Finite Group Databasebeta

← #14666770

Subgroups — #14666770

Order 2816.

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

normal subgroups only

This group has 394 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#13073989C211yesmaximal, characteristic
2#13067624C212yesmaximal
3#13066621C212yesmaximal
4#13066562C211yesmaximal, characteristic
5C11×#2060C211yesmaximal, characteristic
6C11×#544C2211yescharacteristic
7C2×C4×Dic22—21no—
8C11×#428—21no—
9C11×#384C2211yescharacteristic
10#10622656—22no—
11#10622598—22no—
12#10622596—21no—
13#10622596C2212yes—
14#10622587—22no—
15C11×#343C2211yescharacteristic
16C11×#339—21no—
17#10622176—22no—
18#10622166C2212yes—
19C22×Dic22—21no—
20C2×C11×M16—21no—
21C11×C4⋊Q8—41no—
22C11×#125—41no—
23C11×C22⋊Q8—22no—
24C11×#117—21no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C4⋊C4C2311yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11D412yes—
32C2×Dic11⋊C4—22no—
33C2×C4×Dic11—22no—
34C4×Dic22—42no—
35C4×Dic22—42no—
36C11×#107—41no—
37C11×#106—41no—
38#66899—42no—
39C11⋊#95—21no—
40C11⋊#95—22no—
41C11⋊#95—22no—
42C11⋊#95D412yes—
43C22⋊(C11⋊C8)—22no—
44#66872—42no—
45#12247—111nomaximal, Sylow
46C2×Q8×C11—22no—
47C22×C4×C11—21no—
48C22×C4×C11—21no—
49C22×C4×C11C2×D411yescharacteristic
50C22×C4×C11C2×D412yes—
51C22×Dic11—22no—
52C22×Dic11—22no—
53C2×Dic22—24no—
54C2×Dic22—42no—
55C2×Dic22—42no—
56C11×M16—22no—
57C11×M16—41no—
58C2×C8×C11—41no—
59C11×C4⋊C4—22no—
60C11×C4⋊C4—21no—
61C11×C4⋊C4—21no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—44no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—41no—
66C11×C22⋊C4—41no—
67C42×C11—21no—
68C42×C11—41no—
69C42×C11SD1612yes—
70C4⋊Dic11—42no—
71C4⋊Dic11—42no—
72C4⋊Dic11—81no—
73Dic11⋊C4—42no—
74Dic11⋊C4—42no—
75C4×Dic11—44no—
76C2×C11⋊C8—42no—
77#2582—111no—
78#2060D1111yescharacteristic
79#1611—112no—
80#1346—112no—
81#1325—111no—
82C23×C11#12011yescharacteristic
83Q8×C11—82no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—41no—
95C2×C4×C11C2×SD1611yescharacteristic
96C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
97C2×Dic11—24no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103Dic22—48no—
104C8×C11—42no—
105C11⋊C8—82no—
106#544C2×D1111yescharacteristic
107C2×C4×Q8—221no—
108#483—222no—
109#428—21no—
110#398—112no—
111#398—221no—
112#391—222no—
113#389—222no—
114#384C2×D1111yescharacteristic
115#343C2×D1111yescharacteristic
116#339—21no—
117#328—222no—
118#324—112no—
119C22×C11—21no—
120C22×C11—21no—
121C22×C11#45011yescharacteristic
122C22×C11#45611yescharacteristic
123C22×C11B(4,𝔽2)11yescharacteristic
124C4×C11—24no—
125C4×C11—21no—
126C4×C11—21no—
127C4×C11—42no—
128C4×C11—81no—
129C4×C11—81no—
130C4×C11—81no—
131Dic11—44no—
132Dic11—82no—
133C22×Q8—221no—
134C2×M16—21no—
135C4⋊Q8—41no—
136#125—41no—
137C22⋊Q8—22no—
138C4×Q8—442no—
139C4×Q8—442no—
140#117—21no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—112no—
143C2×C4⋊C4—221no—
144C2×C4⋊C4—222no—
145C2×C4⋊C4—221no—
146C2×C4⋊C4C22⋊D1111yescharacteristic
147C2×C4⋊C4C22×D1111yescharacteristic
148C2×C42—222no—
149C2×C42C22⋊D1111yescharacteristic
150#107—41no—
151#106—41no—
152#106—442no—
153#103—442no—
154C22⋊C8—222no—
155#95—112no—
156#95—222no—
157#95—221no—
158#95—222no—
159C2×C11—21no—
160C2×C11—21no—
161C2×C11#160411yescharacteristic
162C2×C11#219811yescharacteristic
163C2×C11#220511yescharacteristic
164C2×Q8—22no—
165C2×Q8—224no—
166C2×Q8—442no—
167C2×Q8—442no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—222no—
171C22×C4—222no—
172C22×C4D4×D1112yes—
173C22×C4C2×C22⋊D1111yescharacteristic
174M16—22no—
175M16—41no—
176C2×C8—41no—
177C2×C8—442no—
178C4⋊C4—21no—
179C4⋊C4—22no—
180C4⋊C4—21no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—44no—
184C4⋊C4—42no—
185C4⋊C4—442no—
186C4⋊C4—442no—
187C4⋊C4—442no—
188C4⋊C4—442no—
189C4⋊C4—881no—
190C22⋊C4—41no—
191C42—21no—
192C42—41no—
193C42—444no—
194C42#432512yes—
195C11#1224711yescharacteristic, complemented, Sylow
196C23#6699011yescharacteristic
197Q8—82no—
198Q8—448no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—224no—
211C2×C4—442no—
212C2×C4—442no—
213C2×C4—442no—
214C2×C4—442no—
215C2×C4—442no—
216C2×C4C2×#432511yescharacteristic
217C2×C4#6700211yescharacteristic
218C8—42no—
219C8—882no—
220C22—21no—
221C22—21no—
222C22#1062264511yescharacteristic
223C22#1062265911yescharacteristic
224C22#1062270811yescharacteristic
225C4—24no—
226C4—21no—
227C4—21no—
228C4—42no—
229C4—81no—
230C4—81no—
231C4—81no—
232C4—444no—
233C4—882no—
234C2—21no—
235C2—21no—
236C2#1306758411yescharacteristic
237C2#1307061111yescharacteristic
238C2#1307064511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2060C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2060D11
hypocenterC11#12247
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2060

Complements

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

NH ≅ G/Ntype
195. C11#12247semidirect

Maximal subgroups

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

subgroupindex
#130739892
#130676242
#130666212
#130665622
C11×#20602
#1224711