Finite Group Databasebeta

← #14645127

Subgroups — #14645127

Order 2816.

810 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 171 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#13068684C212yesmaximal
2C2×#10622166C214yesmaximal
3C22×C11×#125C211yesmaximal, characteristic
4C2×C11×#125—28no—
5C2×C11×#125—24no—
6C22×C11×C4⋊C4C411yescharacteristic
7C22×C11×C4⋊C4C412yes—
8C22×C11×C4⋊C4C411yescharacteristic
9C22×C11×C4⋊C4C2212yes—
10C22×C42×C11C2211yescharacteristic
11C2×C22⋊(C11⋊C8)C2214yes—
12#10622166—28no—
13#10622162—24no—
14C23×C4×C11C2×C411yescharacteristic
15C23×C4×C11C2×C411yescharacteristic
16C23×C4×C11C2×C412yes—
17C23×C4×C11C2×C412yes—
18C23×C4×C11C2311yescharacteristic
19C11×#125—232no—
20C2×C11×C4⋊C4—24no—
21C2×C11×C4⋊C4—24no—
22C2×C11×C4⋊C4—24no—
23C2×C11×C4⋊C4—24no—
24C2×C11×C4⋊C4—24no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—24no—
28C2×C11×C4⋊C4—24no—
29C2×C11×C4⋊C4D418yes—
30C2×C42×C11—24no—
31C2×C42×C11D414yes—
32C22×C11⋊C8—24no—
33C22⋊(C11⋊C8)—28no—
34#8306—111nomaximal, Sylow
35C24×C11C22×C411yescharacteristic
36C22×C4×C11—22no—
37C22×C4×C11—24no—
38C22×C4×C11—22no—
39C22×C4×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11—22no—
42C22×C4×C11—22no—
43C22×C4×C11—24no—
44C22×C4×C11—28no—
45C22×C4×C11—42no—
46C22×C4×C11—44no—
47C22×C4×C11C22⋊C412yes—
48C22×C4×C11C22⋊C414yes—
49C22×C4×C11C22⋊C412yes—
50C22×C4×C11C22⋊C414yes—
51C22×C4×C11C2×D412yes—
52C22×C4×C11C2×D414yes—
53C11×C4⋊C4—28no—
54C11×C4⋊C4—28no—
55C11×C4⋊C4—216no—
56C11×C4⋊C4—216no—
57C42×C11—28no—
58C2×C11⋊C8—48no—
59C2×C11⋊C8—44no—
60C22×#125D1111yescharacteristic
61#1817—112no—
62C2×#324—114no—
63C23×C11—22no—
64C23×C11—22no—
65C23×C11C2×C22⋊C412yes—
66C23×C11C2×C22⋊C411yescharacteristic
67C23×C11#13114yes—
68C2×C4×C11—28no—
69C2×C4×C11—22no—
70C2×C4×C11—24no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—24no—
74C2×C4×C11—24no—
75C2×C4×C11—28no—
76C2×C4×C11—24no—
77C2×C4×C11—44no—
78C2×C4×C11—44no—
79C2×C4×C11—44no—
80C2×C4×C11—44no—
81C2×C4×C11—44no—
82C2×C4×C11—44no—
83C2×C4×C11—44no—
84C2×C4×C11#10114yes—
85C2×C4×C11#12014yes—
86C11⋊C8—84no—
87C2×#125—28no—
88C2×#125—24no—
89C22×C4⋊C4Dic1111yescharacteristic
90C22×C4⋊C4Dic1112yes—
91C22×C4⋊C4Dic1111yescharacteristic
92C22×C4⋊C4C2×D1112yes—
93C22×C42C2×D1111yescharacteristic
94C2×C22⋊C8—114no—
95#336—224no—
96#324—228no—
97C22×C11—28no—
98C22×C11—22no—
99C22×C11—22no—
100C22×C11#37911yescharacteristic
101C22×C11#40814yes—
102C22×C11#40812yes—
103C22×C11#41012yes—
104C22×C11C2×#10112yes—
105C4×C11—24no—
106C4×C11—24no—
107C4×C11—42no—
108C4×C11—44no—
109C4×C11—44no—
110C23×C4C2×Dic1112yes—
111C23×C4C2×Dic1111yescharacteristic
112C23×C4C2×Dic1111yescharacteristic
113C23×C4C2×Dic1112yes—
114C23×C4C22×D1111yescharacteristic
115C22×C8—224no—
116#125—232no—
117C2×C4⋊C4—24no—
118C2×C4⋊C4—24no—
119C2×C4⋊C4—24no—
120C2×C4⋊C4—24no—
121C2×C4⋊C4—24no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—24no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4C22⋊D1118yes—
127C2×C42—24no—
128C2×C42C22⋊D1114yes—
129C22⋊C8—228no—
130C2×C11—24no—
131C2×C11#147014yes—
132C2×C11#178011yescharacteristic
133C2×C11#178211yescharacteristic
134C2×C11#178411yescharacteristic
135C24C22×Dic1111yescharacteristic
136C22×C4—22no—
137C22×C4—24no—
138C22×C4—28no—
139C22×C4—24no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—42no—
146C22×C4—44no—
147C22×C4C22⋊Dic1114yes—
148C22×C4C22⋊Dic1112yes—
149C22×C4C22⋊Dic1112yes—
150C22×C4C22⋊Dic1114yes—
151C22×C4C2×C22⋊D1112yes—
152C22×C4C2×C22⋊D1114yes—
153C2×C8—448no—
154C2×C8—444no—
155C4⋊C4—28no—
156C4⋊C4—28no—
157C4⋊C4—216no—
158C4⋊C4—216no—
159C42—28no—
160C11#830611yescharacteristic, complemented, Sylow
161C23—22no—
162C23—22no—
163C23#6700114yes—
164C23C2×C22⋊Dic1112yes—
165C23C2×C22⋊Dic1111yescharacteristic
166C2×C4—28no—
167C2×C4—22no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—28no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—44no—
176C2×C4—44no—
177C2×C4—44no—
178C2×C4—44no—
179C2×C4—44no—
180C2×C4—44no—
181C2×C4—44no—
182C2×C4#6690014yes—
183C2×C4#6700614yes—
184C8—884no—
185C22—28no—
186C22—22no—
187C22—22no—
188C22C2×#6690012yes—
189C22#1062284714yes—
190C22#1062284712yes—
191C22#1062285312yes—
192C22#1062286011yescharacteristic
193C4—24no—
194C4—24no—
195C4—42no—
196C4—44no—
197C4—44no—
198C2—24no—
199C2#1306697214yes—
200C2#1306852811yescharacteristic
201C2#1306853411yescharacteristic
202C2#1306854011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutator, prime radicalC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#125C2
socleC23×C11C2×C22⋊C4
cosocleC23×C4×C11C23
hypercenterC22×#125D11
hypocenterC11#8306
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
160. C11#8306semidirect

Maximal subgroups

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

subgroupindex
#130686842
C2×#106221662
C22×C11×#1252
#830611