Finite Group Databasebeta

← #14667319

Subgroups — #14667319

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#13081626C211yesmaximal, characteristic
2#13070872C211yesmaximal, characteristic
3#13070666C211yesmaximal, characteristic, complemented
4#13067987C211yesmaximal, characteristic, complemented
5#13066661C211yesmaximal, characteristic
6#13066596C211yesmaximal, characteristic, complemented
7C11×#1332C211yesmaximal, characteristic, complemented
8#10623116—21no—
9C4×C11×Q16C2211yescharacteristic
10#10622804—21no—
11C2×#66893—21no—
12#10622640—21no—
13C2×#66864—22no—
14#10622485—21no—
15#10622464—21no—
16#10622432—22no—
17#10622312C2211yescharacteristic
18#10622308C2211yescharacteristic
19C8×Dic22C2211yescharacteristic
20C4×C11×C16C2211yescharacteristic
21C11×#335C2211yescharacteristic
22#10622130—21no—
23#10622124—21no—
24C4⋊(C11⋊C16)C2211yescharacteristic
25C2×C11×Q16D411yescharacteristic
26C4×Q8×C11—21no—
27#67000—22no—
28C2×#4325—22no—
29C2×Dic44—21no—
30C2×Dic44—21no—
31C2×D88—21no—
32C2×D88D412yes—
33#66947—42no—
34#66946—22no—
35#66928—41no—
36#66927—21no—
37C4×D44—41no—
38#66922—21no—
39C4×Dic22D411yescharacteristic
40C2×C11×C16—21no—
41C11×#107D411yescharacteristic
42C11×C4⋊C8—21no—
43C11×#103—21no—
44C4×C8×C11C2311yescharacteristic
45#66893—42no—
46#66881—41no—
47#66880—41no—
48Dic11⋊C8—21no—
49C8×Dic11—21no—
50C2×C11⋊C16—21no—
51#66873—22no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#66864—44no—
54#12333—111nomaximal, Sylow
55C2×Q8×C11—21no—
56C2×D44—22no—
57C2×D44—41no—
58C2×D44—41no—
59C2×C4×D11—42no—
60C2×Dic22—41no—
61C2×Dic22D811yescharacteristic
62C11×Q16—21no—
63C11×Q16—21no—
64C2×C8×C11—41no—
65C2×C8×C11C2×D411yescharacteristic
66C2×C8×C11C2×D411yescharacteristic
67C11×C4⋊C4—21no—
68C11×C4⋊C4—41no—
69C42×C11—41no—
70C42×C11C2×D411yescharacteristic
71#4325—82no—
72(C2×D11)⋊C4—42no—
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—42no—
75C4⋊Dic11—41no—
76C4⋊Dic11—41no—
77C4⋊Dic11D811yescharacteristic
78Dic11⋊C4—21no—
79C4×Dic11—21no—
80C2×C11⋊C8—21no—
81Dic44—42no—
82Dic44—41no—
83Dic44—41no—
84D88—42no—
85D88—41no—
86D88—41no—
87C11×C16—22no—
88C11⋊C16—41no—
89#3396—111no—
90#2248—111no—
91#2209—111no—
92#1670—111no—
93#1361—111no—
94Q8⋊C16—111no—
95#1332D1111yescharacteristic, complemented
96C22×D11—42no—
97Q8×C11—41no—
98Q8×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11#12011yescharacteristic
102C2×C4×C11C2×D811yescharacteristic
103C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
104C2×Dic11—21no—
105C2×Dic11—21no—
106C2×Dic11—81no—
107D44—42no—
108D44—42no—
109D44—81no—
110D44—81no—
111D44—161no—
112C4×D11—162no—
113Dic22—21no—
114Dic22—21no—
115Dic22—81no—
116Dic22—81no—
117C8×C11—21no—
118C8×C11—81no—
119C8×C11#13511yescharacteristic
120C8×C11AGL(1,ℤ/8)11yescharacteristic
121C11⋊C8—41no—
122#559—221no—
123C2×Q32—221no—
124C2×SD32—222no—
125#495—221no—
126#494—111no—
127#493—111no—
128#475—221no—
129#463—222no—
130#460—221no—
131C8×Q8—111no—
132C4×Q16C2×D1111yescharacteristic
133C4×D8—221no—
134C4⋊C16—111no—
135#358—221no—
136C4×C16C2×D1111yescharacteristic
137#335C2×D1111yescharacteristic
138#332—221no—
139C22×C11#44711yescharacteristic
140C2×D11—82no—
141C2×D11—82no—
142C2×D11—82no—
143C4×C11—21no—
144C4×C11—81no—
145C4×C11—81no—
146C4×C11#44911yescharacteristic
147C4×C11#45311yescharacteristic
148C4×C11#50811yescharacteristic
149C4×C11#51011yescharacteristic
150Dic11—41no—
151Dic11—41no—
152Dic11—161no—
153C2×Q16—221no—
154C2×Q16—221no—
155C2×Q16D4411yescharacteristic
156C2×SD16—222no—
157C2×D8—112no—
158C2×D8—221no—
159C4⋊Q8—221no—
160#127—221no—
161#124—222no—
162#124—441no—
163#123—442no—
164C4×Q8—21no—
165C4×Q8—111no—
166C4×D4—222no—
167C4×D4—441no—
168Q32—442no—
169SD32—444no—
170C2×C16—21no—
171C2×C16—221no—
172#107D4411yescharacteristic
173#106—441no—
174C4⋊C8—21no—
175C4⋊C8—111no—
176C4⋊C8—221no—
177#103—21no—
178#103—441no—
179#102—222no—
180C4×C8—221no—
181C4×C8C22×D1111yescharacteristic
182C2×C11#162111yescharacteristic
183C2×C11#218911yescharacteristic
184C2×C11#219411yescharacteristic
185D11—162no—
186C2×Q8—21no—
187C2×Q8—111no—
188C2×Q8—441no—
189C2×D4—222no—
190C2×D4—441no—
191C2×D4—441no—
192C22×C4—442no—
193Q16—21no—
194Q16—21no—
195Q16—442no—
196Q16—441no—
197Q16—441no—
198SD16—882no—
199D8—442no—
200D8—441no—
201D8—441no—
202C2×C8—41no—
203C2×C8—221no—
204C2×C8C2×D4411yescharacteristic
205C2×C8D4×D1111yescharacteristic
206C4⋊C4—21no—
207C4⋊C4—41no—
208C4⋊C4—111no—
209C4⋊C4—221no—
210C4⋊C4—441no—
211C4⋊C4—441no—
212C22⋊C4—442no—
213C22⋊C4—442no—
214C22⋊C4—442no—
215C42—41no—
216C42—221no—
217C42D4×D1111yescharacteristic
218C16—22no—
219C16—441no—
220C11#1233311yescharacteristic, complemented, Sylow
221C23—442no—
222Q8—41no—
223Q8—41no—
224Q8—221no—
225Q8—221no—
226Q8—881no—
227Q8—881no—
228D4—442no—
229D4—442no—
230D4—881no—
231D4—881no—
232D4—1761no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—221no—
236C2×C4—221no—
237C2×C4—881no—
238C2×C4—1762no—
239C2×C4#6693511yescharacteristic
240C2×C4D8×D1111yescharacteristic
241C2×C4#6696711yescharacteristic
242C8—21no—
243C8—81no—
244C8—441no—
245C8#6695711yescharacteristic
246C8#6696111yescharacteristic
247C22—882no—
248C22—882no—
249C22—882no—
250C22#1062238611yescharacteristic
251C4—21no—
252C4—81no—
253C4—81no—
254C4—441no—
255C4—441no—
256C4—1761no—
257C4#1062234711yescharacteristic
258C4#1062243511yescharacteristic
259C4#1062252911yescharacteristic
260C4#1062253111yescharacteristic
261C2—1762no—
262C2#1306768411yescharacteristic
263C2#1307055911yescharacteristic
264C2#1307058811yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1332C2
socleC22×C11#447
prime radical#10622308C22
hypercenter#1332D11
hypocenterC11#12333
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
3. #13070666C2semidirect
4. #13067987C2semidirect
6. #13066596C2semidirect
7. C11×#1332C2semidirect
95. #1332D11semidirect
220. C11#12333semidirect

Maximal subgroups

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

subgroupindex
#130816262
#130708722
#130706662
#130679872
#130666612
#130665962
C11×#13322
#1233311