Finite Group Databasebeta

← #14667497

Subgroups — #14667497

Order 2816.

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

normal subgroups only

This group has 296 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#13081481C211yesmaximal, characteristic
2#13070843C211yesmaximal, characteristic, complemented
3#13067983C211yesmaximal, characteristic, complemented
4#13066673C211yesmaximal, characteristic, complemented
5#13066594C211yesmaximal, characteristic, complemented
6#13066577C211yesmaximal, characteristic
7C11×#2208C211yesmaximal, characteristic
8#10623074—21no—
9C2×C11×SD32—21no—
10C11×#494C2211yescharacteristic
11C4×C11×D8C2211yescharacteristic
12D8×Dic11—21no—
13#10622707—21no—
14#10622621—21no—
15#10622491—21no—
16#10622379—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×D8D411yescharacteristic
28C11×C4⋊Q8—21no—
29C4×D4×C11—21no—
30D4×Dic11—22no—
31C2×C4⋊Dic11—41no—
32#66977—41no—
33#66943—22no—
34#66931—42no—
35#66922—21no—
36C4×Dic22D411yescharacteristic
37C11×SD32—42no—
38C2×C11×C16—21no—
39C11×#107D411yescharacteristic
40C11×#102—21no—
41C4×C8×C11C2311yescharacteristic
42#66896—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#12359—111nomaximal, Sylow
54C2×Q8×C11—41no—
55C2×D4×C11—21no—
56C22×C4×C11—41no—
57C22×Dic11—42no—
58C2×Dic22—41no—
59C2×Dic22D811yescharacteristic
60C11×Q16—42no—
61C11×Q16—41no—
62C11×Q16—41no—
63C11×D8—21no—
64C11×D8SD1612yes—
65C2×C8×C11C2×D411yescharacteristic
66C2×C8×C11C2×D411yescharacteristic
67C11×C4⋊C4—21no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C11×C22⋊C4—41no—
71C42×C11C2×D411yescharacteristic
72C22⋊Dic11—42no—
73C4⋊Dic11—22no—
74C4⋊Dic11—42no—
75C4⋊Dic11—41no—
76C4⋊Dic11D811yescharacteristic
77Dic11⋊C4—21no—
78Dic11⋊C4—42no—
79C4×Dic11—21no—
80C2×C11⋊C8—21no—
81C2×C11⋊C8—41no—
82C11×C16—41no—
83C11⋊C16—41no—
84#3380—111no—
85#2241—111no—
86#2208D1111yescharacteristic
87#1670—111no—
88#1365—111no—
89Q8⋊C16—111no—
90#1331—111no—
91C23×C11—41no—
92Q8×C11—81no—
93Q8×C11—81no—
94D4×C11—22no—
95D4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11—81no—
98C2×C4×C11—81no—
99C2×C4×C11—81no—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11C2×D811yescharacteristic
102C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
103C2×Dic11—21no—
104C2×Dic11—21no—
105C2×Dic11—42no—
106C2×Dic11—162no—
107Dic22—21no—
108Dic22—21no—
109Dic22—161no—
110C8×C11—21no—
111C8×C11C2×SD1611yescharacteristic
112C8×C11#13711yescharacteristic
113C11⋊C8—41no—
114C11⋊C8—81no—
115#554—221no—
116C2×SD32—21no—
117#500—111no—
118#499—221no—
119#494C2×D1111yescharacteristic
120#478—222no—
121#476—221no—
122#475—221no—
123C8×Q8—111no—
124C4×D8—221no—
125C4×D8C2×D1111yescharacteristic
126C4⋊C16C2×D1111yescharacteristic
127#358—21no—
128#358—222no—
129C4×C16—111no—
130#335—111no—
131#332—221no—
132C22×C11—42no—
133C22×C11—81no—
134C22×C11—81no—
135C22×C11#44711yescharacteristic
136C4×C11—21no—
137C4×C11—81no—
138C4×C11—161no—
139C4×C11#44811yescharacteristic
140C4×C11#45411yescharacteristic
141C4×C11#50811yescharacteristic
142C4×C11#51011yescharacteristic
143Dic11—41no—
144Dic11—41no—
145Dic11—82no—
146C2×Q16—21no—
147C2×Q16—21no—
148C2×D8C22⋊D1111yescharacteristic
149C4⋊Q8—21no—
150C4⋊Q8—221no—
151#125—222no—
152C22⋊Q8—442no—
153C22⋊Q8—441no—
154C4×Q8—111no—
155C4×D4—21no—
156C4×D4—222no—
157C2×C4⋊C4—441no—
158SD32—42no—
159C2×C16—21no—
160C2×C16—221no—
161#107—112no—
162#107—221no—
163#107C22⋊D1111yescharacteristic
164#106—222no—
165#106—441no—
166C4⋊C8—111no—
167C4⋊C8—221no—
168C4⋊C8—221no—
169#103—441no—
170#102—21no—
171#102—222no—
172C4×C8—221no—
173C4×C8C22×D1111yescharacteristic
174C2×C11—82no—
175C2×C11#162711yescharacteristic
176C2×C11#218911yescharacteristic
177C2×C11#219411yescharacteristic
178C2×Q8—41no—
179C2×Q8—111no—
180C2×Q8—441no—
181C2×D4—21no—
182C22×C4—41no—
183C22×C4—442no—
184Q16—42no—
185Q16—41no—
186Q16—41no—
187D8—21no—
188D8#432412yes—
189C2×C8—221no—
190C2×C8—441no—
191C2×C8D4×D1111yescharacteristic
192C2×C8C2×C22⋊D1111yescharacteristic
193C4⋊C4—21no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—111no—
197C4⋊C4—221no—
198C4⋊C4—222no—
199C4⋊C4—442no—
200C4⋊C4—442no—
201C4⋊C4—441no—
202C22⋊C4—41no—
203C22⋊C4—442no—
204C42—221no—
205C42D4×D1111yescharacteristic
206C16—41no—
207C16—441no—
208C11#1235911yescharacteristic, complemented, Sylow
209C23—41no—
210Q8—81no—
211Q8—81no—
212Q8—221no—
213Q8—221no—
214Q8—1761no—
215D4—22no—
216D4—41no—
217C2×C4—41no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—81no—
221C2×C4—221no—
222C2×C4—221no—
223C2×C4—442no—
224C2×C4—1762no—
225C2×C4D8×D1111yescharacteristic
226C2×C4#6696411yescharacteristic
227C2×C4#6699011yescharacteristic
228C8—21no—
229C8—441no—
230C8—881no—
231C8C2×#432411yescharacteristic
232C8#6700411yescharacteristic
233C22—42no—
234C22—81no—
235C22—81no—
236C22#1062276911yescharacteristic
237C4—21no—
238C4—81no—
239C4—161no—
240C4—441no—
241C4—441no—
242C4—882no—
243C4#1062252811yescharacteristic
244C4#1062252911yescharacteristic
245C4#1062265311yescharacteristic
246C4#1062281411yescharacteristic
247C2—82no—
248C2#1306771811yescharacteristic
249C2#1307055311yescharacteristic
250C2#1307058411yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2208C2
socleC22×C11#447
prime radicalC2×C11×D8D4
hypercenter#2208D11
hypocenterC11#12359
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
2. #13070843C2semidirect
3. #13067983C2semidirect
4. #13066673C2semidirect
5. #13066594C2semidirect
208. C11#12359semidirect

Maximal subgroups

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

subgroupindex
#130814812
#130708432
#130679832
#130666732
#130665942
#130665772
C11×#22082
#1235911