Finite Group Databasebeta

← #14653270

Subgroups — #14653270

Order 2816.

390 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 127 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#13068754C211yesmaximal, characteristic
2#13067301C212yesmaximal
3#13067297C212yesmaximal
4#13066908C211yesmaximal, characteristic
5C2×C11×#500C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2212yes—
7C11×#500—22no—
8C11×#500C414yes—
9C2×C11×#107—22no—
10C2×C4×C8×C11C2211yescharacteristic
11#10622538C2211yescharacteristic
12#10622538C2211yescharacteristic
13#10622537C2212yes—
14#10622190—22no—
15#10622185—24no—
16#10622184—24no—
17#10622092—22no—
18C22×Q8×C11—22no—
19C22×C8×C11D412yes—
20C11×C4⋊Q8—22no—
21C11×C4⋊Q8—22no—
22C11×C4⋊Q8—22no—
23C11×C4⋊Q8C2×C414yes—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4—22no—
26C2×C42×C11C2311yescharacteristic
27C2×#4318—22no—
28C11×#107—28no—
29C4×C8×C11C2×C412yes—
30C4×C8×C11D412yes—
31C22⋊(C11⋊C8)—21no—
32C22⋊(C11⋊C8)—21no—
33C4⋊(C11⋊C8)—22no—
34C4⋊(C11⋊C8)—22no—
35C4⋊(C11⋊C8)D412yes—
36C4⋊(C11⋊C8)D412yes—
37C4×C11⋊C8—21no—
38C4×C11⋊C8—21no—
39#9778—111nomaximal, Sylow
40C2×Q8×C11—24no—
41C2×Q8×C11—42no—
42C2×Q8×C11—84no—
43C22×C4×C11—42no—
44C22×C4×C11C2×D411yescharacteristic
45C22×C4×C11#4111yescharacteristic
46C22×C4×C11#4111yescharacteristic
47C2×C8×C11—24no—
48C2×C8×C11C22⋊C414yes—
49C11×C4⋊C4—24no—
50C11×C4⋊C4—24no—
51C11×C4⋊C4—42no—
52C11×C4⋊C4—42no—
53C42×C11C22×C411yescharacteristic
54C42×C11C2×D411yescharacteristic
55C42×C11C2×D411yescharacteristic
56C42×C11C2×D411yescharacteristic
57#4318—44no—
58C2×C11⋊C8—22no—
59C2×C11⋊C8—22no—
60C2×C11⋊C8—42no—
61C2×#500D1111yescharacteristic
62#1837—111no—
63#1549—112no—
64#1548—112no—
65#1452—111no—
66C23×C11#12411yescharacteristic
67Q8×C11—84no—
68Q8×C11—84no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—44no—
72C2×C4×C11—84no—
73C2×C4×C11C2×C22⋊C411yescharacteristic
74C2×C4×C11C4×D411yescharacteristic
75C2×C4×C11C4×D411yescharacteristic
76C2×C4×C11#12111yescharacteristic
77C2×C4×C11#12111yescharacteristic
78C2×C4×C11#12711yescharacteristic
79C2×C4×C11#13714yes—
80C8×C11—24no—
81C11⋊C8—42no—
82C11⋊C8—42no—
83C11⋊C8—82no—
84C2×C4⋊Q8C2×D1112yes—
85#500—22no—
86#500Dic1114yes—
87#431—111no—
88#431—111no—
89C2×#107—22no—
90#423—112no—
91C2×C4×C8C2×D1111yescharacteristic
92#341—222no—
93#333—224no—
94#332—224no—
95#322—222no—
96C22×C11—21no—
97C22×C11—21no—
98C22×C11#39011yescharacteristic
99C22×C11#49112yes—
100C4×C11—21no—
101C4×C11—21no—
102C4×C11—84no—
103C4×C11#41912yes—
104C4×C11#47212yes—
105C4×C11#47312yes—
106C4×C11#49712yes—
107C22×Q8—22no—
108C2×M16—222no—
109C22×C8C22⋊D1112yes—
110C4⋊Q8—22no—
111C4⋊Q8—22no—
112C4⋊Q8—22no—
113C4⋊Q8C2×Dic1114yes—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—22no—
116C2×C42C22×D1111yescharacteristic
117#107—28no—
118C4⋊C8—112no—
119C4⋊C8—112no—
120C4⋊C8—222no—
121C4⋊C8—222no—
122C22⋊C8—221no—
123C22⋊C8—221no—
124C4×C8—221no—
125C4×C8—221no—
126C4×C8C2×Dic1112yes—
127C4×C8C22⋊D1112yes—
128C2×C11—22no—
129C2×C11#196011yescharacteristic
130C2×C11#197811yescharacteristic
131C2×C11#197911yescharacteristic
132C2×Q8—24no—
133C2×Q8—42no—
134C2×Q8—84no—
135C22×C4—42no—
136C22×C4#434111yescharacteristic
137C22×C4#434111yescharacteristic
138C22×C4C2×C22⋊D1111yescharacteristic
139M16—444no—
140C2×C8—24no—
141C2×C8—222no—
142C2×C8—222no—
143C2×C8—442no—
144C2×C8C22⋊Dic1114yes—
145C4⋊C4—24no—
146C4⋊C4—24no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C42D4×D1111yescharacteristic
150C42D4×D1111yescharacteristic
151C42C22×Dic1111yescharacteristic
152C42C2×C22⋊D1111yescharacteristic
153C11#977811yescharacteristic, complemented, Sylow
154C23#6698911yescharacteristic
155Q8—84no—
156Q8—84no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—44no—
160C2×C4—84no—
161C2×C4D4×Dic1111yescharacteristic
162C2×C4D4×Dic1111yescharacteristic
163C2×C4#6699111yescharacteristic
164C2×C4#6699111yescharacteristic
165C2×C4#6699311yescharacteristic
166C2×C4#6699514yes—
167C2×C4C2×C22⋊Dic1111yescharacteristic
168C8—24no—
169C8—442no—
170C8—442no—
171C8—882no—
172C22—21no—
173C22—21no—
174C22#1062269512yes—
175C22#1062283411yescharacteristic
176C4—21no—
177C4—21no—
178C4—84no—
179C4#1062269912yes—
180C4#1062277312yes—
181C4#1062280512yes—
182C4#1062283812yes—
183C2—22no—
184C2#1306943711yescharacteristic
185C2#1306952711yescharacteristic
186C2#1306953211yescharacteristic
subgroupG/H
centerC22#10622834
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#500C2
socleC22×C11#390
prime radicalC23×C11#124
cosocleC2×C42×C11C23
hypercenterC2×#500D11
hypocenterC11#9778
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
153. C11#9778semidirect

Maximal subgroups

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

subgroupindex
#130687542
#130673012
#130672972
#130669082
C2×C11×#5002
#977811