Finite Group Databasebeta

← #14641404

Subgroups — #14641404

Order 2816.

198 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 41 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#13069961C211yesmaximal, characteristic
2#13066499C211yesmaximal, characteristic
3C11×#1325C211yesmaximal, characteristic
4#10623031C411yescharacteristic
5C11×#384C2211yescharacteristic
6#10622577—21no—
7C2×C4⋊(C11⋊C8)—21no—
8C11×#324—21no—
9#10622168C411yescharacteristic
10#10622161—21no—
11C2×C11×C4⋊C4—41no—
12C2×C11×C4⋊C4C2×C411yescharacteristic
13C2×C11×C4⋊C4D411yescharacteristic
14C2×C42×C11D411yescharacteristic
15#66979—21no—
16#66977—41no—
17C2×#4318—21no—
18C22×C11⋊C8—41no—
19#66943—41no—
20#66941—41no—
21C11×C22⋊C8—41no—
22#66872—41no—
23#66871—41no—
24C4⋊(C11⋊C8)—22no—
25C4⋊(C11⋊C8)—41no—
26#7443—111nomaximal, Sylow
27C22×C4×C11—21no—
28C22×C4×C11—21no—
29C22×C4×C11—21no—
30C22×C4×C11C22⋊C411yescharacteristic
31C2×Dic22—41no—
32C2×C8×C11—81no—
33C11×C4⋊C4—41no—
34C11×C4⋊C4—41no—
35C11×C4⋊C4—81no—
36C11×C4⋊C4—81no—
37C42×C11—21no—
38C42×C11SD1611yescharacteristic
39C42×C11Q1611yescharacteristic
40C22⋊Dic11—41no—
41C4⋊Dic11—21no—
42C4⋊Dic11—21no—
43C4⋊Dic11—41no—
44Dic11⋊C4—42no—
45C4×Dic11—41no—
46#4318—22no—
47#4318—41no—
48C2×C11⋊C8—41no—
49C2×C11⋊C8—42no—
50C2×C11⋊C8—81no—
51C2×C11⋊C8—81no—
52#2060—111no—
53#1325D1111yescharacteristic
54#1296—111no—
55C23×C11#9911yescharacteristic
56C2×C4×C11—21no—
57C2×C4×C11—21no—
58C2×C4×C11—21no—
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—21no—
64C2×C4×C11—41no—
65C2×C4×C11—41no—
66C2×C4×C11—81no—
67C2×C4×C11—81no—
68C2×C4×C11#10311yescharacteristic
69C2×C4×C11#10411yescharacteristic
70C2×Dic11—41no—
71C2×Dic11—41no—
72Dic22—161no—
73C8×C11—161no—
74C11⋊C8—42no—
75C11⋊C8—82no—
76#544—111no—
77#428—221no—
78C2×C4⋊C8—221no—
79#384C2×D1111yescharacteristic
80#343—111no—
81#339—221no—
82#324—21no—
83C22×C11—21no—
84C22×C11—21no—
85C22×C11#32811yescharacteristic
86C22×C11AΣL(1,𝔽16)11yescharacteristic
87C22×C11#35611yescharacteristic
88C4×C11—21no—
89C4×C11—21no—
90C4×C11—21no—
91C4×C11—21no—
92C4×C11—21no—
93C4×C11—21no—
94C4×C11—81no—
95C4×C11—81no—
96Dic11—81no—
97Dic11—81no—
98C2×M16—221no—
99C22×C8—441no—
100C4⋊Q8—441no—
101#125—441no—
102C22⋊Q8—441no—
103#117—221no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4C4×D1111yescharacteristic
106C2×C4⋊C4C22⋊D1111yescharacteristic
107C2×C42D4411yescharacteristic
108#107—441no—
109#106—441no—
110C4⋊C8—222no—
111C4⋊C8—441no—
112C22⋊C8—41no—
113C2×C11—21no—
114C2×C11—21no—
115C2×C11#135411yescharacteristic
116C2×C11#140211yescharacteristic
117C2×C11#140511yescharacteristic
118C2×Q8—441no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4(C2×D11)⋊C411yescharacteristic
123M16—222no—
124M16—441no—
125C2×C8—81no—
126C2×C8—441no—
127C2×C8—442no—
128C2×C8—881no—
129C2×C8—881no—
130C4⋊C4—41no—
131C4⋊C4—41no—
132C4⋊C4—81no—
133C4⋊C4—81no—
134C4⋊C4—221no—
135C4⋊C4—221no—
136C4⋊C4—441no—
137C4⋊C4—442no—
138C22⋊C4—441no—
139C42—21no—
140C42—441no—
141C42#431411yescharacteristic
142C42Dic4411yescharacteristic
143C11#744311yescharacteristic, complemented, Sylow
144C23#6687011yescharacteristic
145Q8—1761no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—441no—
159C2×C4—441no—
160C2×C4#6688011yescharacteristic
161C2×C4#6688911yescharacteristic
162C8—161no—
163C8—442no—
164C8—882no—
165C22—21no—
166C22—21no—
167C22#1062210511yescharacteristic
168C22#1062210911yescharacteristic
169C22#1062211611yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—81no—
177C4—81no—
178C4—881no—
179C4—881no—
180C2—21no—
181C2—21no—
182C2#1306664711yescharacteristic
183C2#1306676011yescharacteristic
184C2#1306676911yescharacteristic
subgroupG/H
centerC22#10622109
commutatorC2×C11×C4⋊C4C2×C4
Frattini#384C2×D11
FittingC11×#1325C2
socleC22×C11AΣL(1,𝔽16)
prime radicalC23×C11#99
cosocleC11×#384C22
hypercenter#1325D11
hypocenterC11#7443
LCSG ▷ C2×C11×C4⋊C4 ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1325

Complements

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

NH ≅ G/Ntype
143. C11#7443semidirect

Maximal subgroups

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

subgroupindex
#130699612
#130664992
C11×#13252
#744311