Finite Group Databasebeta

← #14653209

Subgroups — #14653209

Order 2816.

414 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 159 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#13068788C211yesmaximal, characteristic
2#13067301C212yesmaximal
3#13067297C212yesmaximal
4#13066899C211yesmaximal, characteristic
5C2×C11×#498C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2212yes—
7C11×#498—21no—
8C11×#498—21no—
9C11×#498C414yes—
10C2×C11×#106—22no—
11C2×C4×C8×C11C2211yescharacteristic
12C2×#66883—22no—
13#10622538C2212yes—
14#10622537C2211yescharacteristic
15#10622537C2211yescharacteristic
16#10622185—24no—
17#10622184—24no—
18#10622093—21no—
19C8×C11⋊C8—21no—
20C22×Q8×C11—22no—
21C22×C8×C11D412yes—
22C11×C4⋊Q8—22no—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8C2×C414yes—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C42×C11C2311yescharacteristic
29C2×#4318—21no—
30C2×#4318—21no—
31C11×#106—24no—
32C11×#106—24no—
33C4×C8×C11C2×C412yes—
34C4×C8×C11D411yescharacteristic
35C4×C8×C11D411yescharacteristic
36C22⋊(C11⋊C8)—22no—
37#66883—44no—
38C4⋊(C11⋊C8)—22no—
39C4⋊(C11⋊C8)—22no—
40C4⋊(C11⋊C8)D414yes—
41C4×C11⋊C8—22no—
42#9767—111nomaximal, Sylow
43C2×Q8×C11—24no—
44C2×Q8×C11—42no—
45C2×Q8×C11—84no—
46C22×C4×C11—42no—
47C22×C4×C11C2×D411yescharacteristic
48C22×C4×C11#4112yes—
49C2×C8×C11C22⋊C412yes—
50C2×C8×C11C22⋊C412yes—
51C2×C8×C11SD1614yes—
52C2×C8×C11Q1614yes—
53C11×C4⋊C4—24no—
54C11×C4⋊C4—24no—
55C11×C4⋊C4—42no—
56C11×C4⋊C4—42no—
57C42×C11C22×C411yescharacteristic
58C42×C11C2×D411yescharacteristic
59C42×C11C2×D412yes—
60#4318—42no—
61#4318—42no—
62C2×C11⋊C8—24no—
63C2×C11⋊C8—41no—
64C2×C11⋊C8—41no—
65C2×#498D1111yescharacteristic
66#1848—111no—
67#1549—112no—
68#1548—112no—
69#1450—111no—
70C23×C11#12411yescharacteristic
71Q8×C11—84no—
72Q8×C11—84no—
73C2×C4×C11—24no—
74C2×C4×C11—44no—
75C2×C4×C11—84no—
76C2×C4×C11C2×C22⋊C411yescharacteristic
77C2×C4×C11C4×D412yes—
78C2×C4×C11#12112yes—
79C2×C4×C11#12711yescharacteristic
80C2×C4×C11C2×SD1612yes—
81C2×C4×C11C2×Q1612yes—
82C8×C11#10314yes—
83C8×C11#10314yes—
84C11⋊C8—44no—
85C11⋊C8—81no—
86C11⋊C8—81no—
87C2×C4⋊Q8C2×D1112yes—
88#498—21no—
89#498—21no—
90#498Dic1114yes—
91#431—112no—
92C2×#108—222no—
93C2×#106—22no—
94#423—111no—
95#423—111no—
96C2×C4×C8C2×D1111yescharacteristic
97#333—224no—
98#332—224no—
99#322—221no—
100C82—221no—
101C22×C11—22no—
102C22×C11#39011yescharacteristic
103C22×C11#48712yes—
104C4×C11—22no—
105C4×C11—84no—
106C4×C11C2×#10312yes—
107C4×C11#47114yes—
108C4×C11#49211yescharacteristic
109C4×C11#49411yescharacteristic
110C22×Q8—22no—
111C2×M16—221no—
112C2×M16—221no—
113C22×C8C22⋊D1112yes—
114C4⋊Q8—22no—
115C4⋊Q8—22no—
116C4⋊Q8—22no—
117C4⋊Q8C2×Dic1114yes—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—22no—
120C2×C42C22×D1111yescharacteristic
121#108—444no—
122#106—24no—
123#106—24no—
124C4⋊C8—114no—
125C4⋊C8—222no—
126C4⋊C8—222no—
127C22⋊C8—222no—
128C4×C8—222no—
129C4×C8C2×Dic1112yes—
130C4×C8C22⋊D1111yescharacteristic
131C4×C8C22⋊D1111yescharacteristic
132C2×C11—22no—
133C2×C11#195611yescharacteristic
134C2×C11#197712yes—
135C2×Q8—24no—
136C2×Q8—42no—
137C2×Q8—84no—
138C22×C4—42no—
139C22×C4#434112yes—
140C22×C4C2×C22⋊D1111yescharacteristic
141M16—442no—
142M16—442no—
143C2×C8—224no—
144C2×C8—441no—
145C2×C8—441no—
146C2×C8#432514yes—
147C2×C8#432614yes—
148C2×C8C22⋊Dic1112yes—
149C2×C8C22⋊Dic1112yes—
150C4⋊C4—24no—
151C4⋊C4—24no—
152C4⋊C4—42no—
153C4⋊C4—42no—
154C42D4×D1112yes—
155C42C22×Dic1111yescharacteristic
156C42C2×C22⋊D1111yescharacteristic
157C11#976711yescharacteristic, complemented, Sylow
158C23#6698911yescharacteristic
159Q8—84no—
160Q8—84no—
161C2×C4—24no—
162C2×C4—44no—
163C2×C4—84no—
164C2×C4D4×Dic1112yes—
165C2×C4#6699112yes—
166C2×C4#6699311yescharacteristic
167C2×C4C2×#432512yes—
168C2×C4C2×#432612yes—
169C2×C4C2×C22⋊Dic1111yescharacteristic
170C8—444no—
171C8—881no—
172C8—881no—
173C8#6689914yes—
174C8#6689914yes—
175C22—22no—
176C22#1062269412yes—
177C22#1062283411yescharacteristic
178C4—22no—
179C4—84no—
180C4#1062269811yescharacteristic
181C4#1062270511yescharacteristic
182C4#1062279014yes—
183C4C2×#6689912yes—
184C2—22no—
185C2#1306941911yescharacteristic
186C2#1306952112yes—
subgroupG/H
centerC22#10622834
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#498C2
socleC22×C11#390
prime radicalC23×C11#124
cosocleC2×C42×C11C23
hypercenterC2×#498D11
hypocenterC11#9767
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
157. C11#9767semidirect

Maximal subgroups

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

subgroupindex
#130687882
#130673012
#130672972
#130668992
C2×C11×#4982
#976711