Finite Group Databasebeta

← #14913880

Subgroups — #14913880

Order 2816.

3006 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623358C211yesmaximal, characteristic
2C2×#41×Dic11C211yesmaximal, characteristic
3#13071534C214yesmaximal, complemented
4#13071521C2112yesmaximal, complemented
5#13071240C213yesmaximal, complemented
6#13071236C213yesmaximal, complemented
7#13071019C213yesmaximal, complemented
8C2×#10622590C213yesmaximal, complemented
9C2×C11×#520C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C11×#520—28no—
12C2×C4×Q8×C11C2212yes—
13C2×C4×D4×C11C2216yes—
14C2×C11×#117C2213yes—
15C22×C11×C4⋊C4C2213yes—
16#10623358—28no—
17#41×Dic11C4116yescomplemented
18C2×Q8×Dic11C2212yes—
19C2×Q8×Dic11C2212yes—
20C2×D4×Dic11C2216yes—
21C2×D4×Dic11C2216yes—
22C2×#66979C2213yes—
23C2×#66979C2213yes—
24C22×C4⋊Dic11C2213yes—
25C22×C4×Dic11C2213yes—
26#10622823C22112yes—
27C2×C11⋊#95C22112yes—
28#10622590C2216yes—
29#10622590C2213yes—
30#10622590C22112yes—
31#10622590C2211yescharacteristic
32#10622589C2213yes—
33#10622589C2213yes—
34#10622586C22112yes—
35#10622559C22112yes—
36#10622555C22112yes—
37C4×Dic11⋊C4C22112yes—
38#10622541C22112yes—
39C2×C11×#41C2×C418yes—
40C2×C11×#41D418yes—
41C2×C11×#41Q818yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D4×C11C2313yes—
44C23×C4×C11C2316yes—
45C23×C4×C11C2313yes—
46C23×Dic11C2316yes—
47C23×Dic11C2316yes—
48C4×Q8×C11—28no—
49C4×D4×C11—224no—
50C11×#117—212no—
51C2×C11×C4⋊C4—212no—
52C2×C11×C4⋊C4C2316yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2313yes—
55C2×C11×C22⋊C4C2316yes—
56C2×C42×C11C2316yes—
57C2×C22⋊Dic11C2316yes—
58C2×C22⋊Dic11C2316yes—
59Q8×Dic11—28no—
60Q8×Dic11C2×C4116yescomplemented
61D4×Dic11—224no—
62D4×Dic11C2×C4148yescomplemented
63#66979—212no—
64#66979C2×C4124yescomplemented
65C2×C4⋊Dic11—212no—
66C2×C4⋊Dic11C2316yes—
67C2×C4⋊Dic11C2313yes—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2316yes—
70C2×Dic11⋊C4C23112yes—
71C2×Dic11⋊C4C23112yes—
72C2×C4×Dic11C2×C4124yescomplemented
73C2×C4×Dic11C2316yes—
74C2×C4×Dic11C2316yes—
75C2×C4×Dic11C2311yescharacteristic
76C2×C4×Dic11C2313yes—
77C11⋊#95C23124yes—
78C11⋊#95C2314yes—
79C11⋊#95C23112yes—
80#34184—111nomaximal, Sylow
81C24×C11C2413yes—
82C11×#41C4⋊C4164yescomplemented
83C2×Q8×C11C22×C414yes—
84C2×Q8×C11C2×D414yes—
85C2×Q8×C11C2×Q814yes—
86C2×D4×C11C22×C4112yes—
87C2×D4×C11C2×D4112yes—
88C2×D4×C11C2×Q8112yes—
89C22×C4×C11—212no—
90C22×C4×C11—412no—
91C22×C4×C11C22×C4112yes—
92C22×C4×C11C2×D4112yes—
93C22×C4×C11C2×Q8112yes—
94C22×C4×C11C2416yes—
95C22×C4×C11C2412yes—
96C22×C4×C11C2413yes—
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—212no—
99C22×Dic11—46no—
100C22×Dic11—46no—
101C22×Dic11—412no—
102C22×Dic11C22×C4124yes—
103C22×Dic11C2416yes—
104C22×Dic11C2412yes—
105C22×Dic11C2412yes—
106C22×Dic11C2416yes—
107C11×C4⋊C4—26no—
108C11×C4⋊C4—212no—
109C11×C4⋊C4—22no—
110C11×C22⋊C4—212no—
111C42×C11—212no—
112C22⋊Dic11—212no—
113C22⋊Dic11C22×C4124yes—
114C4⋊Dic11—26no—
115C4⋊Dic11—212no—
116C4⋊Dic11—22no—
117C4⋊Dic11C22×C4124yes—
118Dic11⋊C4—412no—
119Dic11⋊C4—412no—
120C4×Dic11—212no—
121C4×Dic11C22×C414yes—
122C4×Dic11C22×C4112yes—
123C4×Dic11C22×C4124yes—
124C2×#520—111no—
125C2×#520D1111yescharacteristic
126C2×C4×#41—111no—
127#2351—114no—
128#2349—1112no—
129#2317—113no—
130#2317—113no—
131#2285—113no—
132C2×#382—113no—
133C23×C11—26no—
134C23×C11—26no—
135C23×C11C23×C416yes—
136C23×C11C22×D416yes—
137C23×C11C22×Q816yes—
138C23×C11C2511yescharacteristic
139Q8×C11C2×C4⋊C4116yes—
140D4×C11C2×C4⋊C4148yes—
141C2×C4×C11—22no—
142C2×C4×C11—26no—
143C2×C4×C11—24no—
144C2×C4×C11—212no—
145C2×C4×C11—812no—
146C2×C4×C11C2×C4⋊C4148yes—
147C2×C4×C11C23×C412yes—
148C2×C4×C11C23×C416yes—
149C2×C4×C11C22×D416yes—
150C2×C4×C11C22×D412yes—
151C2×C4×C11C22×Q812yes—
152C2×C4×C11C22×Q816yes—
153C2×Dic11—26no—
154C2×Dic11—26no—
155C2×Dic11—22no—
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11—26no—
159C2×Dic11—24no—
160C2×Dic11—212no—
161C2×Dic11—424no—
162C2×Dic11—812no—
163C2×Dic11C23×C414yes—
164C2×Dic11C23×C4112yes—
165C22×#41C2×D1111yescharacteristic
166#520—28no—
167#520—228no—
168C4×#41—1116no—
169C2×C4×Q8—112no—
170C2×C4×Q8—112no—
171C2×C4×Q8C2×D1112yes—
172C2×C4×D4—116no—
173C2×C4×D4—116no—
174C2×C4×D4C2×D1116yes—
175C2×#117—113no—
176C2×#117—113no—
177C2×#117C2×D1113yes—
178C22×C4⋊C4—113no—
179C22×C4⋊C4C2×D1113yes—
180C22×C42—113no—
181#389—1112no—
182#389—1112no—
183#385—1112no—
184#385—1112no—
185#384—113no—
186#384—113no—
187#382—116no—
188#382—1112no—
189#382—113no—
190#382—111no—
191#380—1112no—
192C4×C4⋊C4—1112no—
193C2×#95—1112no—
194C22×C11—212no—
195C22×C11—26no—
196C22×C11—26no—
197C22×C11—212no—
198C22×C11C22×C4⋊C4112yes—
199C22×C11C24×C411yescharacteristic
200C22×C11C23×D411yescharacteristic
201C22×C11C23×Q811yescharacteristic
202C22×C11#58512yes—
203C22×C11#58512yes—
204C4×C11—42no—
205C4×C11—46no—
206C4×C11C22×C4⋊C414yes—
207C4×C11C22×C4⋊C4112yes—
208Dic11—24no—
209Dic11—212no—
210Dic11—42no—
211Dic11—46no—
212C2×#41Dic2218yes—
213C2×#41C4×D1118yes—
214C2×#41C22⋊D1118yes—
215C22×Q8C22×D1111yescharacteristic
216C22×D4C22×D1113yes—
217C23×C4—116no—
218C23×C4—116no—
219C23×C4C22×D1116yes—
220C23×C4C22×D1113yes—
221C4×Q8—28no—
222C4×Q8—1116no—
223C4×Q8—228no—
224C4×D4—224no—
225C4×D4—1148no—
226C4×D4—2224no—
227#117—212no—
228#117—1124no—
229#117—2212no—
230C2×C4⋊C4—212no—
231C2×C4⋊C4—116no—
232C2×C4⋊C4—113no—
233C2×C4⋊C4—116no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—1112no—
236C2×C4⋊C4—1112no—
237C2×C4⋊C4—2212no—
238C2×C4⋊C4C22×D1113yes—
239C2×C4⋊C4C22×D1116yes—
240C2×C4⋊C4C22×D1111yescharacteristic
241C2×C22⋊C4—116no—
242C2×C22⋊C4—116no—
243C2×C22⋊C4C22×D1116yes—
244C2×C42—1124no—
245C2×C42—113no—
246C2×C42—116no—
247C2×C42—111no—
248C2×C42—116no—
249C2×C42C22×D1116yes—
250#95—1112no—
251#95—1124no—
252#95—114no—
253C2×C11—212no—
254C2×C11C23×C4⋊C411yescharacteristic
255C2×C11#342812yes—
256C2×C11#350011yescharacteristic
257C2×C11#350011yescharacteristic
258C2×C11#350412yes—
259C24C23×D1113yes—
260#41Dic11⋊C4164yescomplemented
261C2×Q8C2×Dic2214yes—
262C2×Q8C2×C4×D1114yes—
263C2×Q8C2×C22⋊D1114yes—
264C2×D4C2×Dic22112yes—
265C2×D4C2×C4×D11112yes—
266C2×D4C2×C22⋊D11112yes—
267C22×C4—212no—
268C22×C4—412no—
269C22×C4—112no—
270C22×C4—116no—
271C22×C4—1124no—
272C22×C4—116no—
273C22×C4—112no—
274C22×C4—2212no—
275C22×C4—446no—
276C22×C4—446no—
277C22×C4—4412no—
278C22×C4C2×Dic22112yes—
279C22×C4C2×C4×D11112yes—
280C22×C4C2×C22⋊D11112yes—
281C22×C4C23×D1116yes—
282C22×C4C23×D1112yes—
283C22×C4C23×D1113yes—
284C22×C4C23×D1111yescharacteristic
285C4⋊C4—26no—
286C4⋊C4—212no—
287C4⋊C4—22no—
288C4⋊C4—1124no—
289C4⋊C4—226no—
290C4⋊C4—2212no—
291C4⋊C4—222no—
292C4⋊C4—4412no—
293C4⋊C4—4412no—
294C22⋊C4—212no—
295C22⋊C4—1124no—
296C22⋊C4—2212no—
297C42—212no—
298C42—114no—
299C42—1112no—
300C42—1124no—
301C42—2212no—
302C11#3418411yescharacteristic, complemented, Sylow
303C23—26no—
304C23—26no—
305C23C22×Dic2216yes—
306C23C22×C4×D1116yes—
307C23C22×C22⋊D1116yes—
308C23C24×D1111yescharacteristic
309Q8C2×Dic11⋊C4116yes—
310D4C2×Dic11⋊C4148yes—
311C2×C4—212no—
312C2×C4—24no—
313C2×C4—22no—
314C2×C4—26no—
315C2×C4—812no—
316C2×C4—114no—
317C2×C4—1112no—
318C2×C4—226no—
319C2×C4—222no—
320C2×C4—226no—
321C2×C4—222no—
322C2×C4—224no—
323C2×C4—2212no—
324C2×C4—222no—
325C2×C4—226no—
326C2×C4—4424no—
327C2×C4—8812no—
328C2×C4C2×Dic11⋊C4148yes—
329C2×C4C22×Dic2212yes—
330C2×C4C22×Dic2216yes—
331C2×C4C22×C4×D1112yes—
332C2×C4C22×C4×D1116yes—
333C2×C4C22×C22⋊D1116yes—
334C2×C4C22×C22⋊D1112yes—
335C22—26no—
336C22—26no—
337C22—212no—
338C22—212no—
339C22C22×Dic11⋊C4112yes—
340C22C23×Dic2211yescharacteristic
341C22C23×C4×D1111yescharacteristic
342C22#1062345512yes—
343C22#1062345712yes—
344C22C23×C22⋊D1111yescharacteristic
345C4—46no—
346C4—42no—
347C4—224no—
348C4—2212no—
349C4—442no—
350C4—446no—
351C4C22×Dic11⋊C414yes—
352C4C22×Dic11⋊C4112yes—
353C2—212no—
354C2C23×Dic11⋊C411yescharacteristic
355C2#1308181612yes—
356C2#1308240411yescharacteristic
357C2#1308241011yescharacteristic
358C2#1308243812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#520C2
socle, cosocleC23×C11C25
prime radicalC22×C11×#41C22
hypercenterC2×#520D11
hypocenterC11#34184
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
3. #13071534C2semidirect
4. #13071521C2semidirect
5. #13071240C2semidirect
6. #13071236C2semidirect
7. #13071019C2semidirect
8. C2×#10622590C2semidirect
17. #41×Dic11C4semidirect
60. Q8×Dic11C2×C4semidirect
62. D4×Dic11C2×C4semidirect
64. #66979C2×C4semidirect
72. C2×C4×Dic11C2×C4semidirect
82. C11×#41C4⋊C4semidirect
260. #41Dic11⋊C4semidirect
302. C11#34184semidirect

Maximal subgroups

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

subgroupindex
C2×#106233582
C2×#41×Dic112
#130715342
#130715212
#130712402
#130712362
#130710192
C2×#106225902
C2×C11×#5202
#3418411