Finite Group Databasebeta

← #14646801

Subgroups — #14646801

Order 2816.

336 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 109 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#13077551C211yesmaximal, characteristic
2#13067374C212yesmaximal
3#13067354C211yesmaximal, characteristic
4C11⋊#1309C212yesmaximal
5C11×#1561C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C11×#423C2212yes—
8#10622637—22no—
9Q8×C11⋊C8—22no—
10#10622612C412yes—
11#10622610C412yes—
12#10622537C2212yes—
13#10622537C2211yescharacteristic
14C2×C4×C11⋊C8C2211yescharacteristic
15C11×#332—22no—
16#10622185—22no—
17#10622117—22no—
18#10622117—22no—
19C2×C11×M16—22no—
20C11×C4⋊Q8D412yes—
21C11×#125Q812yes—
22C11×C22⋊Q8—22no—
23C4×Q8×C11—22no—
24C11×#117C2×C412yes—
25C2×C42×C11C2311yescharacteristic
26C2×#4318—22no—
27C2×#4318C2×C412yes—
28C22×C11⋊C8C2×C411yescharacteristic
29C22×C11⋊C8C2×C411yescharacteristic
30C11×C4⋊C8—22no—
31C11×C4⋊C8—22no—
32C4⋊(C11⋊C8)—22no—
33C4⋊(C11⋊C8)—24no—
34C4⋊(C11⋊C8)—22no—
35C4⋊(C11⋊C8)—22no—
36#66867—22no—
37C4×C11⋊C8—22no—
38C4×C11⋊C8D412yes—
39C4×C11⋊C8D412yes—
40#8639—111nomaximal, Sylow
41C2×Q8×C11—22no—
42C22×C4×C11C22×C411yescharacteristic
43C22×C4×C11#4112yes—
44C11×M16—82no—
45C2×C8×C11—42no—
46C11×C4⋊C4—22no—
47C11×C4⋊C4—24no—
48C11×C4⋊C4C4⋊C414yes—
49C11×C22⋊C4—22no—
50C42×C11—22no—
51C42×C11C2×D412yes—
52C42×C11C2×D411yescharacteristic
53C42×C11C2×Q811yescharacteristic
54#4318—42no—
55#4318—82no—
56C2×C11⋊C8—22no—
57C2×C11⋊C8—22no—
58C2×C11⋊C8—41no—
59C2×C11⋊C8—42no—
60C2×C11⋊C8C22⋊C411yescharacteristic
61C2×C11⋊C8C22⋊C412yes—
62C2×C11⋊C8C22⋊C411yescharacteristic
63#2960—111no—
64#1567—112no—
65#1561—111no—
66#1561D1111yescharacteristic
67#1309—112no—
68C23×C11#11711yescharacteristic
69Q8×C11—42no—
70Q8×C11—42no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—24no—
76C2×C4×C11C2×C22⋊C411yescharacteristic
77C2×C4×C11C2×C4⋊C411yescharacteristic
78C2×C4×C11#12112yes—
79C2×C4×C11C22⋊Q812yes—
80C8×C11—82no—
81C11⋊C8—21no—
82C11⋊C8—22no—
83C11⋊C8—42no—
84C11⋊C8—82no—
85C11⋊C8#10112yes—
86#533C2×D1111yescharacteristic
87#446—222no—
88C8×Q8—222no—
89#424—112no—
90#423—111no—
91#423—112no—
92#423C2×D1112yes—
93#405—112no—
94C2×C4×C8—111no—
95#335—222no—
96#335—222no—
97#332—22no—
98#332—222no—
99C22×C11—21no—
100C22×C11—22no—
101C22×C11#38011yescharacteristic
102C4×C11—21no—
103C4×C11—22no—
104C4×C11—44no—
105C4×C11C2×#10111yescharacteristic
106C4×C11#41311yescharacteristic
107C4×C11#47212yes—
108C4×C11#47312yes—
109C2×M16—22no—
110C2×M16—112no—
111C2×M16—222no—
112C22×C8—111no—
113C22×C8—111no—
114C4⋊Q8C22⋊D1112yes—
115#125Dic2212yes—
116C22⋊Q8—22no—
117C4×Q8—22no—
118#117C4×D1112yes—
119C2×C42C22×D1111yescharacteristic
120C4⋊C8—22no—
121C4⋊C8—22no—
122C4⋊C8—224no—
123C4⋊C8—222no—
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—22no—
134C22×C4C2×C4×D1111yescharacteristic
135C22×C4#434112yes—
136M16—82no—
137M16—442no—
138M16—882no—
139C2×C8—42no—
140C2×C8—111no—
141C2×C8—111no—
142C2×C8—112no—
143C2×C8—222no—
144C2×C8—222no—
145C2×C8—441no—
146C2×C8—442no—
147C4⋊C4—24no—
148C4⋊C4—22no—
149C4⋊C4Dic11⋊C414yes—
150C22⋊C4—22no—
151C42—22no—
152C42C2×Dic2211yescharacteristic
153C42D4×D1112yes—
154C42C2×C22⋊D1111yescharacteristic
155C11#863911yescharacteristic, complemented, Sylow
156C23#6693011yescharacteristic
157Q8—42no—
158Q8—42no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—24no—
164C2×C4#6693112yes—
165C2×C4C22⋊C4×D1111yescharacteristic
166C2×C4C2×Dic11⋊C411yescharacteristic
167C2×C4#6699212yes—
168C8—82no—
169C8—112no—
170C8—221no—
171C8—222no—
172C8—442no—
173C8—882no—
174C22—21no—
175C22—22no—
176C22#1062255511yescharacteristic
177C4—21no—
178C4—22no—
179C4—44no—
180C4D11×#10111yescharacteristic
181C4#1062236411yescharacteristic
182C4#1062281212yes—
183C4#1062281712yes—
184C2—41no—
185C2#1306861011yescharacteristic
186C2#1306867812yes—
subgroupG/H
centerC22#10622555
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1561C2
socleC22×C11#380
prime radicalC23×C11#117
cosocleC2×C42×C11C23
hypercenter#1561D11
hypocenterC11#8639
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1561

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
#130775512
#130673742
#130673542
C11⋊#13092
C11×#15612
#863911