Finite Group Databasebeta

← #14666521

Subgroups — #14666521

Order 2816.

388 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 59 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#13076653C211yesmaximal, characteristic
2#13069783C211yesmaximal, characteristic
3#13067609C212yesmaximal
4#13066617C212yesmaximal
5C11×#1317C211yesmaximal, characteristic
6C2×#66977—21no—
7#10623014C2211yescharacteristic
8C11×#381C2211yescharacteristic
9#10622824—21no—
10#10622566—21no—
11#10622566C2212yes—
12#10622334—22no—
13#10622272—22no—
14#10622269—22no—
15C11×#323C2212yes—
16#10622165—21no—
17#10622164C2211yescharacteristic
18#10622105—22no—
19C23×C4×C11D411yescharacteristic
20C22×Dic22—21no—
21C2×C11×C22⋊C4D411yescharacteristic
22C2×C11×C22⋊C4C2311yescharacteristic
23C2×C22⋊Dic11—21no—
24C2×C22⋊Dic11—22no—
25C2×C22⋊Dic11—21no—
26C2×C4⋊Dic11—21no—
27C2×C4⋊Dic11—21no—
28C2×C4⋊Dic11D412yes—
29#66977—22no—
30#66977—42no—
31#66977—42no—
32C2×Dic11⋊C4—22no—
33#66931—42no—
34C11×C22⋊C8—22no—
35C11×#95—22no—
36C11⋊#95—22no—
37C11⋊#95—21no—
38C11⋊#95—22no—
39C11⋊#95—42no—
40C11⋊#95D412yes—
41#66881—42no—
42#66880—42no—
43#12207—111nomaximal, Sylow
44C24×C11C2×D411yescharacteristic
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11—41no—
49C22×C4×C11—41no—
50C22×C4×C11SD1612yes—
51C22×C4×C11C2×D412yes—
52C22×Dic11—22no—
53C22×Dic11—22no—
54C22×Dic11—22no—
55C22×Dic11—41no—
56C2×Dic22—22no—
57C2×Dic22—42no—
58C2×Dic22—81no—
59C2×Dic22—81no—
60C2×C8×C11—42no—
61C11×C22⋊C4—41no—
62C11×C22⋊C4—41no—
63C22⋊Dic11—41no—
64C22⋊Dic11—41no—
65C22⋊Dic11—41no—
66C22⋊Dic11—42no—
67C22⋊Dic11—42no—
68C22⋊Dic11—41no—
69C4⋊Dic11—22no—
70C4⋊Dic11—42no—
71C4⋊Dic11—42no—
72C4⋊Dic11—81no—
73Dic11⋊C4—42no—
74Dic11⋊C4—44no—
75#2817—111no—
76#2030—111no—
77#1608—112no—
78#1344—112no—
79#1317D1111yescharacteristic
80C23×C11—21no—
81C23×C11—21no—
82C23×C11—42no—
83C23×C11#12011yescharacteristic
84C23×C11C2×SD1611yescharacteristic
85C23×C11AGL(1,ℤ/8)11yescharacteristic
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11—41no—
94C2×C4×C11—81no—
95C2×Dic11—44no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—82no—
102C2×Dic11—81no—
103C2×Dic11—82no—
104Dic22—84no—
105Dic22—82no—
106C8×C11—82no—
107#543—111no—
108C2×C22⋊Q8—221no—
109#483—222no—
110#400—222no—
111#397—112no—
112#397—221no—
113#395—222no—
114#381—221no—
115#381C2×D1111yescharacteristic
116#342—111no—
117#342—221no—
118#328—222no—
119#323C2×D1112yes—
120C22×C11—22no—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11—42no—
126C22×C11—81no—
127C22×C11#45011yescharacteristic
128C22×C11#45511yescharacteristic
129C22×C11B(4,𝔽2)11yescharacteristic
130C4×C11—42no—
131C4×C11—42no—
132C4×C11—81no—
133Dic11—82no—
134Dic11—82no—
135Dic11—82no—
136Dic11—161no—
137C22×Q8—221no—
138C23×C4D4411yescharacteristic
139C22⋊Q8—222no—
140C22⋊Q8—442no—
141C22⋊Q8—442no—
142C22⋊Q8—442no—
143C2×C4⋊C4—112no—
144C2×C4⋊C4—222no—
145C2×C4⋊C4—221no—
146C2×C4⋊C4—221no—
147C2×C22⋊C4—222no—
148C2×C22⋊C4—221no—
149C2×C22⋊C4—221no—
150C2×C22⋊C4D4411yescharacteristic
151C2×C22⋊C4C22×D1111yescharacteristic
152#106—442no—
153#103—442no—
154C22⋊C8—22no—
155#95—22no—
156#95—112no—
157#95—222no—
158#95—221no—
159#95—222no—
160#95—442no—
161C2×C11—21no—
162C2×C11—21no—
163C2×C11—41no—
164C2×C11—41no—
165C2×C11#160111yescharacteristic
166C2×C11#220112yes—
167C24C2×D4411yescharacteristic
168C2×Q8—222no—
169C2×Q8—442no—
170C2×Q8—881no—
171C2×Q8—881no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—222no—
178C22×C4—222no—
179C22×C4—222no—
180C22×C4—441no—
181C22×C4#431412yes—
182C22×C4D4×D1112yes—
183C2×C8—42no—
184C4⋊C4—222no—
185C4⋊C4—442no—
186C4⋊C4—444no—
187C4⋊C4—442no—
188C4⋊C4—442no—
189C4⋊C4—881no—
190C22⋊C4—41no—
191C22⋊C4—41no—
192C22⋊C4—441no—
193C22⋊C4—441no—
194C22⋊C4—442no—
195C22⋊C4—442no—
196C22⋊C4—441no—
197C22⋊C4—441no—
198C11#1220711yescharacteristic, complemented, Sylow
199C23—21no—
200C23—21no—
201C23—42no—
202C23#6693511yescharacteristic
203C23C2×#431411yescharacteristic
204C23#6696111yescharacteristic
205Q8—882no—
206Q8—884no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—81no—
216C2×C4—444no—
217C2×C4—442no—
218C2×C4—442no—
219C2×C4—442no—
220C2×C4—442no—
221C2×C4—442no—
222C2×C4—882no—
223C2×C4—881no—
224C2×C4—882no—
225C8—82no—
226C22—22no—
227C22—21no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—81no—
233C22#1062234411yescharacteristic
234C22#1062235411yescharacteristic
235C22#1062235911yescharacteristic
236C4—42no—
237C4—42no—
238C4—81no—
239C4—882no—
240C4—882no—
241C4—882no—
242C4—1761no—
243C2—21no—
244C2—21no—
245C2—41no—
246C2—41no—
247C2#1306757011yescharacteristic
248C2#1307063012yes—
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1317C2
socleC22×C11B(4,𝔽2)
prime radicalC24×C11C2×D4
hypercenter#1317D11
hypocenterC11#12207
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
198. C11#12207semidirect

Maximal subgroups

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

subgroupindex
#130766532
#130697832
#130676092
#130666172
C11×#13172
#1220711