Finite Group Databasebeta

← #14664413

Subgroups — #14664413

Order 2816.

378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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#13073978C211yesmaximal, characteristic
2C4×#66900C211yesmaximal, characteristic
3#13066647C212yesmaximal
4#13066644C212yesmaximal
5C11×#1467C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×C4×Dic22C411yescharacteristic
8C11×#432—21no—
9#10622843—21no—
10C2×#66900—21no—
11#10622599C411yescharacteristic
12#10622599C2211yescharacteristic
13#10622592C411yescharacteristic
14#10622592C2211yescharacteristic
15#10622586—21no—
16#10622549C411yescharacteristic
17#10622546—21no—
18#10622546—21no—
19C4×#4318—21no—
20C11×#324—21no—
21C11×#324C2212yes—
22#10622168C2212yes—
23C22×Q8×C11D411yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×C4×Dic11—21no—
39C2×#4318—22no—
40C4×Dic22—41no—
41C4×Dic22—41no—
42C11×C4⋊C8—41no—
43C11×C22⋊C8—22no—
44C11×#97—41no—
45#66900—24no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55#66867—41no—
56C4×C11⋊C8—41no—
57#11792—111nomaximal, Sylow
58C2×Q8×C11—22no—
59C2×Q8×C11—22no—
60C2×Q8×C11—41no—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C2×Dic22—41no—
73C2×Dic22—42no—
74C2×C8×C11—42no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C4⋊Dic11—41no—
85C4⋊Dic11—42no—
86Dic11⋊C4—42no—
87Dic11⋊C4—42no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90C4×Dic11—42no—
91#4318—24no—
92#4318—42no—
93C2×C11⋊C8—42no—
94#2581—111no—
95C4×#101—111no—
96#1467D1111yescharacteristic
97#1354—112no—
98#1353—112no—
99C23×C11C2×C22⋊C411yescharacteristic
100Q8×C11—44no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11#9911yescharacteristic
116C2×C4×C11#9911yescharacteristic
117C2×C4×C11#10412yes—
118C2×C4×C11#13712yes—
119C2×Dic11—22no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122C2×Dic11—41no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—42no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130Dic22—42no—
131Dic22—42no—
132C8×C11—82no—
133C11⋊C8—44no—
134C2×C4×Q8—111no—
135C2×C4×Q8C2×D1111yescharacteristic
136#432—21no—
137C2×#101—221no—
138C4×M16—221no—
139#400—111no—
140#400—111no—
141#395—111no—
142#395—111no—
143#391—221no—
144#389—221no—
145#387—221no—
146#387—221no—
147#382—111no—
148#343—112no—
149#324—21no—
150#324C2×D1112yes—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11C2×#9911yescharacteristic
154C22×C11#41911yescharacteristic
155C22×C11C2×#10411yescharacteristic
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—22no—
159C4×C11—22no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164Dic11—42no—
165Dic11—81no—
166Dic11—81no—
167Dic11—81no—
168C22×Q8—111no—
169C22×Q8D4411yescharacteristic
170C2×M16—222no—
171C4×Q8—41no—
172C4×Q8—41no—
173C4×Q8—441no—
174C4×Q8—441no—
175C2×C4⋊C4—111no—
176C2×C4⋊C4—221no—
177C2×C4⋊C4—221no—
178C2×C4⋊C4—221no—
179C2×C4⋊C4—221no—
180C2×C4⋊C4C4×D1111yescharacteristic
181C2×C4⋊C4C22⋊D1111yescharacteristic
182C2×C4⋊C4C22×D1111yescharacteristic
183C2×C42—221no—
184C2×C42C4×D1111yescharacteristic
185C2×C42D4411yescharacteristic
186C2×C42C22⋊D1111yescharacteristic
187C4⋊C8—41no—
188#101—224no—
189C22⋊C8—22no—
190#97—41no—
191#97—441no—
192C4×C8—441no—
193#95—111no—
194#95—111no—
195#95—221no—
196#95—221no—
197#95—221no—
198#95—221no—
199#95—221no—
200#95—221no—
201#95—221no—
202C2×C11—21no—
203C2×C11—21no—
204C2×C11#150811yescharacteristic
205C2×C11#212011yescharacteristic
206C2×C11#213311yescharacteristic
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8—41no—
210C2×Q8—441no—
211C2×Q8—442no—
212C22×C4—221no—
213C22×C4—221no—
214C22×C4—221no—
215C22×C4—221no—
216C22×C4(C2×D11)⋊C411yescharacteristic
217C22×C4(C2×D11)⋊C411yescharacteristic
218C22×C4(C2×D11)⋊C411yescharacteristic
219C22×C4(C2×D11)⋊C411yescharacteristic
220C22×C4C2×C4×D1111yescharacteristic
221C22×C4C2×D4411yescharacteristic
222C22×C4C2×C22⋊D1111yescharacteristic
223M16—224no—
224M16—442no—
225C2×C8—42no—
226C2×C8—442no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—441no—
231C4⋊C4—442no—
232C4⋊C4—442no—
233C4⋊C4—441no—
234C4⋊C4—441no—
235C4⋊C4—442no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—442no—
243C11#1179211yescharacteristic, complemented, Sylow
244C23C2×(C2×D11)⋊C411yescharacteristic
245Q8—44no—
246Q8—442no—
247Q8—442no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—222no—
263C2×C4—441no—
264C2×C4—441no—
265C2×C4—441no—
266C2×C4—441no—
267C2×C4—441no—
268C2×C4—441no—
269C2×C4—442no—
270C2×C4—441no—
271C2×C4—441no—
272C2×C4—441no—
273C2×C4#6687011yescharacteristic
274C2×C4#6687011yescharacteristic
275C2×C4#6688912yes—
276C2×C4#6696212yes—
277C8—82no—
278C8—444no—
279C22—21no—
280C22—21no—
281C22C2×#6687011yescharacteristic
282C22#1062273311yescharacteristic
283C22C2×#6688911yescharacteristic
284C4—22no—
285C4—22no—
286C4—21no—
287C4—21no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—442no—
293C4—881no—
294C4—881no—
295C4—881no—
296C2—21no—
297C2—21no—
298C2#1306713711yescharacteristic
299C2#1307025511yescharacteristic
300C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1467C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1467D11
hypocenterC11#11792
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
243. C11#11792semidirect

Maximal subgroups

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

subgroupindex
#130739782
C4×#669002
#130666472
#130666442
C11×#14672
#1179211