Finite Group Databasebeta

← #14653860

Subgroups — #14653860

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076968C211yesmaximal, characteristic
2#13066843C211yesmaximal, characteristic
3#13066496C214yesmaximal
4C11×#1749C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C2×#66977—21no—
7C2×#66922C411yescharacteristic, complemented
8C2×C11×C22⋊C8C2212yes—
9C2×C11×#97—21no—
10#10622825—21no—
11#10622825C2212yes—
12C2×C11⋊#95—21no—
13C2×C11⋊#95—21no—
14C2×C11⋊#95C2212yes—
15#10622548C411yescharacteristic, complemented
16#10622542—21no—
17#10622541—21no—
18#10622541C412yescomplemented
19C11×#336—21no—
20C23×C4×C11D411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11C2311yescharacteristic
23C23×Dic11—22no—
24C22×Dic22—21no—
25C22×C8×C11—22no—
26C2×C42×C11—42no—
27C2×C42×C11C2×C411yescharacteristic
28C2×C42×C11C2×C411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C22⋊Dic11—22no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11C2×C412yes—
36C2×C4⋊Dic11C2×C412yes—
37#66977—44no—
38C2×Dic11⋊C4—22no—
39#66922—42no—
40C11×C22⋊C8—22no—
41C11×C22⋊C8Q814yescomplemented
42C11×#97—42no—
43C11⋊#95—24no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—24no—
47C11⋊#95—42no—
48#9889—111nomaximal, Sylow
49C24×C11C2×D411yescharacteristic
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×Q812yes—
65C22×C4×C11#4112yes—
66C22×Dic11—24no—
67C22×Dic11—22no—
68C22×Dic11—22no—
69C22×Dic11—42no—
70C22×Dic11—42no—
71C22×Dic11—42no—
72C22×Dic11—42no—
73C22×Dic11—42no—
74C22×Dic11—42no—
75C2×Dic22—42no—
76C2×Dic22—42no—
77C2×Dic22—42no—
78C2×C8×C11—24no—
79C2×C8×C11—42no—
80C2×C8×C11—42no—
81C42×C11—22no—
82C42×C11—22no—
83C42×C11—41no—
84C42×C11—41no—
85C22⋊Dic11—44no—
86C4⋊Dic11—42no—
87C4⋊Dic11—42no—
88C4⋊Dic11—42no—
89C4⋊Dic11—42no—
90C4⋊Dic11—42no—
91Dic11⋊C4—44no—
92#2857—111no—
93#1749D1111yescharacteristic
94#1434—111no—
95#1294—114no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11C2×C22⋊C411yescharacteristic
101C23×C11#12411yescharacteristic
102C23×C11C4⋊Q811yescharacteristic
103C23×C11AGL(1,ℤ/8)12yes—
104C23×C11#13712yes—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—44no—
122C2×C4×C11—44no—
123C2×C4×C11#9912yes—
124C2×C4×C11#10412yes—
125C2×C4×C11C4×Q812yes—
126C2×C4×C11C22⋊Q812yes—
127C2×Dic11—44no—
128C2×Dic11—44no—
129C2×Dic11—44no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136C2×Dic11—82no—
137C2×Dic11—82no—
138C2×Dic11—82no—
139C2×Dic11—82no—
140Dic22—84no—
141C8×C11—44no—
142C2×C4⋊Q8—111no—
143C2×C22⋊Q8—221no—
144C22×C42C2×D1111yescharacteristic
145C2×C22⋊C8C2×D1112yes—
146C2×#97—21no—
147#391—221no—
148#389—112no—
149#389—221no—
150#384—111no—
151#380—112no—
152#380—221no—
153C2×#95—112no—
154C2×#95—221no—
155C2×#95—221no—
156#336—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—22no—
162C22×C11—22no—
163C22×C11—22no—
164C22×C11—22no—
165C22×C11#39111yescharacteristic
166C22×C11C2×#9911yescharacteristic
167C22×C11#41011yescharacteristic
168C22×C11#41811yescharacteristic
169C22×C11#41911yescharacteristic
170C22×C11C2×#10411yescharacteristic
171C22×C11#42111yescharacteristic
172C22×C11#48912yes—
173C22×C11#50112yes—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—22no—
177C4×C11—22no—
178C4×C11—41no—
179C4×C11—41no—
180Dic11—84no—
181Dic11—82no—
182Dic11—82no—
183C22×Q8—221no—
184C23×C4—222no—
185C23×C4D4411yescharacteristic
186C23×C4D4411yescharacteristic
187C23×C4C22×D1111yescharacteristic
188C22×C8—22no—
189C4⋊Q8—442no—
190C22⋊Q8—444no—
191C2×C4⋊C4—112no—
192C2×C4⋊C4—112no—
193C2×C4⋊C4—221no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C22⋊C4—222no—
198C2×C42—42no—
199C2×C42C4×D1111yescharacteristic
200C2×C42C4×D1111yescharacteristic
201C2×C42C22⋊D1111yescharacteristic
202C2×C42C22⋊D1111yescharacteristic
203C22⋊C8—22no—
204C22⋊C8Dic2214yescomplemented
205#97—42no—
206#95—224no—
207#95—222no—
208#95—222no—
209#95—224no—
210#95—442no—
211C2×C11—22no—
212C2×C11—22no—
213C2×C11#150511yescharacteristic
214C2×C11#150811yescharacteristic
215C2×C11#151011yescharacteristic
216C2×C11#151511yescharacteristic
217C2×C11#198611yescharacteristic
218C2×C11#199311yescharacteristic
219C2×C11#199611yescharacteristic
220C24C2×D4411yescharacteristic
221C2×Q8—442no—
222C2×Q8—442no—
223C2×Q8—442no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—224no—
233C22×C4—222no—
234C22×C4—222no—
235C22×C4—442no—
236C22×C4—442no—
237C22×C4—442no—
238C22×C4—442no—
239C22×C4—442no—
240C22×C4—442no—
241C22×C4(C2×D11)⋊C411yescharacteristic
242C22×C4(C2×D11)⋊C411yescharacteristic
243C22×C4(C2×D11)⋊C411yescharacteristic
244C22×C4(C2×D11)⋊C411yescharacteristic
245C22×C4C2×Dic2212yes—
246C22×C4C2×C4×D1111yescharacteristic
247C22×C4#433912yes—
248C22×C4C2×C22⋊D1111yescharacteristic
249C2×C8—24no—
250C2×C8—42no—
251C2×C8—42no—
252C4⋊C4—442no—
253C4⋊C4—442no—
254C4⋊C4—444no—
255C4⋊C4—442no—
256C4⋊C4—442no—
257C4⋊C4—442no—
258C22⋊C4—444no—
259C42—22no—
260C42—22no—
261C42—41no—
262C42—41no—
263C11#988911yescharacteristic, complemented, Sylow
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#6692211yescharacteristic
269C23#6692811yescharacteristic
270C23#6696112yes—
271C23#6696212yes—
272C23C2×(C2×D11)⋊C411yescharacteristic
273Q8—884no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—444no—
293C2×C4—444no—
294C2×C4—444no—
295C2×C4—442no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4—882no—
302C2×C4—882no—
303C2×C4—882no—
304C2×C4—882no—
305C2×C4#6687012yes—
306C2×C4#6688912yes—
307C2×C4C4×Dic2212yes—
308C2×C4#6697712yes—
309C8—44no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—21no—
317C22—21no—
318C22#1062231512yes—
319C22#1062232712yes—
320C22#1062254211yescharacteristic
321C22C2×#6687011yescharacteristic
322C22#1062261911yescharacteristic
323C22#1062273311yescharacteristic
324C22#1062274411yescharacteristic
325C22C2×#6688911yescharacteristic
326C22#1062275211yescharacteristic
327C4—22no—
328C4—22no—
329C4—22no—
330C4—22no—
331C4—41no—
332C4—41no—
333C4—884no—
334C4—882no—
335C4—882no—
336C2—22no—
337C2—22no—
338C2#1306712511yescharacteristic
339C2#1306713711yescharacteristic
340C2#1306714611yescharacteristic
341C2#1306716811yescharacteristic
342C2#1306956011yescharacteristic
343C2#1306958911yescharacteristic
344C2#1306960111yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1749C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1749D11
hypocenterC11#9889
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
7. C2×#66922C4semidirect
15. #10622548C4semidirect
18. #10622541C4semidirect
41. C11×C22⋊C8Q8semidirect
204. C22⋊C8Dic22semidirect
263. C11#9889semidirect

Maximal subgroups

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

subgroupindex
#130769682
#130668432
#130664962
C11×#17492
#988911