Finite Group Databasebeta

← #14663260

Subgroups — #14663260

Order 2816.

424 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 75 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#13071324C211yesmaximal, characteristic
2#13066958C212yesmaximal, complemented
3#13066562C211yesmaximal, characteristic, complemented
4#13066547C212yesmaximal
5C11×#1325C211yesmaximal, characteristic, complemented
6C2×#66946C411yescharacteristic
7C2×#66940C2211yescharacteristic
8C2×#66928C411yescharacteristic
9C11×#384C2211yescharacteristic
10#10622603—22no—
11#10622602—22no—
12#10622601C2211yescharacteristic
13#10622587C411yescharacteristic
14#10622545C411yescharacteristic
15#10622332—22no—
16C11×#324C2212yes—
17#10622166C2212yes—
18#10622107—22no—
19C22×D44C2×C411yescharacteristic
20C22×C4×D11—21no—
21C22×Dic22C2×C411yescharacteristic
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4C2×C411yescharacteristic
24C2×C11×C4⋊C4C2311yescharacteristic
25C2×C42×C11C2×C411yescharacteristic
26C2×(C2×D11)⋊C4—22no—
27C2×(C2×D11)⋊C4—21no—
28C2×(C2×D11)⋊C4—22no—
29C2×Dic11⋊C4D412yes—
30C2×C4×Dic11C2×C411yescharacteristic
31C2×C4×Dic11C2×C411yescharacteristic
32C2×C4×Dic11D412yes—
33#66946—42no—
34#66940—42no—
35#66928—22no—
36#66928—22no—
37C11×C22⋊C8—22no—
38C11⋊#95—21no—
39C11⋊#95—21no—
40C11⋊#95—22no—
41C22⋊(C11⋊C8)—22no—
42#66879—42no—
43Dic11⋊C8—42no—
44#11534—111nomaximal, Sylow
45C23×D11—21no—
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11C22×C411yescharacteristic
49C22×C4×C11C2×D412yes—
50C22×Dic11—21no—
51C22×Dic11C22⋊C412yes—
52C22×Dic11C22⋊C411yescharacteristic
53C22×Dic11C22⋊C411yescharacteristic
54C2×D44—21no—
55C2×D44—41no—
56C2×D44—41no—
57C2×D44M1612yes—
58C2×C4×D11—42no—
59C2×C4×D11—82no—
60C2×Dic22—21no—
61C2×Dic22—21no—
62C2×Dic22—41no—
63C2×Dic22—41no—
64C2×C8×C11—42no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—82no—
68C42×C11—21no—
69C42×C11M1612yes—
70(C2×D11)⋊C4—28no—
71(C2×D11)⋊C4—42no—
72(C2×D11)⋊C4—82no—
73Dic11⋊C4—42no—
74C4×Dic11—22no—
75C4×Dic11—22no—
76C4×Dic11—22no—
77C4×Dic11—41no—
78C2×C11⋊C8—42no—
79#2326—111no—
80#1467—112no—
81#1325—111no—
82#1325D1111yescharacteristic, complemented
83#1318—112no—
84C23×C11C2×C22⋊C411yescharacteristic
85C22×D11—22no—
86C22×D11—42no—
87C22×D11—42no—
88C22×D11—41no—
89C22×D11—41no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—41no—
99C2×C4×C11C2×M1611yescharacteristic
100C2×C4×C11C2×M1611yescharacteristic
101C2×Dic11—22no—
102C2×Dic11—21no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—41no—
106C2×Dic11—41no—
107C2×Dic11—41no—
108C2×Dic11—41no—
109C2×Dic11—41no—
110C2×Dic11#9912yes—
111D44—42no—
112D44—42no—
113C4×D11—84no—
114Dic22—42no—
115Dic22—42no—
116C8×C11—82no—
117C11⋊C8—82no—
118C2×#124—111no—
119C2×C4×Q8—111no—
120C2×C4×D4—111no—
121#432—222no—
122#391—111no—
123#390—111no—
124#388—222no—
125#385—222no—
126#384C2×D1111yescharacteristic
127#376—111no—
128#324—112no—
129#324—222no—
130#324C2×D1112yes—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11#40711yescharacteristic
134C22×C11C2×#9911yescharacteristic
135C22×C11#41311yescharacteristic
136C2×D11—44no—
137C2×D11—42no—
138C2×D11—82no—
139C2×D11—81no—
140C2×D11—81no—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—42no—
144C4×C11—42no—
145C4×C11—81no—
146Dic11—22no—
147Dic11—41no—
148Dic11—42no—
149Dic11—81no—
150C22×Q8—111no—
151C22×D4—111no—
152C23×C4—221no—
153#124—222no—
154#124—222no—
155C4×Q8—442no—
156C4×D4—442no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—112no—
159C2×C4⋊C4C4×D1111yescharacteristic
160C2×C4⋊C4C22×D1111yescharacteristic
161C2×C22⋊C4—222no—
162C2×C22⋊C4—221no—
163C2×C22⋊C4—222no—
164C2×C42—111no—
165C2×C42—112no—
166C2×C42—111no—
167C2×C42C4×D1111yescharacteristic
168C4⋊C8—442no—
169C22⋊C8—22no—
170C22⋊C8—222no—
171#97—442no—
172#95—221no—
173#95—221no—
174#95—222no—
175C2×C11—21no—
176C2×C11—21no—
177C2×C11#146511yescharacteristic
178C2×C11#212811yescharacteristic
179C2×C11#213311yescharacteristic
180D11—82no—
181C24—221no—
182C2×Q8—221no—
183C2×Q8—221no—
184C2×Q8—441no—
185C2×Q8—441no—
186C2×D4—112no—
187C2×D4—221no—
188C2×D4—441no—
189C2×D4—441no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—111no—
193C22×C4—112no—
194C22×C4—111no—
195C22×C4—221no—
196C22×C4—442no—
197C22×C4—882no—
198C22×C4C2×C4×D1111yescharacteristic
199C22×C4D4×D1112yes—
200C2×C8—42no—
201C2×C8—442no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—82no—
205C4⋊C4—442no—
206C22⋊C4—228no—
207C22⋊C4—442no—
208C22⋊C4—882no—
209C42—21no—
210C42—222no—
211C42—222no—
212C42—222no—
213C42—441no—
214C42#431312yes—
215C11#1153411yescharacteristic, complemented, Sylow
216C23—222no—
217C23—442no—
218C23—442no—
219C23—441no—
220C23—441no—
221C23C22⋊C4×D1111yescharacteristic
222Q8—442no—
223Q8—442no—
224D4—442no—
225D4—442no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—112no—
236C2×C4—222no—
237C2×C4—221no—
238C2×C4—222no—
239C2×C4—222no—
240C2×C4—441no—
241C2×C4—441no—
242C2×C4—441no—
243C2×C4—441no—
244C2×C4—441no—
245C2×C4—884no—
246C2×C4C2×#431311yescharacteristic
247C2×C4M16×D1111yescharacteristic
248C8—82no—
249C8—882no—
250C22—21no—
251C22—21no—
252C22—444no—
253C22—442no—
254C22—882no—
255C22—881no—
256C22—881no—
257C22#1062233911yescharacteristic
258C22D11×#9911yescharacteristic
259C22#1062236411yescharacteristic
260C4—21no—
261C4—21no—
262C4—42no—
263C4—42no—
264C4—81no—
265C4—222no—
266C4—442no—
267C4—441no—
268C4—881no—
269C2—21no—
270C2—21no—
271C2—882no—
272C2#1306695311yescharacteristic
273C2#1307028611yescharacteristic
274C2#1307030411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1325C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1325D11
hypocenterC11#11534
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
2. #13066958C2semidirect
3. #13066562C2semidirect
5. C11×#1325C2semidirect
82. #1325D11semidirect
215. C11#11534semidirect

Maximal subgroups

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

subgroupindex
#130713242
#130669582
#130665622
#130665472
C11×#13252
#1153411