Finite Group Databasebeta

← #15623708

Subgroups — #15623708

Order 2816.

2010 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081913C212yesmaximal, complemented
2#13079327C218yesmaximal, complemented
3#13079316C218yesmaximal, complemented
4#13079062C211yesmaximal, characteristic, complemented
5#13078964C212yesmaximal, complemented
6#13078198C214yesmaximal, complemented
7#13077416C214yesmaximal, complemented
8C2×D11×#97C211yesmaximal, characteristic, complemented
9C11×#3162C211yesmaximal, characteristic, complemented
10C11×#533C2212yes—
11C2×#66957C2214yes—
12C22×C8×D11C2212yes—
13#10623259C2214yes—
14#10623256C2214yes—
15#10623222C2218yes—
16#10623158—24no—
17#10623155—24no—
18#10623111—24no—
19C4×#4343—24no—
20#10623055C2214yes—
21#10623053C2214yes—
22#10623008C2212yes—
23C2×C42×D11C2211yescharacteristic
24C11×#501C2218yescomplemented
25C11×#427C2214yes—
26C2×C11×#97C2211yescharacteristic
27C2×#66879C2212yes—
28#10622702C2218yescomplemented
29#10622682C2214yescomplemented
30#10622680C2214yescomplemented
31#10622615C2218yes—
32C2×#66867C2211yescharacteristic
33#10622502C22116yescomplemented
34#10622500C2218yes—
35#10622496C2218yes—
36#10622482C2218yescomplemented
37#10622477C22116yes—
38#10622466C2218yescomplemented
39#10622328C2214yescomplemented
40#10622325C2214yescomplemented
41D11×#97C2218yes—
42C2×#4343—24no—
43C2×#4339C2314yes—
44C22×C4×D11D412yes—
45C22×C4×D11C2311yescharacteristic
46C22×C8×C11C2312yes—
47C11×C4⋊Q8C2314yes—
48C11×#125C2314yes—
49C11×C22⋊Q8—24no—
50C4×Q8×C11—24no—
51C11×#117C2314yes—
52C2×C42×C11C2311yescharacteristic
53#67000—24no—
54#66999—24no—
55Q8×Dic11—24no—
56#66983—24no—
57C2×C4×Dic11D412yes—
58C2×C4×Dic11C2311yescharacteristic
59C22×C11⋊C8C2312yes—
60C2×Dic44C2314yes—
61#66957—216no—
62C2×D88C2314yes—
63C2×#4314C2318yes—
64C2×C8×D11—28no—
65C2×C8×D11C2318yes—
66#66951—28no—
67#66950C2318yes—
68#66948—24no—
69#66948C2318yes—
70#66947—28no—
71#66946—28no—
72#66946—24no—
73#66946C2318yes—
74#66945—24no—
75#66945—28no—
76#66943—24no—
77#66940C2318yes—
78#66939—24no—
79#66935—24no—
80(C22⋊D11)⋊C4—28no—
81#66928C2314yes—
82#66927C2312yes—
83C4×D44—28no—
84C4×D44—24no—
85#66925—24no—
86C42×D11—24no—
87C42×D11D414yes—
88C42×D11C2314yes—
89#66922C2312yes—
90C11×#107C2318yes—
91C11×#106C2318yes—
92C11×#97C2314yes—
93#66879C2318yes—
94#66874C23116yes—
95#66873C23116yes—
96#66867C2314yes—
97#60688—111nomaximal, Sylow
98C23×D11C2×D411yescharacteristic
99C2×Q8×C11—24no—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2411yescharacteristic
102C2×C22⋊D11—24no—
103C22×Dic11C2×D411yescharacteristic
104C22×Dic11C2×D412yes—
105#4343—416no—
106#4339—216no—
107C2×D44—28no—
108C2×D44—24no—
109C2×D44C2414yes—
110C2×C4×D11—28no—
111C2×C4×D11—24no—
112C2×C4×D11—24no—
113C2×C4×D11—44no—
114C2×C4×D11C2×D412yes—
115C2×C4×D11C2×D414yes—
116C2×C4×D11C2×D414yes—
117C2×C4×D11C2412yes—
118C2×Dic22C2414yes—
119C2×C8×C11#4118yescomplemented
120C2×C8×C11C2414yes—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—28no—
123C11×C4⋊C4C2418yes—
124C11×C22⋊C4—24no—
125C42×C11—24no—
126C42×C11C2×D412yes—
127C42×C11C2412yes—
128(C2×D11)⋊C4—28no—
129(C2×D11)⋊C4—28no—
130(C2×D11)⋊C4—28no—
131(C2×D11)⋊C4—28no—
132C4⋊Dic11—28no—
133C4⋊Dic11—24no—
134Dic11⋊C4—28no—
135C4×Dic11—28no—
136C4×Dic11C2×D412yes—
137C4×Dic11C2×D414yes—
138C4×Dic11C2×D414yes—
139C4×Dic11C2412yes—
140C2×C11⋊C8—24no—
141C2×C11⋊C8C2414yes—
142Dic44—28no—
143D88—28no—
144#4314—216no—
145C8×D11—216no—
146#3444—112no—
147#3181—118no—
148#3180—118no—
149#3162D1111yescharacteristic, complemented
150#3150—111no—
151#3135—112no—
152#3050—114no—
153#2943—114no—
154C22×#97—111no—
155C23×C11C22×D411yescharacteristic
156C22×D11—22no—
157C22×D11—24no—
158C22×D11—24no—
159C22×D11C22×D412yes—
160Q8×C11—48no—
161C2×C4×C11—28no—
162C2×C4×C11—42no—
163C2×C4×C11C22×D414yes—
164C2×C4×C11C22×D411yescharacteristic
165C2×C4×C11C2×#4114yes—
166C2×C4×C11C2511yescharacteristic
167C22⋊D11—48no—
168C2×Dic11—22no—
169C2×Dic11—24no—
170C2×Dic11—42no—
171C2×Dic11C22×D414yes—
172C2×Dic11C22×D412yes—
173D44—28no—
174D44—48no—
175D44—416no—
176C4×D11—28no—
177C4×D11—24no—
178C4×D11—24no—
179C4×D11—44no—
180C4×D11—416no—
181C4×D11—48no—
182Dic22—28no—
183C8×C11C2×#4118yes—
184C11⋊C8—24no—
185C2×#135—114no—
186C23×C8—112no—
187#533—114no—
188#533C2×D1112yes—
189#532—114no—
190#532—112no—
191#529—118no—
192#529—224no—
193#529—224no—
194#525—114no—
195#525—224no—
196C4×#41—114no—
197C4×#41—224no—
198C22×C42—111no—
199#501C2×D1118yescomplemented
200#497—114no—
201#496—114no—
202#491—114no—
203#490—114no—
204#489—118no—
205#467—118no—
206#466—118no—
207#465—1116no—
208#442—118no—
209#441—118no—
210#440—1116no—
211#427C2×D1114yes—
212#416—118no—
213C2×#97—112no—
214C2×#97—111no—
215C2×#97—118no—
216C2×#97C2×D1111yescharacteristic
217C22×C11—22no—
218C22×C11#53212yes—
219C22×C11C23×D411yescharacteristic
220C2×D11—28no—
221C2×D11—22no—
222C2×D11—22no—
223C2×D11—44no—
224C2×D11—48no—
225C2×D11#57514yes—
226C4×C11—24no—
227C4×C11—48no—
228C4×C11#53212yes—
229C4×C11C22×#4112yes—
230Dic11—22no—
231Dic11—24no—
232Dic11—44no—
233C2×#41—114no—
234C2×#41—224no—
235C23×C4—111no—
236C23×C4—112no—
237#135—2216no—
238C2×Q16—114no—
239C2×SD16—118no—
240C2×D8—114no—
241C22×C8—112no—
242C22×C8—118no—
243C22×C8—228no—
244C22×C8C22×D1112yes—
245C4⋊Q8—112no—
246C4⋊Q8C22×D1114yes—
247#127—112no—
248#126—228no—
249#125—224no—
250#125C22×D1114yes—
251#124—114no—
252#124—224no—
253#123—224no—
254#123—228no—
255C22⋊Q8—24no—
256C22⋊Q8—118no—
257C22⋊Q8—224no—
258#121—118no—
259#121—224no—
260#121—224no—
261#120—224no—
262C4×Q8—24no—
263C4×Q8—118no—
264C4×Q8—224no—
265C4×D4—118no—
266C4×D4—228no—
267C4×D4—224no—
268C4×D4—228no—
269C4×D4—228no—
270C4×D4—224no—
271#117—224no—
272#117—228no—
273#117—224no—
274#117C22×D1114yes—
275C2×C42—112no—
276C2×C42—111no—
277C2×C42—114no—
278C2×C42—114no—
279C2×C42—224no—
280C2×C42C22×D1111yescharacteristic
281#107C22×D1118yes—
282#106C22×D1118yes—
283#103—1116no—
284#102—1116no—
285#97—118no—
286#97—114no—
287#97C22×D1114yes—
288C2×C11—22no—
289C2×C11C2×#53211yescharacteristic
290C2×C11C2×#57512yes—
291D11—24no—
292D11—84no—
293C24—111no—
294#41—2216no—
295#41—4416no—
296C2×Q8—24no—
297C2×Q8—114no—
298C2×D4—114no—
299C2×D4—228no—
300C2×D4—224no—
301C2×D4—224no—
302C22×C4—111no—
303C22×C4—112no—
304C22×C4—114no—
305C22×C4—112no—
306C22×C4—112no—
307C22×C4—114no—
308C22×C4—228no—
309C22×C4—224no—
310C22×C4—224no—
311C22×C4—444no—
312C22×C4D4×D1112yes—
313C22×C4C23×D1111yescharacteristic
314Q16—228no—
315SD16—2216no—
316D8—228no—
317C2×C8—114no—
318C2×C8—224no—
319C2×C8—2216no—
320C2×C8#434318yescomplemented
321C2×C8C23×D1114yes—
322C4⋊C4—24no—
323C4⋊C4—28no—
324C4⋊C4—228no—
325C4⋊C4—228no—
326C4⋊C4—224no—
327C4⋊C4C23×D1118yes—
328C22⋊C4—24no—
329C22⋊C4—228no—
330C22⋊C4—228no—
331C22⋊C4—228no—
332C22⋊C4—228no—
333C42—24no—
334C42—114no—
335C42—114no—
336C42—112no—
337C42—112no—
338C42—228no—
339C42D4×D1112yes—
340C42C23×D1112yes—
341C11#6068811yescharacteristic, complemented, Sylow
342C23—112no—
343C23—224no—
344C23—222no—
345C23—224no—
346C23C2×D4×D1111yescharacteristic
347Q8—48no—
348Q8—228no—
349D4—228no—
350D4—448no—
351D4—4416no—
352D4—448no—
353C2×C4—28no—
354C2×C4—42no—
355C2×C4—114no—
356C2×C4—112no—
357C2×C4—228no—
358C2×C4—222no—
359C2×C4—224no—
360C2×C4—224no—
361C2×C4—224no—
362C2×C4—444no—
363C2×C4—4416no—
364C2×C4—442no—
365C2×C4—448no—
366C2×C4C2×D4×D1114yes—
367C2×C4C2×D4×D1111yescharacteristic
368C2×C4C2×#434314yes—
369C2×C4C24×D1111yescharacteristic
370C8—224no—
371C8C2×#434318yes—
372C22—22no—
373C22—114no—
374C22—228no—
375C22—222no—
376C22—222no—
377C22—444no—
378C22—448no—
379C22#1062325612yes—
380C22C22×D4×D1111yescharacteristic
381C4—24no—
382C4—48no—
383C4—222no—
384C4—224no—
385C4—444no—
386C4#1062325612yes—
387C4C22×#434312yes—
388C2—22no—
389C2—224no—
390C2—884no—
391C2C2×#1062325611yescharacteristic
392C2D11×#57512yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3162C2
socleC22×C11C23×D4
hypercenter#3162D11
hypocenterC11#60688
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
1. #13081913C2semidirect
2. #13079327C2semidirect
3. #13079316C2semidirect
4. #13079062C2semidirect
5. #13078964C2semidirect
6. #13078198C2semidirect
7. #13077416C2semidirect
8. C2×D11×#97C2semidirect
9. C11×#3162C2semidirect
24. C11×#501C22semidirect
28. #10622702C22semidirect
29. #10622682C22semidirect
30. #10622680C22semidirect
33. #10622502C22semidirect
36. #10622482C22semidirect
38. #10622466C22semidirect
39. #10622328C22semidirect
40. #10622325C22semidirect
119. C2×C8×C11#41semidirect
149. #3162D11semidirect
199. #501C2×D11semidirect
320. C2×C8#4343semidirect
341. C11#60688semidirect

Maximal subgroups

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

subgroupindex
#130819132
#130793272
#130793162
#130790622
#130789642
#130781982
#130774162
C2×D11×#972
C11×#31622
#6068811