Finite Group Databasebeta

← #15623705

Subgroups — #15623705

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#13081911C212yesmaximal, complemented
2#13079322C218yesmaximal, complemented
3#13079311C218yesmaximal, complemented
4#13079140C211yesmaximal, characteristic, complemented
5#13078961C212yesmaximal, complemented
6#13078193C214yesmaximal, complemented
7#13077417C214yesmaximal, complemented
8C2×D11×#97C211yesmaximal, characteristic, complemented
9C11×#3150C211yesmaximal, characteristic, complemented
10C2×C11×#135C2214yes—
11C11×#532C2212yes—
12#10623359C2214yes—
13#41×Dic11C2214yes—
14C22×C8×D11C2212yes—
15#10623259C2214yes—
16#10623247C2214yes—
17#10623211C2218yes—
18#10623137—24no—
19#10623131—24no—
20#10623088—24no—
21C4×#4341—24no—
22C2×C42×D11C2211yescharacteristic
23#10623001C2212yes—
24C11×#497C2214yescomplemented
25C11×#496C2214yescomplemented
26C2×C11×#97C2211yescharacteristic
27#10622846C2218yes—
28#10622801C2218yes—
29#10622797C2218yescomplemented
30#10622784C22116yes—
31#10622777C22116yescomplemented
32#10622770C2218yes—
33#10622765C2218yescomplemented
34#10622719C2214yes—
35C2×#66879C2212yes—
36#10622695C2214yescomplemented
37#10622684C2214yescomplemented
38#10622668C2218yescomplemented
39C2×#66867C2211yescharacteristic
40D11×#97C2218yes—
41#10622315C2218yescomplemented
42C2×C11×#41C2314yes—
43C2×#4341—24no—
44C22×C4×D11D412yes—
45C22×C4×D11C2311yescharacteristic
46C11×#135—216no—
47C2×C11×Q16C2314yes—
48C2×C11×SD16C2318yes—
49C2×C11×D8C2314yes—
50C22×C8×C11C2312yes—
51C11×C4⋊Q8C2312yes—
52C11×#127C2312yes—
53C11×#124C2314yes—
54C11×#121—24no—
55C4×D4×C11—24no—
56C2×C42×C11C2311yescharacteristic
57#66999C2318yes—
58Q8×Dic11C2318yes—
59#66991—24no—
60#66991C2318yes—
61#66990—24no—
62#66989—24no—
63#66988—24no—
64D4×Dic11—28no—
65D4×Dic11—24no—
66D4×Dic11C2318yes—
67C4×C22⋊D11—28no—
68#66979—24no—
69#66979C2314yes—
70#66977—24no—
71C2×C4×Dic11—24no—
72C2×C4×Dic11D412yes—
73C2×C4×Dic11C2311yescharacteristic
74C22×C11⋊C8C2312yes—
75C2×C8×D11—28no—
76C2×C8×D11C2318yes—
77#66950—24no—
78#66945—24no—
79#66943—24no—
80#66940—24no—
81#66936—28no—
82(C22⋊D11)⋊C4—28no—
83#66932—28no—
84#66930—28no—
85C42×D11D414yes—
86C42×D11C2314yes—
87#66923C2314yes—
88#66922C2314yes—
89C4×Dic22—24no—
90C11×#97C2314yes—
91#66899C23116yes—
92#66896C23116yes—
93#66882C2318yes—
94#66881C2318yes—
95#66879C2318yes—
96#66867C2314yes—
97#60688—111nomaximal, Sylow
98C23×D11C2×D411yescharacteristic
99C11×#41—216no—
100C2×Q8×C11C2414yes—
101C2×D4×C11—24no—
102C2×D4×C11—24no—
103C2×D4×C11C2414yes—
104C22×C4×C11—24no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2411yescharacteristic
107C2×C22⋊D11—28no—
108C22×Dic11—28no—
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D412yes—
111#4341—416no—
112C2×C4×D11—24no—
113C2×C4×D11—44no—
114C2×C4×D11C2×D412yes—
115C2×C4×D11C2×D414yes—
116C2×C4×D11C2×D414yes—
117C2×C4×D11C2412yes—
118C2×Dic22—24no—
119C11×Q16—28no—
120C11×SD16—216no—
121C11×D8—28no—
122C2×C8×C11#4118yescomplemented
123C2×C8×C11C2414yes—
124C11×C4⋊C4—24no—
125C11×C22⋊C4—28no—
126C42×C11C2×D412yes—
127C42×C11C2412yes—
128C22⋊Dic11—28no—
129C22⋊Dic11—28no—
130C22⋊Dic11—24no—
131(C2×D11)⋊C4—28no—
132C4⋊Dic11—28no—
133C4⋊Dic11—24no—
134C4⋊Dic11C2418yes—
135Dic11⋊C4—28no—
136Dic11⋊C4—28no—
137C4×Dic11—28no—
138C4×Dic11—24no—
139C4×Dic11C2×D412yes—
140C4×Dic11C2×D414yes—
141C4×Dic11C2×D414yes—
142C4×Dic11C2412yes—
143C2×C11⋊C8—24no—
144C2×C11⋊C8C2414yes—
145C8×D11—216no—
146#3444—112no—
147#3181—118no—
148#3180—118no—
149#3162—111no—
150#3150D1111yescharacteristic, complemented
151#3135—112no—
152#3050—114no—
153#2943—114no—
154C22×#97—111no—
155C23×C11—24no—
156C23×C11C22×D411yescharacteristic
157C22×D11—22no—
158C22×D11—24no—
159C22×D11C22×D412yes—
160Q8×C11—28no—
161D4×C11—28no—
162D4×C11—48no—
163D4×C11—48no—
164C2×C4×C11—24no—
165C2×C4×C11—42no—
166C2×C4×C11—48no—
167C2×C4×C11C22×D414yes—
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C2×#4114yes—
170C2×C4×C11C2511yescharacteristic
171C22⋊D11—416no—
172C2×Dic11—22no—
173C2×Dic11—28no—
174C2×Dic11—42no—
175C2×Dic11—416no—
176C2×Dic11C22×D414yes—
177C2×Dic11C22×D412yes—
178C4×D11—28no—
179C4×D11—24no—
180C4×D11—24no—
181C4×D11—44no—
182Dic22—48no—
183C8×C11C2×#4118yes—
184C11⋊C8—24no—
185C2×#135C2×D1114yes—
186C23×C8—112no—
187#533—114no—
188#533—112no—
189#532—114no—
190#532C2×D1112yes—
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#501—118no—
200#497C2×D1114yescomplemented
201#496C2×D1114yescomplemented
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#427—114no—
212#416—118no—
213C2×#97—112no—
214C2×#97—111no—
215C2×#97—118no—
216C2×#97C2×D1111yescharacteristic
217C22×C11—22no—
218C22×C11—44no—
219C22×C11—48no—
220C22×C11#53212yes—
221C22×C11C23×D411yescharacteristic
222C2×D11—28no—
223C2×D11—22no—
224C2×D11—22no—
225C2×D11#57514yes—
226C4×C11—24no—
227C4×C11—44no—
228C4×C11#53212yes—
229C4×C11C22×#4112yes—
230Dic11—22no—
231Dic11—24no—
232Dic11—48no—
233C2×#41—224no—
234C2×#41C22×D1114yes—
235C23×C4—111no—
236C23×C4—112no—
237#135—216no—
238C2×Q16C22×D1114yes—
239C2×SD16C22×D1118yes—
240C2×D8C22×D1114yes—
241C22×C8—112no—
242C22×C8—118no—
243C22×C8—228no—
244C22×C8C22×D1112yes—
245C4⋊Q8—114no—
246C4⋊Q8C22×D1112yes—
247#127C22×D1112yes—
248#126—228no—
249#125—114no—
250#125—224no—
251#124—224no—
252#124C22×D1114yes—
253#123—228no—
254#123—224no—
255C22⋊Q8—118no—
256C22⋊Q8—224no—
257C22⋊Q8—224no—
258#121—24no—
259#121—118no—
260#121—224no—
261#120—224no—
262C4×Q8—118no—
263C4×Q8—224no—
264C4×Q8—224no—
265C4×D4—24no—
266C4×D4—118no—
267C4×D4—224no—
268C4×D4—228no—
269C4×D4—228no—
270C4×D4—228no—
271#117—114no—
272#117—228no—
273#117—224no—
274#117—224no—
275C2×C42—112no—
276C2×C42—111no—
277C2×C42—114no—
278C2×C42—114no—
279C2×C42—224no—
280C2×C42C22×D1111yescharacteristic
281#107—118no—
282#106—118no—
283#103—1116no—
284#102—1116no—
285#97—118no—
286#97—114no—
287#97C22×D1114yes—
288C2×C11—22no—
289C2×C11—84no—
290C2×C11C2×#53211yescharacteristic
291C2×C11C2×#57512yes—
292D11—24no—
293C24—111no—
294#41—216no—
295#41—4416no—
296C2×Q8—224no—
297C2×Q8C23×D1114yes—
298C2×D4—24no—
299C2×D4—24no—
300C2×D4—228no—
301C2×D4C23×D1114yes—
302C22×C4—24no—
303C22×C4—111no—
304C22×C4—112no—
305C22×C4—114no—
306C22×C4—112no—
307C22×C4—112no—
308C22×C4—114no—
309C22×C4—228no—
310C22×C4—224no—
311C22×C4—444no—
312C22×C4D4×D1112yes—
313C22×C4C23×D1111yescharacteristic
314Q16—28no—
315SD16—216no—
316D8—28no—
317C2×C8—114no—
318C2×C8—224no—
319C2×C8—2216no—
320C2×C8#434118yescomplemented
321C2×C8C23×D1114yes—
322C4⋊C4—24no—
323C4⋊C4—118no—
324C4⋊C4—228no—
325C4⋊C4—228no—
326C4⋊C4—224no—
327C4⋊C4—228no—
328C22⋊C4—28no—
329C22⋊C4—228no—
330C22⋊C4—228no—
331C22⋊C4—228no—
332C22⋊C4—224no—
333C42—114no—
334C42—114no—
335C42—112no—
336C42—112no—
337C42—228no—
338C42—224no—
339C42D4×D1112yes—
340C42C23×D1112yes—
341C11#6068811yescharacteristic, complemented, Sylow
342C23—24no—
343C23—112no—
344C23—224no—
345C23—222no—
346C23C2×D4×D1111yescharacteristic
347Q8—28no—
348Q8—448no—
349D4—28no—
350D4—48no—
351D4—48no—
352D4—4416no—
353C2×C4—24no—
354C2×C4—42no—
355C2×C4—48no—
356C2×C4—114no—
357C2×C4—112no—
358C2×C4—228no—
359C2×C4—222no—
360C2×C4—224no—
361C2×C4—224no—
362C2×C4—228no—
363C2×C4—444no—
364C2×C4—442no—
365C2×C4—4416no—
366C2×C4C2×D4×D1114yes—
367C2×C4C2×D4×D1111yescharacteristic
368C2×C4C2×#434114yes—
369C2×C4C24×D1111yescharacteristic
370C8—224no—
371C8C2×#434118yes—
372C22—22no—
373C22—44no—
374C22—48no—
375C22—114no—
376C22—228no—
377C22—222no—
378C22—222no—
379C22#1062324712yes—
380C22C22×D4×D1111yescharacteristic
381C4—24no—
382C4—44no—
383C4—222no—
384C4—224no—
385C4—448no—
386C4#1062324712yes—
387C4C22×#434112yes—
388C2—22no—
389C2—84no—
390C2—224no—
391C2C2×#1062324711yescharacteristic
392C2D11×#57512yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3150C2
socleC22×C11C23×D4
hypercenter#3150D11
hypocenterC11#60688
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3150

Complements

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

NH ≅ G/Ntype
1. #13081911C2semidirect
2. #13079322C2semidirect
3. #13079311C2semidirect
4. #13079140C2semidirect
5. #13078961C2semidirect
6. #13078193C2semidirect
7. #13077417C2semidirect
8. C2×D11×#97C2semidirect
9. C11×#3150C2semidirect
24. C11×#497C22semidirect
25. C11×#496C22semidirect
29. #10622797C22semidirect
31. #10622777C22semidirect
33. #10622765C22semidirect
36. #10622695C22semidirect
37. #10622684C22semidirect
38. #10622668C22semidirect
41. #10622315C22semidirect
122. C2×C8×C11#41semidirect
150. #3150D11semidirect
200. #497C2×D11semidirect
201. #496C2×D11semidirect
320. C2×C8#4341semidirect
341. C11#60688semidirect

Maximal subgroups

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

subgroupindex
#130819112
#130793222
#130793112
#130791402
#130789612
#130781932
#130774172
C2×D11×#972
C11×#31502
#6068811