Finite Group Databasebeta

← #15623434

Subgroups — #15623434

Order 2816.

1890 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C212yesmaximal
2#13079166C218yesmaximal, complemented
3#13079160C218yesmaximal, complemented
4#13079139C214yesmaximal, complemented
5#13079128C214yesmaximal, complemented
6#13077206C211yesmaximal, characteristic
7#13077205C212yesmaximal
8C2×M16×Dic11C211yesmaximal, characteristic
9C11×#2911C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2212yes—
12C2×#66979C2212yes—
13C22×C4×Dic11C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15#10623048—24no—
16#10623048—24no—
17#10623048C2214yes—
18#10623048C2214yes—
19#10623048C2214yes—
20#10623048C2214yes—
21C2×#66943C2214yes—
22C2×#66941C2214yes—
23C2×#66931—24no—
24C2×C4×Dic22—24no—
25C11×#428C2218yes—
26C11×#427C2214yes—
27#10622734C2218yes—
28M16×Dic11C2214yes—
29M16×Dic11C2214yes—
30#10622719C2214yes—
31C2×#66879C2212yes—
32C2×C8×Dic11C2212yes—
33#10622611C2218yes—
34#10622608C2218yes—
35#10622577C2218yes—
36#10622491C2218yescomplemented
37#10622489C22116yescomplemented
38#10622487C2218yescomplemented
39#10622471C2218yescomplemented
40#10622469C22116yescomplemented
41#10622468C2218yescomplemented
42C23×C4×C11C2311yescharacteristic
43C23×Dic11D412yes—
44C22×Dic22—24no—
45C2×C11×M16Q818yescomplemented
46C2×C11×M16C2314yes—
47C22×C8×C11C2312yes—
48C11×#117—22no—
49C11×#117—22no—
50C11×#117C2314yes—
51C11×#117C2314yes—
52C2×C11×C4⋊C4C2314yes—
53C2×C11×C22⋊C4—22no—
54C2×C42×C11—22no—
55C2×C22⋊Dic11—22no—
56#66979—22no—
57#66979—22no—
58#66979C2314yes—
59#66979C2314yes—
60C2×C4⋊Dic11—24no—
61C2×C4⋊Dic11C2314yes—
62C2×Dic11⋊C4—24no—
63C2×Dic11⋊C4—24no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11D414yes—
66C2×C4×Dic11D412yes—
67C2×C4×Dic11C2312yes—
68C2×C4×Dic11C2312yes—
69C2×C4×Dic11C2311yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C2×#4318Q818yescomplemented
72C2×#4318C2314yes—
73C22×C11⋊C8C2312yes—
74#66943—24no—
75#66943—24no—
76#66943C2318yes—
77#66943C2318yes—
78#66941—24no—
79#66941—24no—
80#66941C2318yes—
81#66941C2318yes—
82#66931—28no—
83#66931—28no—
84#66931—28no—
85#66931—28no—
86C4×Dic22—28no—
87C4×Dic22—28no—
88C4×Dic22—28no—
89C4×Dic22—28no—
90C11×#107C2318yes—
91C11×#106C2318yes—
92#66882C2318yes—
93#66881C2318yes—
94#66879C2318yes—
95C8×Dic11C2314yes—
96C8×Dic11C2314yes—
97#66872C23116yes—
98#66871C23116yes—
99#60663—111nomaximal, Sylow
100C24×C11C2×D411yescharacteristic
101C22×C4×C11—24no—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×Q814yes—
105C22×C4×C11C2×Q814yes—
106C22×C4×C11C2411yescharacteristic
107C22×C4×C11C2412yes—
108C22×Dic11—24no—
109C22×Dic11—44no—
110C22×Dic11C2×D412yes—
111C22×Dic11C2×D414yes—
112C22×Dic11C2×D412yes—
113C22×Dic11C2×D414yes—
114C2×Dic22—28no—
115C2×Dic22—28no—
116C2×Dic22—416no—
117C11×M16C2×Q8116yescomplemented
118C2×C8×C11C2×Q818yescomplemented
119C2×C8×C11C2414yes—
120C11×C4⋊C4—24no—
121C11×C4⋊C4C2418yes—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—24no—
124C42×C11—24no—
125C42×C11—24no—
126C22⋊Dic11—24no—
127C22⋊Dic11—24no—
128C4⋊Dic11—28no—
129C4⋊Dic11—28no—
130C4⋊Dic11—24no—
131C4⋊Dic11C2418yes—
132Dic11⋊C4—28no—
133Dic11⋊C4—28no—
134Dic11⋊C4—28no—
135Dic11⋊C4—28no—
136C4×Dic11—24no—
137C4×Dic11—24no—
138C4×Dic11C2×D412yes—
139C4×Dic11C2×D412yes—
140C4×Dic11C2×D414yes—
141C4×Dic11C2×D414yes—
142C4×Dic11C2411yescharacteristic
143C4×Dic11C2411yescharacteristic
144C4×Dic11C2412yes—
145#4318C2×Q8116yescomplemented
146C2×C11⋊C8C2×Q818yescomplemented
147C2×C11⋊C8C2414yes—
148C2×#533—112no—
149#3166—118no—
150#3165—118no—
151#3162—114no—
152#3160—114no—
153#2911—111no—
154#2911—112no—
155#2911D1111yescharacteristic
156C2×C4×M16—111no—
157C23×C11—42no—
158C23×C11C4⋊Q814yes—
159C23×C11C22×D411yescharacteristic
160C23×C11C22×D412yes—
161C2×C4×C11—28no—
162C2×C4×C11—48no—
163C2×C4×C11C4⋊Q818yes—
164C2×C4×C11C4⋊Q814yes—
165C2×C4×C11C22×D412yes—
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C22×Q812yes—
168C2×C4×C11C22×Q814yes—
169C2×C4×C11C22×Q812yes—
170C2×C4×C11C22×Q814yes—
171C2×C4×C11C2511yescharacteristic
172C2×Dic11—28no—
173C2×Dic11—24no—
174C2×Dic11—28no—
175C2×Dic11—42no—
176C2×Dic11—44no—
177C2×Dic11—48no—
178C2×Dic11C22×D412yes—
179C2×Dic11C22×D414yes—
180C2×Dic11C22×D412yes—
181Dic22—416no—
182Dic22—416no—
183C8×C11C22×Q818yes—
184C11⋊C8C22×Q818yes—
185C22×M16—111no—
186C22×M16C2×D1111yescharacteristic
187#533—114no—
188#533—114no—
189#533—114no—
190#533—114no—
191#533—224no—
192#533—224no—
193C2×C4⋊Q8—114no—
194C2×#125—114no—
195C2×C22⋊Q8—224no—
196C2×C4×Q8—224no—
197C2×#117—112no—
198C2×#117C2×D1112yes—
199C22×C42—111no—
200#501—1116no—
201#501—1116no—
202#500—118no—
203#499—118no—
204#499—118no—
205#498—118no—
206#428—118no—
207#428—118no—
208#428—118no—
209#428C2×D1118yes—
210#427—114no—
211#427—118no—
212#427C2×D1114yes—
213C4×M16—114no—
214C4×M16—114no—
215C2×#97—112no—
216C2×C4×C8—112no—
217C22×C11—24no—
218C22×C11—22no—
219C22×C11—44no—
220C22×C11C2×C4⋊Q812yes—
221C22×C11C2×C4⋊Q814yes—
222C22×C11C23×D411yescharacteristic
223C4×C11—48no—
224C4×C11C2×C4⋊Q814yes—
225C4×C11C2×C4⋊Q812yes—
226C4×C11C23×Q811yescharacteristic
227C4×C11C23×Q811yescharacteristic
228Dic11—24no—
229Dic11—22no—
230Dic11—48no—
231Dic11#57514yes—
232C22×Q8—224no—
233C23×C4—112no—
234C23×C4C22×D1111yescharacteristic
235C2×M16—118no—
236C2×M16—114no—
237C2×M16Dic2218yescomplemented
238C2×M16C22×D1114yes—
239C22×C8—112no—
240C22×C8C22×D1112yes—
241C4⋊Q8—118no—
242C4⋊Q8—118no—
243C4⋊Q8—224no—
244C4⋊Q8—224no—
245#125—118no—
246#125—118no—
247#125—224no—
248#125—224no—
249C22⋊Q8—228no—
250C22⋊Q8—228no—
251C22⋊Q8—228no—
252C22⋊Q8—228no—
253C4×Q8—228no—
254C4×Q8—228no—
255C4×Q8—228no—
256C4×Q8—228no—
257#117—22no—
258#117—22no—
259#117—114no—
260#117—114no—
261#117—222no—
262#117—222no—
263#117C22×D1114yes—
264#117C22×D1114yes—
265C2×C4⋊C4—114no—
266C2×C4⋊C4—224no—
267C2×C4⋊C4—224no—
268C2×C4⋊C4—224no—
269C2×C4⋊C4C22×D1114yes—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—222no—
272C2×C42—22no—
273C2×C42—114no—
274C2×C42—112no—
275C2×C42—112no—
276C2×C42—112no—
277C2×C42—111no—
278C2×C42—111no—
279C2×C42—222no—
280#107—118no—
281#107—1116no—
282#107C22×D1118yes—
283#106—118no—
284#106—1116no—
285#106C22×D1118yes—
286#97—118no—
287C4×C8—114no—
288C4×C8—114no—
289C2×C11—24no—
290C2×C11—22no—
291C2×C11C22×C4⋊Q811yescharacteristic
292C2×C11C2×#57512yes—
293C24D4×D1111yescharacteristic
294C2×Q8—228no—
295C2×Q8—228no—
296C2×Q8—4416no—
297C22×C4—24no—
298C22×C4—114no—
299C22×C4—112no—
300C22×C4—114no—
301C22×C4—112no—
302C22×C4—224no—
303C22×C4—444no—
304C22×C4C2×Dic2214yes—
305C22×C4D4×D1111yescharacteristic
306C22×C4D4×D1112yes—
307C22×C4Q8×D1114yes—
308C22×C4C23×D1112yes—
309C22×C4C23×D1111yescharacteristic
310M16—1116no—
311M16C2×Dic22116yescomplemented
312C2×C8—118no—
313C2×C8—114no—
314C2×C8C2×Dic2218yescomplemented
315C2×C8C23×D1114yes—
316C4⋊C4—24no—
317C4⋊C4—118no—
318C4⋊C4—228no—
319C4⋊C4—228no—
320C4⋊C4—228no—
321C4⋊C4—228no—
322C4⋊C4—228no—
323C4⋊C4—228no—
324C4⋊C4—224no—
325C4⋊C4C23×D1118yes—
326C22⋊C4—24no—
327C22⋊C4—24no—
328C22⋊C4—224no—
329C22⋊C4—224no—
330C42—24no—
331C42—24no—
332C42—114no—
333C42—114no—
334C42—112no—
335C42—112no—
336C42—111no—
337C42—111no—
338C42—112no—
339C42—224no—
340C42—224no—
341C11#6066311yescharacteristic, complemented, Sylow
342C23—42no—
343C23#6694114yes—
344C23C2×D4×D1111yescharacteristic
345C23C2×D4×D1112yes—
346Q8—4416no—
347Q8—4416no—
348C2×C4—28no—
349C2×C4—48no—
350C2×C4—112no—
351C2×C4—112no—
352C2×C4—114no—
353C2×C4—228no—
354C2×C4—224no—
355C2×C4—228no—
356C2×C4—442no—
357C2×C4—444no—
358C2×C4—448no—
359C2×C4#6694114yes—
360C2×C4#6694118yes—
361C2×C4C22×Dic2212yes—
362C2×C4C22×Dic2214yes—
363C2×C4C2×D4×D1112yes—
364C2×C4C2×D4×D1111yescharacteristic
365C2×C4C2×Q8×D1112yes—
366C2×C4C2×Q8×D1114yes—
367C2×C4C24×D1111yescharacteristic
368C8—118no—
369C8C22×Dic2218yes—
370C22—24no—
371C22—22no—
372C22—44no—
373C22C2×#6694112yes—
374C22C2×#6694114yes—
375C22C22×D4×D1111yescharacteristic
376C4—48no—
377C4—114no—
378C4—224no—
379C4—222no—
380C4—448no—
381C4C2×#6694114yes—
382C4C2×#6694112yes—
383C4C23×Dic2211yescharacteristic
384C4C22×Q8×D1111yescharacteristic
385C2—24no—
386C2—22no—
387C2C22×#6694111yescharacteristic
388C2D11×#57512yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2911C2
socleC22×C11C23×D4
prime radicalC24×C11C2×D4
hypercenter#2911D11
hypocenterC11#60663
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2911

Complements

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

NH ≅ G/Ntype
2. #13079166C2semidirect
3. #13079160C2semidirect
4. #13079139C2semidirect
5. #13079128C2semidirect
36. #10622491C22semidirect
37. #10622489C22semidirect
38. #10622487C22semidirect
39. #10622471C22semidirect
40. #10622469C22semidirect
41. #10622468C22semidirect
45. C2×C11×M16Q8semidirect
71. C2×#4318Q8semidirect
117. C11×M16C2×Q8semidirect
118. C2×C8×C11C2×Q8semidirect
145. #4318C2×Q8semidirect
146. C2×C11⋊C8C2×Q8semidirect
237. C2×M16Dic22semidirect
311. M16C2×Dic22semidirect
314. C2×C8C2×Dic22semidirect
341. C11#60663semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
#130791662
#130791602
#130791392
#130791282
#130772062
#130772052
C2×M16×Dic112
C11×#29112
#6066311