Finite Group Databasebeta

← #14665293

Subgroups — #14665293

Order 2816.

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

normal subgroups only

This group has 268 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#13079275C211yesmaximal, characteristic
2#13070432C211yesmaximal, characteristic
3#13066678C212yesmaximal, complemented
4#13066654C212yesmaximal, complemented
5C11×#2153C211yesmaximal, characteristic
6#10623049C412yes—
7C2×C11×M32—21no—
8C11×#405C2211yescharacteristic
9#10622750—21no—
10#10622729—21no—
11#10622329—21no—
12#10622316C412yes—
13#10622312C2211yescharacteristic
14C4×Dic44—21no—
15#10622296C2211yescharacteristic
16C11×#364—21no—
17C11×#364C2212yes—
18#10622191—21no—
19#10622104—21no—
20#10622101C2212yes—
21C2×C11×M16D411yescharacteristic
22C22×C8×C11D411yescharacteristic
23C11×#117C2×C411yescharacteristic
24#66977—22no—
25C2×Dic44—21no—
26C2×Dic44—21no—
27#66942—42no—
28#66932—42no—
29#66923C2×C412yes—
30#66922C2×C412yes—
31C4×Dic22—22no—
32C11×M32—22no—
33C11×M32—41no—
34C2×C11×C16—41no—
35C11×#97C2×C411yescharacteristic
36C11×#97D411yescharacteristic
37C4×C8×C11D411yescharacteristic
38C4×C8×C11C2311yescharacteristic
39#66882—21no—
40#66881—21no—
41#66880—22no—
42#66880—22no—
43#66876—22no—
44#11990—111nomaximal, Sylow
45C22×C4×C11C22⋊C411yescharacteristic
46C2×Dic22—22no—
47C11×M16—22no—
48C2×C8×C11—21no—
49C2×C8×C11—21no—
50C2×C8×C11C22⋊C411yescharacteristic
51C2×C8×C11C22⋊C411yescharacteristic
52C2×C8×C11C2×D411yescharacteristic
53C2×C8×C11C2×D411yescharacteristic
54C11×C4⋊C4—21no—
55C11×C22⋊C4—21no—
56C42×C11C22⋊C411yescharacteristic
57C42×C11C22×C411yescharacteristic
58C22⋊Dic11—42no—
59C4⋊Dic11—22no—
60C4⋊Dic11—42no—
61Dic11⋊C4—42no—
62Dic11⋊C4—42no—
63Dic11⋊C4—42no—
64C4×Dic11—42no—
65Dic44—42no—
66Dic44—41no—
67Dic44—41no—
68C11×C16—42no—
69C11⋊C16—42no—
70#3177—111no—
71#2166—111no—
72#2153D1111yescharacteristic
73#1366—112no—
74#1358—112no—
75C23×C11#10011yescharacteristic
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11#10011yescharacteristic
81C2×C4×C11C2×C22⋊C411yescharacteristic
82C2×Dic11—42no—
83C2×Dic11—42no—
84Dic22—42no—
85Dic22—42no—
86C8×C11—21no—
87C8×C11—21no—
88C8×C11#13512yes—
89C8×C11AGL(1,ℤ/8)11yescharacteristic
90C8×C11#13711yescharacteristic
91#541—112no—
92C2×M32—21no—
93#499—111no—
94#494—111no—
95#491—112no—
96#470—221no—
97#467—221no—
98#441—221no—
99C4×Q16—221no—
100#405C2×D1111yescharacteristic
101#364—21no—
102#364—112no—
103#364C2×D1112yes—
104#349—221no—
105#347—221no—
106C22×C11—21no—
107C22×C11—41no—
108C22×C11C2×#10011yescharacteristic
109C4×C11—21no—
110C4×C11—41no—
111C4×C11—41no—
112C4×C11#41611yescharacteristic
113C4×C11#41711yescharacteristic
114Dic11—82no—
115Dic11—82no—
116C2×Q16—221no—
117C2×Q16—221no—
118C2×M16D4411yescharacteristic
119C22×C8C22⋊D1111yescharacteristic
120C4⋊Q8—112no—
121#126—442no—
122#125—112no—
123#125—442no—
124C22⋊Q8—222no—
125C4×Q8—222no—
126#117C4×D1111yescharacteristic
127M32—22no—
128M32—41no—
129M32—222no—
130C2×C16—41no—
131#107—221no—
132#106—221no—
133#103—222no—
134#103—222no—
135#97C4×D1111yescharacteristic
136#97D4411yescharacteristic
137C4×C8C22⋊D1111yescharacteristic
138C4×C8C22×D1111yescharacteristic
139C2×C11—21no—
140C2×C11—41no—
141C2×C11#155111yescharacteristic
142C2×Q8—222no—
143C22×C4(C2×D11)⋊C411yescharacteristic
144Q16—442no—
145Q16—441no—
146Q16—441no—
147M16—22no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8(C2×D11)⋊C411yescharacteristic
151C2×C8(C2×D11)⋊C411yescharacteristic
152C2×C8C2×D4411yescharacteristic
153C2×C8C2×C22⋊D1111yescharacteristic
154C4⋊C4—21no—
155C4⋊C4—222no—
156C4⋊C4—442no—
157C4⋊C4—442no—
158C4⋊C4—442no—
159C4⋊C4—442no—
160C22⋊C4—21no—
161C22⋊C4—442no—
162C42—442no—
163C42(C2×D11)⋊C411yescharacteristic
164C42C2×C4×D1111yescharacteristic
165C16—42no—
166C16—442no—
167C11#1199011yescharacteristic, complemented, Sylow
168C23#6688711yescharacteristic
169Q8—442no—
170Q8—442no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—442no—
176C2×C4—442no—
177C2×C4#6688711yescharacteristic
178C2×C4C2×(C2×D11)⋊C411yescharacteristic
179C8—21no—
180C8—21no—
181C8#6695712yes—
182C8#6698511yescharacteristic
183C8#6699511yescharacteristic
184C22—21no—
185C22—41no—
186C22C2×#6688711yescharacteristic
187C4—21no—
188C4—41no—
189C4—41no—
190C4—882no—
191C4—882no—
192C4#1062257911yescharacteristic
193C4#1062272611yescharacteristic
194C2—21no—
195C2—41no—
196C2#1306730911yescharacteristic
subgroupG/H
centerC2#13067309
commutatorC42×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#2153C2
socleC2×C11#1551
prime radicalC23×C11#100
cosocleC4×C8×C11C23
hypercenter#2153D11
hypocenterC11#11990
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2153

Complements

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

NH ≅ G/Ntype
3. #13066678C2semidirect
4. #13066654C2semidirect
167. C11#11990semidirect

Maximal subgroups

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

subgroupindex
#130792752
#130704322
#130666782
#130666542
C11×#21532
#1199011