Finite Group Databasebeta

← #14641389

Subgroups — #14641389

Order 2816.

174 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 37 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#13070169C211yesmaximal, characteristic
2#13066737C211yesmaximal, characteristic
3C11×#1315C211yesmaximal, characteristic
4C11×#408C2211yescharacteristic
5#10622853—21no—
6#10622849—21no—
7#10622738C411yescharacteristic, complemented
8#10622715—21no—
9C11×C22⋊C16—21no—
10#10622195C411yescharacteristic, complemented
11C2×C11×#41D411yescharacteristic
12C2×C11×M16C2×C411yescharacteristic
13C22×C8×C11D411yescharacteristic
14#66979—21no—
15#66979—41no—
16C2×#4318—21no—
17C2×C11×C16—41no—
18C11×C22⋊C8—41no—
19#66901—42no—
20#66898—22no—
21#66898—41no—
22#66883—41no—
23Dic11⋊C8—42no—
24#7438—111nomaximal, Sylow
25C11×#41—41no—
26C11×#41—41no—
27C2×Q8×C11Q1611yescharacteristic
28C2×D4×C11—21no—
29C2×D4×C11SD1611yescharacteristic
30C22×C4×C11—21no—
31C22×C4×C11C22⋊C411yescharacteristic
32C11×M16—41no—
33C2×C8×C11—21no—
34C2×C8×C11—21no—
35C2×C8×C11—41no—
36C22⋊Dic11—42no—
37C22⋊Dic11—41no—
38C4⋊Dic11—41no—
39C4⋊Dic11—81no—
40C4×Dic11—22no—
41C4×Dic11—81no—
42#4318—41no—
43#4318—41no—
44C2×C11⋊C8—41no—
45C11×C16—81no—
46#2098—111no—
47#1391—111no—
48#1315D1111yescharacteristic
49C23×C11—21no—
50C23×C11#10411yescharacteristic
51Q8×C11—41no—
52D4×C11—41no—
53D4×C11—81no—
54C2×C4×C11—21no—
55C2×C4×C11—21no—
56C2×C4×C11—21no—
57C2×C4×C11—41no—
58C2×C4×C11—41no—
59C2×C4×C11#9911yescharacteristic
60C2×C4×C11#10311yescharacteristic
61C2×Dic11—42no—
62C2×Dic11—82no—
63C8×C11—41no—
64C8×C11—41no—
65C11⋊C8—81no—
66#430—111no—
67#424—221no—
68#421—221no—
69#410—221no—
70#408C2×D1111yescharacteristic
71C22⋊C16—21no—
72H(3,ℤ/4)—111no—
73C22×C11—21no—
74C22×C11—41no—
75C22×C11—41no—
76C22×C11—81no—
77C22×C11#32811yescharacteristic
78C4×C11—21no—
79C4×C11—41no—
80C4×C11#35211yescharacteristic
81C4×C11#35311yescharacteristic
82Dic11—82no—
83Dic11—162no—
84C2×#41D4411yescharacteristic
85C2×M16—221no—
86C2×M16C4×D1111yescharacteristic
87C22×C8C22⋊D1111yescharacteristic
88#117—221no—
89#117—441no—
90C2×C16—41no—
91#108—441no—
92C4⋊C8—442no—
93#104—442no—
94#99—222no—
95#99—441no—
96C22⋊C8—41no—
97C2×C11—21no—
98C2×C11—41no—
99C2×C11—81no—
100C2×C11#135211yescharacteristic
101#41—41no—
102#41—41no—
103C2×Q8Dic4411yescharacteristic
104C2×D4—21no—
105C2×D4#431411yescharacteristic
106C22×C4—21no—
107C22×C4(C2×D11)⋊C411yescharacteristic
108M16—41no—
109M16—441no—
110M16—441no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—41no—
114C2×C8—441no—
115C4⋊C4—441no—
116C4⋊C4—881no—
117C22⋊C4—441no—
118C22⋊C4—442no—
119C42—222no—
120C42—881no—
121C16—81no—
122C11#743811yescharacteristic, complemented, Sylow
123C23—21no—
124C23#6688911yescharacteristic
125Q8—41no—
126D4—41no—
127D4—81no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—442no—
134C2×C4—882no—
135C2×C4#6687011yescharacteristic
136C2×C4#6688011yescharacteristic
137C8—41no—
138C8—41no—
139C8—881no—
140C22—21no—
141C22—41no—
142C22—41no—
143C22—81no—
144C22#1062210511yescharacteristic
145C4—21no—
146C4—41no—
147C4—882no—
148C4—1762no—
149C4#1062211211yescharacteristic
150C4#1062211411yescharacteristic
151C2—21no—
152C2—41no—
153C2—81no—
154C2#1306664111yescharacteristic
subgroupG/H
centerC4#10622112
commutatorC2×C11×M16C2×C4
Frattini#408C2×D11
FittingC11×#1315C2
socleC2×C11#1352
prime radicalC2×C11×#41D4
cosocleC11×#408C22
hypercenter#1315D11
hypocenterC11#7438
LCSG ▷ C2×C11×M16 ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #408 ◁ #1315

Complements

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

NH ≅ G/Ntype
7. #10622738C4semidirect
10. #10622195C4semidirect
122. C11#7438semidirect

Maximal subgroups

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

subgroupindex
#130701692
#130667372
C11×#13152
#743811