Finite Group Databasebeta

← #14666621

Subgroups — #14666621

Order 2816.

336 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 63 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#13069777C211yesmaximal, characteristic
2#13067657C212yesmaximal
3#13066643C212yesmaximal
4#13066550C211yesmaximal, characteristic
5C11×#2809C211yesmaximal, characteristic
6#10623031C2211yescharacteristic
7C11×#400C2212yes—
8C11×#398—22no—
9C11×#391—21no—
10C11×#391C2211yescharacteristic
11C11×#389—21no—
12C11×#387—22no—
13#10622838—21no—
14#10622583—22no—
15#10622168C2211yescharacteristic
16#10622166C2212yes—
17#10622161—21no—
18#10622090—22no—
19C22×Q8×C11D411yescharacteristic
20C2×C11×C4⋊C4—22no—
21C2×C11×C4⋊C4—21no—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4D412yes—
25C2×C11×C4⋊C4C2311yescharacteristic
26C2×C42×C11—21no—
27C2×C42×C11D411yescharacteristic
28#66979—21no—
29#66977—22no—
30C2×#4318—21no—
31#66943—41no—
32#66941—41no—
33C11×#95—22no—
34C11×#95—22no—
35C11×#95—22no—
36C11×#95—22no—
37C11×#95D412yes—
38#66899—41no—
39#66899—41no—
40C22⋊(C11⋊C8)—22no—
41#66874—42no—
42#66871—42no—
43#12225—111nomaximal, Sylow
44C2×Q8×C11—21no—
45C2×Q8×C11—41no—
46C2×Q8×C11—41no—
47C2×Q8×C11Q1612yes—
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11C2×D412yes—
54C2×Dic22—22no—
55C11×C4⋊C4—41no—
56C11×C4⋊C4—44no—
57C11×C4⋊C4—42no—
58C11×C4⋊C4—42no—
59C11×C4⋊C4—81no—
60C11×C4⋊C4—81no—
61C42×C11—41no—
62C42×C11—81no—
63C22⋊Dic11—41no—
64C4⋊Dic11—22no—
65C4⋊Dic11—21no—
66C4⋊Dic11—21no—
67Dic11⋊C4—42no—
68C4×Dic11—41no—
69#4318—41no—
70#4318—41no—
71C2×C11⋊C8—42no—
72C2×C11⋊C8—41no—
73#2809D1111yescharacteristic
74#2028—111no—
75#1617—112no—
76#1353—112no—
77#1319—111no—
78C23×C11#12011yescharacteristic
79Q8×C11—42no—
80Q8×C11—81no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11—42no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11C2×Q1611yescharacteristic
98C2×C4×C11#13711yescharacteristic
99C2×Dic11—41no—
100C2×Dic11—41no—
101Dic22—82no—
102C11⋊C8—81no—
103C11⋊C8—82no—
104#544—111no—
105#484—222no—
106#419—221no—
107#400C2×D1112yes—
108#398—22no—
109#391—21no—
110#391C2×D1111yescharacteristic
111#389—21no—
112#387—22no—
113#343—111no—
114#339—221no—
115#328—222no—
116#324—112no—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11#45111yescharacteristic
120C22×C11#45511yescharacteristic
121C22×C11B(4,𝔽2)11yescharacteristic
122C4×C11—21no—
123C4×C11—21no—
124C4×C11—42no—
125C4×C11—42no—
126C4×C11—42no—
127C4×C11—82no—
128C4×C11—82no—
129Dic11—81no—
130Dic11—81no—
131C22×Q8C22⋊D1111yescharacteristic
132C2×M16—221no—
133C4⋊Q8—441no—
134#125—441no—
135C22⋊Q8—222no—
136#117—221no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4C22⋊D1112yes—
142C2×C4⋊C4C22×D1111yescharacteristic
143C2×C42—21no—
144C2×C42C22⋊D1111yescharacteristic
145#107—442no—
146#103—442no—
147#103—441no—
148#103—441no—
149C22⋊C8—222no—
150#95—22no—
151#95—22no—
152#95—22no—
153#95—22no—
154#95C22⋊D1112yes—
155C2×C11—21no—
156C2×C11—21no—
157C2×C11#160211yescharacteristic
158C2×C11#220111yescharacteristic
159C2×C11#220411yescharacteristic
160C2×Q8—21no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8—222no—
164C2×Q8#432612yes—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4C2×C22⋊D1111yescharacteristic
170C22×C4C2×C22⋊D1112yes—
171M16—441no—
172M16—441no—
173C2×C8—442no—
174C2×C8—441no—
175C4⋊C4—41no—
176C4⋊C4—42no—
177C4⋊C4—44no—
178C4⋊C4—42no—
179C4⋊C4—81no—
180C4⋊C4—81no—
181C4⋊C4—221no—
182C4⋊C4—221no—
183C4⋊C4—222no—
184C4⋊C4—442no—
185C22⋊C4—441no—
186C42—41no—
187C42—81no—
188C42—441no—
189C11#1222511yescharacteristic, complemented, Sylow
190C23#6700611yescharacteristic
191Q8—42no—
192Q8—81no—
193Q8—882no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—441no—
211C2×C4—441no—
212C2×C4#6699511yescharacteristic
213C2×C4C2×#432611yescharacteristic
214C8—881no—
215C8—882no—
216C22—21no—
217C22—21no—
218C22#1062284111yescharacteristic
219C22#1062285511yescharacteristic
220C22#1062285711yescharacteristic
221C4—21no—
222C4—21no—
223C4—42no—
224C4—42no—
225C4—42no—
226C4—82no—
227C4—82no—
228C4—881no—
229C4—881no—
230C2—21no—
231C2—21no—
232C2#1306757311yescharacteristic
233C2#1307062911yescharacteristic
234C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2809C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2809D11
hypocenterC11#12225
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2809

Complements

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

NH ≅ G/Ntype
189. C11#12225semidirect

Maximal subgroups

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

subgroupindex
#130697772
#130676572
#130666432
#130665502
C11×#28092
#1222511