Finite Group Databasebeta

← #14667313

Subgroups — #14667313

Order 2816.

324 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 65 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#13081630C211yesmaximal, characteristic
2#13070663C211yesmaximal, characteristic, complemented
3#13067983C211yesmaximal, characteristic, complemented
4#13066662C211yesmaximal, characteristic
5#13066596C211yesmaximal, characteristic, complemented
6#13066581C211yesmaximal, characteristic, complemented
7C11×#2248C211yesmaximal, characteristic
8#10623244—21no—
9C2×C11×SD32—22no—
10C11×#494C2211yescharacteristic
11C11×#493C2211yescharacteristic
12C2×#66893—21no—
13#10622768—21no—
14#10622766—22no—
15D8×Dic11—21no—
16#10622707—21no—
17#10622688—21no—
18C4×Dic44C2211yescharacteristic
19C8×Dic22C2211yescharacteristic
20C4×C11×C16C2211yescharacteristic
21#10622202—21no—
22#10622185—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16—21no—
27C2×C11×D8—21no—
28C2×C11×D8D412yes—
29C11×C4⋊Q8—21no—
30C11×#127—21no—
31#66989—22no—
32#66989—41no—
33#66988—42no—
34D4×Dic11—22no—
35D4×Dic11—41no—
36C2×#4324—22no—
37C2×Dic44D411yescharacteristic
38C4×Dic22—21no—
39C4×Dic22D411yescharacteristic
40C11×SD32—44no—
41C2×C11×C16—21no—
42C4×C8×C11C2311yescharacteristic
43#66896—22no—
44#66893—42no—
45#66882D411yescharacteristic
46#66880—21no—
47Dic11⋊C8—21no—
48C8×Dic11—21no—
49C2×C11⋊C16—21no—
50#66874—41no—
51#66872—41no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)D411yescharacteristic
54#12333—111nomaximal, Sylow
55C2×Q8×C11—41no—
56C2×D4×C11—22no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C22×Dic11—42no—
60C2×Dic22—21no—
61C2×Dic22D811yescharacteristic
62C11×Q16—42no—
63C11×Q16—41no—
64C11×Q16—41no—
65C11×D8—41no—
66C11×D8—41no—
67C11×D8—42no—
68C2×C8×C11C2×D411yescharacteristic
69C2×C8×C11C2×D411yescharacteristic
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C42×C11C2×D411yescharacteristic
73C22⋊Dic11—42no—
74C22⋊Dic11—42no—
75C22⋊Dic11—42no—
76#4324—82no—
77C4⋊Dic11—21no—
78C4⋊Dic11D811yescharacteristic
79Dic11⋊C4—21no—
80Dic11⋊C4—41no—
81C4×Dic11—21no—
82C4×Dic11—41no—
83C2×C11⋊C8—21no—
84C2×C11⋊C8—41no—
85Dic44—21no—
86Dic44—21no—
87C11×C16—22no—
88C11⋊C16—41no—
89#3396—111no—
90#2248D1111yescharacteristic
91#2209—111no—
92#1670—111no—
93#1361—111no—
94Q8⋊C16—111no—
95#1332—111no—
96C23×C11—42no—
97Q8×C11—81no—
98Q8×C11—81no—
99D4×C11—42no—
100D4×C11—42no—
101D4×C11—81no—
102D4×C11—81no—
103D4×C11—161no—
104C2×C4×C11—81no—
105C2×C4×C11#12011yescharacteristic
106C2×C4×C11C2×D811yescharacteristic
107C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11—41no—
111C2×Dic11—41no—
112C2×Dic11—162no—
113Dic22—21no—
114Dic22—21no—
115Dic22—41no—
116Dic22—41no—
117C8×C11—21no—
118C8×C11#13511yescharacteristic
119C8×C11AGL(1,ℤ/8)11yescharacteristic
120C11⋊C8—41no—
121C11⋊C8—81no—
122#559—221no—
123C2×Q32—221no—
124C2×SD32—22no—
125#495—221no—
126#494C2×D1111yescharacteristic
127#493C2×D1111yescharacteristic
128#475—221no—
129#463—222no—
130#460—221no—
131C8×Q8—111no—
132C4×Q16—111no—
133C4×D8—221no—
134C4⋊C16—111no—
135#358—221no—
136C4×C16C2×D1111yescharacteristic
137#335—111no—
138#332—221no—
139C22×C11—82no—
140C22×C11—82no—
141C22×C11—82no—
142C22×C11#44711yescharacteristic
143C4×C11—21no—
144C4×C11—161no—
145C4×C11#44911yescharacteristic
146C4×C11#45311yescharacteristic
147C4×C11#50811yescharacteristic
148C4×C11#51011yescharacteristic
149Dic11—41no—
150Dic11—41no—
151Dic11—81no—
152Dic11—81no—
153C2×Q16—21no—
154C2×Q16—21no—
155C2×Q16—111no—
156C2×SD16—222no—
157C2×D8—21no—
158C2×D8C22⋊D1112yes—
159C4⋊Q8—21no—
160#127—21no—
161#124—222no—
162#124—441no—
163#123—442no—
164C4×Q8—111no—
165C4×Q8—221no—
166C4×D4—222no—
167C4×D4—441no—
168Q32—442no—
169SD32—44no—
170C2×C16—21no—
171C2×C16—221no—
172#107—111no—
173#106—441no—
174C4⋊C8—111no—
175C4⋊C8—221no—
176C4⋊C8—221no—
177#103—221no—
178#103—441no—
179#102—222no—
180C4×C8—221no—
181C4×C8C22×D1111yescharacteristic
182C2×C11—162no—
183C2×C11#162111yescharacteristic
184C2×C11#218911yescharacteristic
185C2×C11#219411yescharacteristic
186C2×Q8—41no—
187C2×Q8—111no—
188C2×Q8—221no—
189C2×D4—22no—
190C2×D4—41no—
191C2×D4—41no—
192C22×C4—442no—
193Q16—42no—
194Q16—41no—
195Q16—41no—
196Q16—221no—
197Q16—221no—
198SD16—882no—
199D8—42no—
200D8—41no—
201D8—41no—
202C2×C8—221no—
203C2×C8—441no—
204C2×C8D4×D1111yescharacteristic
205C2×C8C2×C22⋊D1111yescharacteristic
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—111no—
209C4⋊C4—221no—
210C4⋊C4—221no—
211C4⋊C4—441no—
212C22⋊C4—442no—
213C22⋊C4—442no—
214C22⋊C4—442no—
215C42—221no—
216C42—441no—
217C42D4×D1111yescharacteristic
218C16—22no—
219C16—441no—
220C11#1233311yescharacteristic, complemented, Sylow
221C23—42no—
222Q8—81no—
223Q8—81no—
224Q8—221no—
225Q8—221no—
226Q8—441no—
227Q8—441no—
228D4—42no—
229D4—42no—
230D4—81no—
231D4—81no—
232D4—161no—
233C2×C4—81no—
234C2×C4—221no—
235C2×C4—221no—
236C2×C4—441no—
237C2×C4—441no—
238C2×C4—1762no—
239C2×C4D8×D1111yescharacteristic
240C2×C4#6696411yescharacteristic
241C2×C4#6699011yescharacteristic
242C8—21no—
243C8—441no—
244C8—881no—
245C8#6696411yescharacteristic
246C8#6696511yescharacteristic
247C22—82no—
248C22—82no—
249C22—82no—
250C22#1062276911yescharacteristic
251C4—21no—
252C4—161no—
253C4—441no—
254C4—441no—
255C4—881no—
256C4—881no—
257C4#1062252811yescharacteristic
258C4#1062252911yescharacteristic
259C4#1062269011yescharacteristic
260C4#1062277111yescharacteristic
261C2—162no—
262C2#1306767811yescharacteristic
263C2#1307055311yescharacteristic
264C2#1307058611yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2248C2
socleC22×C11#447
prime radicalC11×#493C22
hypercenter#2248D11
hypocenterC11#12333
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
2. #13070663C2semidirect
3. #13067983C2semidirect
5. #13066596C2semidirect
6. #13066581C2semidirect
220. C11#12333semidirect

Maximal subgroups

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

subgroupindex
#130816302
#130706632
#130679832
#130666622
#130665962
#130665812
C11×#22482
#1233311