Finite Group Databasebeta

← #14668180

Subgroups — #14668180

Order 2816.

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

normal subgroups only

This group has 186 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#13070789C211yesmaximal, characteristic
2#13070694C211yesmaximal, characteristic
3#13070459C211yesmaximal, characteristic
4#13066684C211yesmaximal, characteristic, complemented
5#13066677C211yesmaximal, characteristic, complemented
6#13066655C211yesmaximal, characteristic, complemented
7C11×#2245C211yesmaximal, characteristic, complemented
8C11×#499C2211yescharacteristic
9C11×#494C2211yescharacteristic
10#10622792—21no—
11#10622514—21no—
12#10622313C2211yescharacteristic
13C11×#358—21no—
14C11×#358—21no—
15C11×#346C2211yescharacteristic
16#10622203—21no—
17#10622146—21no—
18#10622126—21no—
19#10622125—21no—
20#10622101C2211yescharacteristic
21#10622101C2211yescharacteristic
22#10622101C2211yescharacteristic
23C2×C11×Q16—21no—
24C2×C11×Q16—21no—
25C11×C4⋊Q8—21no—
26C11×#125—21no—
27#66957D411yescharacteristic
28#66954—21no—
29C2×C11×C16D411yescharacteristic
30C2×C11×C16D411yescharacteristic
31C11×#107—21no—
32C11×#106—21no—
33C4×C8×C11C2311yescharacteristic
34#66893—41no—
35#66892—41no—
36#66883D411yescharacteristic
37#66876—21no—
38#66876—21no—
39#66876—21no—
40#66869—21no—
41#66862—41no—
42C16×D11—41no—
43#12466—111nomaximal, Sylow
44C2×Q8×C11—41no—
45#4339—21no—
46C11×Q16—41no—
47C11×Q16—41no—
48C11×Q16—41no—
49C11×Q16—41no—
50C2×C8×C11C2×D411yescharacteristic
51C2×C8×C11C2×D411yescharacteristic
52C11×C4⋊C4—41no—
53C11×C4⋊C4—81no—
54C11×C4⋊C4—81no—
55C42×C11#4111yescharacteristic
56#4318—21no—
57Dic44SD1611yescharacteristic
58D88SD1611yescharacteristic
59#4314—21no—
60#4313—41no—
61C8×D11—41no—
62C11×C16—21no—
63C11×C16—21no—
64C11⋊C16—41no—
65C11⋊C16—41no—
66C11⋊C16—41no—
67#2245D1111yescharacteristic, complemented
68#2231—111no—
69#2214—111no—
70#2171—111no—
71#1369—111no—
72#1366—111no—
73#1358—111no—
74Q8×C11—81no—
75Q8×C11—81no—
76C2×C4×C11—21no—
77C2×C4×C11—81no—
78C2×C4×C11—81no—
79C2×C4×C11#12111yescharacteristic
80C22⋊D11—41no—
81D44—21no—
82C4×D11—41no—
83Dic22—21no—
84C8×C11C2×SD1611yescharacteristic
85C8×C11#13511yescharacteristic
86C8×C11#13511yescharacteristic
87C8×C11AGL(1,ℤ/8)11yescharacteristic
88C11⋊C8—41no—
89#510—221no—
90#504—221no—
91#499C2×D1111yescharacteristic
92#494C2×D1111yescharacteristic
93#443—111no—
94#365—221no—
95#364—111no—
96#364—111no—
97#364—111no—
98#362—221no—
99#360—221no—
100#358—21no—
101#358—21no—
102#350—221no—
103#346C2×D1111yescharacteristic
104C22×C11#47211yescharacteristic
105C2×D11—41no—
106C4×C11—41no—
107C4×C11—161no—
108C4×C11—161no—
109C4×C11#46311yescharacteristic
110C4×C11#46511yescharacteristic
111Dic11—41no—
112#135—111no—
113C2×Q16—21no—
114C2×Q16—21no—
115#131—221no—
116C4⋊Q8—21no—
117#125—21no—
118Q32—441no—
119SD32—441no—
120M32—221no—
121M32—221no—
122M32—221no—
123M32—441no—
124C2×C16—441no—
125C2×C16C22⋊D1111yescharacteristic
126C2×C16C22⋊D1111yescharacteristic
127#108—111no—
128#107—21no—
129#106—21no—
130#104—221no—
131C4×C8C22×D1111yescharacteristic
132C2×C11—21no—
133C2×C11#167711yescharacteristic
134D11—81no—
135#41—221no—
136C2×Q8—41no—
137Q16—41no—
138Q16—41no—
139Q16—41no—
140Q16—41no—
141Q16—111no—
142SD16—221no—
143D8—111no—
144M16—221no—
145M16—441no—
146C2×C8—441no—
147C2×C8D4×D1111yescharacteristic
148C2×C8C2×C22⋊D1111yescharacteristic
149C4⋊C4—41no—
150C4⋊C4—81no—
151C4⋊C4—81no—
152C42#434111yescharacteristic
153C16—21no—
154C16—21no—
155C16—441no—
156C16—441no—
157C16—441no—
158C11#1246611yescharacteristic, complemented, Sylow
159Q8—81no—
160Q8—81no—
161Q8—221no—
162D4—221no—
163D4—441no—
164C2×C4—21no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—441no—
168C2×C4#6699111yescharacteristic
169C8—441no—
170C8SD16×D1111yescharacteristic
171C8#6696911yescharacteristic
172C8#6700211yescharacteristic
173C8#6700311yescharacteristic
174C22—441no—
175C22#1062277311yescharacteristic
176C4—41no—
177C4—161no—
178C4—161no—
179C4—441no—
180C4#1062267011yescharacteristic
181C4#1062278411yescharacteristic
182C2—21no—
183C2—881no—
184C2#1306802211yescharacteristic
subgroupG/H
centerC2#13068022
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2245C2
socleC2×C11#1677
prime radical#66957D4
hypercenter#2245D11
hypocenterC11#12466
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2245

Complements

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

NH ≅ G/Ntype
4. #13066684C2semidirect
5. #13066677C2semidirect
6. #13066655C2semidirect
7. C11×#2245C2semidirect
67. #2245D11semidirect
158. C11#12466semidirect

Maximal subgroups

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

subgroupindex
#130707892
#130706942
#130704592
#130666842
#130666772
#130666552
C11×#22452
#1246611