Finite Group Databasebeta

← #14909887

Subgroups — #14909887

Order 2816.

504 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079195C211yesmaximal, characteristic
2#13070896C211yesmaximal, characteristic, complemented
3#13070889C211yesmaximal, characteristic, complemented
4#13070841C211yesmaximal, characteristic, complemented
5#13070841C211yesmaximal, characteristic, complemented
6#13070807C214yesmaximal, complemented
7#13070770C214yesmaximal, complemented
8#13070415C211yesmaximal, characteristic, complemented
9C11×#3160C211yesmaximal, characteristic, complemented
10C11×#533—21no—
11#10623008—21no—
12C11×#500C2211yescharacteristic
13C11×#500C2211yescharacteristic
14C11×#499—21no—
15C11×#499C2212yes—
16C11×#498—21no—
17C11×#427—21no—
18C11×#427C2212yes—
19C2×C4×C8×C11C2211yescharacteristic
20#10622728—21no—
21#10622728C2212yes—
22#10622308C2211yescharacteristic
23#10622307—21no—
24C4×D88—21no—
25C4×D88C2212yes—
26#10622295C2211yescharacteristic
27C22⋊(C11⋊C16)C2212yes—
28#10622129C2214yes—
29#10622129C2214yes—
30#10622128C2214yes—
31#10622127C2214yes—
32C4⋊(C11⋊C16)C2212yes—
33C4×C11⋊C16C2211yescharacteristic
34C4×C11⋊C16C2211yescharacteristic
35C2×#4339—41no—
36C22×C8×C11D411yescharacteristic
37C22×C8×C11C2311yescharacteristic
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×#125—22no—
41C11×C22⋊Q8—41no—
42C11×C22⋊Q8—41no—
43C4×Q8×C11—41no—
44C4×Q8×C11—41no—
45C11×#117—22no—
46C2×C42×C11D411yescharacteristic
47#66983—22no—
48#66983—41no—
49C2×D88—21no—
50C2×D88C2312yes—
51#66928—41no—
52#66927—21no—
53C4×D44—22no—
54C4×D44—41no—
55#66922—21no—
56C11×#107—21no—
57C11×#107—21no—
58C11×#107C2312yes—
59C11×#107C2312yes—
60C11×#106—22no—
61C11×#106—22no—
62C4×C8×C11D411yescharacteristic
63C4×C8×C11D411yescharacteristic
64C4×C8×C11C2311yescharacteristic
65C4×C8×C11C2311yescharacteristic
66#66885—22no—
67#66885—22no—
68#66882—21no—
69#66882C2312yes—
70C2×C11⋊C16C2312yes—
71C2×C11⋊C16C2312yes—
72#33794—111nomaximal, Sylow
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C22×C4×C11D811yescharacteristic
76C22×C4×C11D811yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11—42no—
79#4339—84no—
80C2×D44—22no—
81C2×D44—41no—
82C2×D44—41no—
83C2×C4×D11—42no—
84C2×Dic22—41no—
85C2×C8×C11—22no—
86C2×C8×C11—22no—
87C2×C8×C11C2×D411yescharacteristic
88C2×C8×C11C2×D411yescharacteristic
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2411yescharacteristic
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—42no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—42no—
98C42×C11—42no—
99C42×C11D811yescharacteristic
100C42×C11D811yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—42no—
105C4⋊Dic11—22no—
106C4⋊Dic11—41no—
107D88—24no—
108D88—42no—
109C11⋊C16—22no—
110C11⋊C16—22no—
111#3169—111no—
112#3160D1111yescharacteristic, complemented
113#2254—111no—
114#2252—111no—
115#2240—111no—
116#2240—111no—
117#2234—114no—
118#2228—114no—
119#2162—111no—
120C23×C11C2×D811yescharacteristic
121C22×D11—42no—
122Q8×C11—82no—
123Q8×C11—82no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11C2×D811yescharacteristic
131C2×C4×C11C2×D811yescharacteristic
132C2×C4×C11C2×D811yescharacteristic
133C2×C4×C11C2×D811yescharacteristic
134C2×C4×C11C2×D811yescharacteristic
135C2×C4×C11C22×D411yescharacteristic
136C22⋊D11—84no—
137C2×Dic11—42no—
138D44—42no—
139D44—42no—
140D44—82no—
141D44—82no—
142C4×D11—84no—
143Dic22—82no—
144C8×C11—21no—
145C8×C11—21no—
146C8×C11#13712yes—
147C8×C112−1+412yes—
148#533—21no—
149#532—221no—
150#500—111no—
151#500C2×D1111yescharacteristic
152#500C2×D1111yescharacteristic
153#499—21no—
154#499C2×D1112yes—
155#498—21no—
156#493—111no—
157#486—221no—
158#466—112no—
159#466—221no—
160C4×D8—112no—
161C4×D8—221no—
162#427—21no—
163#427C2×D1112yes—
164C2×C4×C8C2×D1111yescharacteristic
165#367—114no—
166#366—114no—
167C4⋊C16—112no—
168#357—114no—
169#357—114no—
170C22⋊C16—112no—
171C4×C16—111no—
172C4×C16—111no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11C22×D811yescharacteristic
177C2×D11—82no—
178C2×D11—82no—
179C2×D11—82no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—82no—
184C4×C11—82no—
185C4×C11#50812yes—
186C4×C11#50912yes—
187C4×C11#53611yescharacteristic
188C4×C11C2×#13711yescharacteristic
189Dic11—82no—
190C2×#41—441no—
191C2×D8—112no—
192C2×D8—221no—
193C22×C8C22⋊D1111yescharacteristic
194C22×C8C22×D1111yescharacteristic
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—221no—
198#127—221no—
199#125—22no—
200#124—441no—
201C22⋊Q8—41no—
202C22⋊Q8—41no—
203#121—222no—
204#121—441no—
205C4×Q8—41no—
206C4×Q8—41no—
207C4×D4—222no—
208C4×D4—441no—
209#117—22no—
210C2×C42C22⋊D1111yescharacteristic
211C2×C16—112no—
212C2×C16—112no—
213#107—21no—
214#107—21no—
215#107—112no—
216#107—221no—
217#107C22×D1112yes—
218#107C22×D1112yes—
219#106—22no—
220#106—22no—
221#102—222no—
222#102—222no—
223C4×C8C22⋊D1111yescharacteristic
224C4×C8C22⋊D1111yescharacteristic
225C4×C8C22×D1111yescharacteristic
226C4×C8C22×D1111yescharacteristic
227C2×C11—41no—
228C2×C11#322611yescharacteristic
229C2×C11C2×#50811yescharacteristic
230C2×C11C2×#50911yescharacteristic
231D11—162no—
232#41—884no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—441no—
236C2×D4—222no—
237C2×D4—442no—
238C2×D4—441no—
239C2×D4—441no—
240C22×C4—442no—
241C22×C4#432311yescharacteristic
242C22×C4#432311yescharacteristic
243C22×C4C2×C22⋊D1111yescharacteristic
244D8—224no—
245D8—442no—
246C2×C8—22no—
247C2×C8—22no—
248C2×C8C2×C22⋊D1111yescharacteristic
249C2×C8C2×C22⋊D1111yescharacteristic
250C2×C8C2×C22⋊D1111yescharacteristic
251C2×C8C23×D1111yescharacteristic
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—222no—
259C4⋊C4—441no—
260C22⋊C4—42no—
261C22⋊C4—442no—
262C22⋊C4—442no—
263C42—42no—
264C42#432311yescharacteristic
265C42#432311yescharacteristic
266C42C2×C22⋊D1111yescharacteristic
267C42C2×C22⋊D1111yescharacteristic
268C16—222no—
269C16—222no—
270C11#3379411yescharacteristic, complemented, Sylow
271C23—442no—
272C23C2×#432311yescharacteristic
273Q8—82no—
274Q8—82no—
275Q8—882no—
276D4—442no—
277D4—442no—
278D4—884no—
279D4—882no—
280D4—882no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—442no—
288C2×C4—884no—
289C2×C4C2×#432311yescharacteristic
290C2×C4C2×#432311yescharacteristic
291C2×C4C2×#432311yescharacteristic
292C2×C4C2×#432311yescharacteristic
293C2×C4C2×#432311yescharacteristic
294C2×C4C22×C22⋊D1111yescharacteristic
295C8—21no—
296C8—21no—
297C8#6699512yes—
298C8#6704012yes—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—882no—
303C22—882no—
304C22—882no—
305C22C22×#432311yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—82no—
310C4—82no—
311C4—882no—
312C4#1062280612yes—
313C4#1062280712yes—
314C4C2×#6699511yescharacteristic
315C4#1062334711yescharacteristic
316C2—41no—
317C2—1762no—
318C2#1307973711yescharacteristic
319C2C2×#1062280711yescharacteristic
320C2C2×#1062280611yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3160C2
socleC22×C11C22×D8
prime radical#13079195C2
hypercenter#3160D11
hypocenterC11#33794
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3160

Complements

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

NH ≅ G/Ntype
2. #13070896C2semidirect
3. #13070889C2semidirect
4. #13070841C2semidirect
5. #13070841C2semidirect
6. #13070807C2semidirect
7. #13070770C2semidirect
8. #13070415C2semidirect
9. C11×#3160C2semidirect
112. #3160D11semidirect
270. C11#33794semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130708962
#130708892
#130708412
#130708072
#130707702
#130704152
C11×#31602
#3379411