Finite Group Databasebeta

← #14673457

Subgroups — #14673457

Order 2816.

416 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 81 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#13068830C213yesmaximal
2#13066743C213yesmaximal
3C11×#2811C211yesmaximal, characteristic
4#10623343C2211yescharacteristic
5C11×#395—23no—
6C11×#391—23no—
7C11×#391C2213yes—
8C2×#66900C2213yes—
9#10622577—23no—
10#10622161—23no—
11C22×Q8×C11—21no—
12C22×Q8×C11—21no—
13C22×Q8×C11C2311yescharacteristic
14C2×C11×C4⋊C4—23no—
15C2×C11×C4⋊C4D413yes—
16C2×C42×C11D413yes—
17Q8×Dic11—41no—
18Q8×Dic11—41no—
19#66979—23no—
20C2×#4318—23no—
21C11×#95—23no—
22C11×#95—26no—
23#66900—23no—
24#66900Q816yescomplemented
25#66872—43no—
26#66871—43no—
27#13464—111nomaximal, Sylow
28C2×Q8×C11—24no—
29C2×Q8×C11—41no—
30C2×Q8×C11—41no—
31C2×Q8×C11—81no—
32C2×Q8×C11—81no—
33C2×Q8×C11—82no—
34C2×Q8×C11—81no—
35C2×Q8×C11C2×Q813yes—
36C2×Q8×C11#4111yescharacteristic
37C22×C4×C11—23no—
38C22×C4×C11—23no—
39C22×C4×C11C2×D413yes—
40C11×C4⋊C4—43no—
41C11×C4⋊C4—83no—
42C42×C11—43no—
43C22⋊Dic11—41no—
44C4⋊Dic11—23no—
45C4⋊Dic11—23no—
46C4×Dic11—43no—
47#4318—26no—
48#4318—43no—
49C2×C11⋊C8—43no—
50#2811D1111yescharacteristic
51#1857—113no—
52#1394—113no—
53C23×C11#12011yescharacteristic
54Q8×C11—43no—
55Q8×C11—41no—
56Q8×C11—84no—
57Q8×C11—84no—
58C2×C4×C11—23no—
59C2×C4×C11—23no—
60C2×C4×C11—26no—
61C2×C4×C11—43no—
62C2×C4×C11—43no—
63C2×C4×C11—46no—
64C2×C4×C11—43no—
65C2×C4×C11C22⋊Q813yes—
66C2×C4×C11C4⋊Q813yes—
67C2×Dic11—41no—
68C2×Dic11—41no—
69C11⋊C8—46no—
70#519—111no—
71#428—223no—
72C2×#101—113no—
73#395—23no—
74#391—23no—
75#391C2×D1113yes—
76#339—223no—
77C22×C11—21no—
78C22×C11—21no—
79C22×C11#39511yescharacteristic
80C22×C11B(4,𝔽2)11yescharacteristic
81C22×C11#45811yescharacteristic
82C4×C11—23no—
83C4×C11—23no—
84C4×C11—46no—
85C4×C11—83no—
86Dic11—81no—
87Dic11—81no—
88C22×Q8—21no—
89C22×Q8—21no—
90C22×Q8C22×D1111yescharacteristic
91C2×M16—223no—
92C4×Q8—441no—
93C4×Q8—441no—
94#117—223no—
95C2×C4⋊C4—23no—
96C2×C4⋊C4C22⋊D1113yes—
97C2×C42C22⋊D1113yes—
98#107—443no—
99#106—443no—
100#101—116no—
101#101—223no—
102#95—23no—
103#95—26no—
104C2×C11—21no—
105C2×C11—21no—
106C2×C11#206211yescharacteristic
107C2×C11#220211yescharacteristic
108C2×C11#220511yescharacteristic
109C2×Q8—24no—
110C2×Q8—41no—
111C2×Q8—41no—
112C2×Q8—81no—
113C2×Q8—81no—
114C2×Q8—82no—
115C2×Q8—81no—
116C2×Q8Q8×D1113yes—
117C2×Q8#434311yescharacteristic
118C22×C4—23no—
119C22×C4—23no—
120C22×C4C2×C22⋊D1113yes—
121M16—226no—
122M16—443no—
123C2×C8—443no—
124C4⋊C4—43no—
125C4⋊C4—83no—
126C4⋊C4—223no—
127C4⋊C4—223no—
128C22⋊C4—441no—
129C42—43no—
130C42—443no—
131C11#1346411yescharacteristic, complemented, Sylow
132C23#6700611yescharacteristic
133Q8—43no—
134Q8—41no—
135Q8—84no—
136Q8—84no—
137C2×C4—23no—
138C2×C4—23no—
139C2×C4—26no—
140C2×C4—43no—
141C2×C4—43no—
142C2×C4—46no—
143C2×C4—43no—
144C2×C4—441no—
145C2×C4—441no—
146C2×C4#6699713yes—
147C2×C4#6699913yes—
148C8—446no—
149C22—21no—
150C22—21no—
151C22#1062284211yescharacteristic
152C22#1062285611yescharacteristic
153C22#1062285711yescharacteristic
154C4—23no—
155C4—23no—
156C4—46no—
157C4—83no—
158C4—881no—
159C4—881no—
160C2—21no—
161C2—21no—
162C2#1306996811yescharacteristic
163C2#1307063311yescharacteristic
164C2#1307064611yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC22×Q8×C11C23
FrattiniC22×Q8C22×D11
FittingC11×#2811C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2811D11
hypocenterC11#13464
LCSG ▷ C22×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #2811

Complements

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

NH ≅ G/Ntype
24. #66900Q8semidirect
131. C11#13464semidirect

Maximal subgroups

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

subgroupindex
#130688302
#130667432
C11×#28112
#1346411