Finite Group Databasebeta

← #14735853

Subgroups — #14735853

Order 2816.

876 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 876 conjugacy classes of subgroups — too many to draw. Only its 179 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#13078992C213yesmaximal
2#13067918C218yesmaximal, complemented
3#13067211C213yesmaximal, complemented
4C11×#3556C211yesmaximal, characteristic, complemented
5C11×#564C2214yescomplemented
6C11×#557—26no—
7C11×#541—26no—
8C11×#533C2213yes—
9C2×#66927C2211yescharacteristic
10#10622701—26no—
11#10622680C22112yes—
12#10622614—26no—
13C4×#4318C2213yes—
14#10622181C22112yescomplemented
15C22×D44—23no—
16C11×C4⋊Q8—26no—
17C11×C4⋊Q8D416yes—
18C11×#126—28no—
19C11×#125—26no—
20C11×#125—224no—
21C11×#125C2316yes—
22C11×C22⋊Q8—26no—
23C4×Q8×C11—212no—
24C4×Q8×C11—26no—
25C11×#117D416yes—
26C2×C42×C11C2311yescharacteristic
27C2×#4318—23no—
28#66927—23no—
29#66927C2312yes—
30#66873—224no—
31#66867C2316yes—
32C4×C11⋊C8—23no—
33#19083—111nomaximal, Sylow
34C23×D11—41no—
35C2×Q8×C11—26no—
36C22×C4×C11C2×D413yes—
37C2×D44—26no—
38C2×D44—412no—
39C2×D44—43no—
40C11×C4⋊C4—224no—
41C11×C4⋊C4—26no—
42C11×C4⋊C4—212no—
43C11×C4⋊C4C2×D4112yes—
44C11×C22⋊C4—26no—
45C42×C11—28no—
46C42×C11—26no—
47C42×C11C2×D413yes—
48C42×C11C2411yescharacteristic
49#4318—46no—
50C2×C11⋊C8—26no—
51#3556D1111yescharacteristic, complemented
52#3138—113no—
53#1658—118no—
54#1526—113no—
55C23×C11#12011yescharacteristic
56C22×D11—42no—
57C22×D11—86no—
58Q8×C11—412no—
59C2×C4×C11—26no—
60C2×C4×C11—212no—
61C2×C4×C11#12013yes—
62C2×C4×C11C22×D413yes—
63D44—412no—
64D44—86no—
65C11⋊C8—46no—
66#564C2×D1114yescomplemented
67#557—26no—
68#541—26no—
69#533C2×D1113yes—
70C2×#127—111no—
71#490—1112no—
72#486—226no—
73#418—226no—
74C4×M16—113no—
75#330—1112no—
76C22×C11—23no—
77C22×C11C2×#12011yescharacteristic
78C2×D11—86no—
79C2×D11—164no—
80C4×C11—23no—
81C4×C11—412no—
82C4×C11#45416yes—
83C22×D4—223no—
84C2×M16—223no—
85C4⋊Q8—26no—
86C4⋊Q8C22⋊D1116yes—
87#127—112no—
88#127—223no—
89#126—28no—
90#125—26no—
91#125—224no—
92#125C22×D1116yes—
93C22⋊Q8—26no—
94C4×Q8—212no—
95C4×Q8—26no—
96#117C22⋊D1116yes—
97C2×C42C22×D1111yescharacteristic
98#102—2224no—
99#97—116no—
100C4×C8—223no—
101C2×C11—41no—
102C2×C11C2×#45413yes—
103D11—162no—
104C24—441no—
105C2×Q8—26no—
106C2×D4—226no—
107C2×D4—4412no—
108C2×D4—443no—
109C22×C4C2×C22⋊D1113yes—
110M16—446no—
111C2×C8—226no—
112C4⋊C4—224no—
113C4⋊C4—26no—
114C4⋊C4—212no—
115C4⋊C4C2×C22⋊D11112yes—
116C22⋊C4—26no—
117C42—28no—
118C42—26no—
119C42C2×C22⋊D1113yes—
120C42C23×D1111yescharacteristic
121C11#1908311yescharacteristic, complemented, Sylow
122C23—442no—
123C23—886no—
124C23#6700611yescharacteristic
125Q8—412no—
126D4—4412no—
127D4—886no—
128C2×C4—26no—
129C2×C4—212no—
130C2×C4#6700613yes—
131C2×C4C22×C22⋊D1113yes—
132C8—446no—
133C22—23no—
134C22—886no—
135C22—1764no—
136C22C2×#6700611yescharacteristic
137C4—23no—
138C4—412no—
139C4#1062285816yes—
140C2—41no—
141C2—1762no—
142C2C2×#1062285813yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3556C2
socleC22×C11C2×#120
prime radicalC2×#66927C22
hypercenter#3556D11
hypocenterC11#19083
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3556

Complements

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

NH ≅ G/Ntype
2. #13067918C2semidirect
3. #13067211C2semidirect
4. C11×#3556C2semidirect
5. C11×#564C22semidirect
14. #10622181C22semidirect
51. #3556D11semidirect
66. #564C2×D11semidirect
121. C11#19083semidirect

Maximal subgroups

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

subgroupindex
#130789922
#130679182
#130672112
C11×#35562
#1908311