Finite Group Databasebeta

← #14913822

Subgroups — #14913822

Order 2816.

2446 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
1C22×#66930C211yesmaximal, characteristic
2#13071470C2116yesmaximal, complemented
3#13071228C212yesmaximal
4#13071216C214yesmaximal, complemented
5#13071010C214yesmaximal, complemented
6C2×#10622556C212yesmaximal
7#13070969C211yesmaximal, characteristic
8C11×#2273C211yesmaximal, characteristic
9C24×Dic11C2211yescharacteristic
10C22×C11×C22⋊C4C2212yes—
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic11C2212yes—
13C22×C22⋊Dic11C2211yescharacteristic
14C22×Dic11⋊C4C2212yes—
15C22×C4×Dic11C2212yes—
16C2×#66930C4116yescomplemented
17C2×#66930C2218yes—
18C4×C11×C22⋊C4C2218yes—
19C4×C11×C22⋊C4C2214yes—
20#10622823C2218yes—
21C4×C22⋊Dic11C2214yes—
22C2×C11⋊#95C2218yes—
23#10622559C2218yes—
24#10622556C2218yes—
25#10622556C2214yes—
26#10622556C2214yes—
27#10622555C2218yes—
28C22⋊C4×Dic11C2218yes—
29#10622546C22116yescomplemented
30#10622545C2218yescomplemented
31C4×Dic11⋊C4C2218yescomplemented
32#10622265C22116yescomplemented
33#10622264C2218yescomplemented
34#10622263C2218yescomplemented
35C25×C11C2311yescharacteristic
36C23×C4×C11C2314yes—
37C23×C4×C11C2312yes—
38C23×Dic11—28no—
39C23×Dic11C2×C418yes—
40C23×Dic11C2314yes—
41C23×Dic11C2311yescharacteristic
42C23×Dic11C2311yescharacteristic
43C23×Dic11C2314yes—
44C23×Dic11C2312yes—
45C2×C11×C22⋊C4—28no—
46C2×C11×C22⋊C4C2×C418yes—
47C2×C11×C22⋊C4C2314yes—
48C2×C11×C22⋊C4C2314yes—
49C2×C11×C22⋊C4C2314yes—
50C2×C42×C11C2318yes—
51C2×C22⋊Dic11—28no—
52C2×C22⋊Dic11C2×C418yes—
53C2×C22⋊Dic11C2314yes—
54C2×C22⋊Dic11C2314yes—
55C2×C22⋊Dic11C2314yes—
56C2×Dic11⋊C4C2×C4116yescomplemented
57C2×Dic11⋊C4C23116yes—
58C2×Dic11⋊C4C2318yes—
59C2×C4×Dic11C2×C4116yescomplemented
60C2×C4×Dic11C2318yes—
61C2×C4×Dic11C2314yes—
62C2×C4×Dic11C2314yes—
63#66930C2×C4164yescomplemented
64C11×#95C2318yes—
65C11⋊#95C23116yes—
66C11⋊#95C2318yes—
67C11⋊#95C23116yes—
68C11⋊#95C23116yes—
69#34177—111nomaximal, Sylow
70C24×C11—44no—
71C24×C11C22×C414yes—
72C24×C11#4118yes—
73C24×C11C2412yes—
74C24×C11C2411yescharacteristic
75C22×C4×C11—28no—
76C22×C4×C11—44no—
77C22×C4×C11—48no—
78C22×C4×C11C22×C418yes—
79C22×C4×C11C2418yes—
80C22×C4×C11C2414yes—
81C22×Dic11—232no—
82C22×Dic11—24no—
83C22×Dic11—24no—
84C22×Dic11—28no—
85C22×Dic11—28no—
86C22×Dic11—28no—
87C22×Dic11—44no—
88C22×Dic11—48no—
89C22×Dic11C22×C4116yes—
90C22×Dic11C22×C414yes—
91C22×Dic11C22×C414yes—
92C22×Dic11C22×C418yes—
93C22×Dic11C2418yes—
94C22×Dic11C2412yes—
95C22×Dic11C2412yes—
96C22×Dic11C2414yes—
97C11×C22⋊C4—28no—
98C11×C22⋊C4—28no—
99C11×C22⋊C4C22×C4116yes—
100C42×C11—48no—
101C22⋊Dic11—28no—
102C22⋊Dic11—28no—
103C22⋊Dic11C22×C4116yes—
104Dic11⋊C4—416no—
105Dic11⋊C4C22×C4132yes—
106C4×Dic11—48no—
107C4×Dic11C22×C4116yes—
108C4×Dic11C22×C4116yes—
109C22×#117—111no—
110#2343—1116no—
111#2315—112no—
112#2313—114no—
113#2283—114no—
114C2×#381—112no—
115#2273—111no—
116#2273D1111yescharacteristic
117C23×C11—24no—
118C23×C11—28no—
119C23×C11—48no—
120C23×C11—416no—
121C23×C11#117116yes—
122C23×C11C23×C414yes—
123C23×C11C23×C412yes—
124C23×C11C2×#4114yes—
125C23×C11C2×#4114yes—
126C23×C11C2×#4114yes—
127C23×C11C2511yescharacteristic
128C2×C4×C11—28no—
129C2×C4×C11—28no—
130C2×C4×C11—216no—
131C2×C4×C11—48no—
132C2×C4×C11—88no—
133C2×C4×C11C23×C418yes—
134C2×Dic11—232no—
135C2×Dic11—28no—
136C2×Dic11—28no—
137C2×Dic11—24no—
138C2×Dic11—24no—
139C2×Dic11—28no—
140C2×Dic11—28no—
141C2×Dic11—216no—
142C2×Dic11—48no—
143C2×Dic11—88no—
144C2×Dic11C23×C414yes—
145C2×Dic11C23×C418yes—
146C2×Dic11C23×C414yes—
147C24×C4—111no—
148C2×#117—118no—
149C2×#117—1116no—
150C22×C4⋊C4—112no—
151C22×C22⋊C4—111no—
152C22×C22⋊C4—112no—
153C22×C22⋊C4C2×D1112yes—
154C22×C22⋊C4C2×D1111yescharacteristic
155C22×C42—112no—
156#387—1116no—
157#387—1116no—
158#385—118no—
159#385—118no—
160#383—118no—
161#382—118no—
162#381—114no—
163#381—118no—
164#381—114no—
165#380—118no—
166C4×C4⋊C4—118no—
167C4×C22⋊C4—114no—
168C4×C22⋊C4—118no—
169C4×C22⋊C4C2×D1114yes—
170C4×C22⋊C4C2×D1118yes—
171#376—118no—
172C2×#95—118no—
173C22×C11—24no—
174C22×C11—28no—
175C22×C11—28no—
176C22×C11—28no—
177C22×C11—28no—
178C22×C11—416no—
179C22×C11C2×#11718yes—
180C22×C11C2×#11714yes—
181C22×C11C24×C411yescharacteristic
182C22×C11C22×#4112yes—
183C22×C11#58514yes—
184C4×C11—28no—
185C4×C11—48no—
186Dic11—24no—
187Dic11—24no—
188Dic11—28no—
189Dic11—48no—
190C25C22×D1111yescharacteristic
191C23×C4—118no—
192C23×C4—111no—
193C23×C4—114no—
194C23×C4—111no—
195C23×C4—112no—
196C23×C4—114no—
197C23×C4—228no—
198C23×C4C22×D1114yes—
199C23×C4C22×D1112yes—
200#117—1164no—
201C2×C4⋊C4—1116no—
202C2×C4⋊C4—118no—
203C2×C4⋊C4—1116no—
204C2×C22⋊C4—28no—
205C2×C22⋊C4—118no—
206C2×C22⋊C4—114no—
207C2×C22⋊C4—114no—
208C2×C22⋊C4—114no—
209C2×C22⋊C4—228no—
210C2×C22⋊C4C4×D1118yes—
211C2×C22⋊C4C22×D1114yes—
212C2×C22⋊C4C22×D1114yes—
213C2×C22⋊C4C22×D1114yes—
214C2×C42—1116no—
215C2×C42—114no—
216C2×C42—114no—
217C2×C42—118no—
218C2×C42C22×D1118yes—
219#95—1116no—
220#95—1116no—
221#95—1116no—
222#95—118no—
223#95C22×D1118yes—
224C2×C11—24no—
225C2×C11—28no—
226C2×C11C22×#11711yescharacteristic
227C2×C11#342812yes—
228C2×C11#349114yes—
229C24—44no—
230C24C2×C4×D1114yes—
231C24#433918yes—
232C24C23×D1112yes—
233C24C23×D1111yescharacteristic
234C22×C4—28no—
235C22×C4—44no—
236C22×C4—48no—
237C22×C4—114no—
238C22×C4—114no—
239C22×C4—1116no—
240C22×C4—112no—
241C22×C4—112no—
242C22×C4—114no—
243C22×C4—118no—
244C22×C4—118no—
245C22×C4—2232no—
246C22×C4—224no—
247C22×C4—224no—
248C22×C4—228no—
249C22×C4—228no—
250C22×C4—228no—
251C22×C4—444no—
252C22×C4—448no—
253C22×C4C2×C4×D1118yes—
254C22×C4C23×D1118yes—
255C22×C4C23×D1114yes—
256C4⋊C4—1132no—
257C4⋊C4—4416no—
258C22⋊C4—28no—
259C22⋊C4—28no—
260C22⋊C4—1116no—
261C22⋊C4—228no—
262C22⋊C4—228no—
263C22⋊C4C2×C4×D11116yes—
264C42—48no—
265C42—1116no—
266C42—1116no—
267C42—448no—
268C11#3417711yescharacteristic, complemented, Sylow
269C23—28no—
270C23—24no—
271C23—48no—
272C23—416no—
273C23#66925116yes—
274C23C22×C4×D1114yes—
275C23C22×C4×D1112yes—
276C23C2×#433914yes—
277C23C2×#433914yes—
278C23C2×#433914yes—
279C23C24×D1111yescharacteristic
280C2×C4—28no—
281C2×C4—28no—
282C2×C4—216no—
283C2×C4—48no—
284C2×C4—88no—
285C2×C4—114no—
286C2×C4—118no—
287C2×C4—114no—
288C2×C4—228no—
289C2×C4—228no—
290C2×C4—2232no—
291C2×C4—224no—
292C2×C4—224no—
293C2×C4—228no—
294C2×C4—228no—
295C2×C4—2216no—
296C2×C4—448no—
297C2×C4—888no—
298C2×C4C22×C4×D1118yes—
299C22—28no—
300C22—28no—
301C22—28no—
302C22—24no—
303C22—28no—
304C22—416no—
305C22C2×#6692518yes—
306C22C2×#6692514yes—
307C22C23×C4×D1111yescharacteristic
308C22C22×#433912yes—
309C22#1062345514yes—
310C4—28no—
311C4—48no—
312C4—224no—
313C4—224no—
314C4—228no—
315C4—448no—
316C2—28no—
317C2—24no—
318C2C22×#6692511yescharacteristic
319C2#1308181412yes—
320C2#1308230914yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2273C2
socle, cosocleC23×C11C25
prime radicalC25×C11C23
hypercenter#2273D11
hypocenterC11#34177
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2273

Complements

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

NH ≅ G/Ntype
2. #13071470C2semidirect
4. #13071216C2semidirect
5. #13071010C2semidirect
16. C2×#66930C4semidirect
29. #10622546C22semidirect
30. #10622545C22semidirect
31. C4×Dic11⋊C4C22semidirect
32. #10622265C22semidirect
33. #10622264C22semidirect
34. #10622263C22semidirect
56. C2×Dic11⋊C4C2×C4semidirect
59. C2×C4×Dic11C2×C4semidirect
63. #66930C2×C4semidirect
268. C11#34177semidirect

Maximal subgroups

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

subgroupindex
C22×#669302
#130714702
#130712282
#130712162
#130710102
C2×#106225562
#130709692
C11×#22732
#3417711