Finite Group Databasebeta

← #14664625

Subgroups — #14664625

Order 2816.

280 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 79 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#13070428C211yesmaximal, characteristic
2#13068765C211yesmaximal, characteristic
3#13066610C212yesmaximal
4#13066604C212yesmaximal
5C11×#3185C211yesmaximal, characteristic
6C11×#533—21no—
7C11×#498C411yescharacteristic, complemented
8C11×#494C411yescharacteristic, complemented
9C11×#487—21no—
10C11×#470—21no—
11C11×#470C2212yes—
12C11×#441—21no—
13C11×#441C412yescomplemented
14C4×C11×M16C2211yescharacteristic
15C11⋊#338C2211yescharacteristic
16#10622195C2211yescharacteristic
17#10622194—21no—
18#10622191C2212yes—
19#10622161—21no—
20#10622104—21no—
21#10622101—21no—
22C2×C11×Q16—21no—
23C2×C11×Q16C2×C412yes—
24C2×C11×M16D411yescharacteristic
25C2×C11×M16C2311yescharacteristic
26C11×C4⋊Q8—21no—
27C11×C4⋊Q8—21no—
28C11×#125—41no—
29C11×C22⋊Q8—22no—
30C11×C22⋊Q8—41no—
31C4×Q8×C11—22no—
32C4×Q8×C11—41no—
33C11×#117—41no—
34C2×C42×C11D411yescharacteristic
35#66979—21no—
36C2×#4318—21no—
37C11×#106—21no—
38C11×#106C2×C412yes—
39C11×#103—22no—
40C11×#103—22no—
41C11×#97C2×C411yescharacteristic
42C11×#97D411yescharacteristic
43C4×C8×C11C2×C411yescharacteristic
44C4×C8×C11D411yescharacteristic
45#66876—22no—
46#11838—111nomaximal, Sylow
47C2×Q8×C11—22no—
48C2×Q8×C11—41no—
49C22×C4×C11—21no—
50C22×C4×C11C2×D411yescharacteristic
51C11×Q16—42no—
52C11×Q16—42no—
53C11×M16—41no—
54C11×M16—41no—
55C2×C8×C11C22⋊C411yescharacteristic
56C2×C8×C11C22⋊C411yescharacteristic
57C2×C8×C11C22×C411yescharacteristic
58C2×C8×C11C2×D411yescharacteristic
59C11×C4⋊C4—22no—
60C11×C4⋊C4—41no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—42no—
65C11×C22⋊C4—42no—
66C42×C11—21no—
67C42×C11—42no—
68C42×C11C22⋊C411yescharacteristic
69C42×C11C22⋊C411yescharacteristic
70C22⋊Dic11—41no—
71C4⋊Dic11—41no—
72C4×Dic11—41no—
73#4318—41no—
74#4318—41no—
75C2×C11⋊C8—41no—
76C11⋊C16—42no—
77#3185D1111yescharacteristic
78#2165—111no—
79#1841—111no—
80#1342—112no—
81#1340—112no—
82C23×C11AGL(1,ℤ/8)11yescharacteristic
83Q8×C11—42no—
84Q8×C11—42no—
85Q8×C11—82no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11C2×C22⋊C411yescharacteristic
94C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
95C2×Dic11—81no—
96C8×C11—21no—
97C8×C11—21no—
98C8×C11—21no—
99C8×C11—21no—
100C11⋊C8—81no—
101#533—21no—
102#498Dic1111yescharacteristic, complemented
103#494Dic1111yescharacteristic, complemented
104#487—21no—
105#470—21no—
106#470C2×D1112yes—
107#441—21no—
108#441Dic1112yescomplemented
109C4×M16C2×D1111yescharacteristic
110#364—221no—
111#349—112no—
112#347—221no—
113#344—221no—
114#339—221no—
115#338—111no—
116H(3,ℤ/4)—111no—
117C22×C11—21no—
118C22×C11—41no—
119C22×C11#41811yescharacteristic
120C4×C11—22no—
121C4×C11—21no—
122C4×C11—41no—
123C4×C11—82no—
124C4×C11—82no—
125C4×C11#41011yescharacteristic
126C4×C11#42111yescharacteristic
127Dic11—161no—
128C2×Q16—21no—
129C2×Q16C2×Dic1112yes—
130C2×M16—221no—
131C2×M16C22⋊D1111yescharacteristic
132C2×M16C22×D1111yescharacteristic
133C4⋊Q8—21no—
134C4⋊Q8—21no—
135#125—41no—
136C22⋊Q8—22no—
137C22⋊Q8—41no—
138C4×Q8—22no—
139C4×Q8—41no—
140#117—41no—
141#117—221no—
142C2×C42C22⋊D1111yescharacteristic
143M32—222no—
144#106—21no—
145#106C2×Dic1112yes—
146#103—22no—
147#103—22no—
148#97C2×Dic1111yescharacteristic
149#97C22⋊D1111yescharacteristic
150C4×C8C2×Dic1111yescharacteristic
151C4×C8C22⋊D1111yescharacteristic
152C2×C11—21no—
153C2×C11—41no—
154C2×C11#151411yescharacteristic
155C2×Q8—22no—
156C2×Q8—41no—
157C22×C4—21no—
158C22×C4C2×C22⋊D1111yescharacteristic
159Q16—42no—
160Q16—42no—
161M16—41no—
162M16—41no—
163M16—441no—
164M16—441no—
165C2×C8—441no—
166C2×C8C22⋊Dic1111yescharacteristic
167C2×C8C22⋊Dic1111yescharacteristic
168C2×C8C22×Dic1111yescharacteristic
169C2×C8C2×C22⋊D1111yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—42no—
174C4⋊C4—41no—
175C4⋊C4—42no—
176C4⋊C4—441no—
177C22⋊C4—42no—
178C22⋊C4—441no—
179C42—21no—
180C42—42no—
181C42—441no—
182C42C22⋊Dic1111yescharacteristic
183C42C22⋊Dic1111yescharacteristic
184C16—442no—
185C11#1183811yescharacteristic, complemented, Sylow
186C23#6698511yescharacteristic
187Q8—42no—
188Q8—42no—
189Q8—82no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—881no—
198C2×C4#6698511yescharacteristic
199C2×C4C2×C22⋊Dic1111yescharacteristic
200C8—21no—
201C8—21no—
202C8—21no—
203C8—21no—
204C8—881no—
205C22—21no—
206C22—41no—
207C22#1062282811yescharacteristic
208C4—22no—
209C4—21no—
210C4—41no—
211C4—82no—
212C4—82no—
213C4—1761no—
214C4#1062284911yescharacteristic
215C4#1062285311yescharacteristic
216C2—21no—
217C2—41no—
218C2#1306716311yescharacteristic
subgroupG/H
centerC2#13067163
commutatorC2×C8×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#3185C2
socleC2×C11#1514
prime radicalC23×C11AGL(1,ℤ/8)
cosocleC2×C11×M16C23
hypercenter#3185D11
hypocenterC11#11838
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #3185

Complements

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

NH ≅ G/Ntype
7. C11×#498C4semidirect
8. C11×#494C4semidirect
13. C11×#441C4semidirect
102. #498Dic11semidirect
103. #494Dic11semidirect
108. #441Dic11semidirect
185. C11#11838semidirect

Maximal subgroups

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

subgroupindex
#130704282
#130687652
#130666102
#130666042
C11×#31852
#1183811