Finite Group Databasebeta

← #14663249

Subgroups — #14663249

Order 2816.

460 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 99 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#13066954C212yesmaximal
2#13066560C212yesmaximal, complemented
3#13066550C212yesmaximal, complemented
4C4×C11×#124C211yesmaximal, characteristic
5C2×C11×#124C411yescharacteristic
6C2×C4×Q8×C11C411yescharacteristic
7C2×C4×D4×C11C2211yescharacteristic
8C11×#391C2211yescharacteristic
9C11×#390C411yescharacteristic
10C11×#388—22no—
11C11×#382C2211yescharacteristic
12C4×C11×C22⋊C4—22no—
13C43×C11C411yescharacteristic
14#10622820—22no—
15#10622166C2214yes—
16#10622163—22no—
17C22×Q8×C11C2×C411yescharacteristic
18C22×D4×C11C2×C411yescharacteristic
19C23×C4×C11D412yes—
20C11×#124—22no—
21C11×#124—22no—
22C4×Q8×C11—41no—
23C4×Q8×C11—41no—
24C4×D4×C11—41no—
25C4×D4×C11—41no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4C2311yescharacteristic
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4D412yes—
32C2×C42×C11—21no—
33C2×C42×C11—21no—
34C2×C42×C11—21no—
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11C2×C411yescharacteristic
38C2×#4318—42no—
39C11×#95—22no—
40C11×#95—22no—
41C22⋊(C11⋊C8)—24no—
42C22⋊(C11⋊C8)—42no—
43#11531—111nomaximal, Sylow
44C24×C11C22⋊C412yes—
45C2×Q8×C11—21no—
46C2×Q8×C11—41no—
47C2×Q8×C11—41no—
48C2×Q8×C11M1612yescomplemented
49C2×D4×C11—21no—
50C2×D4×C11—21no—
51C2×D4×C11—41no—
52C2×D4×C11—41no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—21no—
59C22×C4×C11—44no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D412yes—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—41no—
67C11×C22⋊C4—28no—
68C11×C22⋊C4—42no—
69C11×C22⋊C4—44no—
70C42×C11—21no—
71C42×C11—21no—
72C42×C11—21no—
73C42×C11—42no—
74C42×C11—42no—
75C42×C11—41no—
76C42×C11—41no—
77C42×C11—41no—
78C42×C11M1612yescomplemented
79#4318—84no—
80C2×C11⋊C8—44no—
81C4×#124D1111yescharacteristic
82#1465—112no—
83#1324—112no—
84#1319—112no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—22no—
88C23×C11—42no—
89C23×C11—42no—
90C23×C11C2×C22⋊C411yescharacteristic
91Q8×C11—42no—
92Q8×C11—42no—
93D4×C11—42no—
94D4×C11—42no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—44no—
110C2×C4×C11—41no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—41no—
114C2×C4×C11—82no—
115C2×C4×C11#9911yescharacteristic
116C2×C4×C11#9911yescharacteristic
117C2×C4×C11C2×M1611yescharacteristic
118C2×C4×C11C2×M1611yescharacteristic
119C11⋊C8—84no—
120C2×#124Dic1111yescharacteristic
121C2×C4×Q8Dic1111yescharacteristic
122C2×C4×D4C2×D1111yescharacteristic
123#407—222no—
124#391C2×D1111yescharacteristic
125#390Dic1111yescharacteristic
126#388—22no—
127#382C2×D1111yescharacteristic
128C4×C22⋊C4—22no—
129C43Dic1111yescharacteristic
130#324—114no—
131#323—222no—
132C22×C11—21no—
133C22×C11—21no—
134C22×C11—44no—
135C22×C11—42no—
136C22×C11—42no—
137C22×C11—42no—
138C22×C11—82no—
139C22×C11#40711yescharacteristic
140C22×C11C2×#9911yescharacteristic
141C22×C11#41311yescharacteristic
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—21no—
145C4×C11—42no—
146C4×C11—42no—
147C4×C11—42no—
148C4×C11—41no—
149C4×C11—42no—
150C4×C11—81no—
151C4×C11#35412yes—
152C22×Q8C2×Dic1111yescharacteristic
153C22×D4C2×Dic1111yescharacteristic
154C23×C4C22⋊D1112yes—
155C2×M16—442no—
156#124—22no—
157#124—22no—
158C4×Q8—41no—
159C4×Q8—41no—
160C4×D4—41no—
161C4×D4—41no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4C2×Dic1111yescharacteristic
164C2×C4⋊C4C22×D1111yescharacteristic
165C2×C22⋊C4—22no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4C22⋊D1112yes—
168C2×C42—21no—
169C2×C42—21no—
170C2×C42—21no—
171C2×C42C2×Dic1111yescharacteristic
172C2×C42C2×Dic1111yescharacteristic
173C2×C42C2×Dic1111yescharacteristic
174C22⋊C8—224no—
175C22⋊C8—442no—
176#95—22no—
177#95—22no—
178C2×C11—21no—
179C2×C11—21no—
180C2×C11—82no—
181C2×C11#146511yescharacteristic
182C2×C11C2×#35411yescharacteristic
183C2×C11#213211yescharacteristic
184C24C22⋊Dic1112yes—
185C2×Q8—21no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8#431812yescomplemented
189C2×D4—21no—
190C2×D4—21no—
191C2×D4—41no—
192C2×D4—41no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—21no—
199C22×C4—44no—
200C22×C4C22⋊Dic1111yescharacteristic
201C22×C4C22⋊Dic1111yescharacteristic
202C22×C4C22×Dic1111yescharacteristic
203C22×C4C2×C22⋊D1112yes—
204M16—884no—
205C2×C8—444no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—42no—
209C22⋊C4—28no—
210C22⋊C4—42no—
211C22⋊C4—44no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—41no—
216C42—42no—
217C42—42no—
218C42—41no—
219C42—41no—
220C42#431812yescomplemented
221C11#1153111yescharacteristic, complemented, Sylow
222C23—22no—
223C23—22no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23C2×C22⋊Dic1111yescharacteristic
228Q8—42no—
229Q8—42no—
230D4—42no—
231D4—42no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—44no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—82no—
252C2×C4#6689811yescharacteristic
253C2×C4#6689811yescharacteristic
254C2×C4C2×#431811yescharacteristic
255C2×C4C2×#431811yescharacteristic
256C8—884no—
257C22—21no—
258C22—21no—
259C22—44no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—82no—
264C22#1062282011yescharacteristic
265C22C2×#6689811yescharacteristic
266C22#1062285011yescharacteristic
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—42no—
272C4—42no—
273C4—42no—
274C4—41no—
275C4—81no—
276C4#1062217912yes—
277C2—21no—
278C2—21no—
279C2—82no—
280C2#1306695411yescharacteristic
281C2C2×#1062217911yescharacteristic
282C2#1307030111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC4×C11×#124C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenterC4×#124D11
hypocenterC11#11531
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
2. #13066560C2semidirect
3. #13066550C2semidirect
48. C2×Q8×C11M16semidirect
78. C42×C11M16semidirect
188. C2×Q8#4318semidirect
220. C42#4318semidirect
221. C11#11531semidirect

Maximal subgroups

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

subgroupindex
#130669542
#130665602
#130665502
C4×C11×#1242
#1153111