Finite Group Databasebeta

← #14664966

Subgroups — #14664966

Order 2816.

326 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 71 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#13078991C211yesmaximal, characteristic
2#13070428C211yesmaximal, characteristic, complemented
3#13066648C214yesmaximal, complemented
4C11×#2165C211yesmaximal, characteristic, complemented
5C2×#66927C411yescharacteristic
6#10623001C411yescharacteristic
7C4×C11×M16C2211yescharacteristic
8#10622744—21no—
9#10622744—21no—
10#10622326C412yes—
11#10622326C2212yes—
12#10622307—21no—
13#10622307—21no—
14C11×#364—21no—
15C11×#349—21no—
16C11×#347C2212yescomplemented
17#10622191—21no—
18#10622104C2212yescomplemented
19#10622101—21no—
20C22×D44—21no—
21C22×D44—41no—
22C2×C11×M16D411yescharacteristic
23C2×C11×M16D411yescharacteristic
24C2×C42×C11C2×C411yescharacteristic
25#66979—21no—
26#66977—41no—
27#66927—21no—
28#66927—41no—
29#66927C2×C412yes—
30#66923C2×C412yes—
31#66922—21no—
32C4×Dic22—41no—
33C11×M32—22no—
34C11×#97C2×C411yescharacteristic
35C11×#97C2311yescharacteristic
36C4×C8×C11D411yescharacteristic
37C4×C8×C11D411yescharacteristic
38#66885—22no—
39#66885—22no—
40#66885—22no—
41#66885—22no—
42#66876—22no—
43#11915—111nomaximal, Sylow
44C23×D11—41no—
45C22×C4×C11—21no—
46C22×C4×C11C22⋊C411yescharacteristic
47C2×D44—22no—
48C2×D44—42no—
49C2×D44—42no—
50C2×D44—42no—
51C2×D44—42no—
52C2×D44—41no—
53C2×D44—84no—
54C2×Dic22—41no—
55C11×M16—41no—
56C11×M16—41no—
57C2×C8×C11C22⋊C411yescharacteristic
58C2×C8×C11C22⋊C411yescharacteristic
59C2×C8×C11C2×D411yescharacteristic
60C2×C8×C11C2×D411yescharacteristic
61C42×C11—21no—
62C42×C11C22⋊C411yescharacteristic
63C42×C11C22×C411yescharacteristic
64C22⋊Dic11—41no—
65C4⋊Dic11—22no—
66C4⋊Dic11—41no—
67Dic11⋊C4—42no—
68C4×Dic11—41no—
69C11×C16—42no—
70C11⋊C16—42no—
71#3138—111no—
72#2165—111no—
73#2165D1111yescharacteristic, complemented
74#1355—114no—
75C23×C11#10011yescharacteristic
76C22×D11—42no—
77C22×D11—82no—
78C22×D11—84no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—42no—
84C2×C4×C11#10011yescharacteristic
85C2×C4×C11C2×C22⋊C411yescharacteristic
86C2×Dic11—42no—
87D44—42no—
88D44—42no—
89D44—82no—
90D44—84no—
91D44—84no—
92Dic22—82no—
93C8×C11—21no—
94C8×C11—21no—
95C8×C11—21no—
96C8×C11—21no—
97#533—111no—
98C2×#127—111no—
99#490—112no—
100#490—112no—
101#486—221no—
102#486—221no—
103#418—221no—
104#418—221no—
105C4×M16C2×D1111yescharacteristic
106#364—21no—
107#364—221no—
108#349—21no—
109#349—221no—
110#347—112no—
111#347C2×D1112yescomplemented
112C22×C11—21no—
113C22×C11—41no—
114C22×C11C2×#10011yescharacteristic
115C2×D11—84no—
116C2×D11—82no—
117C2×D11—164no—
118C4×C11—22no—
119C4×C11—21no—
120C4×C11—41no—
121C4×C11#42111yescharacteristic
122C4×C11#42111yescharacteristic
123Dic11—82no—
124C22×D4—221no—
125C22×D4—441no—
126C2×M16D4411yescharacteristic
127C2×M16C22⋊D1111yescharacteristic
128C4⋊Q8—221no—
129#127—112no—
130#127—221no—
131#127—441no—
132#125—112no—
133C22⋊Q8—441no—
134C4×Q8—441no—
135#117—221no—
136C2×C42C4×D1111yescharacteristic
137M32—22no—
138M32—222no—
139#102—222no—
140#102—222no—
141#102—222no—
142#102—222no—
143#97C4×D1111yescharacteristic
144#97C22×D1111yescharacteristic
145C4×C8D4411yescharacteristic
146C4×C8C22⋊D1111yescharacteristic
147C2×C11—21no—
148C2×C11—41no—
149C2×C11#153311yescharacteristic
150D11—162no—
151C24—441no—
152C2×Q8—441no—
153C2×D4—222no—
154C2×D4—442no—
155C2×D4—442no—
156C2×D4—442no—
157C2×D4—442no—
158C2×D4—441no—
159C2×D4—884no—
160C22×C4—21no—
161C22×C4(C2×D11)⋊C411yescharacteristic
162M16—41no—
163M16—41no—
164C2×C8(C2×D11)⋊C411yescharacteristic
165C2×C8(C2×D11)⋊C411yescharacteristic
166C2×C8C2×D4411yescharacteristic
167C2×C8C2×C22⋊D1111yescharacteristic
168C4⋊C4—222no—
169C4⋊C4—442no—
170C4⋊C4—441no—
171C22⋊C4—441no—
172C42—21no—
173C42—441no—
174C42(C2×D11)⋊C411yescharacteristic
175C42C2×C4×D1111yescharacteristic
176C16—42no—
177C16—442no—
178C11#1191511yescharacteristic, complemented, Sylow
179C23—442no—
180C23—882no—
181C23—884no—
182C23#6688711yescharacteristic
183Q8—882no—
184D4—442no—
185D4—442no—
186D4—882no—
187D4—884no—
188D4—884no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—42no—
194C2×C4—442no—
195C2×C4#6688711yescharacteristic
196C2×C4C2×(C2×D11)⋊C411yescharacteristic
197C8—21no—
198C8—21no—
199C8—21no—
200C8—21no—
201C22—21no—
202C22—41no—
203C22—884no—
204C22—882no—
205C22—1764no—
206C22C2×#6688711yescharacteristic
207C4—22no—
208C4—21no—
209C4—41no—
210C4—882no—
211C4#1062261811yescharacteristic
212C4#1062275211yescharacteristic
213C2—21no—
214C2—41no—
215C2—1762no—
216C2#1306723911yescharacteristic
subgroupG/H
centerC2#13067239
commutatorC42×C11C22×C4
Frattini#97C22×D11
FittingC11×#2165C2
socleC2×C11#1533
prime radicalC2×#66927C4
cosocleC11×#97C23
hypercenter#2165D11
hypocenterC11#11915
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
2. #13070428C2semidirect
3. #13066648C2semidirect
4. C11×#2165C2semidirect
16. C11×#347C22semidirect
18. #10622104C22semidirect
73. #2165D11semidirect
111. #347C2×D11semidirect
178. C11#11915semidirect

Maximal subgroups

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

subgroupindex
#130789912
#130704282
#130666482
C11×#21652
#1191511