Finite Group Databasebeta

← #14668017

Subgroups — #14668017

Order 2816.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#13070868C211yesmaximal, characteristic, complemented
2#13070698C211yesmaximal, characteristic
3#13070694C211yesmaximal, characteristic
4#13070452C211yesmaximal, characteristic
5#13066691C211yesmaximal, characteristic, complemented
6#13066654C211yesmaximal, characteristic, complemented
7C11×#1358C211yesmaximal, characteristic, complemented
8C11×#494C2211yescharacteristic
9C2×#66893—21no—
10C2×#66893—21no—
11#10622792—21no—
12#10622522—21no—
13#10622520—21no—
14#10622313C2211yescharacteristic
15#10622312C2211yescharacteristic
16C11×#364C2211yescharacteristic
17C11×#364C2211yescharacteristic
18#10622203—21no—
19#10622155—21no—
20#10622153—21no—
21#10622101C2211yescharacteristic
22C4×C11⋊C16C2211yescharacteristic
23C2×C11×Q16—21no—
24C2×C11×Q16—21no—
25C11×C4⋊Q8—21no—
26C2×Dic44—21no—
27C2×Dic44—21no—
28#66957D411yescharacteristic
29#66954—21no—
30#66922—21no—
31C11×M32—21no—
32C11×M32—21no—
33C4×C8×C11C2311yescharacteristic
34#66893—42no—
35#66893—41no—
36#66893—41no—
37#66893—41no—
38#66892—41no—
39#66883D411yescharacteristic
40#66876—21no—
41C2×C11⋊C16D411yescharacteristic
42C2×C11⋊C16D411yescharacteristic
43#66869—21no—
44Dic88—41no—
45#66864—41no—
46#66862—41no—
47C16×D11—41no—
48#12437—111nomaximal, Sylow
49C2×Q8×C11—41no—
50#4339—21no—
51C2×Dic22—41no—
52C11×Q16—41no—
53C11×Q16—41no—
54C11×Q16—41no—
55C11×Q16—41no—
56C2×C8×C11C2×D411yescharacteristic
57C2×C8×C11C2×D411yescharacteristic
58C11×C4⋊C4—81no—
59C42×C11#4111yescharacteristic
60C4⋊Dic11—81no—
61#4318—21no—
62Dic44—41no—
63Dic44—41no—
64Dic44—41no—
65Dic44—41no—
66Dic44D811yescharacteristic
67D88D811yescharacteristic
68#4314—21no—
69#4313—41no—
70C8×D11—41no—
71C11×C16—41no—
72C11×C16—41no—
73C11⋊C16—21no—
74C11⋊C16—41no—
75C11⋊C16D811yescharacteristic
76C11⋊C16D811yescharacteristic
77#2247—111no—
78#2214—111no—
79#2214—111no—
80#2170—111no—
81#1373—111no—
82#1358—111no—
83#1358D1111yescharacteristic, complemented
84Q8×C11—81no—
85Q8×C11—81no—
86C2×C4×C11—21no—
87C2×C4×C11—81no—
88C2×C4×C11#12111yescharacteristic
89C22⋊D11—41no—
90C2×Dic11—81no—
91D44—21no—
92C4×D11—41no—
93Dic22—21no—
94Dic22—81no—
95Dic22—81no—
96C8×C11C2×D811yescharacteristic
97C8×C11C2×D811yescharacteristic
98C8×C11#13511yescharacteristic
99C8×C11AGL(1,ℤ/8)11yescharacteristic
100C11⋊C8—41no—
101#510—221no—
102#510—221no—
103C2×Q32—221no—
104C2×Q32—221no—
105#504—221no—
106#494—111no—
107#494C2×D1111yescharacteristic
108#443—111no—
109#364—111no—
110#364C2×D1111yescharacteristic
111#364C2×D1111yescharacteristic
112#362—221no—
113#362—221no—
114#350—221no—
115C4×C16—111no—
116C22×C11#47211yescharacteristic
117C2×D11—41no—
118C4×C11—22no—
119C4×C11—161no—
120C4×C11#45911yescharacteristic
121C4×C11#46611yescharacteristic
122Dic11—41no—
123Dic11—161no—
124#135—111no—
125C2×Q16—21no—
126C2×Q16—21no—
127C2×Q16—221no—
128C2×Q16—221no—
129#131—221no—
130C4⋊Q8—21no—
131C4⋊Q8—221no—
132Q32—441no—
133Q32—441no—
134Q32—441no—
135Q32—442no—
136Q32—441no—
137SD32—441no—
138SD32—441no—
139M32—21no—
140M32—21no—
141M32—221no—
142M32—441no—
143C2×C16—111no—
144C2×C16—111no—
145C2×C16—441no—
146#108—111no—
147#104—221no—
148C4×C8C22×D1111yescharacteristic
149C2×C11—21no—
150C2×C11#166711yescharacteristic
151D11—81no—
152#41—221no—
153C2×Q8—41no—
154C2×Q8—441no—
155Q16—41no—
156Q16—41no—
157Q16—41no—
158Q16—41no—
159Q16—111no—
160Q16—441no—
161Q16—441no—
162Q16—441no—
163Q16—441no—
164SD16—221no—
165D8—111no—
166M16—221no—
167M16—441no—
168C2×C8—441no—
169C2×C8D4×D1111yescharacteristic
170C2×C8D4×D1111yescharacteristic
171C4⋊C4—81no—
172C4⋊C4—881no—
173C42#433911yescharacteristic
174C16—41no—
175C16—41no—
176C16—111no—
177C16—111no—
178C16—221no—
179C16—441no—
180C11#1243711yescharacteristic, complemented, Sylow
181Q8—81no—
182Q8—81no—
183Q8—221no—
184Q8—881no—
185Q8—881no—
186D4—221no—
187D4—441no—
188C2×C4—21no—
189C2×C4—81no—
190C2×C4—441no—
191C2×C4—881no—
192C2×C4#6693711yescharacteristic
193C8—441no—
194C8D8×D1111yescharacteristic
195C8D8×D1111yescharacteristic
196C8#6696711yescharacteristic
197C8#6696911yescharacteristic
198C22—441no—
199C22#1062236211yescharacteristic
200C4—22no—
201C4—161no—
202C4—441no—
203C4—1761no—
204C4#1062238811yescharacteristic
205C4#1062239911yescharacteristic
206C2—21no—
207C2—881no—
208C2#1306797011yescharacteristic
subgroupG/H
centerC2#13067970
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1358C2
socleC2×C11#1667
prime radical#66957D4
hypercenter#1358D11
hypocenterC11#12437
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1358

Complements

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

NH ≅ G/Ntype
1. #13070868C2semidirect
5. #13066691C2semidirect
6. #13066654C2semidirect
7. C11×#1358C2semidirect
83. #1358D11semidirect
180. C11#12437semidirect

Maximal subgroups

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

subgroupindex
#130708682
#130706982
#130706942
#130704522
#130666912
#130666542
C11×#13582
#1243711