Finite Group Databasebeta

← #14640402

Subgroups — #14640402

Order 2816.

194 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 51 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#13066540C212yesmaximal
2C11×#1818C211yesmaximal, characteristic
3C2×C11×#117C411yescharacteristic
4C2×C11×C22⋊C8C411yescharacteristic
5C2×C11×C22⋊C8C2211yescharacteristic
6C11×#336—22no—
7C22⋊(C11⋊C16)—22no—
8C23×C4×C11C2×C411yescharacteristic
9C22×C8×C11—21no—
10C22×C8×C11D412yes—
11C11×#117—41no—
12C11×#117—41no—
13C2×C11×C4⋊C4C811yescharacteristic
14C2×C11×C4⋊C4C811yescharacteristic
15C2×C11×C22⋊C4—21no—
16C2×C42×C11—21no—
17C11×C22⋊C8—41no—
18C11×C22⋊C8—41no—
19C2×C11⋊C16—42no—
20#7059—111nomaximal, Sylow
21C24×C11M1611yescharacteristic
22C22×C4×C11—21no—
23C22×C4×C11—21no—
24C22×C4×C11—21no—
25C22×C4×C11—21no—
26C22×C4×C11—42no—
27C22×C4×C11C22⋊C411yescharacteristic
28C22×C4×C11C2×C811yescharacteristic
29C2×C8×C11—22no—
30C2×C8×C11—42no—
31C2×C8×C11—42no—
32C2×C8×C11—41no—
33C11×C4⋊C4—41no—
34C11×C4⋊C4—41no—
35C11×C22⋊C4—42no—
36C42×C11—41no—
37C42×C11—41no—
38C11⋊C16—82no—
39#1818D1111yescharacteristic
40#1314—112no—
41C23×C11—21no—
42C23×C11—22no—
43C23×C11—41no—
44C23×C11—41no—
45C23×C11C22⋊C811yescharacteristic
46C2×C4×C11—22no—
47C2×C4×C11—21no—
48C2×C4×C11—42no—
49C2×C4×C11—42no—
50C2×C4×C11—41no—
51C2×C4×C11—42no—
52C2×C4×C11—41no—
53C2×C4×C11—41no—
54C2×C4×C11—42no—
55C2×C4×C11#9911yescharacteristic
56C2×C4×C11#10011yescharacteristic
57C8×C11—42no—
58C8×C11—81no—
59C2×#117Dic1111yescharacteristic
60C2×C22⋊C8Dic1111yescharacteristic
61C2×C22⋊C8C2×D1111yescharacteristic
62C22⋊C16—222no—
63#336—22no—
64C22×C11—21no—
65C22×C11—21no—
66C22×C11—41no—
67C22×C11—41no—
68C22×C11—41no—
69C22×C11—82no—
70C22×C11#32311yescharacteristic
71C22×C11#35012yes—
72C4×C11—21no—
73C4×C11—41no—
74C4×C11—81no—
75C4×C11—81no—
76C4×C11#35212yes—
77C23×C4C2×Dic1111yescharacteristic
78C22×C8—21no—
79C22×C8C22⋊D1112yes—
80#117—41no—
81#117—41no—
82C2×C4⋊C4C11⋊C811yescharacteristic
83C2×C4⋊C4C11⋊C811yescharacteristic
84C2×C22⋊C4—21no—
85C2×C42—21no—
86C2×C16—442no—
87C22⋊C8—41no—
88C22⋊C8—41no—
89C2×C11—22no—
90C2×C11—81no—
91C2×C11#131511yescharacteristic
92C2×C11#131711yescharacteristic
93C2×C11#132111yescharacteristic
94C24#431811yescharacteristic
95C22×C4—21no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—21no—
99C22×C4—42no—
100C22×C4C2×C11⋊C811yescharacteristic
101C22×C4C22⋊Dic1111yescharacteristic
102C2×C8—22no—
103C2×C8—42no—
104C2×C8—42no—
105C2×C8—41no—
106C4⋊C4—41no—
107C4⋊C4—41no—
108C22⋊C4—42no—
109C42—41no—
110C42—41no—
111C16—882no—
112C11#705911yescharacteristic, complemented, Sylow
113C23—21no—
114C23—22no—
115C23—41no—
116C23—41no—
117C23C22⋊(C11⋊C8)11yescharacteristic
118C2×C4—22no—
119C2×C4—21no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—41no—
123C2×C4—42no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—42no—
127C2×C4#6689711yescharacteristic
128C2×C4#6689811yescharacteristic
129C8—42no—
130C8—81no—
131C22—21no—
132C22—21no—
133C22—41no—
134C22—41no—
135C22—41no—
136C22—82no—
137C22#1062216311yescharacteristic
138C22#1062219912yes—
139C4—21no—
140C4—41no—
141C4—81no—
142C4—81no—
143C4#1062217712yes—
144C2—22no—
145C2—81no—
146C2#1306654211yescharacteristic
147C2#1306654611yescharacteristic
148C2#1306655411yescharacteristic
subgroupG/H
centerC2×C4#66898
commutatorC22×C4×C11C2×C8
FrattiniC2×C22⋊C8C2×D11
FittingC11×#1818C2
socleC22×C11#323
prime radicalC24×C11M16
cosocleC2×C11×C22⋊C8C22
hypercenter#1818D11
hypocenterC11#7059
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1818

Complements

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

NH ≅ G/Ntype
112. C11#7059semidirect

Maximal subgroups

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

subgroupindex
#130665402
C11×#18182
#705911