Finite Group Databasebeta

← #14667314

Subgroups — #14667314

Order 2816.

324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 67 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#13081629C211yesmaximal, characteristic
2#13070873C211yesmaximal, characteristic
3#13070663C211yesmaximal, characteristic, complemented
4#13066661C211yesmaximal, characteristic
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066579C211yesmaximal, characteristic, complemented
7C11×#1670C211yesmaximal, characteristic, complemented
8#10623116—21no—
9C11×#494C2211yescharacteristic
10C11×#475—21no—
11C8×Q8×C11C2211yescharacteristic
12C2×#66893—21no—
13C2×#66892—22no—
14#10622461—21no—
15#10622457—22no—
16C4×Dic44C2211yescharacteristic
17#10622309—21no—
18#10622308C2211yescharacteristic
19C4×D88—21no—
20C11×#335C2211yescharacteristic
21C11×#332—21no—
22#10622202—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24C4×C11⋊C16C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16—21no—
27C11×C4⋊Q8—21no—
28C4×Q8×C11D411yescharacteristic
29#67000—41no—
30C2×Dic44D411yescharacteristic
31C2×D88—21no—
32C2×D88D412yes—
33C2×#4314—22no—
34#66947—42no—
35#66946—41no—
36#66928—22no—
37#66927—21no—
38C4×D44—22no—
39C4×Dic22—21no—
40C11×#106—41no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8D411yescharacteristic
44C11×#103—41no—
45C4×C8×C11—21no—
46C4×C8×C11C2311yescharacteristic
47#66893—42no—
48#66892—44no—
49#66885—22no—
50#66882D411yescharacteristic
51#66880—21no—
52C2×C11⋊C16—21no—
53C2×C11⋊C16—21no—
54#12333—111nomaximal, Sylow
55C2×Q8×C11—41no—
56C2×Q8×C11D811yescharacteristic
57C2×D44—22no—
58C2×D44—41no—
59C2×D44—41no—
60C2×C4×D11—42no—
61C2×Dic22—21no—
62C11×Q16—42no—
63C11×Q16—41no—
64C11×Q16—41no—
65C2×C8×C11—21no—
66C2×C8×C11—41no—
67C2×C8×C11C2×D411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4D811yescharacteristic
73C42×C11—21no—
74C42×C11C2×D411yescharacteristic
75(C2×D11)⋊C4—42no—
76(C2×D11)⋊C4—42no—
77(C2×D11)⋊C4—42no—
78C4⋊Dic11—21no—
79Dic11⋊C4—41no—
80C4×Dic11—41no—
81Dic44—21no—
82Dic44—21no—
83D88—42no—
84D88—41no—
85D88—41no—
86#4314—82no—
87C11⋊C16—22no—
88C11⋊C16—41no—
89#3396—111no—
90#2248—111no—
91#2209—111no—
92#1670D1111yescharacteristic, complemented
93#1361—111no—
94Q8⋊C16—111no—
95#1332—111no—
96C22×D11—42no—
97Q8×C11—21no—
98Q8×C11—21no—
99Q8×C11—81no—
100Q8×C11—81no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—81no—
104C2×C4×C11#12011yescharacteristic
105C2×C4×C11C2×D811yescharacteristic
106C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
107C2×Dic11—41no—
108C2×Dic11—41no—
109D44—42no—
110D44—42no—
111D44—81no—
112D44—81no—
113D44—161no—
114C4×D11—162no—
115Dic22—41no—
116Dic22—41no—
117C8×C11—21no—
118C8×C11—41no—
119C8×C11—81no—
120C8×C11#13511yescharacteristic
121C8×C11AGL(1,ℤ/8)11yescharacteristic
122#559—221no—
123C2×Q32—221no—
124C2×SD32—222no—
125#495—221no—
126#494C2×D1111yescharacteristic
127#493—111no—
128#475—21no—
129#463—222no—
130#460—221no—
131C8×Q8C2×D1111yescharacteristic
132C4×Q16—111no—
133C4×D8—221no—
134C4⋊C16—111no—
135#358—221no—
136C4×C16—111no—
137#335C2×D1111yescharacteristic
138#332—21no—
139C22×C11#44711yescharacteristic
140C2×D11—82no—
141C2×D11—82no—
142C2×D11—82no—
143C4×C11—21no—
144C4×C11—41no—
145C4×C11—41no—
146C4×C11—161no—
147C4×C11#44911yescharacteristic
148C4×C11#45311yescharacteristic
149C4×C11#50811yescharacteristic
150C4×C11#51011yescharacteristic
151Dic11—81no—
152Dic11—81no—
153C2×Q16—21no—
154C2×Q16—21no—
155C2×Q16—111no—
156C2×SD16—222no—
157C2×D8—112no—
158C2×D8—221no—
159C4⋊Q8—21no—
160#127—221no—
161#124—222no—
162#124—441no—
163#123—442no—
164C4×Q8—221no—
165C4×Q8C22⋊D1111yescharacteristic
166C4×D4—222no—
167C4×D4—441no—
168Q32—442no—
169SD32—444no—
170C2×C16—221no—
171C2×C16—221no—
172#107—111no—
173#106—41no—
174C4⋊C8—21no—
175C4⋊C8—21no—
176C4⋊C8C22⋊D1111yescharacteristic
177#103—41no—
178#103—221no—
179#102—222no—
180C4×C8—21no—
181C4×C8C22×D1111yescharacteristic
182C2×C11#162111yescharacteristic
183C2×C11#218911yescharacteristic
184C2×C11#219411yescharacteristic
185D11—162no—
186C2×Q8—41no—
187C2×Q8—221no—
188C2×Q8#432311yescharacteristic
189C2×D4—222no—
190C2×D4—441no—
191C2×D4—441no—
192C22×C4—442no—
193Q16—42no—
194Q16—41no—
195Q16—41no—
196Q16—221no—
197Q16—221no—
198SD16—882no—
199D8—442no—
200D8—441no—
201D8—441no—
202C2×C8—21no—
203C2×C8—41no—
204C2×C8D4×D1111yescharacteristic
205C2×C8D4×D1111yescharacteristic
206C4⋊C4—21no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—221no—
210C4⋊C4—441no—
211C4⋊C4#432311yescharacteristic
212C22⋊C4—442no—
213C22⋊C4—442no—
214C22⋊C4—442no—
215C42—21no—
216C42—441no—
217C42C2×C22⋊D1111yescharacteristic
218C16—222no—
219C16—441no—
220C11#1233311yescharacteristic, complemented, Sylow
221C23—442no—
222Q8—21no—
223Q8—21no—
224Q8—81no—
225Q8—81no—
226Q8—441no—
227Q8—441no—
228D4—442no—
229D4—442no—
230D4—881no—
231D4—881no—
232D4—1761no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—81no—
236C2×C4—441no—
237C2×C4—441no—
238C2×C4—1762no—
239C2×C4C2×#432311yescharacteristic
240C2×C4#6699011yescharacteristic
241C2×C4#6700211yescharacteristic
242C8—21no—
243C8—41no—
244C8—81no—
245C8#6696711yescharacteristic
246C8#6696911yescharacteristic
247C22—882no—
248C22—882no—
249C22—882no—
250C22#1062264911yescharacteristic
251C4—21no—
252C4—41no—
253C4—41no—
254C4—161no—
255C4—881no—
256C4—881no—
257C4#1062278511yescharacteristic
258C4#1062279211yescharacteristic
259C4#1062280711yescharacteristic
260C4#1062281111yescharacteristic
261C2—1762no—
262C2#1306767911yescharacteristic
263C2#1307055411yescharacteristic
264C2#1307058511yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1670C2
socleC22×C11#447
prime radical#10622308C22
hypercenter#1670D11
hypocenterC11#12333
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1670

Complements

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

NH ≅ G/Ntype
3. #13070663C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
6. #13066579C2semidirect
7. C11×#1670C2semidirect
92. #1670D11semidirect
220. C11#12333semidirect

Maximal subgroups

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

subgroupindex
#130816292
#130708732
#130706632
#130666612
Q8⋊(C11⋊C16)2
#130665792
C11×#16702
#1233311