Finite Group Databasebeta

← #14666998

Subgroups — #14666998

Order 2816.

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

normal subgroups only

This group has 344 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#13079391C211yesmaximal, characteristic
2#13070819C212yesmaximal, complemented
3#13070044C211yesmaximal, characteristic
4#13066629C212yesmaximal, complemented
5C11×#1314C211yesmaximal, characteristic
6C2×#66977—21no—
7C2×C11×C22⋊C8C2211yescharacteristic
8#10622825—21no—
9#10622729—21no—
10#10622729C2212yes—
11C2×#66882C2211yescharacteristic
12#10622352—22no—
13#10622335—22no—
14C11×C22⋊C16C2212yes—
15#10622189—21no—
16#10622189C2211yescharacteristic
17#10622142—22no—
18#10622141—22no—
19C23×C4×C11D411yescharacteristic
20C22×Dic22—21no—
21C22×C8×C11D411yescharacteristic
22C22×C8×C11C2311yescharacteristic
23C2×C22⋊Dic11—41no—
24C2×C22⋊Dic11—41no—
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—21no—
27C2×C4⋊Dic11—21no—
28#66977—22no—
29#66977—22no—
30#66977—41no—
31#66977—41no—
32C2×Dic11⋊C4—41no—
33C2×Dic44—21no—
34C2×Dic44D412yes—
35C2×C11×C16—22no—
36C11×C22⋊C8—22no—
37C11⋊#95—41no—
38#66882—21no—
39#66882—22no—
40#66882D412yes—
41#66880—22no—
42#66880—22no—
43#12282—111nomaximal, Sylow
44C24×C11D811yescharacteristic
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11—41no—
48C22×C4×C11—41no—
49C22×C4×C11D811yescharacteristic
50C22×C4×C11C2×D411yescharacteristic
51C22×Dic11—41no—
52C22×Dic11—41no—
53C22×Dic11—41no—
54C22×Dic11—41no—
55C2×Dic22—22no—
56C2×Dic22—41no—
57C2×Dic22—81no—
58C2×Dic22—81no—
59C2×C8×C11—21no—
60C2×C8×C11—41no—
61C2×C8×C11—41no—
62C2×C8×C11C2×D412yes—
63C22⋊Dic11—42no—
64C22⋊Dic11—42no—
65C22⋊Dic11—82no—
66C4⋊Dic11—22no—
67C4⋊Dic11—41no—
68C4⋊Dic11—41no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71C4⋊Dic11—41no—
72Dic11⋊C4—42no—
73Dic11⋊C4—42no—
74Dic44—42no—
75Dic44—81no—
76C11×C16—42no—
77#3189—111no—
78#2236—112no—
79#2076—111no—
80#1348—112no—
81#1314D1111yescharacteristic
82C23×C11—21no—
83C23×C11—21no—
84C23×C11—41no—
85C23×C11—41no—
86C23×C11Q3212yes—
87C23×C11C2×D811yescharacteristic
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—81no—
95C2×C4×C11#12011yescharacteristic
96C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—82no—
100C2×Dic11—82no—
101C2×Dic11—81no—
102C2×Dic11—81no—
103C2×Dic11—81no—
104C2×Dic11—81no—
105C2×Dic11—81no—
106C2×Dic11—81no—
107Dic22—42no—
108Dic22—42no—
109Dic22—82no—
110C8×C11—22no—
111C8×C11—41no—
112C2×C22⋊Q8—221no—
113#484—222no—
114#467—112no—
115#467—221no—
116#451—222no—
117C2×#107—111no—
118C2×C22⋊C8C2×D1111yescharacteristic
119#380—221no—
120#366—222no—
121#358—222no—
122C22⋊C16C2×D1112yes—
123#340—111no—
124#340—221no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11—22no—
128C22×C11—42no—
129C22×C11—41no—
130C22×C11—41no—
131C22×C11—81no—
132C22×C11#44711yescharacteristic
133C22×C11C2×Q3211yescharacteristic
134C22×C11#51011yescharacteristic
135C4×C11—21no—
136C4×C11—41no—
137C4×C11#45511yescharacteristic
138C4×C11#45811yescharacteristic
139Dic11—82no—
140Dic11—82no—
141Dic11—161no—
142Dic11—161no—
143C22×Q8—221no—
144C23×C4D4411yescharacteristic
145C2×Q16—112no—
146C2×Q16—221no—
147C22×C8D4411yescharacteristic
148C22×C8C22×D1111yescharacteristic
149C22⋊Q8—222no—
150C22⋊Q8—222no—
151C22⋊Q8—441no—
152C22⋊Q8—441no—
153C2×C4⋊C4—221no—
154C2×C4⋊C4—221no—
155C2×C4⋊C4—221no—
156C2×C4⋊C4—441no—
157C2×C22⋊C4—441no—
158C2×C22⋊C4—441no—
159C2×C16—22no—
160#107—112no—
161#107—221no—
162#107—222no—
163#103—222no—
164#103—222no—
165C22⋊C8—22no—
166#95—441no—
167C2×C11—21no—
168C2×C11—21no—
169C2×C11—42no—
170C2×C11#160711yescharacteristic
171C2×C11#218811yescharacteristic
172C2×C11#219011yescharacteristic
173C24D8811yescharacteristic
174C2×Q8—222no—
175C2×Q8—441no—
176C2×Q8—881no—
177C2×Q8—881no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—441no—
183C22×C4—441no—
184C22×C4—441no—
185C22×C4—441no—
186C22×C4D8811yescharacteristic
187C22×C4C2×D4411yescharacteristic
188Q16—442no—
189Q16—881no—
190C2×C8—21no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8D4×D1112yes—
194C4⋊C4—222no—
195C4⋊C4—441no—
196C4⋊C4—442no—
197C4⋊C4—441no—
198C4⋊C4—441no—
199C4⋊C4—442no—
200C4⋊C4—441no—
201C4⋊C4—441no—
202C22⋊C4—442no—
203C22⋊C4—442no—
204C22⋊C4—882no—
205C16—42no—
206C11#1228211yescharacteristic, complemented, Sylow
207C23—21no—
208C23—21no—
209C23—41no—
210C23—41no—
211C23Dic8812yes—
212C23C2×D8811yescharacteristic
213Q8—442no—
214Q8—442no—
215Q8—882no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—81no—
223C2×C4—442no—
224C2×C4—442no—
225C2×C4—882no—
226C2×C4—882no—
227C2×C4—881no—
228C2×C4—881no—
229C2×C4—881no—
230C2×C4—881no—
231C2×C4—881no—
232C2×C4—881no—
233C2×C4#6693511yescharacteristic
234C2×C4#6696111yescharacteristic
235C8—22no—
236C8—41no—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—81no—
244C22#1062234511yescharacteristic
245C22C2×Dic8811yescharacteristic
246C22#1062252211yescharacteristic
247C4—21no—
248C4—41no—
249C4—882no—
250C4—882no—
251C4—1761no—
252C4—1761no—
253C4#1062235511yescharacteristic
254C4#1062235911yescharacteristic
255C2—21no—
256C2—21no—
257C2—42no—
258C2#1306760411yescharacteristic
259C2#1307055211yescharacteristic
260C2#1307056411yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1314C2
socleC22×C11#447
prime radicalC24×C11D8
hypercenter#1314D11
hypocenterC11#12282
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #13070819C2semidirect
4. #13066629C2semidirect
206. C11#12282semidirect

Maximal subgroups

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

subgroupindex
#130793912
#130708192
#130700442
#130666292
C11×#13142
#1228211