Finite Group Databasebeta

← #14959883

Subgroups — #14959883

Order 2816.

2502 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C212yesmaximal
2#13077014C211yesmaximal, characteristic, complemented
3#13076993C212yesmaximal, complemented
4#13076977C214yesmaximal, complemented
5#13076969C214yesmaximal
6#13076963C214yesmaximal
7C4⋊Q8×Dic11C214yesmaximal, complemented
8#13071183C214yesmaximal, complemented
9#13071021C214yesmaximal
10C43×D11C211yesmaximal, characteristic
11C11×#2868C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2212yes—
13C2×C11×C4⋊Q8C2214yes—
14C2×#66999C2214yes—
15C2×Q8×Dic11C2214yes—
16#10623259—216no—
17C2×#66950C2214yes—
18C2×#66945C2214yes—
19C2×#66943C2214yes—
20C2×#66940C2214yes—
21C2×C42×D11C2212yes—
22C2×C42×D11C2212yes—
23C2×C42×D11C2211yescharacteristic
24C2×C42×D11C2212yes—
25C2×#66922C2212yes—
26C2×#66922C2214yes—
27C11×#384C2214yes—
28C11×#384C2214yes—
29C43×C11C2211yescharacteristic
30#10622843C2218yes—
31#10622600C22116yes—
32#10622598C22116yes—
33#10622590C2218yes—
34C4⋊C4×Dic11C22116yes—
35#10622587C2218yes—
36#10622586C22116yes—
37#10622548C2214yes—
38#10622548C2214yes—
39C42×Dic11C2211yescharacteristic
40C42×Dic11C2212yes—
41C42×Dic11C2212yes—
42C42×Dic11C2212yes—
43C22×Q8×C11C2314yes—
44C22×C4×D11C2311yescharacteristic
45C22×C4×D11C2311yescharacteristic
46C22×C4×D11C2314yes—
47C22×C4×D11C2311yescharacteristic
48C22×Dic22C2314yes—
49C11×C4⋊Q8—28no—
50C11×C4⋊Q8—216no—
51C2×C11×C4⋊C4C2314yes—
52C2×C11×C4⋊C4C2314yes—
53C2×C11×C4⋊C4C23116yes—
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2312yes—
56C2×C42×C11C2312yes—
57C2×C42×C11C2312yes—
58#66999—216no—
59Q8×Dic11—216no—
60C2×(C2×D11)⋊C4C2318yes—
61C2×C4⋊Dic11C2314yes—
62C2×C4⋊Dic11C2314yes—
63C2×C4⋊Dic11C23116yes—
64C2×C4⋊Dic11C2318yes—
65C2×Dic11⋊C4C2318yes—
66C2×C4×Dic11C2314yes—
67C2×C4×Dic11C2312yes—
68C2×C4×Dic11C2312yes—
69C2×C4×Dic11C2314yes—
70C2×C4×Dic11C2318yes—
71C2×C4×Dic11C2311yescharacteristic
72C2×C4×Dic11C2311yescharacteristic
73C2×C4×Dic11C2311yescharacteristic
74C2×C4×Dic11C2314yes—
75C2×C4×Dic11C2312yes—
76#66950—216no—
77#66945—216no—
78#66943—216no—
79#66940—216no—
80C42×D11—28no—
81C42×D11—28no—
82C42×D11D418yes—
83C42×D11Q8116yescomplemented
84#66922—28no—
85#66922—216no—
86C11⋊#95C23132yes—
87#36645—111nomaximal, Sylow
88C23×D11C2411yescharacteristic
89C2×Q8×C11—28no—
90C2×Q8×C11—216no—
91C22×C4×C11C2418yes—
92C22×C4×C11C2411yescharacteristic
93C22×C4×C11C2411yescharacteristic
94C22×C4×C11C2411yescharacteristic
95C22×C4×C11C2414yes—
96C22×Dic11C2418yes—
97C22×Dic11C2411yescharacteristic
98C22×Dic11C2411yescharacteristic
99C22×Dic11C2414yes—
100C22×Dic11C2411yescharacteristic
101C2×C4×D11—24no—
102C2×C4×D11—28no—
103C2×C4×D11—24no—
104C2×C4×D11—28no—
105C2×C4×D11C2×D414yes—
106C2×C4×D11C2×D414yes—
107C2×C4×D11C2×D414yes—
108C2×C4×D11C2×Q8116yes—
109C2×C4×D11C2×Q818yes—
110C2×Dic22—28no—
111C2×Dic22—216no—
112C11×C4⋊C4—28no—
113C11×C4⋊C4—28no—
114C11×C4⋊C4—232no—
115C42×C11C2×D414yes—
116C42×C11C2×Q818yes—
117C42×C11#4118yes—
118C42×C11#4118yes—
119(C2×D11)⋊C4—216no—
120C4⋊Dic11—216no—
121C4⋊Dic11—28no—
122C4⋊Dic11—28no—
123C4⋊Dic11—232no—
124Dic11⋊C4—216no—
125C4×Dic11—216no—
126C4×Dic11—24no—
127C4×Dic11—28no—
128C4×Dic11—24no—
129C4×Dic11—28no—
130C4×Dic11C2×D414yes—
131C4×Dic11C2×D414yes—
132C4×Dic11C2×D414yes—
133C4×Dic11C2×Q818yes—
134C4×Dic11C2×Q8116yes—
135C2×#533—112no—
136#2868—111no—
137#2868D1111yescharacteristic, complemented
138#2862—112no—
139#2859—114no—
140#2857—114no—
141#2857—114no—
142C4×C4⋊Q8—114no—
143C4×C4⋊Q8—114no—
144#2285—114no—
145C2×C43—111no—
146C23×C11C2511yescharacteristic
147C22×D11—22no—
148C22×D11—22no—
149C22×D11C22×D412yes—
150C22×D11C22×Q814yes—
151Q8×C11—416no—
152C2×C4×C11—28no—
153C2×C4×C11—216no—
154C2×C4×C11C22×D412yes—
155C2×C4×C11C22×D412yes—
156C2×C4×C11C22×D412yes—
157C2×C4×C11C22×Q814yes—
158C2×C4×C11C22×Q818yes—
159C2×C4×C11C2×#4114yes—
160C2×C4×C11C2×#4118yes—
161C2×C4×C11C2×#4114yes—
162C2×C4×C11C2×#4118yes—
163C2×Dic11—22no—
164C2×Dic11—24no—
165C2×Dic11—22no—
166C2×Dic11—24no—
167C2×Dic11—28no—
168C2×Dic11—216no—
169C2×Dic11C22×D412yes—
170C2×Dic11C22×D412yes—
171C2×Dic11C22×D412yes—
172C2×Dic11C22×Q818yes—
173C2×Dic11C22×Q814yes—
174C4×D11—28no—
175C4×D11—28no—
176C4×D11—232no—
177C4×D11C4⋊Q8116yescomplemented
178Dic22—416no—
179#533—2216no—
180C2×C4⋊Q8—114no—
181C2×C4⋊Q8—112no—
182C2×C4⋊Q8C2×D1114yes—
183C2×C4⋊Q8C2×D1112yes—
184C2×#125—114no—
185C2×C22⋊Q8—114no—
186C2×C22⋊Q8—114no—
187C2×C4×Q8—114no—
188C2×C4×Q8—114no—
189C2×#117—114no—
190C22×C42—111no—
191C22×C42—112no—
192C22×C42—112no—
193C22×C42—112no—
194#391—118no—
195#391—118no—
196#389—1116no—
197#389—1116no—
198#384—114no—
199#384—114no—
200#384C2×D1114yes—
201#384C2×D1114yes—
202#382—118no—
203#380—1116no—
204C4×C4⋊C4—1116no—
205C43—112no—
206C43—112no—
207C43—112no—
208C43—111no—
209C43C2×D1111yescharacteristic
210C22×C11C23×D411yescharacteristic
211C22×C11C23×Q812yes—
212C22×C11C22×#4112yes—
213C22×C11C22×#4112yes—
214C2×D11—22no—
215C2×D11—22no—
216C2×D11—28no—
217C2×D11C2×C4⋊Q814yes—
218C4×C11—48no—
219C4×C11C2×C4⋊Q814yes—
220C4×C11#53214yes—
221C4×C11#53214yes—
222C4×C11#533116yescomplemented
223Dic11—22no—
224Dic11—22no—
225Dic11—28no—
226Dic11—48no—
227Dic11C2×C4⋊Q814yes—
228C22×Q8—114no—
229C22×Q8C22×D1114yes—
230C23×C4—111no—
231C23×C4—111no—
232C23×C4—111no—
233C23×C4—114no—
234C4⋊Q8—28no—
235C4⋊Q8—216no—
236C4⋊Q8—228no—
237C4⋊Q8—2216no—
238#125—2216no—
239C22⋊Q8—2216no—
240C22⋊Q8—2216no—
241C4×Q8—2216no—
242C4×Q8—2216no—
243#117—2216no—
244C2×C4⋊C4—114no—
245C2×C4⋊C4—118no—
246C2×C4⋊C4—118no—
247C2×C4⋊C4—114no—
248C2×C4⋊C4—1116no—
249C2×C4⋊C4C22×D1114yes—
250C2×C4⋊C4C22×D1114yes—
251C2×C4⋊C4C22×D11116yes—
252C2×C22⋊C4—118no—
253C2×C42—111no—
254C2×C42—111no—
255C2×C42—111no—
256C2×C42—114no—
257C2×C42—112no—
258C2×C42—118no—
259C2×C42—1116no—
260C2×C42—118no—
261C2×C42—114no—
262C2×C42—114no—
263C2×C42—112no—
264C2×C42—112no—
265C2×C42—228no—
266C2×C42—228no—
267C2×C42C22×D1111yescharacteristic
268C2×C42C22×D1112yes—
269C2×C42C22×D1112yes—
270C2×C42C22×D1112yes—
271#95—1132no—
272C2×C11C22×C4⋊Q811yescharacteristic
273C2×C11C2×#53211yescharacteristic
274C2×C11C2×#53211yescharacteristic
275C2×C11C2×#53314yes—
276D11—24no—
277C24—111no—
278C2×Q8—28no—
279C2×Q8—216no—
280C2×Q8—228no—
281C2×Q8—2216no—
282C22×C4—111no—
283C22×C4—114no—
284C22×C4—118no—
285C22×C4—114no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—114no—
289C22×C4—114no—
290C22×C4—1116no—
291C22×C4—118no—
292C22×C4—224no—
293C22×C4—228no—
294C22×C4—224no—
295C22×C4—228no—
296C22×C4C23×D1118yes—
297C22×C4C23×D1111yescharacteristic
298C22×C4C23×D1111yescharacteristic
299C22×C4C23×D1111yescharacteristic
300C22×C4C23×D1114yes—
301C4⋊C4—28no—
302C4⋊C4—28no—
303C4⋊C4—232no—
304C4⋊C4—2216no—
305C4⋊C4—2216no—
306C4⋊C4—228no—
307C4⋊C4—228no—
308C4⋊C4—2232no—
309C22⋊C4—2216no—
310C42—114no—
311C42—114no—
312C42—114no—
313C42—1116no—
314C42—118no—
315C42—2216no—
316C42—224no—
317C42—228no—
318C42—224no—
319C42—228no—
320C42D4×D1114yes—
321C42#434118yes—
322C42Q8×D1118yes—
323C42#434318yes—
324C11#3664511yescharacteristic, complemented, Sylow
325C23—112no—
326C23—114no—
327C23—222no—
328C23—222no—
329C23C24×D1111yescharacteristic
330Q8—416no—
331Q8—4416no—
332C2×C4—28no—
333C2×C4—216no—
334C2×C4—112no—
335C2×C4—114no—
336C2×C4—1116no—
337C2×C4—112no—
338C2×C4—112no—
339C2×C4—118no—
340C2×C4—222no—
341C2×C4—224no—
342C2×C4—222no—
343C2×C4—224no—
344C2×C4—228no—
345C2×C4—228no—
346C2×C4—2232no—
347C2×C4—228no—
348C2×C4—2216no—
349C2×C4C2×D4×D1112yes—
350C2×C4C2×D4×D1112yes—
351C2×C4C2×D4×D1112yes—
352C2×C4C2×#434114yes—
353C2×C4C2×#434118yes—
354C2×C4C2×Q8×D1114yes—
355C2×C4C2×Q8×D1118yes—
356C2×C4C2×#434314yes—
357C2×C4C2×#434318yes—
358C22—114no—
359C22—222no—
360C22—222no—
361C22—228no—
362C22C22×D4×D1111yescharacteristic
363C22C22×#434112yes—
364C22C22×Q8×D1112yes—
365C22C22×#434312yes—
366C4—48no—
367C4—114no—
368C4—222no—
369C4—222no—
370C4—228no—
371C4—448no—
372C4#1062324714yes—
373C4D11×C4⋊Q814yes—
374C4#1062325614yes—
375C4#10623259116yescomplemented
376C2—224no—
377C2C2×D11×C4⋊Q811yescharacteristic
378C2C2×#1062324711yescharacteristic
379C2C2×#1062325611yescharacteristic
380C2C2×#1062325914yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2868C2
prime radicalC23×D11C24
hypercenter#2868D11
hypocenterC11#36645
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2868

Complements

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

NH ≅ G/Ntype
2. #13077014C2semidirect
3. #13076993C2semidirect
4. #13076977C2semidirect
7. C4⋊Q8×Dic11C2semidirect
8. #13071183C2semidirect
11. C11×#2868C2semidirect
83. C42×D11Q8semidirect
137. #2868D11semidirect
177. C4×D11C4⋊Q8semidirect
222. C4×C11#533semidirect
324. C11#36645semidirect
375. C4#10623259semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130770142
#130769932
#130769772
#130769692
#130769632
C4⋊Q8×Dic112
#130711832
#130710212
C43×D112
C11×#28682
#3664511