×#10411yescharacteristic
130Dic11—82no—
131Dic11—82no—
132C2×D8—112no—
133C2×D8—221no—
134C2×M16—221no—
135C2×M16C22×D1111yescharacteristic
136C22×C8D4411yescharacteristic
137#127—221no—
138#125—221no—
139#123—442no—
140#121—222no—
141#121—442no—
142C4×D4—222no—
143#117—221no—
144#117D4411yescharacteristic
145M32—22no—
146#107—221no—
147#106—112no—
148#102—222no—
149#102—222no—
150#97—222no—
151#97C4×D1111yescharacteristic
152#97C22⋊D1111yescharacteristic
153C4×C8—222no—
154C4×C8C4×D1111yescharacteristic
155C4×C8C22⋊D1111yescharacteristic
156C2×C11—21no—
157C2×C11—41no—
158C2×C11#150511yescharacteristic
159D11—162no—
160C2×D4—222no—
161C2×D4—442no—
162C2×D4—442no—
163C22×C4—442no—
164C22×C4C2×D4411yescharacteristic
165D8—442no—
166D8—441no—
167D8—441no—
168M16—41no—
169M16—441no—
170M16—441no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—222no—
174C2×C8(C2×D11)⋊C411yescharacteristic
175C2×C8(C2×D11)⋊C411yescharacteristic
176C2×C8C2×C4×D1111yescharacteristic
177C2×C8C2×C22⋊D1111yescharacteristic
178C4⋊C4—21no—
179C4⋊C4—222no—
180C4⋊C4—441no—
181C4⋊C4—442no—
182C22⋊C4—21no—
183C22⋊C4—442no—
184C22⋊C4—441no—
185C22⋊C4—442no—
186C42—222no—
187C42(C2×D11)⋊C411yescharacteristic
188C42(C2×D11)⋊C411yescharacteristic
189C16—42no—
190C11#1177011yescharacteristic, complemented, Sylow
191C23—442no—
192C23#6696111yescharacteristic
193D4—442no—
194D4—442no—
195D4—1762no—
196D4—1762no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—442no—
202C2×C4—442no—
203C2×C4—1762no—
204C2×C4#6696111yescharacteristic
205C2×C4C2×(C2×D11)⋊C411yescharacteristic
206C8—21no—
207C8—21no—
208C8—21no—
209C8—442no—
210C8#6688911yescharacteristic
211C8#6688911yescharacteristic
212C22—21no—
213C22—41no—
214C22—882no—
215C22—882no—
216C22—882no—
217C22#1062274411yescharacteristic
218C4—21no—
219C4—41no—
220C4—41no—
221C4—882no—
222C4—882no—
223C4#1062261911yescharacteristic
224C4C2×#6688911yescharacteristic
225C2—21no—
226C2—41no—
227C2—1762no—
228C2#1306712511yescharacteristic
subgroupG/H
centerC2#13067125
commutatorC2×C8×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#2166C2
socleC2×C11#1505
prime radical#13079266C2
cosocleC2×C11×M16C23
hypercenter#2166D11
hypocenterC11#11770
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
2. #13068371C2semidirect
3. #13066608C2semidirect
4. #13066602C2semidirect
5. C11×#2166C2semidirect
12. #10622324C4semidirect
13. #10622308C4semidirect
15. #10622296C4semidirect
78. #2166D11semidirect
190. C11#11770semidirect

Maximal subgroups

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

subgroupindex
#130792662
#130683712
#130666082
#130666022
C11×#21662
#1177011