Finite Group Databasebeta

← #14667301

Subgroups — #14667301

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#13081602C211yesmaximal, characteristic, complemented
2#13070871C211yesmaximal, characteristic, complemented
3#13067973C211yesmaximal, characteristic, complemented
4#13066666C211yesmaximal, characteristic, complemented
5#13066594C211yesmaximal, characteristic, complemented
6#13066577C211yesmaximal, characteristic, complemented
7C11×#2206C211yesmaximal, characteristic
8#10623073—21no—
9C2×C11×D16—21no—
10C11×#493C2211yescharacteristic
11C4×C11×D8C2211yescharacteristic
12#10622768—21no—
13C2×#66891—22no—
14#10622688—21no—
15#10622632—21no—
16#10622486—21no—
17#10622380—22no—
18#10622312C2211yescharacteristic
19C8×Dic22C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C11×#357—21no—
22#10622182—21no—
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×D8—21no—
26C2×C11×D8—21no—
27C2×C11×D8D411yescharacteristic
28C11×#127—21no—
29C4×D4×C11—21no—
30#66989—22no—
31C2×#4324—22no—
32C2×#4324—41no—
33#66979—41no—
34#66977—41no—
35C2×Dic44—21no—
36C2×Dic44D412yes—
37#66940—22no—
38#66932—42no—
39#66922—21no—
40C4×Dic22D411yescharacteristic
41C11×D16—42no—
42C2×C11×C16—21no—
43C11×#107D411yescharacteristic
44C11×#102—21no—
45C4×C8×C11C2311yescharacteristic
46#66896—41no—
47#66891—44no—
48Dic11⋊C8—21no—
49C8×Dic11—21no—
50C2×C11⋊C16—21no—
51#66874—22no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)D411yescharacteristic
54#12331—111nomaximal, Sylow
55C2×D4×C11—21no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C22×C4×C11—41no—
60C2×Dic22—22no—
61C2×Dic22D811yescharacteristic
62C11×D8—21no—
63C11×D8—21no—
64C11×D8—42no—
65C11×D8—41no—
66C11×D8—41no—
67C2×C8×C11C2×D411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C11×C4⋊C4—21no—
70C11×C22⋊C4—41no—
71C42×C11C2×D411yescharacteristic
72C22⋊Dic11—42no—
73C22⋊Dic11—42no—
74#4324—82no—
75#4324—82no—
76C4⋊Dic11—41no—
77C4⋊Dic11—41no—
78C4⋊Dic11D811yescharacteristic
79Dic11⋊C4—21no—
80Dic11⋊C4—42no—
81C4×Dic11—21no—
82C4×Dic11—42no—
83C2×C11⋊C8—21no—
84C2×C11⋊C8—41no—
85Dic44—42no—
86Dic44—41no—
87Dic44—41no—
88C11×C16—41no—
89C11⋊C16—22no—
90#3393—111no—
91#2248—111no—
92#2206D1111yescharacteristic
93#1668—111no—
94#1362—111no—
95Q8⋊C16—111no—
96#1331—111no—
97C23×C11—41no—
98C23×C11—81no—
99D4×C11—41no—
100D4×C11—41no—
101D4×C11—81no—
102D4×C11—81no—
103D4×C11—81no—
104D4×C11—81no—
105D4×C11—161no—
106C2×C4×C11—41no—
107C2×C4×C11—81no—
108C2×C4×C11—81no—
109C2×C4×C11#12011yescharacteristic
110C2×C4×C11C2×D811yescharacteristic
111C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—42no—
115Dic22—21no—
116Dic22—21no—
117Dic22—42no—
118Dic22—42no—
119C8×C11—21no—
120C8×C11#13511yescharacteristic
121C8×C11AGL(1,ℤ/8)11yescharacteristic
122C11⋊C8—41no—
123C11⋊C8—81no—
124#556—221no—
125C2×SD32—222no—
126C2×D16—21no—
127#495—221no—
128#494—111no—
129#493C2×D1111yescharacteristic
130#464—222no—
131#461—221no—
132#460—221no—
133C8×Q8—111no—
134C4×Q16—221no—
135C4×D8C2×D1111yescharacteristic
136C4⋊C16C2×D1111yescharacteristic
137#357—21no—
138C4×C16—111no—
139#335—111no—
140#331—221no—
141C22×C11—81no—
142C22×C11—81no—
143C22×C11—81no—
144C22×C11—161no—
145C22×C11—161no—
146C22×C11—161no—
147C22×C11#44711yescharacteristic
148C4×C11—21no—
149C4×C11—81no—
150C4×C11#44911yescharacteristic
151C4×C11#45311yescharacteristic
152C4×C11#50811yescharacteristic
153C4×C11#50911yescharacteristic
154Dic11—41no—
155Dic11—41no—
156Dic11—82no—
157C2×Q16—112no—
158C2×Q16—221no—
159C2×SD16—222no—
160C2×SD16—441no—
161C2×D8—21no—
162C2×D8—21no—
163C2×D8C22⋊D1111yescharacteristic
164C4⋊Q8—221no—
165#127—21no—
166#126—442no—
167#124—222no—
168C22⋊Q8—441no—
169C4×Q8—111no—
170C4×Q8—222no—
171C4×D4—21no—
172#117—441no—
173SD32—444no—
174D16—42no—
175C2×C16—21no—
176C2×C16—221no—
177#107C22⋊D1111yescharacteristic
178C4⋊C8—111no—
179C4⋊C8—221no—
180C4⋊C8—221no—
181#103—222no—
182#102—21no—
183#102—441no—
184C4×C8—221no—
185C4×C8C22×D1111yescharacteristic
186C2×C11—161no—
187C2×C11—321no—
188C2×C11#162111yescharacteristic
189C2×C11#218611yescharacteristic
190C2×C11#219311yescharacteristic
191C2×Q8—111no—
192C2×Q8—222no—
193C2×D4—21no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—41no—
197C22×C4—41no—
198Q16—442no—
199Q16—441no—
200Q16—441no—
201SD16—882no—
202SD16—882no—
203D8—21no—
204D8—21no—
205D8—42no—
206D8—41no—
207D8—41no—
208C2×C8—221no—
209C2×C8—441no—
210C2×C8D4×D1111yescharacteristic
211C2×C8C2×C22⋊D1111yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—111no—
214C4⋊C4—221no—
215C4⋊C4—442no—
216C4⋊C4—441no—
217C4⋊C4—441no—
218C22⋊C4—41no—
219C22⋊C4—442no—
220C22⋊C4—442no—
221C42—221no—
222C42—442no—
223C42D4×D1111yescharacteristic
224C16—41no—
225C16—222no—
226C11#1233111yescharacteristic, complemented, Sylow
227C23—41no—
228C23—81no—
229Q8—221no—
230Q8—221no—
231Q8—442no—
232Q8—442no—
233D4—41no—
234D4—41no—
235D4—81no—
236D4—81no—
237D4—81no—
238D4—81no—
239D4—161no—
240C2×C4—41no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—221no—
244C2×C4—221no—
245C2×C4—442no—
246C2×C4D8×D1111yescharacteristic
247C2×C4#6696411yescharacteristic
248C2×C4#6699011yescharacteristic
249C8—21no—
250C8—441no—
251C8—881no—
252C8#6698511yescharacteristic
253C8#6700311yescharacteristic
254C22—81no—
255C22—81no—
256C22—81no—
257C22—161no—
258C22—161no—
259C22—161no—
260C22#1062276911yescharacteristic
261C4—21no—
262C4—81no—
263C4—441no—
264C4—441no—
265C4—882no—
266C4#1062252411yescharacteristic
267C4#1062252511yescharacteristic
268C4#1062265011yescharacteristic
269C4#1062281111yescharacteristic
270C2—161no—
271C2—321no—
272C2#1306768011yescharacteristic
273C2#1307053611yescharacteristic
274C2#1307057711yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
Fitting, prime radicalC11×#2206C2
socleC22×C11#447
hypercenter#2206D11
hypocenterC11#12331
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #13081602C2semidirect
2. #13070871C2semidirect
3. #13067973C2semidirect
4. #13066666C2semidirect
5. #13066594C2semidirect
6. #13066577C2semidirect
226. C11#12331semidirect

Maximal subgroups

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

subgroupindex
#130816022
#130708712
#130679732
#130666662
#130665942
#130665772
C11×#22062
#1233111