Finite Group Databasebeta

← #14667299

Subgroups — #14667299

Order 2816.

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

normal subgroups only

This group has 328 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#13081606C211yesmaximal, characteristic, complemented
2#13070648C211yesmaximal, characteristic
3#13067973C211yesmaximal, characteristic, complemented
4#13066665C211yesmaximal, characteristic, complemented
5#13066596C211yesmaximal, characteristic, complemented
6#13066578C211yesmaximal, characteristic, complemented
7C11×#2248C211yesmaximal, characteristic, complemented
8#10623263—21no—
9C2×C11×SD32—22no—
10C11×#494C2211yescharacteristic
11C11×#493C2211yescharacteristic
12#10622804—21no—
13#10622798—22no—
14Q16×Dic11—21no—
15C2×#66890—21no—
16#10622696—21no—
17#10622688—21no—
18C4×D88C2211yescharacteristic
19C8×Dic22C2211yescharacteristic
20C4×C11×C16C2211yescharacteristic
21#10622200—21no—
22#10622182—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16D412yes—
27C2×C11×D8—21no—
28C2×C11×D8—21no—
29C11×C4⋊Q8—21no—
30C11×#127—21no—
31#67000—22no—
32Q8×Dic11—22no—
33C2×#4325—22no—
34C2×#4324—41no—
35C2×D88D411yescharacteristic
36#66951—42no—
37#66950—41no—
38#66945—41no—
39C4×D44—21no—
40C4×Dic22D411yescharacteristic
41C11×SD32—44no—
42C2×C11×C16—21no—
43C4×C8×C11C2311yescharacteristic
44#66899—22no—
45#66896—41no—
46#66890—42no—
47#66885—21no—
48#66882D411yescharacteristic
49Dic11⋊C8—21no—
50C8×Dic11—21no—
51C2×C11⋊C16—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)D411yescharacteristic
54#12331—111nomaximal, Sylow
55C2×Q8×C11—22no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×D44—21no—
60C2×C4×D11—41no—
61C2×Dic22D811yescharacteristic
62C11×Q16—41no—
63C11×Q16—41no—
64C11×Q16—42no—
65C11×D8—42no—
66C11×D8—41no—
67C11×D8—41no—
68C2×C8×C11C2×D411yescharacteristic
69C2×C8×C11C2×D411yescharacteristic
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C42×C11C2×D411yescharacteristic
73#4325—82no—
74#4324—82no—
75(C2×D11)⋊C4—42no—
76(C2×D11)⋊C4—42no—
77(C2×D11)⋊C4—41no—
78C4⋊Dic11—21no—
79C4⋊Dic11—42no—
80C4⋊Dic11D811yescharacteristic
81Dic11⋊C4—21no—
82C4×Dic11—21no—
83C4×Dic11—42no—
84C2×C11⋊C8—21no—
85C2×C11⋊C8—41no—
86D88—21no—
87D88—21no—
88C11×C16—22no—
89C11⋊C16—41no—
90#3393—111no—
91#2248D1111yescharacteristic, complemented
92#2206—111no—
93#1668—111no—
94#1362—111no—
95Q8⋊C16—111no—
96#1331—111no—
97C23×C11—81no—
98C22×D11—41no—
99Q8×C11—42no—
100Q8×C11—42no—
101D4×C11—81no—
102D4×C11—81no—
103D4×C11—81no—
104D4×C11—81no—
105D4×C11—161no—
106C2×C4×C11—42no—
107C2×C4×C11#12011yescharacteristic
108C2×C4×C11C2×D811yescharacteristic
109C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
110C2×Dic11—21no—
111C2×Dic11—21no—
112C2×Dic11—41no—
113D44—41no—
114D44—41no—
115C4×D11—81no—
116C4×D11—81no—
117Dic22—21no—
118Dic22—21no—
119C8×C11—21no—
120C8×C11#13511yescharacteristic
121C8×C11AGL(1,ℤ/8)11yescharacteristic
122C11⋊C8—41no—
123C11⋊C8—81no—
124#556—221no—
125C2×SD32—22no—
126C2×D16—221no—
127#495—221no—
128#494C2×D1111yescharacteristic
129#493C2×D1111yescharacteristic
130#464—222no—
131#461—221no—
132#460—221no—
133C8×Q8—111no—
134C4×Q16—221no—
135C4×D8—111no—
136C4⋊C16—111no—
137#357—221no—
138C4×C16C2×D1111yescharacteristic
139#335—111no—
140#331—221no—
141C22×C11—161no—
142C22×C11—161no—
143C22×C11—161no—
144C22×C11#44711yescharacteristic
145C2×D11—81no—
146C2×D11—81no—
147C2×D11—81no—
148C4×C11—21no—
149C4×C11—82no—
150C4×C11#44911yescharacteristic
151C4×C11#45311yescharacteristic
152C4×C11#50811yescharacteristic
153C4×C11#50911yescharacteristic
154Dic11—41no—
155Dic11—41no—
156Dic11—81no—
157C2×Q16—21no—
158C2×Q16C22⋊D1112yes—
159C2×SD16—222no—
160C2×SD16—441no—
161C2×D8—21no—
162C2×D8—21no—
163C2×D8—111no—
164C4⋊Q8—21no—
165#127—21no—
166#126—442no—
167#124—222no—
168C22⋊Q8—441no—
169C4×Q8—111no—
170C4×Q8—222no—
171C4×D4—221no—
172#117—441no—
173SD32—44no—
174D16—442no—
175C2×C16—21no—
176C2×C16—221no—
177#107—111no—
178C4⋊C8—111no—
179C4⋊C8—221no—
180C4⋊C8—221no—
181#103—222no—
182#102—221no—
183#102—441no—
184C4×C8—221no—
185C4×C8C22×D1111yescharacteristic
186C2×C11—321no—
187C2×C11#162111yescharacteristic
188C2×C11#218611yescharacteristic
189C2×C11#219311yescharacteristic
190D11—161no—
191C2×Q8—22no—
192C2×Q8—111no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—221no—
197C22×C4—441no—
198Q16—42no—
199Q16—41no—
200Q16—41no—
201SD16—882no—
202SD16—882no—
203D8—42no—
204D8—41no—
205D8—41no—
206D8—221no—
207D8—221no—
208C2×C8—221no—
209C2×C8—441no—
210C2×C8D4×D1111yescharacteristic
211C2×C8C2×C22⋊D1111yescharacteristic
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—111no—
215C4⋊C4—221no—
216C4⋊C4—221no—
217C4⋊C4—442no—
218C22⋊C4—442no—
219C22⋊C4—442no—
220C22⋊C4—441no—
221C42—221no—
222C42—442no—
223C42D4×D1111yescharacteristic
224C16—22no—
225C16—441no—
226C11#1233111yescharacteristic, complemented, Sylow
227C23—81no—
228C23—441no—
229Q8—42no—
230Q8—42no—
231Q8—221no—
232Q8—221no—
233D4—81no—
234D4—81no—
235D4—81no—
236D4—81no—
237D4—161no—
238D4—441no—
239D4—441no—
240C2×C4—42no—
241C2×C4—221no—
242C2×C4—221no—
243C2×C4—441no—
244C2×C4—881no—
245C2×C4—881no—
246C2×C4D8×D1111yescharacteristic
247C2×C4#6696411yescharacteristic
248C2×C4#6699011yescharacteristic
249C8—21no—
250C8—441no—
251C8—881no—
252C8#6696411yescharacteristic
253C8#6696511yescharacteristic
254C22—161no—
255C22—161no—
256C22—161no—
257C22—881no—
258C22—881no—
259C22—881no—
260C22#1062276911yescharacteristic
261C4—21no—
262C4—82no—
263C4—441no—
264C4—441no—
265C4—881no—
266C4#1062252711yescharacteristic
267C4#1062252911yescharacteristic
268C4#1062269011yescharacteristic
269C4#1062277111yescharacteristic
270C2—321no—
271C2—1761no—
272C2#1306767811yescharacteristic
273C2#1307053811yescharacteristic
274C2#1307057911yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2248C2
socleC22×C11#447
prime radical#13070648C2
hypercenter#2248D11
hypocenterC11#12331
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #13081606C2semidirect
3. #13067973C2semidirect
4. #13066665C2semidirect
5. #13066596C2semidirect
6. #13066578C2semidirect
7. C11×#2248C2semidirect
91. #2248D11semidirect
226. C11#12331semidirect

Maximal subgroups

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

subgroupindex
#130816062
#130706482
#130679732
#130666652
#130665962
#130665782
C11×#22482
#1233111