Finite Group Databasebeta

← #15618743

Subgroups — #15618743

Order 2816.

1974 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic
2#13077704C218yesmaximal, complemented
3#13077699C216yesmaximal, complemented
4#13077697C211yesmaximal, characteristic, complemented
5Q8×#4313C218yesmaximal, complemented
6#13077244C216yesmaximal
7C11×#2982C211yesmaximal, characteristic, complemented
8C22×Q8×D11C411yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×Q8×Dic11C411yescharacteristic
11C4×Q8×D11C414yes—
12C4×Q8×D11C414yes—
13C4×Q8×D11C2214yes—
14C4×Q8×D11C2214yes—
15C2×C4⋊C4×D11C413yes—
16C2×#66940C413yes—
17C2×C42×D11C2213yes—
18C2×C4×Dic22C2213yes—
19C8×Q8×C11C2218yescomplemented
20C11×#431C2216yes—
21Q8×C11⋊C8C2218yescomplemented
22#10622538C2216yes—
23#10622450C22112yes—
24#10622448C22112yes—
25#10622444C22124yescomplemented
26#10622339C2214yes—
27#10622332C22112yes—
28C4×#4313C22112yes—
29#10622298C22112yes—
30#10622292C22124yescomplemented
31C22×Q8×C11C2×C411yescharacteristic
32C2×Q8×D11—28no—
33C2×Q8×D11C2×C414yes—
34C2×Q8×D11C2×C414yes—
35C22×C4×D11C2×C413yes—
36C22×C4×D11C2×C413yes—
37C22×C4×D11C2311yescharacteristic
38C22×Dic22C2×C413yes—
39C4×Q8×C11C2×C414yes—
40C4×Q8×C11C2314yes—
41C2×C11×C4⋊C4C2×C413yes—
42C2×C42×C11C2313yes—
43Q8×Dic11C2×C414yes—
44Q8×Dic11C2×C414yes—
45C2×C4⋊Dic11C2×C413yes—
46C2×Dic11⋊C4C2×C416yes—
47C2×C4×Dic11C2×C413yes—
48C2×C4×Dic11C2×C413yes—
49C2×C4×Dic11C2313yes—
50C2×#4313C2318yes—
51C4⋊C4×D11C2×C4112yes—
52C4⋊C4×D11C2×C4112yes—
53#66940C2×C4112yes—
54#66940C2×C4112yes—
55C42×D11C2×C416yes—
56C42×D11C2×C416yes—
57C42×D11C2316yes—
58C42×D11C2316yes—
59C4×Dic22C2×C4112yes—
60C4×Dic22C23112yes—
61C11×C4⋊C8C23112yes—
62C11×C22⋊C8C2314yes—
63C4×C8×C11C23112yes—
64C22⋊(C11⋊C8)C2314yes—
65(C2×D11)⋊C8C2318yes—
66#66879C23124yes—
67Dic11⋊C8C23124yes—
68C4⋊(C11⋊C8)C23112yes—
69C4×C11⋊C8C23112yes—
70#60248—111nomaximal, Sylow
71C23×D11C22×C411yescharacteristic
72C2×Q8×C11M1618yescomplemented
73C2×Q8×C11C22×C414yes—
74C22×C4×C11C22×C413yes—
75C22×C4×C11C22×C413yes—
76C22×C4×C11C2411yescharacteristic
77C22×Dic11C22×C411yescharacteristic
78C22×Dic11C22×C413yes—
79C22×Dic11C22×C413yes—
80Q8×D11—216no—
81Q8×D11—216no—
82C2×C4×D11—24no—
83C2×C4×D11—212no—
84C2×C4×D11—46no—
85C2×C4×D11C22×C411yescharacteristic
86C2×C4×D11C22×C411yescharacteristic
87C2×C4×D11C22×C416yes—
88C2×C4×D11C22×C416yes—
89C2×C4×D11C22×C416yes—
90C2×C4×D11C22×C416yes—
91C2×C4×D11C2411yescharacteristic
92C2×C4×D11C2411yescharacteristic
93C2×Dic22—212no—
94C2×Dic22C22×C4112yes—
95C2×C8×C11C2418yes—
96C11×C4⋊C4C22×C4112yes—
97C42×C11C22×C416yes—
98C42×C11C2416yes—
99C4⋊Dic11C22×C4112yes—
100Dic11⋊C4C22×C4124yes—
101C4×Dic11C22×C416yes—
102C4×Dic11C22×C416yes—
103C4×Dic11C22×C416yes—
104C4×Dic11C22×C416yes—
105C4×Dic11C22×C416yes—
106C4×Dic11C2416yes—
107C2×C11⋊C8C2418yes—
108#4313—216no—
109C22×C4×Q8—111no—
110#2984—118no—
111#2983—116no—
112#2982—111no—
113#2982D1111yescharacteristic, complemented
114Q8×M16—118no—
115#2920—116no—
116C23×C11C23×C411yescharacteristic
117C22×D11—22no—
118C22×D11—22no—
119C22×D11—22no—
120C22×D11C23×C411yescharacteristic
121C22×D11C23×C411yescharacteristic
122Q8×C11C2×M16116yes—
123C2×C4×C11—22no—
124C2×C4×C11—43no—
125C2×C4×C11C2×M16112yes—
126C2×C4×C11C23×C411yescharacteristic
127C2×C4×C11C23×C416yes—
128C2×C4×C11C23×C416yes—
129C2×C4×C11C2511yescharacteristic
130C2×Dic11—26no—
131C2×Dic11—22no—
132C2×Dic11—43no—
133C2×Dic11C23×C411yescharacteristic
134C2×Dic11C23×C416yes—
135C2×Dic11C23×C416yes—
136C2×Dic11C23×C411yescharacteristic
137C4×D11—22no—
138C4×D11—212no—
139C4×D11—212no—
140C4×D11—212no—
141C4×D11—22no—
142C4×D11—22no—
143C4×D11—46no—
144C4×D112−1+414yes—
145Dic22—224no—
146C8×C11—28no—
147C11⋊C8—28no—
148C23×Q8—111no—
149C2×C4×Q8—111no—
150C2×C4×Q8—114no—
151C2×C4×Q8—114no—
152C2×C4×Q8—114no—
153C2×C4×Q8—114no—
154C2×C4×Q8—113no—
155C2×C4×Q8—113no—
156C2×C4×Q8C2×D1111yescharacteristic
157C22×C4⋊C4—113no—
158C22×C42—113no—
159#446—1124no—
160#446—1124no—
161C8×Q8—118no—
162C8×Q8C2×D1118yescomplemented
163#432—1112no—
164#432—1112no—
165#431—116no—
166#431—1112no—
167#431C2×D1116yes—
168#423—1112no—
169#407—114no—
170C4×M16—1112no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11C22×M1612yes—
174C22×C11C24×C411yescharacteristic
175C2×D11—28no—
176C2×D11—21no—
177C2×D11—21no—
178C2×D11—21no—
179C2×D11—21no—
180C2×D11#51912yes—
181C2×D11#56812yes—
182C4×C11—21no—
183C4×C11—26no—
184C4×C11C22×M16112yes—
185C4×C11C2×2−1+412yes—
186Dic11—21no—
187Dic11—26no—
188Dic11—26no—
189Dic11#51912yes—
190C22×Q8—114no—
191C22×Q8—114no—
192C22×Q8—113no—
193C22×Q8—228no—
194C22×Q8C4×D1111yescharacteristic
195C23×C4—113no—
196C23×C4—111no—
197C23×C4—113no—
198C2×M16—118no—
199C4×Q8—114no—
200C4×Q8—114no—
201C4×Q8—1112no—
202C4×Q8—1112no—
203C4×Q8—1112no—
204C4×Q8—1112no—
205C4×Q8C4×D1114yes—
206C4×Q8C22×D1114yes—
207C2×C4⋊C4—116no—
208C2×C4⋊C4—113no—
209C2×C4⋊C4—1112no—
210C2×C4⋊C4—1112no—
211C2×C4⋊C4C4×D1113yes—
212C2×C42—113no—
213C2×C42—113no—
214C2×C42—113no—
215C2×C42—116no—
216C2×C42—116no—
217C2×C42—116no—
218C2×C42—116no—
219C2×C42C22×D1113yes—
220C4⋊C8—1124no—
221C4⋊C8—1112no—
222C4⋊C8C22×D11112yes—
223C22⋊C8—114no—
224C22⋊C8—118no—
225C22⋊C8C22×D1114yes—
226#97—1124no—
227C4×C8—1112no—
228C4×C8C22×D11112yes—
229C2×C11—22no—
230C2×C11C2×#51911yescharacteristic
231C2×C11C23×M1611yescharacteristic
232C2×C11C2×#56811yescharacteristic
233D11—22no—
234D11—22no—
235C24—111no—
236C2×Q8—1112no—
237C2×Q8—2216no—
238C2×Q8—2216no—
239C2×Q8—2212no—
240C2×Q8#431318yescomplemented
241C2×Q8C2×C4×D1114yes—
242C22×C4—111no—
243C22×C4—111no—
244C22×C4—113no—
245C22×C4—113no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—116no—
249C22×C4—116no—
250C22×C4—116no—
251C22×C4—111no—
252C22×C4—116no—
253C22×C4—224no—
254C22×C4—2212no—
255C22×C4—446no—
256C22×C4C2×C4×D1113yes—
257C22×C4C2×C4×D1113yes—
258C22×C4C23×D1111yescharacteristic
259M16—2216no—
260C2×C8—118no—
261C2×C8C23×D1118yes—
262C4⋊C4—1124no—
263C4⋊C4—1112no—
264C4⋊C4C2×C4×D11112yes—
265C42—116no—
266C42—116no—
267C42—116no—
268C42—116no—
269C42—116no—
270C42—116no—
271C42C2×C4×D1116yes—
272C42C23×D1116yes—
273C11#6024811yescharacteristic, complemented, Sylow
274C23—111no—
275C23—111no—
276C23—222no—
277C23—222no—
278C23—222no—
279C23C22×C4×D1111yescharacteristic
280Q8—2224no—
281Q8C2×#4313116yes—
282C2×C4—22no—
283C2×C4—43no—
284C2×C4—111no—
285C2×C4—114no—
286C2×C4—111no—
287C2×C4—116no—
288C2×C4—116no—
289C2×C4—222no—
290C2×C4—222no—
291C2×C4—2212no—
292C2×C4—222no—
293C2×C4—226no—
294C2×C4—2212no—
295C2×C4—2212no—
296C2×C4—222no—
297C2×C4—446no—
298C2×C4—443no—
299C2×C4C2×#4313112yes—
300C2×C4C22×C4×D1111yescharacteristic
301C2×C4C22×C4×D1116yes—
302C2×C4C22×C4×D1116yes—
303C2×C4C24×D1111yescharacteristic
304C8—28no—
305C8—228no—
306C22—21no—
307C22—21no—
308C22—112no—
309C22—112no—
310C22—228no—
311C22—221no—
312C22—221no—
313C22—221no—
314C22—221no—
315C22C22×#431312yes—
316C22C23×C4×D1111yescharacteristic
317C4—26no—
318C4—21no—
319C4—112no—
320C4—226no—
321C4—226no—
322C4—221no—
323C4C22×#4313112yes—
324C4D11×2−1+412yes—
325C2—22no—
326C2—222no—
327C2—222no—
328C2D11×#51911yescharacteristic
329C2C23×#431311yescharacteristic
330C2D11×#56811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2982C2
prime radicalC23×D11C22×C4
cosocleC2×C4×C11C25
hypercenter#2982D11
hypocenterC11#60248
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #13077704C2semidirect
3. #13077699C2semidirect
4. #13077697C2semidirect
5. Q8×#4313C2semidirect
7. C11×#2982C2semidirect
19. C8×Q8×C11C22semidirect
21. Q8×C11⋊C8C22semidirect
25. #10622444C22semidirect
30. #10622292C22semidirect
72. C2×Q8×C11M16semidirect
113. #2982D11semidirect
162. C8×Q8C2×D11semidirect
240. C2×Q8#4313semidirect
273. C11#60248semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
#130777042
#130776992
#130776972
Q8×#43132
#130772442
C11×#29822
#6024811