Finite Group Databasebeta

← #14641379

Subgroups — #14641379

Order 2816.

224 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 43 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#13066741C211yesmaximal, characteristic
2#13066548C211yesmaximal, characteristic
3C11×#2094C211yesmaximal, characteristic
4C2×C11×#106—21no—
5C2×C11×#102—21no—
6C11×#390C2211yescharacteristic
7C11×#384C411yescharacteristic, complemented
8C2×#66898—21no—
9C11×#336C411yescharacteristic, complemented
10#10622166—21no—
11C22×D4×C11D411yescharacteristic
12C22×C8×C11—21no—
13C2×C11×C4⋊C4—21no—
14C2×C11×C4⋊C4—41no—
15C2×C11×C4⋊C4D411yescharacteristic
16C2×C11×C22⋊C4—41no—
17C2×C42×C11C2×C411yescharacteristic
18C2×C22⋊Dic11—41no—
19C11×#106—42no—
20C11×#102—42no—
21#66898—22no—
22#66898—41no—
23C22⋊(C11⋊C8)—41no—
24#7435—111nomaximal, Sylow
25C24×C11—21no—
26C2×D4×C11—21no—
27C2×D4×C11—41no—
28C2×D4×C11—41no—
29C2×D4×C11SD1611yescharacteristic
30C2×D4×C11Q1611yescharacteristic
31C22×C4×C11—21no—
32C22×C4×C11—21no—
33C22×C4×C11—41no—
34C22×C4×C11C22⋊C411yescharacteristic
35C22×Dic11—81no—
36C2×C8×C11—22no—
37C2×C8×C11—41no—
38C2×C8×C11—41no—
39C11×C4⋊C4—41no—
40C11×C4⋊C4—41no—
41C11×C4⋊C4—41no—
42C11×C4⋊C4—82no—
43C11×C22⋊C4—82no—
44C42×C11—41no—
45C22⋊Dic11—42no—
46C22⋊Dic11—81no—
47C2×C11⋊C8—81no—
48#2094D1111yescharacteristic
49#1393—111no—
50#1318—111no—
51C23×C11—21no—
52C23×C11—21no—
53C23×C11—41no—
54C23×C11—41no—
55C23×C11—81no—
56C23×C11—81no—
57C23×C11#9911yescharacteristic
58D4×C11—41no—
59D4×C11—41no—
60D4×C11—81no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—22no—
64C2×C4×C11—41no—
65C2×C4×C11—41no—
66C2×C4×C11—41no—
67C2×C4×C11—81no—
68C2×C4×C11—82no—
69C2×C4×C11—81no—
70C2×C4×C11#10311yescharacteristic
71C2×C4×C11#10411yescharacteristic
72C2×Dic11—82no—
73C2×Dic11—161no—
74C2×Dic11—161no—
75C8×C11—42no—
76C11⋊C8—161no—
77C2×#106—21no—
78C2×#102—21no—
79C2×#99—221no—
80#390C2×D1111yescharacteristic
81#384Dic1111yescharacteristic, complemented
82#336Dic1111yescharacteristic, complemented
83#324—221no—
84C22×C11—21no—
85C22×C11—21no—
86C22×C11—41no—
87C22×C11—41no—
88C22×C11—81no—
89C22×C11—81no—
90C22×C11—81no—
91C22×C11—81no—
92C22×C11—161no—
93C22×C11#32811yescharacteristic
94C22×C11#35211yescharacteristic
95C22×C11#35311yescharacteristic
96C4×C11—21no—
97C4×C11—21no—
98C4×C11—42no—
99C4×C11—81no—
100C4×C11—161no—
101Dic11—162no—
102C22×D4C22⋊D1111yescharacteristic
103C22×C8—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4C22⋊D1111yescharacteristic
107C2×C22⋊C4—41no—
108C2×C22⋊C4—441no—
109C2×C42C2×Dic1111yescharacteristic
110#106—42no—
111#102—42no—
112#99—222no—
113#99—441no—
114C22⋊C8—441no—
115C2×C11—21no—
116C2×C11—21no—
117C2×C11—81no—
118C2×C11—81no—
119C2×C11#135211yescharacteristic
120C2×C11#140611yescharacteristic
121C2×C11#140911yescharacteristic
122C24—21no—
123C2×D4—21no—
124C2×D4—41no—
125C2×D4—41no—
126C2×D4#432511yescharacteristic
127C2×D4#432611yescharacteristic
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—41no—
131C22×C4—881no—
132C22×C4C22⋊Dic1111yescharacteristic
133C2×C8—22no—
134C2×C8—41no—
135C2×C8—41no—
136C2×C8—881no—
137C4⋊C4—41no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—82no—
141C22⋊C4—82no—
142C22⋊C4—442no—
143C22⋊C4—881no—
144C42—41no—
145C11#743511yescharacteristic, complemented, Sylow
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—81no—
151C23—81no—
152C23#6689811yescharacteristic
153D4—41no—
154D4—41no—
155D4—81no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—81no—
163C2×C4—82no—
164C2×C4—81no—
165C2×C4—882no—
166C2×C4—1761no—
167C2×C4—1761no—
168C2×C4#6689911yescharacteristic
169C2×C4#6690111yescharacteristic
170C8—42no—
171C8—1761no—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—161no—
181C22#1062217611yescharacteristic
182C22#1062217711yescharacteristic
183C22#1062218311yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—81no—
188C4—161no—
189C4—1762no—
190C2—21no—
191C2—21no—
192C2—81no—
193C2—81no—
194C2#1306664011yescharacteristic
195C2#1306677311yescharacteristic
196C2#1306678111yescharacteristic
subgroupG/H
centerC22#10622183
commutatorC2×C42×C11C2×C4
Frattini#390C2×D11
FittingC11×#2094C2
socleC22×C11#353
prime radicalC22×D4×C11D4
cosocleC11×#390C22
hypercenter#2094D11
hypocenterC11#7435
LCSG ▷ C2×C42×C11 ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #2094

Complements

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

NH ≅ G/Ntype
7. C11×#384C4semidirect
9. C11×#336C4semidirect
81. #384Dic11semidirect
82. #336Dic11semidirect
145. C11#7435semidirect

Maximal subgroups

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

subgroupindex
#130667412
#130665482
C11×#20942
#743511