Finite Group Databasebeta

← #14646790

Subgroups — #14646790

Order 2816.

404 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 101 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#13077327C211yesmaximal, characteristic
2#13067371C212yesmaximal, complemented
3#13067349C212yesmaximal
4C11⋊#1309C211yesmaximal, characteristic, complemented
5C11×#1309C211yesmaximal, characteristic, complemented
6C2×#66960C412yes—
7#10623008C2211yescharacteristic
8C11×#423C2212yes—
9C11×#423C2211yescharacteristic
10#10622742C412yes—
11#10622537C2212yes—
12C2×C4×C11⋊C8C2211yescharacteristic
13#10622451—22no—
14#10622447—22no—
15#10622123—22no—
16#10622119—22no—
17#10622118—22no—
18#10622118—22no—
19C2×#4339C2×C412yes—
20C2×C11×M16—22no—
21C2×C11×M16C2×C412yes—
22C2×C42×C11C2311yescharacteristic
23#66983—22no—
24C2×#4318—22no—
25C22×C11⋊C8C2×C411yescharacteristic
26C22×C11⋊C8C2×C411yescharacteristic
27#66960—44no—
28C2×#4313—22no—
29C2×C8×D11—22no—
30#66928Q812yes—
31#66927D411yescharacteristic
32C4×D44—22no—
33#66922D411yescharacteristic
34C11×C4⋊C8—22no—
35C11×C4⋊C8—22no—
36C11×C4⋊C8—22no—
37(C2×D11)⋊C8—24no—
38C4⋊(C11⋊C8)—22no—
39C4⋊(C11⋊C8)—22no—
40C4×C11⋊C8D412yes—
41C4×C11⋊C8D412yes—
42#8636—111nomaximal, Sylow
43C22×C4×C11C22×C411yescharacteristic
44C22×C4×C11#4112yes—
45C2×C22⋊D11—22no—
46#4339—42no—
47#4339—42no—
48C2×D44—22no—
49C2×D44C4⋊C412yes—
50C2×C4×D11—22no—
51C2×Dic22C4⋊C412yes—
52C11×M16—42no—
53C11×M16—82no—
54C2×C8×C11—22no—
55C2×C8×C11—42no—
56C42×C11C2×D412yes—
57C42×C11C2×D411yescharacteristic
58C42×C11C2×Q811yescharacteristic
59(C2×D11)⋊C4—24no—
60C4⋊Dic11—22no—
61#4318—82no—
62C2×C11⋊C8—22no—
63C2×C11⋊C8—41no—
64C2×C11⋊C8—42no—
65C2×C11⋊C8C22⋊C412yes—
66C2×C11⋊C8C22⋊C411yescharacteristic
67C2×C11⋊C8C22⋊C411yescharacteristic
68#4313—44no—
69C8×D11—44no—
70#2931—111no—
71#1566—112no—
72#1560—112no—
73#1309—111no—
74#1309D1111yescharacteristic, complemented
75C23×C11#11711yescharacteristic
76C22×D11—22no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11C2×C22⋊C411yescharacteristic
82C2×C4×C11C2×C4⋊C411yescharacteristic
83C2×C4×C11#12112yes—
84C2×C4×C11C22⋊Q812yes—
85C22⋊D11—44no—
86C2×Dic11—22no—
87D44—42no—
88D44—42no—
89D44—42no—
90C4×D11—42no—
91C4×D11—42no—
92Dic22—42no—
93C8×C11—42no—
94C8×C11—82no—
95C11⋊C8—21no—
96C11⋊C8—22no—
97C11⋊C8—82no—
98C11⋊C8#10012yes—
99C2×#131—112no—
100#532—111no—
101#436—222no—
102C8×D4—222no—
103#423—112no—
104#423C2×D1112yes—
105#423C2×D1111yescharacteristic
106#408—112no—
107C2×C4×C8—111no—
108#334—222no—
109#334—222no—
110#333—222no—
111#331—222no—
112C22×C11—21no—
113C22×C11—22no—
114C22×C11#38011yescharacteristic
115C2×D11—42no—
116C2×D11—44no—
117C4×C11—21no—
118C4×C11—22no—
119C4×C11C2×#10011yescharacteristic
120C4×C11#41311yescharacteristic
121C4×C11#47112yes—
122C4×C11#47112yes—
123Dic11—42no—
124C2×#41—112no—
125#131—444no—
126C2×M16—22no—
127C2×M16—222no—
128C2×M16—222no—
129C2×M16C4×D1112yes—
130C22×C8—111no—
131C22×C8—111no—
132C22×C8—222no—
133C4⋊Q8—111no—
134#127—111no—
135#124—112no—
136#121—222no—
137C4×D4—222no—
138C2×C42C22×D1111yescharacteristic
139C4⋊C8—22no—
140C4⋊C8—22no—
141C4⋊C8—22no—
142C4⋊C8—222no—
143C4⋊C8—222no—
144C22⋊C8—224no—
145C4×C8—112no—
146C4×C8—112no—
147C2×C11—41no—
148C2×C11#180011yescharacteristic
149C2×C11#181512yes—
150D11—82no—
151#41—442no—
152#41—442no—
153C2×Q8—112no—
154C2×D4—112no—
155C2×D4—222no—
156C2×D4—222no—
157C22×C4—222no—
158C22×C4C2×C4×D1111yescharacteristic
159C22×C4#433912yes—
160M16—42no—
161M16—82no—
162M16—444no—
163M16—882no—
164C2×C8—22no—
165C2×C8—42no—
166C2×C8—111no—
167C2×C8—112no—
168C2×C8—111no—
169C2×C8—222no—
170C2×C8—444no—
171C2×C8—441no—
172C2×C8—442no—
173C4⋊C4—222no—
174C22⋊C4—224no—
175C42D4×D1112yes—
176C42D4×D1111yescharacteristic
177C42Q8×D1111yescharacteristic
178C11#863611yescharacteristic, complemented, Sylow
179C23—222no—
180C23#6692511yescharacteristic
181Q8—442no—
182D4—442no—
183D4—444no—
184D4—442no—
185D4—442no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—222no—
191C2×C4—442no—
192C2×C4—442no—
193C2×C4C22⋊C4×D1111yescharacteristic
194C2×C4#6693712yes—
195C2×C4C4⋊C4×D1111yescharacteristic
196C2×C4#6694912yes—
197C8—42no—
198C8—82no—
199C8—112no—
200C8—221no—
201C8—222no—
202C8—882no—
203C22—21no—
204C22—22no—
205C22—442no—
206C22—444no—
207C22#1062228011yescharacteristic
208C4—21no—
209C4—22no—
210C4—442no—
211C4D11×#10011yescharacteristic
212C4#1062236112yes—
213C4#1062236411yescharacteristic
214C4#1062236712yes—
215C2—41no—
216C2—882no—
217C2#1306860711yescharacteristic
218C2#1306867412yes—
subgroupG/H
centerC22#10622280
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1309C2
socleC22×C11#380
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1309D11
hypocenterC11#8636
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1309

Complements

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

NH ≅ G/Ntype
2. #13067371C2semidirect
4. C11⋊#1309C2semidirect
5. C11×#1309C2semidirect
74. #1309D11semidirect
178. C11#8636semidirect

Maximal subgroups

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

subgroupindex
#130773272
#130673712
#130673492
C11⋊#13092
C11×#13092
#863611