Finite Group Databasebeta

← #14668010

Subgroups — #14668010

Order 2816.

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

normal subgroups only

This group has 234 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#13070689C212yesmaximal, complemented
2#13070454C211yesmaximal, characteristic, complemented
3#13066692C211yesmaximal, characteristic, complemented
4#13066653C212yesmaximal, complemented
5C11×#2246C211yesmaximal, characteristic, complemented
6C2×C11×D16—21no—
7C2×C11×D16—21no—
8C11×#493C2212yes—
9#10622760—22no—
10#10622514—21no—
11#10622313C2211yescharacteristic
12C4×C11×C16C2211yescharacteristic
13#10622201—22no—
14#10622146—21no—
15#10622101C2212yes—
16#10622101C2211yescharacteristic
17C2×C11×D8—22no—
18C2×C11×D8—22no—
19C11×#127—22no—
20#66957D411yescharacteristic
21#66954—21no—
22C11×D16—42no—
23C11×D16—41no—
24C11×D16—41no—
25C2×C11×C16D411yescharacteristic
26C2×C11×C16D411yescharacteristic
27C4×C8×C11C2311yescharacteristic
28#66891—42no—
29#66890—42no—
30#66883D411yescharacteristic
31#66876—22no—
32#66876—21no—
33#66869—21no—
34#66862—41no—
35C16×D11—41no—
36#12436—111nomaximal, Sylow
37C2×D4×C11—42no—
38C2×D4×C11—82no—
39#4339—21no—
40C11×D8—42no—
41C11×D8—42no—
42C11×D8—42no—
43C11×D8—42no—
44C2×C8×C11C2×D411yescharacteristic
45C2×C8×C11C2×D411yescharacteristic
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#2246D1111yescharacteristic, complemented
59#2213—112no—
60#2170—111no—
61#1373—111no—
62#1357—112no—
63C23×C11—82no—
64D4×C11—82no—
65D4×C11—82no—
66D4×C11—164no—
67C2×C4×C11—21no—
68C2×C4×C11#12111yescharacteristic
69C22⋊D11—41no—
70D44—21no—
71C4×D11—41no—
72Dic22—21no—
73C8×C11C2×D811yescharacteristic
74C8×C11C2×D811yescharacteristic
75C8×C11#13511yescharacteristic
76C8×C11AGL(1,ℤ/8)11yescharacteristic
77C11⋊C8—41no—
78#509—222no—
79C2×D16—21no—
80C2×D16—21no—
81#504—221no—
82#493C2×D1112yes—
83#443—111no—
84#364—111no—
85#364—112no—
86#361—222no—
87#350—221no—
88C4×C16C2×D1111yescharacteristic
89C22×C11—164no—
90C22×C11—162no—
91C22×C11#47211yescharacteristic
92C2×D11—41no—
93C4×C11—22no—
94C4×C11#45911yescharacteristic
95C4×C11#46611yescharacteristic
96Dic11—41no—
97#135—111no—
98C2×D8—22no—
99C2×D8—22no—
100#131—221no—
101#127—22no—
102SD32—442no—
103D16—42no—
104D16—41no—
105D16—41no—
106D16—442no—
107M32—222no—
108M32—221no—
109M32—441no—
110C2×C16—441no—
111C2×C16C22⋊D1111yescharacteristic
112C2×C16C22⋊D1111yescharacteristic
113#108—111no—
114#104—221no—
115C4×C8C22×D1111yescharacteristic
116C2×C11—21no—
117C2×C11—322no—
118C2×C11#166711yescharacteristic
119D11—81no—
120#41—221no—
121C2×D4—42no—
122C2×D4—82no—
123Q16—111no—
124SD16—221no—
125D8—42no—
126D8—42no—
127D8—42no—
128D8—42no—
129D8—111no—
130M16—221no—
131M16—441no—
132C2×C8—441no—
133C2×C8D4×D1111yescharacteristic
134C2×C8C2×C22⋊D1111yescharacteristic
135C42#434111yescharacteristic
136C16—21no—
137C16—442no—
138C16—441no—
139C16#432311yescharacteristic
140C16#432311yescharacteristic
141C11#1243611yescharacteristic, complemented, Sylow
142C23—82no—
143Q8—221no—
144D4—82no—
145D4—82no—
146D4—164no—
147D4—221no—
148D4—441no—
149C2×C4—21no—
150C2×C4—441no—
151C2×C4#6699111yescharacteristic
152C8—441no—
153C8D8×D1111yescharacteristic
154C8#6696511yescharacteristic
155C8C2×#432311yescharacteristic
156C8#6698511yescharacteristic
157C22—164no—
158C22—162no—
159C22—441no—
160C22#1062277311yescharacteristic
161C4—22no—
162C4—441no—
163C4#1062268511yescharacteristic
164C4#1062277011yescharacteristic
165C2—21no—
166C2—322no—
167C2—881no—
168C2#1306796811yescharacteristic
subgroupG/H
centerC2#13067968
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2246C2
socleC2×C11#1667
hypercenter#2246D11
hypocenterC11#12436
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2246

Complements

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

NH ≅ G/Ntype
1. #13070689C2semidirect
2. #13070454C2semidirect
3. #13066692C2semidirect
4. #13066653C2semidirect
5. C11×#2246C2semidirect
58. #2246D11semidirect
141. C11#12436semidirect

Maximal subgroups

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

subgroupindex
#130706892
#130704542
#130666922
#130666532
C11×#22462
#1243611