Finite Group Databasebeta

← #14651377

Subgroups — #14651377

Order 2816.

400 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 107 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#13078998C211yesmaximal, characteristic
2#13067354C211yesmaximal, characteristic
3#13067300C212yesmaximal
4#13066507C212yesmaximal
5C11×#2986C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C2×#66922C2211yescharacteristic
8C11×#446—22no—
9C8×Q8×C11—22no—
10C11×#433—22no—
11C11×#431C2212yes—
12#10622706—22no—
13#10622682C414yes—
14#10622617—22no—
15#10622537C2212yes—
16C4×#4318C2211yescharacteristic
17#10622185—22no—
18#10622120—22no—
19#10622120—22no—
20C22×Dic22—21no—
21C11×C4⋊Q8D412yes—
22C11×#125C2×C412yes—
23C11×C22⋊Q8—22no—
24C4×Q8×C11—22no—
25C11×#117D412yes—
26C2×C42×C11C2311yescharacteristic
27C2×C4⋊Dic11—22no—
28C2×#4318—21no—
29C2×#4318—22no—
30#66922—22no—
31#66922—21no—
32#66922C2×C412yes—
33C11×C4⋊C8—24no—
34C11×C4⋊C8D412yes—
35C11×C4⋊C8D412yes—
36C11×C22⋊C8—22no—
37C11×#97—22no—
38C4×C8×C11—22no—
39C4×C8×C11—22no—
40#66874—28no—
41C4⋊(C11⋊C8)—22no—
42C4⋊(C11⋊C8)—22no—
43#66867C2×C412yes—
44C4×C11⋊C8—21no—
45#9436—111nomaximal, Sylow
46C2×Q8×C11—22no—
47C22×C4×C11C2×D411yescharacteristic
48C22×C4×C11#4112yes—
49C22×Dic11—41no—
50C2×Dic22—22no—
51C2×Dic22—44no—
52C2×Dic22—41no—
53C2×C8×C11—22no—
54C2×C8×C11—22no—
55C11×C4⋊C4—24no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4C22⋊C414yes—
58C11×C22⋊C4—22no—
59C42×C11—22no—
60C42×C11C22×C411yescharacteristic
61C42×C11C2×D411yescharacteristic
62C42×C11C2×D412yes—
63C4⋊Dic11—24no—
64C4⋊Dic11—42no—
65#4318—42no—
66#4318—82no—
67C2×C11⋊C8—22no—
68C2×C11⋊C8—42no—
69#3139—111no—
70#2986D1111yescharacteristic
71#1561—111no—
72#1549—112no—
73#1299—112no—
74C23×C11#12311yescharacteristic
75Q8×C11—42no—
76Q8×C11—42no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—24no—
81C2×C4×C11C2×C22⋊C411yescharacteristic
82C2×C4×C11C4×D412yes—
83C2×C4×C11#12011yescharacteristic
84C2×C4×C11#12112yes—
85C2×Dic11—42no—
86C2×Dic11—82no—
87Dic22—44no—
88Dic22—82no—
89C8×C11—42no—
90C8×C11—42no—
91C11⋊C8—42no—
92C11⋊C8—82no—
93#533C2×D1111yescharacteristic
94C2×C4⋊Q8—111no—
95#491—114no—
96#487—222no—
97#446—22no—
98C8×Q8—22no—
99#433—22no—
100#431C2×D1112yes—
101#423—112no—
102#419—222no—
103C4×M16—111no—
104#332—222no—
105#332—222no—
106#332—222no—
107C22×C11—21no—
108C22×C11—22no—
109C22×C11#38611yescharacteristic
110C4×C11—21no—
111C4×C11—22no—
112C4×C11—44no—
113C4×C11#45412yes—
114C4×C11#47112yes—
115C4×C11#47312yes—
116Dic11—82no—
117C22×Q8—221no—
118C2×M16—221no—
119C2×M16—222no—
120C4⋊Q8—112no—
121C4⋊Q8—221no—
122C4⋊Q8—222no—
123C4⋊Q8D4412yes—
124#125C4×D1112yes—
125C22⋊Q8—22no—
126C4×Q8—22no—
127#117C22⋊D1112yes—
128C2×C4⋊C4—222no—
129C2×C42C22×D1111yescharacteristic
130C4⋊C8—24no—
131C4⋊C8—222no—
132C4⋊C8—222no—
133C4⋊C8C22⋊D1112yes—
134C4⋊C8C22⋊D1112yes—
135#103—228no—
136C22⋊C8—22no—
137#97—22no—
138#97—112no—
139C4×C8—22no—
140C4×C8—22no—
141C4×C8—221no—
142C2×C11—41no—
143C2×C11#188811yescharacteristic
144C2×C11#190812yes—
145C2×Q8—22no—
146C2×Q8—222no—
147C2×Q8—444no—
148C2×Q8—441no—
149C22×C4—441no—
150C22×C4#433912yes—
151C22×C4C2×C22⋊D1111yescharacteristic
152M16—442no—
153M16—882no—
154C2×C8—22no—
155C2×C8—22no—
156C2×C8—222no—
157C2×C8—442no—
158C4⋊C4—24no—
159C4⋊C4—22no—
160C4⋊C4—224no—
161C4⋊C4—442no—
162C4⋊C4(C2×D11)⋊C414yes—
163C22⋊C4—22no—
164C42—22no—
165C42C2×C4×D1111yescharacteristic
166C42C2×D4411yescharacteristic
167C42C2×C22⋊D1112yes—
168C11#943611yescharacteristic, complemented, Sylow
169C23#6698211yescharacteristic
170Q8—42no—
171Q8—42no—
172Q8—444no—
173Q8—882no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—442no—
179C2×C4—882no—
180C2×C4C2×(C2×D11)⋊C411yescharacteristic
181C2×C4C4×C22⋊D1112yes—
182C2×C4#6698312yes—
183C2×C4#6700611yescharacteristic
184C8—42no—
185C8—42no—
186C8—442no—
187C8—882no—
188C22—22no—
189C22—21no—
190C22#1062282611yescharacteristic
191C4—22no—
192C4—21no—
193C4—44no—
194C4—882no—
195C4#1062275412yes—
196C4#1062275612yes—
197C4#1062285812yes—
198C2—41no—
199C2#1306901911yescharacteristic
200C2#1306913112yes—
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2986C2
socleC22×C11#386
prime radicalC23×C11#123
cosocleC2×C42×C11C23
hypercenter#2986D11
hypocenterC11#9436
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2986

Complements

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

NH ≅ G/Ntype
168. C11#9436semidirect

Maximal subgroups

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

subgroupindex
#130789982
#130673542
#130673002
#130665072
C11×#29862
#943611