Finite Group Databasebeta

← #14656842

Subgroups — #14656842

Order 2816.

484 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 93 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#13069439C213yesmaximal
2#13066497C213yesmaximal, complemented
3C11×#2844C211yesmaximal, characteristic, complemented
4C2×#66927C2211yescharacteristic
5C11×#400—23no—
6C11×#395—23no—
7C11×#382C2213yes—
8C2×#66873—23no—
9C2×#66873—23no—
10C2×#66867C2213yes—
11C22×Q8×C11—21no—
12C22×D44—23no—
13C2×C11×C4⋊C4—23no—
14C2×C11×C4⋊C4D413yes—
15C2×C11×C4⋊C4D413yes—
16C2×C42×C11C2311yescharacteristic
17C22×C11⋊C8—23no—
18#66927—23no—
19#66927Q812yescomplemented
20C11×#95—23no—
21C11×#95—21no—
22C11×#95—26no—
23#66873—46no—
24#66873—46no—
25#66867—26no—
26#10358—111nomaximal, Sylow
27C23×D11—41no—
28C2×Q8×C11—83no—
29C22×C4×C11—23no—
30C22×C4×C11—23no—
31C22×C4×C11C2×D413yes—
32C2×D44—26no—
33C2×D44—43no—
34C2×D44—43no—
35C2×D44—43no—
36C2×D44—43no—
37C2×D44—43no—
38C11×C4⋊C4—43no—
39C11×C4⋊C4—43no—
40C11×C4⋊C4—83no—
41C42×C11C2×Q811yescharacteristic
42C42×C11#4113yes—
43C2×C11⋊C8—26no—
44C2×C11⋊C8—43no—
45C2×C11⋊C8—43no—
46#2844D1111yescharacteristic, complemented
47#1961—113no—
48#1295—113no—
49C23×C11#12011yescharacteristic
50C22×D11—42no—
51C22×D11—83no—
52C22×D11—83no—
53Q8×C11—84no—
54C2×C4×C11—23no—
55C2×C4×C11—23no—
56C2×C4×C11—43no—
57C2×C4×C11—43no—
58C2×C4×C11—46no—
59C2×C4×C11—46no—
60C2×C4×C11C22⋊Q813yes—
61C2×C4×C11#12413yes—
62D44—46no—
63D44—46no—
64D44—83no—
65D44—83no—
66C11⋊C8—46no—
67C2×#127—111no—
68C2×#102—223no—
69C2×#102—223no—
70C2×#97—113no—
71#400—23no—
72#395—23no—
73#382C2×D1113yes—
74C22×C11#39311yescharacteristic
75C22×C11#45313yes—
76C22×C11#45413yes—
77C2×D11—86no—
78C2×D11—161no—
79C2×D11—163no—
80C4×C11—23no—
81C4×C11—23no—
82C4×C11—83no—
83C4×C11—83no—
84C22×Q8—21no—
85C22×D4—223no—
86C22×C8—223no—
87#127—112no—
88#127—223no—
89C2×C4⋊C4—23no—
90C2×C4⋊C4C22⋊D1113yes—
91C2×C4⋊C4C22⋊D1113yes—
92C2×C42C22×D1111yescharacteristic
93#102—446no—
94#102—446no—
95#97—226no—
96#95—23no—
97#95—21no—
98#95—26no—
99C2×C11#165511yescharacteristic
100C2×C11#165713yes—
101C2×C11#202713yes—
102D11—162no—
103C24—441no—
104C2×Q8—83no—
105C2×D4—226no—
106C2×D4—443no—
107C2×D4—443no—
108C2×D4—443no—
109C2×D4—443no—
110C2×D4—443no—
111C22×C4—23no—
112C22×C4—23no—
113C22×C4C2×C22⋊D1113yes—
114C2×C8—226no—
115C2×C8—443no—
116C2×C8—443no—
117C4⋊C4—43no—
118C4⋊C4—43no—
119C4⋊C4—83no—
120C42Q8×D1111yescharacteristic
121C42#434313yes—
122C11#1035811yescharacteristic, complemented, Sylow
123C23—442no—
124C23—883no—
125C23—883no—
126C23#6700611yescharacteristic
127Q8—84no—
128D4—446no—
129D4—446no—
130D4—883no—
131D4—883no—
132C2×C4—23no—
133C2×C4—23no—
134C2×C4—43no—
135C2×C4—43no—
136C2×C4—46no—
137C2×C4—46no—
138C2×C4#6699913yes—
139C2×C4#6700013yes—
140C8—446no—
141C22—886no—
142C22—1761no—
143C22—1763no—
144C22#1062284411yescharacteristic
145C22#1062285413yes—
146C22#1062285813yes—
147C4—23no—
148C4—23no—
149C4—83no—
150C4—83no—
151C2—1762no—
152C2#1306790511yescharacteristic
153C2#1306791413yes—
154C2#1306976913yes—
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2844C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenter#2844D11
hypocenterC11#10358
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2844

Complements

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

NH ≅ G/Ntype
2. #13066497C2semidirect
3. C11×#2844C2semidirect
19. #66927Q8semidirect
46. #2844D11semidirect
122. C11#10358semidirect

Maximal subgroups

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

subgroupindex
#130694392
#130664972
C11×#28442
#1035811