Finite Group Databasebeta

← #14658784

Subgroups — #14658784

Order 2816.

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

normal subgroups only

This group has 354 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#13069448C211yesmaximal, characteristic
2#13068770C211yesmaximal, characteristic, complemented
3#13067387C212yesmaximal, complemented
4#13067016C212yesmaximal
5C11×#1274C211yesmaximal, characteristic, complemented
6#10623008C2211yescharacteristic
7C11×#431C2212yes—
8C11×#376C2211yescharacteristic
9C2×#66869—22no—
10#10622537C2211yescharacteristic
11C2×C4⋊(C11⋊C8)—22no—
12C2×C4⋊(C11⋊C8)C2212yes—
13#10622097—24no—
14#10622095—24no—
15C2×#4339—21no—
16C2×C42×C11D412yes—
17C2×C42×C11C2311yescharacteristic
18#66983—22no—
19C2×#4318—21no—
20C22×C11⋊C8—22no—
21#66928—21no—
22#66927Q811yescharacteristic
23C4×D44—22no—
24#66922Q811yescharacteristic
25C11×C4⋊C8—22no—
26C11×C22⋊C8—22no—
27C4×C8×C11D414yes—
28C11×#95—22no—
29#66869—44no—
30C4⋊(C11⋊C8)—22no—
31C4⋊(C11⋊C8)—22no—
32C4⋊(C11⋊C8)—22no—
33C4⋊(C11⋊C8)—44no—
34#10666—111nomaximal, Sylow
35C22×C4×C11—22no—
36C22×C4×C11C2×D411yescharacteristic
37C22×C4×C11#4112yes—
38C2×C22⋊D11—41no—
39#4339—42no—
40#4339—42no—
41C2×D44—22no—
42C2×D44—21no—
43C2×C4×D11—41no—
44C2×Dic22—21no—
45C2×C8×C11—24no—
46C42×C11—22no—
47C42×C11SD1614yes—
48C42×C11C2×D412yes—
49C42×C11C2×Q811yescharacteristic
50C42×C11#4111yescharacteristic
51(C2×D11)⋊C4—42no—
52C4⋊Dic11—22no—
53#4318—42no—
54C2×C11⋊C8—42no—
55C2×C11⋊C8—41no—
56C2×C11⋊C8—44no—
57#1963—111no—
58#1843—111no—
59#1570—112no—
60#1480—112no—
61#1274D1111yescharacteristic, complemented
62C23×C11#12311yescharacteristic
63C22×D11—41no—
64C2×C4×C11—24no—
65C2×C4×C11—42no—
66C2×C4×C11—44no—
67C2×C4×C11C22⋊Q812yes—
68C2×C4×C11C22⋊Q811yescharacteristic
69C2×C4×C11#12312yes—
70C2×C4×C11#12711yescharacteristic
71C2×C4×C11C2×SD1612yes—
72C2×C4×C11AGL(1,ℤ/8)12yes—
73C22⋊D11—82no—
74C2×Dic11—41no—
75D44—44no—
76D44—42no—
77C4×D11—81no—
78C4×D11—81no—
79Dic22—42no—
80C8×C11—44no—
81C11⋊C8—81no—
82C11⋊C8—82no—
83#532—111no—
84#431C2×D1112yes—
85#423—111no—
86C2×C4⋊C8—112no—
87C2×C4⋊C8—222no—
88C2×#104—222no—
89#376C2×D1111yescharacteristic
90#334—224no—
91D4⋊C8—224no—
92C22×C11—22no—
93C22×C11#39911yescharacteristic
94C22×C11#48112yes—
95C2×D11—81no—
96C2×D11—82no—
97C4×C11—22no—
98C4×C11—22no—
99C4×C11—44no—
100C4×C11#47612yes—
101C4×C11#49211yescharacteristic
102C4×C11#49611yescharacteristic
103Dic11—81no—
104C2×#41—221no—
105C2×M16—221no—
106C22×C8—222no—
107C4⋊Q8—111no—
108#127—111no—
109#124—221no—
110#121—222no—
111C4×D4—222no—
112C2×C42D4412yes—
113C2×C42C22×D1111yescharacteristic
114C4⋊C8—22no—
115C4⋊C8—222no—
116C4⋊C8—222no—
117C4⋊C8—222no—
118C4⋊C8—444no—
119#104—444no—
120C22⋊C8—22no—
121C4×C8D4414yes—
122#95—22no—
123C2×C11—22no—
124C2×C11#209411yescharacteristic
125C2×C11#209812yes—
126D11—161no—
127#41—442no—
128#41—442no—
129C2×Q8—221no—
130C2×D4—222no—
131C2×D4—221no—
132C2×D4—441no—
133C22×C4—22no—
134C22×C4—441no—
135C22×C4C2×D4411yescharacteristic
136C22×C4#434112yes—
137M16—442no—
138C2×C8—24no—
139C2×C8—442no—
140C2×C8—441no—
141C2×C8—444no—
142C4⋊C4—222no—
143C22⋊C4—442no—
144C42—22no—
145C42#431414yes—
146C42C2×D4412yes—
147C42#434111yescharacteristic
148C42Q8×D1111yescharacteristic
149C11#1066611yescharacteristic, complemented, Sylow
150C23—441no—
151C23#6693911yescharacteristic
152Q8—442no—
153D4—444no—
154D4—442no—
155D4—882no—
156C2×C4—24no—
157C2×C4—42no—
158C2×C4—44no—
159C2×C4—441no—
160C2×C4—881no—
161C2×C4—881no—
162C2×C4#6692711yescharacteristic
163C2×C4#6693912yes—
164C2×C4#6695012yes—
165C2×C4#6695011yescharacteristic
166C2×C4C2×#431412yes—
167C2×C4#6696112yes—
168C8—44no—
169C8—881no—
170C8—882no—
171C22—22no—
172C22—881no—
173C22—882no—
174C22#1062229011yescharacteristic
175C22#1062234812yes—
176C4—22no—
177C4—22no—
178C4—44no—
179C4—881no—
180C4#1062230611yescharacteristic
181C4#1062232511yescharacteristic
182C4#1062245512yes—
183C2—22no—
184C2—1761no—
185C2#1307014811yescharacteristic
186C2#1307017012yes—
subgroupG/H
centerC2×C4#66927
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1274C2
socleC22×C11#399
prime radical#10623008C22
hypercenter#1274D11
hypocenterC11#10666
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
2. #13068770C2semidirect
3. #13067387C2semidirect
5. C11×#1274C2semidirect
61. #1274D11semidirect
149. C11#10666semidirect

Maximal subgroups

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

subgroupindex
#130694482
#130687702
#130673872
#130670162
C11×#12742
#1066611