Finite Group Databasebeta

← #14719952

Subgroups — #14719952

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077701C212yesmaximal, complemented
2#13066985C214yesmaximal
3#13066972C214yesmaximal, complemented
4#13066960C212yesmaximal, complemented
5#13066950C212yesmaximal
6C2×C11×#541C211yesmaximal, characteristic
7C11×#541—28no—
8C2×C11×C4⋊Q8C411yescharacteristic
9C2×C11×#126C412yes—
10C2×C11×#126C2212yes—
11C2×C11×#125C411yescharacteristic
12C2×C11×#125C412yes—
13C2×C11×#125C2212yes—
14C2×C11×C22⋊Q8C411yescharacteristic
15C2×C11×C22⋊Q8C411yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19#10622637—28no—
20#10622539C2214yes—
21#10622539C2214yes—
22#10622538C2214yes—
23#10622166C2214yes—
24#10622166C2218yes—
25#10622163C2214yes—
26C22×Q8×C11C2×C411yescharacteristic
27C22×Q8×C11C2×C411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C11×C4⋊Q8—24no—
30C11×#126—28no—
31C11×#126—24no—
32C11×#126—24no—
33C11×#125—24no—
34C11×#125—28no—
35C11×#125—24no—
36C11×#125—24no—
37C11×C22⋊Q8—24no—
38C11×C22⋊Q8—24no—
39C4×Q8×C11—24no—
40C4×Q8×C11D418yes—
41C11×#117—24no—
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C11×C4⋊C4C2×C411yescharacteristic
44C2×C11×C4⋊C4C2×C412yes—
45C2×C11×C4⋊C4C2×C412yes—
46C2×C11×C4⋊C4C2×C412yes—
47C2×C11×C4⋊C4C2×C412yes—
48C2×C11×C4⋊C4C2×C412yes—
49C2×C11×C4⋊C4C2×C412yes—
50C2×C11×C4⋊C4C2×C411yescharacteristic
51C2×C11×C4⋊C4C2×C412yes—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4C2×C411yescharacteristic
55C2×C11×C22⋊C4C2×C412yes—
56C2×C11×C22⋊C4C2×C412yes—
57C2×C11×C22⋊C4C2311yescharacteristic
58C2×C42×C11C2×C411yescharacteristic
59C2×C42×C11C2×C412yes—
60C2×C42×C11C2312yes—
61C2×C42×C11C2311yescharacteristic
62C22⋊(C11⋊C8)C2318yes—
63C4⋊(C11⋊C8)—24no—
64C4⋊(C11⋊C8)—24no—
65C4⋊(C11⋊C8)—24no—
66#66867—24no—
67#66867—24no—
68C4×C11⋊C8—24no—
69#17410—111nomaximal, Sylow
70C24×C11C22×C411yescharacteristic
71C2×Q8×C11—22no—
72C2×Q8×C11—42no—
73C2×Q8×C11—42no—
74C2×Q8×C11C22⋊C414yes—
75C22×C4×C11—22no—
76C22×C4×C11—42no—
77C22×C4×C11C22×C412yes—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C22×C412yes—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C22×C412yes—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C22×C412yes—
86C22×C4×C11C2411yescharacteristic
87C11×C4⋊C4—22no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—24no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4C22⋊C414yes—
99C11×C4⋊C4C22⋊C418yes—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—22no—
104C42×C11—22no—
105C42×C11—24no—
106C42×C11C2×D414yes—
107C42×C11C2×D414yes—
108C42×C11C2×D414yes—
109C2×C11⋊C8—28no—
110C2×#541D1111yescharacteristic
111#2983—112no—
112#1473—114no—
113#1470—114no—
114#1467—112no—
115#1464—112no—
116C23×C11—21no—
117C23×C11—22no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11C23×C411yescharacteristic
121Q8×C11—44no—
122Q8×C11—44no—
123C2×C4×C11—22no—
124C2×C4×C11—24no—
125C2×C4×C11—21no—
126C2×C4×C11—22no—
127C2×C4×C11—21no—
128C2×C4×C11—22no—
129C2×C4×C11—21no—
130C2×C4×C11—22no—
131C2×C4×C11—24no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—41no—
135C2×C4×C11—44no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—41no—
139C2×C4×C11C2×C22⋊C412yes—
140C2×C4×C11C2×C22⋊C412yes—
141C2×C4×C11C2×C22⋊C414yes—
142C2×C4×C11C2×C22⋊C414yes—
143C2×C4×C11C22×D412yes—
144C11⋊C8—48no—
145#541—28no—
146C2×C4⋊Q8Dic1111yescharacteristic
147C2×#126Dic1112yes—
148C2×#126C2×D1112yes—
149C2×#125Dic1111yescharacteristic
150C2×#125Dic1112yes—
151C2×#125C2×D1112yes—
152C2×C22⋊Q8Dic1111yescharacteristic
153C2×C22⋊Q8Dic1111yescharacteristic
154C2×C4×Q8C2×D1111yescharacteristic
155C2×C4×Q8C2×D1111yescharacteristic
156C2×#117C2×D1111yescharacteristic
157#446—228no—
158#432—114no—
159#432—114no—
160#431—114no—
161#324—114no—
162#324—118no—
163#323—114no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—82no—
170C22×C11C22×C22⋊C411yescharacteristic
171C22×C11#56812yes—
172C4×C11—22no—
173C4×C11—24no—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—24no—
177C4×C11—41no—
178C4×C11—42no—
179C4×C11—41no—
180C4×C11—42no—
181C4×C11—41no—
182C22×Q8C2×Dic1111yescharacteristic
183C22×Q8C2×Dic1111yescharacteristic
184C23×C4C2×Dic1111yescharacteristic
185C4⋊Q8—24no—
186#126—28no—
187#126—24no—
188#126—24no—
189#125—24no—
190#125—28no—
191#125—24no—
192#125—24no—
193C22⋊Q8—24no—
194C22⋊Q8—24no—
195C4×Q8—24no—
196C4×Q8C22⋊D1118yes—
197#117—24no—
198C2×C4⋊C4C2×Dic1111yescharacteristic
199C2×C4⋊C4C2×Dic1111yescharacteristic
200C2×C4⋊C4C2×Dic1112yes—
201C2×C4⋊C4C2×Dic1112yes—
202C2×C4⋊C4C2×Dic1112yes—
203C2×C4⋊C4C2×Dic1112yes—
204C2×C4⋊C4C2×Dic1112yes—
205C2×C4⋊C4C2×Dic1112yes—
206C2×C4⋊C4C2×Dic1111yescharacteristic
207C2×C4⋊C4C2×Dic1112yes—
208C2×C4⋊C4C22×D1111yescharacteristic
209C2×C4⋊C4C22×D1112yes—
210C2×C22⋊C4C2×Dic1111yescharacteristic
211C2×C22⋊C4C2×Dic1112yes—
212C2×C22⋊C4C2×Dic1112yes—
213C2×C22⋊C4C22×D1111yescharacteristic
214C2×C42C2×Dic1111yescharacteristic
215C2×C42C2×Dic1112yes—
216C2×C42C22×D1111yescharacteristic
217C2×C42C22×D1112yes—
218C4⋊C8—224no—
219C4⋊C8—224no—
220C4⋊C8—224no—
221C22⋊C8—118no—
222#97—224no—
223#97—224no—
224C4×C8—224no—
225C2×C11—22no—
226C2×C11—81no—
227C2×C11#287911yescharacteristic
228C2×C11#288411yescharacteristic
229C2×C11#288911yescharacteristic
230C24C22×Dic1111yescharacteristic
231C2×Q8—22no—
232C2×Q8—42no—
233C2×Q8—42no—
234C2×Q8C22⋊Dic1114yes—
235C22×C4—22no—
236C22×C4—42no—
237C22×C4C22×Dic1112yes—
238C22×C4C22×Dic1111yescharacteristic
239C22×C4C22×Dic1111yescharacteristic
240C22×C4C22×Dic1112yes—
241C22×C4C22×Dic1111yescharacteristic
242C22×C4C22×Dic1111yescharacteristic
243C22×C4C22×Dic1112yes—
244C22×C4C22×Dic1111yescharacteristic
245C22×C4C22×Dic1112yes—
246C22×C4C23×D1111yescharacteristic
247C2×C8—228no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4C22⋊Dic1114yes—
260C4⋊C4C22⋊Dic1118yes—
261C22⋊C4—22no—
262C22⋊C4—24no—
263C22⋊C4—24no—
264C22⋊C4—22no—
265C42—22no—
266C42—24no—
267C42C2×C22⋊D1114yes—
268C42C2×C22⋊D1114yes—
269C42C2×C22⋊D1114yes—
270C11#1741011yescharacteristic, complemented, Sylow
271C23—21no—
272C23—22no—
273C23—41no—
274C23—41no—
275C23C23×Dic1111yescharacteristic
276Q8—44no—
277Q8—44no—
278C2×C4—22no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—44no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4C2×C22⋊Dic1112yes—
295C2×C4C2×C22⋊Dic1112yes—
296C2×C4C2×C22⋊Dic1114yes—
297C2×C4C2×C22⋊Dic1114yes—
298C2×C4C22×C22⋊D1112yes—
299C8—448no—
300C22—21no—
301C22—21no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—82no—
306C22#1062335012yes—
307C22C22×C22⋊Dic1111yescharacteristic
308C4—22no—
309C4—24no—
310C4—22no—
311C4—22no—
312C4—24no—
313C4—41no—
314C4—42no—
315C4—41no—
316C4—42no—
317C4—41no—
318C2—22no—
319C2—81no—
320C2#1307706111yescharacteristic
321C2#1307708011yescharacteristic
322C2#1307709911yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#541C2
socleC22×C11C22×C22⋊C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC2×#541D11
hypocenterC11#17410
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #13077701C2semidirect
3. #13066972C2semidirect
4. #13066960C2semidirect
270. C11#17410semidirect

Maximal subgroups

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

subgroupindex
#130777012
#130669852
#130669722
#130669602
#130669502
C2×C11×#5412
#1741011