Finite Group Databasebeta

← #14666797

Subgroups — #14666797

Order 2816.

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

normal subgroups only

This group has 342 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#13076684C211yesmaximal, characteristic
2#13069966C211yesmaximal, characteristic
3#13067626C212yesmaximal
4#13066623C212yesmaximal
5C11×#1324C211yesmaximal, characteristic
6#10623031C2211yescharacteristic
7C2×#66923—21no—
8C11×#382C2211yescharacteristic
9#10622596—21no—
10#10622596C2212yes—
11#10622577—21no—
12#10622334—22no—
13#10622274—22no—
14#10622272—22no—
15C11×#324C2212yes—
16#10622168C2211yescharacteristic
17#10622161—21no—
18#10622105—22no—
19C2×C11×C4⋊C4D411yescharacteristic
20C2×C11×C4⋊C4C2311yescharacteristic
21C2×C42×C11D411yescharacteristic
22#66979—21no—
23C2×C4⋊Dic11—21no—
24C2×C4⋊Dic11—21no—
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11D412yes—
27#66977—22no—
28C2×Dic11⋊C4—22no—
29C2×Dic11⋊C4—22no—
30C2×#4318—21no—
31#66943—41no—
32#66941—41no—
33#66923—42no—
34#66923—42no—
35C11×C22⋊C8—22no—
36C11×#95—22no—
37C11⋊#95—21no—
38C11⋊#95—22no—
39C11⋊#95—22no—
40C11⋊#95D412yes—
41#66881—42no—
42#66880—42no—
43#66872—41no—
44#66871—41no—
45#12251—111nomaximal, Sylow
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11C2×D411yescharacteristic
49C22×C4×C11C2×D412yes—
50C22×Dic11—22no—
51C22×Dic11—22no—
52C2×Dic22—22no—
53C2×C8×C11—42no—
54C11×C4⋊C4—41no—
55C11×C4⋊C4—41no—
56C42×C11—21no—
57C42×C11SD1612yes—
58C22⋊Dic11—41no—
59C4⋊Dic11—21no—
60C4⋊Dic11—21no—
61C4⋊Dic11—22no—
62C4⋊Dic11—42no—
63C4⋊Dic11—42no—
64C4⋊Dic11—42no—
65C4⋊Dic11—81no—
66Dic11⋊C4—44no—
67Dic11⋊C4—42no—
68Dic11⋊C4—42no—
69Dic11⋊C4—42no—
70C4×Dic11—41no—
71#4318—22no—
72#4318—41no—
73C2×C11⋊C8—41no—
74#2822—111no—
75#2061—111no—
76#1611—112no—
77#1346—112no—
78#1324D1111yescharacteristic
79C23×C11#12011yescharacteristic
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—41no—
85C2×C4×C11—41no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11—41no—
89C2×C4×C11C2×SD1611yescharacteristic
90C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
91C2×Dic11—42no—
92C2×Dic11—42no—
93C2×Dic11—42no—
94C2×Dic11—42no—
95C2×Dic11—42no—
96C2×Dic11—41no—
97C2×Dic11—41no—
98C2×Dic11—42no—
99Dic22—82no—
100C8×C11—82no—
101C11⋊C8—42no—
102#544—111no—
103C2×#125—221no—
104#483—222no—
105#428—221no—
106#400—222no—
107#398—112no—
108#398—222no—
109#398—221no—
110#382C2×D1111yescharacteristic
111#343—111no—
112#339—221no—
113#328—222no—
114#324C2×D1112yes—
115C22×C11—21no—
116C22×C11—21no—
117C22×C11#45011yescharacteristic
118C22×C11#45611yescharacteristic
119C22×C11B(4,𝔽2)11yescharacteristic
120C4×C11—21no—
121C4×C11—21no—
122C4×C11—42no—
123C4×C11—42no—
124C4×C11—81no—
125Dic11—82no—
126Dic11—82no—
127Dic11—81no—
128Dic11—81no—
129C2×M16—221no—
130C4⋊Q8—441no—
131#125—442no—
132#125—441no—
133#125—442no—
134C22⋊Q8—222no—
135#117—221no—
136C2×C4⋊C4—112no—
137C2×C4⋊C4—221no—
138C2×C4⋊C4—222no—
139C2×C4⋊C4—221no—
140C2×C4⋊C4—222no—
141C2×C4⋊C4—221no—
142C2×C4⋊C4D4411yescharacteristic
143C2×C4⋊C4C22×D1111yescharacteristic
144C2×C42D4411yescharacteristic
145#107—441no—
146#106—441no—
147#106—442no—
148#103—442no—
149C22⋊C8—22no—
150#95—22no—
151#95—112no—
152#95—222no—
153#95—221no—
154#95—222no—
155C2×C11—21no—
156C2×C11—21no—
157C2×C11#160411yescharacteristic
158C2×C11#220111yescharacteristic
159C2×C11#220311yescharacteristic
160C2×Q8—222no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—222no—
164C22×C4—222no—
165C22×C4C2×D4411yescharacteristic
166C22×C4D4×D1112yes—
167M16—222no—
168M16—441no—
169C2×C8—42no—
170C2×C8—441no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—221no—
174C4⋊C4—222no—
175C4⋊C4—221no—
176C4⋊C4—442no—
177C4⋊C4—444no—
178C4⋊C4—442no—
179C4⋊C4—442no—
180C4⋊C4—442no—
181C4⋊C4—442no—
182C4⋊C4—442no—
183C4⋊C4—881no—
184C22⋊C4—441no—
185C42—21no—
186C42—441no—
187C42#431412yes—
188C11#1225111yescharacteristic, complemented, Sylow
189C23#6693511yescharacteristic
190Q8—882no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—442no—
201C2×C4—442no—
202C2×C4—442no—
203C2×C4—442no—
204C2×C4—441no—
205C2×C4—441no—
206C2×C4—442no—
207C2×C4—442no—
208C2×C4C2×#431411yescharacteristic
209C2×C4#6696111yescharacteristic
210C8—82no—
211C8—442no—
212C22—21no—
213C22—21no—
214C22#1062234411yescharacteristic
215C22#1062235411yescharacteristic
216C22#1062236511yescharacteristic
217C4—21no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—81no—
222C4—882no—
223C4—881no—
224C4—881no—
225C4—882no—
226C2—21no—
227C2—21no—
228C2#1306758711yescharacteristic
229C2#1307063111yescharacteristic
230C2#1307063911yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1324C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#1324D11
hypocenterC11#12251
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
188. C11#12251semidirect

Maximal subgroups

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

subgroupindex
#130766842
#130699662
#130676262
#130666232
C11×#13242
#1225111