Finite Group Databasebeta

← #15618182

Subgroups — #15618182

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C211yesmaximal, characteristic
2#13077560C2116yesmaximal, complemented
3#13077556C214yesmaximal, complemented
4#13077550C214yesmaximal, complemented
5#13077180C211yesmaximal, characteristic
6C2×#10622715C212yesmaximal
7#13077034C212yesmaximal
8C2×C11×#405C211yesmaximal, characteristic
9C22×C11×M16C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2212yes—
13C22×#4318C2212yes—
14#10623050C418yes—
15#10623048C2218yes—
16#10623031C414yes—
17#10623014C414yes—
18#10623001C2214yes—
19C11×#405C2218yes—
20C2×C11×#97C2212yes—
21C2×C4×C8×C11C2212yes—
22#10622735C2218yes—
23M16×Dic11C2218yes—
24#10622715C2214yes—
25#10622715C2214yes—
26#10622715C2218yes—
27#10622714C2218yes—
28C2×Dic11⋊C8C2218yes—
29#10622612C2218yes—
30#10622537C2214yes—
31#10622314C22132yescomplemented
32#10622292C22116yescomplemented
33C8×Dic22C22116yescomplemented
34C23×C4×C11C2311yescharacteristic
35C2×C11×M16Q818yescomplemented
36C2×C11×M16C2314yes—
37C22×C8×C11—24no—
38C22×C8×C11C2311yescharacteristic
39C22×C8×C11C2311yescharacteristic
40C22×C8×C11C2314yes—
41C22×C8×C11C2312yes—
42C11×#117C2×C414yes—
43C11×#117C2314yes—
44C2×C11×C4⋊C4C2×C412yes—
45C2×C11×C22⋊C4C2×C412yes—
46C2×C42×C11C2312yes—
47C2×C22⋊Dic11C2×C414yes—
48#66979C2×C414yes—
49#66979C2×C414yes—
50#66979C2314yes—
51#66979C2314yes—
52C2×C4⋊Dic11C2×C414yes—
53#66977C2×C4116yes—
54C2×C4×Dic11C2314yes—
55C2×#4318—28no—
56C2×#4318C2314yes—
57C2×#4318C2314yes—
58C22×C11⋊C8C2314yes—
59#66943C2×C4116yes—
60#66941C2×C4116yes—
61#66931C2×C4132yes—
62#66923C2×C418yes—
63#66922C2×C418yes—
64C4×Dic22C23116yes—
65C11×#97C2318yes—
66C4×C8×C11C2318yes—
67#66879C23116yes—
68Dic11⋊C8C23116yes—
69Dic11⋊C8C23116yes—
70C8×Dic11C23116yes—
71C4⋊(C11⋊C8)C23116yes—
72#60193—111nomaximal, Sylow
73C24×C11C22×C411yescharacteristic
74C22×C4×C11C22×C414yes—
75C22×C4×C11C22×C412yes—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×Q814yes—
78C22×C4×C11#4114yes—
79C22×C4×C11C2412yes—
80C22×C4×C11C2411yescharacteristic
81C22×Dic11C22×C418yes—
82C2×Dic22C22×C4116yes—
83C11×M16C2×Q8116yes—
84C2×C8×C11—28no—
85C2×C8×C11—22no—
86C2×C8×C11—22no—
87C2×C8×C11C2×Q818yes—
88C2×C8×C11C2412yes—
89C2×C8×C11C2412yes—
90C2×C8×C11C2414yes—
91C11×C4⋊C4C22×C418yes—
92C11×C22⋊C4C22×C418yes—
93C42×C11C22×C414yes—
94C42×C11C2414yes—
95C22⋊Dic11C22×C418yes—
96C22⋊Dic11C22×C418yes—
97C4⋊Dic11C22×C4116yes—
98C4⋊Dic11C22×C418yes—
99C4⋊Dic11C22×C418yes—
100Dic11⋊C4C22×C4132yes—
101C4×Dic11C22×C418yes—
102C4×Dic11C2418yes—
103#4318—28no—
104#4318—28no—
105C2×C11⋊C8—28no—
106C2×C11⋊C8C2418yes—
107#3458—111no—
108#2962—1116no—
109#2961—114no—
110#2960—114no—
111#2905—111no—
112C2×#424—112no—
113#2873—112no—
114C2×#405D1111yescharacteristic
115C23×C11—42no—
116C23×C11C4×Q814yes—
117C23×C11C23×C411yescharacteristic
118C23×C11C23×C412yes—
119C2×C4×C11—44no—
120C2×C4×C11C4×Q818yes—
121C2×C4×C11C4×Q814yes—
122C2×C4×C11C23×C418yes—
123C2×C4×C11C23×C412yes—
124C2×C4×C11C23×C411yescharacteristic
125C2×C4×C11C22×Q812yes—
126C2×C4×C11C22×Q814yes—
127C2×C4×C11C2×#4114yes—
128C2×C4×C11C2×#4112yes—
129C2×C4×C11C2511yescharacteristic
130C2×Dic11—48no—
131C2×Dic11C23×C4116yes—
132Dic22—416no—
133C8×C11—22no—
134C8×C11—22no—
135C8×C11C22×Q818yes—
136C11⋊C8—28no—
137C22×M16—112no—
138C22×M16C2×D1111yescharacteristic
139C23×C8C2×D1111yescharacteristic
140#544—118no—
141#544—114no—
142#543—114no—
143#533—118no—
144#533—114no—
145C2×#117—112no—
146C2×#117C2×D1111yescharacteristic
147#446—1132no—
148#446—1116no—
149C8×Q8—1116no—
150#424—114no—
151#424—114no—
152#424—118no—
153#424—118no—
154#423—114no—
155C2×C4⋊C8—118no—
156#405—118no—
157#405—118no—
158#405C2×D1118yes—
159C4×M16—118no—
160C2×#97C2×D1112yes—
161C2×C4×C8C2×D1112yes—
162C22×C11—22no—
163C22×C11—24no—
164C22×C11—44no—
165C22×C11C2×C4×Q812yes—
166C22×C11C2×C4×Q814yes—
167C22×C11C24×C411yescharacteristic
168C4×C11—28no—
169C4×C11C2×C4×Q814yes—
170C4×C11C2×C4×Q812yes—
171C4×C11C23×Q811yescharacteristic
172C4×C11C22×#4111yescharacteristic
173Dic11—216no—
174C23×C4C22×D1111yescharacteristic
175C2×M16—114no—
176C2×M16—114no—
177C2×M16—228no—
178C2×M16Dic2218yescomplemented
179C2×M16C22×D1114yes—
180C22×C8—24no—
181C22×C8—114no—
182C22×C8C22×D1111yescharacteristic
183C22×C8C22×D1111yescharacteristic
184C22×C8C22×D1114yes—
185C22×C8C22×D1112yes—
186C4⋊Q8—1116no—
187C4⋊Q8—118no—
188#125—1116no—
189#125—118no—
190C22⋊Q8—1116no—
191C22⋊Q8—1132no—
192C4×Q8—1116no—
193#117—114no—
194#117—114no—
195#117—114no—
196#117—114no—
197#117C4×D1114yes—
198#117C22×D1114yes—
199C2×C4⋊C4—114no—
200C2×C4⋊C4C4×D1112yes—
201C2×C22⋊C4—114no—
202C2×C22⋊C4C4×D1112yes—
203C2×C42—114no—
204C2×C42C22×D1112yes—
205C4⋊C8—1116no—
206C4⋊C8—1116no—
207C4⋊C8—1116no—
208#97—1116no—
209#97C22×D1118yes—
210C4×C8—1116no—
211C4×C8C22×D1118yes—
212C2×C11—22no—
213C2×C11—24no—
214C2×C11C22×C4×Q811yescharacteristic
215C2×C11#357312yes—
216C24C2×C4×D1111yescharacteristic
217C2×Q8—1116no—
218C22×C4—118no—
219C22×C4C2×Dic2214yes—
220C22×C4C2×C4×D1114yes—
221C22×C4C2×C4×D1112yes—
222C22×C4C2×C4×D1111yescharacteristic
223C22×C4#433914yes—
224C22×C4C23×D1112yes—
225C22×C4C23×D1111yescharacteristic
226M16—228no—
227M16—228no—
228M16C2×Dic22116yes—
229C2×C8—28no—
230C2×C8—22no—
231C2×C8—22no—
232C2×C8—118no—
233C2×C8—228no—
234C2×C8C2×Dic2218yes—
235C2×C8C23×D1112yes—
236C2×C8C23×D1112yes—
237C2×C8C23×D1114yes—
238C4⋊C4—118no—
239C4⋊C4—118no—
240C4⋊C4—1132no—
241C4⋊C4—1116no—
242C4⋊C4C2×C4×D1118yes—
243C22⋊C4—118no—
244C22⋊C4—118no—
245C22⋊C4C2×C4×D1118yes—
246C42—118no—
247C42—118no—
248C42C2×C4×D1114yes—
249C42C23×D1114yes—
250C11#6019311yescharacteristic, complemented, Sylow
251C23—42no—
252C23C4×Dic2214yes—
253C23C22×C4×D1111yescharacteristic
254C23C22×C4×D1112yes—
255Q8—4416no—
256C2×C4—44no—
257C2×C4—1116no—
258C2×C4—448no—
259C2×C4C4×Dic2218yes—
260C2×C4C4×Dic2214yes—
261C2×C4C22×Dic2212yes—
262C2×C4C22×Dic2214yes—
263C2×C4C22×C4×D1118yes—
264C2×C4C22×C4×D1112yes—
265C2×C4C22×C4×D1111yescharacteristic
266C2×C4C2×#433914yes—
267C2×C4C2×#433912yes—
268C2×C4C24×D1111yescharacteristic
269C8—22no—
270C8—22no—
271C8—228no—
272C8C22×Dic2218yes—
273C22—22no—
274C22—24no—
275C22—44no—
276C22C2×C4×Dic2212yes—
277C22C2×C4×Dic2214yes—
278C22C23×C4×D1111yescharacteristic
279C4—28no—
280C4—2216no—
281C4C2×C4×Dic2212yes—
282C4C2×C4×Dic2214yes—
283C4C23×Dic2211yescharacteristic
284C4C22×#433911yescharacteristic
285C2—22no—
286C2—24no—
287C2C22×C4×Dic2211yescharacteristic
288C2#1308332712yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC2×C11×#405C2
prime radicalC24×C11C22×C4
cosocleC2×C4×C11C25
hypercenterC2×#405D11
hypocenterC11#60193
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. #13077560C2semidirect
3. #13077556C2semidirect
4. #13077550C2semidirect
31. #10622314C22semidirect
32. #10622292C22semidirect
33. C8×Dic22C22semidirect
35. C2×C11×M16Q8semidirect
178. C2×M16Dic22semidirect
250. C11#60193semidirect

Maximal subgroups

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

subgroupindex
#130820212
#130775602
#130775562
#130775502
#130771802
C2×#106227152
#130770342
C2×C11×#4052
#6019311