Finite Group Databasebeta

← #14781190

Subgroups — #14781190

Order 2816.

1178 conjugacy classes of subgroups; only the 275 normal subgroups are shown.

normal subgroups only

This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 275 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#13071200C213yesmaximal
2#13069782C218yesmaximal
3#13068349C213yesmaximal
4C11×#3458C211yesmaximal, characteristic
5C23×Dic22C2211yescharacteristic
6C11×#544—26no—
7C11×#543C2214yes—
8C11×#533—26no—
9C2×C11×#117C2213yes—
10C2×#66979C2213yes—
11#10622587—26no—
12#10622556C22112yes—
13#10622542—26no—
14#10622164C22112yes—
15C23×C4×C11C2311yescharacteristic
16C23×Dic11C2312yes—
17C22×Dic22—23no—
18C22×Dic22—23no—
19C22×Dic22—26no—
20C22×Dic22Q814yescomplemented
21C11×C4⋊Q8—212no—
22C11×#125—212no—
23C11×C22⋊Q8—224no—
24C4×Q8×C11—28no—
25C11×#117—26no—
26C11×#117—26no—
27C2×C11×C4⋊C4D416yes—
28C2×C11×C22⋊C4C2316yes—
29C2×C42×C11D416yes—
30C2×C22⋊Dic11C2316yes—
31#66979—212no—
32C2×C4⋊Dic11—23no—
33C2×C4×Dic11—23no—
34C11⋊#95—224no—
35#23470—111nomaximal, Sylow
36C24×C11C2411yescharacteristic
37C2×Q8×C11—28no—
38C22×C4×C11C2×D4112yes—
39C22×C4×C11C2×D413yes—
40C22×C4×C11C2×D413yes—
41C22×C4×C11C2×Q812yes—
42C22×C4×C11#4116yes—
43C22×Dic11—26no—
44C22×Dic11—26no—
45C22×Dic11—26no—
46C22×Dic11C2×Q814yes—
47C2×Dic22—212no—
48C2×Dic22—212no—
49C2×Dic22—41no—
50C2×Dic22—43no—
51C2×Dic22—46no—
52C2×Dic22—46no—
53C11×C4⋊C4—224no—
54C11×C4⋊C4—212no—
55C11×C22⋊C4—212no—
56C42×C11—26no—
57C42×C11—26no—
58C22⋊Dic11—212no—
59C4⋊Dic11—46no—
60C4×Dic11—46no—
61#3458D1111yescharacteristic
62#2310—113no—
63#2030—118no—
64#1740—113no—
65C23×C11—42no—
66C23×C11C22×D413yes—
67C23×C11C22×Q811yescharacteristic
68C23×C11C2×#4113yes—
69Q8×C11—88no—
70C2×C4×C11—212no—
71C2×C4×C11—412no—
72C2×C4×C11#12011yescharacteristic
73C2×C4×C11#12013yes—
74C2×C4×C11C22⋊Q816yes—
75C2×C4×C11C22⋊Q816yes—
76C2×C4×C11#12416yes—
77C2×C4×C11#12416yes—
78C2×Dic11—212no—
79C2×Dic11—42no—
80C2×Dic11—46no—
81C2×Dic11—412no—
82C2×Dic11—46no—
83Dic22—44no—
84Dic22—412no—
85C23×Q8—111no—
86#544—26no—
87#543C2×D1114yes—
88#533—26no—
89C2×#117—113no—
90C2×#117C2×D1113yes—
91#391—226no—
92#391—226no—
93#381—1112no—
94#342—1112no—
95C22×C11—26no—
96C22×C11—41no—
97C22×C11—43no—
98C22×C11C2×#12011yescharacteristic
99C22×C11C2×C22⋊Q813yes—
100C22×C11C2×#12413yes—
101C4×C11—412no—
102C4×C11#39312yes—
103C4×C11#39316yes—
104Dic11—44no—
105Dic11—86no—
106C22×Q8—114no—
107C22×Q8—226no—
108C22×Q8—223no—
109C22×Q8—223no—
110C23×C4—112no—
111C23×C4C22×D1111yescharacteristic
112C4⋊Q8—212no—
113#125—212no—
114C22⋊Q8—224no—
115C4×Q8—28no—
116#117—26no—
117#117—26no—
118#117—2212no—
119C2×C4⋊C4—223no—
120C2×C4⋊C4C22⋊D1116yes—
121C2×C22⋊C4—116no—
122C2×C22⋊C4C22×D1116yes—
123C2×C42—223no—
124C2×C42C22⋊D1116yes—
125#95—2224no—
126C2×C11—23no—
127C2×C11—23no—
128C2×C11C2×#39311yescharacteristic
129C2×C11#302812yes—
130C24C23×D1111yescharacteristic
131C2×Q8—28no—
132C2×Q8—2212no—
133C2×Q8—2212no—
134C2×Q8—446no—
135C2×Q8—446no—
136C2×Q8—441no—
137C2×Q8—443no—
138C22×C4—114no—
139C22×C4—226no—
140C22×C4—226no—
141C22×C4—226no—
142C22×C4Q8×D1112yes—
143C22×C4#434316yes—
144C22×C4C2×C22⋊D11112yes—
145C22×C4C2×C22⋊D1113yes—
146C22×C4C2×C22⋊D1113yes—
147C4⋊C4—224no—
148C4⋊C4—212no—
149C4⋊C4—446no—
150C22⋊C4—212no—
151C22⋊C4—2212no—
152C42—26no—
153C42—26no—
154C42—446no—
155C11#2347011yescharacteristic, complemented, Sylow
156C23—42no—
157C23C2×Q8×D1111yescharacteristic
158C23C2×#434313yes—
159C23C22×C22⋊D1113yes—
160Q8—88no—
161Q8—4412no—
162Q8—444no—
163C2×C4—212no—
164C2×C4—412no—
165C2×C4—2212no—
166C2×C4—446no—
167C2×C4—442no—
168C2×C4—4412no—
169C2×C4—446no—
170C2×C4#6699916yes—
171C2×C4#6699916yes—
172C2×C4#6700016yes—
173C2×C4#6700016yes—
174C2×C4#6700611yescharacteristic
175C2×C4#6700613yes—
176C22—26no—
177C22—41no—
178C22—43no—
179C22C2×#6699913yes—
180C22C2×#6700013yes—
181C22C2×#6700611yescharacteristic
182C4—412no—
183C4—444no—
184C4—886no—
185C4#1062284416yes—
186C4#1062284412yes—
187C2—23no—
188C2—23no—
189C2C2×#1062284411yescharacteristic
190C2#1307802212yes—
subgroupG/H
centerC22C2×#67006
commutator, prime radical, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#3458C2
socleC22×C11C2×#120
hypercenter#3458D11
hypocenterC11#23470
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3458

Complements

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

NH ≅ G/Ntype
20. C22×Dic22Q8semidirect
155. C11#23470semidirect

Maximal subgroups

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

subgroupindex
#130712002
#130697822
#130683492
C11×#34582
#2347011