Finite Group Databasebeta

← #14658583

Subgroups — #14658583

Order 2816.

294 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 87 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#13068757C211yesmaximal, characteristic
2#13067288C212yesmaximal
3#13066474C212yesmaximal
4#13066461C211yesmaximal, characteristic
5C11×#1960C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×#103—22no—
8C2×C11×#97C2211yescharacteristic
9C11×#382C2211yescharacteristic
10#10622538C2212yes—
11#10622537C2212yes—
12#10622190—22no—
13#10622185—24no—
14C22×Q8×C11—21no—
15C22×C8×C11D412yes—
16C11×C4⋊Q8—22no—
17C11×C4⋊Q8—21no—
18C11×C4⋊Q8D412yes—
19C2×C11×C4⋊C4—22no—
20C2×C11×C4⋊C4—21no—
21C2×C42×C11C2311yescharacteristic
22C2×#4318—22no—
23C11×#103—44no—
24C11×#97—22no—
25C11×#95—22no—
26C22⋊(C11⋊C8)—22no—
27C4⋊(C11⋊C8)—22no—
28C4⋊(C11⋊C8)—22no—
29C4⋊(C11⋊C8)—22no—
30C4×C11⋊C8—22no—
31#10635—111nomaximal, Sylow
32C2×Q8×C11—22no—
33C2×Q8×C11—41no—
34C2×Q8×C11—42no—
35C2×Q8×C11—42no—
36C22×C4×C11—41no—
37C22×C4×C11—41no—
38C22×C4×C11C2×D411yescharacteristic
39C22×C4×C11#4112yes—
40C2×C8×C11—22no—
41C2×C8×C11—22no—
42C2×C8×C11—22no—
43C11×C4⋊C4—24no—
44C11×C4⋊C4—42no—
45C11×C4⋊C4—42no—
46C42×C11C2×D411yescharacteristic
47C42×C11#4111yescharacteristic
48C42×C11#4112yes—
49#4318—42no—
50#4318—42no—
51C2×C11⋊C8—42no—
52C2×C11⋊C8—42no—
53#1960D1111yescharacteristic
54#1838—111no—
55#1546—112no—
56#1286—112no—
57#1281—111no—
58C23×C11#12411yescharacteristic
59Q8×C11—44no—
60Q8×C11—82no—
61C2×C4×C11—42no—
62C2×C4×C11—42no—
63C2×C4×C11—81no—
64C2×C4×C11—81no—
65C2×C4×C11—82no—
66C2×C4×C11—81no—
67C2×C4×C11#12111yescharacteristic
68C2×C4×C11#12312yes—
69C2×C4×C11#12311yescharacteristic
70C2×C4×C11#12612yes—
71C2×C4×C11#13512yes—
72C2×C4×C11AGL(1,ℤ/8)12yes—
73C8×C11—42no—
74C11⋊C8—82no—
75C11⋊C8—82no—
76C2×C4⋊Q8C2×D1111yescharacteristic
77#431—112no—
78#423—112no—
79C2×#103—22no—
80C2×#97C2×D1111yescharacteristic
81#382C2×D1111yescharacteristic
82#341—222no—
83#332—224no—
84C22×C11—22no—
85C22×C11#39711yescharacteristic
86C22×C11#48811yescharacteristic
87C22×C11#49011yescharacteristic
88C4×C11—22no—
89C4×C11—22no—
90C4×C11—82no—
91C4×C11—161no—
92C4×C11#46312yes—
93C4×C11#48212yes—
94C22×Q8—21no—
95C2×M16—222no—
96C22×C8C22⋊D1112yes—
97C4⋊Q8—21no—
98C4⋊Q8—22no—
99C4⋊Q8D4412yes—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—21no—
102C2×C42C22×D1111yescharacteristic
103C4⋊C8—222no—
104C4⋊C8—222no—
105C4⋊C8—222no—
106#103—44no—
107C22⋊C8—222no—
108#97—22no—
109C4×C8—222no—
110#95—22no—
111C2×C11—21no—
112C2×C11—21no—
113C2×C11#207311yescharacteristic
114C2×C11#208212yes—
115C2×Q8—22no—
116C2×Q8—41no—
117C2×Q8—42no—
118C2×Q8—42no—
119C22×C4—41no—
120C22×C4—41no—
121C22×C4#434112yes—
122C22×C4C2×C22⋊D1111yescharacteristic
123M16—442no—
124M16—442no—
125C2×C8—22no—
126C2×C8—22no—
127C2×C8—22no—
128C2×C8—442no—
129C2×C8—442no—
130C4⋊C4—24no—
131C4⋊C4—42no—
132C4⋊C4—42no—
133C42C2×D4411yescharacteristic
134C42#433911yescharacteristic
135C42#434112yes—
136C11#1063511yescharacteristic, complemented, Sylow
137C23#6698911yescharacteristic
138Q8—44no—
139Q8—82no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—81no—
143C2×C4—81no—
144C2×C4—82no—
145C2×C4—81no—
146C2×C4#6693212yes—
147C2×C4#6693912yes—
148C2×C4#6698311yescharacteristic
149C2×C4#6698512yes—
150C2×C4#6698811yescharacteristic
151C2×C4#6700312yes—
152C8—42no—
153C8—882no—
154C8—882no—
155C22—22no—
156C22#1062256611yescharacteristic
157C22#1062266911yescharacteristic
158C22#1062268411yescharacteristic
159C4—22no—
160C4—22no—
161C4—82no—
162C4—161no—
163C4#1062262912yes—
164C4#1062264812yes—
165C2—21no—
166C2—21no—
167C2#1307002911yescharacteristic
168C2#1307008012yes—
subgroupG/H
centerC22#10622566
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1960C2
socleC22×C11#397
prime radicalC23×C11#124
hypercenter#1960D11
hypocenterC11#10635
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
136. C11#10635semidirect

Maximal subgroups

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

subgroupindex
#130687572
#130672882
#130664742
#130664612
C11×#19602
#1063511