Finite Group Databasebeta

← #14667483

Subgroups — #14667483

Order 2816.

282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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#13081505C211yesmaximal, characteristic
2#13070843C211yesmaximal, characteristic
3#13067983C211yesmaximal, characteristic
4#13066670C211yesmaximal, characteristic
5#13066594C211yesmaximal, characteristic
6#13066580C211yesmaximal, characteristic
7C11×#2209C211yesmaximal, characteristic
8#10623101—21no—
9C2×C11×Q32—21no—
10C11×#494C2211yescharacteristic
11C4×C11×Q16C2211yescharacteristic
12Q16×Dic11—21no—
13#10622707—21no—
14#10622633—21no—
15#10622491—21no—
16#10622409—22no—
17#10622295C2211yescharacteristic
18C8×Dic22C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C11×#358—21no—
21#10622202—22no—
22#10622185—21no—
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16—21no—
27C2×C11×Q16D411yescharacteristic
28C11×C4⋊Q8—21no—
29C4×Q8×C11—21no—
30Q8×Dic11—22no—
31#66943—22no—
32#66943—42no—
33#66922—21no—
34#66922—41no—
35C4×Dic22—41no—
36C4×Dic22D411yescharacteristic
37C11×Q32—42no—
38C2×C11×C16—21no—
39C11×#107D411yescharacteristic
40C11×#103—21no—
41C4×C8×C11C2311yescharacteristic
42#66899—22no—
43#66882—21no—
44#66882D412yes—
45Dic11⋊C8—21no—
46C8×Dic11—21no—
47C2×C11⋊C16—21no—
48#66874—41no—
49#66872—22no—
50#66872—41no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#12357—111nomaximal, Sylow
54C2×Q8×C11—21no—
55C2×Q8×C11—41no—
56C2×Dic22—41no—
57C2×Dic22D811yescharacteristic
58C11×Q16—21no—
59C11×Q16—42no—
60C11×Q16—41no—
61C11×Q16—41no—
62C11×Q16SD1612yes—
63C2×C8×C11C2×D411yescharacteristic
64C2×C8×C11C2×D411yescharacteristic
65C11×C4⋊C4—21no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C42×C11—41no—
70C42×C11C2×D411yescharacteristic
71C4⋊Dic11—22no—
72C4⋊Dic11—42no—
73C4⋊Dic11—42no—
74C4⋊Dic11—41no—
75C4⋊Dic11D811yescharacteristic
76Dic11⋊C4—21no—
77Dic11⋊C4—42no—
78C4×Dic11—21no—
79C4×Dic11—42no—
80C2×C11⋊C8—21no—
81C2×C11⋊C8—41no—
82C11×C16—41no—
83C11⋊C16—41no—
84#3383—111no—
85#2241—111no—
86#2209D1111yescharacteristic
87#1670—111no—
88#1364—111no—
89Q8⋊C16—111no—
90#1332—111no—
91Q8×C11—22no—
92Q8×C11—41no—
93Q8×C11—81no—
94Q8×C11—81no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11—81no—
98C2×C4×C11#12011yescharacteristic
99C2×C4×C11C2×D811yescharacteristic
100C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
101C2×Dic11—21no—
102C2×Dic11—21no—
103C2×Dic11—42no—
104Dic22—21no—
105Dic22—21no—
106Dic22—81no—
107Dic22—81no—
108C8×C11—21no—
109C8×C11C2×SD1611yescharacteristic
110C8×C11#13711yescharacteristic
111C11⋊C8—41no—
112C11⋊C8—81no—
113#557—221no—
114C2×Q32—21no—
115#500—111no—
116#499—221no—
117#494C2×D1111yescharacteristic
118#479—222no—
119#475—221no—
120#475—221no—
121C8×Q8—111no—
122C4×Q16—221no—
123C4×Q16C2×D1111yescharacteristic
124C4⋊C16C2×D1111yescharacteristic
125#358—21no—
126#358—222no—
127C4×C16—111no—
128#335—111no—
129#332—221no—
130C22×C11#44711yescharacteristic
131C4×C11—21no—
132C4×C11—42no—
133C4×C11—81no—
134C4×C11—161no—
135C4×C11#44811yescharacteristic
136C4×C11#45411yescharacteristic
137C4×C11#50811yescharacteristic
138C4×C11#51011yescharacteristic
139Dic11—41no—
140Dic11—41no—
141Dic11—82no—
142C2×Q16—21no—
143C2×Q16—21no—
144C2×Q16C22⋊D1111yescharacteristic
145C4⋊Q8—21no—
146C4⋊Q8—221no—
147C4⋊Q8—441no—
148#125—222no—
149#125—442no—
150C4×Q8—21no—
151C4×Q8—111no—
152C4×Q8—222no—
153C4×Q8—441no—
154Q32—42no—
155C2×C16—21no—
156C2×C16—221no—
157#107—112no—
158#107—221no—
159#107C22⋊D1111yescharacteristic
160#106—222no—
161#106—441no—
162C4⋊C8—111no—
163C4⋊C8—221no—
164C4⋊C8—221no—
165#103—21no—
166#103—222no—
167#103—441no—
168C4×C8—221no—
169C4×C8C22×D1111yescharacteristic
170C2×C11#162711yescharacteristic
171C2×C11#218911yescharacteristic
172C2×C11#219511yescharacteristic
173C2×Q8—21no—
174C2×Q8—41no—
175C2×Q8—111no—
176C2×Q8—441no—
177Q16—21no—
178Q16—42no—
179Q16—41no—
180Q16—41no—
181Q16#432412yes—
182C2×C8—221no—
183C2×C8—441no—
184C2×C8D4×D1111yescharacteristic
185C2×C8C2×C22⋊D1111yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—111no—
191C4⋊C4—221no—
192C4⋊C4—222no—
193C4⋊C4—442no—
194C4⋊C4—442no—
195C4⋊C4—442no—
196C4⋊C4—441no—
197C42—41no—
198C42—221no—
199C42—442no—
200C42D4×D1111yescharacteristic
201C16—41no—
202C16—441no—
203C11#1235711yescharacteristic, complemented, Sylow
204Q8—22no—
205Q8—41no—
206Q8—81no—
207Q8—81no—
208Q8—221no—
209Q8—221no—
210Q8—881no—
211Q8—881no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—81no—
215C2×C4—221no—
216C2×C4—221no—
217C2×C4—442no—
218C2×C4D8×D1111yescharacteristic
219C2×C4#6696411yescharacteristic
220C2×C4#6699011yescharacteristic
221C8—21no—
222C8—441no—
223C8—881no—
224C8C2×#432411yescharacteristic
225C8#6700411yescharacteristic
226C22#1062276911yescharacteristic
227C4—21no—
228C4—42no—
229C4—81no—
230C4—161no—
231C4—441no—
232C4—441no—
233C4—882no—
234C4#1062253111yescharacteristic
235C4#1062253211yescharacteristic
236C4#1062265311yescharacteristic
237C4#1062281411yescharacteristic
238C2#1306771811yescharacteristic
239C2#1307055511yescharacteristic
240C2#1307059111yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2209C2
socle, prime radicalC22×C11#447
hypercenter#2209D11
hypocenterC11#12357
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
203. C11#12357semidirect

Maximal subgroups

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

subgroupindex
#130815052
#130708432
#130679832
#130666702
#130665942
#130665802
C11×#22092
#1235711