Finite Group Databasebeta

← #14640992

Subgroups — #14640992

Order 2816.

250 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 75 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#13066940C212yesmaximal
2C11×#1985C211yesmaximal, characteristic
3C2×C4×Q8×C11C2211yescharacteristic
4C2×C11×C4⋊C8C411yescharacteristic
5C2×C11×#97C411yescharacteristic
6#10622538—22no—
7C11×#336—22no—
8#10622166—22no—
9#10622166C414yes—
10C22×Q8×C11Q811yescharacteristic
11C22×C8×C11—21no—
12C22×C8×C11—21no—
13C4×Q8×C11—41no—
14C4×Q8×C11—41no—
15C2×C11×C4⋊C4C2×C412yes—
16C2×C11×C4⋊C4D411yescharacteristic
17C2×C42×C11C2×C411yescharacteristic
18C2×C42×C11D412yes—
19C11×C4⋊C8—41no—
20C11×#97—41no—
21C22⋊(C11⋊C8)—24no—
22C4⋊(C11⋊C8)—42no—
23C4×C11⋊C8—42no—
24#7286—111nomaximal, Sylow
25C2×Q8×C11—24no—
26C2×Q8×C11—41no—
27C22×C4×C11C4211yescharacteristic
28C22×C4×C11C22⋊C411yescharacteristic
29C22×C4×C11C22⋊C412yes—
30C22×C4×C11C4⋊C411yescharacteristic
31C22×C4×C11C4⋊C412yes—
32C2×C8×C11—22no—
33C2×C8×C11—41no—
34C2×C8×C11—42no—
35C2×C8×C11—41no—
36C2×C8×C11—41no—
37C11×C4⋊C4—42no—
38C11×C4⋊C4—41no—
39C42×C11—22no—
40C42×C11—22no—
41C42×C11—21no—
42C42×C11—21no—
43C2×C11⋊C8—44no—
44#1985D1111yescharacteristic
45#1461—112no—
46C23×C11#9511yescharacteristic
47Q8×C11—44no—
48C2×C4×C11—22no—
49C2×C4×C11—22no—
50C2×C4×C11—21no—
51C2×C4×C11—21no—
52C2×C4×C11—22no—
53C2×C4×C11—22no—
54C2×C4×C11—21no—
55C2×C4×C11—21no—
56C2×C4×C11—41no—
57C2×C4×C11—42no—
58C2×C4×C11#9911yescharacteristic
59C2×C4×C11#9911yescharacteristic
60C2×C4×C11#10814yes—
61C8×C11—42no—
62C8×C11—81no—
63C11⋊C8—84no—
64C2×C4×Q8C2×D1111yescharacteristic
65#431—222no—
66C2×C4⋊C8Dic1111yescharacteristic
67C2×#97Dic1111yescharacteristic
68#336—22no—
69#324—114no—
70#324—222no—
71C22×C11—21no—
72C22×C11—21no—
73C22×C11#34112yes—
74C22×C11#34211yescharacteristic
75C4×C11—24no—
76C4×C11—21no—
77C4×C11—41no—
78C4×C11—41no—
79C4×C11—42no—
80C4×C11#35511yescharacteristic
81C4×C11#35611yescharacteristic
82C22×Q8Dic2211yescharacteristic
83C22×C8—21no—
84C22×C8—21no—
85C4×Q8—41no—
86C4×Q8—41no—
87C2×C4⋊C4C4×D1112yes—
88C2×C4⋊C4D4411yescharacteristic
89C2×C42C2×Dic1111yescharacteristic
90C2×C42C22⋊D1112yes—
91C4⋊C8—41no—
92C4⋊C8—442no—
93C22⋊C8—224no—
94#97—41no—
95C4×C8—442no—
96C2×C11—22no—
97C2×C11#129811yescharacteristic
98C2×C11#139111yescharacteristic
99C2×C11#139411yescharacteristic
100C2×Q8—24no—
101C2×Q8—41no—
102C22×C4C4×Dic1111yescharacteristic
103C22×C4Dic11⋊C412yes—
104C22×C4C4⋊Dic1111yescharacteristic
105C22×C4(C2×D11)⋊C412yes—
106C22×C4C22⋊Dic1111yescharacteristic
107C2×C8—22no—
108C2×C8—41no—
109C2×C8—41no—
110C2×C8—42no—
111C2×C8—41no—
112C2×C8—444no—
113C4⋊C4—42no—
114C4⋊C4—41no—
115C42—21no—
116C42—22no—
117C42—22no—
118C42—21no—
119C11#728611yescharacteristic, complemented, Sylow
120C23C11⋊#9511yescharacteristic
121Q8—44no—
122C2×C4—22no—
123C2×C4—22no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—22no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—22no—
130C2×C4—41no—
131C2×C4—42no—
132C2×C4#6688614yes—
133C2×C4#6689811yescharacteristic
134C2×C4#6689811yescharacteristic
135C8—42no—
136C8—81no—
137C8—884no—
138C22—21no—
139C22—21no—
140C22#1062216411yescharacteristic
141C22#1062219612yes—
142C4—24no—
143C4—21no—
144C4—41no—
145C4—42no—
146C4—41no—
147C4#1062218011yescharacteristic
148C4#1062218611yescharacteristic
149C2—22no—
150C2#1306650311yescharacteristic
151C2#1306673711yescharacteristic
152C2#1306674311yescharacteristic
subgroupG/H
centerC2×C4#66898
commutatorC22×C4×C11C42
FrattiniC2×C4×Q8C2×D11
FittingC11×#1985C2
socleC22×C11#342
prime radicalC23×C11#95
cosocleC2×C4×Q8×C11C22
hypercenter#1985D11
hypocenterC11#7286
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1985

Complements

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

NH ≅ G/Ntype
119. C11#7286semidirect

Maximal subgroups

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

subgroupindex
#130669402
C11×#19852
#728611