Finite Group Databasebeta

← #14668181

Subgroups — #14668181

Order 2816.

186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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#13070861C211yesmaximal, characteristic, complemented
2#13070792C211yesmaximal, characteristic
3#13070458C211yesmaximal, characteristic
4#13066683C211yesmaximal, characteristic, complemented
5#13066676C211yesmaximal, characteristic, complemented
6#13066655C211yesmaximal, characteristic, complemented
7C11×#2214C211yesmaximal, characteristic
8C11×#510—21no—
9C11×#494C2211yescharacteristic
10C11×#443C2211yescharacteristic
11#10622753—21no—
12#10622296C2211yescharacteristic
13C11×#364C2211yescharacteristic
14C11×#362—21no—
15#10622204—21no—
16#10622202—21no—
17#10622202—21no—
18#10622199—21no—
19#10622132—21no—
20#10622101C2211yescharacteristic
21#10622101C2211yescharacteristic
22#10622099C2211yescharacteristic
23C11×#135D411yescharacteristic
24C2×C11×Q16—21no—
25C2×C11×Q16—21no—
26C11×#131—21no—
27C11×C4⋊Q8—21no—
28#66923—21no—
29C11×Q32—41no—
30C11×SD32—41no—
31C11×M32—21no—
32C11×#108D411yescharacteristic
33C11×#104—21no—
34C4×C8×C11C2311yescharacteristic
35#66882—21no—
36#66881—21no—
37#66876—21no—
38#66876—21no—
39#66876—41no—
40C2×C11⋊C16—41no—
41C2×C11⋊C16D411yescharacteristic
42C2×C11⋊C16D411yescharacteristic
43#12466—111nomaximal, Sylow
44C11×#41—21no—
45C2×Q8×C11—41no—
46C11×Q16—41no—
47C11×Q16—41no—
48C11×Q16—41no—
49C11×Q16—41no—
50C11×Q16SD1611yescharacteristic
51C11×SD16—21no—
52C11×D8SD1611yescharacteristic
53C11×M16—21no—
54C11×M16—41no—
55C2×C8×C11—41no—
56C2×C8×C11C2×D411yescharacteristic
57C2×C8×C11C2×D411yescharacteristic
58C11×C4⋊C4—81no—
59C42×C11#4111yescharacteristic
60C4⋊Dic11—41no—
61Dic11⋊C4—81no—
62C11×C16—41no—
63C11⋊C16—21no—
64C11⋊C16—21no—
65C11⋊C16—41no—
66C11⋊C16—41no—
67#2245—111no—
68#2231—111no—
69#2214D1111yescharacteristic
70#2171—111no—
71#1369—111no—
72#1366—111no—
73#1358—111no—
74Q8×C11—21no—
75Q8×C11—81no—
76Q8×C11—81no—
77D4×C11—21no—
78D4×C11—41no—
79C2×C4×C11—21no—
80C2×C4×C11—41no—
81C2×C4×C11—81no—
82C2×C4×C11#12111yescharacteristic
83C2×Dic11—81no—
84C8×C11—41no—
85C8×C11C2×SD1611yescharacteristic
86C8×C11#13511yescharacteristic
87C8×C11#13511yescharacteristic
88C8×C11AGL(1,ℤ/8)11yescharacteristic
89#510—21no—
90#504—221no—
91#499—111no—
92#494C2×D1111yescharacteristic
93#443C2×D1111yescharacteristic
94#365—221no—
95#364—111no—
96#364—111no—
97#364C2×D1111yescharacteristic
98#362—21no—
99#360—221no—
100#358—221no—
101#358—221no—
102#350—221no—
103#346—111no—
104C22×C11—41no—
105C22×C11#47211yescharacteristic
106C4×C11—41no—
107C4×C11—41no—
108C4×C11—161no—
109C4×C11#46311yescharacteristic
110C4×C11#46511yescharacteristic
111Dic11—161no—
112#135C22⋊D1111yescharacteristic
113C2×Q16—21no—
114C2×Q16—21no—
115#131—21no—
116C4⋊Q8—21no—
117#125—221no—
118Q32—41no—
119SD32—41no—
120M32—21no—
121M32—221no—
122M32—221no—
123M32—441no—
124C2×C16—111no—
125C2×C16—111no—
126C2×C16—441no—
127#108C22⋊D1111yescharacteristic
128#107—221no—
129#106—221no—
130#104—21no—
131C4×C8C22×D1111yescharacteristic
132C2×C11—21no—
133C2×C11—81no—
134C2×C11#167711yescharacteristic
135#41—21no—
136C2×Q8—41no—
137Q16—41no—
138Q16—41no—
139Q16—41no—
140Q16—41no—
141Q16#432411yescharacteristic
142SD16—21no—
143D8#432411yescharacteristic
144M16—21no—
145M16—41no—
146C2×C8—41no—
147C2×C8D4×D1111yescharacteristic
148C2×C8C2×C22⋊D1111yescharacteristic
149C4⋊C4—81no—
150C4⋊C4—441no—
151C4⋊C4—881no—
152C42#434111yescharacteristic
153C16—41no—
154C16—221no—
155C16—221no—
156C16—441no—
157C16—441no—
158C11#1246611yescharacteristic, complemented, Sylow
159Q8—21no—
160Q8—81no—
161Q8—81no—
162D4—21no—
163D4—41no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—81no—
167C2×C4—881no—
168C2×C4#6699211yescharacteristic
169C8—41no—
170C8#6696411yescharacteristic
171C8#6696511yescharacteristic
172C8C2×#432411yescharacteristic
173C8#6700311yescharacteristic
174C22—41no—
175C22#1062281211yescharacteristic
176C4—41no—
177C4—41no—
178C4—161no—
179C4—1761no—
180C4#1062265411yescharacteristic
181C4#1062276611yescharacteristic
182C2—21no—
183C2—81no—
184C2#1306802311yescharacteristic
subgroupG/H
centerC2#13068023
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2214C2
socleC2×C11#1677
prime radicalC11×#135D4
hypercenter#2214D11
hypocenterC11#12466
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2214

Complements

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

NH ≅ G/Ntype
1. #13070861C2semidirect
4. #13066683C2semidirect
5. #13066676C2semidirect
6. #13066655C2semidirect
158. C11#12466semidirect

Maximal subgroups

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

subgroupindex
#130708612
#130707922
#130704582
#130666832
#130666762
#130666552
C11×#22142
#1246611