Finite Group Databasebeta

← #14654732

Subgroups — #14654732

Order 2816.

468 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 85 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#13078742C212yesmaximal
2#13069555C211yesmaximal, characteristic
3#13067231C212yesmaximal
4#13066486C211yesmaximal, characteristic
5C11×#3249C211yesmaximal, characteristic
6C11×#533C2212yes—
7C2×C4×Dic22C2211yescharacteristic
8C11×#477—22no—
9C11×#467—22no—
10C11×#462—22no—
11C2×C11×C4⋊C8C2211yescharacteristic
12#10622707—22no—
13#10622703—22no—
14#10622663—22no—
15#10622656—22no—
16#10622643—24no—
17#10622539C2212yes—
18C2×#66867C2211yescharacteristic
19#10622188—22no—
20#10622181—24no—
21C22×Dic22D411yescharacteristic
22C2×C11×Q16—22no—
23C22×C8×C11D412yes—
24C11×C4⋊Q8D412yes—
25C11×C4⋊Q8D412yes—
26C11×#125—22no—
27C11×C22⋊Q8—22no—
28C11×C22⋊Q8—22no—
29C4×Q8×C11—22no—
30C4×Q8×C11—22no—
31C11×#117—22no—
32C2×C42×C11C2311yescharacteristic
33C2×#4326—24no—
34C2×C4⋊Dic11D411yescharacteristic
35C2×Dic11⋊C4—21no—
36C2×C4×Dic11—21no—
37C22×C11⋊C8—21no—
38C4×Dic22—22no—
39C4×Dic22—22no—
40C11×#107—22no—
41C11×C4⋊C8—22no—
42C11×#103—24no—
43#66899—24no—
44C22⋊(C11⋊C8)—22no—
45#66874—24no—
46#66872—24no—
47C4⋊(C11⋊C8)—22no—
48#66867—22no—
49#66867D414yes—
50#10031—111nomaximal, Sylow
51C2×Q8×C11—22no—
52C2×Q8×C11—22no—
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11#4111yescharacteristic
56C22×Dic11—21no—
57C22×Dic11—21no—
58C2×Dic22—22no—
59C2×Dic22—42no—
60C11×Q16—82no—
61C2×C8×C11—22no—
62C2×C8×C11—42no—
63C11×C4⋊C4—22no—
64C11×C4⋊C4—22no—
65C11×C4⋊C4—22no—
66C11×C4⋊C4—22no—
67C11×C4⋊C4—42no—
68C11×C4⋊C4—42no—
69C11×C22⋊C4—42no—
70C42×C11—42no—
71C42×C11C2×D412yes—
72C42×C11C2×D412yes—
73#4326—48no—
74C4⋊Dic11—22no—
75Dic11⋊C4—42no—
76C4×Dic11—41no—
77C4×Dic11—41no—
78C2×C11⋊C8—22no—
79C2×C11⋊C8—24no—
80C2×C11⋊C8—41no—
81C2×C11⋊C8—41no—
82#3249D1111yescharacteristic
83#3113—112no—
84#1985—111no—
85#1531—112no—
86#1290—111no—
87C23×C11#12111yescharacteristic
88Q8×C11—44no—
89Q8×C11—42no—
90Q8×C11—42no—
91C2×C4×C11—22no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—41no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11#12012yes—
98C2×C4×C11#12011yescharacteristic
99C2×C4×C11#12112yes—
100C2×C4×C11#12711yescharacteristic
101C2×Dic11—22no—
102C2×Dic11—41no—
103C2×Dic11—41no—
104C2×Dic11—41no—
105C2×Dic11—42no—
106Dic22—24no—
107Dic22—42no—
108C8×C11—42no—
109C11⋊C8—42no—
110C11⋊C8—44no—
111#533C2×D1112yes—
112C2×C4×Q8—111no—
113#483—222no—
114#477—22no—
115#475—222no—
116#467—22no—
117#462—22no—
118#462—222no—
119#451—222no—
120#441—224no—
121#432—112no—
122C2×C4⋊C8C2×D1111yescharacteristic
123C2×#97—111no—
124#336—222no—
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—82no—
134C4×C11—82no—
135C4×C11#45511yescharacteristic
136C4×C11#45611yescharacteristic
137Dic11—42no—
138Dic11—81no—
139C22×Q8—111no—
140C2×Q16—22no—
141C2×Q16—224no—
142C22×C8—221no—
143C22×C8C22⋊D1112yes—
144C4⋊Q8C22⋊D1112yes—
145C4⋊Q8C22⋊D1112yes—
146#125—22no—
147C22⋊Q8—22no—
148C22⋊Q8—22no—
149C4×Q8—22no—
150C4×Q8—22no—
151C4×Q8—222no—
152C4×Q8—222no—
153#117—22no—
154C2×C4⋊C4—111no—
155C2×C4⋊C4—221no—
156C2×C42—221no—
157C2×C42C22×D1111yescharacteristic
158#107—22no—
159#106—224no—
160C4⋊C8—22no—
161C4⋊C8—222no—
162#103—24no—
163#103—224no—
164#103—224no—
165C22⋊C8—222no—
166#97—114no—
167#97—222no—
168C2×C11—22no—
169C2×C11#200711yescharacteristic
170C2×C11#201011yescharacteristic
171C2×C11#202011yescharacteristic
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—222no—
175C2×Q8—442no—
176C22×C4—221no—
177C22×C4—221no—
178C22×C4D4×D1111yescharacteristic
179C22×C4#434111yescharacteristic
180C22×C4C2×C22⋊D1111yescharacteristic
181Q16—82no—
182Q16—448no—
183C2×C8—22no—
184C2×C8—42no—
185C2×C8—222no—
186C2×C8—224no—
187C2×C8—441no—
188C2×C8—441no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—222no—
196C4⋊C4—442no—
197C22⋊C4—42no—
198C42—42no—
199C42—441no—
200C42—441no—
201C42D4×D1112yes—
202C42C2×C22⋊D1112yes—
203C11#1003111yescharacteristic, complemented, Sylow
204C23#6699111yescharacteristic
205Q8—44no—
206Q8—42no—
207Q8—42no—
208Q8—224no—
209Q8—442no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—222no—
217C2×C4—441no—
218C2×C4—441no—
219C2×C4—442no—
220C2×C4—441no—
221C2×C4#6699012yes—
222C2×C4#6699212yes—
223C2×C4#6699311yescharacteristic
224C2×C4#6700611yescharacteristic
225C8—42no—
226C8—442no—
227C8—444no—
228C22—21no—
229C22—21no—
230C22#1062280512yes—
231C22#1062283611yescharacteristic
232C4—21no—
233C4—22no—
234C4—22no—
235C4—82no—
236C4—82no—
237C4—442no—
238C4—881no—
239C4#1062285511yescharacteristic
240C4#1062285911yescharacteristic
241C2—22no—
242C2#1306966311yescharacteristic
243C2#1306968011yescharacteristic
244C2#1306973511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3249C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3249D11
hypocenterC11#10031
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

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
#130787422
#130695552
#130672312
#130664862
C11×#32492
#1003111