Finite Group Databasebeta

← #14656888

Subgroups — #14656888

Order 2816.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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#13069444C211yesmaximal, characteristic
2#13067175C212yesmaximal
3#13066474C212yesmaximal, complemented
4#13066449C211yesmaximal, characteristic, complemented
5C11×#2864C211yesmaximal, characteristic, complemented
6#10623008C2211yescharacteristic
7C11×#389—22no—
8C11×#387—24no—
9C11×#382C2212yes—
10C43×C11C2211yescharacteristic
11C2×#66869—22no—
12#10622538C2212yes—
13#10622537C2211yescharacteristic
14#10622089—24no—
15C2×#4339—21no—
16C2×C11×C4⋊C4—24no—
17C2×C11×C4⋊C4—22no—
18C2×C42×C11—22no—
19C2×C42×C11D412yes—
20C2×C42×C11C2311yescharacteristic
21#66983—22no—
22C2×#4318—21no—
23#66928—21no—
24#66927Q811yescharacteristic
25C4×D44—22no—
26#66922Q811yescharacteristic
27C11×#95—24no—
28C11×#95—22no—
29C11×#95D414yes—
30C22⋊(C11⋊C8)—22no—
31#66869—44no—
32C4⋊(C11⋊C8)—22no—
33C4⋊(C11⋊C8)—22no—
34C4×C11⋊C8—22no—
35#10368—111nomaximal, Sylow
36C22×C4×C11—22no—
37C22×C4×C11—24no—
38C22×C4×C11C2×D412yes—
39C22×C4×C11C2×D411yescharacteristic
40C2×C22⋊D11—41no—
41#4339—42no—
42#4339—42no—
43C2×D44—21no—
44C2×D44—22no—
45C2×C4×D11—41no—
46C2×Dic22—21no—
47C11×C4⋊C4—48no—
48C11×C4⋊C4—42no—
49C11×C4⋊C4—42no—
50C42×C11—22no—
51C42×C11—22no—
52C42×C11—44no—
53C42×C11C2×Q811yescharacteristic
54C42×C11#4111yescharacteristic
55C42×C11#4112yes—
56(C2×D11)⋊C4—42no—
57C4⋊Dic11—22no—
58#4318—42no—
59C2×C11⋊C8—42no—
60C2×C11⋊C8—41no—
61#2864D1111yescharacteristic, complemented
62#1962—111no—
63#1517—112no—
64#1286—112no—
65#1276—111no—
66C23×C11#12011yescharacteristic
67C22×D11—41no—
68C2×C4×C11—24no—
69C2×C4×C11—42no—
70C2×C4×C11—42no—
71C2×C4×C11—42no—
72C2×C4×C11—48no—
73C2×C4×C11—44no—
74C2×C4×C11C22⋊Q812yes—
75C2×C4×C11C22⋊Q811yescharacteristic
76C2×C4×C11#12412yes—
77C2×C4×C11#12411yescharacteristic
78C2×C4×C11#13512yes—
79C2×C4×C11AGL(1,ℤ/8)12yes—
80C22⋊D11—82no—
81C2×Dic11—41no—
82D44—42no—
83D44—82no—
84C4×D11—81no—
85C4×D11—81no—
86Dic22—42no—
87C11⋊C8—82no—
88C11⋊C8—81no—
89#532—111no—
90#431—112no—
91#423—111no—
92C2×#104—222no—
93#389—22no—
94#387—24no—
95#382C2×D1112yes—
96C43C2×D1111yescharacteristic
97#327—224no—
98C22×C11—22no—
99C22×C11#39311yescharacteristic
100C22×C11#44912yes—
101C2×D11—81no—
102C2×D11—82no—
103C4×C11—22no—
104C4×C11—22no—
105C4×C11—44no—
106C4×C11—84no—
107C4×C11#47812yes—
108C4×C11#48811yescharacteristic
109C4×C11#49011yescharacteristic
110Dic11—81no—
111C2×#41—221no—
112C2×M16—221no—
113C4⋊Q8—111no—
114#127—111no—
115#124—221no—
116#121—222no—
117C4×D4—222no—
118C2×C4⋊C4—24no—
119C2×C4⋊C4—22no—
120C2×C42—22no—
121C2×C42C22⋊D1112yes—
122C2×C42C22×D1111yescharacteristic
123C4⋊C8—222no—
124C4⋊C8—222no—
125#104—444no—
126C22⋊C8—222no—
127C4×C8—222no—
128#95—24no—
129#95—22no—
130#95C22⋊D1114yes—
131C2×C11—22no—
132C2×C11#202511yescharacteristic
133C2×C11#203112yes—
134D11—161no—
135#41—442no—
136#41—442no—
137C2×Q8—221no—
138C2×D4—221no—
139C2×D4—222no—
140C2×D4—441no—
141C22×C4—22no—
142C22×C4—24no—
143C22×C4—441no—
144C22×C4C2×C22⋊D1112yes—
145C22×C4C2×C22⋊D1111yescharacteristic
146M16—442no—
147C2×C8—442no—
148C2×C8—441no—
149C4⋊C4—48no—
150C4⋊C4—42no—
151C4⋊C4—42no—
152C4⋊C4—222no—
153C22⋊C4—442no—
154C42—22no—
155C42—22no—
156C42—44no—
157C42Q8×D1111yescharacteristic
158C42#434311yescharacteristic
159C42#434312yes—
160C11#1036811yescharacteristic, complemented, Sylow
161C23—441no—
162C23#6700611yescharacteristic
163Q8—442no—
164D4—442no—
165D4—882no—
166D4—882no—
167C2×C4—24no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—48no—
172C2×C4—44no—
173C2×C4—441no—
174C2×C4—881no—
175C2×C4—881no—
176C2×C4#6699912yes—
177C2×C4#6699911yescharacteristic
178C2×C4#6700012yes—
179C2×C4#6700011yescharacteristic
180C2×C4#6700212yes—
181C2×C4#6700312yes—
182C8—882no—
183C8—881no—
184C22—22no—
185C22—881no—
186C22—882no—
187C22#1062284411yescharacteristic
188C22#1062285112yes—
189C4—22no—
190C4—22no—
191C4—44no—
192C4—84no—
193C4—881no—
194C4#1062267912yes—
195C4#1062268011yescharacteristic
196C4#1062268111yescharacteristic
197C2—22no—
198C2—1761no—
199C2#1306975911yescharacteristic
200C2#1306978512yes—
subgroupG/H
centerC22#10622844
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2864C2
socleC22×C11#393
prime radical#10623008C22
hypercenter#2864D11
hypocenterC11#10368
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2864

Complements

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

NH ≅ G/Ntype
3. #13066474C2semidirect
4. #13066449C2semidirect
5. C11×#2864C2semidirect
61. #2864D11semidirect
160. C11#10368semidirect

Maximal subgroups

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

subgroupindex
#130694442
#130671752
#130664742
#130664492
C11×#28642
#1036811