Finite Group Databasebeta

← #14667399

Subgroups — #14667399

Order 2816.

290 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 290 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#13081048C211yesmaximal, characteristic
2#13070843C211yesmaximal, characteristic, complemented
3#13067978C211yesmaximal, characteristic
4#13066670C211yesmaximal, characteristic, complemented
5#13066580C211yesmaximal, characteristic, complemented
6#13066570C211yesmaximal, characteristic
7C11×#2209C211yesmaximal, characteristic, complemented
8#10623115—21no—
9C2×C11×Q32—21no—
10C11×#494C2211yescharacteristic
11C4×C11×Q16C2211yescharacteristic
12#10622801—21no—
13#10622700—21no—
14#10622633—21no—
15#10622493—21no—
16#10622427—22no—
17C8×D44C2211yescharacteristic
18#10622295C2211yescharacteristic
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×Q16D411yescharacteristic
28C11×C4⋊Q8—21no—
29C4×Q8×C11—21no—
30#66999—22no—
31C2×C8×D11—21no—
32#66951—42no—
33#66945—22no—
34#66928—41no—
35C4×D44D411yescharacteristic
36#66922—21no—
37C4×Dic22—41no—
38C11×Q32—42no—
39C2×C11×C16—21no—
40C11×#107D411yescharacteristic
41C11×#103—21no—
42C4×C8×C11C2311yescharacteristic
43#66899—22no—
44(C2×D11)⋊C8—21no—
45#66882—21no—
46#66882D412yes—
47C2×C11⋊C16—21no—
48#66873—41no—
49#66872—22no—
50#66871—41no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#12345—111nomaximal, Sylow
54C2×Q8×C11—21no—
55C2×Q8×C11—41no—
56C2×D44D811yescharacteristic
57C2×C4×D11—21no—
58C2×Dic22—41no—
59C11×Q16—21no—
60C11×Q16—21no—
61C11×Q16—42no—
62C11×Q16—41no—
63C11×Q16—41no—
64C2×C8×C11C2×D411yescharacteristic
65C2×C8×C11C2×D411yescharacteristic
66C11×C4⋊C4—21no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C42×C11—41no—
71C42×C11C2×D411yescharacteristic
72(C2×D11)⋊C4—21no—
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—42no—
75C4⋊Dic11—22no—
76C4⋊Dic11—41no—
77C4⋊Dic11D811yescharacteristic
78Dic11⋊C4—42no—
79C4×Dic11—42no—
80C2×C11⋊C8—21no—
81C2×C11⋊C8—41no—
82C8×D11—41no—
83C8×D11—41no—
84C11×C16—41no—
85C11⋊C16—41no—
86#3342—111no—
87#2241—111no—
88#2209D1111yescharacteristic, complemented
89#1669—111no—
90#1364—111no—
91#1332—111no—
92D4⋊C16—111no—
93C22×D11—21no—
94Q8×C11—41no—
95Q8×C11—41no—
96Q8×C11—81no—
97Q8×C11—81no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—81no—
101C2×C4×C11#12011yescharacteristic
102C2×C4×C11C2×D811yescharacteristic
103C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
104C2×Dic11—21no—
105C2×Dic11—42no—
106D44—21no—
107D44—21no—
108C4×D11—41no—
109C4×D11—41no—
110Dic22—81no—
111Dic22—81no—
112C8×C11—21no—
113C8×C11#13511yescharacteristic
114C8×C11AGL(1,ℤ/8)11yescharacteristic
115C11⋊C8—41no—
116C11⋊C8—81no—
117#556—221no—
118C2×Q32—21no—
119#500—111no—
120#494C2×D1111yescharacteristic
121#485—222no—
122#475—221no—
123#474—221no—
124#467—221no—
125C4×Q16C2×D1111yescharacteristic
126C8×D4—111no—
127#427—221no—
128C4⋊C16C2×D1111yescharacteristic
129#358—21no—
130#358—222no—
131C4×C16—111no—
132#335—111no—
133#332—221no—
134C22×C11#44711yescharacteristic
135C2×D11—41no—
136C2×D11—41no—
137C2×D11—41no—
138C4×C11—21no—
139C4×C11—81no—
140C4×C11—81no—
141C4×C11—161no—
142C4×C11#44911yescharacteristic
143C4×C11#45411yescharacteristic
144C4×C11#50811yescharacteristic
145C4×C11#51011yescharacteristic
146Dic11—41no—
147Dic11—82no—
148C2×Q16—21no—
149C2×Q16—21no—
150C2×Q16C22⋊D1111yescharacteristic
151C22×C8—221no—
152C4⋊Q8—21no—
153C4⋊Q8—221no—
154#126—442no—
155#124—441no—
156C22⋊Q8—222no—
157C4×Q8—21no—
158C4×Q8—441no—
159C4×D4—111no—
160#117—222no—
161Q32—42no—
162C2×C16—21no—
163C2×C16—221no—
164#107—112no—
165#107—221no—
166#107—441no—
167#107C22⋊D1111yescharacteristic
168#106—222no—
169C4⋊C8—111no—
170C4⋊C8—221no—
171#103—21no—
172#103—222no—
173#102—441no—
174C22⋊C8—221no—
175C4×C8C22×D1111yescharacteristic
176C2×C11#162511yescharacteristic
177C2×C11#218911yescharacteristic
178C2×C11#219511yescharacteristic
179D11—81no—
180C2×Q8—21no—
181C2×Q8—41no—
182C2×Q8—441no—
183C2×D4—111no—
184C22×C4—221no—
185Q16—21no—
186Q16—21no—
187Q16—42no—
188Q16—41no—
189Q16—41no—
190C2×C8—221no—
191C2×C8—441no—
192C2×C8—441no—
193C2×C8—441no—
194C2×C8D4×D1111yescharacteristic
195C2×C8C2×C22⋊D1111yescharacteristic
196C4⋊C4—21no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—111no—
201C4⋊C4—222no—
202C4⋊C4—442no—
203C4⋊C4—441no—
204C22⋊C4—221no—
205C22⋊C4—442no—
206C22⋊C4—442no—
207C42—41no—
208C42—442no—
209C42D4×D1111yescharacteristic
210C16—41no—
211C16—441no—
212C11#1234511yescharacteristic, complemented, Sylow
213C23—221no—
214Q8—41no—
215Q8—41no—
216Q8—81no—
217Q8—81no—
218Q8—881no—
219Q8—881no—
220D4—221no—
221D4—221no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—81no—
225C2×C4—221no—
226C2×C4—441no—
227C2×C4—441no—
228C2×C4—442no—
229C2×C4D8×D1111yescharacteristic
230C2×C4#6696411yescharacteristic
231C2×C4#6699011yescharacteristic
232C8—21no—
233C8—441no—
234C8—881no—
235C8#6698511yescharacteristic
236C8#6700311yescharacteristic
237C22—441no—
238C22—441no—
239C22—441no—
240C22#1062276911yescharacteristic
241C4—21no—
242C4—81no—
243C4—81no—
244C4—161no—
245C4—441no—
246C4—882no—
247C4#1062253111yescharacteristic
248C4#1062253211yescharacteristic
249C4#1062265011yescharacteristic
250C4#1062281411yescharacteristic
251C2—881no—
252C2#1306770411yescharacteristic
253C2#1307055511yescharacteristic
254C2#1307059111yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2209C2
socleC22×C11#447
prime radicalC2×D44D8
hypercenter#2209D11
hypocenterC11#12345
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
2. #13070843C2semidirect
4. #13066670C2semidirect
5. #13066580C2semidirect
7. C11×#2209C2semidirect
88. #2209D11semidirect
212. C11#12345semidirect

Maximal subgroups

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

subgroupindex
#130810482
#130708432
#130679782
#130666702
#130665802
#130665702
C11×#22092
#1234511