Finite Group Databasebeta

← #14668173

Subgroups — #14668173

Order 2816.

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

normal subgroups only

This group has 196 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, complemented
2#13070689C211yesmaximal, characteristic
3#13070459C211yesmaximal, characteristic, complemented
4#13066684C211yesmaximal, characteristic, complemented
5#13066677C211yesmaximal, characteristic, complemented
6#13066653C211yesmaximal, characteristic, complemented
7C11×#2244C211yesmaximal, characteristic, complemented
8C11×#499C2211yescharacteristic
9C11×#493C2211yescharacteristic
10#10622760—21no—
11#10622514—21no—
12#10622313C2211yescharacteristic
13C11×#357—21no—
14C11×#357—21no—
15C11×#346C2211yescharacteristic
16#10622201—21no—
17#10622146—21no—
18#10622126—21no—
19#10622125—21no—
20#10622101C2211yescharacteristic
21#10622101C2211yescharacteristic
22#10622101C2211yescharacteristic
23C2×C11×D8—21no—
24C2×C11×D8—21no—
25C11×#127—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#66891—41no—
35#66890—41no—
36#66883D411yescharacteristic
37#66876—21no—
38#66876—21no—
39#66876—21no—
40#66869—21no—
41#66862—41no—
42C16×D11—41no—
43#12465—111nomaximal, Sylow
44C2×D4×C11—41no—
45C2×D4×C11—81no—
46#4339—21no—
47C11×D8—41no—
48C11×D8—41no—
49C11×D8—41no—
50C11×D8—41no—
51C2×C8×C11C2×D411yescharacteristic
52C2×C8×C11C2×D411yescharacteristic
53C11×C4⋊C4—41no—
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#2244D1111yescharacteristic, complemented
68#2231—111no—
69#2213—111no—
70#2171—111no—
71#1369—111no—
72#1366—111no—
73#1357—111no—
74C23×C11—81no—
75D4×C11—81no—
76D4×C11—81no—
77D4×C11—162no—
78C2×C4×C11—21no—
79C2×C4×C11—81no—
80C2×C4×C11#12111yescharacteristic
81C22⋊D11—41no—
82D44—21no—
83C4×D11—41no—
84Dic22—21no—
85C8×C11C2×SD1611yescharacteristic
86C8×C11#13511yescharacteristic
87C8×C11#13511yescharacteristic
88C8×C11AGL(1,ℤ/8)11yescharacteristic
89C11⋊C8—41no—
90#509—221no—
91#504—221no—
92#499C2×D1111yescharacteristic
93#493C2×D1111yescharacteristic
94#443—111no—
95#365—221no—
96#364—111no—
97#364—111no—
98#364—111no—
99#361—221no—
100#360—221no—
101#357—21no—
102#357—21no—
103#350—221no—
104#346C2×D1111yescharacteristic
105C22×C11—162no—
106C22×C11—161no—
107C22×C11#47211yescharacteristic
108C2×D11—41no—
109C4×C11—41no—
110C4×C11—161no—
111C4×C11#46311yescharacteristic
112C4×C11#46511yescharacteristic
113Dic11—41no—
114#135—111no—
115C2×D8—21no—
116C2×D8—21no—
117#131—221no—
118#127—21no—
119#125—21no—
120SD32—441no—
121D16—441no—
122M32—221no—
123M32—221no—
124M32—221no—
125M32—441no—
126C2×C16—441no—
127C2×C16C22⋊D1111yescharacteristic
128C2×C16C22⋊D1111yescharacteristic
129#108—111no—
130#107—21no—
131#106—21no—
132#104—221no—
133C4×C8C22×D1111yescharacteristic
134C2×C11—21no—
135C2×C11—321no—
136C2×C11#167711yescharacteristic
137D11—81no—
138#41—221no—
139C2×D4—41no—
140C2×D4—81no—
141Q16—111no—
142SD16—221no—
143D8—41no—
144D8—41no—
145D8—41no—
146D8—41no—
147D8—111no—
148M16—221no—
149M16—441no—
150C2×C8—441no—
151C2×C8D4×D1111yescharacteristic
152C2×C8C2×C22⋊D1111yescharacteristic
153C4⋊C4—41no—
154C4⋊C4—81no—
155C42#434111yescharacteristic
156C16—21no—
157C16—21no—
158C16—441no—
159C16—441no—
160C16—441no—
161C11#1246511yescharacteristic, complemented, Sylow
162C23—81no—
163Q8—221no—
164D4—81no—
165D4—81no—
166D4—162no—
167D4—221no—
168D4—441no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—441no—
172C2×C4#6699111yescharacteristic
173C8—441no—
174C8SD16×D1111yescharacteristic
175C8#6696911yescharacteristic
176C8#6700211yescharacteristic
177C8#6700311yescharacteristic
178C22—162no—
179C22—161no—
180C22—441no—
181C22#1062277311yescharacteristic
182C4—41no—
183C4—161no—
184C4—441no—
185C4#1062267011yescharacteristic
186C4#1062278411yescharacteristic
187C2—21no—
188C2—321no—
189C2—881no—
190C2#1306802211yescharacteristic
subgroupG/H
centerC2#13068022
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2244C2
socleC2×C11#1677
prime radical#13070689C2
hypercenter#2244D11
hypocenterC11#12465
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2244

Complements

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

NH ≅ G/Ntype
1. #13070789C2semidirect
3. #13070459C2semidirect
4. #13066684C2semidirect
5. #13066677C2semidirect
6. #13066653C2semidirect
7. C11×#2244C2semidirect
67. #2244D11semidirect
161. C11#12465semidirect

Maximal subgroups

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

subgroupindex
#130707892
#130706892
#130704592
#130666842
#130666772
#130666532
C11×#22442
#1246511