Finite Group Databasebeta

← #15623561

Subgroups — #15623561

Order 2816.

1998 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C212yesmaximal, complemented
2#13079222C218yesmaximal, complemented
3#13079211C218yesmaximal, complemented
4#13079140C211yesmaximal, characteristic, complemented
5#13079062C211yesmaximal, characteristic, complemented
6#13078962C212yesmaximal, complemented
7#13078225C214yesmaximal, complemented
8C4×#66957C214yesmaximal, complemented
9C2×C4×C11×M16C211yesmaximal, characteristic, complemented
10C22×C11×M16C2212yes—
11C22×C42×C11C2211yescharacteristic
12#10623322—24no—
13#10623322C2214yes—
14C2×#66957C2214yes—
15#10623010—24no—
16#10623010—24no—
17#10623010C2218yes—
18#10623008C2212yes—
19#10623008C2214yes—
20C4×#4339—24no—
21C4×#4339C2214yes—
22#10623001C2212yes—
23#10623001C2214yes—
24C4×C11×M16C2218yes—
25C2×C11×#97C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C2×C4×C8×C11C2212yes—
28#10622750C2218yes—
29#10622748C2218yes—
30#10622747C22116yes—
31#10622726C2218yes—
32#10622719C2214yes—
33#10622328C2214yescomplemented
34#10622327C2218yescomplemented
35#10622326C2214yescomplemented
36#10622325C2214yescomplemented
37#10622316C2214yescomplemented
38#10622315C2218yescomplemented
39C4×Dic44C2218yescomplemented
40C4×D88C2218yescomplemented
41C4×#4314C22116yescomplemented
42C23×C4×C11D412yes—
43C23×C4×C11C2311yescharacteristic
44C2×#4339—24no—
45C2×#4339C2314yes—
46C2×C11×M16—28no—
47C2×C11×M16C2318yes—
48C22×C8×C11C2312yes—
49C22×C8×C11C2312yes—
50C2×C42×C11D412yes—
51C2×C42×C11D412yes—
52C2×C42×C11D412yes—
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2314yes—
55C2×C42×C11C2311yescharacteristic
56#67006—24no—
57#66983—24no—
58#66983—24no—
59#66983C2318yes—
60#66982—24no—
61#66982—28no—
62C4×C22⋊D11—28no—
63C4×C22⋊D11—28no—
64C4×C22⋊D11—28no—
65#66979—24no—
66#66979C2314yes—
67#66977—24no—
68#66977—24no—
69#66977C2318yes—
70C2×Dic44C2314yes—
71#66957—216no—
72C2×D88C2314yes—
73C2×#4314C2318yes—
74#66929—28no—
75#66928—24no—
76#66928C2314yes—
77#66927C2312yes—
78C4×D44—24no—
79C4×D44—24no—
80C4×D44C2318yes—
81#66925—28no—
82#66925—24no—
83C42×D11—24no—
84#66923—24no—
85#66923C2314yes—
86#66922C2312yes—
87#66922C2314yes—
88C4×Dic22—24no—
89C4×Dic22—24no—
90C4×Dic22C2318yes—
91C11×#97C2314yes—
92C11×#97C2314yes—
93C4×C8×C11C2318yes—
94#66885C23116yes—
95#66882C2318yes—
96#66881C2318yes—
97#66880C23116yes—
98#60676—111nomaximal, Sylow
99C24×C11C2×D411yescharacteristic
100C22×C4×C11—24no—
101C22×C4×C11—44no—
102C22×C4×C11C2×D414yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D414yes—
108C22×C4×C11C2412yes—
109C22×C4×C11C2411yescharacteristic
110C2×C22⋊D11—24no—
111C2×C22⋊D11—28no—
112#4339—216no—
113#4339—416no—
114C2×D44—24no—
115C2×D44C2414yes—
116C2×C4×D11—24no—
117C2×C4×D11—28no—
118C2×Dic22—24no—
119C2×Dic22C2414yes—
120C11×M16—216no—
121C2×C8×C11—24no—
122C2×C8×C11#4118yescomplemented
123C2×C8×C11C2414yes—
124C2×C8×C11C2414yes—
125C42×C11C2×D412yes—
126C42×C11C2×D414yes—
127C42×C11C2×D414yes—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11C2412yes—
131C42×C11C2412yes—
132C22⋊Dic11—24no—
133C22⋊Dic11—28no—
134(C2×D11)⋊C4—28no—
135(C2×D11)⋊C4—28no—
136(C2×D11)⋊C4—28no—
137C4⋊Dic11—24no—
138C4⋊Dic11—24no—
139C4⋊Dic11C2418yes—
140Dic11⋊C4—28no—
141Dic11⋊C4—28no—
142Dic11⋊C4—28no—
143C4×Dic11—24no—
144C4×Dic11—28no—
145Dic44—28no—
146D88—28no—
147#4314—216no—
148#3444—112no—
149#3172—118no—
150#3171—118no—
151#3162—111no—
152#3150—111no—
153#3135—112no—
154#3054—114no—
155C4×#135—114no—
156C2×C4×M16D1111yescharacteristic, complemented
157C23×C11—22no—
158C23×C11—42no—
159C23×C11C22×D412yes—
160C23×C11C22×D411yescharacteristic
161C22×D11—24no—
162C2×C4×C11—22no—
163C2×C4×C11—24no—
164C2×C4×C11—28no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—44no—
168C2×C4×C11—42no—
169C2×C4×C11C22×D412yes—
170C2×C4×C11C22×D412yes—
171C2×C4×C11C22×D414yes—
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C22×D412yes—
174C2×C4×C11C2×#4114yes—
175C2×C4×C11C2511yescharacteristic
176C22⋊D11—416no—
177C22⋊D11—48no—
178C2×Dic11—24no—
179C2×Dic11—28no—
180D44—28no—
181D44—48no—
182C4×D11—48no—
183C4×D11—416no—
184Dic22—28no—
185Dic22—48no—
186C8×C11—24no—
187C8×C11C2×#4118yes—
188C2×#135—114no—
189C22×M16C2×D1112yes—
190#533—112no—
191#533—114no—
192#532—114no—
193#532—112no—
194#529—118no—
195#529—224no—
196#529—224no—
197#525—114no—
198#525—224no—
199C4×#41—114no—
200C4×#41—224no—
201C22×C42C2×D1111yescharacteristic
202#501—118no—
203#497—114no—
204#496—114no—
205#491—114no—
206#490—114no—
207#489—118no—
208#470—118no—
209#469—118no—
210#468—1116no—
211C4×Q16—118no—
212C4×SD16—1116no—
213C4×D8—118no—
214#427—114no—
215#416—118no—
216C4×M16C2×D1118yes—
217C2×#97C2×D1111yescharacteristic
218C2×#97C2×D1111yescharacteristic
219C2×C4×C8C2×D1112yes—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—24no—
223C22×C11—44no—
224C22×C11#53212yes—
225C22×C11C23×D411yescharacteristic
226C2×D11—44no—
227C2×D11—48no—
228C4×C11—22no—
229C4×C11—22no—
230C4×C11—24no—
231C4×C11#53212yes—
232C4×C11#57514yes—
233C4×C11C22×#4112yes—
234Dic11—44no—
235Dic11—48no—
236C2×#41—114no—
237C2×#41—224no—
238C23×C4D4412yes—
239C23×C4C22×D1111yescharacteristic
240#135—2216no—
241C2×Q16—114no—
242C2×SD16—118no—
243C2×D8—114no—
244C2×M16—28no—
245C2×M16C22×D1118yes—
246C22×C8C22×D1112yes—
247C22×C8C22×D1112yes—
248C4⋊Q8—114no—
249C4⋊Q8—112no—
250#127—112no—
251#126—228no—
252#125—114no—
253#125—224no—
254#124—114no—
255#124—224no—
256#123—224no—
257#123—228no—
258C22⋊Q8—118no—
259C22⋊Q8—224no—
260C22⋊Q8—224no—
261#121—118no—
262#121—224no—
263#121—224no—
264#120—224no—
265C4×Q8—118no—
266C4×Q8—224no—
267C4×Q8—224no—
268C4×D4—118no—
269C4×D4—228no—
270C4×D4—228no—
271C4×D4—228no—
272C4×D4—224no—
273C4×D4—224no—
274#117—114no—
275#117—224no—
276#117—224no—
277#117—228no—
278C2×C42—224no—
279C2×C42D4412yes—
280C2×C42D4412yes—
281C2×C42D4412yes—
282C2×C42C22×D1114yes—
283C2×C42C22×D1111yescharacteristic
284C2×C42C22×D1111yescharacteristic
285#107—118no—
286#106—118no—
287#103—1116no—
288#102—1116no—
289#97C22×D1114yes—
290#97C22×D1114yes—
291C4×C8C22×D1118yes—
292C2×C11—22no—
293C2×C11—42no—
294C2×C11C2×#53211yescharacteristic
295C2×C11C2×#57512yes—
296D11—84no—
297C24C2×D4411yescharacteristic
298#41—2216no—
299#41—4416no—
300C2×Q8—114no—
301C2×Q8—224no—
302C2×D4—114no—
303C2×D4—228no—
304C2×D4—224no—
305C2×D4—224no—
306C22×C4—24no—
307C22×C4—44no—
308C22×C4—228no—
309C22×C4—224no—
310C22×C4C2×D4414yes—
311C22×C4C2×D4412yes—
312C22×C4C2×D4412yes—
313C22×C4C2×D4411yescharacteristic
314C22×C4C2×D4412yes—
315C22×C4C2×D4414yes—
316C22×C4C23×D1112yes—
317C22×C4C23×D1111yescharacteristic
318Q16—228no—
319SD16—2216no—
320D8—228no—
321M16—216no—
322C2×C8—24no—
323C2×C8#433918yescomplemented
324C2×C8C23×D1114yes—
325C2×C8C23×D1114yes—
326C4⋊C4—118no—
327C4⋊C4—228no—
328C4⋊C4—224no—
329C4⋊C4—224no—
330C4⋊C4—228no—
331C4⋊C4—228no—
332C22⋊C4—224no—
333C22⋊C4—228no—
334C22⋊C4—228no—
335C22⋊C4—228no—
336C22⋊C4—228no—
337C42—224no—
338C42—228no—
339C42C2×D4411yescharacteristic
340C42C2×D4414yes—
341C42C2×D4412yes—
342C42C2×D4414yes—
343C42C2×D4411yescharacteristic
344C42C23×D1112yes—
345C42C23×D1112yes—
346C11#6067611yescharacteristic, complemented, Sylow
347C23—22no—
348C23—42no—
349C23—224no—
350C23C22×D4412yes—
351C23C22×D4411yescharacteristic
352Q8—228no—
353Q8—448no—
354D4—228no—
355D4—448no—
356D4—4416no—
357D4—448no—
358C2×C4—22no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—28no—
362C2×C4—24no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—228no—
366C2×C4—224no—
367C2×C4—448no—
368C2×C4—4416no—
369C2×C4C22×D4412yes—
370C2×C4C22×D4412yes—
371C2×C4C22×D4414yes—
372C2×C4C22×D4411yescharacteristic
373C2×C4C22×D4412yes—
374C2×C4C2×#433914yes—
375C2×C4C24×D1111yescharacteristic
376C8—24no—
377C8C2×#433918yes—
378C22—22no—
379C22—22no—
380C22—24no—
381C22—44no—
382C22—444no—
383C22—448no—
384C22#1062300812yes—
385C22C23×D4411yescharacteristic
386C4—22no—
387C4—24no—
388C4—22no—
389C4—444no—
390C4—448no—
391C4#1062300812yes—
392C4#1062327914yes—
393C4C22×#433912yes—
394C2—22no—
395C2—42no—
396C2—884no—
397C2C2×#1062300811yescharacteristic
398C2C2×#1062327912yes—
subgroupG/H
centerC42C2×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×M16C2
socleC22×C11C23×D4
hypercenterC2×C4×M16D11
hypocenterC11#60676
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C42 ◁ C22×C42 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
1. #13081912C2semidirect
2. #13079222C2semidirect
3. #13079211C2semidirect
4. #13079140C2semidirect
5. #13079062C2semidirect
6. #13078962C2semidirect
7. #13078225C2semidirect
8. C4×#66957C2semidirect
9. C2×C4×C11×M16C2semidirect
33. #10622328C22semidirect
34. #10622327C22semidirect
35. #10622326C22semidirect
36. #10622325C22semidirect
37. #10622316C22semidirect
38. #10622315C22semidirect
39. C4×Dic44C22semidirect
40. C4×D88C22semidirect
41. C4×#4314C22semidirect
122. C2×C8×C11#41semidirect
156. C2×C4×M16D11semidirect
323. C2×C8#4339semidirect
346. C11#60676semidirect

Maximal subgroups

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

subgroupindex
#130819122
#130792222
#130792112
#130791402
#130790622
#130789622
#130782252
C4×#669572
C2×C4×C11×M162
#6067611