Finite Group Databasebeta

← #14668015

Subgroups — #14668015

Order 2816.

214 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 59 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#13070694C212yesmaximal
2#13070454C211yesmaximal, characteristic
3#13066692C211yesmaximal, characteristic, complemented
4#13066655C212yesmaximal, complemented
5C11×#2247C211yesmaximal, characteristic, complemented
6C2×C11×Q32—21no—
7C2×C11×Q32—21no—
8C11×#494C2212yes—
9#10622792—22no—
10#10622514—21no—
11#10622313C2211yescharacteristic
12C4×C11×C16C2211yescharacteristic
13#10622203—22no—
14#10622146—21no—
15#10622101C2212yes—
16#10622101C2211yescharacteristic
17C2×C11×Q16—22no—
18C2×C11×Q16—22no—
19C11×C4⋊Q8—22no—
20#66957D411yescharacteristic
21#66954—21no—
22C11×Q32—42no—
23C11×Q32—41no—
24C11×Q32—41no—
25C2×C11×C16D411yescharacteristic
26C2×C11×C16D411yescharacteristic
27C4×C8×C11C2311yescharacteristic
28#66893—42no—
29#66892—42no—
30#66883D411yescharacteristic
31#66876—21no—
32#66876—22no—
33#66869—21no—
34#66862—41no—
35C16×D11—41no—
36#12437—111nomaximal, Sylow
37C2×Q8×C11—42no—
38#4339—21no—
39C11×Q16—42no—
40C11×Q16—42no—
41C11×Q16—42no—
42C11×Q16—42no—
43C2×C8×C11C2×D411yescharacteristic
44C2×C8×C11C2×D411yescharacteristic
45C11×C4⋊C4—82no—
46C42×C11#4111yescharacteristic
47#4318—21no—
48Dic44D811yescharacteristic
49D88D811yescharacteristic
50#4314—21no—
51#4313—41no—
52C8×D11—41no—
53C11×C16—21no—
54C11×C16D811yescharacteristic
55C11×C16D811yescharacteristic
56C11⋊C16—41no—
57C11⋊C16—42no—
58#2247D1111yescharacteristic, complemented
59#2214—112no—
60#2170—111no—
61#1373—111no—
62#1358—112no—
63Q8×C11—82no—
64Q8×C11—82no—
65C2×C4×C11—21no—
66C2×C4×C11—82no—
67C2×C4×C11#12111yescharacteristic
68C22⋊D11—41no—
69D44—21no—
70C4×D11—41no—
71Dic22—21no—
72C8×C11C2×D811yescharacteristic
73C8×C11C2×D811yescharacteristic
74C8×C11#13511yescharacteristic
75C8×C11AGL(1,ℤ/8)11yescharacteristic
76C11⋊C8—41no—
77#510—222no—
78C2×Q32—21no—
79C2×Q32—21no—
80#504—221no—
81#494C2×D1112yes—
82#443—111no—
83#364—111no—
84#364—112no—
85#362—222no—
86#350—221no—
87C4×C16C2×D1111yescharacteristic
88C22×C11#47211yescharacteristic
89C2×D11—41no—
90C4×C11—22no—
91C4×C11—162no—
92C4×C11#45911yescharacteristic
93C4×C11#46611yescharacteristic
94Dic11—41no—
95#135—111no—
96C2×Q16—22no—
97C2×Q16—22no—
98#131—221no—
99C4⋊Q8—22no—
100Q32—42no—
101Q32—41no—
102Q32—41no—
103Q32—442no—
104SD32—442no—
105M32—222no—
106M32—221no—
107M32—441no—
108C2×C16—441no—
109C2×C16C22⋊D1111yescharacteristic
110C2×C16C22⋊D1111yescharacteristic
111#108—111no—
112#104—221no—
113C4×C8C22×D1111yescharacteristic
114C2×C11—21no—
115C2×C11#166711yescharacteristic
116D11—81no—
117#41—221no—
118C2×Q8—42no—
119Q16—42no—
120Q16—42no—
121Q16—42no—
122Q16—42no—
123Q16—111no—
124SD16—221no—
125D8—111no—
126M16—221no—
127M16—441no—
128C2×C8—441no—
129C2×C8D4×D1111yescharacteristic
130C2×C8C2×C22⋊D1111yescharacteristic
131C4⋊C4—82no—
132C42#434111yescharacteristic
133C16—21no—
134C16—442no—
135C16—441no—
136C16#432311yescharacteristic
137C16#432311yescharacteristic
138C11#1243711yescharacteristic, complemented, Sylow
139Q8—82no—
140Q8—82no—
141Q8—221no—
142D4—221no—
143D4—441no—
144C2×C4—21no—
145C2×C4—82no—
146C2×C4—441no—
147C2×C4#6699111yescharacteristic
148C8—441no—
149C8D8×D1111yescharacteristic
150C8#6696511yescharacteristic
151C8C2×#432311yescharacteristic
152C8#6698511yescharacteristic
153C22—441no—
154C22#1062277311yescharacteristic
155C4—22no—
156C4—162no—
157C4—441no—
158C4#1062268511yescharacteristic
159C4#1062277011yescharacteristic
160C2—21no—
161C2—881no—
162C2#1306796811yescharacteristic
subgroupG/H
centerC2#13067968
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2247C2
socleC2×C11#1667
prime radical#66957D4
hypercenter#2247D11
hypocenterC11#12437
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2247

Complements

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

NH ≅ G/Ntype
3. #13066692C2semidirect
4. #13066655C2semidirect
5. C11×#2247C2semidirect
58. #2247D11semidirect
138. C11#12437semidirect

Maximal subgroups

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

subgroupindex
#130706942
#130704542
#130666922
#130666552
C11×#22472
#1243711