Finite Group Databasebeta

← #14909754

Subgroups — #14909754

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079202C211yesmaximal, characteristic, complemented
2#13070888C212yesmaximal, complemented
3#13070852C212yesmaximal, complemented
4#13070675C214yesmaximal, complemented
5#13070550C212yesmaximal, complemented
6#13070545C212yesmaximal
7#13070419C211yesmaximal, characteristic, complemented
8C2×C11×#495C211yesmaximal, characteristic
9C22×C11×Q16C2211yescharacteristic
10C22×C11×SD16—21no—
11C22×C11×D8C2211yescharacteristic
12C2×C11×#124—21no—
13#10623001—21no—
14C11×#495—21no—
15C11×#495—21no—
16C11×#495C2212yes—
17C11×#495C2212yes—
18C2×C4×C8×C11C2211yescharacteristic
19C2×#66893C2214yescomplemented
20C2×#66891C2214yes—
21#10622729—21no—
22#10622729C2212yes—
23#10622312C2211yescharacteristic, complemented
24C4×Dic44—21no—
25C4×Dic44C2212yescomplemented
26#10622295C2211yescharacteristic, complemented
27#10622294—21no—
28#10622202C2214yescomplemented
29#10622200C2214yes—
30C22⋊(C11⋊C16)C2212yes—
31C4⋊(C11⋊C16)C2212yescomplemented
32#10622099C2212yescomplemented
33C22×Q8×C11—21no—
34C22×D4×C11—21no—
35C2×C11×Q16—21no—
36C2×C11×Q16—42no—
37C2×C11×Q16C2312yes—
38C2×C11×SD16—22no—
39C2×C11×SD16—22no—
40C2×C11×SD16—44no—
41C2×C11×D8—21no—
42C2×C11×D8—42no—
43C2×C11×D8C2312yes—
44C22×C8×C11D411yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C11×#124—22no—
47C11×#124—22no—
48C11×#124—41no—
49C11×#124—41no—
50C2×C11×C22⋊C4—41no—
51C2×C11×C22⋊C4—41no—
52C2×C42×C11D411yescharacteristic
53#66979—41no—
54#66977—22no—
55#66977—41no—
56C2×Dic44—21no—
57C2×Dic44C2312yes—
58#66923—41no—
59#66922—21no—
60#66922—21no—
61C4×Dic22—22no—
62C4×Dic22—41no—
63C4×C8×C11D411yescharacteristic
64C4×C8×C11D411yescharacteristic
65C4×C8×C11C2311yescharacteristic
66C4×C8×C11C2311yescharacteristic
67#66893—44no—
68#66891—44no—
69#66882—21no—
70#66882C2312yes—
71#66880—22no—
72#66880—22no—
73C2×C11⋊C16C2314yes—
74#33781—111nomaximal, Sylow
75C24×C11—41no—
76C2×Q8×C11—22no—
77C2×Q8×C11—42no—
78C2×Q8×C11—42no—
79C2×Q8×C11—41no—
80C2×D4×C11—22no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11D811yescharacteristic
86C22×C4×C11D811yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C2×Dic22—22no—
89C2×Dic22—41no—
90C11×Q16—24no—
91C11×Q16—42no—
92C11×SD16—44no—
93C11×SD16—44no—
94C11×D8—24no—
95C11×D8—42no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2411yescharacteristic
102C11×C22⋊C4—42no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—42no—
105C11×C22⋊C4—42no—
106C42×C11D811yescharacteristic
107C42×C11D811yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C22⋊Dic11—42no—
111C4⋊Dic11—22no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115Dic11⋊C4—42no—
116Dic11⋊C4—42no—
117C4×Dic11—42no—
118Dic44—24no—
119Dic44—42no—
120C11⋊C16—24no—
121#3170—111no—
122C2×#495D1111yescharacteristic
123#2251—112no—
124#2243—112no—
125#2211—114no—
126#2188—112no—
127#2187—112no—
128#2163—111no—
129C23×C11—42no—
130C23×C11—82no—
131C23×C11—82no—
132C23×C11—82no—
133C23×C11C2×D811yescharacteristic
134Q8×C11—42no—
135Q8×C11—42no—
136Q8×C11—82no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—82no—
140C2×C4×C11—22no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—82no—
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C22×D411yescharacteristic
152C2×Dic11—42no—
153C2×Dic11—42no—
154Dic22—42no—
155Dic22—42no—
156Dic22—82no—
157C8×C11—21no—
158C8×C11—21no—
159C8×C11AGL(1,ℤ/8)12yes—
160C8×C11H(5,𝔽2)12yes—
161C22×Q16C2×D1111yescharacteristic
162C22×SD16—21no—
163C22×D8C2×D1111yescharacteristic
164#533—221no—
165C2×#124—21no—
166C2×Q32—114no—
167C2×SD32—114no—
168#500—111no—
169#495—21no—
170#495—21no—
171#495C2×D1112yes—
172#495C2×D1112yes—
173#494—111no—
174#487—221no—
175#467—112no—
176#467—221no—
177C4×Q16—112no—
178C4×Q16—221no—
179C2×C4×C8C2×D1111yescharacteristic
180C4⋊C16—112no—
181#358—114no—
182#357—114no—
183C22⋊C16—112no—
184#346—112no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—82no—
188C22×C11—82no—
189C22×C11—82no—
190C22×C11—164no—
191C22×C11#51012yes—
192C22×C11C22×D811yescharacteristic
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—82no—
199C4×C11#53511yescharacteristic
200C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
201Dic11—82no—
202Dic11—82no—
203C22×Q8—21no—
204C22×D4—21no—
205C2×Q16—21no—
206C2×Q16—42no—
207C2×Q16—112no—
208C2×Q16—221no—
209C2×Q16C22×D1112yes—
210C2×SD16—22no—
211C2×SD16—22no—
212C2×SD16—44no—
213C2×D8—21no—
214C2×D8—42no—
215C2×D8C22×D1112yes—
216C22×C8C22⋊D1111yescharacteristic
217C22×C8C22×D1111yescharacteristic
218C4⋊Q8—221no—
219C4⋊Q8—221no—
220#125—441no—
221#124—22no—
222#124—22no—
223#124—41no—
224#124—41no—
225C22⋊Q8—222no—
226C22⋊Q8—441no—
227C4×Q8—222no—
228C4×Q8—441no—
229#117—441no—
230C2×C22⋊C4—41no—
231C2×C22⋊C4—41no—
232C2×C42C22⋊D1111yescharacteristic
233Q32—444no—
234SD32—444no—
235C2×C16—114no—
236#107—112no—
237#107—221no—
238#103—222no—
239#103—222no—
240C4×C8C22⋊D1111yescharacteristic
241C4×C8C22⋊D1111yescharacteristic
242C4×C8C22×D1111yescharacteristic
243C4×C8C22×D1111yescharacteristic
244C2×C11—22no—
245C2×C11—162no—
246C2×C11#320511yescharacteristic
247C2×C11C2×#51011yescharacteristic
248C2×C11#341411yescharacteristic
249C24—41no—
250C2×Q8—22no—
251C2×Q8—42no—
252C2×Q8—42no—
253C2×Q8—41no—
254C2×Q8—222no—
255C2×Q8—441no—
256C2×D4—22no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—41no—
260C22×C4—41no—
261C22×C4#432311yescharacteristic
262C22×C4#432311yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264Q16—24no—
265Q16—42no—
266Q16—224no—
267Q16—442no—
268SD16—44no—
269SD16—44no—
270D8—24no—
271D8—42no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8C2×C22⋊D1111yescharacteristic
275C2×C8C2×C22⋊D1111yescharacteristic
276C2×C8C2×C22⋊D1111yescharacteristic
277C2×C8C23×D1111yescharacteristic
278C4⋊C4—222no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—442no—
282C4⋊C4—442no—
283C4⋊C4—441no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—442no—
289C42—442no—
290C42#432311yescharacteristic
291C42#432311yescharacteristic
292C42C2×C22⋊D1111yescharacteristic
293C42C2×C22⋊D1111yescharacteristic
294C16—224no—
295C11#3378111yescharacteristic, complemented, Sylow
296C23—42no—
297C23—82no—
298C23—82no—
299C23—82no—
300C23C2×#432311yescharacteristic
301Q8—42no—
302Q8—42no—
303Q8—82no—
304Q8—442no—
305Q8—442no—
306Q8—882no—
307D4—42no—
308D4—42no—
309D4—82no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—82no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4C2×#432311yescharacteristic
319C2×C4C2×#432311yescharacteristic
320C2×C4C2×#432311yescharacteristic
321C2×C4C2×#432311yescharacteristic
322C2×C4C2×#432311yescharacteristic
323C2×C4C22×C22⋊D1111yescharacteristic
324C8—21no—
325C8—21no—
326C8#6698512yes—
327C8#6703712yes—
328C22—21no—
329C22—21no—
330C22—82no—
331C22—82no—
332C22—82no—
333C22—164no—
334C22#1062280812yes—
335C22C22×#432311yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—82no—
342C4—882no—
343C4—882no—
344C4C2×#6698511yescharacteristic
345C4#1062333611yescharacteristic
346C2—22no—
347C2—162no—
348C2#1307953411yescharacteristic
349C2C2×#1062280811yescharacteristic
350C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#495C2
socleC22×C11C22×D8
prime radicalC22×C11×D8C22
hypercenterC2×#495D11
hypocenterC11#33781
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. #13079202C2semidirect
2. #13070888C2semidirect
3. #13070852C2semidirect
4. #13070675C2semidirect
5. #13070550C2semidirect
7. #13070419C2semidirect
19. C2×#66893C22semidirect
23. #10622312C22semidirect
25. C4×Dic44C22semidirect
26. #10622295C22semidirect
28. #10622202C22semidirect
31. C4⋊(C11⋊C16)C22semidirect
32. #10622099C22semidirect
295. C11#33781semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130708882
#130708522
#130706752
#130705502
#130705452
#130704192
C2×C11×#4952
#3378111