Finite Group Databasebeta

← #14666518

Subgroups — #14666518

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#13067607C212yesmaximal
3#13066615C212yesmaximal
4#13066546C211yesmaximal, characteristic
5C11×#2030C211yesmaximal, characteristic
6C11×#543C2211yescharacteristic
7C2×#66977—21no—
8C11×#381—21no—
9C11×#381C2211yescharacteristic
10#10622656—22no—
11#10622566—21no—
12#10622566C2212yes—
13#10622272—22no—
14#10622269—22no—
15C11×#342—21no—
16C11×#342C2211yescharacteristic
17#10622176—22no—
18#10622163C2212yes—
19C23×C4×C11D411yescharacteristic
20C22×Dic22—21no—
21C11×C22⋊Q8—22no—
22C11×C22⋊Q8—42no—
23C2×C11×C22⋊C4—21no—
24C2×C11×C22⋊C4—21no—
25C2×C11×C22⋊C4D411yescharacteristic
26C2×C11×C22⋊C4C2311yescharacteristic
27C2×C22⋊Dic11—22no—
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11D412yes—
31#66977—42no—
32#66977—42no—
33C2×Dic11⋊C4—22no—
34C11×#95—22no—
35C11×#95—42no—
36#66899—42no—
37C11⋊#95—22no—
38C11⋊#95—21no—
39C11⋊#95—22no—
40C11⋊#95D412yes—
41C22⋊(C11⋊C8)—22no—
42#66872—42no—
43#12207—111nomaximal, Sylow
44C24×C11C2×D411yescharacteristic
45C2×Q8×C11—22no—
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11—21no—
49C22×C4×C11—22no—
50C22×C4×C11—41no—
51C22×C4×C11—41no—
52C22×C4×C11—41no—
53C22×C4×C11SD1612yes—
54C22×C4×C11C2×D412yes—
55C22×Dic11—22no—
56C22×Dic11—22no—
57C2×Dic22—42no—
58C2×Dic22—81no—
59C2×Dic22—81no—
60C11×C4⋊C4—22no—
61C11×C4⋊C4—42no—
62C11×C22⋊C4—41no—
63C11×C22⋊C4—41no—
64C11×C22⋊C4—41no—
65C11×C22⋊C4—41no—
66C11×C22⋊C4—41no—
67C11×C22⋊C4—41no—
68C22⋊Dic11—42no—
69C22⋊Dic11—42no—
70C4⋊Dic11—42no—
71C4⋊Dic11—42no—
72C4⋊Dic11—81no—
73Dic11⋊C4—44no—
74C2×C11⋊C8—42no—
75#2817—111no—
76#2030D1111yescharacteristic
77#1608—112no—
78#1344—112no—
79#1317—111no—
80C23×C11—21no—
81C23×C11—21no—
82C23×C11—42no—
83C23×C11#12011yescharacteristic
84C23×C11C2×SD1611yescharacteristic
85C23×C11AGL(1,ℤ/8)11yescharacteristic
86Q8×C11—82no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11—42no—
94C2×C4×C11—41no—
95C2×C4×C11—42no—
96C2×C4×C11—81no—
97C2×C4×C11—82no—
98C2×C4×C11—81no—
99C2×C4×C11—82no—
100C2×Dic11—44no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105Dic22—84no—
106C11⋊C8—82no—
107#543C2×D1111yescharacteristic
108C2×C22⋊Q8—221no—
109#483—222no—
110#400—222no—
111#397—112no—
112#397—221no—
113#395—222no—
114#381—21no—
115#381C2×D1111yescharacteristic
116#342—21no—
117#342C2×D1111yescharacteristic
118#328—222no—
119#323—112no—
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—
133C4×C11—82no—
134C4×C11—161no—
135Dic11—82no—
136Dic11—82no—
137C22×Q8—221no—
138C23×C4C22⋊D1111yescharacteristic
139C22⋊Q8—22no—
140C22⋊Q8—42no—
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—21no—
148C2×C22⋊C4—21no—
149C2×C22⋊C4—222no—
150C2×C22⋊C4C22⋊D1111yescharacteristic
151C2×C22⋊C4C22×D1111yescharacteristic
152#106—442no—
153#103—442no—
154C22⋊C8—222no—
155#95—22no—
156#95—42no—
157#95—112no—
158#95—222no—
159#95—221no—
160#95—222no—
161C2×C11—21no—
162C2×C11—21no—
163C2×C11—41no—
164C2×C11—41no—
165C2×C11#160111yescharacteristic
166C2×C11#220112yes—
167C24C2×C22⋊D1111yescharacteristic
168C2×Q8—22no—
169C2×Q8—442no—
170C2×Q8—881no—
171C2×Q8—881no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4#432512yes—
182C22×C4D4×D1112yes—
183C2×C8—442no—
184C4⋊C4—22no—
185C4⋊C4—42no—
186C4⋊C4—442no—
187C4⋊C4—444no—
188C4⋊C4—442no—
189C4⋊C4—881no—
190C22⋊C4—41no—
191C22⋊C4—41no—
192C22⋊C4—41no—
193C22⋊C4—41no—
194C22⋊C4—41no—
195C22⋊C4—41no—
196C22⋊C4—442no—
197C22⋊C4—442no—
198C11#1220711yescharacteristic, complemented, Sylow
199C23—21no—
200C23—21no—
201C23—42no—
202C23#6699011yescharacteristic
203C23C2×#432511yescharacteristic
204C23#6700211yescharacteristic
205Q8—82no—
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—42no—
215C2×C4—41no—
216C2×C4—81no—
217C2×C4—82no—
218C2×C4—81no—
219C2×C4—82no—
220C2×C4—444no—
221C2×C4—442no—
222C2×C4—442no—
223C2×C4—442no—
224C2×C4—442no—
225C8—882no—
226C22—22no—
227C22—21no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—81no—
233C22#1062264511yescharacteristic
234C22#1062265911yescharacteristic
235C22#1062267411yescharacteristic
236C4—42no—
237C4—42no—
238C4—81no—
239C4—82no—
240C4—161no—
241C4—882no—
242C4—882no—
243C2—21no—
244C2—21no—
245C2—41no—
246C2—41no—
247C2#1306756711yescharacteristic
248C2#1307062712yes—
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2030C2
socleC22×C11B(4,𝔽2)
prime radicalC24×C11C2×D4
hypercenter#2030D11
hypocenterC11#12207
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2030

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
#130676072
#130666152
#130665462
C11×#20302
#1220711