Finite Group Databasebeta

← #14653265

Subgroups — #14653265

Order 2816.

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

normal subgroups only

This group has 506 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, complemented
2#13067288C212yesmaximal, complemented
3#13067284C212yesmaximal
4#13066908C211yesmaximal, characteristic, complemented
5C2×C11×#492C211yesmaximal, characteristic
6C22×C11×SD16—22no—
7C2×C11×C4⋊Q8C2211yescharacteristic
8C2×C11×#127C2211yescharacteristic
9C11×#492—22no—
10C11×#492C414yes—
11C2×C4×C8×C11C2211yescharacteristic
12#10622538C2212yes—
13#10622537C2212yes—
14#10622190—22no—
15#10622185—24no—
16#10622182—24no—
17#10622092—22no—
18C22×Q8×C11—21no—
19C22×D4×C11—21no—
20C22×D4×C11—22no—
21C2×C11×SD16—28no—
22C2×C11×SD16—48no—
23C22×C8×C11D412yes—
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8—21no—
26C11×C4⋊Q8C2×C412yes—
27C11×#127—21no—
28C11×#127—22no—
29C11×#127C2×C412yes—
30C2×C11×C4⋊C4—22no—
31C2×C42×C11C2311yescharacteristic
32C2×#4318—22no—
33C4×C8×C11C2×C412yes—
34C4×C8×C11D412yes—
35C22⋊(C11⋊C8)—22no—
36C4⋊(C11⋊C8)—22no—
37C4⋊(C11⋊C8)—22no—
38C4⋊(C11⋊C8)D414yes—
39C4×C11⋊C8—22no—
40#9777—111nomaximal, Sylow
41C24×C11—41no—
42C2×Q8×C11—22no—
43C2×Q8×C11—41no—
44C2×Q8×C11—44no—
45C2×D4×C11—22no—
46C2×D4×C11—24no—
47C2×D4×C11—42no—
48C2×D4×C11—41no—
49C2×D4×C11—44no—
50C2×D4×C11—84no—
51C22×C4×C11—41no—
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11#4112yes—
54C11×SD16—416no—
55C2×C8×C11—24no—
56C2×C8×C11C22⋊C414yes—
57C11×C4⋊C4—24no—
58C11×C4⋊C4—42no—
59C42×C11C22×C411yescharacteristic
60C42×C11C2×D411yescharacteristic
61C42×C11C2×D412yes—
62#4318—44no—
63C2×C11⋊C8—24no—
64C2×C11⋊C8—42no—
65C2×#492D1111yescharacteristic
66#1837—111no—
67#1546—112no—
68#1545—112no—
69#1452—111no—
70C23×C11—42no—
71C23×C11—84no—
72C23×C11—82no—
73C23×C11#12411yescharacteristic
74Q8×C11—44no—
75Q8×C11—82no—
76D4×C11—44no—
77D4×C11—84no—
78D4×C11—84no—
79D4×C11—82no—
80C2×C4×C11—24no—
81C2×C4×C11—42no—
82C2×C4×C11—82no—
83C2×C4×C11C2×C22⋊C411yescharacteristic
84C2×C4×C11C4×D412yes—
85C2×C4×C11#12112yes—
86C2×C4×C11#12711yescharacteristic
87C2×C4×C11AGL(1,ℤ/8)14yes—
88C8×C11—24no—
89C11⋊C8—44no—
90C11⋊C8—82no—
91C22×SD16—22no—
92C2×C4⋊Q8C2×D1111yescharacteristic
93C2×#127C2×D1111yescharacteristic
94#492—22no—
95#492Dic1114yes—
96#431—112no—
97#423—112no—
98C2×C4×C8C2×D1111yescharacteristic
99#341—222no—
100#332—224no—
101#331—224no—
102#322—222no—
103C22×C11—22no—
104C22×C11—82no—
105C22×C11—84no—
106C22×C11—164no—
107C22×C11#39011yescharacteristic
108C22×C11#49012yes—
109C4×C11—22no—
110C4×C11—82no—
111C4×C11#41812yes—
112C4×C11#47114yes—
113C4×C11#49612yes—
114C22×Q8—21no—
115C22×D4—22no—
116C22×D4—21no—
117C2×SD16—28no—
118C2×SD16—48no—
119C2×M16—222no—
120C22×C8C22⋊D1112yes—
121C4⋊Q8—22no—
122C4⋊Q8—21no—
123C4⋊Q8C2×Dic1112yes—
124#127—22no—
125#127—21no—
126#127C2×Dic1112yes—
127C2×C4⋊C4—22no—
128C2×C42C22×D1111yescharacteristic
129C4⋊C8—114no—
130C4⋊C8—222no—
131C4⋊C8—222no—
132C22⋊C8—222no—
133C4×C8—222no—
134C4×C8C2×Dic1112yes—
135C4×C8C22⋊D1112yes—
136C2×C11—22no—
137C2×C11—162no—
138C2×C11#196111yescharacteristic
139C2×C11#197712yes—
140C24—41no—
141C2×Q8—22no—
142C2×Q8—41no—
143C2×Q8—44no—
144C2×D4—24no—
145C2×D4—22no—
146C2×D4—44no—
147C2×D4—42no—
148C2×D4—41no—
149C2×D4—84no—
150C22×C4—41no—
151C22×C4#434112yes—
152C22×C4C2×C22⋊D1111yescharacteristic
153SD16—416no—
154M16—444no—
155C2×C8—24no—
156C2×C8—224no—
157C2×C8—442no—
158C2×C8C22⋊Dic1114yes—
159C4⋊C4—24no—
160C4⋊C4—42no—
161C42D4×D1112yes—
162C42C22×Dic1111yescharacteristic
163C42C2×C22⋊D1111yescharacteristic
164C11#977711yescharacteristic, complemented, Sylow
165C23—42no—
166C23—84no—
167C23—82no—
168C23#6698911yescharacteristic
169Q8—44no—
170Q8—82no—
171D4—44no—
172D4—84no—
173D4—84no—
174D4—82no—
175C2×C4—24no—
176C2×C4—42no—
177C2×C4—82no—
178C2×C4#6698514yes—
179C2×C4D4×Dic1112yes—
180C2×C4#6699112yes—
181C2×C4#6699311yescharacteristic
182C2×C4C2×C22⋊Dic1111yescharacteristic
183C8—24no—
184C8—444no—
185C8—882no—
186C22—22no—
187C22—82no—
188C22—84no—
189C22—164no—
190C22#1062268412yes—
191C22#1062283411yescharacteristic
192C4—22no—
193C4—82no—
194C4#1062268712yes—
195C4#1062279014yes—
196C4#1062282812yes—
197C2—22no—
198C2—162no—
199C2#1306944111yescharacteristic
200C2#1306952112yes—
subgroupG/H
centerC22#10622834
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#492C2
socleC22×C11#390
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenterC2×#492D11
hypocenterC11#9777
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
1. #13068754C2semidirect
2. #13067288C2semidirect
4. #13066908C2semidirect
164. C11#9777semidirect

Maximal subgroups

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

subgroupindex
#130687542
#130672882
#130672842
#130669082
C2×C11×#4922
#977711