Finite Group Databasebeta

← #14654734

Subgroups — #14654734

Order 2816.

468 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 83 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#13079961C211yesmaximal, characteristic
2#13078746C212yesmaximal
3#13067230C212yesmaximal
4#13066486C211yesmaximal, characteristic
5C11×#1985C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7#10623001C2212yes—
8C2×C11×C4⋊C8C2211yescharacteristic
9C2×C11×#97C2211yescharacteristic
10#10622841—22no—
11#10622729—22no—
12#10622644—22no—
13#10622643—24no—
14#10622633—22no—
15#10622584—22no—
16#10622539C2212yes—
17#10622463—22no—
18#10622462—22no—
19C11×#336—22no—
20#10622103—24no—
21C22×Q8×C11D411yescharacteristic
22C22×C8×C11—21no—
23C22×C8×C11D412yes—
24C4×Q8×C11—22no—
25C4×Q8×C11—22no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C42×C11—21no—
29C2×C42×C11C2311yescharacteristic
30C2×#4326—24no—
31#66979—22no—
32#66977—22no—
33#66977—22no—
34C2×Dic44—22no—
35#66923—22no—
36#66922D412yes—
37#66922D412yes—
38C4×Dic22—22no—
39C4×Dic22—22no—
40C11×C4⋊C8—22no—
41C11×#97—22no—
42#66899—24no—
43C22⋊(C11⋊C8)—22no—
44#66882—22no—
45#66880—24no—
46#66874—24no—
47#66872—24no—
48C4⋊(C11⋊C8)—22no—
49#66867D414yes—
50#10031—111nomaximal, Sylow
51C2×Q8×C11—22no—
52C2×Q8×C11—42no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11#4111yescharacteristic
58C2×Dic22—22no—
59C2×Dic22—22no—
60C2×C8×C11—22no—
61C2×C8×C11—22no—
62C2×C8×C11—42no—
63C2×C8×C11—41no—
64C2×C8×C11—41no—
65C11×C4⋊C4—22no—
66C11×C4⋊C4—42no—
67C42×C11—41no—
68C42×C11—41no—
69C42×C11C2×D412yes—
70C42×C11C2×D412yes—
71C22⋊Dic11—42no—
72#4326—48no—
73C4⋊Dic11—22no—
74C4⋊Dic11—22no—
75C4⋊Dic11—22no—
76C4⋊Dic11—22no—
77Dic11⋊C4—42no—
78Dic11⋊C4—42no—
79C4×Dic11—42no—
80C2×C11⋊C8—24no—
81Dic44—82no—
82#3249—111no—
83#3113—112no—
84#1985D1111yescharacteristic
85#1531—112no—
86#1290—111no—
87C23×C11#12111yescharacteristic
88Q8×C11—24no—
89Q8×C11—42no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11—42no—
99C2×C4×C11#12012yes—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11#12112yes—
102C2×C4×C11#12711yescharacteristic
103C2×Dic11—42no—
104C2×Dic11—42no—
105Dic22—44no—
106Dic22—42no—
107Dic22—42no—
108C8×C11—42no—
109C8×C11—42no—
110C11⋊C8—44no—
111#533—112no—
112C2×C4×Q8C2×D1111yescharacteristic
113#483—222no—
114#477—222no—
115#475—222no—
116#467—222no—
117#462—222no—
118#462—222no—
119#451—222no—
120#441—224no—
121#432—112no—
122C2×C4⋊C8C2×D1111yescharacteristic
123C2×#97C2×D1111yescharacteristic
124#336—22no—
125#330—224no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11#39211yescharacteristic
129C22×C11#47312yes—
130C4×C11—21no—
131C4×C11—22no—
132C4×C11—22no—
133C4×C11—42no—
134C4×C11—81no—
135C4×C11#45511yescharacteristic
136C4×C11#45611yescharacteristic
137Dic11—82no—
138Dic11—82no—
139C22×Q8D4411yescharacteristic
140C2×Q16—222no—
141C2×Q16—224no—
142C22×C8—21no—
143C22×C8C22⋊D1112yes—
144C4⋊Q8—112no—
145C4⋊Q8—112no—
146#125—222no—
147C22⋊Q8—222no—
148C22⋊Q8—222no—
149C4×Q8—22no—
150C4×Q8—22no—
151C4×Q8—222no—
152C4×Q8—222no—
153#117—222no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4D4411yescharacteristic
156C2×C42—21no—
157C2×C42C22×D1111yescharacteristic
158#107—222no—
159#106—224no—
160C4⋊C8—22no—
161C4⋊C8—222no—
162#103—224no—
163#103—224no—
164#103—224no—
165C22⋊C8—222no—
166#97—22no—
167#97—114no—
168C2×C11—22no—
169C2×C11#200711yescharacteristic
170C2×C11#201011yescharacteristic
171C2×C11#202011yescharacteristic
172C2×Q8—22no—
173C2×Q8—42no—
174C2×Q8—222no—
175C2×Q8—222no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4C2×D4411yescharacteristic
179C22×C4#433911yescharacteristic
180C22×C4C2×C22⋊D1111yescharacteristic
181Q16—448no—
182Q16—882no—
183C2×C8—22no—
184C2×C8—22no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—42no—
188C2×C8—224no—
189C4⋊C4—22no—
190C4⋊C4—42no—
191C4⋊C4—222no—
192C4⋊C4—222no—
193C4⋊C4—222no—
194C4⋊C4—222no—
195C4⋊C4—442no—
196C4⋊C4—442no—
197C22⋊C4—442no—
198C42—41no—
199C42—41no—
200C42—442no—
201C42D4×D1112yes—
202C42D4×D1112yes—
203C11#1003111yescharacteristic, complemented, Sylow
204C23#6698311yescharacteristic
205Q8—24no—
206Q8—42no—
207Q8—444no—
208Q8—442no—
209Q8—442no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—442no—
220C2×C4—442no—
221C2×C4#6693512yes—
222C2×C4#6693712yes—
223C2×C4#6699011yescharacteristic
224C2×C4#6699311yescharacteristic
225C8—42no—
226C8—42no—
227C8—444no—
228C22—21no—
229C22—21no—
230C22#1062257311yescharacteristic
231C22#1062275612yes—
232C4—21no—
233C4—22no—
234C4—22no—
235C4—42no—
236C4—81no—
237C4—882no—
238C4—882no—
239C4#1062267411yescharacteristic
240C4#1062270811yescharacteristic
241C2—22no—
242C2#1306966211yescharacteristic
243C2#1306968311yescharacteristic
244C2#1306973711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1985C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1985D11
hypocenterC11#10031
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
203. C11#10031semidirect

Maximal subgroups

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

subgroupindex
#130799612
#130787462
#130672302
#130664862
C11×#19852
#1003111