Finite Group Databasebeta

← #14651500

Subgroups — #14651500

Order 2816.

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

normal subgroups only

This group has 528 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#13073090C211yesmaximal, characteristic
2#13071219C211yesmaximal, characteristic
3#13067150C212yesmaximal
4#13066470C212yesmaximal
5C11×#1821C211yesmaximal, characteristic
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66977C2211yescharacteristic
8C11×#407C2212yes—
9#10622825—21no—
10#10622824C2212yes—
11#10622823—21no—
12#10622823—21no—
13C4×C22⋊Dic11—21no—
14C4×C22⋊Dic11C2211yescharacteristic
15#10622594—24no—
16#10622593—22no—
17#10622589C412yescomplemented
18#10622587C412yescomplemented
19C11×#343—22no—
20#10622105—24no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C2×C11×M16—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4C2×C412yes—
29C2×C11×C4⋊C4D412yes—
30C2×C22⋊Dic11—21no—
31C2×C22⋊Dic11—21no—
32C2×C22⋊Dic11—22no—
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11C2×C411yescharacteristic
35#66977—22no—
36#66977—22no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—22no—
39C2×Dic11⋊C4—22no—
40C2×C4×Dic11—22no—
41C2×C4×Dic11C2×C412yes—
42C11×C22⋊C8—22no—
43C11×C22⋊C8—22no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95—21no—
49C11⋊#95—22no—
50C11⋊#95D414yes—
51#9461—111nomaximal, Sylow
52C24×C11C2×D411yescharacteristic
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—42no—
58C22×C4×C11—81no—
59C22×C4×C11—81no—
60C22×C4×C11C22⋊C412yes—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D412yes—
65C22×C4×C11#4112yes—
66C22×Dic11—22no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—24no—
70C2×Dic22—22no—
71C2×Dic22—42no—
72C11×M16—44no—
73C2×C8×C11—42no—
74C11×C4⋊C4—24no—
75C11×C4⋊C4—24no—
76C22⋊Dic11—24no—
77C22⋊Dic11—44no—
78C22⋊Dic11—41no—
79C22⋊Dic11—41no—
80C4⋊Dic11—22no—
81C4⋊Dic11—82no—
82Dic11⋊C4—42no—
83Dic11⋊C4—82no—
84Dic11⋊C4—82no—
85C4×Dic11—42no—
86C4×Dic11—82no—
87#2502—111no—
88#2313—111no—
89#1821D1111yescharacteristic
90#1511—112no—
91#1284—112no—
92C23×C11—22no—
93C23×C11—22no—
94C23×C11—41no—
95C23×C11C2×C22⋊C411yescharacteristic
96C23×C11#12011yescharacteristic
97C23×C11#12311yescharacteristic
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—81no—
109C2×C4×C11—81no—
110C2×C4×C11C4×D412yes—
111C2×C4×C11#12112yes—
112C2×Dic11—24no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—44no—
116C2×Dic11—42no—
117C2×Dic11—44no—
118C2×Dic11—41no—
119C2×Dic11—41no—
120C2×Dic11—42no—
121C2×Dic11—44no—
122Dic22—82no—
123C8×C11—82no—
124C2×C22⋊Q8—111no—
125C22×C4⋊C4C2×D1111yescharacteristic
126#407C2×D1112yes—
127#398—222no—
128#391—112no—
129#387—224no—
130#385—221no—
131#385—221no—
132#384—112no—
133#381—112no—
134#380—221no—
135C4×C22⋊C4—111no—
136C4×C22⋊C4—221no—
137#343—22no—
138#328—224no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—44no—
147C22×C11#38611yescharacteristic
148C22×C11#41012yes—
149C22×C11#45612yes—
150C4×C11—22no—
151C4×C11—22no—
152C4×C11—42no—
153C4×C11—42no—
154Dic11—44no—
155Dic11—84no—
156Dic11—81no—
157Dic11—81no—
158C22×Q8—111no—
159C23×C4D4411yescharacteristic
160C23×C4D4411yescharacteristic
161C23×C4C22×D1111yescharacteristic
162C2×M16—22no—
163C22⋊Q8—222no—
164C22⋊Q8—222no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—221no—
169C2×C4⋊C4—222no—
170C2×C4⋊C4—222no—
171C2×C4⋊C4—222no—
172C2×C4⋊C4C4×D1112yes—
173C2×C4⋊C4C22⋊D1112yes—
174C2×C22⋊C4—221no—
175C2×C22⋊C4—221no—
176C2×C22⋊C4—222no—
177C2×C42—112no—
178C2×C42—222no—
179C22⋊C8—22no—
180C22⋊C8—22no—
181#95—114no—
182#95—222no—
183#95—222no—
184#95—222no—
185#95—222no—
186#95—222no—
187#95—221no—
188C2×C11—22no—
189C2×C11—22no—
190C2×C11—41no—
191C2×C11#188611yescharacteristic
192C2×C11#189911yescharacteristic
193C2×C11#191111yescharacteristic
194C24C2×D4411yescharacteristic
195C2×Q8—222no—
196C2×Q8—442no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—42no—
202C22×C4—81no—
203C22×C4—81no—
204C22×C4—222no—
205C22×C4—224no—
206C22×C4—221no—
207C22×C4—221no—
208C22×C4(C2×D11)⋊C412yes—
209C22×C4(C2×D11)⋊C412yes—
210C22×C4C2×C4×D1111yescharacteristic
211C22×C4D4×D1112yes—
212C22×C4#434112yes—
213C22×C4C2×C22⋊D1111yescharacteristic
214M16—44no—
215C2×C8—42no—
216C4⋊C4—24no—
217C4⋊C4—24no—
218C4⋊C4—222no—
219C4⋊C4—442no—
220C4⋊C4—882no—
221C4⋊C4—882no—
222C4⋊C4—882no—
223C22⋊C4—224no—
224C22⋊C4—444no—
225C22⋊C4—441no—
226C22⋊C4—441no—
227C42—442no—
228C42—882no—
229C11#946111yescharacteristic, complemented, Sylow
230C23—22no—
231C23—22no—
232C23—41no—
233C23#6693511yescharacteristic
234C23#6693911yescharacteristic
235C23C2×(C2×D11)⋊C411yescharacteristic
236Q8—882no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—224no—
250C2×C4—442no—
251C2×C4—442no—
252C2×C4—444no—
253C2×C4—444no—
254C2×C4—442no—
255C2×C4—441no—
256C2×C4—441no—
257C2×C4—442no—
258C2×C4—444no—
259C2×C4(C22⋊D11)⋊C412yes—
260C2×C4#6699212yes—
261C8—82no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—44no—
270C22#1062236512yes—
271C22#1062257111yescharacteristic
272C22#1062261912yes—
273C4—22no—
274C4—22no—
275C4—42no—
276C4—42no—
277C4—444no—
278C4—884no—
279C4—881no—
280C4—881no—
281C2—22no—
282C2—22no—
283C2—41no—
284C2#1306900711yescharacteristic
285C2#1306907211yescharacteristic
286C2#1306914611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1821C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1821D11
hypocenterC11#9461
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
17. #10622589C4semidirect
18. #10622587C4semidirect
229. C11#9461semidirect

Maximal subgroups

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

subgroupindex
#130730902
#130712192
#130671502
#130664702
C11×#18212
#946111