Finite Group Databasebeta

← #14752583

Subgroups — #14752583

Order 2816.

1006 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic
2C4×#66979C211yesmaximal, characteristic
3#13068488C214yesmaximal, complemented
4#13068471C212yesmaximal, complemented
5C4⋊C8×Dic11C212yesmaximal, complemented
6#13068395C212yesmaximal
7#13068390C212yesmaximal
8C2×C11×#432C211yesmaximal, characteristic
9C22×C42×C11C2211yescharacteristic
10C2×#66979C412yes—
11C23×C11⋊C8C2212yes—
12C11×#432C418yescomplemented
13C2×C11×C4⋊C8C2212yes—
14C2×C11×C22⋊C8C2212yes—
15C2×C11×#97C2212yes—
16C4×C22⋊Dic11C412yes—
17C4×C22⋊Dic11C2211yescharacteristic
18C4×C22⋊Dic11C2211yescharacteristic
19C2×#66879C2214yes—
20C2×C8×Dic11C2214yes—
21C4×C4⋊Dic11C412yes—
22C4×C4⋊Dic11C2212yes—
23#10622545C412yes—
24C42×Dic11C2212yes—
25C2×C4⋊(C11⋊C8)C418yescomplemented
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2212yes—
29#10622188C2214yes—
30#10622188C2214yes—
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C22×C8×C11C2314yes—
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11C2×C414yes—
38C2×C42×C11C2×C414yes—
39C2×C42×C11C2311yescharacteristic
40C2×C42×C11C2311yescharacteristic
41C2×C22⋊Dic11C2×C412yes—
42C2×C22⋊Dic11C2×C412yes—
43#66979—28no—
44C2×C4⋊Dic11C2×C414yes—
45C2×C4×Dic11C2×C414yes—
46C2×C4×Dic11C2×C414yes—
47C2×C4×Dic11C2312yes—
48C2×C4×Dic11C2312yes—
49C22×C11⋊C8—44no—
50C22×C11⋊C8C2×C418yes—
51C22×C11⋊C8C2312yes—
52C22×C11⋊C8C2312yes—
53C11×C4⋊C8C2×C418yes—
54C11×C22⋊C8C2×C418yes—
55C11×#97C2×C418yes—
56C11⋊#95C2×C412yes—
57C11⋊#95C2×C412yes—
58C11⋊#95C2×C414yes—
59#66879—44no—
60C8×Dic11—44no—
61C4⋊(C11⋊C8)C2×C414yes—
62C4⋊(C11⋊C8)C2×C414yes—
63C4⋊(C11⋊C8)C2×C418yes—
64#20546—111nomaximal, Sylow
65C24×C11C22×C411yescharacteristic
66C22×C4×C11—24no—
67C22×C4×C11—24no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11C4214yes—
71C22×C4×C11C4214yes—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C22×C412yes—
77C22×C4×C11C22×C412yes—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2411yescharacteristic
80C22×Dic11C22×C414yes—
81C22×Dic11C22×C414yes—
82C2×C8×C11—24no—
83C2×C8×C11—24no—
84C2×C8×C11C22×C418yes—
85C42×C11C4214yes—
86C42×C11C4214yes—
87C42×C11C22×C412yes—
88C42×C11C22×C412yes—
89C42×C11C22×C412yes—
90C42×C11C22×C412yes—
91C22⋊Dic11—24no—
92C22⋊Dic11M1618yes—
93C4⋊Dic11—28no—
94C4×Dic11—28no—
95C4×Dic11—28no—
96C4×Dic11—22no—
97C4×Dic11—22no—
98C4×Dic11—22no—
99C4×Dic11—22no—
100C2×C11⋊C8—24no—
101C2×C11⋊C8—24no—
102C2×C11⋊C8—48no—
103C2×C11⋊C8C22×C414yes—
104C2×C11⋊C8C22×C414yes—
105C2×#432D1111yescharacteristic
106C22×C4⋊C8—111no—
107C4×#117—111no—
108#1771—114no—
109#1767—112no—
110C4×C4⋊C8—112no—
111#1752—112no—
112C8×C22⋊C4—112no—
113C23×C11—22no—
114C23×C11—22no—
115C23×C11C2×C4212yes—
116C23×C11C2×M1614yes—
117C23×C11C23×C411yescharacteristic
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—28no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—24no—
126C2×C4×C11—28no—
127C2×C4×C11C2×C4212yes—
128C2×C4×C11C2×C4212yes—
129C2×C4×C11C2×C4212yes—
130C2×C4×C11C2×C4212yes—
131C2×C4×C11C2×C4212yes—
132C2×C4×C11#13114yes—
133C2×C4×C11C23×C411yescharacteristic
134C2×C4×C11C23×C411yescharacteristic
135C2×C4×C11H(5,𝔽2)12yes—
136C2×C4×C112−1+412yes—
137C2×Dic11—24no—
138C2×Dic11—24no—
139C2×Dic11—24no—
140C2×Dic11—24no—
141C2×Dic11—24no—
142C2×Dic11C2×M1618yes—
143C8×C11—28no—
144C11⋊C8—24no—
145C11⋊C8—24no—
146C23×C8—112no—
147C2×#117—112no—
148C22×C42C2×D1111yescharacteristic
149#432Dic1118yescomplemented
150C2×C4⋊C8—111no—
151C2×C4⋊C8—111no—
152C2×C4⋊C8—112no—
153C2×C4⋊C8—118no—
154C2×C4⋊C8C2×D1112yes—
155C2×C22⋊C8C2×D1112yes—
156C2×#97—114no—
157C2×#97C2×D1112yes—
158C2×C4×C8—114no—
159C4×C4⋊C4—112no—
160C4×C4⋊C4—112no—
161C4×C22⋊C4—111no—
162C4×C22⋊C4—111no—
163C4×C22⋊C4—112no—
164#376—112no—
165C43—112no—
166#336—114no—
167#336—114no—
168C22×C11—22no—
169C22×C11—28no—
170C22×C11—22no—
171C22×C11C4×M1614yes—
172C22×C11C22×C4211yescharacteristic
173C22×C11#52012yes—
174C22×C11C22×M1612yes—
175C22×C11C2×#13112yes—
176C4×C11—22no—
177C4×C11—22no—
178C4×C11—22no—
179C4×C11—22no—
180C4×C11#40514yes—
181C4×C11#51811yescharacteristic
182C4×C11#51911yescharacteristic
183C4×C11#52012yes—
184Dic11—28no—
185Dic11—44no—
186C23×C4C4×D1111yescharacteristic
187C23×C4C4×D1111yescharacteristic
188C23×C4C22×D1111yescharacteristic
189C22×C8—112no—
190C22×C8—112no—
191C22×C8—118no—
192C22×C8—444no—
193C22×C8C22×D1114yes—
194#117—228no—
195C2×C4⋊C4—114no—
196C2×C22⋊C4—112no—
197C2×C22⋊C4—112no—
198C2×C42—114no—
199C2×C42—114no—
200C2×C42—112no—
201C2×C42—112no—
202C2×C42C4×D1111yescharacteristic
203C2×C42C4×D1111yescharacteristic
204C2×C42C4×D1114yes—
205C2×C42C2×Dic1114yes—
206C2×C42C22×D1111yescharacteristic
207C2×C42C22×D1111yescharacteristic
208C4⋊C8—114no—
209C4⋊C8—114no—
210C4⋊C8—118no—
211C4⋊C8C2×Dic1118yes—
212C22⋊C8C2×Dic1118yes—
213#97—444no—
214#97C2×Dic1118yes—
215C4×C8—444no—
216#95—112no—
217#95—114no—
218#95—112no—
219C2×C11—24no—
220C2×C11#227411yescharacteristic
221C2×C11C2×C4×M1611yescharacteristic
222C2×C11C2×#40511yescharacteristic
223C2×C11#299014yes—
224C24C2×C4×D1111yescharacteristic
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—114no—
230C22×C4—114no—
231C22×C4C4×Dic1114yes—
232C22×C4C4×Dic1114yes—
233C22×C4C2×C4×D1111yescharacteristic
234C22×C4C2×C4×D1111yescharacteristic
235C22×C4C2×C4×D1111yescharacteristic
236C22×C4C2×C4×D1111yescharacteristic
237C22×C4C2×C4×D1112yes—
238C22×C4C2×C4×D1111yescharacteristic
239C22×C4C22×Dic1112yes—
240C22×C4C23×D1111yescharacteristic
241C2×C8—24no—
242C2×C8—24no—
243C2×C8—114no—
244C2×C8—114no—
245C2×C8—224no—
246C2×C8—224no—
247C2×C8—448no—
248C2×C8C22×Dic1118yes—
249C4⋊C4—228no—
250C22⋊C4—118no—
251C22⋊C4—224no—
252C42—228no—
253C42—228no—
254C42—222no—
255C42—222no—
256C42—222no—
257C42—222no—
258C42C4×Dic1114yes—
259C42C4×Dic1114yes—
260C42C2×C4×D1112yes—
261C42C2×C4×D1112yes—
262C42C22×Dic1112yes—
263C42C22×Dic1112yes—
264C11#2054611yescharacteristic, complemented, Sylow
265C23—22no—
266C23—22no—
267C23M16×D1114yes—
268C23C2×C4×Dic1112yes—
269C23C22×C4×D1111yescharacteristic
270C2×C4—28no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—28no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—118no—
280C2×C4—224no—
281C2×C4—224no—
282C2×C4—224no—
283C2×C4—224no—
284C2×C4—224no—
285C2×C4#6696014yes—
286C2×C4C2×C4×Dic1112yes—
287C2×C4C2×C4×Dic1112yes—
288C2×C4C2×C4×Dic1112yes—
289C2×C4C2×C4×Dic1112yes—
290C2×C4C2×C4×Dic1112yes—
291C2×C4C22×C4×D1111yescharacteristic
292C2×C4#6704212yes—
293C2×C4#6704312yes—
294C2×C4C23×Dic1111yescharacteristic
295C8—28no—
296C8—224no—
297C8—224no—
298C22—22no—
299C22—22no—
300C22—28no—
301C22M16×Dic1114yes—
302C22#1062305412yes—
303C22C2×M16×D1112yes—
304C22C2×#6696012yes—
305C22C22×C4×Dic1111yescharacteristic
306C4—22no—
307C4—22no—
308C4—22no—
309C4—22no—
310C4—228no—
311C4—444no—
312C4#1062273514yes—
313C4#1062304711yescharacteristic
314C4#1062305211yescharacteristic
315C4#1062335812yes—
316C2—24no—
317C2#1307097211yescharacteristic
318C2C2×M16×Dic1111yescharacteristic
319C2C2×#1062273511yescharacteristic
320C2#1307774314yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#432C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC2×#432D11
hypocenterC11#20546
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
3. #13068488C2semidirect
4. #13068471C2semidirect
5. C4⋊C8×Dic11C2semidirect
12. C11×#432C4semidirect
25. C2×C4⋊(C11⋊C8)C4semidirect
149. #432Dic11semidirect
264. C11#20546semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊(C11⋊C8)2
C4×#669792
#130684882
#130684712
C4⋊C8×Dic112
#130683952
#130683902
C2×C11×#4322
#2054611