Finite Group Databasebeta

← #14642272

Subgroups — #14642272

Order 2816.

530 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076926C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic
3#13066440C212yesmaximal, complemented
4#13066438C212yesmaximal, complemented
5C2×C11×#336C211yesmaximal, characteristic
6C23×C8×C11—21no—
7C22×C42×C11C2211yescharacteristic
8C2×#66923C411yescharacteristic
9#10622825C411yescharacteristic
10#10622825C411yescharacteristic
11#10622823—21no—
12#10622823—21no—
13C2×C22⋊(C11⋊C8)—21no—
14#10622549C411yescharacteristic
15#10622546—21no—
16#10622546—21no—
17#10622541C2211yescharacteristic
18#10622541C2211yescharacteristic
19C2×#66867—21no—
20C11×#336—21no—
21C11×#336C2212yes—
22#10622162C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C8×C11—24no—
27C22×C8×C11—22no—
28C22×C8×C11—42no—
29C22×C8×C11—42no—
30C2×C42×C11—42no—
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C22×C11⋊C8—22no—
46#66923—42no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C22⋊(C11⋊C8)—24no—
54#66867—42no—
55#7691—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C2×C8×C11—24no—
78C2×C8×C11—48no—
79C2×C8×C11—42no—
80C2×C8×C11—42no—
81C42×C11—22no—
82C42×C11—22no—
83C42×C11—41no—
84C42×C11—41no—
85C22⋊Dic11—42no—
86C22⋊Dic11—42no—
87C4⋊Dic11—22no—
88C4⋊Dic11—22no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91Dic11⋊C4—42no—
92Dic11⋊C4—42no—
93Dic11⋊C4—42no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96C2×C11⋊C8—24no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—42no—
99#2851—111no—
100#1749—111no—
101C2×#336D1111yescharacteristic
102#1271—112no—
103#1271—112no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11#10112yes—
109C23×C11#10412yes—
110C23×C11#10412yes—
111C23×C11C2×C22⋊C411yescharacteristic
112C2×C4×C11—24no—
113C2×C4×C11—24no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—44no—
129C2×C4×C11—44no—
130C2×C4×C11#9912yes—
131C2×C4×C11#13112yes—
132C2×C4×C11#13512yes—
133C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C8×C11—44no—
148C11⋊C8—44no—
149C23×C8—21no—
150C2×#125—111no—
151C22×C42C2×D1111yescharacteristic
152C2×C22⋊C8—221no—
153C2×#97—221no—
154#389—111no—
155#389—111no—
156#387—221no—
157#387—221no—
158#385—221no—
159#385—221no—
160#382—111no—
161#380—111no—
162#380—111no—
163#336—21no—
164#336—112no—
165#336C2×D1112yes—
166C22×C11—22no—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11—22no—
170C22×C11—22no—
171C22×C11—22no—
172C22×C11#33014yes—
173C22×C11#40811yescharacteristic
174C22×C11C2×#9911yescharacteristic
175C22×C11C2×#10111yescharacteristic
176C22×C11#41611yescharacteristic
177C22×C11#41711yescharacteristic
178C22×C11C2×#10411yescharacteristic
179C22×C11C2×#10411yescharacteristic
180C4×C11—22no—
181C4×C11—22no—
182C4×C11—22no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—41no—
186C4×C11—41no—
187Dic11—81no—
188Dic11—81no—
189Dic11—81no—
190Dic11—81no—
191C23×C4C4×D1111yescharacteristic
192C23×C4D4411yescharacteristic
193C23×C4C22⋊D1111yescharacteristic
194C22×C8—24no—
195C22×C8—22no—
196C22×C8—42no—
197C22×C8—42no—
198C22×C8—222no—
199#125—442no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210C2×C42—42no—
211C2×C42C4×D1111yescharacteristic
212C2×C42D4411yescharacteristic
213C2×C42C22⋊D1111yescharacteristic
214C2×C42C22×D1111yescharacteristic
215C22⋊C8—224no—
216#97—442no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223C2×C11—24no—
224C2×C11#147211yescharacteristic
225C2×C11#148311yescharacteristic
226C2×C11#149411yescharacteristic
227C2×C11#150111yescharacteristic
228C2×C11#150411yescharacteristic
229C2×C11C2×#33011yescharacteristic
230C2×C11#155211yescharacteristic
231C24(C2×D11)⋊C411yescharacteristic
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4(C2×D11)⋊C411yescharacteristic
247C22×C4(C2×D11)⋊C411yescharacteristic
248C22×C4(C2×D11)⋊C411yescharacteristic
249C22×C4C2×C4×D1111yescharacteristic
250C22×C4C2×D4411yescharacteristic
251C22×C4C2×C22⋊D1111yescharacteristic
252C2×C8—24no—
253C2×C8—48no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—224no—
257C2×C8—442no—
258C2×C8—442no—
259C4⋊C4—222no—
260C4⋊C4—222no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—442no—
264C4⋊C4—442no—
265C4⋊C4—442no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C22⋊C4—442no—
269C22⋊C4—442no—
270C42—22no—
271C42—22no—
272C42—41no—
273C42—41no—
274C11#769111yescharacteristic, complemented, Sylow
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23#6686912yes—
280C23#6688812yes—
281C23#6688912yes—
282C23C2×(C2×D11)⋊C411yescharacteristic
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4#6687012yes—
314C2×C4#6695412yes—
315C2×C4#6695712yes—
316C2×C4#6698511yescharacteristic
317C2×C4#6699511yescharacteristic
318C8—44no—
319C8—444no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22#1062210314yes—
327C22C2×#6686911yescharacteristic
328C22C2×#6687011yescharacteristic
329C22#1062257911yescharacteristic
330C22#1062272311yescharacteristic
331C22#1062272611yescharacteristic
332C22C2×#6688811yescharacteristic
333C22C2×#6688911yescharacteristic
334C4—22no—
335C4—21no—
336C4—22no—
337C4—21no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—881no—
342C4—881no—
343C4—881no—
344C4—881no—
345C2—24no—
346C2#1306697911yescharacteristic
347C2#1306702711yescharacteristic
348C2#1306707711yescharacteristic
349C2#1306710811yescharacteristic
350C2#1306711811yescharacteristic
351C2C2×#1062210311yescharacteristic
352C2#1306731411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#336C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#336D11
hypocenterC11#7691
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. #13066440C2semidirect
4. #13066438C2semidirect
274. C11#7691semidirect

Maximal subgroups

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

subgroupindex
#130769262
#130683782
#130664402
#130664382
C2×C11×#3362
#769111