Finite Group Databasebeta

← #14658579

Subgroups — #14658579

Order 2816.

346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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#13069440C211yesmaximal, characteristic
2#13067285C212yesmaximal
3#13066476C212yesmaximal, complemented
4#13066461C211yesmaximal, characteristic, complemented
5C11×#1838C211yesmaximal, characteristic, complemented
6C2×#66927C2211yescharacteristic
7C11×#423C2212yes—
8C2×C11×#97C2211yescharacteristic
9C2×#66885—22no—
10#10622549C2211yescharacteristic
11#10622538C2212yes—
12C11×#341—22no—
13#10622123—24no—
14C22×D44—21no—
15C22×D44—22no—
16C2×C11×M16—22no—
17C22×C8×C11D412yes—
18C2×C42×C11C2311yescharacteristic
19C2×C4⋊Dic11—21no—
20#66927—22no—
21#66927—21no—
22#66927D412yes—
23C11×C4⋊C8—22no—
24C11×C4⋊C8—22no—
25C11×#97—22no—
26C11⋊#95—22no—
27C22⋊(C11⋊C8)—22no—
28#66885—44no—
29C4⋊(C11⋊C8)—22no—
30C4×C11⋊C8—22no—
31#10634—111nomaximal, Sylow
32C23×D11—41no—
33C22×C4×C11C2×D411yescharacteristic
34C22×C4×C11#4112yes—
35C22×Dic11—41no—
36C2×D44—22no—
37C2×D44—24no—
38C2×D44—41no—
39C2×D44—42no—
40C2×D44—42no—
41C2×D44—42no—
42C2×D44—84no—
43C11×M16—42no—
44C11×M16—42no—
45C2×C8×C11—22no—
46C2×C8×C11—22no—
47C2×C8×C11—22no—
48C2×C8×C11—42no—
49C42×C11C2×D411yescharacteristic
50C42×C11#4111yescharacteristic
51C42×C11#4112yes—
52C4⋊Dic11—42no—
53C2×C11⋊C8—42no—
54#1961—111no—
55#1838D1111yescharacteristic, complemented
56#1545—112no—
57#1286—112no—
58#1281—111no—
59C23×C11#12411yescharacteristic
60C22×D11—42no—
61C22×D11—84no—
62C22×D11—81no—
63C22×D11—81no—
64C2×C4×C11—42no—
65C2×C4×C11#12111yescharacteristic
66C2×C4×C11#12312yes—
67C2×C4×C11#12311yescharacteristic
68C2×C4×C11#12612yes—
69C2×C4×C11#13512yes—
70C2×C4×C11AGL(1,ℤ/8)12yes—
71C2×Dic11—82no—
72C2×Dic11—81no—
73D44—44no—
74D44—84no—
75D44—84no—
76D44—82no—
77C8×C11—42no—
78C8×C11—82no—
79C11⋊C8—82no—
80C2×#127—111no—
81#431—112no—
82#423C2×D1112yes—
83C2×#102—222no—
84C2×#97C2×D1111yescharacteristic
85#382—111no—
86#341—22no—
87#331—224no—
88C22×C11—22no—
89C22×C11#39711yescharacteristic
90C22×C11#48811yescharacteristic
91C22×C11#49011yescharacteristic
92C2×D11—82no—
93C2×D11—84no—
94C2×D11—162no—
95C2×D11—162no—
96C4×C11—22no—
97C4×C11—22no—
98C4×C11#46312yes—
99C4×C11#48212yes—
100Dic11—161no—
101C22×D4—222no—
102C22×D4—221no—
103C2×M16—22no—
104C22×C8C22⋊D1112yes—
105#127—112no—
106#127—222no—
107#127—221no—
108C2×C4⋊C4—221no—
109C2×C42C22×D1111yescharacteristic
110C4⋊C8—22no—
111C4⋊C8—22no—
112C4⋊C8—222no—
113#102—444no—
114C22⋊C8—222no—
115#97—22no—
116C4×C8—222no—
117#95—222no—
118C2×C11—21no—
119C2×C11—21no—
120C2×C11#207311yescharacteristic
121C2×C11#208112yes—
122D11—162no—
123C24—441no—
124C2×D4—224no—
125C2×D4—222no—
126C2×D4—442no—
127C2×D4—441no—
128C2×D4—442no—
129C2×D4—442no—
130C2×D4—884no—
131C22×C4—441no—
132C22×C4#434312yes—
133C22×C4C2×C22⋊D1111yescharacteristic
134M16—42no—
135M16—42no—
136C2×C8—22no—
137C2×C8—22no—
138C2×C8—22no—
139C2×C8—42no—
140C2×C8—442no—
141C4⋊C4—442no—
142C42#433912yes—
143C42D4×D1111yescharacteristic
144C42#434111yescharacteristic
145C11#1063411yescharacteristic, complemented, Sylow
146C23—442no—
147C23—884no—
148C23—881no—
149C23—881no—
150C23#6700011yescharacteristic
151D4—444no—
152D4—884no—
153D4—884no—
154D4—882no—
155C2×C4—42no—
156C2×C4—882no—
157C2×C4—881no—
158C2×C4#6694712yes—
159C2×C4#6695112yes—
160C2×C4#6698211yescharacteristic
161C2×C4#6699111yescharacteristic
162C2×C4#6700212yes—
163C2×C4#6700312yes—
164C8—42no—
165C8—82no—
166C8—882no—
167C22—22no—
168C22—882no—
169C22—884no—
170C22—1762no—
171C22—1762no—
172C22#1062260611yescharacteristic
173C22#1062268011yescharacteristic
174C22#1062268111yescharacteristic
175C4—22no—
176C4—22no—
177C4—1761no—
178C4#1062261612yes—
179C4#1062267012yes—
180C2—21no—
181C2—21no—
182C2—1762no—
183C2#1307003011yescharacteristic
184C2#1307007412yes—
subgroupG/H
centerC22#10622606
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1838C2
socleC22×C11#397
prime radicalC2×#66927C22
hypercenter#1838D11
hypocenterC11#10634
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1838

Complements

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

NH ≅ G/Ntype
3. #13066476C2semidirect
4. #13066461C2semidirect
5. C11×#1838C2semidirect
55. #1838D11semidirect
145. C11#10634semidirect

Maximal subgroups

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

subgroupindex
#130694402
#130672852
#130664762
#130664612
C11×#18382
#1063411