Finite Group Databasebeta

← #14913842

Subgroups — #14913842

Order 2816.

2390 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071509C218yesmaximal, complemented
2#13071501C218yesmaximal, complemented
3#13071234C212yesmaximal, complemented
4#13071214C214yesmaximal
5#13071014C214yesmaximal, complemented
6#13070999C212yesmaximal
7#13070973C212yesmaximal, complemented
8C22×C11×#117C211yesmaximal, characteristic
9C24×C4×C11C2211yescharacteristic
10C2×C11×#117C4116yescomplemented
11C2×C11×#117C2214yes—
12C2×C11×#117C2214yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C42×C11C2212yes—
17C2×#66979C2214yes—
18#10622860C2214yes—
19#10622825C2218yes—
20#10622825C2214yes—
21#10622825C2214yes—
22#10622824C2214yes—
23C4×C22⋊Dic11C2218yes—
24C4×C22⋊Dic11C2214yes—
25C4×C22⋊Dic11C2214yes—
26#10622598C22116yescomplemented
27C4⋊C4×Dic11C22116yescomplemented
28#10622564C22132yes—
29#10622550C2218yescomplemented
30#10622549C2218yescomplemented
31C4×C4⋊Dic11C2218yescomplemented
32#10622545C2218yescomplemented
33C25×C11C2311yescharacteristic
34C23×C4×C11—28no—
35C23×C4×C11C2×C418yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C11×#117C2×C4132yes—
43C11×#117C2×C4132yes—
44C2×C11×C4⋊C4C2×C418yes—
45C2×C11×C4⋊C4C2×C418yes—
46C2×C11×C4⋊C4C2314yes—
47C2×C11×C4⋊C4C2314yes—
48C2×C11×C22⋊C4C2×C4116yes—
49C2×C11×C22⋊C4C2318yes—
50C2×C42×C11C2×C4116yes—
51C2×C42×C11C2314yes—
52C2×C42×C11C2314yes—
53C2×C22⋊Dic11C2318yes—
54C2×C22⋊Dic11C2318yes—
55C2×C22⋊Dic11C2318yes—
56#66979—216no—
57C2×C4⋊Dic11C2318yes—
58C2×C4⋊Dic11C23116yes—
59C2×C4×Dic11C2318yes—
60C2×C4×Dic11C23116yes—
61C11⋊#95C2318yes—
62C11⋊#95C23116yes—
63C11⋊#95C2318yes—
64C11⋊#95C23116yes—
65#34179—111nomaximal, Sylow
66C24×C11—24no—
67C24×C11—42no—
68C24×C11—42no—
69C24×C11C22×C414yes—
70C24×C11C2412yes—
71C24×C11C2411yescharacteristic
72C22×C4×C11—24no—
73C22×C4×C11—232no—
74C22×C4×C11—28no—
75C22×C4×C11—28no—
76C22×C4×C11—44no—
77C22×C4×C11—44no—
78C22×C4×C11C22×C414yes—
79C22×C4×C11C22×C418yes—
80C22×C4×C11C22×C418yes—
81C22×C4×C11C22×C418yes—
82C22×C4×C11C22×C418yes—
83C22×C4×C11C22×C414yes—
84C22×C4×C11#4118yes—
85C22×C4×C11C2411yescharacteristic
86C22×C4×C11C2411yescharacteristic
87C22×C4×C11C2414yes—
88C22×C4×C11C2414yes—
89C22×C4×C11C2412yes—
90C22×Dic11C24116yes—
91C11×C4⋊C4C22×C4116yes—
92C11×C4⋊C4C22×C4116yes—
93C11×C22⋊C4C22×C4132yes—
94C42×C11C22×C4116yes—
95C42×C11C22×C4116yes—
96C22⋊Dic11—216no—
97C22⋊Dic11—48no—
98C22⋊Dic11—48no—
99C4⋊Dic11—216no—
100C4⋊Dic11—416no—
101C4×Dic11—216no—
102C4×Dic11—416no—
103C22×#117D1111yescharacteristic
104#2347—118no—
105#2346—118no—
106#2316—112no—
107#2312—114no—
108#2283—114no—
109#2280—112no—
110#2274—112no—
111C23×C11—22no—
112C23×C11—22no—
113C23×C11—28no—
114C23×C11—24no—
115C23×C11—24no—
116C23×C11—24no—
117C23×C11—44no—
118C23×C11—44no—
119C23×C11—416no—
120C23×C11C23×C414yes—
121C23×C11C23×C412yes—
122C23×C11C2×#4114yes—
123C23×C11C2511yescharacteristic
124C2×C4×C11—28no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—28no—
128C2×C4×C11—28no—
129C2×C4×C11—216no—
130C2×C4×C11—216no—
131C2×C4×C11—48no—
132C2×C4×C11—48no—
133C2×C4×C11#117116yes—
134C2×C4×C11C23×C412yes—
135C2×C4×C11C23×C412yes—
136C2×C4×C11C23×C418yes—
137C2×C4×C11C23×C418yes—
138C2×C4×C11C23×C414yes—
139C2×C4×C11C2×#4118yes—
140C2×Dic11—216no—
141C2×Dic11—216no—
142C2×Dic11—216no—
143C24×C4C2×D1111yescharacteristic
144C2×#117—114no—
145C2×#117Dic11116yescomplemented
146C2×#117C2×D1114yes—
147C2×#117C2×D1114yes—
148C22×C4⋊C4C2×D1111yescharacteristic
149C22×C4⋊C4C2×D1111yescharacteristic
150C22×C22⋊C4C2×D1112yes—
151C22×C42C2×D1112yes—
152#389—1116no—
153#388—1132no—
154#383—118no—
155#382—118no—
156#381—114no—
157#380—118no—
158#380—114no—
159#380—114no—
160#379—114no—
161C4×C4⋊C4—1116no—
162C4×C4⋊C4—118no—
163C4×C22⋊C4—118no—
164C4×C22⋊C4—114no—
165C4×C22⋊C4—114no—
166#376—118no—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11—28no—
170C22×C11—24no—
171C22×C11—24no—
172C22×C11—24no—
173C22×C11—416no—
174C22×C11—48no—
175C22×C11C2×#11714yes—
176C22×C11C24×C411yescharacteristic
177C22×C11C22×#4112yes—
178C22×C11#58512yes—
179C22×C11#58512yes—
180C4×C11—22no—
181C4×C11—22no—
182C4×C11—28no—
183C4×C11—28no—
184C4×C11C2×#11718yes—
185Dic11—416no—
186C25C22×D1111yescharacteristic
187C23×C4—28no—
188C23×C4C2×Dic1118yes—
189C23×C4C22×D1112yes—
190C23×C4C22×D1112yes—
191C23×C4C22×D1111yescharacteristic
192C23×C4C22×D1112yes—
193C23×C4C22×D1112yes—
194C23×C4C22×D1111yescharacteristic
195#117—2216no—
196#117C2×Dic11132yes—
197#117C2×Dic11132yes—
198C2×C4⋊C4—118no—
199C2×C4⋊C4—1116no—
200C2×C4⋊C4C2×Dic1118yes—
201C2×C4⋊C4C2×Dic1118yes—
202C2×C4⋊C4C22×D1114yes—
203C2×C4⋊C4C22×D1114yes—
204C2×C22⋊C4—118no—
205C2×C22⋊C4—118no—
206C2×C22⋊C4—118no—
207C2×C22⋊C4C2×Dic11116yes—
208C2×C22⋊C4C22×D1118yes—
209C2×C42—118no—
210C2×C42—1116no—
211C2×C42C2×Dic11116yes—
212C2×C42C22×D1114yes—
213C2×C42C22×D1114yes—
214#95—118no—
215#95—1116no—
216#95—118no—
217#95—1116no—
218C2×C11—24no—
219C2×C11—44no—
220C2×C11C22×#11711yescharacteristic
221C2×C11#342811yescharacteristic
222C2×C11#342811yescharacteristic
223C2×C11#349314yes—
224C24—24no—
225C24—42no—
226C24—42no—
227C24C22×Dic1114yes—
228C24C23×D1112yes—
229C24C23×D1111yescharacteristic
230C22×C4—24no—
231C22×C4—232no—
232C22×C4—28no—
233C22×C4—28no—
234C22×C4—44no—
235C22×C4—44no—
236C22×C4—1116no—
237C22×C4#433918yes—
238C22×C4C22×Dic1114yes—
239C22×C4C22×Dic1118yes—
240C22×C4C22×Dic1118yes—
241C22×C4C22×Dic1118yes—
242C22×C4C22×Dic1118yes—
243C22×C4C22×Dic1114yes—
244C22×C4C23×D1111yescharacteristic
245C22×C4C23×D1111yescharacteristic
246C22×C4C23×D1114yes—
247C22×C4C23×D1114yes—
248C22×C4C23×D1112yes—
249C4⋊C4—2216no—
250C4⋊C4—4416no—
251C4⋊C4C22×Dic11116yes—
252C4⋊C4C22×Dic11116yes—
253C22⋊C4—2216no—
254C22⋊C4—448no—
255C22⋊C4—448no—
256C22⋊C4C22×Dic11132yes—
257C42—2216no—
258C42—4416no—
259C42C22×Dic11116yes—
260C42C22×Dic11116yes—
261C11#3417911yescharacteristic, complemented, Sylow
262C23—22no—
263C23—22no—
264C23—28no—
265C23—24no—
266C23—24no—
267C23—24no—
268C23—44no—
269C23—44no—
270C23—416no—
271C23C2×#433914yes—
272C23C23×Dic1114yes—
273C23C23×Dic1112yes—
274C23C24×D1111yescharacteristic
275C2×C4—28no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—28no—
279C2×C4—28no—
280C2×C4—216no—
281C2×C4—216no—
282C2×C4—48no—
283C2×C4—48no—
284C2×C4—2216no—
285C2×C4—2216no—
286C2×C4—2216no—
287C2×C4#66979116yes—
288C2×C4C2×#433918yes—
289C2×C4C23×Dic1112yes—
290C2×C4C23×Dic1112yes—
291C2×C4C23×Dic1118yes—
292C2×C4C23×Dic1118yes—
293C2×C4C23×Dic1114yes—
294C22—22no—
295C22—22no—
296C22—28no—
297C22—24no—
298C22—24no—
299C22—24no—
300C22—416no—
301C22—48no—
302C22C2×#6697914yes—
303C22C22×#433912yes—
304C22#1062345312yes—
305C22#1062345312yes—
306C22C24×Dic1111yescharacteristic
307C4—22no—
308C4—22no—
309C4—28no—
310C4—28no—
311C4—4416no—
312C4C2×#6697918yes—
313C2—24no—
314C2—44no—
315C2C22×#6697911yescharacteristic
316C2#1308181911yescharacteristic
317C2#1308181911yescharacteristic
318C2#1308233614yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC22×C11×#117C2
socle, cosocleC23×C11C25
prime radicalC25×C11C23
hypercenterC22×#117D11
hypocenterC11#34179
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. #13071509C2semidirect
2. #13071501C2semidirect
3. #13071234C2semidirect
5. #13071014C2semidirect
7. #13070973C2semidirect
10. C2×C11×#117C4semidirect
26. #10622598C22semidirect
27. C4⋊C4×Dic11C22semidirect
29. #10622550C22semidirect
30. #10622549C22semidirect
31. C4×C4⋊Dic11C22semidirect
32. #10622545C22semidirect
145. C2×#117Dic11semidirect
261. C11#34179semidirect

Maximal subgroups

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

subgroupindex
#130715092
#130715012
#130712342
#130712142
#130710142
#130709992
#130709732
C22×C11×#1172
#3417911