Finite Group Databasebeta

← #14663281

Subgroups — #14663281

Order 2816.

270 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 91 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#13070432C212yesmaximal
2#13066569C212yesmaximal
3#13066567C212yesmaximal
4C11×#2960C211yesmaximal, characteristic
5C11×#533C411yescharacteristic
6C11×#446—22no—
7C8×Q8×C11—22no—
8C11×#424C411yescharacteristic
9C11×#424C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#405C411yescharacteristic
12C11×#405C2211yescharacteristic
13C2×C4×C8×C11C411yescharacteristic
14#10622191C2214yes—
15#10622104—22no—
16#10622101—22no—
17C2×C11×M16C2×C411yescharacteristic
18C2×C11×M16C2311yescharacteristic
19C22×C8×C11C2×C411yescharacteristic
20C22×C8×C11C2×C411yescharacteristic
21C11×C4⋊Q8—21no—
22C11×#125—21no—
23C11×C22⋊Q8—22no—
24C4×Q8×C11—22no—
25C11×#117C2×C411yescharacteristic
26C11×#117C2×C411yescharacteristic
27C2×C42×C11C2×C411yescharacteristic
28C11×C4⋊C8—22no—
29C11×C4⋊C8—22no—
30C11×C4⋊C8—22no—
31C11×#97—21no—
32C11×#97D412yes—
33C4×C8×C11—21no—
34C4×C8×C11—21no—
35C4×C8×C11—21no—
36C4×C8×C11D412yes—
37#66876—24no—
38#11539—111nomaximal, Sylow
39C2×Q8×C11—22no—
40C22×C4×C11—21no—
41C22×C4×C11C22×C411yescharacteristic
42C11×M16—41no—
43C11×M16—41no—
44C2×C8×C11—22no—
45C2×C8×C11—21no—
46C2×C8×C11—21no—
47C2×C8×C11—41no—
48C2×C8×C11C22⋊C411yescharacteristic
49C2×C8×C11C22⋊C411yescharacteristic
50C2×C8×C11C2×D412yes—
51C11×C4⋊C4—24no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4—21no—
55C11×C22⋊C4—21no—
56C11×C22⋊C4M1612yes—
57C42×C11—21no—
58C42×C11—21no—
59C42×C11C22⋊C412yes—
60C42×C11M1611yescharacteristic
61C42×C11M1611yescharacteristic
62C11⋊C16—44no—
63#2960D1111yescharacteristic
64#2166—112no—
65#1328—112no—
66#1327—112no—
67C23×C11C2×M1611yescharacteristic
68Q8×C11—44no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—42no—
76C2×C4×C11C2×C22⋊C411yescharacteristic
77C2×C4×C11C2×M1611yescharacteristic
78C8×C11—22no—
79C8×C11—21no—
80C8×C11—41no—
81C8×C11—41no—
82C8×C11#10112yes—
83#533Dic1111yescharacteristic
84#446—22no—
85C8×Q8—22no—
86#424Dic1111yescharacteristic
87#424C2×D1111yescharacteristic
88#423C2×D1111yescharacteristic
89#405Dic1111yescharacteristic
90#405C2×D1111yescharacteristic
91C2×C4×C8Dic1111yescharacteristic
92#364—222no—
93#349—114no—
94#347—222no—
95C22×C11—21no—
96C22×C11—41no—
97C22×C11#40711yescharacteristic
98C4×C11—22no—
99C4×C11—21no—
100C4×C11—41no—
101C4×C11—42no—
102C4×C11—42no—
103C4×C11#41011yescharacteristic
104C4×C11C2×#10111yescharacteristic
105C2×M16C2×Dic1111yescharacteristic
106C2×M16C22×D1111yescharacteristic
107C22×C8C2×Dic1111yescharacteristic
108C22×C8C2×Dic1111yescharacteristic
109C4⋊Q8—21no—
110#125—21no—
111C22⋊Q8—22no—
112C4×Q8—22no—
113#117C2×Dic1111yescharacteristic
114#117C2×Dic1111yescharacteristic
115C2×C42C2×Dic1111yescharacteristic
116M32—224no—
117C4⋊C8—22no—
118C4⋊C8—22no—
119C4⋊C8—22no—
120#97—21no—
121#97C22⋊D1112yes—
122C4×C8—21no—
123C4×C8—21no—
124C4×C8—21no—
125C4×C8C22⋊D1112yes—
126C2×C11—21no—
127C2×C11—41no—
128C2×C11#146711yescharacteristic
129C2×Q8—22no—
130C22×C4—21no—
131C22×C4C22×Dic1111yescharacteristic
132M16—41no—
133M16—41no—
134C2×C8—22no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—41no—
138C2×C8C22⋊Dic1111yescharacteristic
139C2×C8C22⋊Dic1111yescharacteristic
140C2×C8C2×C22⋊D1112yes—
141C4⋊C4—24no—
142C4⋊C4—22no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4#431812yes—
147C42—21no—
148C42—21no—
149C42#431811yescharacteristic
150C42#431811yescharacteristic
151C42C22⋊Dic1112yes—
152C16—444no—
153C11#1153911yescharacteristic, complemented, Sylow
154C23C2×#431811yescharacteristic
155Q8—44no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4C2×#431811yescharacteristic
164C2×C4C2×C22⋊Dic1111yescharacteristic
165C8—21no—
166C8—22no—
167C8—41no—
168C8—41no—
169C8#6690012yes—
170C22—21no—
171C22—41no—
172C22#1062282011yescharacteristic
173C4—22no—
174C4—21no—
175C4—41no—
176C4—42no—
177C4—42no—
178C4C2×#6690011yescharacteristic
179C4#1062285311yescharacteristic
180C2—21no—
181C2—41no—
182C2#1306696011yescharacteristic
subgroupG/H
centerC4#10622853
commutatorC22×C4×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#2960C2
socleC2×C11#1467
prime radicalC23×C11C2×M16
cosocleC2×C11×M16C23
hypercenter#2960D11
hypocenterC11#11539
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C8 ◁ #405 ◁ #2960

Complements

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

NH ≅ G/Ntype
153. C11#11539semidirect

Maximal subgroups

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

subgroupindex
#130704322
#130665692
#130665672
C11×#29602
#1153911