Finite Group Databasebeta

← #14646767

Subgroups — #14646767

Order 2816.

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

normal subgroups only

This group has 320 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#13077551C211yesmaximal, characteristic
2#13067377C212yesmaximal
3#13067254C211yesmaximal, characteristic
4#13066526C212yesmaximal
5C11×#1537C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C11×#432C2212yes—
8#10622637—22no—
9Q8×C11⋊C8—22no—
10#10622612C412yes—
11#10622610C412yes—
12#10622539C2212yes—
13#10622537C2211yescharacteristic
14C2×C4×C11⋊C8C2211yescharacteristic
15C11×#330—22no—
16#10622181—22no—
17#10622118—22no—
18#10622117—22no—
19C11×C4⋊Q8Q812yes—
20C11×#125D412yes—
21C11×C22⋊Q8—22no—
22C4×Q8×C11—22no—
23C11×#117C2×C412yes—
24C2×C42×C11C2311yescharacteristic
25C2×#4318C2×C412yes—
26C22×C11⋊C8C2×C411yescharacteristic
27C22×C11⋊C8C2×C411yescharacteristic
28C11×C4⋊C8—22no—
29C11×C22⋊C8—22no—
30C11×#97—22no—
31C22⋊(C11⋊C8)—22no—
32C4⋊(C11⋊C8)—22no—
33C4⋊(C11⋊C8)—24no—
34C4⋊(C11⋊C8)—22no—
35#66867—22no—
36#66867—22no—
37C4×C11⋊C8—22no—
38C4×C11⋊C8D412yes—
39C4×C11⋊C8D412yes—
40#8631—111nomaximal, Sylow
41C2×Q8×C11—22no—
42C22×C4×C11C22×C411yescharacteristic
43C22×C4×C11#4112yes—
44C2×C8×C11—42no—
45C11×C4⋊C4—24no—
46C11×C4⋊C4—22no—
47C11×C4⋊C4C4⋊C414yes—
48C11×C22⋊C4—22no—
49C42×C11—22no—
50C42×C11C2×D412yes—
51C42×C11C2×D411yescharacteristic
52C42×C11C2×Q811yescharacteristic
53#4318—42no—
54C2×C11⋊C8—22no—
55C2×C11⋊C8—22no—
56C2×C11⋊C8—41no—
57C2×C11⋊C8—42no—
58C2×C11⋊C8C22⋊C411yescharacteristic
59C2×C11⋊C8C22⋊C412yes—
60C2×C11⋊C8C22⋊C411yescharacteristic
61#2960—111no—
62#1568—112no—
63#1537—111no—
64#1537D1111yescharacteristic
65#1307—112no—
66C23×C11#11711yescharacteristic
67Q8×C11—44no—
68C2×C4×C11—21no—
69C2×C4×C11—21no—
70C2×C4×C11—24no—
71C2×C4×C11—42no—
72C2×C4×C11C2×C22⋊C411yescharacteristic
73C2×C4×C11C2×C4⋊C411yescharacteristic
74C2×C4×C11#12112yes—
75C2×C4×C11C22⋊Q812yes—
76C8×C11—82no—
77C11⋊C8—21no—
78C11⋊C8—22no—
79C11⋊C8—42no—
80C11⋊C8—82no—
81C11⋊C8#10112yes—
82#533C2×D1111yescharacteristic
83#446—222no—
84C8×Q8—222no—
85#432—112no—
86#432C2×D1112yes—
87#424—112no—
88#423—111no—
89#405—112no—
90C2×C4×C8—111no—
91#335—222no—
92#334—222no—
93#330—22no—
94#330—222no—
95C22×C11—21no—
96C22×C11—22no—
97C22×C11#38011yescharacteristic
98C4×C11—21no—
99C4×C11—22no—
100C4×C11—22no—
101C4×C11—44no—
102C4×C11C2×#10111yescharacteristic
103C4×C11#41311yescharacteristic
104C2×M16—112no—
105C22×C8—111no—
106C22×C8—111no—
107C4⋊Q8Dic2212yes—
108#125C22⋊D1112yes—
109C22⋊Q8—22no—
110C4×Q8—22no—
111#117C4×D1112yes—
112C2×C42C22×D1111yescharacteristic
113C4⋊C8—22no—
114C4⋊C8—224no—
115C4⋊C8—222no—
116C4⋊C8—222no—
117C22⋊C8—22no—
118C22⋊C8—222no—
119#97—22no—
120#97—222no—
121#97—222no—
122C4×C8—112no—
123C4×C8—112no—
124C4×C8—222no—
125C2×C11—41no—
126C2×C11#180111yescharacteristic
127C2×C11#181412yes—
128C2×Q8—22no—
129C22×C4C2×C4×D1111yescharacteristic
130C22×C4#434112yes—
131M16—442no—
132C2×C8—42no—
133C2×C8—111no—
134C2×C8—111no—
135C2×C8—112no—
136C2×C8—222no—
137C2×C8—222no—
138C2×C8—441no—
139C2×C8—442no—
140C4⋊C4—22no—
141C4⋊C4—24no—
142C4⋊C4Dic11⋊C414yes—
143C22⋊C4—22no—
144C42—22no—
145C42C2×Dic2211yescharacteristic
146C42D4×D1112yes—
147C42C2×C22⋊D1111yescharacteristic
148C11#863111yescharacteristic, complemented, Sylow
149C23#6693011yescharacteristic
150Q8—44no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—24no—
154C2×C4—42no—
155C2×C4#6693112yes—
156C2×C4C22⋊C4×D1111yescharacteristic
157C2×C4C2×Dic11⋊C411yescharacteristic
158C2×C4#6699212yes—
159C8—82no—
160C8—112no—
161C8—221no—
162C8—222no—
163C8—442no—
164C8—882no—
165C22—21no—
166C22—22no—
167C22#1062255511yescharacteristic
168C4—21no—
169C4—22no—
170C4—22no—
171C4—44no—
172C4D11×#10111yescharacteristic
173C4#1062236411yescharacteristic
174C2—41no—
175C2#1306861011yescharacteristic
176C2#1306866812yes—
subgroupG/H
centerC22#10622555
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1537C2
socleC22×C11#380
prime radicalC23×C11#117
cosocleC2×C42×C11C23
hypercenter#1537D11
hypocenterC11#8631
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1537

Complements

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

NH ≅ G/Ntype
148. C11#8631semidirect

Maximal subgroups

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

subgroupindex
#130775512
#130673772
#130672542
#130665262
C11×#15372
#863111