Finite Group Databasebeta

← #14853448

Subgroups — #14853448

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077003C211yesmaximal, characteristic, complemented
2C4×#66927C211yesmaximal, characteristic
3#13070180C212yesmaximal, complemented
4#13069851C212yesmaximal
5#13069299C214yesmaximal, complemented
6#13068627C212yesmaximal, complemented
7#13068627C212yesmaximal, complemented
8C4×C11×C4⋊C8C211yesmaximal, characteristic, complemented
9C2×#66927C2211yescharacteristic
10C2×C4×D44—22no—
11C2×C4×D44C2212yes—
12C2×C11×C4⋊C8C2212yes—
13C2×C4×C8×C11C2212yes—
14C43×C11C2211yescharacteristic
15C2×#66885C2214yes—
16C2×#66885C2214yes—
17#10622552—22no—
18#10622552C2212yes—
19#10622549C2211yescharacteristic
20#10622549C2211yescharacteristic
21#10622548C2211yescharacteristic
22#10622546—22no—
23#10622546—22no—
24#10622541C2212yes—
25#10622541C2212yes—
26C11×#336C2212yes—
27#10622189C2214yes—
28#10622189C2214yes—
29C22×D44—22no—
30C22×D44C2312yes—
31C22×C4×D11—22no—
32C22×C8×C11C2314yes—
33C2×C42×C11D412yes—
34C2×C42×C11D412yes—
35C2×C42×C11C2311yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C2×(C2×D11)⋊C4—24no—
39C2×(C2×D11)⋊C4—22no—
40C2×C4⋊Dic11—22no—
41C2×C4⋊Dic11C2312yes—
42C2×C4⋊Dic11C2312yes—
43C2×C4⋊Dic11C2312yes—
44C2×Dic11⋊C4—22no—
45C2×Dic11⋊C4—22no—
46#66927—24no—
47C4×D44—24no—
48C4×D44—24no—
49C4×D44—48no—
50C11×C4⋊C8—24no—
51C4×C8×C11—42no—
52C11⋊#95—22no—
53C11⋊#95—22no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58#66885—28no—
59#66885—44no—
60#29124—111nomaximal, Sylow
61C23×D11—22no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D412yes—
65C22×C4×C11C2×D412yes—
66C22×C4×C11C2411yescharacteristic
67C22×Dic11—22no—
68C22×Dic11—22no—
69C22×Dic11—22no—
70C2×D44—28no—
71C2×D44—22no—
72C2×D44—22no—
73C2×D44—22no—
74C2×D44—22no—
75C2×D44—22no—
76C2×D44—44no—
77C2×D44—44no—
78C2×D44#4114yes—
79C2×C4×D11—48no—
80C2×C4×D11—44no—
81C2×C8×C11—24no—
82C2×C8×C11—24no—
83C2×C8×C11—24no—
84C42×C11—24no—
85C42×C11—24no—
86C42×C11—22no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11#4114yes—
90(C2×D11)⋊C4—44no—
91(C2×D11)⋊C4—48no—
92C4⋊Dic11—24no—
93C4⋊Dic11—22no—
94C4⋊Dic11—22no—
95C4⋊Dic11—22no—
96C4⋊Dic11—22no—
97C4⋊Dic11—44no—
98Dic11⋊C4—44no—
99Dic11⋊C4—44no—
100#2864—111no—
101C4×#127—111no—
102#2100—112no—
103#2041—112no—
104#1934—114no—
105#1804—112no—
106#1804—112no—
107C4×C4⋊C8D1111yescharacteristic, complemented
108C23×C11C22×D411yescharacteristic
109C22×D11—24no—
110C22×D11—42no—
111C22×D11—42no—
112C22×D11—44no—
113C22×D11—44no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11#12412yes—
121C2×C4×C11#12412yes—
122C2×C4×C11#13514yes—
123C2×C4×C11AGL(1,ℤ/8)14yes—
124C2×C4×C11C2×#4112yes—
125C2×C4×C11C2×#4112yes—
126C2×C4×C11H(5,𝔽2)11yescharacteristic
127C2×C4×C112−1+411yescharacteristic
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—44no—
136D44—24no—
137D44—24no—
138D44—416no—
139D44—42no—
140D44—42no—
141C4×D11—88no—
142C8×C11—44no—
143C2×#127—111no—
144C2×C4×D4—112no—
145C2×C4×D4—222no—
146C2×C4⋊C8C2×D1112yes—
147C2×#102—114no—
148C2×#102—114no—
149C2×C4×C8C2×D1112yes—
150#390—112no—
151#390—222no—
152#389—112no—
153#389—112no—
154#387—222no—
155#387—222no—
156#384—111no—
157#382—111no—
158#382—111no—
159C43C2×D1111yescharacteristic
160#340—114no—
161#340—114no—
162#336C2×D1112yes—
163C22×C11#52511yescharacteristic
164C22×C11C2×#12411yescharacteristic
165C22×C11#53711yescharacteristic
166C22×C11C2×#13512yes—
167C22×C11C2×AGL(1,ℤ/8)12yes—
168C2×D11—44no—
169C2×D11—48no—
170C2×D11—82no—
171C2×D11—82no—
172C2×D11—84no—
173C4×C11—24no—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—24no—
177C4×C11#55212yes—
178C4×C11#55312yes—
179Dic11—82no—
180Dic11—82no—
181Dic11—82no—
182C22×D4—112no—
183C22×D4—222no—
184C23×C4—222no—
185C22×C8C22×D1114yes—
186#127—224no—
187C4×D4—224no—
188C4×D4—224no—
189C4×D4—448no—
190C2×C4⋊C4—112no—
191C2×C4⋊C4—112no—
192C2×C4⋊C4—112no—
193C2×C4⋊C4—222no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4—222no—
196C2×C22⋊C4—222no—
197C2×C22⋊C4—224no—
198C2×C42D4412yes—
199C2×C42D4412yes—
200C2×C42C22×D1111yescharacteristic
201C2×C42C22×D1111yescharacteristic
202C2×C42C22×D1111yescharacteristic
203C4⋊C8—24no—
204#102—228no—
205#102—444no—
206C4×C8—42no—
207#95—221no—
208#95—221no—
209#95—221no—
210#95—221no—
211#95—222no—
212#95—222no—
213C2×C11#256211yescharacteristic
214C2×C11#310512yes—
215C2×C11#313111yescharacteristic
216C2×C11#313811yescharacteristic
217C2×C11#324712yes—
218D11—84no—
219C24—222no—
220C2×D4—114no—
221C2×D4—228no—
222C2×D4—222no—
223C2×D4—222no—
224C2×D4—222no—
225C2×D4—222no—
226C2×D4—222no—
227C2×D4—444no—
228C2×D4—444no—
229C22×C4—222no—
230C22×C4—222no—
231C22×C4—222no—
232C22×C4—448no—
233C22×C4—444no—
234C22×C4C2×D4411yescharacteristic
235C22×C4C2×D4411yescharacteristic
236C22×C4C2×D4412yes—
237C22×C4C2×D4412yes—
238C22×C4C23×D1111yescharacteristic
239C2×C8—24no—
240C2×C8—24no—
241C2×C8—24no—
242C4⋊C4—222no—
243C4⋊C4—222no—
244C4⋊C4—222no—
245C4⋊C4—222no—
246C4⋊C4—224no—
247C4⋊C4—444no—
248C4⋊C4—444no—
249C4⋊C4—444no—
250C22⋊C4—444no—
251C22⋊C4—448no—
252C42—24no—
253C42—24no—
254C42—21no—
255C42—21no—
256C42—22no—
257C42#433914yes—
258C11#2912411yescharacteristic, complemented, Sylow
259C23—224no—
260C23—442no—
261C23—444no—
262C23—444no—
263C23—442no—
264C23C22×D4411yescharacteristic
265D4—224no—
266D4—224no—
267D4—4416no—
268D4—442no—
269D4—442no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—442no—
277C2×C4—442no—
278C2×C4—442no—
279C2×C4—444no—
280C2×C4—442no—
281C2×C4—442no—
282C2×C4—442no—
283C2×C4—442no—
284C2×C4—888no—
285C2×C4#6692812yes—
286C2×C4#6692812yes—
287C2×C4#6695714yes—
288C2×C4#6696114yes—
289C2×C4C2×#433912yes—
290C2×C4#6703711yescharacteristic
291C2×C4#6704011yescharacteristic
292C2×C4#41×D1112yes—
293C8—44no—
294C22—444no—
295C22—448no—
296C22—884no—
297C22—882no—
298C22—882no—
299C22C2×#6692811yescharacteristic
300C22#1062304111yescharacteristic
301C22#1062305511yescharacteristic
302C22C2×#6695712yes—
303C22C2×#6696112yes—
304C4—24no—
305C4—24no—
306C4—22no—
307C4—22no—
308C4—882no—
309C4—882no—
310C4—882no—
311C4#1062308912yes—
312C4#1062311212yes—
313C2—884no—
314C2#1307377711yescharacteristic
315C2#1307866512yes—
316C2#1307893911yescharacteristic
317C2#1307899111yescharacteristic
318C2#1307994312yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×C4⋊C8C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenterC4×C4⋊C8D11
hypocenterC11#29124
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #13077003C2semidirect
3. #13070180C2semidirect
5. #13069299C2semidirect
6. #13068627C2semidirect
7. #13068627C2semidirect
8. C4×C11×C4⋊C8C2semidirect
107. C4×C4⋊C8D11semidirect
258. C11#29124semidirect

Maximal subgroups

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

subgroupindex
#130770032
C4×#669272
#130701802
#130698512
#130692992
#130686272
C4×C11×C4⋊C82
#2912411