Finite Group Databasebeta

← #14656873

Subgroups — #14656873

Order 2816.

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

normal subgroups only

This group has 400 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#13069593C211yesmaximal, characteristic
2#13067179C212yesmaximal
3#13066474C212yesmaximal
4#13066449C211yesmaximal, characteristic
5C11×#2859C211yesmaximal, characteristic
6C2×C11×#125—21no—
7#10623001C2211yescharacteristic
8C11×#389—24no—
9C11×#384—21no—
10C11×#382C2212yes—
11C43×C11C2211yescharacteristic
12#10622538C2212yes—
13#10622537C2211yescharacteristic
14#10622161—21no—
15#10622161—21no—
16#10622090—24no—
17C11×#125—42no—
18C11×#125—42no—
19C2×C11×C4⋊C4—24no—
20C2×C11×C4⋊C4—24no—
21C2×C11×C4⋊C4—22no—
22C2×C42×C11—22no—
23C2×C42×C11D411yescharacteristic
24C2×C42×C11D411yescharacteristic
25C2×C42×C11C2311yescharacteristic
26#66979—21no—
27#66977—22no—
28C2×#4318—21no—
29#66923—21no—
30#66922Q812yes—
31C4×Dic22—22no—
32C11×#95—22no—
33C11×#95D414yes—
34C22⋊(C11⋊C8)—22no—
35C4⋊(C11⋊C8)—22no—
36C4⋊(C11⋊C8)—22no—
37C4×C11⋊C8—22no—
38#10365—111nomaximal, Sylow
39C22×C4×C11—21no—
40C22×C4×C11—21no—
41C22×C4×C11—24no—
42C22×C4×C11C2×D412yes—
43C22×C4×C11C2×D411yescharacteristic
44C2×Dic22—22no—
45C11×C4⋊C4—48no—
46C11×C4⋊C4—48no—
47C11×C4⋊C4—42no—
48C11×C4⋊C4—42no—
49C42×C11—21no—
50C42×C11—21no—
51C42×C11—44no—
52C42×C11SD1612yes—
53C42×C11Q1612yes—
54C42×C11C2×Q811yescharacteristic
55C42×C11#4111yescharacteristic
56C42×C11#4112yes—
57C22⋊Dic11—41no—
58C4⋊Dic11—22no—
59C4⋊Dic11—22no—
60Dic11⋊C4—42no—
61C4×Dic11—41no—
62#4318—41no—
63#4318—41no—
64C2×C11⋊C8—42no—
65C2×C11⋊C8—41no—
66#2859D1111yescharacteristic
67#1994—111no—
68#1518—112no—
69#1286—112no—
70#1276—111no—
71C23×C11#12011yescharacteristic
72C2×C4×C11—24no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—42no—
76C2×C4×C11—42no—
77C2×C4×C11—48no—
78C2×C4×C11—44no—
79C2×C4×C11C22⋊Q812yes—
80C2×C4×C11C22⋊Q811yescharacteristic
81C2×C4×C11#12412yes—
82C2×C4×C11#12411yescharacteristic
83C2×C4×C11C2×SD1611yescharacteristic
84C2×C4×C11C2×Q1611yescharacteristic
85C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
86C2×C4×C11#13711yescharacteristic
87C2×Dic11—42no—
88Dic22—82no—
89C11⋊C8—82no—
90C11⋊C8—81no—
91#533—111no—
92C2×#125—21no—
93#431—112no—
94#423—111no—
95#389—24no—
96#384—21no—
97#382C2×D1112yes—
98C43C2×D1111yescharacteristic
99#339—221no—
100#339—221no—
101#328—224no—
102C22×C11—22no—
103C22×C11#39311yescharacteristic
104C22×C11#45011yescharacteristic
105C22×C11#45111yescharacteristic
106C4×C11—24no—
107C4×C11—22no—
108C4×C11—22no—
109C4×C11—42no—
110C4×C11—84no—
111C4×C11#47511yescharacteristic
112C4×C11#47711yescharacteristic
113C4×C11#48711yescharacteristic
114C4×C11#48911yescharacteristic
115Dic11—82no—
116C2×M16—221no—
117C4⋊Q8—112no—
118#125—42no—
119#125—42no—
120#125—221no—
121C22⋊Q8—222no—
122C4×Q8—222no—
123#117—221no—
124C2×C4⋊C4—24no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4—22no—
127C2×C42—22no—
128C2×C42C22⋊D1111yescharacteristic
129C2×C42C22⋊D1111yescharacteristic
130C2×C42C22×D1111yescharacteristic
131C4⋊C8—222no—
132C4⋊C8—222no—
133C22⋊C8—222no—
134C4×C8—222no—
135#95—22no—
136#95C22⋊D1114yes—
137C2×C11—21no—
138C2×C11—21no—
139C2×C11#202411yescharacteristic
140C2×C11#203112yes—
141C2×Q8—222no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—24no—
145C22×C4C2×C22⋊D1112yes—
146C22×C4C2×C22⋊D1111yescharacteristic
147M16—441no—
148M16—441no—
149C2×C8—442no—
150C2×C8—441no—
151C4⋊C4—48no—
152C4⋊C4—48no—
153C4⋊C4—42no—
154C4⋊C4—42no—
155C4⋊C4—222no—
156C4⋊C4—222no—
157C4⋊C4—442no—
158C22⋊C4—441no—
159C42—21no—
160C42—21no—
161C42—44no—
162C42—441no—
163C42#432412yes—
164C42#432612yes—
165C42Q8×D1111yescharacteristic
166C42#434311yescharacteristic
167C42#434312yes—
168C11#1036511yescharacteristic, complemented, Sylow
169C23#6700611yescharacteristic
170Q8—882no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—48no—
177C2×C4—44no—
178C2×C4—442no—
179C2×C4#6698511yescharacteristic
180C2×C4C2×#432411yescharacteristic
181C2×C4#6699511yescharacteristic
182C2×C4C2×#432611yescharacteristic
183C2×C4#6699912yes—
184C2×C4#6699911yescharacteristic
185C2×C4#6700012yes—
186C2×C4#6700011yescharacteristic
187C8—882no—
188C8—881no—
189C22—22no—
190C22#1062283111yescharacteristic
191C22#1062284111yescharacteristic
192C22#1062284411yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—84no—
198C4—882no—
199C4#1062270211yescharacteristic
200C4#1062270411yescharacteristic
201C4#1062270611yescharacteristic
202C4#1062270711yescharacteristic
203C2—21no—
204C2—21no—
205C2#1306975411yescharacteristic
206C2#1306978512yes—
subgroupG/H
centerC22#10622844
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2859C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#2859D11
hypocenterC11#10365
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2859

Complements

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

NH ≅ G/Ntype
168. C11#10365semidirect

Maximal subgroups

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

subgroupindex
#130695932
#130671792
#130664742
#130664492
C11×#28592
#1036511