Finite Group Databasebeta

← #14641390

Subgroups — #14641390

Order 2816.

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

normal subgroups only

This group has 170 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#13066542C211yesmaximal, characteristic
3C11×#1392C211yesmaximal, characteristic
4C11×#413—21no—
5C11×#408C2211yescharacteristic
6#10622849—21no—
7#10622738C411yescharacteristic
8#10622715—21no—
9#10622195C411yescharacteristic
10C22⋊(C11⋊C16)—21no—
11C2×C11×#41D411yescharacteristic
12C2×C11×M16—41no—
13C2×C11×M16C2×C411yescharacteristic
14C22×C8×C11D411yescharacteristic
15#66979—21no—
16C2×#4318—21no—
17C11×#101—41no—
18C11×#100—22no—
19C11×C22⋊C8—41no—
20#66901—42no—
21#66883—41no—
22Dic11⋊C8—42no—
23C2×C11⋊C16—41no—
24#7439—111nomaximal, Sylow
25C11×#41—41no—
26C11×#41—41no—
27C2×Q8×C11SD1611yescharacteristic
28C2×D4×C11—21no—
29C2×D4×C11Q1611yescharacteristic
30C22×C4×C11—21no—
31C22×C4×C11C22⋊C411yescharacteristic
32C11×M16—41no—
33C11×M16—42no—
34C11×M16—81no—
35C2×C8×C11—21no—
36C2×C8×C11—21no—
37C2×C8×C11—41no—
38C2×C8×C11—81no—
39C22⋊Dic11—41no—
40C4⋊Dic11—41no—
41C4×Dic11—22no—
42#4318—41no—
43#4318—41no—
44C2×C11⋊C8—41no—
45C11⋊C16—81no—
46#2098—111no—
47#1392D1111yescharacteristic
48#1315—111no—
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—
62C8×C11—41no—
63C8×C11—41no—
64C8×C11—82no—
65C11⋊C8—81no—
66#430—111no—
67#424—221no—
68#421—221no—
69#413—21no—
70#408C2×D1111yescharacteristic
71C22⋊C16—221no—
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—
83C2×#41C22⋊D1111yescharacteristic
84C2×M16—41no—
85C2×M16—221no—
86C2×M16C4×D1111yescharacteristic
87C22×C8D4411yescharacteristic
88#117—221no—
89C2×C16—441no—
90#108—441no—
91C4⋊C8—442no—
92#104—442no—
93#101—41no—
94#100—22no—
95C22⋊C8—41no—
96C2×C11—21no—
97C2×C11—41no—
98C2×C11—81no—
99C2×C11#135211yescharacteristic
100#41—41no—
101#41—41no—
102C2×Q8#432411yescharacteristic
103C2×D4—21no—
104C2×D4#432611yescharacteristic
105C22×C4—21no—
106C22×C4(C2×D11)⋊C411yescharacteristic
107M16—41no—
108M16—42no—
109M16—81no—
110M16—441no—
111M16—441no—
112C2×C8—21no—
113C2×C8—21no—
114C2×C8—41no—
115C2×C8—81no—
116C2×C8—441no—
117C4⋊C4—441no—
118C22⋊C4—441no—
119C42—222no—
120C16—881no—
121C11#743911yescharacteristic, complemented, Sylow
122C23—21no—
123C23#6686911yescharacteristic
124Q8—41no—
125D4—41no—
126D4—81no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—442no—
133C2×C4#6687011yescharacteristic
134C2×C4#6687411yescharacteristic
135C8—41no—
136C8—41no—
137C8—82no—
138C8—881no—
139C22—21no—
140C22—41no—
141C22—41no—
142C22—81no—
143C22#1062209011yescharacteristic
144C4—21no—
145C4—41no—
146C4—882no—
147C4#1062211011yescharacteristic
148C4#1062211211yescharacteristic
149C2—21no—
150C2—41no—
151C2—81no—
152C2#1306663911yescharacteristic
subgroupG/H
centerC4#10622112
commutatorC2×C11×M16C2×C4
Frattini#408C2×D11
FittingC11×#1392C2
socleC2×C11#1352
prime radicalC2×C11×#41D4
cosocleC11×#408C22
hypercenter#1392D11
hypocenterC11#7439
LCSG ▷ C2×C11×M16 ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #408 ◁ #1392

Complements

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

NH ≅ G/Ntype
121. C11#7439semidirect

Maximal subgroups

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

subgroupindex
#130701692
#130665422
C11×#13922
#743911