Finite Group Databasebeta

← #14654436

Subgroups — #14654436

Order 2816.

502 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 79 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#13078564C212yesmaximal
2#13076653C211yesmaximal, characteristic
3#13067148C212yesmaximal
4#13066524C211yesmaximal, characteristic
5C11×#1820C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C2×#66977C2212yes—
8C11×#381C2211yescharacteristic
9C11×#381C2211yescharacteristic
10#10622820C2212yes—
11#10622617—22no—
12#10622609—24no—
13#10622608—22no—
14#10622584—22no—
15#10622583—22no—
16#10622566—22no—
17#10622272—22no—
18#10622269—22no—
19C11×#342—22no—
20#10622090—24no—
21C23×C4×C11C2311yescharacteristic
22C22×Dic22D412yes—
23C11×#117—22no—
24C11×#117—22no—
25C2×C11×C4⋊C4D412yes—
26C2×C11×C22⋊C4—21no—
27C2×C11×C22⋊C4—21no—
28C2×C11×C22⋊C4D412yes—
29C2×C42×C11—21no—
30C2×C22⋊Dic11—22no—
31C2×C4⋊Dic11—22no—
32C2×C4⋊Dic11D412yes—
33#66977—22no—
34#66977—22no—
35#66977—22no—
36#66977—22no—
37C2×Dic11⋊C4—22no—
38C2×#4318—22no—
39C11×#95—22no—
40C11×#95—22no—
41C11⋊#95—24no—
42C11⋊#95—22no—
43C22⋊(C11⋊C8)—22no—
44C22⋊(C11⋊C8)D414yes—
45#66874—24no—
46#66874—24no—
47#66872—24no—
48#66871—24no—
49#9985—111nomaximal, Sylow
50C24×C11C2×D411yescharacteristic
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—42no—
54C22×C4×C11—41no—
55C22×C4×C11C2×D412yes—
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11C2×D412yes—
58C22×C4×C11#4111yescharacteristic
59C22×Dic11—22no—
60C22×Dic11—22no—
61C2×Dic22—22no—
62C2×Dic22—22no—
63C2×Dic22—44no—
64C11×C4⋊C4—22no—
65C11×C4⋊C4—22no—
66C11×C22⋊C4—41no—
67C11×C22⋊C4—41no—
68C11×C22⋊C4—42no—
69C11×C22⋊C4—42no—
70C42×C11—42no—
71C22⋊Dic11—42no—
72C22⋊Dic11—42no—
73C4⋊Dic11—22no—
74C4⋊Dic11—22no—
75C4⋊Dic11—82no—
76Dic11⋊C4—42no—
77Dic11⋊C4—42no—
78#4318—44no—
79C2×C11⋊C8—24no—
80#3095—112no—
81#2817—111no—
82#1820D1111yescharacteristic
83#1511—112no—
84#1306—111no—
85C23×C11—22no—
86C23×C11—42no—
87C23×C11#12011yescharacteristic
88C23×C11#12111yescharacteristic
89C23×C11#12711yescharacteristic
90C2×C4×C11—24no—
91C2×C4×C11—41no—
92C2×C4×C11—42no—
93C2×C4×C11—41no—
94C2×C4×C11—44no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—82no—
98C2×C4×C11—81no—
99C2×C4×C11—82no—
100C2×C4×C11#12012yes—
101C2×C4×C11#12112yes—
102C2×Dic11—44no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—44no—
106Dic22—44no—
107Dic22—82no—
108C11⋊C8—44no—
109C2×C22⋊Q8—112no—
110C2×#117C2×D1111yescharacteristic
111#485—224no—
112#484—222no—
113#483—222no—
114#428—222no—
115#419—222no—
116#407—112no—
117#400—222no—
118#397—222no—
119#395—222no—
120#381C2×D1111yescharacteristic
121#381C2×D1111yescharacteristic
122#342—22no—
123#328—224no—
124C22×C11—22no—
125C22×C11—22no—
126C22×C11—22no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11—82no—
130C22×C11#39211yescharacteristic
131C22×C11#45812yes—
132C4×C11—22no—
133C4×C11—22no—
134C4×C11—82no—
135C4×C11—82no—
136C4×C11—161no—
137Dic11—82no—
138Dic11—82no—
139C22×Q8—112no—
140C23×C4C22×D1111yescharacteristic
141C2×M16—222no—
142C22⋊Q8—222no—
143C22⋊Q8—222no—
144C22⋊Q8—222no—
145C22⋊Q8—222no—
146#117—22no—
147#117—22no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—222no—
150C2×C4⋊C4—222no—
151C2×C4⋊C4D4412yes—
152C2×C22⋊C4—21no—
153C2×C22⋊C4—21no—
154C2×C22⋊C4—222no—
155C2×C22⋊C4C22⋊D1112yes—
156C2×C42—21no—
157#107—224no—
158#106—224no—
159#103—224no—
160#103—224no—
161C22⋊C8—114no—
162C22⋊C8—222no—
163#95—22no—
164#95—22no—
165#95—224no—
166#95—222no—
167C2×C11—22no—
168C2×C11—41no—
169C2×C11—41no—
170C2×C11#200912yes—
171C2×C11#202211yescharacteristic
172C24C2×C22⋊D1111yescharacteristic
173C2×Q8—222no—
174C2×Q8—222no—
175C2×Q8—444no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—42no—
179C22×C4—41no—
180C22×C4—222no—
181C22×C4—222no—
182C22×C4C2×D4411yescharacteristic
183C22×C4#433911yescharacteristic
184C22×C4D4×D1112yes—
185C22×C4D4×D1112yes—
186M16—444no—
187C2×C8—224no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—222no—
191C4⋊C4—222no—
192C4⋊C4—442no—
193C4⋊C4—442no—
194C4⋊C4—882no—
195C22⋊C4—41no—
196C22⋊C4—41no—
197C22⋊C4—42no—
198C22⋊C4—42no—
199C22⋊C4—442no—
200C22⋊C4—442no—
201C42—42no—
202C11#998511yescharacteristic, complemented, Sylow
203C23—22no—
204C23—42no—
205C23#6698311yescharacteristic
206C23#6699011yescharacteristic
207C23#6699311yescharacteristic
208Q8—444no—
209Q8—882no—
210C2×C4—24no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—82no—
218C2×C4—81no—
219C2×C4—82no—
220C2×C4—444no—
221C2×C4—442no—
222C2×C4—442no—
223C2×C4—444no—
224C2×C4#6693512yes—
225C2×C4#6693712yes—
226C8—444no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—21no—
232C22—82no—
233C22#1062257311yescharacteristic
234C22#1062266612yes—
235C4—22no—
236C4—22no—
237C4—82no—
238C4—82no—
239C4—161no—
240C4—882no—
241C4—882no—
242C2—22no—
243C2—41no—
244C2—41no—
245C2#1306967512yes—
246C2#1306974711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1820C2
socleC22×C11#392
prime radicalC24×C11C2×D4
hypercenter#1820D11
hypocenterC11#9985
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
202. C11#9985semidirect

Maximal subgroups

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

subgroupindex
#130785642
#130766532
#130671482
#130665242
C11×#18202
#998511