Finite Group Databasebeta

← #14641167

Subgroups — #14641167

Order 2816.

164 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 39 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#13069596C211yesmaximal, characteristic
2#13066567C211yesmaximal, characteristic
3C11×#1327C211yesmaximal, characteristic
4#10623001C411yescharacteristic
5C11×#423C2211yescharacteristic
6#10622545C411yescharacteristic
7C11×#349—21no—
8#10622193—21no—
9#10622193—21no—
10#10622191—21no—
11C2×C11×M16D411yescharacteristic
12C2×C11×M16D411yescharacteristic
13C2×C42×C11C2×C411yescharacteristic
14#66979—21no—
15#66977—41no—
16C2×C4×Dic11—21no—
17#66923C812yes—
18#66922—21no—
19C4×Dic22—41no—
20C11×M32—41no—
21C11×C4⋊C8—41no—
22C11⋊#95—41no—
23#66876—41no—
24#7360—111nomaximal, Sylow
25C22×C4×C11—21no—
26C22×C4×C11C22⋊C411yescharacteristic
27C22×Dic11—41no—
28C2×Dic22—41no—
29C11×M16—41no—
30C11×M16—41no—
31C2×C8×C11—21no—
32C2×C8×C11—21no—
33C42×C11—21no—
34C42×C11C2×C811yescharacteristic
35C42×C11M1611yescharacteristic
36C22⋊Dic11—41no—
37C4⋊Dic11—22no—
38C4⋊Dic11—41no—
39Dic11⋊C4—42no—
40C4×Dic11—22no—
41C4×Dic11—41no—
42C4×Dic11—41no—
43C11×C16—81no—
44C11⋊C16—81no—
45#1995—111no—
46#1327—111no—
47#1327D1111yescharacteristic
48C23×C11#10011yescharacteristic
49C2×C4×C11—21no—
50C2×C4×C11—21no—
51C2×C4×C11—21no—
52C2×C4×C11—21no—
53C2×C4×C11—81no—
54C2×C4×C11C22⋊C811yescharacteristic
55C2×C4×C11#9911yescharacteristic
56C2×Dic11—42no—
57C2×Dic11—42no—
58C2×Dic11—82no—
59Dic22—82no—
60C8×C11—41no—
61C8×C11—41no—
62#533—111no—
63#423C2×D1111yescharacteristic
64#376—111no—
65#349—21no—
66#349—221no—
67#339—221no—
68#339—221no—
69C22×C11—21no—
70C22×C11—41no—
71C22×C11#32311yescharacteristic
72C4×C11—21no—
73C4×C11—41no—
74C4×C11—41no—
75C4×C11#35411yescharacteristic
76C4×C11#35611yescharacteristic
77Dic11—82no—
78Dic11—82no—
79C2×M16D4411yescharacteristic
80C2×M16C22⋊D1111yescharacteristic
81C4⋊Q8—221no—
82#125—112no—
83C22⋊Q8—441no—
84C4×Q8—441no—
85#117—221no—
86C2×C42—221no—
87C2×C42C4×D1111yescharacteristic
88M32—41no—
89M32—441no—
90C4⋊C8—41no—
91#95—441no—
92C2×C11—21no—
93C2×C11—41no—
94C2×C11#131911yescharacteristic
95C2×Q8—441no—
96C22×C4—21no—
97C22×C4—441no—
98C22×C4(C2×D11)⋊C411yescharacteristic
99M16—41no—
100M16—41no—
101C2×C8—21no—
102C2×C8—21no—
103C4⋊C4—222no—
104C4⋊C4—442no—
105C4⋊C4—441no—
106C22⋊C4—441no—
107C42—21no—
108C42—222no—
109C42—441no—
110C42—441no—
111C42C8×D1111yescharacteristic
112C42#431311yescharacteristic
113C16—81no—
114C16—881no—
115C11#736011yescharacteristic, complemented, Sylow
116C23#6688711yescharacteristic
117Q8—882no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—81no—
123C2×C4—442no—
124C2×C4—442no—
125C2×C4—882no—
126C2×C4#6687011yescharacteristic
127C2×C4(C2×D11)⋊C811yescharacteristic
128C8—41no—
129C8—41no—
130C22—21no—
131C22—41no—
132C22#1062210611yescharacteristic
133C4—21no—
134C4—41no—
135C4—41no—
136C4—882no—
137C4—882no—
138C4#1062211111yescharacteristic
139C4#1062211611yescharacteristic
140C2—21no—
141C2—41no—
142C2#1306654911yescharacteristic
subgroupG/H
centerC4#10622111
commutatorC42×C11C2×C8
Frattini#423C2×D11
FittingC11×#1327C2
socleC2×C11#1319
prime radicalC23×C11#100
cosocleC11×#423C22
hypercenter#1327D11
hypocenterC11#7360
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ #1327

Complements

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

NH ≅ G/Ntype
115. C11#7360semidirect

Maximal subgroups

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

subgroupindex
#130695962
#130665672
C11×#13272
#736011