Finite Group Databasebeta

← #14664412

Subgroups — #14664412

Order 2816.

378 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C4×#66900C211yesmaximal, characteristic
2#13066960C211yesmaximal, characteristic
3#13066646C212yesmaximal
4#13066643C212yesmaximal
5C11×#2581C211yesmaximal, characteristic
6C2×C4×Q8×C11C411yescharacteristic
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#400C411yescharacteristic
9C11×#400C2211yescharacteristic
10C11×#395C411yescharacteristic
11C11×#395C2211yescharacteristic
12C11×#391—21no—
13C11×#389—21no—
14C11×#387—21no—
15C11×#387—21no—
16C11×#382C411yescharacteristic
17C2×#66900—21no—
18#10622539—21no—
19C4×#4318—21no—
20#10622168C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C22×Q8×C11D411yescharacteristic
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C4×Q8×C11—41no—
28C4×Q8×C11—41no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4C2311yescharacteristic
37C2×C42×C11—21no—
38C2×C42×C11C2×C411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×#4318—22no—
42C11×#95—21no—
43C11×#95—21no—
44C11×#95—21no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95C2×C411yescharacteristic
50C11×#95C2×C411yescharacteristic
51#66900—24no—
52C22⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—41no—
54#66867—41no—
55#66867—41no—
56C4×C11⋊C8—41no—
57#11792—111nomaximal, Sylow
58C2×Q8×C11—22no—
59C2×Q8×C11—22no—
60C2×Q8×C11—41no—
61C2×Q8×C11—42no—
62C2×Q8×C11—41no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—42no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—42no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—42no—
90#4318—24no—
91#4318—42no—
92C2×C11⋊C8—42no—
93C2×C11⋊C8—42no—
94#2581D1111yescharacteristic
95C4×#101—111no—
96#1467—111no—
97#1354—112no—
98#1353—112no—
99C23×C11C2×C22⋊C411yescharacteristic
100Q8×C11—44no—
101Q8×C11—42no—
102Q8×C11—42no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11#9911yescharacteristic
129C2×C4×C11#9911yescharacteristic
130C2×C4×C11#10412yes—
131C2×C4×C11#13712yes—
132C11⋊C8—44no—
133C11⋊C8—82no—
134C2×C4×Q8Dic1111yescharacteristic
135C2×C4×Q8C2×D1111yescharacteristic
136#432—221no—
137C2×#101—221no—
138C4×M16—221no—
139#400Dic1111yescharacteristic
140#400C2×D1111yescharacteristic
141#395Dic1111yescharacteristic
142#395C2×D1111yescharacteristic
143#391—21no—
144#389—21no—
145#387—21no—
146#387—21no—
147#382Dic1111yescharacteristic
148#343—112no—
149#324—112no—
150#324—221no—
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—42no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—81no—
166C4×C11—81no—
167C4×C11—81no—
168C22×Q8C2×Dic1111yescharacteristic
169C22×Q8C22⋊D1111yescharacteristic
170C2×M16—222no—
171C4×Q8—41no—
172C4×Q8—41no—
173C4×Q8—41no—
174C4×Q8—41no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4C2×Dic1111yescharacteristic
180C2×C4⋊C4C2×Dic1111yescharacteristic
181C2×C4⋊C4C22⋊D1111yescharacteristic
182C2×C4⋊C4C22×D1111yescharacteristic
183C2×C42—21no—
184C2×C42C2×Dic1111yescharacteristic
185C2×C42C22⋊D1111yescharacteristic
186C2×C42C22⋊D1111yescharacteristic
187C4⋊C8—441no—
188#101—224no—
189C22⋊C8—222no—
190#97—441no—
191#97—441no—
192C4×C8—441no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95C2×Dic1111yescharacteristic
201#95C2×Dic1111yescharacteristic
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—42no—
211C2×Q8—41no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4C22⋊Dic1111yescharacteristic
217C22×C4C22⋊Dic1111yescharacteristic
218C22×C4C22⋊Dic1111yescharacteristic
219C22×C4C22⋊Dic1111yescharacteristic
220C22×C4C22×Dic1111yescharacteristic
221C22×C4C2×C22⋊D1111yescharacteristic
222C22×C4C2×C22⋊D1111yescharacteristic
223M16—224no—
224M16—442no—
225C2×C8—442no—
226C2×C8—442no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—42no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—42no—
243C11#1179211yescharacteristic, complemented, Sylow
244C23C2×C22⋊Dic1111yescharacteristic
245Q8—44no—
246Q8—42no—
247Q8—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4#6689811yescharacteristic
274C2×C4#6689811yescharacteristic
275C2×C4#6690112yes—
276C2×C4#6699512yes—
277C8—444no—
278C8—882no—
279C22—21no—
280C22—21no—
281C22C2×#6689811yescharacteristic
282C22#1062283811yescharacteristic
283C22C2×#6690111yescharacteristic
284C4—22no—
285C4—22no—
286C4—21no—
287C4—21no—
288C4—41no—
289C4—41no—
290C4—42no—
291C4—41no—
292C4—41no—
293C4—81no—
294C4—81no—
295C4—81no—
296C2—21no—
297C2—21no—
298C2#1306713611yescharacteristic
299C2#1307025711yescharacteristic
300C2#1307030511yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2581C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2581D11
hypocenterC11#11792
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2581

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
C4×#669002
#130669602
#130666462
#130666432
C11×#25812
#1179211