Finite Group Databasebeta

← #14643031

Subgroups — #14643031

Order 2816.

698 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 95 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#13070149C213yesmaximal, complemented
2#13066437C213yesmaximal, complemented
3C11×#2679C211yesmaximal, characteristic
4C2×C11×#120—23no—
5C11×#394—23no—
6C11×#390C2213yes—
7C2×#66896—23no—
8C2×#66872—23no—
9#10622548C2211yescharacteristic, complemented
10#10622162C2213yescomplemented
11C25×C11—21no—
12C22×D4×C11—23no—
13C22×D4×C11D413yes—
14C11×#120—46no—
15C11×#120—46no—
16C2×C11×C4⋊C4D413yes—
17C2×C11×C22⋊C4—23no—
18C2×C11×C22⋊C4—26no—
19C2×C42×C11C2311yescharacteristic
20C2×C4⋊Dic11—23no—
21C22×C11⋊C8—23no—
22C11×#95—21no—
23#66896—46no—
24#66872—46no—
25#7822—111nomaximal, Sylow
26C24×C11—23no—
27C24×C11—46no—
28C24×C11—83no—
29C24×C11—81no—
30C2×D4×C11—23no—
31C2×D4×C11—43no—
32C2×D4×C11—43no—
33C2×D4×C11—412no—
34C2×D4×C11—83no—
35C2×D4×C11SD1616yes—
36C22×C4×C11—23no—
37C22×C4×C11C2×D413yes—
38C22×Dic11—41no—
39C11×C4⋊C4—43no—
40C11×C22⋊C4—46no—
41C11×C22⋊C4—46no—
42C11×C22⋊C4—46no—
43C42×C11—41no—
44C4⋊Dic11—43no—
45C4⋊Dic11—43no—
46C2×C11⋊C8—26no—
47C2×C11⋊C8—43no—
48C2×C11⋊C8—43no—
49#2679D1111yescharacteristic
50#2094—113no—
51#1270—113no—
52C23×C11—26no—
53C23×C11—46no—
54C23×C11—43no—
55C23×C11—46no—
56C23×C11—43no—
57C23×C11—812no—
58C23×C11—812no—
59C23×C11—84no—
60C23×C11#12011yescharacteristic
61D4×C11—46no—
62D4×C11—83no—
63D4×C11—812no—
64C2×C4×C11—23no—
65C2×C4×C11—23no—
66C2×C4×C11—46no—
67C2×C4×C11—43no—
68C2×C4×C11C2×SD1613yes—
69C2×C4×C11AGL(1,ℤ/8)13yes—
70C2×Dic11—83no—
71C11⋊C8—46no—
72C2×#120—23no—
73C2×#106—223no—
74C2×#102—223no—
75#394—23no—
76#390C2×D1113yes—
77#384—111no—
78#336—113no—
79C22×C11—46no—
80C22×C11—412no—
81C22×C11—816no—
82C22×C11—86no—
83C22×C11—83no—
84C22×C11—83no—
85C22×C11#45013yes—
86C22×C11#45313yes—
87C22×C11#45811yescharacteristic
88C4×C11—23no—
89C4×C11—23no—
90C4×C11—83no—
91Dic11—161no—
92C25—21no—
93C22×D4—23no—
94C22×D4C22⋊D1113yes—
95C22×C8—223no—
96#120—46no—
97#120—46no—
98C2×C4⋊C4—223no—
99C2×C4⋊C4C22⋊D1113yes—
100C2×C22⋊C4—23no—
101C2×C22⋊C4—26no—
102C2×C42C22×D1111yescharacteristic
103#106—446no—
104#102—446no—
105#95—21no—
106C2×C11—86no—
107C2×C11#161313yes—
108C2×C11#162913yes—
109C2×C11#165511yescharacteristic
110C24—23no—
111C24—46no—
112C24—83no—
113C24—81no—
114C2×D4—23no—
115C2×D4—43no—
116C2×D4—43no—
117C2×D4—412no—
118C2×D4—83no—
119C2×D4#432416yes—
120C22×C4—23no—
121C22×C4—441no—
122C22×C4C2×C22⋊D1113yes—
123C2×C8—226no—
124C2×C8—443no—
125C2×C8—443no—
126C4⋊C4—43no—
127C4⋊C4—443no—
128C4⋊C4—443no—
129C22⋊C4—46no—
130C22⋊C4—46no—
131C22⋊C4—46no—
132C42—41no—
133C11#782211yescharacteristic, complemented, Sylow
134C23—26no—
135C23—46no—
136C23—43no—
137C23—46no—
138C23—43no—
139C23—812no—
140C23—812no—
141C23—84no—
142C23#6700611yescharacteristic
143D4—46no—
144D4—83no—
145D4—812no—
146C2×C4—23no—
147C2×C4—23no—
148C2×C4—46no—
149C2×C4—43no—
150C2×C4—883no—
151C2×C4#6698513yes—
152C2×C4C2×#432413yes—
153C8—446no—
154C22—46no—
155C22—412no—
156C22—816no—
157C22—86no—
158C22—83no—
159C22—83no—
160C22#1062283113yes—
161C22#1062285413yes—
162C22#1062285611yescharacteristic
163C4—23no—
164C4—23no—
165C4—83no—
166C4—1761no—
167C2—86no—
168C2#1306763613yes—
169C2#1306773213yes—
170C2#1306790511yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#2679C2
socleC23×C11#120
hypercenter#2679D11
hypocenterC11#7822
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2679

Complements

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

NH ≅ G/Ntype
1. #13070149C2semidirect
2. #13066437C2semidirect
9. #10622548C22semidirect
10. #10622162C22semidirect
133. C11#7822semidirect

Maximal subgroups

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

subgroupindex
#130701492
#130664372
C11×#26792
#782211