Finite Group Databasebeta

← #14664315

Subgroups — #14664315

Order 2816.

316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 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#13070432C211yesmaximal, characteristic, complemented
2#13068371C211yesmaximal, characteristic, complemented
3#13066607C212yesmaximal, complemented
4#13066601C212yesmaximal, complemented
5C11×#3176C211yesmaximal, characteristic
6C11×#540—21no—
7C11×#499C411yescharacteristic, complemented
8C11×#493C411yescharacteristic, complemented
9C11×#490—21no—
10C11×#469C2212yes—
11C11×#466—21no—
12C11×#442C412yescomplemented
13C4×C11×D8—21no—
14C11×#405C2211yescharacteristic
15#10622714—21no—
16C11⋊#338C2211yescharacteristic
17#10622195C2211yescharacteristic
18#10622191C2212yes—
19#10622169—21no—
20#10622104—21no—
21#10622101—21no—
22C2×C11×D8—21no—
23C2×C11×D8C2×C412yes—
24C2×C11×M16C2311yescharacteristic
25C22×C8×C11D411yescharacteristic
26C11×#127—21no—
27C11×#125—21no—
28C11×#123—42no—
29C11×#121—22no—
30C11×#121—42no—
31C4×D4×C11—22no—
32C11×#117D411yescharacteristic
33#66979—21no—
34C2×#4318—21no—
35C11×#107—21no—
36C11×#106C2×C412yes—
37C11×#102—22no—
38C11×#102—22no—
39C11×#97C2×C411yescharacteristic
40C11×#97D411yescharacteristic
41C4×C8×C11C2×C411yescharacteristic
42C4×C8×C11D411yescharacteristic
43#66879—22no—
44C8×Dic11—22no—
45#66876—22no—
46#11770—111nomaximal, Sylow
47C2×D4×C11—22no—
48C2×D4×C11—42no—
49C2×D4×C11—42no—
50C22×C4×C11—42no—
51C22×C4×C11C2×D411yescharacteristic
52C11×D8—41no—
53C11×D8—41no—
54C11×D8—42no—
55C11×M16—41no—
56C2×C8×C11—21no—
57C2×C8×C11—21no—
58C2×C8×C11C22⋊C411yescharacteristic
59C2×C8×C11C22⋊C411yescharacteristic
60C2×C8×C11C22×C411yescharacteristic
61C2×C8×C11C2×D411yescharacteristic
62C11×C4⋊C4—21no—
63C11×C4⋊C4—22no—
64C11×C4⋊C4—42no—
65C11×C22⋊C4—21no—
66C11×C22⋊C4—42no—
67C11×C22⋊C4—42no—
68C42×C11C22⋊C411yescharacteristic
69C42×C11C22⋊C411yescharacteristic
70C22⋊Dic11—41no—
71C4⋊Dic11—41no—
72C4×Dic11—22no—
73#4318—41no—
74#4318—41no—
75C2×C11⋊C8—22no—
76C11⋊C16—42no—
77#3176D1111yescharacteristic
78#2166—111no—
79#1747—111no—
80#1341—112no—
81#1339—112no—
82C23×C11—42no—
83C23×C11AGL(1,ℤ/8)11yescharacteristic
84D4×C11—42no—
85D4×C11—42no—
86D4×C11—162no—
87D4×C11—162no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—42no—
93C2×C4×C11—162no—
94C2×C4×C11C2×C22⋊C411yescharacteristic
95C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
96C2×Dic11—42no—
97C8×C11—21no—
98C8×C11—21no—
99C8×C11—21no—
100C8×C11#10411yescharacteristic
101C8×C11#10411yescharacteristic
102C11⋊C8—42no—
103#540—21no—
104#499Dic1111yescharacteristic, complemented
105#493Dic1111yescharacteristic, complemented
106#490—21no—
107#469C2×D1112yes—
108#466—21no—
109#442Dic1112yescomplemented
110C4×D8—21no—
111#405—221no—
112#405C2×D1111yescharacteristic
113#364—221no—
114#349—112no—
115#347—221no—
116#338—111no—
117H(3,ℤ/4)—111no—
118H(3,ℤ/4)—221no—
119C22×C11—21no—
120C22×C11—41no—
121C22×C11—82no—
122C22×C11—82no—
123C22×C11—82no—
124C22×C11#41811yescharacteristic
125C4×C11—21no—
126C4×C11—41no—
127C4×C11—41no—
128C4×C11—82no—
129C4×C11#41011yescharacteristic
130C4×C11C2×#10411yescharacteristic
131Dic11—82no—
132C2×D8—21no—
133C2×D8C2×Dic1112yes—
134C2×M16—221no—
135C2×M16C22×D1111yescharacteristic
136C22×C8C22⋊D1111yescharacteristic
137#127—21no—
138#125—21no—
139#123—42no—
140#121—22no—
141#121—42no—
142C4×D4—22no—
143#117—221no—
144#117C22⋊D1111yescharacteristic
145M32—222no—
146#107—21no—
147#106C2×Dic1112yes—
148#102—22no—
149#102—22no—
150#97—222no—
151#97C2×Dic1111yescharacteristic
152#97C22⋊D1111yescharacteristic
153C4×C8—222no—
154C4×C8C2×Dic1111yescharacteristic
155C4×C8C22⋊D1111yescharacteristic
156C2×C11—21no—
157C2×C11—41no—
158C2×C11—162no—
159C2×C11#150511yescharacteristic
160C2×D4—22no—
161C2×D4—42no—
162C2×D4—42no—
163C22×C4—42no—
164C22×C4C2×C22⋊D1111yescharacteristic
165D8—42no—
166D8—41no—
167D8—41no—
168M16—41no—
169M16—441no—
170M16—441no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—222no—
174C2×C8C22⋊Dic1111yescharacteristic
175C2×C8C22⋊Dic1111yescharacteristic
176C2×C8C22×Dic1111yescharacteristic
177C2×C8C2×C22⋊D1111yescharacteristic
178C4⋊C4—21no—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—441no—
182C22⋊C4—21no—
183C22⋊C4—42no—
184C22⋊C4—42no—
185C22⋊C4—441no—
186C42—222no—
187C42C22⋊Dic1111yescharacteristic
188C42C22⋊Dic1111yescharacteristic
189C16—442no—
190C11#1177011yescharacteristic, complemented, Sylow
191C23—42no—
192C23#6698511yescharacteristic
193D4—42no—
194D4—42no—
195D4—162no—
196D4—162no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—162no—
203C2×C4—442no—
204C2×C4#6698511yescharacteristic
205C2×C4C2×C22⋊Dic1111yescharacteristic
206C8—21no—
207C8—21no—
208C8—21no—
209C8—442no—
210C8#6690111yescharacteristic
211C8#6690111yescharacteristic
212C22—21no—
213C22—41no—
214C22—82no—
215C22—82no—
216C22—82no—
217C22#1062282811yescharacteristic
218C4—21no—
219C4—41no—
220C4—41no—
221C4—82no—
222C4—882no—
223C4C2×#6690111yescharacteristic
224C4#1062285311yescharacteristic
225C2—21no—
226C2—41no—
227C2—162no—
228C2#1306712411yescharacteristic
subgroupG/H
centerC2#13067124
commutatorC2×C8×C11C22×C4
FrattiniC2×M16C22×D11
Fitting, prime radicalC11×#3176C2
socleC2×C11#1505
cosocleC2×C11×M16C23
hypercenter#3176D11
hypocenterC11#11770
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #3176

Complements

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

NH ≅ G/Ntype
1. #13070432C2semidirect
2. #13068371C2semidirect
3. #13066607C2semidirect
4. #13066601C2semidirect
7. C11×#499C4semidirect
8. C11×#493C4semidirect
12. C11×#442C4semidirect
104. #499Dic11semidirect
105. #493Dic11semidirect
109. #442Dic11semidirect
190. C11#11770semidirect

Maximal subgroups

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

subgroupindex
#130704322
#130683712
#130666072
#130666012
C11×#31762
#1177011