Finite Group Databasebeta

← #14667495

Subgroups — #14667495

Order 2816.

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

normal subgroups only

This group has 296 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#13081485C211yesmaximal, characteristic
2#13070658C211yesmaximal, characteristic
3#13067983C211yesmaximal, characteristic, complemented
4#13066674C211yesmaximal, characteristic, complemented
5#13066596C211yesmaximal, characteristic, complemented
6#13066578C211yesmaximal, characteristic
7C11×#2241C211yesmaximal, characteristic, complemented
8#10623261—21no—
9C11×#500C2211yescharacteristic
10C11×#494C2211yescharacteristic
11C2×#66892—21no—
12#10622707—21no—
13#10622697—21no—
14#10622504—22no—
15#10622491—21no—
16#10622485—21no—
17C4×D88C2211yescharacteristic
18C8×Dic22C2211yescharacteristic
19C11×#358—22no—
20C4×C11×C16C2211yescharacteristic
21#10622202—21no—
22#10622185—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16—21no—
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29#66999—42no—
30C2×D88D411yescharacteristic
31#66950—41no—
32#66946—22no—
33C4⋊C4×D11—41no—
34#66943—22no—
35C4×D44—21no—
36C4×Dic22D411yescharacteristic
37C2×C11×C16—21no—
38C11×#107—21no—
39C11×#107D412yes—
40C4×C8×C11C2311yescharacteristic
41#66892—42no—
42#66885—21no—
43#66882D411yescharacteristic
44Dic11⋊C8—21no—
45C8×Dic11—21no—
46C2×C11⋊C16—21no—
47#66874—41no—
48#66873—22no—
49#66872—22no—
50#66872—41no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#12359—111nomaximal, Sylow
54C2×Q8×C11—41no—
55C2×Q8×C11—41no—
56C2×D44—21no—
57C2×C4×D11—42no—
58C2×C4×D11—41no—
59C2×Dic22D811yescharacteristic
60C11×Q16—42no—
61C11×Q16—41no—
62C11×Q16—41no—
63C2×C8×C11C2×D411yescharacteristic
64C2×C8×C11C2×D411yescharacteristic
65C11×C4⋊C4—22no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C42×C11C2×D411yescharacteristic
70(C2×D11)⋊C4—42no—
71(C2×D11)⋊C4—41no—
72C4⋊Dic11—21no—
73C4⋊Dic11—42no—
74C4⋊Dic11D811yescharacteristic
75Dic11⋊C4—21no—
76Dic11⋊C4—42no—
77C4×Dic11—21no—
78C2×C11⋊C8—21no—
79C2×C11⋊C8—41no—
80D88—21no—
81D88SD1612yes—
82C11×C16—41no—
83C11⋊C16—41no—
84#3380—111no—
85#2241D1111yescharacteristic, complemented
86#2208—111no—
87#1670—111no—
88#1365—111no—
89Q8⋊C16—111no—
90#1331—111no—
91C22×D11—41no—
92Q8×C11—81no—
93Q8×C11—81no—
94Q8×C11—161no—
95C2×C4×C11—42no—
96C2×C4×C11—81no—
97C2×C4×C11#12011yescharacteristic
98C2×C4×C11C2×D811yescharacteristic
99C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—41no—
103D44—22no—
104D44—41no—
105C4×D11—81no—
106C4×D11—81no—
107C4×D11—162no—
108Dic22—21no—
109Dic22—21no—
110C8×C11—21no—
111C8×C11C2×SD1611yescharacteristic
112C8×C11#13711yescharacteristic
113C11⋊C8—41no—
114C11⋊C8—81no—
115#554—221no—
116C2×SD32—221no—
117#500C2×D1111yescharacteristic
118#499—221no—
119#494C2×D1111yescharacteristic
120#478—222no—
121#476—221no—
122#475—221no—
123C8×Q8—111no—
124C4×D8—111no—
125C4×D8—221no—
126C4⋊C16—111no—
127#358—22no—
128#358—221no—
129C4×C16C2×D1111yescharacteristic
130#335—111no—
131#332—221no—
132C22×C11#44711yescharacteristic
133C2×D11—42no—
134C2×D11—81no—
135C2×D11—81no—
136C4×C11—21no—
137C4×C11—82no—
138C4×C11—161no—
139C4×C11#44811yescharacteristic
140C4×C11#45411yescharacteristic
141C4×C11#50811yescharacteristic
142C4×C11#51011yescharacteristic
143Dic11—41no—
144Dic11—41no—
145Dic11—81no—
146C2×Q16—21no—
147C2×Q16—21no—
148C2×D8—111no—
149C4⋊Q8—21no—
150C4⋊Q8—21no—
151#125—222no—
152C22⋊Q8—441no—
153C22⋊Q8—442no—
154C4×Q8—111no—
155C4×D4—222no—
156C4×D4—221no—
157C2×C4⋊C4—441no—
158SD32—442no—
159C2×C16—21no—
160C2×C16—221no—
161#107—21no—
162#107—111no—
163#107C22⋊D1112yes—
164#106—222no—
165#106—441no—
166C4⋊C8—111no—
167C4⋊C8—221no—
168C4⋊C8—221no—
169#103—441no—
170#102—222no—
171#102—221no—
172C4×C8—221no—
173C4×C8C22×D1111yescharacteristic
174C2×C11#162711yescharacteristic
175C2×C11#218911yescharacteristic
176C2×C11#219411yescharacteristic
177D11—82no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—111no—
181C2×D4—221no—
182C22×C4—442no—
183C22×C4—441no—
184Q16—42no—
185Q16—41no—
186Q16—41no—
187D8—112no—
188D8—221no—
189C2×C8—221no—
190C2×C8—441no—
191C2×C8D4×D1111yescharacteristic
192C2×C8C2×C22⋊D1111yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—111no—
198C4⋊C4—221no—
199C4⋊C4—221no—
200C4⋊C4—442no—
201C4⋊C4—442no—
202C22⋊C4—442no—
203C22⋊C4—441no—
204C42—221no—
205C42D4×D1111yescharacteristic
206C16—41no—
207C16—441no—
208C11#1235911yescharacteristic, complemented, Sylow
209C23—441no—
210Q8—81no—
211Q8—81no—
212Q8—161no—
213Q8—221no—
214Q8—221no—
215D4—222no—
216D4—441no—
217C2×C4—42no—
218C2×C4—81no—
219C2×C4—221no—
220C2×C4—221no—
221C2×C4—441no—
222C2×C4—881no—
223C2×C4—881no—
224C2×C4—1762no—
225C2×C4D8×D1111yescharacteristic
226C2×C4#6696411yescharacteristic
227C2×C4#6699011yescharacteristic
228C8—21no—
229C8—441no—
230C8—881no—
231C8SD16×D1111yescharacteristic
232C8#6696811yescharacteristic
233C22—442no—
234C22—881no—
235C22—881no—
236C22#1062276911yescharacteristic
237C4—21no—
238C4—82no—
239C4—161no—
240C4—441no—
241C4—441no—
242C4—881no—
243C4#1062253111yescharacteristic
244C4#1062253211yescharacteristic
245C4#1062267511yescharacteristic
246C4#1062278311yescharacteristic
247C2—882no—
248C2#1306771611yescharacteristic
249C2#1307055511yescharacteristic
250C2#1307058611yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2241C2
socleC22×C11#447
prime radicalC2×D88D4
hypercenter#2241D11
hypocenterC11#12359
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

Complements

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

NH ≅ G/Ntype
3. #13067983C2semidirect
4. #13066674C2semidirect
5. #13066596C2semidirect
7. C11×#2241C2semidirect
85. #2241D11semidirect
208. C11#12359semidirect

Maximal subgroups

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

subgroupindex
#130814852
#130706582
#130679832
#130666742
#130665962
#130665782
C11×#22412
#1235911