Finite Group Databasebeta

← #14664612

Subgroups — #14664612

Order 2816.

286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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#13079345C211yesmaximal, characteristic
2#13070428C211yesmaximal, characteristic, complemented
3#13066609C211yesmaximal, characteristic, complemented
4#13066606C211yesmaximal, characteristic
5#13066603C211yesmaximal, characteristic, complemented
6#13066600C211yesmaximal, characteristic
7C11×#1841C211yesmaximal, characteristic, complemented
8#10623010—21no—
9C4×C11×M16C2211yescharacteristic
10#10622750C2211yescharacteristic
11#10622748C2211yescharacteristic
12#10622747—21no—
13#10622329C411yescharacteristic, complemented
14#10622324C411yescharacteristic, complemented
15#10622323—21no—
16#10622310—21no—
17#10622309C411yescharacteristic, complemented
18#10622296C411yescharacteristic, complemented
19C11×#344—21no—
20C11×#339—21no—
21C11×#338C2211yescharacteristic
22C11×H(3,ℤ/4)C2211yescharacteristic
23#10622191C2211yescharacteristic
24#10622191C2211yescharacteristic
25#10622104—21no—
26#10622101—21no—
27C2×C11×M16—21no—
28C2×C11×M16D411yescharacteristic
29C2×C11×M16C2311yescharacteristic
30C11×#117—21no—
31C2×C42×C11D411yescharacteristic
32#66983—21no—
33#66982—41no—
34C4×C22⋊D11—41no—
35#66977—21no—
36C2×Dic44C2×C411yescharacteristic
37C2×D88C2×C411yescharacteristic
38C2×#4314—21no—
39#66929—41no—
40#66928—21no—
41C4×D44—21no—
42#66925—41no—
43#66923—21no—
44C4×Dic22—21no—
45C11×#97C2×C411yescharacteristic
46C11×#97D411yescharacteristic
47C4×C8×C11C2×C411yescharacteristic
48C4×C8×C11D411yescharacteristic
49#66885—21no—
50#66885—21no—
51#66882—21no—
52#66881C2×C411yescharacteristic
53#66881C2×C411yescharacteristic
54#66880—21no—
55#66880—21no—
56#66876—21no—
57#66876—21no—
58#11836—111nomaximal, Sylow
59C22×C4×C11—21no—
60C22×C4×C11C2×D411yescharacteristic
61C2×C22⋊D11—41no—
62C2×D44—21no—
63C2×C4×D11—41no—
64C2×Dic22—21no—
65C11×M16—41no—
66C11×M16—41no—
67C11×M16—41no—
68C11×M16—41no—
69C2×C8×C11—41no—
70C2×C8×C11C22⋊C411yescharacteristic
71C2×C8×C11C22⋊C411yescharacteristic
72C2×C8×C11C22×C411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—41no—
75C11×C22⋊C4—41no—
76C42×C11—21no—
77C42×C11—41no—
78C42×C11C22⋊C411yescharacteristic
79C42×C11C22⋊C411yescharacteristic
80C22⋊Dic11—41no—
81(C2×D11)⋊C4—41no—
82(C2×D11)⋊C4—41no—
83(C2×D11)⋊C4—41no—
84(C2×D11)⋊C4—41no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91C4×Dic11—41no—
92Dic44—41no—
93D88—41no—
94#4314—42no—
95C11⋊C16—41no—
96C11⋊C16—41no—
97#3183—111no—
98#2165—111no—
99#1841D1111yescharacteristic, complemented
100#1342—111no—
101#1341—111no—
102#1340—111no—
103#1339—111no—
104C23×C11AGL(1,ℤ/8)11yescharacteristic
105C22×D11—41no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—81no—
111C2×C4×C11—81no—
112C2×C4×C11C2×C22⋊C411yescharacteristic
113C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
114C22⋊D11—82no—
115C2×Dic11—41no—
116C2×Dic11—41no—
117C2×Dic11—41no—
118D44—41no—
119D44—41no—
120C4×D11—82no—
121Dic22—41no—
122Dic22—41no—
123C8×C11—21no—
124C8×C11—21no—
125C8×C11—21no—
126C8×C11—21no—
127C8×C11—81no—
128#529—221no—
129#499—111no—
130#495—111no—
131#488—221no—
132#470—111no—
133#469—111no—
134#468—221no—
135#442—111no—
136#441—111no—
137#440—221no—
138C4×M16C2×D1111yescharacteristic
139#364—221no—
140#349—111no—
141#349—111no—
142#347—221no—
143#344—21no—
144#339—21no—
145#338C2×D1111yescharacteristic
146H(3,ℤ/4)C2×D1111yescharacteristic
147C22×C11—21no—
148C22×C11—41no—
149C22×C11#41811yescharacteristic
150C2×D11—81no—
151C2×D11—81no—
152C2×D11—81no—
153C4×C11—21no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11—161no—
157C4×C11#41011yescharacteristic
158C4×C11#42111yescharacteristic
159Dic11—81no—
160Dic11—81no—
161Dic11—81no—
162C2×Q16—111no—
163C2×SD16—221no—
164C2×D8—111no—
165C2×M16—21no—
166C2×M16C22⋊D1111yescharacteristic
167C2×M16C22×D1111yescharacteristic
168#126—441no—
169#125—221no—
170#124—221no—
171#123—441no—
172C22⋊Q8—221no—
173#121—221no—
174C4×Q8—221no—
175C4×D4—221no—
176C4×D4—441no—
177#117—21no—
178#117—441no—
179C2×C42C22⋊D1111yescharacteristic
180M32—221no—
181M32—221no—
182#107—221no—
183#106—111no—
184#106—111no—
185#103—221no—
186#103—221no—
187#102—221no—
188#102—221no—
189#97C4×D1111yescharacteristic
190#97D4411yescharacteristic
191C4×C8C4×D1111yescharacteristic
192C4×C8D4411yescharacteristic
193C2×C11—21no—
194C2×C11—41no—
195C2×C11#151411yescharacteristic
196D11—161no—
197C2×Q8—221no—
198C2×D4—221no—
199C2×D4—441no—
200C22×C4—21no—
201C22×C4—441no—
202C22×C4C2×C22⋊D1111yescharacteristic
203Q16—441no—
204SD16—442no—
205D8—441no—
206M16—41no—
207M16—41no—
208M16—41no—
209M16—41no—
210C2×C8—41no—
211C2×C8(C2×D11)⋊C411yescharacteristic
212C2×C8(C2×D11)⋊C411yescharacteristic
213C2×C8C2×C4×D1111yescharacteristic
214C2×C8C2×D4411yescharacteristic
215C4⋊C4—41no—
216C4⋊C4—221no—
217C4⋊C4—221no—
218C4⋊C4—441no—
219C4⋊C4—441no—
220C4⋊C4—441no—
221C4⋊C4—441no—
222C22⋊C4—41no—
223C22⋊C4—441no—
224C22⋊C4—441no—
225C22⋊C4—441no—
226C22⋊C4—441no—
227C22⋊C4—441no—
228C42—21no—
229C42—41no—
230C42—441no—
231C42(C2×D11)⋊C411yescharacteristic
232C42(C2×D11)⋊C411yescharacteristic
233C16—441no—
234C16—441no—
235C11#1183611yescharacteristic, complemented, Sylow
236C23—441no—
237C23#6700211yescharacteristic
238Q8—441no—
239Q8—441no—
240D4—441no—
241D4—441no—
242D4—882no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—441no—
250C2×C4—441no—
251C2×C4—441no—
252C2×C4—882no—
253C2×C4C2×(C2×D11)⋊C411yescharacteristic
254C2×C4#6700211yescharacteristic
255C8—21no—
256C8—21no—
257C8—21no—
258C8—21no—
259C8—81no—
260C22—21no—
261C22—41no—
262C22—881no—
263C22—881no—
264C22—881no—
265C22#1062261411yescharacteristic
266C4—21no—
267C4—41no—
268C4—41no—
269C4—161no—
270C4—881no—
271C4—881no—
272C4—881no—
273C4#1062261811yescharacteristic
274C4#1062261911yescharacteristic
275C2—21no—
276C2—41no—
277C2—1761no—
278C2#1306716211yescharacteristic
subgroupG/H
centerC2#13067162
commutatorC2×C8×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#1841C2
socleC2×C11#1514
prime radical#10622748C22
cosocleC2×C11×M16C23
hypercenter#1841D11
hypocenterC11#11836
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #1841

Complements

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

NH ≅ G/Ntype
2. #13070428C2semidirect
3. #13066609C2semidirect
5. #13066603C2semidirect
7. C11×#1841C2semidirect
13. #10622329C4semidirect
14. #10622324C4semidirect
17. #10622309C4semidirect
18. #10622296C4semidirect
99. #1841D11semidirect
235. C11#11836semidirect

Maximal subgroups

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

subgroupindex
#130793452
#130704282
#130666092
#130666062
#130666032
#130666002
C11×#18412
#1183611