Finite Group Databasebeta

← #14666304

Subgroups — #14666304

Order 2816.

340 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 59 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#13070566C212yesmaximal
2#13069903C211yesmaximal, characteristic
3#13066610C212yesmaximal, complemented
4#13066567C211yesmaximal, characteristic, complemented
5C11×#3255C211yesmaximal, characteristic, complemented
6C11×#533—21no—
7#10623279C2211yescharacteristic
8C11×#475—22no—
9C11×#470—21no—
10C11×#470C2212yes—
11C11×#462—22no—
12C11×#423C2211yescharacteristic
13#10622792—22no—
14#10622745—21no—
15C2×#66869—21no—
16C11⋊#338C2211yescharacteristic
17#10622191C2212yes—
18#10622126—22no—
19C2×#4339—21no—
20C2×C11×Q16—21no—
21C2×C11×Q16D412yes—
22C2×C11×M16D411yescharacteristic
23C2×C11×M16C2311yescharacteristic
24C11×C4⋊Q8—21no—
25C11×C4⋊Q8—21no—
26C11×#125—41no—
27C11×C22⋊Q8—22no—
28C11×C22⋊Q8—41no—
29C4×Q8×C11—22no—
30C4×Q8×C11—41no—
31C11×#117—41no—
32C2×C42×C11D411yescharacteristic
33C2×#4318—21no—
34#66962—41no—
35#66961—41no—
36#66957—22no—
37C11×#106—21no—
38C11×#106D412yes—
39C11×C4⋊C8—22no—
40C11×#103—22no—
41C11×#103—22no—
42#66893—42no—
43#66892—42no—
44#66888—41no—
45#66887—41no—
46#66876—22no—
47#66869—41no—
48#66869—41no—
49#12174—111nomaximal, Sylow
50C2×Q8×C11—22no—
51C2×Q8×C11—41no—
52C22×C4×C11—21no—
53C22×C4×C11C2×D411yescharacteristic
54C2×C22⋊D11—41no—
55#4339—41no—
56#4339—41no—
57#4339—41no—
58#4339—41no—
59C2×D44—21no—
60C2×C4×D11—41no—
61C2×Dic22—21no—
62C11×Q16—42no—
63C11×Q16—81no—
64C11×M16—41no—
65C11×M16—41no—
66C2×C8×C11—21no—
67C2×C8×C11C2×D412yes—
68C11×C4⋊C4—22no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—42no—
74C11×C22⋊C4—42no—
75C42×C11—21no—
76C42×C11—42no—
77C42×C11D811yescharacteristic
78C42×C11D811yescharacteristic
79#4318—41no—
80#4318—41no—
81C2×C11⋊C8—41no—
82Dic44—22no—
83D88—22no—
84#4314—42no—
85C11⋊C16—42no—
86#3255D1111yescharacteristic, complemented
87#2191—112no—
88#2050—111no—
89#1342—112no—
90#1327—111no—
91C23×C11AGL(1,ℤ/8)11yescharacteristic
92C22×D11—41no—
93Q8×C11—42no—
94Q8×C11—42no—
95Q8×C11—82no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11#12011yescharacteristic
104C2×C4×C11C2×D811yescharacteristic
105C22⋊D11—81no—
106C22⋊D11—81no—
107C2×Dic11—41no—
108D44—41no—
109D44—41no—
110C4×D11—81no—
111C4×D11—81no—
112Dic22—41no—
113Dic22—41no—
114C8×C11—22no—
115C8×C11—41no—
116C11⋊C8—81no—
117#575—111no—
118#533—21no—
119#510—222no—
120#475—22no—
121#470—21no—
122#470C2×D1112yes—
123#462—22no—
124#423C2×D1111yescharacteristic
125C2×#104—221no—
126#413—221no—
127#360—222no—
128#349—112no—
129#338—111no—
130C22×C11—21no—
131C22×C11—41no—
132C22×C11#44711yescharacteristic
133C2×D11—81no—
134C2×D11—161no—
135C4×C11—22no—
136C4×C11—21no—
137C4×C11—41no—
138C4×C11—82no—
139C4×C11—82no—
140C4×C11#45411yescharacteristic
141C4×C11B(4,𝔽2)11yescharacteristic
142Dic11—81no—
143C2×#41—221no—
144#137—441no—
145AGL(1,ℤ/8)—441no—
146#135—222no—
147C2×Q16—21no—
148C2×Q16C22⋊D1112yes—
149C2×M16—221no—
150C2×M16C22⋊D1111yescharacteristic
151C2×M16C22×D1111yescharacteristic
152C4⋊Q8—21no—
153C4⋊Q8—21no—
154#125—41no—
155C22⋊Q8—22no—
156C22⋊Q8—41no—
157C4×Q8—22no—
158C4×Q8—41no—
159#117—41no—
160C2×C42C22⋊D1111yescharacteristic
161Q32—442no—
162SD32—442no—
163M32—222no—
164#106—21no—
165#106C22⋊D1112yes—
166C4⋊C8—22no—
167#104—441no—
168#104—441no—
169#103—22no—
170#103—22no—
171#101—441no—
172#100—441no—
173C2×C11—21no—
174C2×C11—41no—
175C2×C11#159811yescharacteristic
176D11—161no—
177#41—441no—
178#41—441no—
179#41—441no—
180#41—441no—
181C2×Q8—22no—
182C2×Q8—41no—
183C2×Q8—221no—
184C2×D4—221no—
185C2×D4—441no—
186C22×C4—21no—
187C22×C4—441no—
188C22×C4C2×C22⋊D1111yescharacteristic
189Q16—42no—
190Q16—81no—
191Q16—222no—
192SD16—442no—
193D8—222no—
194M16—41no—
195M16—41no—
196M16—441no—
197M16—441no—
198C2×C8—21no—
199C2×C8—441no—
200C2×C8C2×C22⋊D1112yes—
201C4⋊C4—22no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C22⋊C4—42no—
208C42—21no—
209C42—42no—
210C42#432311yescharacteristic
211C42#432311yescharacteristic
212C16—442no—
213C11#1217411yescharacteristic, complemented, Sylow
214C23—441no—
215C23#6698511yescharacteristic
216Q8—42no—
217Q8—42no—
218Q8—82no—
219Q8—441no—
220Q8—441no—
221D4—441no—
222D4—441no—
223D4—881no—
224D4—881no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—441no—
233C2×C4—881no—
234C2×C4—881no—
235C2×C4C2×#432311yescharacteristic
236C2×C4#6700611yescharacteristic
237C8—22no—
238C8—41no—
239C8—881no—
240C22—21no—
241C22—41no—
242C22—881no—
243C22—1761no—
244C22#1062283011yescharacteristic
245C4—22no—
246C4—21no—
247C4—41no—
248C4—82no—
249C4—82no—
250C4—881no—
251C4#1062285711yescharacteristic
252C4#1062285811yescharacteristic
253C2—21no—
254C2—41no—
255C2—1761no—
256C2#1306755111yescharacteristic
subgroupG/H
centerC2#13067551
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
FittingC11×#3255C2
socleC2×C11#1598
prime radical#10623279C22
hypercenter#3255D11
hypocenterC11#12174
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3255

Complements

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

NH ≅ G/Ntype
3. #13066610C2semidirect
4. #13066567C2semidirect
5. C11×#3255C2semidirect
86. #3255D11semidirect
213. C11#12174semidirect

Maximal subgroups

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

subgroupindex
#130705662
#130699032
#130666102
#130665672
C11×#32552
#1217411