Finite Group Databasebeta

← #14663258

Subgroups — #14663258

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#13071326C211yesmaximal, characteristic
2#13066958C212yesmaximal, complemented
3#13066561C212yesmaximal, complemented
4#13066548C211yesmaximal, characteristic
5C11×#1318C211yesmaximal, characteristic
6C2×#66989C411yescharacteristic
7C2×D4×Dic11C411yescharacteristic
8C2×#66940C2211yescharacteristic
9C11×#390C2211yescharacteristic
10#10622589C2211yescharacteristic
11#10622559—22no—
12#10622558—22no—
13#10622545C411yescharacteristic
14#10622542C411yescharacteristic
15#10622332—22no—
16C11×#324C2212yes—
17#10622166C2212yes—
18#10622107—22no—
19C22×D4×C11C2×C411yescharacteristic
20C23×Dic11—21no—
21C22×Dic22C2×C411yescharacteristic
22C2×C11×C4⋊C4C2311yescharacteristic
23C2×C11×C22⋊C4—22no—
24C2×C42×C11C2×C411yescharacteristic
25C2×C22⋊Dic11—22no—
26C2×C22⋊Dic11—21no—
27#66989—22no—
28#66989—22no—
29D4×Dic11—42no—
30C2×C4⋊Dic11C2×C411yescharacteristic
31C2×Dic11⋊C4—22no—
32C2×Dic11⋊C4D412yes—
33C2×C4×Dic11C2×C411yescharacteristic
34C2×C4×Dic11C2×C411yescharacteristic
35C2×C4×Dic11D412yes—
36#66940—42no—
37C11×C22⋊C8—22no—
38C11⋊#95—22no—
39C11⋊#95—21no—
40C11⋊#95—21no—
41C22⋊(C11⋊C8)—22no—
42#66879—42no—
43Dic11⋊C8—42no—
44#11534—111nomaximal, Sylow
45C24×C11—21no—
46C2×D4×C11—21no—
47C2×D4×C11—41no—
48C2×D4×C11—41no—
49C2×D4×C11M1612yes—
50C22×C4×C11—21no—
51C22×C4×C11C22×C411yescharacteristic
52C22×C4×C11C2×D412yes—
53C22×Dic11—21no—
54C22×Dic11—21no—
55C22×Dic11—42no—
56C22×Dic11—82no—
57C22×Dic11C22⋊C412yes—
58C22×Dic11C22⋊C411yescharacteristic
59C22×Dic11C22⋊C411yescharacteristic
60C2×Dic22—21no—
61C2×Dic22—21no—
62C2×Dic22—41no—
63C2×Dic22—41no—
64C2×C8×C11—42no—
65C11×C4⋊C4—41no—
66C11×C22⋊C4—82no—
67C42×C11—41no—
68C22⋊Dic11—28no—
69C22⋊Dic11—42no—
70C4⋊Dic11—41no—
71Dic11⋊C4—42no—
72Dic11⋊C4—82no—
73C4×Dic11—22no—
74C4×Dic11—22no—
75C4×Dic11—22no—
76C4×Dic11—21no—
77C4×Dic11M1612yes—
78C2×C11⋊C8—42no—
79#2326—111no—
80#1467—112no—
81#1325—112no—
82#1318—111no—
83#1318D1111yescharacteristic
84C23×C11—22no—
85C23×C11—42no—
86C23×C11—42no—
87C23×C11—41no—
88C23×C11—41no—
89C23×C11C2×C22⋊C411yescharacteristic
90D4×C11—42no—
91D4×C11—42no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—22no—
95C2×C4×C11—42no—
96C2×C4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11—41no—
99C2×C4×C11C2×M1611yescharacteristic
100C2×C4×C11C2×M1611yescharacteristic
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—21no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—41no—
107C2×Dic11—41no—
108C2×Dic11—41no—
109C2×Dic11—41no—
110C2×Dic11—42no—
111C2×Dic11—41no—
112C2×Dic11—84no—
113C2×Dic11#9912yes—
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#390C2×D1111yescharacteristic
124#388—222no—
125#385—222no—
126#384—111no—
127#376—111no—
128#324—112no—
129#324—222no—
130#324C2×D1112yes—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11—44no—
134C22×C11—42no—
135C22×C11—82no—
136C22×C11—81no—
137C22×C11—81no—
138C22×C11#40711yescharacteristic
139C22×C11C2×#9911yescharacteristic
140C22×C11#41311yescharacteristic
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—42no—
144C4×C11—81no—
145Dic11—22no—
146Dic11—42no—
147Dic11—41no—
148Dic11—42no—
149Dic11—81no—
150C22×Q8—111no—
151C22×D4C4×D1111yescharacteristic
152C23×C4—221no—
153#124—222no—
154#124—222no—
155C4×Q8—442no—
156C4×D4—442no—
157C2×C4⋊C4—112no—
158C2×C4⋊C4—111no—
159C2×C4⋊C4—222no—
160C2×C4⋊C4C22×D1111yescharacteristic
161C2×C22⋊C4—22no—
162C2×C22⋊C4—222no—
163C2×C22⋊C4—221no—
164C2×C42—111no—
165C2×C42—111no—
166C2×C42—112no—
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—82no—
178C2×C11#146511yescharacteristic
179C2×C11#212811yescharacteristic
180C2×C11#213311yescharacteristic
181C24—21no—
182C2×Q8—221no—
183C2×Q8—221no—
184C2×Q8—441no—
185C2×Q8—441no—
186C2×D4—21no—
187C2×D4—41no—
188C2×D4—41no—
189C2×D4#431312yes—
190C22×C4—21no—
191C22×C4—111no—
192C22×C4—112no—
193C22×C4—111no—
194C22×C4—221no—
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—442no—
204C4⋊C4—441no—
205C4⋊C4—882no—
206C22⋊C4—82no—
207C22⋊C4—228no—
208C22⋊C4—442no—
209C42—41no—
210C42—112no—
211C42—222no—
212C42—222no—
213C42—222no—
214C42—221no—
215C11#1153411yescharacteristic, complemented, Sylow
216C23—22no—
217C23—42no—
218C23—42no—
219C23—41no—
220C23—41no—
221C23C22⋊C4×D1111yescharacteristic
222Q8—442no—
223Q8—442no—
224D4—42no—
225D4—42no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—112no—
234C2×C4—222no—
235C2×C4—222no—
236C2×C4—221no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4—441no—
240C2×C4—441no—
241C2×C4—441no—
242C2×C4—441no—
243C2×C4—442no—
244C2×C4—441no—
245C2×C4—884no—
246C2×C4C2×#431311yescharacteristic
247C2×C4M16×D1111yescharacteristic
248C8—82no—
249C8—882no—
250C22—21no—
251C22—21no—
252C22—44no—
253C22—42no—
254C22—82no—
255C22—81no—
256C22—81no—
257C22#1062233911yescharacteristic
258C22D11×#9911yescharacteristic
259C22#1062235811yescharacteristic
260C4—21no—
261C4—21no—
262C4—42no—
263C4—81no—
264C4—222no—
265C4—442no—
266C4—442no—
267C4—441no—
268C4—881no—
269C2—21no—
270C2—21no—
271C2—82no—
272C2#1306695111yescharacteristic
273C2#1307028611yescharacteristic
274C2#1307030211yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1318C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1318D11
hypocenterC11#11534
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #13066958C2semidirect
3. #13066561C2semidirect
215. C11#11534semidirect

Maximal subgroups

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

subgroupindex
#130713262
#130669582
#130665612
#130665482
C11×#13182
#1153411