Finite Group Databasebeta

← #14646802

Subgroups — #14646802

Order 2816.

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

normal subgroups only

This group has 336 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#13077546C211yesmaximal, characteristic
2#13067374C212yesmaximal
3#13067353C212yesmaximal
4C11⋊#1309C211yesmaximal, characteristic
5C11×#1309C211yesmaximal, characteristic
6#10623001C2211yescharacteristic
7C11×#423C2212yes—
8C11×#423C2211yescharacteristic
9#10622735C412yes—
10#10622732C412yes—
11#10622537C2212yes—
12C2×C4×C11⋊C8C2211yescharacteristic
13#10622444—22no—
14#10622443—22no—
15#10622124—22no—
16#10622120—22no—
17#10622117—22no—
18#10622117—22no—
19C2×C11×M16—22no—
20C2×C11×M16C2×C412yes—
21C2×C42×C11C2311yescharacteristic
22#66979C2×C412yes—
23#66977—22no—
24C2×#4318—22no—
25C22×C11⋊C8C2×C411yescharacteristic
26C22×C11⋊C8C2×C411yescharacteristic
27#66923Q812yes—
28#66922D412yes—
29C4×Dic22—22no—
30C11×C4⋊C8—22no—
31C11×C4⋊C8—22no—
32C11×C4⋊C8—22no—
33#66879—22no—
34Dic11⋊C8—24no—
35C8×Dic11—22no—
36C4⋊(C11⋊C8)—22no—
37C4⋊(C11⋊C8)—22no—
38C4×C11⋊C8D412yes—
39C4×C11⋊C8D412yes—
40#8639—111nomaximal, Sylow
41C22×C4×C11C22×C411yescharacteristic
42C22×C4×C11#4112yes—
43C2×Dic22—22no—
44C11×M16—42no—
45C11×M16—82no—
46C2×C8×C11—22no—
47C2×C8×C11—42no—
48C42×C11C2×D412yes—
49C42×C11C2×D411yescharacteristic
50C42×C11C2×Q811yescharacteristic
51C22⋊Dic11—22no—
52C4⋊Dic11—22no—
53C4⋊Dic11C4⋊C414yes—
54Dic11⋊C4—24no—
55C4×Dic11—22no—
56#4318—82no—
57C2×C11⋊C8—22no—
58C2×C11⋊C8—41no—
59C2×C11⋊C8—42no—
60C2×C11⋊C8C22⋊C412yes—
61C2×C11⋊C8C22⋊C411yescharacteristic
62C2×C11⋊C8C22⋊C411yescharacteristic
63#2960—111no—
64#1567—112no—
65#1561—112no—
66#1309—111no—
67#1309D1111yescharacteristic
68C23×C11#11711yescharacteristic
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11C2×C22⋊C411yescharacteristic
74C2×C4×C11C2×C4⋊C411yescharacteristic
75C2×C4×C11#12112yes—
76C2×C4×C11C22⋊Q812yes—
77C2×Dic11—24no—
78Dic22—42no—
79Dic22—42no—
80C8×C11—42no—
81C8×C11—82no—
82C11⋊C8—21no—
83C11⋊C8—22no—
84C11⋊C8—82no—
85C11⋊C8#10112yes—
86#533—111no—
87#446—222no—
88C8×Q8—222no—
89#424—112no—
90#423—112no—
91#423C2×D1112yes—
92#423C2×D1111yescharacteristic
93#405—112no—
94C2×C4×C8—111no—
95#335—222no—
96#335—222no—
97#332—222no—
98#332—222no—
99C22×C11—21no—
100C22×C11—22no—
101C22×C11#38011yescharacteristic
102C4×C11—21no—
103C4×C11—22no—
104C4×C11C2×#10111yescharacteristic
105C4×C11#41311yescharacteristic
106C4×C11#47212yes—
107C4×C11#47312yes—
108Dic11—44no—
109C2×M16—22no—
110C2×M16—222no—
111C2×M16C4×D1112yes—
112C22×C8—111no—
113C22×C8—111no—
114C4⋊Q8—112no—
115#125—112no—
116C22⋊Q8—222no—
117C4×Q8—222no—
118#117—112no—
119C2×C42C22×D1111yescharacteristic
120C4⋊C8—22no—
121C4⋊C8—22no—
122C4⋊C8—22no—
123C4⋊C8—224no—
124C4⋊C8—222no—
125C4⋊C8—222no—
126#97—222no—
127C4×C8—112no—
128C4×C8—112no—
129C4×C8—222no—
130C2×C11—41no—
131C2×C11#180111yescharacteristic
132C2×C11#181612yes—
133C2×Q8—222no—
134C22×C4C2×C4×D1111yescharacteristic
135C22×C4#433912yes—
136M16—42no—
137M16—82no—
138M16—882no—
139C2×C8—22no—
140C2×C8—42no—
141C2×C8—111no—
142C2×C8—111no—
143C2×C8—112no—
144C2×C8—222no—
145C2×C8—441no—
146C2×C8—442no—
147C4⋊C4—114no—
148C4⋊C4—222no—
149C4⋊C4—224no—
150C22⋊C4—222no—
151C42—222no—
152C42D4×D1112yes—
153C42D4×D1111yescharacteristic
154C42Q8×D1111yescharacteristic
155C11#863911yescharacteristic, complemented, Sylow
156C23#6692511yescharacteristic
157Q8—442no—
158Q8—442no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—224no—
164C2×C4C22⋊C4×D1111yescharacteristic
165C2×C4#6693712yes—
166C2×C4C4⋊C4×D1111yescharacteristic
167C2×C4#6694912yes—
168C8—42no—
169C8—82no—
170C8—112no—
171C8—222no—
172C8—221no—
173C8—882no—
174C22—21no—
175C22—22no—
176C22#1062228011yescharacteristic
177C4—21no—
178C4—22no—
179C4—444no—
180C4#1062235811yescharacteristic
181C4#1062236212yes—
182C4D11×#10111yescharacteristic
183C4#1062236812yes—
184C2—41no—
185C2#1306861111yescharacteristic
186C2#1306867912yes—
subgroupG/H
centerC22#10622280
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1309C2
socleC22×C11#380
prime radicalC23×C11#117
cosocleC2×C42×C11C23
hypercenter#1309D11
hypocenterC11#8639
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1309

Complements

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

NH ≅ G/Ntype
155. C11#8639semidirect

Maximal subgroups

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

subgroupindex
#130775462
#130673742
#130673532
C11⋊#13092
C11×#13092
#863911