Finite Group Databasebeta

← #14752827

Subgroups — #14752827

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622292C211yesmaximal, characteristic
2C2×#10622443C211yesmaximal, characteristic
3#13071090C211yesmaximal, characteristic
4#13068489C212yesmaximal
5#13068485C211yesmaximal, characteristic
6C8×Dic11⋊C4C212yesmaximal
7#13068474C212yesmaximal
8C4⋊C8×Dic11C211yesmaximal, characteristic
9#13068366C212yesmaximal
10#13068361C211yesmaximal, characteristic
11C8×C11×C4⋊C4C211yesmaximal, characteristic
12C2×C4×Dic22C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C4×C8×C11C2212yes—
15C2×C4×C8×C11C2211yescharacteristic
16C4×C11×C4⋊C4C2211yescharacteristic
17C2×#66879C2212yes—
18C2×Dic11⋊C8C2212yes—
19C2×Dic11⋊C8C2212yes—
20C2×C8×Dic11C2212yes—
21C2×C8×Dic11C2212yes—
22#10622587C412yes—
23#10622586C412yes—
24#10622545C2212yes—
25C4×Dic11⋊C4C2212yes—
26C42×Dic11C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C2×#66867C2212yes—
29C2×C4×C11⋊C8C2211yescharacteristic
30#10622443C418yescomplemented
31#10622292C418yescomplemented
32#10622265C414yes—
33C11×#336C2212yes—
34#10622188C2211yescharacteristic
35#10622188C2211yescharacteristic
36#10622188C2211yescharacteristic
37#10622188C2211yescharacteristic
38#10622188C2212yes—
39#10622162C2212yes—
40C22×Dic22C2×C411yescharacteristic
41C22×C8×C11C2311yescharacteristic
42C22×C8×C11C2312yes—
43C22×C8×C11C2311yescharacteristic
44C2×C11×C4⋊C4C2×C412yes—
45C2×C42×C11C2312yes—
46C2×C42×C11C2311yescharacteristic
47C2×C4⋊Dic11C2×C411yescharacteristic
48C2×Dic11⋊C4C2×C414yes—
49C2×Dic11⋊C4C2×C412yes—
50C2×C4×Dic11C2×C412yes—
51C2×C4×Dic11C2×C412yes—
52C2×C4×Dic11C2311yescharacteristic
53C2×C4×Dic11C2311yescharacteristic
54C2×C4×Dic11C2312yes—
55C22×C11⋊C8C2311yescharacteristic
56C22×C11⋊C8C2311yescharacteristic
57C22×C11⋊C8C2312yes—
58C4×Dic22C2×C414yes—
59C4×Dic22C2×C414yes—
60C11×C4⋊C8C2×C414yes—
61C4×C8×C11—42no—
62C4×C8×C11C2×C414yes—
63C11×#95C2×C412yes—
64C11⋊#95C2×C414yes—
65C11⋊#95C2×C414yes—
66C11⋊#95C2×C414yes—
67#66879C2×C418yes—
68Dic11⋊C8C2×C418yes—
69Dic11⋊C8C2×C418yes—
70C8×Dic11—42no—
71C8×Dic11C2×C418yes—
72C4⋊(C11⋊C8)C2×C414yes—
73#66867—42no—
74C4×C11⋊C8C2×C414yes—
75#20571—111nomaximal, Sylow
76C22×C4×C11C22×C414yes—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2411yescharacteristic
80C22×Dic11C22×C412yes—
81C22×Dic11C22×C412yes—
82C22×Dic11C22×C412yes—
83C22×Dic11C22×C412yes—
84C2×Dic22—24no—
85C2×Dic22C4214yes—
86C2×C8×C11—22no—
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11—22no—
92C2×C8×C11C22×C414yes—
93C2×C8×C11C22×C412yes—
94C2×C8×C11C22×C412yes—
95C11×C4⋊C4—24no—
96C42×C11—22no—
97C42×C11—22no—
98C42×C11C22×C412yes—
99C42×C11C22×C412yes—
100C4⋊Dic11C4214yes—
101Dic11⋊C4—28no—
102Dic11⋊C4C4218yes—
103C4×Dic11—24no—
104C4×Dic11—24no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11C22×C414yes—
110C4×Dic11C22×C414yes—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—21no—
116C2×C11⋊C8—21no—
117C2×C11⋊C8C22×C412yes—
118C2×C11⋊C8C22×C412yes—
119C2×C11⋊C8C22×C414yes—
120C2×#446—111no—
121C2×C8×Q8—111no—
122#2295—111no—
123#1771—112no—
124#1770—111no—
125C8×C4⋊C4—112no—
126C8×C4⋊C4D1111yescharacteristic
127#1768—112no—
128C4×C4⋊C8—111no—
129#1746—112no—
130#1744—111no—
131C23×C11C23×C411yescharacteristic
132C2×C4×C11—22no—
133C2×C4×C11—24no—
134C2×C4×C11—24no—
135C2×C4×C11—24no—
136C2×C4×C11C2×C4212yes—
137C2×C4×C11C2×C4212yes—
138C2×C4×C11#13114yes—
139C2×C4×C11C23×C411yescharacteristic
140C2×C4×C11C23×C411yescharacteristic
141C2×C4×C11H(5,𝔽2)11yescharacteristic
142C2×C4×C112−1+411yescharacteristic
143C2×C4×C112−1+411yescharacteristic
144C2×C4×C112−1+411yescharacteristic
145C2×Dic11—22no—
146C2×Dic11—22no—
147C2×Dic11—24no—
148C2×Dic11—24no—
149C2×Dic11—22no—
150C2×Dic11—22no—
151C2×Dic11—22no—
152C2×Dic11C2×C4214yes—
153C2×Dic11C2×C4214yes—
154C2×Dic11#13114yes—
155Dic22—28no—
156C8×C11—22no—
157C8×C11—22no—
158C8×C11—24no—
159C11⋊C8—22no—
160C11⋊C8—24no—
161C11⋊C8—22no—
162C2×C4×Q8—111no—
163#446—118no—
164C8×Q8—118no—
165C2×C4⋊C8—112no—
166C2×C4⋊C8—112no—
167C2×C4⋊C8—111no—
168C2×C4⋊C8C2×D1111yescharacteristic
169C2×#97—112no—
170C2×#97—112no—
171C2×C4×C8—112no—
172C2×C4×C8—111no—
173C2×C4×C8—112no—
174C2×C4×C8C2×D1112yes—
175C2×C4×C8C2×D1111yescharacteristic
176#391—112no—
177#389—112no—
178#387—114no—
179C4×C4⋊C4—112no—
180C4×C4⋊C4C2×D1111yescharacteristic
181#376—112no—
182C43—111no—
183#336—111no—
184#336—111no—
185#336—111no—
186#336—111no—
187#336—112no—
188#336—112no—
189#336C2×D1112yes—
190C22×C11C22×C4211yescharacteristic
191C22×C11#51911yescharacteristic
192C22×C11#52011yescharacteristic
193C22×C11C2×#13112yes—
194C22×C11C2×#13112yes—
195C4×C11—22no—
196C4×C11—44no—
197C4×C11#40514yes—
198C4×C11#51911yescharacteristic
199C4×C11#51911yescharacteristic
200C4×C11#52011yescharacteristic
201C4×C11#52011yescharacteristic
202Dic11—24no—
203Dic11—24no—
204Dic11—24no—
205Dic11—42no—
206C22×Q8—111no—
207C22×C8—111no—
208C22×C8—111no—
209C22×C8—112no—
210C22×C8C22×D1111yescharacteristic
211C22×C8C22×D1111yescharacteristic
212C22×C8C22×D1112yes—
213C4×Q8—114no—
214C4×Q8—114no—
215C2×C4⋊C4—112no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—114no—
218C2×C4⋊C4C4×D1112yes—
219C2×C42—112no—
220C2×C42—112no—
221C2×C42—112no—
222C2×C42—111no—
223C2×C42—111no—
224C2×C42C22×D1112yes—
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—118no—
227C4⋊C8—118no—
228C4⋊C8—114no—
229C4⋊C8C4×D1114yes—
230#97—118no—
231#97—442no—
232C4×C8—42no—
233C4×C8—118no—
234C4×C8—114no—
235C4×C8—442no—
236C4×C8C4×D1114yes—
237#95—114no—
238#95—114no—
239#95—114no—
240#95C4×D1112yes—
241C2×C11#227611yescharacteristic
242C2×C11C2×#40511yescharacteristic
243C2×C11C4×#13111yescharacteristic
244C2×C11#298612yes—
245C2×C11#299412yes—
246C2×Q8—114no—
247C2×Q8—224no—
248C22×C4—112no—
249C22×C4—112no—
250C22×C4—112no—
251C22×C4—112no—
252C22×C4C2×C4×D1114yes—
253C22×C4C2×C4×D1111yescharacteristic
254C22×C4C2×C4×D1111yescharacteristic
255C22×C4C23×D1111yescharacteristic
256C2×C8—21no—
257C2×C8—22no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—22no—
262C2×C8—112no—
263C2×C8—112no—
264C2×C8—114no—
265C2×C8—222no—
266C2×C8—221no—
267C2×C8—222no—
268C2×C8—221no—
269C2×C8—221no—
270C2×C8—221no—
271C2×C8C2×C4×D1114yes—
272C2×C8C2×C4×D1112yes—
273C2×C8C2×C4×D1112yes—
274C4⋊C4—24no—
275C4⋊C4—118no—
276C4⋊C4—114no—
277C4⋊C4—228no—
278C42—22no—
279C42—22no—
280C42—114no—
281C42—114no—
282C42—224no—
283C42—224no—
284C42—221no—
285C42—221no—
286C42—221no—
287C42—221no—
288C42C2×C4×D1112yes—
289C42C2×C4×D1112yes—
290C11#2057111yescharacteristic, complemented, Sylow
291C23C22×C4×D1111yescharacteristic
292Q8—228no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—114no—
298C2×C4—114no—
299C2×C4—114no—
300C2×C4—222no—
301C2×C4—224no—
302C2×C4—224no—
303C2×C4—222no—
304C2×C4—222no—
305C2×C4—222no—
306C2×C4—222no—
307C2×C4C42×D1112yes—
308C2×C4C42×D1112yes—
309C2×C4#6695414yes—
310C2×C4C22×C4×D1111yescharacteristic
311C2×C4C22×C4×D1111yescharacteristic
312C2×C4#6703711yescharacteristic
313C2×C4#6704011yescharacteristic
314C2×C4#6704311yescharacteristic
315C2×C4#6704311yescharacteristic
316C8—22no—
317C8—22no—
318C8—24no—
319C8—224no—
320C8—222no—
321C8—222no—
322C22C2×C42×D1111yescharacteristic
323C22#1062307711yescharacteristic
324C22#1062310311yescharacteristic
325C22C2×#6695412yes—
326C22D11×#13112yes—
327C4—22no—
328C4—44no—
329C4—224no—
330C4—224no—
331C4—224no—
332C4—442no—
333C4#1062230214yes—
334C4#1062303511yescharacteristic
335C4#1062304711yescharacteristic
336C4#1062307711yescharacteristic
337C4#1062310311yescharacteristic
338C2#1307098011yescharacteristic
339C2C2×#1062230211yescharacteristic
340C2#1307703811yescharacteristic
341C2#1307771612yes—
342C2#1307777112yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC8×C11×C4⋊C4C2
socle, prime radicalC23×C11C23×C4
cosocleC22×C4×C11C24
hypercenterC8×C4⋊C4D11
hypocenterC11#20571
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
30. #10622443C4semidirect
31. #10622292C4semidirect
290. C11#20571semidirect

Maximal subgroups

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

subgroupindex
C2×#106222922
C2×#106224432
#130710902
#130684892
#130684852
C8×Dic11⋊C42
#130684742
C4⋊C8×Dic112
#130683662
#130683612
C8×C11×C4⋊C42
#2057111