Finite Group Databasebeta

← #14653879

Subgroups — #14653879

Order 2816.

388 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068469C211yesmaximal, characteristic
2#13068365C211yesmaximal, characteristic
3#13066497C212yesmaximal
4#13066497C212yesmaximal
5C11×#2864C211yesmaximal, characteristic
6C11×#389C411yescharacteristic
7C11×#389C411yescharacteristic
8C11×#389C411yescharacteristic
9C11×#389C411yescharacteristic
10C11×#387—21no—
11C11×#387—21no—
12C11×#387—21no—
13C11×#387—21no—
14C11×#382C2211yescharacteristic
15C11×#382C2211yescharacteristic
16C43×C11C2211yescharacteristic
17C2×C4⋊(C11⋊C8)—21no—
18C2×#66867C2212yes—
19C2×#66867C2212yes—
20#10622162—21no—
21#10622162—21no—
22#10622162—21no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4—21no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C22×C11⋊C8—22no—
39C22×C11⋊C8—22no—
40C11×#95—21no—
41C11×#95—21no—
42C11×#95—21no—
43C11×#95—21no—
44C11×#95—21no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C4⋊(C11⋊C8)—24no—
49#66867—22no—
50#66867—24no—
51#66867Q814yes—
52#9893—111nomaximal, Sylow
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22×C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C11×C4⋊C4—42no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—42no—
72C42×C11—22no—
73C42×C11—41no—
74C42×C11—41no—
75C42×C11—41no—
76C42×C11—41no—
77C42×C11—41no—
78C42×C11C2×Q812yes—
79C42×C11#4112yes—
80C2×C11⋊C8—24no—
81C2×C11⋊C8—24no—
82C2×C11⋊C8—42no—
83C2×C11⋊C8—42no—
84C2×C11⋊C8—42no—
85C2×C11⋊C8—42no—
86#2864D1111yescharacteristic
87#1767—111no—
88#1745—111no—
89#1295—112no—
90#1295—112no—
91C23×C11C2×C22⋊C411yescharacteristic
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11#10412yes—
122C2×C4×C11C4×Q812yes—
123C2×C4×C11C22⋊Q812yes—
124C2×C4×C11#12411yescharacteristic
125C2×C4×C11C4⋊Q811yescharacteristic
126C11⋊C8—44no—
127C11⋊C8—44no—
128C2×C4⋊C8—221no—
129C2×#97—112no—
130C2×#97—112no—
131#389Dic1111yescharacteristic
132#389Dic1111yescharacteristic
133#389Dic1111yescharacteristic
134#389Dic1111yescharacteristic
135#387—21no—
136#387—21no—
137#387—21no—
138#387—21no—
139#382C2×D1111yescharacteristic
140#382C2×D1111yescharacteristic
141C43C2×D1111yescharacteristic
142#336—221no—
143#336—221no—
144#336—221no—
145C22×C11#39111yescharacteristic
146C22×C11#41311yescharacteristic
147C22×C11#41311yescharacteristic
148C22×C11C2×#10411yescharacteristic
149C22×C11#42111yescharacteristic
150C22×C11#42111yescharacteristic
151C22×C11#42111yescharacteristic
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—22no—
155C4×C11—22no—
156C4×C11—22no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—81no—
161C4×C11—81no—
162C4×C11—81no—
163C4×C11—81no—
164C22×C8—222no—
165C22×C8—222no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4C2×Dic1111yescharacteristic
171C2×C4⋊C4C2×Dic1111yescharacteristic
172C2×C4⋊C4C2×Dic1111yescharacteristic
173C2×C4⋊C4C2×Dic1111yescharacteristic
174C2×C42C2×Dic1111yescharacteristic
175C2×C42C2×Dic1111yescharacteristic
176C2×C42C22⋊D1111yescharacteristic
177C2×C42C22⋊D1111yescharacteristic
178C2×C42C22⋊D1111yescharacteristic
179C2×C42C22⋊D1111yescharacteristic
180C2×C42C22×D1111yescharacteristic
181C4⋊C8—224no—
182#97—114no—
183#97—222no—
184#97—224no—
185#95—21no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192#95—21no—
193C2×C11#152911yescharacteristic
194C2×C11#153211yescharacteristic
195C2×C11#153511yescharacteristic
196C2×C11#153511yescharacteristic
197C2×C11#198611yescharacteristic
198C2×C11#199511yescharacteristic
199C2×C11#199811yescharacteristic
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4C22⋊Dic1111yescharacteristic
205C22×C4C22⋊Dic1111yescharacteristic
206C22×C4C22⋊Dic1111yescharacteristic
207C22×C4C22⋊Dic1111yescharacteristic
208C22×C4C22×Dic1111yescharacteristic
209C22×C4C2×C22⋊D1111yescharacteristic
210C22×C4C2×C22⋊D1111yescharacteristic
211C2×C8—224no—
212C2×C8—224no—
213C2×C8—442no—
214C2×C8—442no—
215C2×C8—442no—
216C2×C8—442no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C42—22no—
226C42—41no—
227C42—41no—
228C42—41no—
229C42—41no—
230C42—41no—
231C42Q8×D1112yes—
232C42#434312yes—
233C11#989311yescharacteristic, complemented, Sylow
234C23C2×C22⋊Dic1111yescharacteristic
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4#6690112yes—
265C2×C4#6699711yescharacteristic
266C2×C4Q8×Dic1112yes—
267C2×C4#6699912yes—
268C2×C4#6700011yescharacteristic
269C8—444no—
270C8—444no—
271C22#1062284311yescharacteristic
272C22C2×#6690111yescharacteristic
273C22#1062284911yescharacteristic
274C22#1062284911yescharacteristic
275C22#1062284911yescharacteristic
276C22#1062285011yescharacteristic
277C22#1062285011yescharacteristic
278C4—22no—
279C4—22no—
280C4—22no—
281C4—21no—
282C4—21no—
283C4—41no—
284C4—41no—
285C4—41no—
286C4—81no—
287C4—81no—
288C4—81no—
289C4—81no—
290C2#1306722311yescharacteristic
291C2#1306723611yescharacteristic
292C2#1306724711yescharacteristic
293C2#1306724711yescharacteristic
294C2#1306956111yescharacteristic
295C2#1306959811yescharacteristic
296C2#1306961011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2864C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2864D11
hypocenterC11#9893
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #2864

Complements

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

NH ≅ G/Ntype
233. C11#9893semidirect

Maximal subgroups

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

subgroupindex
#130684692
#130683652
#130664972
C11×#28642
#989311