Finite Group Databasebeta

← #14664614

Subgroups — #14664614

Order 2816.

286 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 79 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#13070428C211yesmaximal, characteristic, complemented
2#13068765C211yesmaximal, characteristic, complemented
3#13066610C211yesmaximal, characteristic, complemented
4#13066607C211yesmaximal, characteristic
5#13066604C211yesmaximal, characteristic, complemented
6#13066601C211yesmaximal, characteristic
7C11×#3183C211yesmaximal, characteristic
8C11×#529—21no—
9C11×#499C411yescharacteristic, complemented
10C11×#495C411yescharacteristic, complemented
11C11×#488—21no—
12C11×#470C2211yescharacteristic
13C11×#469C2211yescharacteristic
14C11×#468—21no—
15C11×#442C411yescharacteristic, complemented
16C11×#441C411yescharacteristic, complemented
17C11×#440—21no—
18C4×C11×M16C2211yescharacteristic
19C11⋊#338C2211yescharacteristic
20#10622195C2211yescharacteristic
21#10622194—21no—
22#10622191C2211yescharacteristic
23#10622191C2211yescharacteristic
24#10622161—21no—
25#10622104—21no—
26#10622101—21no—
27C2×C11×Q16C2×C411yescharacteristic
28C2×C11×SD16—21no—
29C2×C11×D8C2×C411yescharacteristic
30C2×C11×M16D411yescharacteristic
31C2×C11×M16C2311yescharacteristic
32C11×#126—41no—
33C11×#125—21no—
34C11×#124—21no—
35C11×#123—41no—
36C11×C22⋊Q8—21no—
37C11×#121—21no—
38C4×Q8×C11—21no—
39C4×D4×C11—21no—
40C4×D4×C11—41no—
41C11×#117—41no—
42C2×C42×C11D411yescharacteristic
43#66979—21no—
44C2×#4318—21no—
45C11×#107—21no—
46C11×#106C2×C411yescharacteristic
47C11×#106C2×C411yescharacteristic
48C11×#103—21no—
49C11×#103—21no—
50C11×#102—21no—
51C11×#102—21no—
52C11×#97C2×C411yescharacteristic
53C11×#97D411yescharacteristic
54C4×C8×C11C2×C411yescharacteristic
55C4×C8×C11D411yescharacteristic
56#66876—21no—
57#66876—21no—
58#11836—111nomaximal, Sylow
59C2×Q8×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11—41no—
62C22×C4×C11—21no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C11×Q16—41no—
66C11×SD16—42no—
67C11×D8—41no—
68C11×M16—41no—
69C11×M16—41no—
70C2×C8×C11C22⋊C411yescharacteristic
71C2×C8×C11C22⋊C411yescharacteristic
72C2×C8×C11C22×C411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C42×C11—21no—
86C42×C11—41no—
87C42×C11C22⋊C411yescharacteristic
88C42×C11C22⋊C411yescharacteristic
89C22⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4×Dic11—41no—
92#4318—41no—
93#4318—41no—
94C2×C11⋊C8—41no—
95C11⋊C16—41no—
96C11⋊C16—41no—
97#3183D1111yescharacteristic
98#2165—111no—
99#1841—111no—
100#1342—111no—
101#1341—111no—
102#1340—111no—
103#1339—111no—
104C23×C11—41no—
105C23×C11AGL(1,ℤ/8)11yescharacteristic
106Q8×C11—41no—
107Q8×C11—41no—
108D4×C11—41no—
109D4×C11—41no—
110D4×C11—82no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—81no—
119C2×C4×C11—82no—
120C2×C4×C11C2×C22⋊C411yescharacteristic
121C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
122C2×Dic11—81no—
123C8×C11—21no—
124C8×C11—21no—
125C8×C11—21no—
126C8×C11—21no—
127C11⋊C8—81no—
128#529—21no—
129#499Dic1111yescharacteristic, complemented
130#495Dic1111yescharacteristic, complemented
131#488—21no—
132#470C2×D1111yescharacteristic
133#469C2×D1111yescharacteristic
134#468—21no—
135#442Dic1111yescharacteristic, complemented
136#441Dic1111yescharacteristic, complemented
137#440—21no—
138C4×M16C2×D1111yescharacteristic
139#364—221no—
140#349—111no—
141#349—111no—
142#347—221no—
143#344—221no—
144#339—221no—
145#338—111no—
146H(3,ℤ/4)—111no—
147C22×C11—21no—
148C22×C11—41no—
149C22×C11—81no—
150C22×C11—81no—
151C22×C11—81no—
152C22×C11#41811yescharacteristic
153C4×C11—21no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11—81no—
157C4×C11—81no—
158C4×C11—81no—
159C4×C11#41011yescharacteristic
160C4×C11#42111yescharacteristic
161Dic11—161no—
162C2×Q16C2×Dic1111yescharacteristic
163C2×SD16—21no—
164C2×D8C2×Dic1111yescharacteristic
165C2×M16—221no—
166C2×M16C22⋊D1111yescharacteristic
167C2×M16C22×D1111yescharacteristic
168#126—41no—
169#125—21no—
170#124—21no—
171#123—41no—
172C22⋊Q8—21no—
173#121—21no—
174C4×Q8—21no—
175C4×D4—21no—
176C4×D4—41no—
177#117—41no—
178#117—221no—
179C2×C42C22⋊D1111yescharacteristic
180M32—221no—
181M32—221no—
182#107—21no—
183#106C2×Dic1111yescharacteristic
184#106C2×Dic1111yescharacteristic
185#103—21no—
186#103—21no—
187#102—21no—
188#102—21no—
189#97C2×Dic1111yescharacteristic
190#97C22⋊D1111yescharacteristic
191C4×C8C2×Dic1111yescharacteristic
192C4×C8C22⋊D1111yescharacteristic
193C2×C11—21no—
194C2×C11—41no—
195C2×C11—161no—
196C2×C11#151411yescharacteristic
197C2×Q8—21no—
198C2×D4—21no—
199C2×D4—41no—
200C22×C4—21no—
201C22×C4—41no—
202C22×C4C2×C22⋊D1111yescharacteristic
203Q16—41no—
204SD16—42no—
205D8—41no—
206M16—41no—
207M16—41no—
208M16—441no—
209M16—441no—
210C2×C8—441no—
211C2×C8C22⋊Dic1111yescharacteristic
212C2×C8C22⋊Dic1111yescharacteristic
213C2×C8C22×Dic1111yescharacteristic
214C2×C8C2×C22⋊D1111yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—441no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—441no—
228C42—21no—
229C42—41no—
230C42—441no—
231C42C22⋊Dic1111yescharacteristic
232C42C22⋊Dic1111yescharacteristic
233C16—441no—
234C16—441no—
235C11#1183611yescharacteristic, complemented, Sylow
236C23—41no—
237C23#6698511yescharacteristic
238Q8—41no—
239Q8—41no—
240D4—41no—
241D4—41no—
242D4—82no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—81no—
251C2×C4—82no—
252C2×C4—881no—
253C2×C4#6698511yescharacteristic
254C2×C4C2×C22⋊Dic1111yescharacteristic
255C8—21no—
256C8—21no—
257C8—21no—
258C8—21no—
259C8—881no—
260C22—21no—
261C22—41no—
262C22—81no—
263C22—81no—
264C22—81no—
265C22#1062282811yescharacteristic
266C4—21no—
267C4—41no—
268C4—41no—
269C4—81no—
270C4—81no—
271C4—81no—
272C4—1761no—
273C4#1062284911yescharacteristic
274C4#1062285311yescharacteristic
275C2—21no—
276C2—41no—
277C2—161no—
278C2#1306716311yescharacteristic
subgroupG/H
centerC2#13067163
commutatorC2×C8×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#3183C2
socleC2×C11#1514
prime radicalC11×#469C22
cosocleC2×C11×M16C23
hypercenter#3183D11
hypocenterC11#11836
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #3183

Complements

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

NH ≅ G/Ntype
1. #13070428C2semidirect
2. #13068765C2semidirect
3. #13066610C2semidirect
5. #13066604C2semidirect
9. C11×#499C4semidirect
10. C11×#495C4semidirect
15. C11×#442C4semidirect
16. C11×#441C4semidirect
129. #499Dic11semidirect
130. #495Dic11semidirect
135. #442Dic11semidirect
136. #441Dic11semidirect
235. C11#11836semidirect

Maximal subgroups

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

subgroupindex
#130704282
#130687652
#130666102
#130666072
#130666042
#130666012
C11×#31832
#1183611