Finite Group Databasebeta

← #14668012

Subgroups — #14668012

Order 2816.

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

normal subgroups only

This group has 234 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#13070865C211yesmaximal, characteristic, complemented
2#13070693C211yesmaximal, characteristic, complemented
3#13070689C211yesmaximal, characteristic, complemented
4#13070452C211yesmaximal, characteristic, complemented
5#13066691C211yesmaximal, characteristic, complemented
6#13066652C211yesmaximal, characteristic, complemented
7C11×#1357C211yesmaximal, characteristic, complemented
8C11×#493C2211yescharacteristic
9#10622760—21no—
10C2×#66890—21no—
11C2×#66890—21no—
12#10622521—21no—
13#10622520—21no—
14#10622313C2211yescharacteristic
15#10622308C2211yescharacteristic
16C11×#364C2211yescharacteristic
17C11×#364C2211yescharacteristic
18#10622201—21no—
19#10622154—21no—
20#10622153—21no—
21#10622101C2211yescharacteristic
22C4×C11⋊C16C2211yescharacteristic
23C2×C11×D8—21no—
24C2×C11×D8—21no—
25C11×#127—21no—
26#66957D411yescharacteristic
27C2×D88—21no—
28C2×D88—21no—
29#66954—21no—
30#66927—21no—
31C11×M32—21no—
32C11×M32—21no—
33C4×C8×C11C2311yescharacteristic
34#66891—41no—
35#66890—42no—
36#66890—41no—
37#66890—41no—
38#66890—41no—
39#66883D411yescharacteristic
40#66876—21no—
41C2×C11⋊C16D411yescharacteristic
42C2×C11⋊C16D411yescharacteristic
43#66869—21no—
44#66864—41no—
45D176—41no—
46#66862—41no—
47C16×D11—41no—
48#12436—111nomaximal, Sylow
49C2×D4×C11—41no—
50C2×D4×C11—81no—
51#4339—21no—
52C2×D44—41no—
53C2×D44—81no—
54C11×D8—41no—
55C11×D8—41no—
56C11×D8—41no—
57C11×D8—41no—
58C2×C8×C11C2×D411yescharacteristic
59C2×C8×C11C2×D411yescharacteristic
60C42×C11#4111yescharacteristic
61#4318—21no—
62Dic44D811yescharacteristic
63D88—41no—
64D88—41no—
65D88—41no—
66D88—41no—
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#2246—111no—
78#2213—111no—
79#2213—111no—
80#2170—111no—
81#1373—111no—
82#1357—111no—
83#1357D1111yescharacteristic, complemented
84C23×C11—81no—
85C22×D11—81no—
86D4×C11—81no—
87D4×C11—81no—
88D4×C11—162no—
89C2×C4×C11—21no—
90C2×C4×C11#12111yescharacteristic
91C22⋊D11—41no—
92D44—21no—
93D44—81no—
94D44—81no—
95D44—162no—
96C4×D11—41no—
97Dic22—21no—
98C8×C11C2×D811yescharacteristic
99C8×C11C2×D811yescharacteristic
100C8×C11#13511yescharacteristic
101C8×C11AGL(1,ℤ/8)11yescharacteristic
102C11⋊C8—41no—
103#509—221no—
104#509—221no—
105C2×D16—221no—
106C2×D16—221no—
107#504—221no—
108#493—111no—
109#493C2×D1111yescharacteristic
110#443—111no—
111#364—111no—
112#364C2×D1111yescharacteristic
113#364C2×D1111yescharacteristic
114#361—221no—
115#361—221no—
116#350—221no—
117C4×C16—111no—
118C22×C11—162no—
119C22×C11—161no—
120C22×C11#47211yescharacteristic
121C2×D11—41no—
122C2×D11—162no—
123C2×D11—161no—
124C4×C11—22no—
125C4×C11#45911yescharacteristic
126C4×C11#46611yescharacteristic
127Dic11—41no—
128#135—111no—
129C2×D8—21no—
130C2×D8—21no—
131C2×D8—221no—
132C2×D8—221no—
133#131—221no—
134#127—21no—
135#127—221no—
136SD32—441no—
137SD32—441no—
138D16—441no—
139D16—441no—
140D16—441no—
141D16—442no—
142D16—441no—
143M32—21no—
144M32—21no—
145M32—221no—
146M32—441no—
147C2×C16—111no—
148C2×C16—111no—
149C2×C16—441no—
150#108—111no—
151#104—221no—
152C4×C8C22×D1111yescharacteristic
153C2×C11—21no—
154C2×C11—321no—
155C2×C11#166711yescharacteristic
156D11—81no—
157D11—321no—
158#41—221no—
159C2×D4—41no—
160C2×D4—81no—
161C2×D4—441no—
162C2×D4—881no—
163Q16—111no—
164SD16—221no—
165D8—41no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—111no—
170D8—441no—
171D8—441no—
172D8—441no—
173D8—441no—
174M16—221no—
175M16—441no—
176C2×C8—441no—
177C2×C8D4×D1111yescharacteristic
178C2×C8D4×D1111yescharacteristic
179C42#433911yescharacteristic
180C16—41no—
181C16—41no—
182C16—111no—
183C16—111no—
184C16—221no—
185C16—441no—
186C11#1243611yescharacteristic, complemented, Sylow
187C23—81no—
188C23—881no—
189Q8—221no—
190D4—81no—
191D4—81no—
192D4—162no—
193D4—221no—
194D4—441no—
195D4—881no—
196D4—881no—
197D4—1762no—
198C2×C4—21no—
199C2×C4—441no—
200C2×C4#6693711yescharacteristic
201C8—441no—
202C8D8×D1111yescharacteristic
203C8D8×D1111yescharacteristic
204C8#6696711yescharacteristic
205C8#6696911yescharacteristic
206C22—162no—
207C22—161no—
208C22—441no—
209C22—1762no—
210C22—1761no—
211C22#1062236211yescharacteristic
212C4—22no—
213C4—441no—
214C4#1062238811yescharacteristic
215C4#1062239911yescharacteristic
216C2—21no—
217C2—321no—
218C2—881no—
219C2—3521no—
220C2#1306797011yescharacteristic
subgroupG/H
centerC2#13067970
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1357C2
socleC2×C11#1667
hypercenter#1357D11
hypocenterC11#12436
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1357

Complements

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

NH ≅ G/Ntype
1. #13070865C2semidirect
2. #13070693C2semidirect
3. #13070689C2semidirect
4. #13070452C2semidirect
5. #13066691C2semidirect
6. #13066652C2semidirect
7. C11×#1357C2semidirect
83. #1357D11semidirect
186. C11#12436semidirect

Maximal subgroups

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

subgroupindex
#130708652
#130706932
#130706892
#130704522
#130666912
#130666522
C11×#13572
#1243611