Finite Group Databasebeta

← #14656887

Subgroups — #14656887

Order 2816.

364 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 89 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#13077003C211yesmaximal, characteristic
2#13069593C211yesmaximal, characteristic
3#13067181C212yesmaximal
4#13066475C212yesmaximal
5C11×#1276C211yesmaximal, characteristic
6#10623001C2211yescharacteristic
7C11×#431C2212yes—
8C43×C11C2211yescharacteristic
9#10622549C2212yes—
10#10622546—24no—
11#10622541—22no—
12#10622537C2211yescharacteristic
13#10622161—22no—
14#10622105—24no—
15C2×C42×C11—22no—
16C2×C42×C11D412yes—
17C2×C42×C11C2311yescharacteristic
18#66979—21no—
19C2×C4⋊Dic11—22no—
20#66977—22no—
21C2×Dic11⋊C4—24no—
22C2×#4318—21no—
23#66923—21no—
24#66922Q812yes—
25C4×Dic22—22no—
26C11×C4⋊C8—22no—
27C11×C22⋊C8—22no—
28C4×C8×C11—22no—
29C11⋊#95—24no—
30C11⋊#95—22no—
31C11⋊#95D414yes—
32C4⋊(C11⋊C8)—22no—
33#10367—111nomaximal, Sylow
34C22×C4×C11—22no—
35C22×C4×C11C2×D412yes—
36C22×C4×C11C2×D411yescharacteristic
37C22×Dic11—24no—
38C2×Dic22—22no—
39C2×C8×C11—42no—
40C42×C11—22no—
41C42×C11—22no—
42C42×C11—44no—
43C42×C11C2×Q811yescharacteristic
44C42×C11#4112yes—
45C42×C11#4111yescharacteristic
46C22⋊Dic11—41no—
47C4⋊Dic11—22no—
48C4⋊Dic11—22no—
49C4⋊Dic11—42no—
50C4⋊Dic11—42no—
51Dic11⋊C4—48no—
52Dic11⋊C4—42no—
53C4×Dic11—41no—
54#4318—42no—
55C2×C11⋊C8—41no—
56#2864—111no—
57#1994—111no—
58#1518—112no—
59#1286—112no—
60#1276D1111yescharacteristic
61C23×C11#12011yescharacteristic
62C2×C4×C11—24no—
63C2×C4×C11—42no—
64C2×C4×C11—42no—
65C2×C4×C11—42no—
66C2×C4×C11C22⋊Q812yes—
67C2×C4×C11C22⋊Q811yescharacteristic
68C2×C4×C11#12411yescharacteristic
69C2×C4×C11#12412yes—
70C2×C4×C11#13512yes—
71C2×C4×C11#13712yes—
72C2×Dic11—48no—
73C2×Dic11—42no—
74C2×Dic11—44no—
75Dic22—82no—
76C8×C11—82no—
77C11⋊C8—81no—
78#533—111no—
79#431C2×D1112yes—
80#423—111no—
81#389—222no—
82#387—224no—
83#382—112no—
84C43C2×D1111yescharacteristic
85#339—222no—
86#328—224no—
87C22×C11—22no—
88C22×C11#39311yescharacteristic
89C22×C11#45212yes—
90C4×C11—22no—
91C4×C11—22no—
92C4×C11—44no—
93C4×C11#47912yes—
94C4×C11#48811yescharacteristic
95C4×C11#49111yescharacteristic
96Dic11—84no—
97Dic11—82no—
98C2×M16—221no—
99C4⋊Q8—112no—
100#125—221no—
101C22⋊Q8—222no—
102C4×Q8—222no—
103#117—221no—
104C2×C4⋊C4—224no—
105C2×C4⋊C4—222no—
106C2×C42—22no—
107C2×C42D4412yes—
108C2×C42C22×D1111yescharacteristic
109C4⋊C8—22no—
110C4⋊C8—222no—
111C22⋊C8—22no—
112C4×C8—22no—
113#95—114no—
114#95—224no—
115#95—222no—
116C2×C11—22no—
117C2×C11#202611yescharacteristic
118C2×C11#203112yes—
119C2×Q8—222no—
120C22×C4—22no—
121C22×C4—224no—
122C22×C4C2×D4411yescharacteristic
123C22×C4D4×D1112yes—
124M16—442no—
125C2×C8—42no—
126C2×C8—441no—
127C4⋊C4—222no—
128C4⋊C4—222no—
129C4⋊C4—448no—
130C4⋊C4—442no—
131C4⋊C4—442no—
132C4⋊C4—442no—
133C22⋊C4—441no—
134C42—22no—
135C42—22no—
136C42—44no—
137C42—441no—
138C42#433912yes—
139C42#434111yescharacteristic
140C42Q8×D1111yescharacteristic
141C11#1036711yescharacteristic, complemented, Sylow
142C23#6693511yescharacteristic
143Q8—882no—
144C2×C4—24no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—448no—
149C2×C4—442no—
150C2×C4—444no—
151C2×C4#6692811yescharacteristic
152C2×C4#6693812yes—
153C2×C4#6694912yes—
154C2×C4#6695011yescharacteristic
155C2×C4#6695712yes—
156C2×C4#6696212yes—
157C8—82no—
158C8—881no—
159C22—22no—
160C22#1062228611yescharacteristic
161C22#1062234612yes—
162C4—22no—
163C4—22no—
164C4—44no—
165C4—884no—
166C4—882no—
167C4#1062231011yescharacteristic
168C4#1062231611yescharacteristic
169C4#1062244212yes—
170C2—22no—
171C2#1306976811yescharacteristic
172C2#1306978912yes—
subgroupG/H
centerC22#10622286
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1276C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1276D11
hypocenterC11#10367
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
141. C11#10367semidirect

Maximal subgroups

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

subgroupindex
#130770032
#130695932
#130671812
#130664752
C11×#12762
#1036711