Finite Group Databasebeta

← #14667329

Subgroups — #14667329

Order 2816.

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

normal subgroups only

This group has 312 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
2#13070868C211yesmaximal, characteristic, complemented
3#13067983C211yesmaximal, characteristic, complemented
4#13066666C211yesmaximal, characteristic, complemented
5#13066594C211yesmaximal, characteristic, complemented
6#13066577C211yesmaximal, characteristic
7C11×#2208C211yesmaximal, characteristic
8#10623073—21no—
9C2×C11×SD32—21no—
10C11×#494C2211yescharacteristic
11C4×C11×D8C2211yescharacteristic
12C2×#66893—22no—
13#10622768—21no—
14#10622707—21no—
15#10622632—21no—
16#10622486—21no—
17#10622380—22no—
18#10622312C2211yescharacteristic
19C8×Dic22C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C11×#358—21no—
22#10622185—21no—
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16—21no—
27C2×C11×D8D411yescharacteristic
28C11×C4⋊Q8—21no—
29C4×D4×C11—21no—
30#66989—22no—
31C2×#4324—22no—
32#66979—41no—
33#66977—41no—
34C2×Dic44—21no—
35C2×Dic44D412yes—
36#66940—22no—
37#66932—42no—
38#66922—21no—
39C4×Dic22D411yescharacteristic
40C11×SD32—42no—
41C2×C11×C16—21no—
42C11×#107D411yescharacteristic
43C11×#102—21no—
44C4×C8×C11C2311yescharacteristic
45#66893—44no—
46Dic11⋊C8—21no—
47C8×Dic11—21no—
48C2×C11⋊C16—21no—
49#66874—22no—
50#66874—41no—
51#66872—41no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)D411yescharacteristic
54#12335—111nomaximal, Sylow
55C2×Q8×C11—41no—
56C2×D4×C11—21no—
57C22×C4×C11—41no—
58C2×Dic22—22no—
59C2×Dic22D811yescharacteristic
60C11×Q16—42no—
61C11×Q16—41no—
62C11×Q16—41no—
63C11×D8—21no—
64C11×D8—21no—
65C2×C8×C11C2×D411yescharacteristic
66C2×C8×C11C2×D411yescharacteristic
67C11×C4⋊C4—21no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C11×C22⋊C4—41no—
71C42×C11C2×D411yescharacteristic
72C22⋊Dic11—42no—
73C22⋊Dic11—42no—
74#4324—82no—
75C4⋊Dic11—41no—
76C4⋊Dic11—41no—
77C4⋊Dic11D811yescharacteristic
78Dic11⋊C4—21no—
79Dic11⋊C4—42no—
80C4×Dic11—21no—
81C4×Dic11—42no—
82C2×C11⋊C8—21no—
83C2×C11⋊C8—41no—
84Dic44—42no—
85Dic44—41no—
86Dic44—41no—
87C11×C16—41no—
88C11⋊C16—22no—
89#3393—111no—
90#2247—111no—
91#2208D1111yescharacteristic
92#1670—111no—
93#1362—111no—
94Q8⋊C16—111no—
95#1331—111no—
96C23×C11—41no—
97Q8×C11—81no—
98Q8×C11—81no—
99D4×C11—41no—
100D4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11—81no—
103C2×C4×C11—81no—
104C2×C4×C11—81no—
105C2×C4×C11#12011yescharacteristic
106C2×C4×C11C2×D811yescharacteristic
107C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11—42no—
111Dic22—21no—
112Dic22—21no—
113Dic22—42no—
114Dic22—42no—
115C8×C11—21no—
116C8×C11#13511yescharacteristic
117C8×C11AGL(1,ℤ/8)11yescharacteristic
118C11⋊C8—41no—
119C11⋊C8—81no—
120#556—221no—
121C2×Q32—222no—
122C2×SD32—21no—
123#495—221no—
124#494—111no—
125#494C2×D1111yescharacteristic
126#475—221no—
127#464—222no—
128#461—221no—
129C8×Q8—111no—
130C4×Q16—221no—
131C4×D8C2×D1111yescharacteristic
132C4⋊C16C2×D1111yescharacteristic
133#358—21no—
134C4×C16—111no—
135#335—111no—
136#332—221no—
137C22×C11—81no—
138C22×C11—81no—
139C22×C11—81no—
140C22×C11#44711yescharacteristic
141C4×C11—21no—
142C4×C11—81no—
143C4×C11—161no—
144C4×C11#44911yescharacteristic
145C4×C11#45311yescharacteristic
146C4×C11#50811yescharacteristic
147C4×C11#51011yescharacteristic
148Dic11—41no—
149Dic11—41no—
150Dic11—82no—
151C2×Q16—21no—
152C2×Q16—21no—
153C2×Q16—112no—
154C2×Q16—221no—
155C2×SD16—222no—
156C2×D8C22⋊D1111yescharacteristic
157C4⋊Q8—21no—
158C4⋊Q8—221no—
159#126—442no—
160#124—222no—
161C22⋊Q8—441no—
162C4×Q8—111no—
163C4×Q8—222no—
164C4×D4—21no—
165#117—441no—
166Q32—444no—
167SD32—42no—
168C2×C16—21no—
169C2×C16—221no—
170#107C22⋊D1111yescharacteristic
171#106—441no—
172C4⋊C8—111no—
173C4⋊C8—221no—
174C4⋊C8—221no—
175#103—222no—
176#103—441no—
177#102—21no—
178C4×C8—221no—
179C4×C8C22×D1111yescharacteristic
180C2×C11—161no—
181C2×C11#162111yescharacteristic
182C2×C11#218911yescharacteristic
183C2×C11#219511yescharacteristic
184C2×Q8—41no—
185C2×Q8—111no—
186C2×Q8—222no—
187C2×D4—21no—
188C22×C4—41no—
189Q16—42no—
190Q16—41no—
191Q16—41no—
192Q16—442no—
193Q16—441no—
194Q16—441no—
195SD16—882no—
196D8—21no—
197D8—21no—
198C2×C8—221no—
199C2×C8—441no—
200C2×C8D4×D1111yescharacteristic
201C2×C8C2×C22⋊D1111yescharacteristic
202C4⋊C4—21no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—111no—
206C4⋊C4—221no—
207C4⋊C4—442no—
208C4⋊C4—441no—
209C4⋊C4—441no—
210C22⋊C4—41no—
211C22⋊C4—442no—
212C22⋊C4—442no—
213C42—221no—
214C42—442no—
215C42D4×D1111yescharacteristic
216C16—41no—
217C16—222no—
218C11#1233511yescharacteristic, complemented, Sylow
219C23—41no—
220Q8—81no—
221Q8—81no—
222Q8—221no—
223Q8—221no—
224Q8—442no—
225Q8—442no—
226D4—41no—
227D4—41no—
228C2×C4—41no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—221no—
233C2×C4—221no—
234C2×C4—442no—
235C2×C4D8×D1111yescharacteristic
236C2×C4#6696411yescharacteristic
237C2×C4#6699011yescharacteristic
238C8—21no—
239C8—441no—
240C8—881no—
241C8#6698511yescharacteristic
242C8#6700311yescharacteristic
243C22—81no—
244C22—81no—
245C22—81no—
246C22#1062276911yescharacteristic
247C4—21no—
248C4—81no—
249C4—161no—
250C4—441no—
251C4—441no—
252C4—882no—
253C4#1062252811yescharacteristic
254C4#1062252911yescharacteristic
255C4#1062265011yescharacteristic
256C4#1062281111yescharacteristic
257C2—161no—
258C2#1306768011yescharacteristic
259C2#1307055311yescharacteristic
260C2#1307059111yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2208C2
socleC22×C11#447
prime radicalC2×C11×D8D4
hypercenter#2208D11
hypocenterC11#12335
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
2. #13070868C2semidirect
3. #13067983C2semidirect
4. #13066666C2semidirect
5. #13066594C2semidirect
218. C11#12335semidirect

Maximal subgroups

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

subgroupindex
#130816022
#130708682
#130679832
#130666662
#130665942
#130665772
C11×#22082
#1233511