Finite Group Databasebeta

← #14647281

Subgroups — #14647281

Order 2816.

786 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 107 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#13068531C212yesmaximal
2C11⋊#1304C214yesmaximal, complemented
3C11×#2309C211yesmaximal, characteristic
4C23×D4×C11C2211yescharacteristic
5C2×C11×#117C412yescomplemented
6C11×#390—24no—
7C11×#379C412yescomplemented
8C11×#379C2212yes—
9#10622860C2214yes—
10C2×#66898—24no—
11C25×C11C2×C411yescharacteristic
12C25×C11C2311yescharacteristic
13C22×D4×C11—24no—
14C22×D4×C11—44no—
15C22×D4×C11D414yes—
16C23×C4×C11C2×C411yescharacteristic
17C11×#117—44no—
18C2×C11×C4⋊C4—22no—
19C2×C11×C22⋊C4—24no—
20C2×C11×C22⋊C4—24no—
21C2×C11×C22⋊C4C2×C414yes—
22C2×C42×C11—22no—
23C2×C22⋊Dic11—24no—
24C2×C22⋊Dic11—28no—
25#66898—48no—
26#8749—111nomaximal, Sylow
27C24×C11—22no—
28C24×C11—42no—
29C24×C11—42no—
30C24×C11—82no—
31C24×C11—82no—
32C24×C11C22⋊C412yes—
33C24×C11C22×C411yescharacteristic
34C24×C11C2×D412yes—
35C24×C11#4114yes—
36C2×D4×C11—28no—
37C2×D4×C11—28no—
38C2×D4×C11—44no—
39C2×D4×C11—416no—
40C22×C4×C11—22no—
41C22×C4×C11—24no—
42C22×C4×C11—24no—
43C22×C4×C11C22⋊C412yes—
44C22×Dic11—44no—
45C11×C4⋊C4—44no—
46C11×C22⋊C4—44no—
47C11×C22⋊C4—84no—
48C11×C22⋊C4—84no—
49C42×C11—44no—
50C22⋊Dic11—48no—
51C22⋊Dic11—88no—
52#2309D1111yescharacteristic
53#1781—112no—
54#1304—114no—
55C23×C11—22no—
56C23×C11—24no—
57C23×C11—22no—
58C23×C11—24no—
59C23×C11—42no—
60C23×C11—48no—
61C23×C11—44no—
62C23×C11—44no—
63C23×C11—44no—
64C23×C11—44no—
65C23×C11—84no—
66C23×C11—88no—
67C23×C11—88no—
68C23×C11C2×C22⋊C411yescharacteristic
69C23×C11#11712yes—
70C23×C11#12314yes—
71D4×C11—416no—
72C2×C4×C11—28no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—48no—
76C2×C4×C11—44no—
77C2×C4×C11#9914yes—
78C2×Dic11—84no—
79C2×Dic11—88no—
80C23×D4C2×D1111yescharacteristic
81C2×#117Dic1112yescomplemented
82C2×#99—224no—
83#390—24no—
84#379—114no—
85#379Dic1112yescomplemented
86#379C2×D1112yes—
87C22×C11—22no—
88C22×C11—22no—
89C22×C11—24no—
90C22×C11—24no—
91C22×C11—28no—
92C22×C11—44no—
93C22×C11—42no—
94C22×C11—44no—
95C22×C11—84no—
96C22×C11—84no—
97C22×C11—88no—
98C22×C11—88no—
99C22×C11#38111yescharacteristic
100C22×C11C2×#9912yes—
101C4×C11—24no—
102C4×C11—84no—
103Dic11—164no—
104C25C2×Dic1111yescharacteristic
105C25C22×D1111yescharacteristic
106C22×D4—24no—
107C22×D4—44no—
108C22×D4C22⋊D1114yes—
109C23×C4C2×Dic1111yescharacteristic
110#117—44no—
111C2×C4⋊C4—22no—
112C2×C22⋊C4—24no—
113C2×C22⋊C4—24no—
114C2×C22⋊C4—224no—
115C2×C22⋊C4—228no—
116C2×C22⋊C4C2×Dic1114yes—
117C2×C42—22no—
118#99—448no—
119C2×C11—22no—
120C2×C11—44no—
121C2×C11—42no—
122C2×C11—82no—
123C2×C11#181911yescharacteristic
124C2×C11#182812yes—
125C24—22no—
126C24—42no—
127C24—42no—
128C24—82no—
129C24—82no—
130C24C22⋊Dic1112yes—
131C24#433914yes—
132C24C22×Dic1111yescharacteristic
133C24C2×C22⋊D1112yes—
134C2×D4—28no—
135C2×D4—28no—
136C2×D4—44no—
137C2×D4—416no—
138C22×C4—22no—
139C22×C4—24no—
140C22×C4—24no—
141C22×C4—444no—
142C22×C4C22⋊Dic1112yes—
143C4⋊C4—44no—
144C22⋊C4—44no—
145C22⋊C4—84no—
146C22⋊C4—84no—
147C22⋊C4—448no—
148C22⋊C4—888no—
149C42—44no—
150C11#874911yescharacteristic, complemented, Sylow
151C23—22no—
152C23—24no—
153C23—22no—
154C23—24no—
155C23—42no—
156C23—44no—
157C23—48no—
158C23—44no—
159C23—44no—
160C23—44no—
161C23—84no—
162C23—88no—
163C23—88no—
164C23#6697912yes—
165C23#6698214yes—
166C23C2×C22⋊Dic1111yescharacteristic
167D4—416no—
168C2×C4—28no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—48no—
172C2×C4—44no—
173C2×C4—884no—
174C2×C4—888no—
175C2×C4#6689814yes—
176C22—22no—
177C22—22no—
178C22—24no—
179C22—28no—
180C22—24no—
181C22—44no—
182C22—42no—
183C22—44no—
184C22—84no—
185C22—84no—
186C22—88no—
187C22—88no—
188C22#1062282411yescharacteristic
189C22C2×#6689812yes—
190C4—24no—
191C4—84no—
192C4—1764no—
193C2—22no—
194C2—44no—
195C2—42no—
196C2—82no—
197C2#1306869011yescharacteristic
198C2#1306872412yes—
subgroupG/H
centerC22#10622824
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC11×#2309C2
socleC22×C11#381
prime radicalC23×D4×C11C22
cosocleC25×C11C23
hypercenter#2309D11
hypocenterC11#8749
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. C11⋊#1304C2semidirect
5. C2×C11×#117C4semidirect
7. C11×#379C4semidirect
81. C2×#117Dic11semidirect
85. #379Dic11semidirect
150. C11#8749semidirect

Maximal subgroups

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

subgroupindex
#130685312
C11⋊#13042
C11×#23092
#874911