Finite Group Databasebeta

← #14651293

Subgroups — #14651293

Order 2816.

384 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 95 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#13077722C211yesmaximal, characteristic
3#13067332C212yesmaximal
4#13066489C212yesmaximal
5C11×#1537C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C2×#66922C2211yescharacteristic
8C11×#432C2212yes—
9#10622706C414yes—
10#10622682—22no—
11#10622637—24no—
12#10622617—22no—
13#10622613—22no—
14#10622539C2212yes—
15C4×#4318C2211yescharacteristic
16C11×#330—22no—
17#10622124—24no—
18C22×Dic22—21no—
19C11×C4⋊Q8C2×C412yes—
20C11×#125D412yes—
21C11×C22⋊Q8—22no—
22C4×Q8×C11—22no—
23C11×#117D412yes—
24C2×C42×C11C2311yescharacteristic
25C2×C4⋊Dic11—22no—
26C2×#4318—21no—
27#66922—22no—
28#66922—21no—
29#66922C2×C412yes—
30C11×C4⋊C8—22no—
31C11×C22⋊C8—22no—
32C11×#97—22no—
33C22⋊(C11⋊C8)—22no—
34#66874—28no—
35C4⋊(C11⋊C8)—24no—
36C4⋊(C11⋊C8)D414yes—
37#66867—22no—
38#66867—21no—
39#66867—22no—
40C4×C11⋊C8—22no—
41C4×C11⋊C8C2×C412yes—
42#9422—111nomaximal, Sylow
43C2×Q8×C11—22no—
44C22×C4×C11C2×D411yescharacteristic
45C22×C4×C11#4112yes—
46C22×Dic11—41no—
47C2×Dic22—22no—
48C2×Dic22—44no—
49C2×Dic22—41no—
50C2×C8×C11—42no—
51C11×C4⋊C4—22no—
52C11×C4⋊C4—24no—
53C11×C4⋊C4C22⋊C414yes—
54C11×C22⋊C4—22no—
55C42×C11—22no—
56C42×C11C22×C411yescharacteristic
57C42×C11C2×D411yescharacteristic
58C42×C11C2×D412yes—
59C4⋊Dic11—24no—
60C4⋊Dic11—42no—
61#4318—42no—
62C2×C11⋊C8—22no—
63C2×C11⋊C8—24no—
64#3139—111no—
65#2987—111no—
66#1556—112no—
67#1537D1111yescharacteristic
68#1291—112no—
69C23×C11#12311yescharacteristic
70Q8×C11—82no—
71C2×C4×C11—22no—
72C2×C4×C11—24no—
73C2×C4×C11—42no—
74C2×C4×C11C2×C22⋊C411yescharacteristic
75C2×C4×C11C4×D412yes—
76C2×C4×C11#12011yescharacteristic
77C2×C4×C11#12112yes—
78C2×Dic11—42no—
79C2×Dic11—82no—
80Dic22—44no—
81Dic22—82no—
82C8×C11—82no—
83C11⋊C8—42no—
84C11⋊C8—44no—
85#533C2×D1111yescharacteristic
86C2×C4⋊Q8—111no—
87#491—222no—
88#487—114no—
89#446—224no—
90#433—222no—
91#432—112no—
92#432C2×D1112yes—
93#419—222no—
94C4×M16—111no—
95#332—224no—
96#330—22no—
97C22×C11—21no—
98C22×C11—22no—
99C22×C11#38611yescharacteristic
100C4×C11—21no—
101C4×C11—22no—
102C4×C11—22no—
103C4×C11—44no—
104C4×C11#45412yes—
105Dic11—82no—
106C22×Q8—221no—
107C2×M16—221no—
108C4⋊Q8—112no—
109C4⋊Q8—222no—
110C4⋊Q8—221no—
111C4⋊Q8C4×D1112yes—
112#125C22⋊D1112yes—
113C22⋊Q8—22no—
114C4×Q8—22no—
115#117D4412yes—
116C2×C4⋊C4—222no—
117C2×C42C22×D1111yescharacteristic
118C4⋊C8—22no—
119C4⋊C8—114no—
120C4⋊C8—224no—
121#103—228no—
122C22⋊C8—22no—
123C22⋊C8—222no—
124#97—22no—
125#97—222no—
126#97—222no—
127#97—221no—
128C4×C8—112no—
129C4×C8—222no—
130C2×C11—41no—
131C2×C11#188811yescharacteristic
132C2×C11#190212yes—
133C2×Q8—22no—
134C2×Q8—222no—
135C2×Q8—444no—
136C2×Q8—441no—
137C22×C4—441no—
138C22×C4C2×D4411yescharacteristic
139C22×C4#434112yes—
140M16—442no—
141C2×C8—42no—
142C2×C8—224no—
143C2×C8—222no—
144C4⋊C4—22no—
145C4⋊C4—24no—
146C4⋊C4—224no—
147C4⋊C4—442no—
148C4⋊C4(C2×D11)⋊C414yes—
149C22⋊C4—22no—
150C42—22no—
151C42C2×C4×D1111yescharacteristic
152C42D4×D1112yes—
153C42C2×C22⋊D1111yescharacteristic
154C11#942211yescharacteristic, complemented, Sylow
155C23#6693911yescharacteristic
156Q8—82no—
157Q8—444no—
158Q8—882no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—42no—
162C2×C4—442no—
163C2×C4—882no—
164C2×C4(C22⋊D11)⋊C412yes—
165C2×C4#6693511yescharacteristic
166C2×C4C2×(C2×D11)⋊C411yescharacteristic
167C2×C4#6699212yes—
168C8—82no—
169C8—442no—
170C8—444no—
171C22—22no—
172C22—21no—
173C22#1062257111yescharacteristic
174C4—22no—
175C4—22no—
176C4—21no—
177C4—44no—
178C4—882no—
179C4#1062236612yes—
180C2—41no—
181C2#1306901711yescharacteristic
182C2#1306908712yes—
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1537C2
socleC22×C11#386
prime radicalC23×C11#123
cosocleC2×C42×C11C23
hypercenter#1537D11
hypocenterC11#9422
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1537

Complements

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

NH ≅ G/Ntype
154. C11#9422semidirect

Maximal subgroups

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

subgroupindex
#130789982
#130777222
#130673322
#130664892
C11×#15372
#942211